Abstract
Title of Dissertation: HIGH-RESOLUTION IMAGING OF
DENSE GAS STRUCTURE AND
KINEMATICS IN NEARBY MOLECULAR
CLOUDS WITH THE CARMA
LARGE AREA STAR FORMATION SURVEY
Shaye Storm, Doctor of Philosophy, 2015
Dissertation directed by: Professor Lee Mundy
Department of Astronomy
This thesis utilizes new observations of dense gas in molecular clouds to develop
an empirical framework for how clouds form structures which evolve into young
cores and stars. Previous observations show the general turbulent and hierarchical
nature of clouds. However, current understanding of the star formation pathway is
limited by existing data that do not combine angular resolution needed to resolve
individual cores with area coverage required to capture entire star-forming regions
and with tracers that can resolve gas motions.
The original contributions of this thesis to astrophysical research are the cre-
ation and analysis of the largest-area high-angular-resolution maps of dense gas in
molecular clouds to-date, and the development of a non-binary dendrogram algo-
rithm to quantify the hierarchical nature and three-dimensional morphology of cloud
structure.
I first describe the CARMA Large Area Star Formation Survey, which provides
spectrally imaged N2H+, HCO+, and HCN (J = 1 → 0) emission across diverse
regions of the Perseus and Serpens Molecular Clouds. I then present a detailed
analysis of the Barnard 1 and L1451 regions in Perseus. A non-binary dendrogram
analysis of Barnard 1 N2H+ emission and all L1451 emission shows that the most hi-
erarchically complex gas corresponds with sub-regions actively forming young stars.
I estimate the typical depth of molecular emission in each region using the spatial
and kinematic properties of dendrogram-identified structures. Barnard 1 appears to
be a sheet-like region at the largest scales with filamentary substructure, while the
L1451 region is composed of more spatially distinct ellipsoidal structures.
I then do a uniform comparison of the hierarchical structure and young stellar
content of all five regions. The more evolved regions with the most young stellar
objects (YSOs) and strongest emission have formed the most hierarchical levels.
However, all regions show similar mean branching properties at each level, sug-
gesting that dense gas fragmentation proceeds in a hierarchically similar way from
earlier to later stages of star formation. Compared to the more evolved YSOs, the
youngest YSOs are preferentially forming within leaves and at high-level locations
in dendrogram hierarchies, indicating that dense gas in molecular clouds must reach
a state of hierarchical complexity before young stars form efficiently.
HIGH-RESOLUTION IMAGING OF
DENSE GAS STRUCTURE AND
KINEMATICS IN NEARBY MOLECULAR
CLOUDS WITH THE CARMA
LARGE AREA STAR FORMATION SURVEY
by
Shaye Storm
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland at College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2015
Advisory Committee:
Professor Lee Mundy, chair
Professor Eve Ostriker
Professor Alberto Bolatto
Dr. Mark Wolfire
Professor Richard Walker, Dean’s representative
c© Copyright by
Shaye Storm
2015
Preface
This thesis contains a combination of research that has already been published and
new results to be published in the future. Chapter 2, entitled “CARMA Large Area
Star Formation Survey: Project Overview with Analysis of Dense Gas Structure and
Kinematics in Barnard 1,” has been published in the Astrophysical Journal (Storm,
S., Mundy, L. G., Ferna´ndez-Lopez, M., et al., 2014, ApJ, 794, 165). Chapter 1,
entitled “Introduction,” includes parts of the introduction from the published work
presented in Chapter 2. Chapter 3, entitled “CARMA Large Area Star Formation
Survey: The Young L1451 Region within Perseus,” is in preparation to be submitted
to the Astrophysical Journal (Storm, S., Mundy, L. G., Lee, I. J., et al., 2015, ApJ,
in preparation). The cross region comparison in Chapter 4 builds from the previous
chapters and from published results of Serpens Main (Lee, K. I., Ferna´ndez-Lo´pez,
M., Storm, S., et al., 2014, ApJ, 797, 76) and results in preparation for Serpens
South (Ferna´ndez-Lo´pez et al. 2015) and NGC 1333 (Mundy et al. 2015).
The thesis observations and research are based on a CARMA Key Project that
was proposed in December 2011. I was a co-investigator on the proposal for the
CARMA Large Area Star Formation Survey, with Professor Lee Mundy as the
Principal Investigator. The project was based on pilot observations of the Perseus
NGC 1333 region, and was approved in February 2012 to observe two additional
regions within Perseus and two regions in Serpens. I led the observations and data
ii
calibration for the Key Project for its entire duration, from April 2012 to August
2013. After the observations were complete, I led the effort to determine the best
mapping techniques. Once the science-ready data cubes for each region were created,
I led the science analysis of the two youngest Perseus regions: Barnard 1 and L1451.
Other team members led the science of NGC 1333 and the Serpens regions, while I
contributed to those works. I was the principal developer of the dendrogram analysis
of all regions that went into each published and upcoming paper mentioned above.
Katherine Lee and Aaron Meisner led the construction of Herschel -based column
density and temperature maps presented in Chapters 3 and 4.
iii
To my family.
iv
Acknowledgements
Graduate school has been the best time of my life. I have many people to
acknowledge and thank. I must thank Lee Mundy for his guidance as an
astronomer, scientist, and negotiator. I always enjoyed our meetings and
discussions, and felt comfortable asking questions and expressing ideas.
I also owe Lee thanks for supporting many trips to observatories and
conferences around the country and world. I want to give a big thank you
to Peter Teuben—this thesis is built on hundreds of hours of CARMA
observations, and it is Peter who played a critical role in processing all
that data. I also want to thank Peter for the countless times he helped me
troubleshoot MIRIAD and other computing problems, for taking great
photos, and for being a great person to bounce ideas off of. Thank you as
well to Marc Pound, who was another vital person for figuring out subtle
MIRIAD tasks and computer needs, and for keeping the atmosphere of
the LMA friendly. I want to thank Eve Ostriker for her guidance in my
research. Eve was an invaluable resource for connecting the observations
in this thesis to theories of star formation. From the time I took her
v
Radiative Processes class, to the end of my grad school career, she was
always willing and able to help me understand the processes in molecular
clouds.
Grad school started off with coursework, and I want to thank the great
professors I had: Eve Ostriker, Andy Harris, Derek Richardson, Alberto
Bolatto, Sylvain Veilleux, Patrick Harrington, Cole Miller, and Stacy
McGaugh. I learned a lot in those classes, and I still refer to Eve and
Alberto’s ISM notes for my research.
I had a great group of classmates to share those classes and the rest of
grad school with. Thanks to Che-Yu for being my star formation theo-
rist companion, to Alex for his soccer coaching, and to DJ for fun nights
in DC. Thanks to Rodrigo for being a great officemate, and for host-
ing us in Chile around his wonderful wedding. Thanks to Katie for the
best (eventually not so-)Secret Santa gift ever. The academically-older
grad students made my early years at Maryland memorable; thanks to
Bevin, Lisa, Stacey, and Hao for making those early years more fun,
and for giving me guidance. And a big thank you to the postdocs and
academically-younger grad students that made my last years more en-
joyable; thanks to David, Amy, Laura, and Maxime.
The Maryland Astronomy Department has an awesome professional staff.
Adrienne Newman and Susan Lehr made my numerous travel expense
forms relatively pain-free and were always willing to help with a smile.
Erik McKenzie and Mary Ann Phillips were always there to take care
of any administrative need, big or small. I also want to thank Stuart
Vogel, who has a been a great department chair for my entire tenure.
vi
I greatly enjoyed my brief teaching assistant tenure under Grace Deming
during my first year. Thanks to Grace for skillfully guiding my first
teaching experience and for all the tasty muffins on test days. Thank
you to Tracy Huard for guiding my research with Lee during my second
year as I was first being introduced to the world of star formation. Thank
you to Mark Wolfire, who has been attentive to any computer or ISM
questions I have had.
As this thesis is built on CARMA data, I must thank the great CARMA
and OVRO staff. I spent thirteen weeks at CARMA as an observer,
and enjoyed every one of those trips. Thank you to: Nikolaus Volgenau,
Cecil Patrick, Mary Daniel, Terry Sepsey, Erik Leitch, James Lamb,
Dave Woody, and any other person I may have interacted with during
my time there. I also need to thank Owens Valley and Cedar Flat,
themselves, for providing immense beauty and clean air.
I had a skilled team supporting my thesis research, and I thank all mem-
bers of the CLASSy collaboration that helped me with data analysis,
science discussions, and paper writing. A special thank you goes out to
Katherine and Manuel for sharing the expansive CLASSy workload.
I developed many great friendships at Maryland. I am grateful to Ka´ri
and Thora for letting me crash at their apartment so much during our
first year, and then for letting me move in with them shortly after.
And for adventurously touring me around Iceland (twice!), and for all
the years of friendship that we shared across Maryland and Virginia.
Thanks to Mary and James for making my first two years more homey,
for helping me get my driver’s license, and then for the fun visits in
California.
vii
My astronomy studies began back in college. I want to thank Susan
Benecchi who led the rooftop observing seminar that got me thinking
astronomy was something worth pursuing in more serious depth. I also
want to thank Jim Elliot for giving me my first astronomy research
experience, during which I spent many nights at Wallace Observatory
and learned my first astronomy-related computer skills. After deciding
to major in the Planetary Science track of Course 12, I was lucky to
do research related to asteroids under Rick Binzel. Rick was a great
advisor and helped propel me to two summer research experiences that
cemented my desire to attend graduate school for astronomy. I want
to thank all the people associated with the Kitt Peak and IfA-Hawaii
REUs, particularly my mentors, Nalin and Bobby.
I am thankful that my great friendships from college have stayed strong
through graduate school. I am grateful to Boris for all of his support
at MIT, for introducing me to what I now consider quality music, for
taking a competitive liking to handball, and for being great at keeping
in touch across long distances. I’d like to thank Sam for being a great
little brother—we complement each other well.
Thanks to Barnet for being the cool uncle that every person would love
to have, and (along with Barbara) for hosting fun weekends for me and
my friends.
I want to thank my great mom, dad, and brother for all their support
during grad school and the years leading up to this thesis. Thanks for the
countless boxes of goodies, for keeping track of my busy travel schedule,
for the visits to DC, for the meetups out west around observing runs,
and for the immense amounts of unconditional love.
viii
And most of all, thank you, Megan. You are the best thing that has ever
happened to me and I am incredibly excited for all of the experiences
we will share throughout our lives.
ix
Contents
List of Tables xiii
List of Figures xiv
1 Introduction 1
1.1 Historical View of Molecular Cloud Observations . . . . . . . . . . . 1
1.2 Properties of Molecular Clouds . . . . . . . . . . . . . . . . . . . . . 4
1.3 Molecular Cloud Surveys . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 CARMA Large Area Star Formation Survey . . . . . . . . . . 8
1.4 The Perseus and Serpens Molecular Clouds . . . . . . . . . . . . . . . 9
1.5 N2H+, HCO+, and HCN As Dense Gas Tracers . . . . . . . . . . . . 12
1.5.1 Chemical Pathways . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.2 Molecular Excitation . . . . . . . . . . . . . . . . . . . . . . . 15
1.5.3 Applications to this Thesis . . . . . . . . . . . . . . . . . . . . 21
1.6 Technical Overview of CARMA . . . . . . . . . . . . . . . . . . . . . 23
1.7 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Project Overview with Analysis of Barnard 1 26
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 CARMA Interferometric Observations . . . . . . . . . . . . . 29
2.2.2 CARMA Single-Dish Observations . . . . . . . . . . . . . . . 34
2.2.3 Joint Deconvolution of Interferometric and Single-Dish Cubes 35
2.2.4 Continuum Mapping . . . . . . . . . . . . . . . . . . . . . . . 36
2.3 Continuum Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4 Morphology of Dense Molecular Gas . . . . . . . . . . . . . . . . . . 40
2.4.1 Main Core Zone . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4.2 Ridge Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4.3 SW Clumps Zone . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5 Kinematics of Dense Molecular Gas . . . . . . . . . . . . . . . . . . . 49
2.6 Dendrogram Analysis of N2H+ . . . . . . . . . . . . . . . . . . . . . . 58
x
2.6.1 The Non-binary Dendrogram . . . . . . . . . . . . . . . . . . 59
2.6.2 Dendrogram Tree Statistics . . . . . . . . . . . . . . . . . . . 62
2.6.3 Dendrogram Spatial Properties . . . . . . . . . . . . . . . . . 66
2.6.4 Dendrogram Kinematic Properties . . . . . . . . . . . . . . . 69
2.7 Size-Linewidth and Cloud Structure . . . . . . . . . . . . . . . . . . . 75
2.7.1 Total Linewidth of Dendrogram Structures . . . . . . . . . . . 76
2.7.2 Resolved Linewidths of Dendrogram Structures . . . . . . . . 78
2.7.3 Inferring Cloud Depth from Resolved Size-Linewidth Relations 80
2.8 Summary of Barnard 1 Results . . . . . . . . . . . . . . . . . . . . . 88
3 The Young L1451 Region 91
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.3 Continuum Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4 Morphology of Dense Molecular Gas . . . . . . . . . . . . . . . . . . 99
3.4.1 Integrated Intensity Emission . . . . . . . . . . . . . . . . . . 99
3.4.2 Channel Emission . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5 Kinematics of Dense Molecular Gas . . . . . . . . . . . . . . . . . . . 111
3.6 Dendrogram Analysis of Molecular Emission . . . . . . . . . . . . . . 114
3.6.1 The Non-binary Dendrograms . . . . . . . . . . . . . . . . . . 114
3.6.2 Dendrogram Spatial and Kinematics Properties . . . . . . . . 117
3.6.3 Tree Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.7 Dust in L1451 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.7.1 L1451 Column Density and Temperature . . . . . . . . . . . . 132
3.7.2 Dendrogram Analysis of Dust . . . . . . . . . . . . . . . . . . 135
3.8 Understanding Star Formation in L1451 . . . . . . . . . . . . . . . . 138
3.8.1 Connecting molecular structures to physical cloud structures . 138
3.8.2 Energy balance of structures . . . . . . . . . . . . . . . . . . . 141
3.8.3 Closer Look at L1451-mm and L1451-west . . . . . . . . . . . 149
3.8.4 Depth of L1451 Structures: A Non-Filamentary Region . . . . 154
3.9 Summary of L1451 Results . . . . . . . . . . . . . . . . . . . . . . . . 160
4 Comparing All CLASSy Regions 165
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.2 Integrated Intensity Maps Across Regions . . . . . . . . . . . . . . . 169
4.3 YSO Statistics Across Regions . . . . . . . . . . . . . . . . . . . . . . 172
4.4 N2H+ Dendrograms Across Regions . . . . . . . . . . . . . . . . . . . 173
4.5 Statistical Comparison of Hierarchies . . . . . . . . . . . . . . . . . . 176
4.6 Linking Stellar Content to Hierarchies . . . . . . . . . . . . . . . . . 181
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
xi
5 Key Findings, Summary, and Future Work 196
5.1 Key Findings of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.2 Summary of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
5.2.1 CLASSy Observations . . . . . . . . . . . . . . . . . . . . . . 199
5.2.2 The Barnard 1 and L1451 Regions . . . . . . . . . . . . . . . 200
5.2.3 A Closer Look At L1451 . . . . . . . . . . . . . . . . . . . . . 205
5.2.4 Comparing All CLASSy Regions . . . . . . . . . . . . . . . . . 206
5.3 Looking Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
A Differences Between Clump-finding and Dendrograms 209
B A New Non-binary Dendrogram Procedure 214
C How to Compare Non-Binary Dendrograms of Different Regions 219
C.1 Noise Dependence of Dendrogram Structure and Statistics . . . . . . 220
C.2 Comparing Regions at Different Distances . . . . . . . . . . . . . . . 227
C.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
D Herschel-identified YSOs 230
Bibliography 230
xii
List of Tables
2.1 Observation Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Correlator Setup Summary . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Observed Properties of Continuum Detections . . . . . . . . . . . . . 38
2.4 Outflow Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5 N2H+ Dendrogram Leaf and Branch Properties . . . . . . . . . . . . 73
2.5 N2H+ Dendrogram Leaf and Branch Properties . . . . . . . . . . . . 74
3.1 Observation Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.2 Correlator Setup Summary . . . . . . . . . . . . . . . . . . . . . . . . 97
3.3 Observed Properties of Continuum Detections . . . . . . . . . . . . . 99
3.4 HCO+ Dendrogram Leaf and Branch Properties . . . . . . . . . . . . 125
3.4 HCO+ Dendrogram Leaf and Branch Properties . . . . . . . . . . . . 126
3.4 HCO+ Dendrogram Leaf and Branch Properties . . . . . . . . . . . . 127
3.5 HCN Dendrogram Leaf and Branch Properties . . . . . . . . . . . . . 128
3.6 N2H+ Dendrogram Leaf and Branch Properties . . . . . . . . . . . . 129
3.7 Tree Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.8 Dust Structure Properties . . . . . . . . . . . . . . . . . . . . . . . . 137
3.9 Virial Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.1 YSO Statistics in CLASSy Regions . . . . . . . . . . . . . . . . . . . 174
4.2 Tree Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.3 YSOs Found Within Leaves . . . . . . . . . . . . . . . . . . . . . . . 183
4.4 Leaves With YSOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
D.1 Non-c2d YSOs Identified with Herschel . . . . . . . . . . . . . . . . . 231
xiii
List of Figures
1.1 Optical view of a molecular cloud . . . . . . . . . . . . . . . . . . . . 2
1.2 Nearby molecular clouds on galactic coordinates . . . . . . . . . . . . 3
1.3 Overview of CLASSy regions in Perseus . . . . . . . . . . . . . . . . . 9
1.4 Overview of CLASSy regions in Serpens . . . . . . . . . . . . . . . . 10
1.5 Excitation Temperature vs. Critical Density . . . . . . . . . . . . . . 17
1.6 Line Temperature as Function of Column Density and Density . . . . 19
1.7 View of CARMA antennas . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1 Barnard 1 mosaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 Continuum detections in Barnard 1 . . . . . . . . . . . . . . . . . . . 37
2.3 Integrated intensity maps of Barnard 1 . . . . . . . . . . . . . . . . . 41
2.4 Example spectra for all molecules from Barnard 1 . . . . . . . . . . . 42
2.5 Integrated intensity maps from the Barnard 1 main core zone . . . . . 44
2.6 HCO+ and HCN outflows in Barnard 1 . . . . . . . . . . . . . . . . . 47
2.7 Integrated intensity maps from the Barnard 1 ridge zone . . . . . . . 49
2.8 Narrow filament discovery in Barnard 1 . . . . . . . . . . . . . . . . . 50
2.9 Integrated intensity maps from the Barnard 1 SW clumps zone . . . . 51
2.10 Maps of centroid velocity and velocity dispersion in Barnard 1 . . . . 56
2.11 Centroid velocities from Barnard 1 main core and ridge zones . . . . 57
2.12 Small-scale kinematics within Barnard 1 . . . . . . . . . . . . . . . . 57
2.13 Non-binary dendrogram for Barnard 1 . . . . . . . . . . . . . . . . . 61
2.14 Barnard 1 dendrogram leaves overplotted on integrated intensity . . . 62
2.15 Dendrogram structures across channels . . . . . . . . . . . . . . . . . 63
2.16 Fitting for dendrogram spatial properties . . . . . . . . . . . . . . . . 68
2.17 Fitting for dendrogram kinematic properties . . . . . . . . . . . . . . 70
2.18 Histograms of Barnard 1 dendrogram structure properties . . . . . . . 75
2.19 Size-linewidth relations using total linewidth . . . . . . . . . . . . . . 78
2.20 Size-linewidth relations using discrete linewidths . . . . . . . . . . . . 79
2.21 Cartoon connecting size-linewidth with cloud depth . . . . . . . . . . 85
2.22 Size-linewidth relations from numerical simulations . . . . . . . . . . 87
3.1 L1451 mosaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
xiv
3.2 L1451 continuum detection . . . . . . . . . . . . . . . . . . . . . . . . 99
3.3 Integrated intensity maps of L1451 . . . . . . . . . . . . . . . . . . . 101
3.4 HCO+ channel maps of L1451 . . . . . . . . . . . . . . . . . . . . . . 107
3.5 HCN channel maps of L1451 . . . . . . . . . . . . . . . . . . . . . . . 108
3.6 N2H+ channel maps of L1451 . . . . . . . . . . . . . . . . . . . . . . 109
3.7 Spectra from Feature A within L1451 . . . . . . . . . . . . . . . . . . 110
3.8 Spectra from Feature B within L1451 . . . . . . . . . . . . . . . . . . 110
3.9 Maps of centroid velocity and velocity dispersion in L1451 . . . . . . 114
3.10 HCO+ non-binary dendrogram from L1451 . . . . . . . . . . . . . . . 118
3.11 HCN non-binary dendrogram from L1451 . . . . . . . . . . . . . . . . 119
3.12 N2H+ non-binary dendrogram from L1451 . . . . . . . . . . . . . . . 119
3.13 Histograms of L1451 HCO+ dendrogram properties . . . . . . . . . . 131
3.14 Histograms of L1451 HCN dendrogram properties . . . . . . . . . . . 131
3.15 Histograms of L1451 N2H+ dendrogram properties . . . . . . . . . . . 132
3.16 Column density map of L1451 . . . . . . . . . . . . . . . . . . . . . . 133
3.17 Dust temperature map of L1451 . . . . . . . . . . . . . . . . . . . . . 134
3.18 Extinction map of L1451 with dust dendrogram structures . . . . . . 136
3.19 L1451 dendrogram branches on column density . . . . . . . . . . . . 139
3.20 L1451 dendrogram leaves on column density . . . . . . . . . . . . . . 139
3.21 CDF of column density with and without molecular emission . . . . . 141
3.22 L1451-mm vs. L1451-west . . . . . . . . . . . . . . . . . . . . . . . . 150
3.23 Size-linewidth relations for all L1451 tracers . . . . . . . . . . . . . . 155
4.1 Cartoon hierarchy of cloud . . . . . . . . . . . . . . . . . . . . . . . . 167
4.2 All N2H+ integrated intensity maps . . . . . . . . . . . . . . . . . . . 169
4.3 Column Density maps for B1 and L1451 . . . . . . . . . . . . . . . . 171
4.4 Column Density versus Integrated Intensity . . . . . . . . . . . . . . 171
4.5 Serpens Main non-binary dendrogram . . . . . . . . . . . . . . . . . . 176
4.6 Serpens South non-binary dendrogram . . . . . . . . . . . . . . . . . 177
4.7 NGC 1333 non-binary dendrogram . . . . . . . . . . . . . . . . . . . 177
4.8 Barnard 1 non-binary dendrogram . . . . . . . . . . . . . . . . . . . . 178
4.9 L1451 non-binary dendrogram . . . . . . . . . . . . . . . . . . . . . . 178
4.10 Serpens Main dendrogram structures and YSOs . . . . . . . . . . . . 188
4.11 Serpens South dendrogram structures and YSOs . . . . . . . . . . . . 189
4.12 NGC 1333 dendrogram structures and YSOs . . . . . . . . . . . . . . 190
4.13 Barnard 1 dendrogram structures and YSOs . . . . . . . . . . . . . . 191
4.14 Separation of YSOs and dendrogram leaves . . . . . . . . . . . . . . . 192
4.15 Dendrogram level of YSOs . . . . . . . . . . . . . . . . . . . . . . . . 193
A.1 Comparing Cloudprops and dendrogram algorithms . . . . . . . . . . 210
A.2 One-dimensional dendrogram example . . . . . . . . . . . . . . . . . 212
xv
B.1 Cartoon explaining new non-binary dendrogram algorithm . . . . . . 216
C.1 Dendrogram structure maps for different noise and parameters . . . . 223
C.2 Dendrograms for different noise and parameters . . . . . . . . . . . . 224
C.3 Dendrogram structure maps for different noise and uniform parameters225
C.4 Dendrograms for different noise and uniform parameters . . . . . . . 226
xvi
Chapter 1
Introduction
Galaxies are gravitationally bound collections of stars, gas, dust, and dark matter.
How stars form within galaxies is a fundamental question of astronomy and human
understanding. The life and death cycle of stars drives the chemical evolution of
the universe and the evolution of galaxies; the population statistics of stars affects
how many habitable exoplanets exist, and our Sun provides energy to support life
on our planet. This thesis is focused on the structure and kinematics of molecular
clouds, which are the birthplace of stars within galaxies. The goal is to achieve a
more complete understanding of how the gas and dust of galaxies turns into stars.
1.1 Historical View of Molecular Cloud Observa-
tions
Modern-day astronomers are interested in molecular clouds because we know they
are collections of molecular gas and dust where stars form; there is a strong cor-
relation between star formation and molecular gas, as opposed to atomic gas (e.g.,
Bigiel et al. 2008; Leroy et al. 2008). However, less than a century ago, molecular
1
clouds were only known as “holes in the heavens” due to the way they obscured op-
tical starlight and produced dark patches in an otherwise bright night sky. Barnard
(1913) was the first to propose that these dark patches were “not vacancies, but
rather some kind of obscuring body lying in the Milky Way, or between us and it,
which cuts out the light from the stars.” Figure 1.1 shows an optical image of a
molecular cloud, where dark patches are easily visible. The first detection of inter-
stellar molecules from these patches came around 1940 from optical stellar absorp-
tion features (e.g., Swings & Rosenfeld 1937; McKellar 1940; Adams 1941). The first
radio telescope detection of molecular emission came in 1963 with the centimeter-
wavelength observation of the OH radical (Weinreb et al. 1963). Detections later
pushed into the millimeter wavelength regime with improved instrumentation, and
the CO line was first detected by Wilson et al. (1970). From the late-1970s on-
ward, mapping molecules in Milky Way and extragalactic molecular clouds from
(sub)millimeter to centimeter wavelengths became common (e.g., Morris & Rickard
1982; Genzel & Stutzki 1989).
Figure 1.1: The Perseus Molecular Cloud, showing examples of optically dark
patches, bright O and B stars, and background stars that have been reddened by
dust. Photo Credit: David Pearson.
2
There have been numerous observations of molecular clouds over the past decades
that have greatly improved our understanding of star formation (see reviews by
Shu et al. 1987; Kennicutt & Evans 2012). In addition to the observation of molecules,
there have been campaigns to observe the thermal continuum emission from cold
cloud dust, as well as the infrared emission from young stellar objects (YSOs) form-
ing in clouds (some of these campaigns are discussed in Section 1.3). The most well-
studied Milky Way molecular clouds are nearby. Specifically, they are in Gould’s
Belt, which Benjamin Gould described as a ring of bright stars (Gould 1874). The
belt is a flattened, elliptical disk several hundred parsecs in radius that contains
numerous bright O- and B-type stars and stellar nurseries (Perrot & Grenier 2003).
Figure 1.2 shows the belt in galactic coordinates, along with the location of several
molecular clouds. The proximity of the belt’s molecular clouds to the Sun makes
them popular targets for observations that desire high spatial resolution. For exam-
ple, Taurus (Torres et al. 2012), Perseus (Hirota et al. 2011), Serpens (Dzib et al.
2010), and Orion (Kim et al. 2008) are ∼133, 235, 415, and 418 pc from the Sun,
respectively. At these distances, 5′′ angular resolution can resolve down to spatial
scales ∼700–2500 AU, meaning it is possible to study individual protostellar cores
and cloud structures that will form stars.
1.2 Properties of Molecular Clouds
Most of the Milky Way interstellar medium (ISM) is atomic due to the dissociation
of molecules by far ultraviolet (FUV) photons (Krumholz et al. 2008). To form a
molecular cloud, gas in the ISM must be accumulated to high enough column den-
sities (i.e., from gravity and turbulence) to shield the gas from the FUV photons—
a minimum visual extinction (AV ) of ∼0.5–1.0 is required (van Dishoeck & Blake
3
Figure 1.2: An IRAS 100 µm map of the galactic plane showing locations
of nearby molecular clouds, including the Perseus and Serpens clouds stud-
ied in this thesis. The solid lines mark the location of the Gould Belt across
galactic coordinates. Image from the JCMT Gould Belt Legacy Survey team:
http://www.eaobservatory.org/jcmt/science/legacy-survey/gbs/.
1998). Once this shielding occurs, HI can form H2 and C+ can turn into CO, lead-
ing to clouds that are readily observable in molecular CO emission (Dobbs et al.
2014). Roman-Duval et al. (2010) did a survey of the 12CO and 13CO in Milky Way
clouds, and found cloud masses between 102–107 M⊙, a median H2 number density
of 230 cm−3, a median surface density of 144 M⊙ pc−2, and a median global velocity
dispersion ∼1.3 km s−1. For a molecule rich galaxy, like the Milky Way, most of the
molecular mass is found in giant molecular clouds (GMCs) that have masses above
104 M⊙ (Williams et al. 2000). The nearby clouds of the Gould Belt are smaller and
less massive than those GMCs, but their proximity to the Sun makes them superior
locations to study the small-scale details of star formation.
The environment of a molecular cloud is magnetized and turbulent. The ratio of
magnetic energy to gravitational potential energy in clouds is not large enough to
prevent gravitational collapse; Crutcher (2012) showed that molecular clouds and
cores, where NH ≥ 1021 cm−2, are magnetically supercritical (cloud mass greater
than magnetic critical mass). Turbulence has more clear influence on molecular
cloud structure. Observations of molecular linewidths show that all molecular clouds
are turbulent, with typical non-thermal velocities ∼1–4 km s−1 on scales ∼1–10 pc
4
(Solomon et al. 1987; Heyer & Brunt 2004). These velocities correspond to super-
sonic motions with Mach numbers of 3–20 in the cold, molecular component of the
ISM, where typical temperatures range from 10–20 K (Ferrie`re 2001) and the corre-
sponding isothermal sound speed is ∼0.2–0.3 km s−1. Supersonic flows are capable
of causing strong density perturbations in clouds, since the gas is highly compress-
ible (Dickman 1985; Scalo 1987; Mac Low & Klessen 2004). Numerical simulations
show that these density perturbations can take the shape of observed cloud struc-
ture, and then fragment and collapse under self-gravity to form dense cores (e.g.,
Gong & Ostriker 2011; Federrath & Klessen 2012; Chen & Ostriker 2014).
Turbulence and self-gravity work together to create a large dynamic range of
spatial and density cloud structure that stretches from the lowest-extinction edge of
a cloud to the highest-extinction clumps within the cloud where stars will actively
form. Observations of 12CO and 13CO reveal that the large-scale cloud is filled
with relatively low-density (n ≤102−3 cm−3), supersonically turbulent gas at all
spatial scales, and can extend for several tens of parsecs (e.g., Kutner et al. 1977;
Lada & Reid 1978; Ridge et al. 2006). Overdensities formed within the low-density
gas create zones of active star formation at parsec scales with n ≥103−5 cm−3, such
as the NGC 1333 region within the Perseus cloud complex that was mapped in N2H+
by Walsh et al. (2007). These parsec-scale overdense regions evolve and fragment
to even higher densities (n ≥105−7 cm−3) as they form pre-stellar and proto-stellar
cores on scales of ∼0.01–0.1 pc (see di Francesco et al. 2007; Ward-Thompson et al.
2007, and references therein).
The progression of molecular cloud structure across spatial scales and densities
can be represented as a hierarchy, where the smaller, denser regions are substructures
of the larger, less-dense regions. Houlahan & Scalo (1992) developed a structure
tree representation of molecular clouds to quantify this nested, hierarchical nature,
5
and that method led to the usage of dendrogram algorithms in the past few years
to analyze hierarchical cloud structure (Rosolowsky et al. 2008b; Goodman et al.
2009). The progression to higher densities also comes with a decreasing volume
filling factor—most of the mass in a cloud is at low densities, so material above
105 cm−3, which is at the hierarchical peak of the cloud density structure, represents
a small percentage of the cloud’s total mass and volume (Mac Low & Klessen 2004).
The formation of overdensities within clouds and their subsequent evolution to
even higher densities, and ultimately to stars, is the focus of active research. It is
known that supersonic turbulent flows, magnetic fields, and self-gravity are all in-
volved, but the interplay between them across a broad range of size scales, and across
different environments, is not fully understood theoretically or observationally.
1.3 Molecular Cloud Surveys
There have been numerous surveys of nearby molecular clouds in the past decades.
The young stellar content of Gould’s Belt clouds was assessed by Spitzer Legacy
Surveys including the c2d survey (e.g., Evans et al. 2009) and the Gould’s Belt sur-
vey (e.g., Gutermuth et al. 2008). Complementary observations of gas and dust are
needed to link those protostars to their environment to understand how they formed.
It is also important to observe regions with pre-stellar cores and condensations to
map the state of clouds before star formation has begun.
A fundamental limitation of existing gas and dust observations is the lack of high-
resolution data tracking the structure and kinematics across complete, parsec-scale
star forming regions. To resolve 10,000-AU envelopes of dense gas and dust that
surround protostars or protostellar multiples, we require at least 3000-AU spatial
resolution to have a few beams across those envelopes. If we want to then understand
6
the environment from which those cores are forming, we need to be sensitive to scales
of one to a few parsecs to track the relationship between the gas and stars as clusters
of stars form.
The thermal continuum emission from molecular cloud dust has been most re-
cently observed throughout large areas of many clouds from 70–500 µm with the
Herschel Gould Belt Survey (Andre´ et al. 2010) and at 450 and 850 µm with the
JCMT Gould Belt Survey (Sadavoy et al. 2013). Those observations are limited
from achieving the goals stated above because the ground-based observations are
not sensitive to structure more than ∼0.17 pc at the distance of Perseus due to
spatial filtering (Sadavoy et al. 2013), while the Herschel observations are limited
to ∼8500 AU spatial resolution at the distance to Perseus for column density and
temperature maps.
The gas structure and kinematics of clouds, commonly traced by CO isotopo-
logues, has been observed by several campaigns, including the FCRAO observations
from the COMPLETE team of Perseus and Ophiucus (Ridge et al. 2006), JCMT
observations of Perseus (Hatchell et al. 2005), and JCMT Gould Belt Legacy Survey
observations (e.g., Buckle et al. 2012). The main observational limitation of these
observations is that the excitation properties of CO make it a better tracer of the
lower-density regions of the clouds than of the higher-density regions where stars are
actively forming, and that the 12C and 13C species are often optically thick in cold
regions preventing a view of the full column of material. Chemically, CO tends to
deplete due to freeze-out onto grains in regions with density above a few ×104 cm−3
(Bacmann et al. 2002) and gas temperature less than 20 K (Collings et al. 2003),
which is another reason it is not a good tracer of the coldest, densest cores where
stars will form. Observations of molecular species and transitions that are excited
at these higher physical densities and column densities are needed to peer through
7
the lower density gas, and to highlight the structure and kinematics of the material
directly feeding into the star formation.
In summary, existing surveys have shown the complex dust and gas structure of
molecular clouds, but they have not adequately captured the wide range of spatial
scales of the high physical density regime where stars form. To do this, new surveys
with higher resolution and larger spatial coverage of the high-density regime are
needed. These new surveys can improve our understanding of the internal physical
state of molecular clouds, with long term goals of understanding what drives and
controls the rate of star formation, why the stellar initial mass function has its
shape, and whether that shape depends on environment. In the near term, such
surveys that follow the structure and kinematics of cloud overdensities over a wide
range of spatial scales can provide a clearer picture of how material fragments along
the pathway to star formation.
1.3.1 CARMA Large Area Star Formation Survey
We started filling the need for new surveys with a Key Project on the Combined
Array for Research in Millimeter-wave Astronomy (CARMA). We carried out a large
area, high angular resolution survey of dense gas in nearby molecular clouds. The
CARMA Large Area Star Formation Survey (CLASSy) spent 700 hours imaging five
large areas of star formation in the N2H+, HCO+, and HCN (J = 1 → 0) molecular
lines. We chose these molecules because they are all tracers of dense gas and sample
a range of chemical/physical environments within a cloud (see Section 1.5). They
are all also observable in a single CARMA correlator setting.
CLASSy observed the Perseus Molecular Cloud Complex towards NGC 1333,
Barnard 1, and L1451 (see Figure 1.3), and the Serpens Molecular Cloud towards
Serpens Main and Serpens South (see Figure 1.4), to capture a range of star-forming
8
environments and evolutionary stages. We mapped each region with ∼1600 and
∼3000 AU spatial resolution at the distances of Perseus and Serpens (235 and
415 pc), respectively, to meet the requirement of resolving individual star-forming
cores (∼10,000 AU). We also covered large enough areas to capture the environ-
ment in which the cores formed—up to linear scales of 1 to 2 pc across each region.
These survey data were combined with many ancillary datasets—Spitzer catalogs
of young stellar objects (YSOs), Herschel images of heating sources, Herschel and
JCMT maps of dust and continuum sources, to name a few—to provide a total
picture of star-forming objects and the structure and kinematics of the dense gas
which is fueling their formation.
We review each CLASSy cloud in Section 1.4, discuss details of each molecule
in Section 1.5, and present the technical details of observations, calibration, and
mapping as part of Chapter 2.
1.4 The Perseus and Serpens Molecular Clouds
The Perseus and Serpens Molecular Clouds were chosen as targets for CLASSy
because they are nearby, and because of the large amounts of existing ancillary data
from other telescopes to combine with new CARMA observations of dense gas. Here
we review basic properties of each cloud.
Perseus is located 235 pc from the Sun (Hirota et al. 2011), and is the closest
cloud that is forming large numbers of low to intermediate-mass stars (Bally et al.
2008). The total mass of the cloud is estimated to be ∼4.8×103 M⊙ based on
extinction maps from 2MASS and Spitzer data (Enoch et al. 2006; Ridge et al. 2006;
Evans et al. 2009). It appears elongated across ∼7◦ (29 pc) of the sky in roughly the
east-west direction, with an estimated total area of ∼70 pc2 based on the AV =3 mag
9
Figure 1.3: Overview of the CLASSy regions in the western portion of the Perseus
Molecular Cloud, as seen by Herschel 350 µm (Andre´ et al. 2010) where the darker
shades of grey represent stronger dust emission relative to the lighter shades of
grey. The approximate areas mapped by CARMA are represented with rectan-
gles; the actual areas are not single rectangular fields for Barnard 1 and L1451.
Projected distances between regions are given, assuming a distance of 235 pc.
contour from 2MASS extinction (Ridge et al. 2006). The star formation within
the cloud is not distributed uniformly across this entire area. The main sites of
clustered star formation can be separated into an eastern and western half. The
most prominent region in the eastern half is the IC 348 star-forming cluster (not
pictured in Figure 1.3), which contains nearly half of the Perseus YSOs identified
by the Spitzer c2d project (Jørgensen et al. 2008). The cluster is considered to be
the oldest region of ongoing star formation in Perseus at 2–4 Myr old (Bally et al.
2008).
The western half of Perseus contains younger, more active clusters of star for-
mation. The most prominent region in this half is the NGC 1333 star-forming
10
Figure 1.4: Overview of CLASSy regions in the Serpens Molecular Cloud, as
seen by Herschel 350 µm (Andre´ et al. 2010). The approximate areas mapped by
CARMA are represented with rectangles; the actual areas are not single rectangu-
lar fields for either region. The Serpens Main data is presented in Lee et al. (2014),
while an analysis of the Serpens South N2H+ filaments is in Ferna´ndez-Lo´pez et al.
(2014).
cluster, which has about 115 associated YSOs (Jørgensen et al. 2008) and dozens of
protostellar outflows and shocks (Arce et al. 2010). NGC 1333 is estimated to be
younger than IC 348, at an age of about 1–2 Myr (Wilking et al. 2004; Bally et al.
2008). There are several smaller regions of star formation within a few parsecs of
NGC 1333, including Barnard 1, L1448, L1455, and L1451, which are thought to be
of a similar age as, or slightly younger than, NGC 1333, based on their star formation
statistics. CLASSy focused on three evolutionarily distinct regions of star formation
in the western half of Perseus that are in close proximity: NGC 1333, Barnard 1,
and L1451. Figure 1.3 shows a view of the cool dust in this region, and we discuss
specifics of each region in later chapters. Chapters 2 and 3 focus on Barnard 1 and
11
L1451, respectively, while Chapter 4 compares the dense gas structure and young
stellar content of all three regions.
The Serpens Molecular Cloud is located 415 pc from the Sun (Dzib et al. 2010).
This measurement was done using the very long baseline array (VLBA), and is from
a souce in the Serpens Main core. Therefore, the distance measurement might not
apply to Serpens South, which is located about 24 pc to the South in the Aquila
Rift system. However, since no VLBA measurements have been made for sources
in Serpens South, and since both regions have gas with similar radial velocities
(Gutermuth et al. 2008), we assume both CLASSy Serpens regions are at 415 pc.
The total mass of the cloud that contains Serpens Main is estimated to be
∼2016 M⊙, with a total area of ∼18 pc2 (Evans et al. 2009). It has two primary
clustered regions with young star formation—one being the aforementioned, well-
studied Serpens Main, and the other being a recently discovered region known as
the Serpens G3YG6 cluster (Djupvik et al. 2006). Serpens Main is the region with
highest extinction and largest concentration of YSOs in the cloud (Harvey et al.
2007), and most of its mass is concentrated into two central clusters (Eiroa et al.
2008). It is estimated to have an age of ∼2 Myr (Erickson et al. 2015). Serpens
South was discovered as part of the Spitzer Gould Belt Legacy Survey in the Serpens-
Aquila Rift (Gutermuth et al. 2008). The region has a bright “hub” of dense gas
with a high fraction of younger YSOs, suggesting a recent burst of star formation
(Gutermuth et al. 2008). Several filaments radiate from the hub, which have made
this region a popular target for studying the role of filaments in star formation
(Kirk et al. 2013; Ferna´ndez-Lo´pez et al. 2014; Nakamura et al. 2014). We note
that we will refer to Serpens Main and Serpens South as both being in the Serpens
Molecular Cloud, even though major surveys, such as Spitzer c2d, did not include
Serpens South in their area coverage.
12
The CLASSy work on Serpens Main and Serpens South has been led by Kather-
ine Lee (Lee et al. 2014) and Manuel Ferna´ndez Lo´pez (Ferna´ndez-Lo´pez et al. 2014),
respectively. These regions are not the focus of the work in this thesis, but are oc-
casionally touched on in comparison to Perseus regions in Chapters 2 and 3, and
are used in Chapter 4 as part of a cross-comparison between all CLASSy regions.
1.5 N2H+, HCO+, and HCN As Dense Gas Trac-
ers
CLASSy utilizes the N2H+, HCO+, and HCN (J = 1 → 0) transitions as probes
of gas distribution and kinematics. In this section, we review important aspects
of their molecular excitation and emission, which are needed to interpret CLASSy
data. In general, the strength of emission seen from a molecule depends on gas
density, molecular column density, gas temperature, and kinematics, whose values
depend on the physical properties and chemistry of the cloud.
1.5.1 Chemical Pathways
Starting with chemistry, a molecule must be present in the gas phase if there is any
chance to observe it. Therefore, it is useful to look at the formation and destruction
paths for our three molecules. The most common chemical pathway for the for-
mation of N2H+ in dense clouds is: H3+ + N2 → N2H+ + H2 (Prasad & Huntress
1980). The H3+ parent is an abundant ion in dense molecular gas, and is formed
through a two-step process: cosmic ray (cr) ionization of H2 to form H2+, followed
by H2+ + H2 → H3+ + H (McCall et al. 1999). The N2 parent is commonly created
from N + NH → N2 + H. A second frequent path to form N2H+ occurs from cosmic
ray ionization of He to form He+, followed by He+ + N2 → N2+ + He, and then
13
N2+ + H2 → N2H+ + H (Prasad & Huntress 1980).
The most common destruction mechanism of N2H+ involves reaction with CO,
which is often the second most abundant molecule in molecular clouds (after H2):
N2H+ + CO → HCO+ + N2 (Prasad & Huntress 1980). Since CO is strongly
depleted from freeze-out onto grains when densities are above a few × 104 cm−3
(Bacmann et al. 2002) and when temperatures get below ∼20 K (Collings et al.
2003), the primary destruction pathway is very depletion-sensitive. In chemical
models and observations, N2H+ is typically one of the last observable species to be
depleted (Bergin & Langer 1997; Caselli et al. 2002). Hence, N2H+ is preferentially
a good tracer of cold material at relatively high density.
The primary production pathway for HCO+ in dense parts of clouds is H3+ +
CO → HCO+ + H2 (Prasad & Huntress 1980). At lower column densities associ-
ated with surfaces of photodissociation regions (PDRs), HCO+ is produced from
CO+ + H2 → HCO+ + H (Young Owl et al. 2000). This shows that HCO+ is
preferentially found in regions with higher CO abundance and higher ionization
fraction. HCO+ is destroyed by dissociative recombination as HCO+ + e− → CO
+ H (Prasad & Huntress 1980), and by charge exchange with neutral Mg and Fe
in denser regions (Young Owl et al. 2000). Thus, HCO+ can be abundant in both
lower density gas with moderate ionization, and in dense, cool gas. The depletion
of CO in the coldest gas will limit the abundance of HCO+ in those regions.
HCN is produced in PDRs and densely clumped regions through reactions in-
cluding H2CN+ + e → HCN + H and CH2 + N → HCN + H (Young Owl et al.
2000; Boger & Sternberg 2005). The main method of HCN destruction in molecu-
lar clouds is cosmic-ray–induced photodissociation (crp) as HCN + crp → CN +
H (Boger & Sternberg 2005), while removal through reaction with C+ and HCO+
is also common (Young Owl et al. 2000). PDR models of Young Owl et al. (2000)
14
predict that HCN has a similar abundance to HCO+, but observations of the Orion
bar in the same paper show that HCN is often more confined to clumps while HCO+
is more diffuse. Young Owl et al. (2000) argue that differences in the molecular ex-
citation of these two molecules, combined with varying cloud density, is a likely
cause for the observed spatial differences in the molecular emission.
The discussion above highlights the differences in chemical pathways and abun-
dances of the three CLASSy molecules: N2H+ will be the most abundant of the
three in high density, cold regions where CO has been depleted, while HCN and
HCO+ are predicted to have similar abundances throughout the cloud, but emit
in distinct spatial locations likely due to differences in excitation (Young Owl et al.
2000). Even with their differences, all three molecules are considered “dense gas
tracers” and are more similar to one another in their emission than any of them is
to CO, which is excited at lower densities. To quantitatively understand at what
cloud densities the J = 1 → 0 rotational transition of each molecule emits most
efficiently, we need to review some basic properties of molecular emission.
1.5.2 Molecular Excitation
The rotational energy levels of linear rotors like N2H+, HCO+, and HCN are quan-
tized according to their angular momentum, J. Their rotational levels are excited
at a temperature on the order of a few to tens of Kelvins. Vibrational modes and
electronic transitions of molecules have energy levels requiring upwards of a few 100–
1000 K for excitation. Since cloud temperatures in the absence of strong internal
heating sources are 10–30 K, there is only enough energy to excite the rotational
modes.
To get a J = 1 → 0 photon, a molecule must make a radiative transition from
the J=1 to J=0 level. If we treat the molecule in the two-level approximation,
15
statistical equilibrium dictates that the total number of collisional and radiative
transitions from the lower-to-upper state is equal to the number of transitions from
an upper-to-lower state1. Therefore, the excitation of the J = 1 → 0 transition can
be determined by the balance of the rate of downward de-excitations with the rate
of upward excitations. The downward rate is controlled by collisional de-excitation
(this has a dependence on the collisional cross-section and density of colliders),
induced photo emission (this has a dependence on the radiation field), and spon-
taneous emission (this value is determined for each molecule and transition based
on the dipole moment of the molecule and the frequency of the transition). The
upward rate is controlled by collisional excitation from the J=0 to J=1 level (this
has a dependence on the cloud kinetic temperature, collisional cross-section, and
density of colliders), and by photo absorption from the J=0 to J=1 level (this has
a dependence on the radiation field).
To summarize these terms in an equation, the rate balance for the two level
system is given as
nU [AUL + γULnH2 +BULJν ] = nL[BLUJν + γLUnH2 ]. (1.1)
On the left hand side of the equation, nU is the population number density of
the upper level, AUL is the Einstein coefficient for spontaneous emission from an
upper-to-lower level transition, γUL is the collisional rate of de-excitation from the
upper-to-lower level, nH2 is the number density of H2, which is the primary collider
species in molecular clouds, BUL is the Einstein coefficient for induced emission
from an upper-to-lower level transition, and Jν is the angle-averaged intensity of
the radiation field at frequency, νUL. On the right hand side of the equation, nL is
1A two-level system that only considers these levels is an approximation that is useful for
describing the statistical equilibrium and excitation of a line, even though molecules have multiple
rotational levels that can be excited in cloud environments.
16
the population number density of the lower level, BLU is the Einstein coefficient for
photo absorption from a lower-to-upper level transition, and γLU is the collisional
rate of excitation from the lower-to-upper level.
To quantify the excitation properties of a molecular transition, Equation 1.1 can
be solved for nU/nL and written in terms of nH2 , AUL, γUL, the kinetic (thermal)
temperature of the gas, Tk, the radiation temperature of the background radia-
tion field, Tr, and the excitation temperature, Tex (see Spitzer 1998, Chapter 4 for
discussion). The formal definition of the excitation temperature, Tex, is
nU
nL
= gUgL
e −hνkTex (1.2)
where gU and gL are the statistical weights of the upper and lower states of the
molecule, and the exponential represents the Boltzmann distribution between the
given energy states. The excitation temperature is the temperature that we would
expect to measure for a system of particles that has a given nU/nL ratio.
Since the full n-level equation for the ratio nU/nL in terms of these values is
complex, for simplicity, the equation of the two-level system in the optically thin
limit can be written as
e −hνkTex =
e
−hν
kTr
1−e
−hν
kTr
+ nH2γULAUL e
−hν
kTk
1
1−e
−hν
kTr
+ nH2γULAUL
, (1.3)
with Figure 1.5 showing how Tex behaves as a function of nH2γUL/AUL.
From Figure 1.5 and Equation 1.3, it is clear that when collisional excitation
and de-excitation dominates in high density gas, Tex approaches Tk; when radiative
processes dominate in low density gas, Tex instead approaches Tr, which is the cosmic
background radiation field in the absence of a significant local radiation field. In the
latter case, the cloud will be in complete thermodynamic equilibrium with the CMB
radiation field meaning that no line will be observed. In Figure 1.5, Tex begins to rise
17
significantly above the background radiation field near nH2γUL/AUL = 1; the nH2
that produces a value of unity for this expression is defined as the critical density
of the given transition.
Figure 1.5: Excitation temperature as a function of critical density for the low
opacity limit.
The curve in Figure 1.5 is an approximation at the optically thin limit with
no radiative trapping, which is not always the case for transitions in dense clouds
where column densities can be high and lines can be optically thick. The effective
critical density would be lower when high column density and photon trapping is
taken into account. Because of this, it is not formulaic to solve for the density at
which a given molecule will start efficiently emitting, and radiative transfer code is
needed to model molecular emission in a variety of non-thermalized conditions to
find the density and column density that will produce emission for a given molecule
in molecular cloud environments.
To demonstrate how molecular emission depends on volume density and column
18
density in a cloud environment, we used the Large Velocity Gradient (LVG; Sobolev
1957; Rybicki & Hummer 1978) radiative transfer code in MIRIAD (Multichannel
Image Reconstruction, Image Analysis and Display; Sault et al. 1995). We made
grids of line emission from a 10 K cloud as a function of H2 density (cm−3) and
molecular column density (cm−2) for HCN and HCO+ (J = 1 → 0), and present
the results in Figure 1.6. The dark areas of the grids are where the excitation tem-
perature of the transition is close to the cosmic background radiation temperature,
meaning that only very weak, or undetectable, emission is produced.
For a fixed, low column density, if the H2 densities are increased, then weak emis-
sion begins to appear as purple intensity in the bottom-right of the grids—these are
the densities needed to collisionally excite the transitions above the cosmic back-
ground radiation field, and correspond to the critical density in Figure 1.5 (solid
vertical line) where Tex begins to rise. For a fixed, low density, if the molecular
column densities are increased, then weak emission begins to appear as purple in-
tensity in the top-left of the grids—these are the column densities needed to excite
the transition through radiative trapping of photons. In the center to upper-right of
the grid, it is clear that increasing density and column density (within these plotted
limits) both lead to stronger line emission.
There are two important things to note from Figure 1.6. First, it is clear that
an observed line temperature can be produced by a combination of different density
and column density. This visualizes the cross-correlation of the two quantities at low
optical depths (TB ∼ Texτ ∝ TexNx for τ ≪ 1), and shows that molecular emission
in clouds is really a tracer of both density and column density, even though it is
often said that a specific molecule “X” traces gas above some density (also see Evans
1999; Shirley 2015). Second, a given J = 1 → 0 line temperature occurs at higher
densities and column densities for HCN than HCO+. This shows that HCN traces
19
Figure 1.6: Grids of HCN and HCO+ brightness temperatures (K) as a function
of H2 density (cm−3) and molecular column density (cm−2), for a fixed kinetic
temperature of 10 K. The grids were calculated using the LVG radiative trans-
fer models in MIRIAD. The solid white contours represent 1–6 K emission line
temperatures, in 1 K increments. The contour at the purple/dark blue transition
corresponds to 1 K. The white region of the grid represents temperatures that
exceed ∼6.5 K.
higher dense gas column densities than HCO+ by about an order of magnitude, and
is why HCN is often referred to as a “higher density gas tracer” than HCO+. We do
not show a grid for N2H+, but it traces slightly higher dense gas column densities
than HCN.
We have focused on emission so far, but self-absorption is also commonly seen
towards molecular clouds. Self-absorption is observed as a dip in the emission profile
of a line, and will be present if emitted photons pass through a significant column
of lower-density or lower temperature material where the species is abundant and
overpopulated in the lower energy level of the transition before reaching the ob-
server. This condition is often met in molecular clouds for HCO+ and HCN: a
cloud naturally has lower-density, larger-scale regions surrounding higher-density,
smaller-scale regions, and from the discussion in Section 1.5.1, we know that HCO+
20
and HCN can be created in both high- and low-density layers of a molecular cloud
(Young Owl et al. 2000). For J = 1 → 0 photons that are emitted from deep inside
the cloud by HCN and HCO+ molecules, if there is a significant column of lower-
density material with HCO+ and HCN in the J=0 state between the cloud and
the observer, then those J = 1 → 0 photons will be readily absorbed in the outer
layer. This will produce a self-absorption dip at the velocity of the lower density
gas. The key point is that low density gas, n ∼ 102− 104 cm−3, can have significant
opacity in the J = 1 → 0 transition yet have very low excitation temperature. This
gas absorbs photons but has nearly no emission. If a transition exhibits significant
self-absorption across a cloud, then it can become challenging to understand cloud
properties. This is one of the reasons most of this thesis focuses on N2H+ emission,
which suffers from the least amount of self-absorption.
1.5.3 Applications to this Thesis
In this thesis, we analyze the N2H+, HCO+, and HCN J = 1 → 0 intensity
(Jy beam−1 units, analogous to line temperature in K units) and integrated in-
tensity (Jy beam−1 km s−1 units, analogous to K km s−1 units) emission structure
of the CLASSy clouds, as opposed to their true density and column density struc-
ture. With only a single transition for each molecule, we are restricted in what
physical properties of the cloud we can measure. To estimate physical densities
using our CLASSy data, a second transition, for example, J = 3 → 2, would need
to be observed at the same high angular resolution. The strength of the two lines
could be used to estimate molecular column density and density.
In theory, the N2H+ J = 1 → 0 transition has hyperfine structure which should
allow for the measurement of opacity (if 1 . τ . 10 in the strongest hyperfine
lines), and hence allow an estimate of the N2H+ column density from the J = 1 → 0
21
line alone. In practice, the signal-to-noise of individual spectra is not high enough
to derive reliable opacity and excitation estimates across large areas of our maps,
and the observed hyperfine ratios are often not consistent with the expected ratios
for local thermodynamic equilibrium (LTE) for a single excitation temperature (e.g.,
Caselli et al. 1995; Matthews et al. 2006; Daniel et al. 2007); this makes any column
density derivation uncertain. Rather than relying on a single molecular transition
to estimate column densities, it is more reliable to derive column densities using
continuum observations at multiple wavelengths, such as those for L1451 in Chap-
ter 3 using Herschel observations from 160–500 µm. However, those observations
are limited in angular resolution compared to our CLASSy data (36′′ for Herschel
at 500 µm versus 7′′ for CLASSy), so they are not ideal for much of the analysis we
set out to do.
Even without knowing precise column density or density values within each
CLASSy beam, we know from the discussion above that the molecular emission
is tracing high physical and column density material. Star formation requires high
physical and column densities—high column density, low volume density regions
will not form stars. Therefore, even though line intensity and integrated intensity
do not directly scale to column density or density, we know they are tracing cloud
regions that are viable locations for star formation. In the analysis that follows in
later chapters, particularly in Chapter 4, we will assume that high (low) intensity
and integrated intensity implies high (low) column density of dense gas.
We can assign ballpark numbers to our discussion of gas emission as a com-
bined tracer of density and column density using a radiative transfer code such as
RADEX (van der Tak et al. 2007). It is possible to excite HCO+ (J = 1 → 0) emis-
sion to above 1 K brightness temperature near densities ∼104 cm−3 with molecular
column density of ∼1013 cm−2 and gas kinetic temperature at ∼10 K. For simi-
22
lar column density and kinetic temperature, HCN (J = 1 → 0) is excited to 1 K
brightness temperature near densities ∼105 cm−3. N2H+ (J = 1 → 0) is typically
an order of magnitude less abundant in molecular clouds relative to HCO+ or HCN
(Blake et al. 1987; Friesen et al. 2010; Sanhueza et al. 2012); for molecular column
density ∼ few × 1012 cm−2 and gas kinetic temperature ∼10 K, N2H+ (J = 1 → 0)
is excited above 1 K brightness temperature near densities of ∼105 cm−3. In general,
if column densities or gas kinetic temperatures are higher than the values used here,
the physical density needed to excite observable lines decreases.
The earlier discussion of chemistry stated that HCO+ and HCN are abundant in
even lower-density, outer regions of clouds. However, those regions do not have the
physical conditions needed to excite the ground state transitions, and mainly play
a role in self-absorption. We also note that these transitions are emitting from even
higher density regions than the ballpark numbers listed, but that the fraction of
total molecular cloud mass decreases with increasing density (Mac Low & Klessen
2004). This means that even if there is gas with densities greater than 106 cm−3, it
will be emitting HCO+ (J = 1 → 0) photons that are a small fraction of the total
number of HCO+ (J = 1 → 0) photons emitted by the cloud. In this sense, a tracer
is most sensitive to the lowest density where it begins to efficiently emit. A caveat
to this argument is that if the observing beam is small enough to isolate the densest
regions, or if an interferometer is used to resolve out all the lower-density emission,
then lower-density photons will not dominate the emission.
23
1.6 Technical Overview of CARMA
This thesis primarily uses data from the Combined Array for Research in Millimeter
Astronomy (CARMA). This section provides a brief technical introduction to the
CARMA facility, with a focus on the systems used for observations in the upcoming
chapters. More details specific to CLASSy observations can be found in Chapter 2.
CARMA is a heterogeneous, 23-element interferometer, located in the eastern
Sierras of California at an elevation of 7217 feet. It has six 10.4-m dishes, nine 6.1-m
dishes, and eight 3.5-m dishes, with a total collecting area of 850 meters squared.
The interferometer can operate as a single 23-element array, or as an independent
15-element array with the larger dishes and an independent 8-element array with
the smaller dishes. The antennas are typically arranged in one of five configurations,
ranging from the most compact, providing baselines between 4.0 and 66 m, to the
largest with baselines between 0.2 and 2 km. The most compact and most extended
arrays provide angular resolution near 11′′ and 0.3′′ respectively at 100 GHz.
Figure 1.7: View of CARMA antennas. Credit: Jens Kauffmann.
CARMA can observe at wavelengths of 1 mm, 3 mm, or 1 cm. All of the
CARMA observations in this thesis were done at the 3 mm wavelength using the
23-element array. All of the 6.1-m and 10.4-m antennas are outfitted with 3 mm
single-polarization, double sideband receivers. The incoming radio frequency signal
is mixed with a local oscillator frequency to produce an intermediate frequency.
24
The sidebands are then separated in the correlator by phase-switching the local
oscillators. The 3.5-m antennas can also observe at 3 mm, though they have single-
sideband receivers, which means that 23-element observations only produce usable
data in the upper sideband. All antennas have 1 cm receivers that can be tuned to
27–36 GHz. The 6.1-m and 10.4-m antennas have 1 mm dual circular polarization,
double sideband receivers that can be tuned to 215–265 GHz.
The CLASSy observations used the CARMA spectral line correlator, which is
a double sideband correlator with 4 GHz of bandwidth per sideband in standard
operation. In 23-element mode, only the upper sideband is used, and four of the
standard eight tunable bands can be configured with bandwidths ranging from 2 to
500 MHz. The channel resolution of those bands depends on the bit level chosen in
the correlator, which can be set to balance sensitivity and spectral resolution. As an
example, for 3-bit observing in 23-element mode, there are 47 channels across the
500 MHz band with 10.4 MHz channel width, and 159 channels across the 8 MHz
band with 0.05 MHz channel width.
1.7 Thesis Outline
This thesis is structured as follows. Chapter 2 presents an overview of the CLASSy
project with a focus on the Barnard 1 region within Perseus. It discusses CLASSy
observations and data calibration, spectral line fitting, dendrogram analysis, and a
method to determine the depth of clouds from size-linewidth relations. Chapter 3
presents the analysis of the L1451 region of CLASSy, with a focus on the state of
star formation in such a young region. Chapter 4 presents a comparison of all five
CLASSy regions, with a dendrogram analysis of their N2H+ integrated intensity
maps, and a comparison between dendrogram structures and young stellar content.
25
A summary and look toward future work is in Chapter 5.
26
Chapter 2
Project Overview with Analysis of
Dense Gas Structure and
Kinematics in the Barnard 1
Region of Perseus
Abstract
We present details of the CARMA Large Area Star Formation Survey (CLASSy),
while focusing on observations of Barnard 1. CLASSy is a CARMA Key Project
that spectrally imaged N2H+, HCO+, and HCN (J = 1 → 0 transitions) across over
800 square arcminutes of the Perseus and Serpens Molecular Clouds. The obser-
vations have angular resolution near 7′′ and spectral resolution near 0.16 km s−1.
We imaged ∼150 square arcminutes of Barnard 1, focusing on the main core, and
the B1 Ridge and clumps to its southwest. N2H+ shows the strongest emission,
with morphology similar to cool dust in the region, while HCO+ and HCN trace
27
several molecular outflows from a collection of protostars in the main core. We iden-
tify a range of kinematic complexity, with N2H+ velocity dispersions ranging from
∼0.05–0.50 km s−1 across the field. Simultaneous continuum mapping at 3 mm
reveals six compact object detections, three of which are new detections. A new,
non-binary dendrogram algorithm is used to analyze dense gas structures in the
N2H+ position-position-velocity (PPV) cube. The projected sizes of dendrogram-
identified structures range from about 0.01–0.34 pc. Size-linewidth relations using
those structures show that non-thermal line-of-sight velocity dispersion varies weakly
with projected size, while rms variation in the centroid velocity rises steeply with
projected size. Comparing these relations, we propose that all dense gas structures
in Barnard 1 have comparable depths into the sky, around 0.1–0.2 pc; this suggests
that over-dense, parsec-scale regions within molecular clouds are better described
as flattened structures rather than spherical collections of gas. Science-ready PPV
cubes for Barnard 1 molecular emission are available for download.
2.1 Introduction
This chapter presents the initial results for the Barnard 1 region. Barnard 1 is
located 3.5 pc to the east of NGC 1333 in the western half of the Perseus Molecular
Cloud (see Figure 1.3 in Chapter 1). We assume a distance of 235 pc based on VLBI
parallax measurements towards nearby sources in Perseus (SVS-13 in NGC 1333
(Hirota et al. 2008) and L1448-C in L1448 (Hirota et al. 2011)). In the context of
the CLASSy campaign, we classify Barnard 1 as a moderate-activity star forming
region, compared to the highly active NGC 1333 region that is dominated by a
complex array of protostellar outflows, and the low-activity L1451 complex that has
only one candidate protostar (Pineda et al. 2011).
28
Previous surveys of the young stellar content and dust in Barnard 1 reveal a
northeast-southwest oriented filament exhibiting a wide range of star formation
(see Figure 2.1)—progressing from a tight collection of pre- and proto-stellar cores
in the northeast “main core” that includes the well-studied B1-b and B1-c cores
(Hirano et al. 1999; Matthews et al. 2006; Hiramatsu et al. 2010), to a long filament
of starless gas and dust known as the B1 Ridge (Enoch et al. 2006), followed by a
collection of gas and dust clumps in the southwest that includes one protostellar
core and several Class II YSOs. In total, the Spitzer c2d team identified thir-
teen young stellar objects (YSOs) in our field (Jørgensen et al. 2006; Rebull et al.
2007; Evans et al. 2009). Twelve dust clumps were identified by Hatchell et al.
(2005) using SCUBA 850 µm data, while Kirk et al. (2006) identified five; the dif-
ference was attributed to different CLUMPFIND (Williams et al. 1994) thresholds.
Jørgensen et al. (2007) associated an embedded YSO with five of the SCUBA dust
clumps, while the rest of the dust clumps appeared starless.
This diversity of star formation activity along a single filament makes Barnard 1
a compelling region to spectrally image at high angular resolution. CLASSy adds to
the large collection of work already done on Barnard 1, and provides the first large
area (150 square arcminute), high angular resolution (7′′; 0.008 pc at 235 pc) spectral
view of the dense gas (n & 104−6 cm−3) across the entire field. This will allow us
to quantify the structure and kinematics of the gas that is actively participating in
the current generation of star formation in greater detail than ever before.
The primary goals of this chapter are to present: (1) the details of our CLASSy
observations and data calibration, (2) an overview of the dense gas morphology and
kinematics in Barnard 1, and (3) a dendrogram analysis of the N2H+ emission. In
Section 2.2, we describe the CARMA observations, data calibration, and imaging.
The continuum detections are summarized in Section 2.3. Section 2.4 provides a
29
large-scale view of the dense gas structure using integrated intensity maps. In Sec-
tion 2.5, we discuss techniques for spectral line fitting and present centroid velocity
and velocity dispersion maps. In Section 2.6, we create a dendrogram representation
of the N2H+ gas and calculate properties of identified dendrogram structures. In
Section 2.7, we use the spatial and kinematic properties of dendrogram-identified
structures to construct size-linewidth relations; these relations are then used to
probe the physical and turbulent nature of Barnard 1. Section 2.8 has a summary
of the initial results. Appendix A compares clump-finding and dendrogram methods
for identifying objects in this region, and Appendix B details our new dendrogram
algorithm that can produce non-binary hierarchies.
2.2 Observations
CARMA is an ideal facility for producing molecular line maps that are sensitive
to a wide range of spatial scales. The newly commissioned CARMA23 mode uses
the cross-correlations from all twenty-three antennas, which increases CARMA’s
imaging capability from the standard CARMA15 mode. Using CARMA23 in concert
with CARMA’s single-dish capability and fast mosaicing can produce large maps
that are sensitive to line-emission at all spatial scales. We detail the observations,
data calibration, and map making in the sections below.
2.2.1 CARMA Interferometric Observations
We mosaiced an approximately 8′ × 20′ area of Barnard 1 using CARMA. The to-
tal observing time (150 hours) was split evenly between DZ and EZ configurations,
which have projected baselines from about 1–40 kλ and 1–30 kλ, respectively. DZ
configuration observations occurred in the Spring and Fall of 2012, and EZ configura-
30
Table 2.1. Observation Summary
Array Dates Total Hours Flux Cal. Gain Cal. Mean Flux (Jy)
DZ April - May 2012 50 Uranus 3C84/3C111 18.3/3.8
October 2012 25 Uranus 3C84/3C111 17.5/2.9
EZ July - September 2012 75 Uranus 3C84/3C111 18.9/3.6
tion observations occurred in the Summer of 2012. Table 2.1 provides a summary of
the observations and calibrators. The “Z” in the DZ and EZ configurations refers to
use of the 23-element observing mode (CARMA23), which utilizes cross-correlations
from all 23 antennas: six 10.4-meter antennas, nine 6.1-meter antennas, and eight
3.5-m antennas. (Standard CARMA15 observing only includes the 10.4-meter and
6.1-meter antennas.)
CARMA23 provides more baselines compared with the CARMA15 mode–this
enhances imaging capabilities by filling in more of the uv -plane. It also offers shorter
baselines, which are important for two reasons: (1) more extended emission, if
present, is recovered, and (2) the increased uv -coverage improves the link between
the zero spacing information from single-dish and the interferometer visibilities when
doing joint deconvolution.
Our CARMA23 mosaic of Barnard 1 is made up of three adjoining rectangular
regions, each at a position angle of 40◦ east of north; it contains 743 individual
pointings in a hexagonal grid with 31′′ spacing. See Figure 2.1 for a depiction of
the pointing centers overlaid on a Herschel 250 µm image (Andre´ et al. 2010). The
reference position of the map, which is the center of the northern rectangle, is at
α=03h33m20s, δ=31◦08′45′′ (J2000); it encompasses the Barnard 1 main core with
the B1-b and B1-c continuum cores. The other two rectangles extending toward the
southwest were chosen to follow the Herschel dust emission.
During each pass through the map, we integrated for 15 seconds on each mosaic
31
Figure 2.1: Mosaic pointing centers overlaid on a Herschel 250 µm image of
Barnard 1 (white is brighter emission, red is fainter emission). We sampled the
field at 31′′ spacing; the smallest CARMA primary beam, from the 10.4-m anten-
nas, is about 77′′ near 90 GHz. We planned the observations to cover the brightest
dust emission in the Barnard 1 main core, and then cover the filamentary emission
that extends to the southwest. Additional pointings around the edge aid in joint
deconvolution by limiting strong emission at the edges of the single-dish maps.
position before moving to the next mosaic position. We used a newly commissioned
“continuous integration” technique that improves on-source efficiency (on-source
integration time compared to wall clock time) of large CARMA mosaics from about
35% to 48%. The improvement comes from continuously taking data, even while
antennas slew to a new mosaic position; the data for a given antenna is automatically
blanked while it is slewing. This technique removes the built-in software delay
32
associated with a slew to a new target or mosaic position. The gain in on-source
efficiency is critically important for large mosaic observations, with many moves
and short integration times between moves. This method should not be confused
with on-the-fly mosaicing, where the antennas are continuously moving while taking
data.
In CARMA23 mode, the correlator has four spectral bands in the upper side
band. The lower side band is not present on the 3.5-m telescopes; it is present but
not used on the 10.4 and 6.1-m telescopes. We tuned to the J = 1 → 0 transitions
of N2H+, HCO+, and HCN, and used a 500 MHz wide band for calibration and
continuum detections. Table 2.2 has an overview of the correlator setup. The
molecular lines were each placed in 8 MHz bands, which have 159 channels that are
0.049 MHz wide in 3-bit mode; this corresponds to ∼0.16 km s−1 velocity resolution
near 90 GHz. All hyperfine components of N2H+ and HCN fit within the 8 MHz
bands. However, there is high-velocity HCO+ and HCN emission from outflows that
lies outside our bandwidth.
Two team members independently inspected, flagged, and calibrated each ob-
serving track during the 150 hour campaign using MIRIAD (Multichannel Im-
age Reconstruction, Image Analysis and Display; Sault et al. 1995). The flags for
each track were then copied to our MIS (MIRIAD Interferometric and Single-Dish;
Teuben et al. 2013) pipeline that has the capability to calibrate all of the tracks
with minimal user input and create combined visibility datasets and maps of all the
observed sources. Standard interferometric calibration steps (e.g., passband, gain,
flux calibration) were performed in the MIS pipeline calibration code. We observed
a nearby quasar every 16 minutes for gain calibration; 3C84 was the main gain cal-
ibrator, and 3C111 was used when 3C84 rose above 80◦ elevation. 3C84 doubled
as a passband calibrator. We observed Uranus for absolute flux calibration during
33
Table 2.2. Correlator Setup Summary
Line Rest Freq. No. Chan. Chan. Width Vel. Coverage Vel. Resolution Chan. RMS Synth. Beama
(GHz) (MHz) (km s−1) (km s−1) (Jy beam−1)
N2H+ 93.173704 159 0.049 24.82 0.157 0.14 7.6′′ × 6.5′′
Continuum 92.7947 47 10.4 1547 33.6 0.0013 8.0′′ × 6.2′′
HCO+ 89.188518 159 0.049 25.92 0.164 0.12 7.8′′ × 6.8′′
HCN 88.631847 159 0.049 26.10 0.165 0.12 7.9′′ × 6.8′′
Note. — aIn principle, the synthesized beam is slightly different for each pointing. Miriad calculates a synthesized
beam for the full mosaic based on all of the pointings.
34
each track and used the bootflux task to determine the absolute flux of the gain
calibrators. The flux of 3C84 varied between 16.0 and 19.4 Jy over the course of the
campaign, while 3C111 varied between 2.8 and 4.5 Jy. The uncertainty in absolute
flux calibration in the 24 combined datasets is about 10%; hereafter, we only report
statistical uncertainties in quoting errors in measured values.
2.2.2 CARMA Single-Dish Observations
Simultaneously with the interferometric observations, we obtained CARMA total
power observations to recover the line emission resolved out by the interferometer
(i.e., CARMA in standard interferometric observing mode). CARMA’s single-dish
mode utilizes the autocorrelation capability of the correlator and intersperses ob-
servations of an emission-free region between on-source integrations. A total power
spectrum can then be constructed from knowledge of the system temperature (Tsys),
the emission region (the ON position), and the emission-free region (the OFF posi-
tion).
The OFF position for Barnard 1 was in a gap of 12CO and 13CO emission 28′ west
and 1.5′ south of the Barnard 1 mosaic reference position. A hole in lower density
CO gas ensured that there was no significant dense gas in that region. We integrated
on the OFF position for 30 seconds every 3.5 minutes if the atmospheric opacity was
stable on the 3.5 minute timescale; otherwise, we observed purely in interferometric
mode. Fourteen of 24 tracks with passing weather grades were observed in single-
dish mode. We flagged the autocorrelation data separately from the cross-correlation
data to account for cases where the opacity deteriorated in a track that was started
in single-dish mode.
We calibrated the autocorrelation data from each antenna in MIRIAD with two
steps: (1) sinbad calculated Tsys ∗ (ON−OFF)/(OFF), and (2) sinpoly removed
35
first-order polynomial baselines from the sinbad spectra. We averaged OFF scans
on both sides of an ON scan in the sinbad calculation to reduce noise introduced
from OFF scans.
We converted the calibrated single-dish spectra from each of the six 10.4-m anten-
nas to six single-dish data cubes using the varmaps routine. We only used the 10.4-m
antennas because they have the highest angular resolution and, hence, best overlap
with the 3.5-m baselines in the uv -plane. The 10.4-m antennas have a halfpower
beamwidth of 77.3′′ (N2H+), 80.7′′ (HCO+), and 81.2′′ (HCN). The routine gridded
each data cube onto 10′′ × 10′′ cells, and used a 50′′ smoothing beam to calculate
the emission in each cell according to the emission at each mosaic pointing. The size
of the smoothing beam was determined empirically; a smaller beam increased the
final noise in the maps, while a larger beam smoothed out structure seen in other
single-dish maps of this region. The final halfpower beamwidth of the calibrated
single-dish cubes is the quadrature sum of the original halfpower beamwidth and
the smoothing beam: 92.1′′ (N2H+), 94.9′′ (HCO+), and 95.4′′ (HCN).
We scaled the data cubes from all six antennas to a single reference antenna
to account for systematic differences of ∼10% arising from physical differences in
each antenna and from differences in bandpass shape of each antenna response. We
calculated the mean of the six data cubes using imstack to improve the signal-
to-noise ratio and limit antenna-based artifacts. The antenna temperature rms
values in the final cubes are 0.025, 0.027, and 0.026 K for N2H+, HCO+, and HCN,
respectively.
36
2.2.3 Joint Deconvolution of Interferometric and Single-Dish
Cubes
The final data product for each observed molecular line transition is a spectral line
cube produced from a joint deconvolution of the interferometric and single-dish data.
The joint deconvolution was done in MIRIAD as summarized below.
We created the interferometric dirty cube and dirty beam from the calibrated
visibility dataset using invert with system temperature and antenna gain weight-
ing, and Briggs’ robustness parameter (Briggs et al. 1999) of −0.5. We de-selected
baselines connecting 10.4 m and 3.5 m dishes due to the illumination of the first
negative sidelobe of the 10.4-m beam by the 3.5-m beam. The dirty cube was then
cleaned with mossdi, a Steer CLEAN algorithm, and the clean components were
carried over to the joint deconvolution to aid in the convergence to a solution. The
single-dish cube was regridded to the interferometric cube axes, and converted to
Jy beam−1 units with a 65 Jy beam−1 K−1 scaling factor1.
The joint deconvolution was done with a maximum entropy algorithm in MIRIAD,
mosmem, that used the interferometric dirty cube, single-dish cube, interferometric
dirty beam, single-dish beam, and interferometric clean components to solve for the
maximum entropy model components. The final cubes are the dirty cube, minus the
maximum entropy model components convolved by the dirty beam, plus the max-
imum entropy model components convolved by the synthesized beam. The noise
levels and synthesize beams for the final data cubes are given in Table 2.2.
1http://www.mmarray.org/memos/carma memo52.pdf
37
2.2.4 Continuum Mapping
A 3 mm continuum map was created from the interferometric data in the 500 MHz
window. We created and cleaned the dirty map in MIRIAD using invert and
mossdi, and restored with a synthesized beam of 8.0′′ × 6.2′′. The rms in the
calibrated continuum map is ∼1.3 mJy beam−1.
The autocorrelation data from the 500 MHz band was not used in continuum
mapping because single-dish continuum observations require fast chopping between
on-position and off-position to cancel out variable sky emission; this observing tech-
nique is not available at CARMA.
2.3 Continuum Results
We detected four compact continuum sources above the 5-σ level; all are associated
with young protostars in the main core. Figure 2.2 shows 3 mm continuum images
toward the previously known Class 0 source, B1-c (Matthews et al. 2006), and the
Class 0 double source, B1-b (Hirano et al. 1999), along with a new 5.8-σ detection
toward a Class I source, SSTc2d J033327.3+310710 (also at the position of the
lower-resolution Per-emb 30 dust source in Enoch et al. 2009).
The structure around B1-c and B1-b is clearly resolved; Per-emb 30 appears to
be nearly unresolved. We used MIRIAD’s imfit to determine the position, peak
brightness, total flux density, size, and position angle of each source with an elliptical
Gaussian approximation (see Table 2.3). The measured position errors are 0.2–0.7′′.
The positions of B1-c and B1-b agree with other interferometric observations of
these sources (Matthews et al. 2006; Chen et al. 2013; Huang & Hirano 2013).
With linear sizes of 1000–2000 AU, the 3 mm emission is arising from compact
cores associated with forming stars. In the optically thin limit, under the assumption
38
Table 2.3. Observed Properties of Continuum Detections
Source Position Pk. Bright. Total Sν Ang. Size P.A. Decon. Size Decon. P.A. Lin. Size Mass
Name (h:m:s, d:′:′′) (mJy beam−1) (mJy) (′′) (◦) (′′) (◦) (AU) (M⊙)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
B1-c 03:33:17.91, +31:09:32.8 23.0 ± 1.8 52.6 ± 4.2 10.7 × 10.7 -33 8.7 × 7.1 -1 2040 × 1670 1.04 ± 0.08
B1-b South 03:33:21.37, +31:07:26.4 29.1 ± 2.3 42.1 ± 3.3 9.8 × 7.4 -79 5.9 × 3.6 -65 1390 × 850 0.84 ± 0.07
B1-b North 03:33:21.23, +31:07:43.7 27.5 ± 2.2 43.0 ± 3.3 10.1 × 7.7 89 6.2 × 4.5 87 1460 × 1060 0.85± 0.07
Per-emb 30 03:33:27.35, +31:07:10.0 6.9 ± 0.8 8.9 ± 1.0 9.7 × 6.6 79 5.5 × 1.7 69 1290 × 400 0.18 ± 0.02
W1 03:33:14.8, +31:07:13 4.1 ± 1.3 ... ... ... ... ... ... a0.08 ± 0.03
W2 03:33:16.7, +31:06:53 4.4 ± 1.3 ... ... ... ... ... ... a0.09 ± 0.03
Note. — (3) Peak brightness, (4) Total flux density, (5) Major and minor axes (FHWM), (6) Position angle (east of north), (7) Deconvolved major and
minor axes (FHWM), (8) Deconvolved position angle, (9) Linear size computed from deconvolved size assuming a distance of 235 pc, (10) Mass calculated using
assumptions in the text (alower-limit mass for weak detections that uses the peak brightness instead of the total flux density).
39
Figure 2.2: The four continuum detections above 5-σ in our field. The synthesized
beam is 8.0′′ × 6.2′′, and the 1-σ sensitivity is ∼1.3 mJy beam−1. B1-c and B1-b
were previously found to have compact continuum emission associated with young
stars. The contour levels in those maps are (±)2, 4, 6, 8, 10, 12, 14, 16, 18 times
1-σ. The compact emission within Per-emb 30 is a new detection that peaks at
5.8-σ. Contour levels in that map are (±)2, 3, 4, 5 times 1-σ. The negative
contours are represented by dashed lines.
of a single temperature, core mass is related to the total flux density as
M = FνD
2
κνBν(Td)
, (2.1)
where M , Fν , D, κν , and Bν(Td), are respectively the total mass, total observed
flux density, distance, mass opacity including dust and gas (assuming a gas-to-dust
ratio of 100), and blackbody intensity at dust temperature, Td. We assume Td =
20 K. To estimate κν , we assumed a power law opacity curve, κν = κo(ν/νo)β,
where νo=1000 GHz and κo=0.1 cm2 g−1 (Beckwith et al. 1990). For a β of 1.5, κν
is 0.0028 cm2 g−1 at 92.79 GHz. The core masses under these assumptions are listed
in Table 2.3; statistical errors are reported using the uncertainty in the total flux
density. The B1-c mass estimate is about three times lower than the mass reported
in Matthews et al. (2006), primarily due to differences in the observed total flux
density near 3.3 mm. The B1-b mass estimates are several times larger than results
from Huang & Hirano (2013), who observed the sources at 1 mm with higher angular
resolution; the disparity increases when adopting their assumed β and Td values.
Since they derived deconvolved sizes of ∼300–500 AU, it is most likely that their
40
mass estimates are not including extended emission in the protostellar envelope.
In addition to these relatively strong detections, we detected two continuum
peaks greater than 3-σ (labeled W1-2 in Table 2.3) that are coincident with a source
in at least one Spitzer or Herschel band. The positions, peak brightnesses, and
lower-limit masses for these sources are listed in Table 2.3. We determined position
using imfit with an elliptical Gaussian approximation. Peak brightness was defined
as the maximum pixel value within the 3-σ contour of the source, with error equal
to the 1-σ sensitivity of the continuum map. The lower-limit mass was calculated
from the peak brightness. W1 is coincident with SSTc2d J033314.3+310710 (Per-
emb 6), and W2 is coincident with SSTc2d J033316.4+310652 (Per-emb 10). Deeper,
follow-up observations are needed to confirm these detections and calculate physical
properties of the sources.
2.4 Morphology of Dense Molecular Gas
Figure 2.3 shows our N2H+, HCN, and HCO+ (J = 1 → 0) integrated intensity
maps, along with a Herschel 250 µm view of Barnard 1 for a qualitative gas-dust
comparison. The angular resolution of the dust map is 18.1′′ in comparison to our
∼7′′ resolution. To facilitate the discussion later in this section, we identify three
zones of emission: the main core zone, the ridge zone, and the SW clumps zone.
Figure 2.4 shows example spectra from each zone at the locations marked by crosses
in Figure 2.3, and the next three sections discuss the three zones in detail.
The N2H+ map was integrated over all seven hyperfine components over veloc-
ity ranges from 14.044 to 10.745 km s−1, 8.860 to 4.775 km s−1, and −0.951 to
−2.766 km s−1. The HCN map was integrated over all three hyperfine compo-
nents, excluding channels with outflows, from 12.117 to 10.961 km s−1, 7.326 to
41
6.005 km s−1, and 0.057 to −1.264 km s−1. The HCO+ map was integrated from
7.161 to 5.849 km s−1, again excluding outflow channels. We integrated N2H+ over
a wider range of velocities compared to the other molecules to include a narrow, red-
shifted filament, which can be seen along the southeastern edge of the thicker N2H+
filament in the ridge zone. This redshifted filament, discussed later in this section,
is also detected in HCN and HCO+, but overlaps in velocity space with HCN and
HCO+ outflow channels that were excluded from these integrated intensity maps.
The rms of the N2H+, HCN, and HCO+ integrated intensity maps in Figure 2.3 are
0.17, 0.10, and 0.06 Jy beam−1 km s−1, respectively.
The peak brightness temperature for a single channel (including channels with
outflows) in the entire field occurs towards the B1-c continuum core; it is 9.5 K,
9.7 K, and 7.1 K in our synthesized beam for N2H+ (2.85 Jy beam−1 to K conversion
factor), HCN (2.91 Jy beam−1 to K conversion factor), and HCO+ (2.91 Jy beam−1
to K conversion factor), respectively.
2.4.1 Main Core Zone
The main core zone, shown in Figure 2.5, is the area of strongest dust emission seen
by Herschel ; it contains the largest cluster of young protostellar objects, and is the
only region where we have detected compact continuum sources (see Section 2.3)
and outflows (see Figure 2.6). The N2H+ emission in this zone follows the overall
structure of the dust, although our improved angular resolution reveals more detail
than ever before. The HCN and HCO+ emission not associated with outflows is
much weaker compared to N2H+, and it does not follow the morphological structure
of the N2H+ or the dust. Figure 2.5 shows the locations of Spitzer YSO candidates
(Jørgensen et al. 2006), Bolocam 1 mm clumps (Enoch et al. 2006), and SCUBA
850 µm clumps (Hatchell et al. 2005).
42
Figure 2.3: Integrated intensity maps of N2H+, HCN, and HCO+ (J = 1 → 0)
emission towards Barnard 1, with a Herschel 250 µm map. Channels containing
outflow emission are excluded from these maps, which is why the narrow filament
(see Section 2.4.2) appears only in N2H+. The rms values of the N2H+, HCN,
and HCO+ maps are 0.17, 0.10, and 0.06 Jy beam−1 km s−1, respectively. We
break the region into three zones based on qualitative features in the dense gas
maps. Crosses in the maps represent the locations of spectra shown in Figure 2.4.
FITS cubes of the PPV data used to make this figure are available in the online
journal version of this chapter.
The spectra from this zone are the most complex in the Barnard 1 field—
Figure 2.4 shows a sample N2H+ spectrum from near the B1-b core that exhibits
broad lines, while the HCN and HCO+ spectra from the same location show evidence
of red-wing outflow emission overlapping with B1-b. The N2H+ emission towards
B1-b shows two resolved peaks. There are emission peaks in HCN and HCO+ to-
43
N2H+ from Main Core
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
HCN from Main Core
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m) only fitting most
isolated hf component
in complex regions w/ outflows
HCO+ from Main Core
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
red outflow
emission
fitting main
emission
N2H+ from Ridge
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
HCN from Ridge
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
HCO+ from Ridge
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
N2H+ from SW Clumps
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
HCN from SW Clumps
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
HCO+ from SW Clumps
-5 0 5 10 15
velocity (km/s)
0.0
0.5
1.0
1.5
2.0
Br
ig
ht
ne
ss
 (J
y/b
m)
Figure 2.4: Example spectra for all three molecules from each zone. The
spectra are averaged over one synthesized beam, and the positions are: α =
03h33m21.633s, δ = 31◦07′38.06′′ for the Main Core Zone, α = 03h33m01.482s, δ
= 31◦04′05.09′′ for the Ridge Zone, and α = 03h32m27.312s, δ = 31◦02′05.36′′ for
the SW Clumps Zone. We fit the spectra and present maps of centroid velocity
and velocity dispersion in Section 2.5. The fits to the main core zone spectra are
shown with solid black lines. The N2H+ has seven resolvable hyperfine compo-
nents in narrow-line regions, and HCN has three resolvable hyperfine components.
The hyperfine structure of N2H+ is shown with vertical bars set within the main
core zone spectrum—the relative brightnesses are representative of the hyperfine
structure, but the absolute values were picked for ease of visualization. As de-
scribed in Section 2.5, we exclude outflow emission from HCN and HCO+ when
doing these fits.
wards B1-b South, but not B1-b North (see Figure 2.5). This agrees with findings
from Huang & Hirano (2013) and supports the idea that carbon-bearing species are
depleted around B1-b North, suggesting it is the younger source of the two.
The N2H+ gas emission is very strong at the location of B1-c, while HCO+ is
only detected in outflows; this agrees with observations from Matthews et al. (2006).
44
HCN gas does exist at the location of B1-c, but is not a strong peak relative to the
rest of the main core, like we see with N2H+. HCN is also detected in outflow
emission.
There are seven Spitzer Class 0/I YSOs in this zone. Two are known to be
associated with the B1-c and Per-emb 30 compact continuum cores, which are sites
of strong N2H+ emission. There are four nearby the larger scale B1-a, B1-b, and
B1-d dust clumps, which are also areas of strong N2H+emission. The seventh YSO,
which lies west of the strongest dense gas in this zone, only has weak dust and gas
emission associated with it. Several of these YSOs are driving outflows, which are
discussed later in this section, and identified in Figure 2.6 and Table 2.4.
There are five Bolocam 1.1 mm cores and six SCUBA 850 µm cores in this
region. All of these lower resolution dust cores are near N2H+ emission peaks, but
not necessarily near HCN or HCO+ peaks. There are several peaks of HCN and
HCO+ that are not associated with strong dust emission.
Figure 2.6 shows HCO+ and HCN dense gas outflows, which are only detected
in this zone. In the HCO+ map, SSTc2d J033317.9+31092 (B1-c) is clearly driving
a bipolar outflow. We detect another bipolar HCO+ outflow, likely associated with
the IRAS 03301+3057 YSO based on a similar detection in CO by Hirano et al.
(1997). There is a red outflow just to the west of SSTc2d J033314.4+310711, another
to the north SSTc2d J033320.3+310721, and a third to the southeast of SSTc2d
J033327.3+310710.
In the HCN map, we again see the bipolar outflow from SSTc2d J033317.9+31092
(B1-c), although the HCN additionally traces an extension of the red part of the
outflow to the west, and an associated knot of emission to the east. The western
extension flares out into two separate, high-velocity outflows that extend beyond
the edge of our spectral window. The eastern knot is likely a bright bow shock
45
Figure 2.5: Integrated intensity maps of N2H+, HCN, and HCO+ (J = 1 → 0)
emission toward the main core zone, along with Herschel 250 µm. Channels
containing outflow emission are excluded from the integrated intensity maps. The
angular resolution of each map is marked with a beam in the lower right corner—
the CARMA synthesized beam is ∼7′′. The Herschel map shows the location
of Spitzer YSOs (stars), Bolocam 1.1 mm cores (squares), and SCUBA 850 µm
cores (circles); all YSOs in this region are Class 0/I. Major dust clumps mentioned
in the text are labeled in the Herschel map. The black boxes in the integrated
intensity maps show the locations of the compact continuum sources that were
discussed in Section 2.3. The rms of the N2H+, HCN, and HCO+ integrated
intensity maps are 0.17, 0.10, and 0.06 Jy beam−1 km s−1, respectively.
from the edge of the outflow interacting with cloud material. We confirmed the
association of these extended features with the main outflow using Spitzer images
that trace the shocked gas. The outflows from IRAS 03301+3057 and SSTc2d
46
J033320.3+310721 are also detected in HCN, while those from J033314.4+310711
and J033327.3+310710 are not.
Figure 2.6: HCO+ and HCN outflows overlaid on N2H+ integrated intensity emis-
sion. Each outflow was integrated over its own range of velocities to minimize noise
introduced from emission-free channels. We are plotting contours of 0.3, 0.4, 0.5,
0.6, 0.7, 0.8, 0.9 times the peak integrated intensity of the outflow, except for the
HCN bipolar outflow from SSTc2d J033317.9+31092 where we extend down to 0.1
and 0.2 times the peak. See Table 2.4 for the velocity ranges and peak integrated
intensity of each outflow—the outflows are identified in the table by the nearest
infrared source plotted in this figure. Spitzer YSO positions are indicated with
black stars; all YSOs are Class 0/I in this region.
2.4.2 Ridge Zone
The ridge zone, shown in Figure 2.7, lies southwest of the main core. The most
striking feature is the backbone of the B1 Ridge that appears as a structure (“Ridge”
in the figure) that measures approximately 260′′ long by 80′′ wide in the N2H+ map.
This corresponds to about 0.30 pc long by 0.09 pc wide at a distance of 235 pc. This
structure has several Bolocam and SCUBA cores running along its spine, which are
strongly clustered in the northeast half where gas emission from all molecules is
the strongest. A single Class 0/I YSO sits at the northeast edge of the structure—
none of the dust cores along the structure have associated protostars, and they
47
Table 2.4. Outflow Identification
Source Identifiera Color Integrated Velocity Range Peak Integrated Intensity
(Red or Blue) (km s−1) (Jy beam−1 km s−1)
HCO+
SSTc2d J033317.9+310932 (B1-c, Per-emb 29) Red 9.62–7.98 1.0
SSTc2d J033317.9+310932 (B1-c, Per-emb 29) Blue 5.36–3.72 1.9
IRAS 03301+3057 (B1-a, Per-emb 40) Red 7.66-7.49 0.5
IRAS 03301+3057 (B1-a, Per-emb 40) Blue 5.36–1.26 2.4
SSTc2d J033327.3+310710 (Per-emb 30) Red 7.82–7.32 0.8
SSTc2d J033320.3+310721 (Per-emb 41) Red 9.95–7.33 1.8
SSTc2d J033314.4+310711 (Per-emb 6) Red 13.73–7.82 4.4
HCN
SSTc2d J033317.9+310932 (B1-c, Per-emb 29) Red 18.89–11.78, 10.13–7.66 12.0
SSTc2d J033317.9+310932 (B1-c, Per-emb 29) Blue 10.63–7.66, 5.67–1.54, (−)1.26–(−)3.08 10.1
SSTc2d J033317.9+310932 (B1-c, Per-emb 29) Blueb (−)1.26–(−)5.72 3.3
IRAS 03301+3057 (B1-a, Per-emb 40) Blue 10.30–9.64, 5.34–4.19 2.1
SSTc2d J033320.3+310721 (Per-emb 41) Red 12.61–12.28, 8.48–7.33, 0.72–0.22 1.5
Note. — (a) Outflows identified by the location of the nearest infrared source. Supplemental Per-emb source identifiers are from Enoch et al. (2009).
(b) This emission corresponds to the blue knot seen in the HCN map of Figure 2.6, east of the main part of the SSTc2d J0333317.9+310932 outflow.
48
are considered pre-stellar. There is a single Bolocam core at the southwestern end
of the structure, where the Herschel map peaks in an area with little molecular
emission; multi-wavelength Herschel images show that this region is brighter at
shorter wavelengths compared to the northeastern section of the structure. This
means it could be a region of slightly higher temperature, which would explain a
lower abundance of dense molecular gas. Figure 2.4 shows sample spectra from
along this structure.
A second molecular feature in this zone is a newly discovered filament that runs
parallel to the main ridge (“Narrow Fil” in Figure 2.7). This filament is extremely
narrow and is offset from the rest of the gas in velocity space by about 1.5 km s−1.
Figure 2.8 shows molecular line contours overlaid on a Herschel 250 µm map. The
filament is about 20′′ wide and 2.5′ long, with a small kink half-way along its length.
At a distance of 235 pc, this corresponds to 0.022 pc wide by 0.17 pc long. The peak
integrated intensity of the filament is 1.2 Jy beam−1 km s−1, 1.4 Jy beam−1 km s−1,
and 0.9 Jy beam−1 km s−1, for N2H+, HCN, and HCO+, respectively. It is not
possible to identify the filament in Herschel maps because it is extremely narrow
and lies along the same line of sight as the western edge of the B1 Ridge. We
briefly discuss the kinematics and possible formation mechanisms of the filament in
Section 2.5.
The third molecular feature is gas in the northern part of the zone that provides
a tenuous link between the main ridge structure and the main core zone. A Class
0/I YSO is located off the southwestern edge of this feature, but there are no dust
condensations directly associated with it.
49
Figure 2.7: Integrated intensity maps as in Figure 2.5, but for the ridge zone.
Since the ridge zone does not have outflows, we included extra channels that
were excluded from Figure 2.5 to capture the narrow filament that is red-
shifted by ∼1.5 km s−1 from the rest of the Barnard 1 gas. The rms values
of these N2H+, HCN, and HCO+ integrated intensity maps are 0.17, 0.12, and
0.08 Jy beam−1 km s−1, respectively.
2.4.3 SW Clumps Zone
The SW clumps zone lies southwest of the B1 Ridge, and is shown in Figure 2.9.
There are five distinct clumps of N2H+ emission, with a sixth clump only detected
in HCN and HCO+. There are three Class II YSOs in this zone that do not correlate
with any gas or dust peaks, which is expected for more evolved protostars. There
is one Class 0/I YSO in this zone that lies at the northeast tip of the western-
50
Figure 2.8: We discovered a narrow filament that is offset by 1.5 km s−1 from
the rest of the gas in Barnard 1. The three figures show the filament detected
in N2H+, HCN, and HCO+, overlaid on the Herschel 250 µm dust image. The
contours represent integrated intensity emission at 0.3, 0.5, 0.7, and 0.9 times the
peak integrated intensity of the HCN filament, which is 1.36 Jy beam−1 km s−1.
most clump. The strongest integrated HCO+ emission across the entire Barnard 1
field is located in this clump—Figure 2.4 shows sample spectra from it. The gas
morphology of this zone is very different from the main core and ridge zones. Those
zones have dense gas peaks embedded within lower-intensity, larger-scale dense gas
structures, while the dense gas peaks in this zone are not joined at weaker emission
levels.
2.5 Kinematics of Dense Molecular Gas
We modeled the spectra in our position-position-velocity (PPV) cubes to derive the
centroid velocity and velocity dispersion for the emission from each molecule along
every line of sight.
The N2H+(J = 1 → 0) line is made up of seven resolvable hyperfine components.
We model all components simultaneously and assume they are Gaussians with the
same dispersion and excitation conditions. The line opacity as a function of velocity,
51
Figure 2.9: Same as Figure 2.5, but for the SW clumps zone. The most western
YSO in this zone is a Class 0/I source, while the others are Class II sources (colored
blue). Like Figure 2.7, since this zone does not have outflows, we included extra
channels to capture the southwestern edge of the narrow filament (best seen in
the HCO+ map) that is redshifted by ∼1.5 km s−1 from the rest of the Barnard 1
gas. The rms values of these N2H+, HCN, and HCO+ integrated intensity maps
are 0.17, 0.12, and 0.08 Jy beam−1 km s−1, respectively.
τ(v), is modeled as:
τ(v) = τ
7
∑
i=0
Cie−(v−Vlsr−vi)
2/2σ2 , (2.2)
where τ is the total opacity of the emission, Ci is the weighted strength of the
ith hyperfine component such that the sum of component strength is unity, Vlsr is
the centroid velocity of the observed emission, vi is the rest velocity of the ith hy-
perfine component, and σ is the velocity dispersion of each hyperfine component.
52
We assigned Ci and vi according to the CDMS catalog listings on the Splatalogue
webpage2 – vi was calculated from the listed νi using the rest frequency of our ob-
servations and the radio Doppler formula. A full observed spectrum is then modeled
as
F (v) = 2kν
2Ω(v)
c2 × Tex(1− e
−τ(v)), (2.3)
where k is Boltzmann’s constant, Ω is the synthesized beam area, v is the velocity
of the observations, and Tex is the excitation temperature.
The four free parameters for the fit are: Vlsr, σ, τ , and Tex. We focus on
the two kinematic parameters in the following sections. We do not address τ and
Tex because they are semi-degenerate, and breaking the degeneracy comes from an
accurate understanding of the optical depth, which is beyond the scope of this initial
analysis.
In the line fitting procedure, a model spectrum is first created from Equations 2.2
and 2.3 with ten times the velocity resolution of our observed data. We then bin
this high-velocity-resolution model spectrum according to our observations’ velocity
resolution, and compare that channelized model spectrum to an observed line. The
fitting is done in IDL with the MPFIT package (Markwardt 2009), which performs
non-linear least-squares minimization of the model fit to an observed spectrum—the
outputs are the best-fit values and errors of the four free parameters. Figure 2.10
(top) shows the best-fit centroid velocity (Vlsr) and velocity dispersion (σ) maps
for N2H+. The pixels that have data values in these maps represent spectra that
pass two robustness criteria: peak signal-to-noise greater than five, and integrated
intensity greater than four times the rms of the N2H+ integrated intensity map.
The vast majority of the field only contains one resolved velocity component
along each line-of-sight, and can be adequately fit with the procedure described
2http://splatalogue.net
53
above. However, we manually inspected the field and identified four locations with
strong evidence for having two resolved velocity components. Three of those loca-
tions are marked with white rectangles in Figure 2.10, and are excluded from the
analysis later in the chapter. The fourth location is the northeastern part of the
narrow filament in the ridge zone; we manually inspected this region and removed
the small number of pixels with confused spectra from the N2H+ maps.
The HCN and HCO+ emission was fit in a similar way; the HCN line is made
up of three resolvable hyperfine components, and HCO+ has no hyperfine structure.
Complications arose from outflows in the main core zone. For lines of sight com-
plicated by outflows, we masked channels with outflow emission before fitting the
spectral line representing the non-outflow gas. This was only done if the outflow
emission was clearly defined in velocity space—we did not fit lines where outflow
emission blended with emission nearest to the centroid velocity of the cloud. For
HCN lines complicated by outflows, we only fit the highest frequency hyperfine
component as it is more isolated in frequency/velocity space from the other two
hyperfine components.
The middle and bottom rows of Figure 2.10 show the best-fit centroid velocity
and velocity dispersion maps for HCN and HCO+, respectively. The integrated
intensity criterion is the same as above. However, the peak signal-to-noise criterion
is eight for HCN, and ten for HCO+, to account for increased uncertainty in fit values
with decreasing number of hyperfine components. It is clear from the sparseness of
the maps that there are far fewer HCN and HCO+ regions strong enough to get
reliable kinematic measurements compared to N2H+. The HCO+ and HCN data
also show evidence for two velocity components in the same regions as N2H+.
Analyzing all the details of these kinematic maps is beyond the scope of this
analysis. However, some features to point out are as follows:
54
1. The most kinematic complexity exists in the main core zone—it has velocity
gradients up to ∼10 km s−1 pc−1 (see Figure 2.11, left), and velocity disper-
sions ranging from 0.05 km s−1 all the way up to 0.5 km s−1. In comparison,
the gas structures in the ridge and SW clump zones show smaller variations
in centroid velocity and velocity dispersion, and the velocity dispersions are
consistently narrower than those found in the main core zone.
2. The narrow filament in the ridge zone, which can be seen in the all three
kinematic maps, is redshifted by 1.5 km s−1 relative to the rest of the Barnard 1
emission. The mean velocity dispersion along the filament is 0.12 km s−1,
0.16 km s−1, and 0.20 km s−1, for N2H+, HCN, and HCO+, respectively.
At an assumed kinetic temperature of 11 K based on Green Bank Telescope
(GBT) data (Rosolowsky et al. 2008a), N2H+ and HCN are detecting subsonic
gas motions and HCO+ is approaching the sonic speed. The 1.5 km s−1 radial
velocity of the filament gas relative to the bulk Barnard 1 gas suggests that
it did not simply fragment from the main reservoir of gas in the region. It is
possible that a nearby flow of material piled onto the larger filament and flowed
around its western edge; this would cause a column density increase along that
edge, thereby strengthening the molecular emission and causing redshift. One
problem with this scenario is that we might expect more turbulent linewidths
for gas involved in a colliding flow. However, this type of flow event could have
happened long enough ago that gravity had time to collect the gas into the
filament we now see. Another possibility is that we are viewing a sheet-like
structure edge on.
3. The largest structure in the ridge zone has a velocity gradient perpendicular
to its major axis (see Figure 2.11, right), which is a feature common in nu-
55
merical simulations of filament formation from planar converging, turbulent
flows (Chen & Ostriker 2014). This type of velocity gradient is seen in sev-
eral CLASSy filaments across our five regions; Serpens South examples are
highlighted in Ferna´ndez-Lo´pez et al. (2014), and we are preparing a paper
linking these observations with the numerical simulations (Mundy et al., in
preparation).
4. Upon close inspection, several regions of the cloud have well-organized N2H+
centroid velocity fields—for example, the dense gas around B1-c shows clear
signatures of envelope rotation that was previously reported in Matthews et al.
(2006). We show other examples of orderly velocity fields in Figure 2.12,
coming from dense gas peaks that are spatially separated from other structures
at low emission levels. One of the examples is the dense gas surrounding the
newly detected compact continuum core within Per-emb 30, while the other
two have no detected protostars at their center. This highlights the ability
of CLASSy data to probe the small-scale velocity structure around cores in
addition to the large-scale velocity structure across the entire region.
5. The best-fit values of the centroid velocity and velocity dispersion toward the
B1-c core are consistent with the results published by Matthews et al. (2006).
We detect the same evidence of a rotating N2H+ envelope in the centroid
velocity map, and detect the same increased velocity dispersion along the
HCO+ and HCN outflow axis. Also, the N2H+ centroid velocities and velocity
dispersions across the field match well with GBT NH3 observations toward
select dust cores (Rosolowsky et al. 2008a).
56
Figure 2.10: Left: Centroid velocity maps of N2H+, HCN, and HCO+ (J = 1 → 0)
emission, from top to bottom. Right: velocity dispersion maps of N2H+, HCN, and
HCO+ (J = 1 → 0) emission, from top to bottom. We masked these maps at different
levels (see Section 2.5 text) to visualize only statistically robust kinematic results. The
color scales are the same across molecules. The ∼7′′ synthesized beam is plotted as a
very small white circle in the lower right corner of the N2H+centroid velocity map. The
small, white rectangles in the N2H+ maps identify regions that likely contain two velocity
components along the-of-sight and are excluded from analysis later in the chapter.
57
Figure 2.11: Left: Zoom-in of the main core zone centroid velocities presented in
Figure 2.10, showing the complex velocity structure seen across this large area.
The two solid lines enclose a region where we calculated the velocity gradient
along the direction indicated by the arrow; we found a peak velocity gradient
∼10 km s−1 pc−1 along this direction. Right: Zoom-in of the ridge zone centroid
velocities. Between the solid white bars, we measured an average velocity differ-
ence ∼0.3 km s−1 perpendicular to the major axis of the filament. The synthesized
beam is shown in the bottom right corner of each image.
Figure 2.12: Zoom-in on three small-scale regions with orderly centroid velocity
fields, highlighting CLASSy’s ability to resolve small-scale kinematic features, in
addition to the large-scale structures seen in Figures 2.10 and 2.11. The color
intensity is centroid velocity, and the contours are integrated intensity (contour
levels in intervals of 10% of the image peak intensity). The left image shows the
dense gas around the compact continuum core toward Per-emb 30 (the continuum
core is identified with a single contour, colored blue). The center image is of gas
south of Per-emb 30 in the main core zone, and the right image is of gas in the
SW clumps zone. The synthesized beam is shown in the lower-right corner of each
image, and a 0.02 pc scale bar is shown in the left image.
58
2.6 Dendrogram Analysis of N2H+
The previous two sections highlighted the dense gas morphology and kinematics
across Barnard 1. Here we quantitatively analyze the N2H+ position-position-
velocity cube to create a census of dense gas structures. We chose N2H+ over
HCN and HCO+ because it is our best tracer of the dense gas that is actively par-
ticipating in star formation—it closely mimics the dust emission and is less affected
by absorption from lower density foreground gas than HCN and HCO+.
Several methods exist for identifying structures in an image or cube, and the
most appropriate method depends on the data and science goals. In Appendix A,
we compare a widely used clump-finding algorithm to the dendrogram method, and
conclude that a dendrogram analysis is more suitable for identifying resolved, dense
gas structures in nearby molecular clouds. A dendrogram tracks emission structure
as a function of isocontour level intensity, and represents the structure as a tree hi-
erarchy made up of leaves and branches (Houlahan & Scalo 1992; Rosolowsky et al.
2008b; Goodman et al. 2009). Leaves are smaller-scale, brighter objects at the top
of the emission hierarchy that do not break-up into further substructure, while
branches are the larger-scale, fainter objects lower in the hierarchy that do break-up
into substructure. The major benefit of a dendrogram analysis over a clump-finding
analysis rests in this ability to represent all of the spatial scales in a dataset, as
opposed to forcing all emission into distinct clumps associated with a local peak.
See Appendix A and Goodman et al. (2009) for more discussion.
In Appendix B, we describe our modifications to the standard dendrogram al-
gorithm that enable non-binary hierarchies, and we argue that non-binary dendro-
grams provide a more statistically meaningful way to represent hierarchical emission
in the presence of noise. The important modifications include: 1) restricting branch-
59
ing to discrete steps, typically to integer values of the 1-σ sensitivity of the data
when only analyzing a single map or data cube, instead of allowing branching at
infinitely small intensity steps, and 2) using an algorithm that can cluster more than
two objects into a single group instead of being restricted to clustering two objects
at a time. These changes create an observable emission hierarchy within the noise
limits of the data, and allow the quantification of the hierarchical complexity of a
dendrogram using tree statistics. The rest of this section focuses on our non-binary
dendrogram analysis of the N2H+ gas in Barnard 1.
2.6.1 The Non-binary Dendrogram
We used our new non-binary dendrogram code to identify gas structures traced by
the isolated hyperfine component of N2H+. We chose to use the isolated hyperfine
component of N2H+ since it is sufficiently separated from other components in ve-
locity space to prevent contaminating our object identification along the velocity
axis. Before running the data through the dendrogram code, we binned the cube by
two velocity channels to improve the signal-to-noise. No velocity information was
lost since there are no lines of sight that contain two or more independent structures
within 1.0 km s−1 of each other. We found that binning by two channels provides
the most improvement to signal-to-noise without biasing the maps towards wide-line
regions. The 1-σ sensitivity of the binned data cube is 0.094 Jy beam−1.
Our non-binary dendrogram code takes the same input parameters as the stan-
dard IDL implementation discussed in Rosolowsky et al. (2008b). We ran it with
the following critical inputs and parameters: (1) a masked cube containing all pixels
greater than or equal to 4-σ intensity, along with adjacent pixels of at least 2.5-σ
intensity, (2) a set of local maxima greater than or equal to all their neighbors in 10′′
by 10′′ by three channel (0.94 km s−1) spatial-velocity pixels, (3) a requirement that
60
a local maximum must peak 2-σ above the intensity where it first merges with an-
other local maximum for it to be considered a leaf (referred to as the “minheight”
parameter in later sections), and (4) a requirement of at least three synthesized
beams of spatial-velocity pixels for a leaf to be considered real (referred to as the
“minpixel” parameter in later sections). The minheight and minpixel parame-
ters act to prevent noise features from being identified as true dendrogram leaves.
An additional input is used in the non-binary algorithm: branching steps restricted
to integer values of the 1-σ sensitivity of the data (referred to as the “stepsize”
parameter in later sections). The stepsize parameter sets the minimum branching
step allowed in a non-binary dendrogram.
The non-binary dendrogram shown in Figure 2.13 contains 41 leaves and 13
branches. The vertical axis of the dendrogram represents the intensity range of the
pixels belonging to a leaf or branch. The horizontal axis does not normally carry
physical meaning, but in this case we arranged the leaves and branches according to
zone. Figure 2.14 shows two-dimensional representations of all leaves overlaid on the
N2H+ integrated intensity map; these representations were created by integrating
over the velocity axis of the leaves and contouring the maximal RA-DEC extent of
the integrated emission. The leaves that peak at least 6-σ in intensity above their
first branch are colored green (leaves 10, 25, and 39). Leaf 25 is the strongest, with
a peak intensity of 1.91 Jy beam−1 (in the binned data cube), and represents the
gas around B1-b. Leaf 39 is the next strongest at 1.77 Jy beam−1, and represents
gas around B1-c. Leaf 10 peaks at 1.04 Jy beam−1, and represents gas around the
newly detected compact continuum source within Per-emb 30. As a reminder that
the identification of leaves and branches was done in three dimensions, Figure 2.15
shows five N2H+ velocity channels near the B1-b cores with the isocontours of leaves
24, 25, and 40, and branch 41, identified with distinct colors.
61
Figure 2.13: The non-binary dendrogram for Barnard 1 is shown; it represents
the hierarchical structure of the N2H+ gas. There are 41 leaves (numbered 0
through 40), and 13 branches (numbered 41 through 53) on the dendrogram. The
vertical axis represents the Jy beam−1 intensity for a given location within the
gas hierarchy. Branching occurs in integer multiples of the 1-σ sensitivity of the
binned data cube used in this analysis. The horizontal axis is ordered according
to zone, though the order within a given zone has no physical meaning. Leaves
10, 25, and 39 (colored green) peak at least 6-σ above their first merge level.
We are using the 6-σ contrast criteria to highlight the strongest leaves before
we are able to confidently discuss the virial boundedness of actual “cores” and
“clumps”—defining bound cores requires accurate measurements of mass to go along
with our high-resolution kinematic information, which is beyond the scope of this
inital analysis. We chose a 6-σ contrast to highlight the gas in Barnard 1 that is
located near existing compact continuum objects—this gas is likely bound. We will
apply the same contrast cut to other CLASSy regions. While we cannot discuss
boundedness of individual gas cores at this stage, we can discuss the properties of
the strongest, highest-column density, dendrogram features and compare them to
weaker features in the field. Leaves with 6-σ or greater contrast will be referred to
as high-contrast leaves later in the chapter, and the rest of the leaves will be called
low-contrast leaves.
The tree structure presented here captures the qualitative hierarchical nature of
the dense gas in Barnard 1, but it does not give quantitative information about the
62
Figure 2.14: The N2H+ integrated intensity map (Jy beam−1 km s−1) is shown
in greyscale. The overplotted contours (green and blue) are two-dimensional rep-
resentations of the three-dimensional (PPV) leaf structures found in Barnard 1.
Green contours represent leaves with contrast greater than 6-σ. Each leaf is la-
beled with its number that can be referenced to Figure 2.13 and Table 2.5.
hierarchy or physical properties of the leaves and branches. Doing science with a
dendrogram requires extracting tree statistics and physical properties of the leaves
and branches, such as size, axis ratio, linewidth, mass, luminosity, etc. We present
three simple tree statistics and the spatial and kinematic properties of leaves and
branches in this chapter. In future papers, we will perform more detailed compar-
isons between dendrogram properties across multiple CLASSy regions.
2.6.2 Dendrogram Tree Statistics
Computation of tree statistics from a non-binary dendrogram is one method of
quantifying a tree structure. Houlahan & Scalo (1992) were the first to develop
tree statistics for the astronomy community in order to quantify the hierarchical
63
Figure 2.15: N2H+ emission surrounding the B1-b double core, viewed across
five binned velocity channels used in the dendrogram analysis, and across the
moment zero map. For the channel maps, the greyscale represents the intensity
of emission (Jy beam−1), and the colored contours (individually colored in the
online version) represent the spatial extent of the dendrogram leaves and branches
in that given channel. The single white contours in all maps represent the 4-σ
detection level of the B1-b continuum sources. In the online version, leaf 25 is
green, 40 is red, and 24 is blue, while branch 41 is cyan. For the moment zero map,
the greyscale represents the integrated intensity of emission (Jy beam−1 km s−1),
and the colored contours represent two-dimensional representations of the three-
dimensional dendrogram structures seen in the channel maps.
nature of molecular cloud structure (see their discussion of “merged trees,” which
are analogous to our non-binary trees). They describe several statistics that can be
computed from non-binary trees; we describe three of the simplest statistics here.
The maximum branching level is the integer number of branching steps needed
to reach the leaves at the top of the hierarchy. A region that has undergone a
lot of hierarchical fragmentation will have more levels than a region that has not
fragmented, or that has fragmented in a single step into several pieces with similar
properties. Branching levels are defined upward from the base of the tree; the
base (0 Jy beam−1 intensity) is considered level 0. An isolated leaf that sprouts
64
directly from the base is at level 0, while a leaf that grows from a branch one level
above the base is at level 1. The maximum branching level in our Barnard 1 N2H+
dendrogram is level 4, where leaves 24, 25, and 40 merge together into branch 41 (see
Figure 2.13). These leaves are in the main core zone, which is the only zone with
detections of 3 mm compact continuum cores and Class 0/I YSOs. It is reasonable
that the largest amount of fragmentation has occurred in the region with the most
young star formation activity. That being said, the ridge zone and SW clumps zone
have maximum branching levels of three and one, respectively, so we are dealing
with small variations of this statistic within Barnard 1.
A related tree statistic is the mean path length of all segments in a dendrogram.
The path length of a segment is defined as the number of branching steps required
to go from a leaf to the bottom of the tree (there are as many path lengths in a
dendrogram as there are leaves). For example, the path length of leaf 25 is four,
while the path length of leaf 37 is three—the path length of leaf 30 is zero because
it directly sprouts from the bottom of the tree. The mean path length in the whole
Barnard 1 N2H+ dendrogram is 1.2 levels, while it is 2.0, 1.2, and 0.5 for the main
core zone, ridge zone, and SW clumps zone, respectively. Again, it is logical that
the main core zone, which is actively fragmenting into young stars, has the largest
mean path length.
It is important to point out that these statistics would be different if we used
the standard dendrogram algorithm instead of our non-binary one. The standard
algorithm forces binary branching by introducing extra branching steps to ensure
that only two objects merge at a time. For example, leaves 24, 25, and 40 would not
all be allowed to merge into branch 41 even though that is what the data suggest is
happening—leaves 24 and 25 would be merged into one branch, which would then
be merged with leaf 40 into a second branch. This inflates the path length of leaves
65
24 and 25, and increases the maximum branching level of the tree. See Appendix B
for more details about differences between the standard dendrogram algorithm and
the new non-binary algorithm.
The third simple tree statistic is the mean branching ratio of all branches in a
tree. The branching ratio for a single branch is defined as the number of substruc-
tures into which it fragments directly above it in the hierarchy. For example, the
branching ratio of branch 41 is three, because it has three leaves directly above it. A
very hierarchical region, where every object fragments into two nested objects, will
have a mean branching ratio of 2, while a region that has fragmented in a single step
into several pieces with similar properties will have a much larger mean branching
ratio. The mean branching ratio in our Barnard 1 N2H+ dendrogram is 3.9. We
include the branching ratio for the base of the tree in this calculation, even though it
is not explicitly defined with a branch number—this ensures that leaves that sprout
directly from the base are factored in. (Note that the branching ratio above the tree
base is always fixed at 2 for the standard dendrogram algorithm that forces binary
branching.)
These simple statistics provide measures of the amount and type of fragmentation
a given region has undergone; a region with a lot of hierarchical fragmentation will
have more levels, a larger mean path length, and a smaller branching ratio, compared
to a region that is just beginning to form strong overdensities. A caveat is that the
absolute values of the branch statistics depend on algorithm parameters and choice
of allowed branching steps (reminder that we restrict branching to intensity steps
equal to integer values of the 1-σ sensitivity of the data instead of allowing branching
at infinitely small intensity steps). However, the statistics can be compared across
trees as a differential measurement if the same algorithm parameters and allowed
branching steps are used; as pointed out by Houlahan & Scalo (1992), the power
66
of tree statistics is strongest when comparing regions with different star formation
properties. We will compare the Barnard 1 tree statistics with the tree statistics of
NGC 1333 and L1451 in Chapter 4 to explore whether the hierarchical complexity of
dense gas represented by tree statistics correlates with the diversity of star formation
activity in the western half of Perseus.
Another caveat arises from linking dendrogram hierarchical complexity to cloud
fragmentation—tree statistics can be affected by projection effects. All observa-
tions suffer from projection effects when transforming the true position-position-
position information of a molecular cloud to observable position-position-velocity
information (for an in-depth discussion of projection effects in spectral line data,
see Beaumont et al. 2013). Projection effects distort optically thick, space-filling
emission more than optically thin emission concentrated in one part of the cloud.
These effects are not overly concerning in our data because the isolated hyperfine
component of N2H+ is optically thin, and the N2H+ emission is arising only from the
densest parts of the cloud. If our data do suffer from projection effects, we assume
that our large mapping areas create a big enough sample of dendrogram structures
so that equal numbers of projection effects occur in each region we will compare.
2.6.3 Dendrogram Spatial Properties
The size of an object is one of its most fundamental properties, but defining the sizes
of irregularly shaped objects in a uniform way is not trivial. This is one challenge
of high-angular-resolution surveys of nearby molecular clouds—CLASSy resolves a
rich morphology of structures with a range of irregular shapes.
When fitting for the size of a leaf or branch, we consider all pixels in its plane-
of-sky footprint (as opposed to only considering the “onion-layer” emission of each
individual branch, which is used to derive kinematic properties in the next section—
67
see Figures 2.16 and 2.17 for examples). We use the regionprops program in
MATLAB to fit an ellipse to the integrated intensity footprint of each dendrogram
object. All pixels are given equal weight so that the ellipse is preferentially fit to
the largest scale of the object—this prevents strong emission at the center of an
object from driving the fit towards a smaller scale. The fit is defined with an RA
centroid, DEC centroid, major axis, minor axis, and position angle. The location,
major axis, minor axis, and position angle are directly determined by the fit, and are
listed in Columns 2–6 in Table 2.5. We do not report formal uncertainties on these
values since the spatial properties of irregularly shaped objects are dependent on
the chosen method, and we do not want to mislead the reader as to the “certainty”
of these values.
To quantify the shape of an object, we use the axis ratio and filling factor of
the fit (Columns 7 and 8 of Table 2.5). The axis ratio is defined as the ratio of
the minor-to-major axis; a circular fit will have an axis ratio of one, and a highly
elongated fit will have an axis ratio approaching zero. The filling factor is defined as
the area of emission within the fitted ellipse divided by the area of the fitted ellipse;
a circular object and an elliptical object will both have a filling factor near one, but
an irregular object will likely have a filling factor much less than one, regardless
of the axis ratio of the fitted ellipse. We lastly define an object size (Column 9
of Table 2.5) as the geometric mean of the major and minor axes. The values
reported in Table 2.5 have been converted to parsecs, assuming a distance of 235 pc.
Figure 2.16 shows example spatial property fitting results for leaves 26 and 39 and
branch 42.
Histograms of the size, filling factor, and axis ratio for all leaves and branches
are plotted in the top row of Figure 2.18. The trend in size is obvious—branches
represent larger structures than the leaves that peak within them. Leaf sizes range
68
Figure 2.16: Example fits for the spatial properties of leaves and branches. The
left panel shows the N2H+ integrated intensity (Jy beam−1 km s−1) within the
two-dimensional footprints of leaves 26 and 39. We estimated the shape of these
leaves with regionprops in MATLAB; the fits are shown with the solid black
ellipses, and the fit parameters are listed. The axis ratio (AR) is the ratio of minor-
to-major axis, and the filling factor (FF) is the number of greyscale pixels within
the fitted ellipse divided by the total number of pixels within the ellipse. The
right panel shows the N2H+ integrated intensity within the footprint of branch
42, with its ellipse fit shown in black, and the ellipse fits of the leaves in grey.
When fitting for the size of a branch, we include emission from the branch itself
and all objects above it in the dendrogram—this results in a filled-in integrated
intensity map for the fitting process, whereas using the emission from a single
branch would give an “onion-layer”-like structure.
from about 0.01 pc to 0.07 pc, while branch sizes range from about 0.08 pc to 0.34 pc.
The high-contrast leaves are larger than the majority of low-contrast leaves. Nearly
25% of leaves have filling factors greater than 0.8, while all branches have filling
factors less than 0.8. This shows that leaves are better fit as regular shapes compared
to branches, but there is still a large population of irregularly-shaped leaves that
are far from round or filamentary. The objects with the maximum axis ratios (leaf
14 and branch 46) are paired with filling factors below 0.8, indicating that they are
not regularly shaped spheroids as the axis ratio alone might be interpreted. There
are no obvious distinctions between high-contrast and low-contrast leaves in filling
factor or axis ratio.
69
2.6.4 Dendrogram Kinematic Properties
One strength of CLASSy data is the kinematic information across a wide range of
spatial scales. We can use the integrated intensity footprints of the dendrogram
objects (leaf footprints shown in Figure 2.14) in combination with the centroid
velocity and velocity dispersion maps in Figure 2.10 to determine the kinematic
properties of leaves and branches. The four properties in Table 2.5 that we focus
on are: the mean and rms centroid velocity (〈Vlsr〉 and ∆Vlsr, respectively), and the
mean and rms velocity dispersion (〈σ〉 and ∆σ, respectively).
We illustrate how we derive these properties for leaves and branches in Fig-
ure 2.17. For leaves, we mask the full N2H+ Vlsr and σ maps with the integrated
intensity footprint of each leaf, and calculate the error weighted mean and stan-
dard deviation of the masked pixels within the masked footprints. For branches, we
mask the full N2H+ Vlsr and σ maps with the integrated intensity footprint of each
branch, excluding pixels associated with any leaves or branches inside the branch
footprint. We calculate the error weighted mean and standard deviation of the re-
maining pixels belonging exclusively to the branch. By excluding leaf pixels, we
are calculating the kinematic properties of branches only at the larger spatial scales
that are not captured by the leaves within them—this method allows us to parse
kinematics across different spatial scales, which enables a size-linewidth analysis in
the next section. We only report kinematic properties of leaves and branches in
Table 2.5 that have three or more synthesized beams worth of kinematic pixels; a
low signal-to-noise feature may be strong enough to be selected as a dendrogram
object, but still too weak to have enough kinematic data points based on our line
fitting criteria discussed in Section 2.5.
70
Figure 2.17: Examples of how we calculate the kinematic properties of leaves and
branches, using the leaf emission towards B1-c, and the branch emission directly sur-
rounding it. Upper left: The integrated intensity footprint of leaf 39 is represented by the
contour (colored red). The best fit centroid velocities (Vlsr) from Figure 2.10 are shown
within that contour; to find the mean centroid velocity (〈Vlsr〉) for leaf 39, we calculate
the weighted mean of those pixels (weighing according to fit error at each pixel), and
to find the rms centroid velocity (∆Vlsr) for leaf 39, we calculate the weighted standard
deviation of those pixels. Lower left: We show the best fit velocity dispersions (σ, not
FWHM) from Figure 2.10 within the contour, and calculate the weighted mean velocity
dispersion (〈σ〉) and rms velocity dispersion (∆σ) as we did for the Vlsr values in the
upper left. Upper right: The integrated intensity footprint of branch 42 is represented by
the outer contour (colored white), while those of leaf 39 and leaf 26 are represented by the
inner contours (colored red). The best fit Vlsr from Figure 2.10 are shown only between
the outer and inner contours. We are using information only at the branch spatial scales
to calculate the kinematic properties of the branch—we exclude the kinematic properties
of the leaves within the branch. As for the upper left figure, to find 〈Vlsr〉 for branch 42,
we calculate the weighted mean of the shown pixels, and to find ∆Vlsr, we calculate the
weighted standard deviation of the shown pixels. Lower right: The best fit σ for branch
42 are shown between the outer and inner contours.
71
Histograms of 〈Vlsr〉, ∆Vlsr, and 〈σ〉 are plotted in the bottom row of Figure 2.18.
The distribution of 〈Vlsr〉 shows that most of the gas in Barnard 1 is near 6.5 km s−1,
while the gas from leaves 0 and 1 and branch 50 (representing the narrow filament
in the ridge zone) is strongly redshifted.
There is a clear offset in the distribution of ∆Vlsr between leaves and branches:
the majority of branches, which represent the largest objects, have larger ∆Vlsr
than the smaller leaves. There are two effects that are likely causing this trend.
The first effect is from organized velocity field motions (e.g., indicative of rotation
or feedback from outflows) that exist towards a leaf and its surrounding branch. For
example, the Vlsr field for the B1-c leaf and parent branch can be seen in Figure 2.17.
The branch that directly surrounds B1-c has a larger ∆Vlsr compared to the B1-c
leaf due to larger differences between the redshifted and blueshifted velocities in
the rotating branch. However, the majority of leaf-branch pairs do not exhibit
matching, well-ordered velocity fields. Therefore, turbulence is the second likely
explanation for this trend. Turbulence has the property of causing scale-dependent
spatial correlations within a velocity field—points separated by larger distances will
have larger rms velocity differences between them than will points that are closer
together (McKee & Ostriker 2007), meaning that branches will have larger ∆Vlsr
values than leaves.
The high-contrast leaves are preferentially shifted to larger ∆Vlsr relative to the
low-contrast leaves. The high-contrast leaves all have known protostellar objects
within them, so their gas motions are most likely dominated by infall, rotation,
or feedback from outflows, all of which increase the variation in the velocity field.
The low-contrast leaves with the largest ∆Vlsr tend to have more organized centroid
velocity patterns (manifested as gradients) than the low-contrast leaves with the
smallest ∆Vlsr, indicating that they may represent gas around pre-stellar cores that
72
are more likely to form stars in the future.
The distribution of 〈σ〉 differs from the distribution of ∆Vlsr. The high-contrast
leaves representing the gas around B1-b and B1-c have the largest 〈σ〉 in the entire
field, and the majority of branches have 〈σ〉 that are similar to those of the majority
of leaves. We would naively expect that if the branches represent the largest objects
projected on the plane of the sky, then they should also represent the most extended
objects along our lines of sight, and should therefore have the largest velocity disper-
sions (assuming velocity dispersion scales proportionally with length-scale, which is
the case for a turbulent cloud; McKee & Ostriker 2007). We explore these results in
more detail in Section 2.7, where we compare the sizes of structures to their ∆Vlsr
and 〈σ〉 in order to probe the physical and turbulent nature of Barnard 1.
73
Table 2.5. N2H+ Dendrogram Leaf and Branch Properties
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈σ〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Leaves
0 03:32:49.1 +31:02:31.9 49.6 12.4 61.8 0.25 0.60 0.028 7.99(1) 0.02(0) 0.08(2) 0.04(1) 0.61 2.9 1
1 03:32:52.1 +31:03:09.3 22.9 8.3 41.1 0.36 0.84 0.016 7.98(1) 0.03(1) 0.08(1) 0.01(1) 0.62 3.0 1
2 03:32:43.4 +30:58:02.4 37.6 22.1 18.1 0.59 0.61 0.033 7.06(1) 0.02(1) 0.08(1) 0.01(0) 0.51 2.9 0
3 03:32:42.1 +30.58:24.3 19.9 9.1 36.7 0.46 0.82 0.015 ... ... ... ... 0.42 2.0 0
4 03:32:43.9 +31:00:02.4 54.7 23.9 4.8 0.44 0.76 0.041 6.86(1) 0.03(0) 0.14(0) 0.02(0) 0.80 4.0 1
5 03:32:25.1 +31:01:36.9 48.5 20.0 55.1 0.41 0.68 0.035 6.99(1) 0.03(1) 0.12(1) 0.02(1) 0.70 4.0 1
6 03:32:54.9 +31:02:06.7 27.9 9.1 68.5 0.33 0.72 0.018 ... ... ... ... 0.47 2.5 0
7 03:33:25.1 +31:05:36.7 66.7 27.8 30.7 0.42 0.67 0.049 6.88(1) 0.05(1) 0.07(0) 0.01(0) 0.82 5.3 1
8 03:33:10.3 +31:05:34.2 23.6 19.6 17.4 0.83 0.75 0.025 ... ... ... ... 0.62 3.5 1
9 03:33:21.7 +31:06:07.8 22.9 8.9 118.2 0.39 0.82 0.016 ... ... ... ... 0.46 2.4 0
10 03:33:27.1 +31:06:58.5 55.3 27.1 174.6 0.49 0.71 0.044 6.97(2) 0.10(1) 0.12(1) 0.03(0) 1.04 7.7 1
11 03:33:29.3 +31:07:26.1 32.5 13.4 101.7 0.41 0.68 0.024 7.02(1) 0.03(1) 0.10(1) 0.01(0) 0.68 3.8 1
12 03:32:46.2 +31:00:04.5 31.3 11.5 144.7 0.37 0.65 0.022 6.71(1) 0.03(1) 0.09(0) 0.01(0) 0.64 2.3 1
13 03:32:28.2 +31:02:13.1 53.1 27.7 37.2 0.52 0.74 0.044 6.66(2) 0.10(1) 0.10(1) 0.02(0) 0.70 4.0 1
14 03:32:53.1 +31:02:26.4 36.5 35.5 48.3 0.97 0.60 0.041 ... ... ... ... 0.59 3.8 0
15 03:32:53.3 +31:02:55.7 16.6 11.4 55.9 0.69 0.83 0.016 ... ... ... ... 0.48 2.1 1
16 03:32:57.3 +31:03:35.4 72.4 36.0 89.5 0.50 0.67 0.058 6.67(1) 0.04(0) 0.09(1) 0.03(0) 1.03 5.9 2
17 03:33:02.0 +31:04:18.4 49.0 26.2 55.7 0.53 0.72 0.041 6.61(1) 0.03(0) 0.15(0) 0.02(0) 0.92 3.8 3
18 03:33:03.0 +31:04:45.0 17.1 13.9 13.9 0.81 0.86 0.018 6.62(1) 0.02(1) 0.14(1) 0.01(0) 0.79 2.3 3
19 03:33:06.4 +31:05:02.2 80.3 40.1 88.8 0.50 0.67 0.065 6.64(1) 0.04(1) 0.13(1) 0.04(0) 1.03 4.9 3
20 03:33:00.3 +31:05:43.4 19.3 13.2 23.7 0.68 0.82 0.018 ... ... ... ... 0.56 3.4 0
21 03:33:02.4 +31:06:15.5 25.8 17.0 38.6 0.66 0.68 0.024 6.67(1) 0.03(1) 0.13(1) 0.03(1) 0.83 4.5 2
22 03:33:25.9 +31:06:13.5 17.7 14.5 33.4 0.82 0.73 0.018 6.78(1) 0.02(1) 0.08(1) 0.01(1) 0.62 3.2 1
23 03:33:05.3 +31:06:38.3 51.4 33.5 69.5 0.65 0.60 0.047 6.60(1) 0.03(0) 0.11(0) 0.02(0) 0.92 5.4 2
24 03:33:15.7 +31:06:56.4 45.2 26.9 142.3 0.60 0.71 0.040 6.47(2) 0.10(2) 0.19(1) 0.03(0) 1.44 4.9 4
25 03:33:20.8 +31:07:33.0 72.7 38.7 11.4 0.53 0.58 0.060 6.62(2) 0.11(1) 0.29(1) 0.05(1) 1.91 9.9 4
26 03:33:18.0 +31:08:57.9 22.0 10.7 99.1 0.49 0.70 0.017 6.66(2) 0.03(1) 0.18(1) 0.02(1) 0.96 2.8 3
27 03:33:13.4 +31:09:10.2 61.2 32.8 73.1 0.54 0.66 0.051 6.51(1) 0.07(1) 0.17(1) 0.03(0) 0.73 4.4 1
28 03:32:37.1 +30.59:10.1 69.4 27.3 3.8 0.39 0.61 0.050 6.47(1) 0.04(1) 0.11(0) 0.02(0) 0.48 2.6 0
29 03:32:27.7 +30:59:18.2 101.8 34.5 59.8 0.34 0.59 0.068 6.44(1) 0.08(1) 0.16(0) 0.03(0) 0.84 5.0 1
30 03:32:36.4 +30:59:51.1 29.1 18.9 13.2 0.65 0.67 0.027 ... ... ... ... 0.52 3.0 0
31 03:32:33.6 +30:59:59.1 32.0 15.4 151.7 0.48 0.58 0.025 ... ... ... ... 0.47 2.5 0
32 03:32:30.8 +31:00:07.1 39.6 18.7 38.9 0.47 0.73 0.031 6.41(1) 0.04(1) 0.11(1) 0.03(0) 0.75 4.0 1
33 03:33:12.2 +31:04:59.9 15.4 10.3 144.5 0.67 0.87 0.014 ... ... ... ... 0.46 2.3 0
74
Table 2.5 (cont’d)
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈σ〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
34 03:33:13.4 +31:04:59.9 17.2 11.7 102.1 0.68 0.90 0.016 ... ... ... ... 0.47 2.5 0
35 03:33:03.6 +31:05:46.4 25.6 14.7 75.3 0.57 0.72 0.022 6.42(2) 0.03(1) 0.13(1) 0.03(1) 0.53 2.2 1
36 03:33:07.7 +31:06:05.4 24.4 16.5 39.8 0.68 0.75 0.023 ... ... ... ... 0.48 2.6 0
37 03:33:22.0 +31:08:53.6 16.5 13.2 139.6 0.80 0.87 0.017 6.32(2) 0.03(1) 0.14(1) 0.01(0) 0.77 2.8 3
38 03:33:09.2 +31:08:53.3 34.7 19.7 52.5 0.57 0.75 0.030 6.46(1) 0.03(1) 0.13(2) 0.04(1) 0.56 3.5 0
39 03:33:18.2 +31:09:32.2 52.1 34.0 164.4 0.65 0.72 0.048 6.24(3) 0.15(2) 0.26(1) 0.04(1) 1.77 11.5 3
40 03:33:16.7 +31:07:17.3 29.1 13.7 79.2 0.47 0.87 0.023 6.11(1) 0.04(1) 0.15(1) 0.02(0) 1.46 5.2 4
Branches
41 03:33:18.2 +31:07:20.6 178.0 103.1 70.6 0.58 0.66 0.154 6.45(2) 0.24(1) 0.21(0) 0.06(0) 0.97 ... 3
42 03:33:17.9 +31:09:21.3 96.6 56.0 178.0 0.58 0.63 0.084 6.47(4) 0.26(3) 0.21(1) 0.06(1) 0.69 ... 2
43 03:33:04.6 +31:04:45.5 153.5 55.3 60.5 0.36 0.59 0.105 6.64(1) 0.04(0) 0.14(1) 0.04(0) 0.57 ... 2
44 03:33:18.1 +31:07:23.5 197.6 116.9 67.0 0.59 0.68 0.173 6.51(2) 0.17(1) 0.17(1) 0.05(0) 0.51 ... 2
45 03:33:01.9 +31:04:23.6 249.6 84.1 55.6 0.34 0.69 0.165 6.63(1) 0.06(0) 0.12(0) 0.04(0) 0.47 ... 1
46 03:32:44.5 +31:00:00.4 79.2 75.1 81.4 0.95 0.76 0.088 6.80(1) 0.07(1) 0.12(0) 0.03(0) 0.43 ... 0
47 03:33:04.9 +31:06:38.4 107.1 38.1 50.3 0.36 0.63 0.073 6.59(1) 0.06(1) 0.12(1) 0.03(1) 0.41 ... 1
48 03:33:17.9 +31:07:47.8 237.1 177.5 17.5 0.75 0.64 0.234 6.54(2) 0.24(2) 0.16(1) 0.06(0) 0.41 ... 1
49 03:32:28.3 +30:59:29.1 148.3 47.8 45.1 0.32 0.69 0.096 6.44(1) 0.07(1) 0.14(1) 0.04(0) 0.37 ... 0
50 03:32:46.4 +31:02:45.5 103.4 18.9 47.8 0.18 0.56 0.050 7.99(2) 0.07(1) 0.12(4) 0.13(3) 0.34 ... 0
51 03:32:27.0 +31:01:58.4 115.7 38.2 47.6 0.33 0.63 0.076 6.70(5) 0.17(4) 0.11(1) 0.03(1) 0.33 ... 0
52 03:33:17.1 +31:07:34.2 324.8 267.3 73.1 0.82 0.50 0.336 6.67(2) 0.23(1) 0.12(0) 0.05(0) 0.32 ... 0
53 03:33:01.8 +31:04:21.9 274.0 90.2 54.4 0.33 0.72 0.179 6.63(2) 0.10(1) 0.12(1) 0.04(0) 0.29 ... 0
Note. — (2)–(6) The position, major axis, minor axis, and position angle were determined from regionprops in MATLAB. We do not report formal uncertainties of these values since
the spatial properties of irregularly shaped objects is dependent on the chosen method.
(7) Axis ratio, defined as the ratio of the minor axis to the major axis.
(8) Filling factor, defined as the area of the leaf or branch inscribed within the fitted ellipse, divided by the area of the fitted ellipse.
(9) Size, defined as the geometric mean of the major and minor axes, for an assumed distance of 235 pc.
(10) The weighted mean Vlsr of all fitted values within a leaf or branch. Weights are determined from the statistical uncertainties reported by the IDL MPFIT program. The error in
the mean is reported in parentheses as the uncertainty in the last digit. It was computed as the standard error of the mean, ∆Vlsr/
√
N , where ∆Vlsr is the value in Column 11 and N
is the number of beams’ worth of pixels within a given object. We report kinematic properties only for objects that have at least three synthesized beams’ worth of kinematic pixels.
(11) The weighted standard deviation of all fitted Vlsr values within a leaf or branch. The error was computed as the standard error of the standard deviation, ∆Vlsr/
√
2(N − 1),
assuming the sample of beams was drawn from a larger sample with a Gaussian velocity distribution.
(12) The weighted mean velocity dispersion of all fitted values within a leaf or branch. The error was computed as the standard error of the mean, ∆σ/
√
N .
(13) The weighted standard deviation of all fitted velocity dispersion values within a leaf or branch. The error was computed as the standard error of the standard deviation,
∆σ/
√
2(N − 1).
(14) For a leaf, this is the peak intensity measured in a single channel of our 2-channel binned dataset used in the dendrogram analysis. For a branch, this is the intensity level where
the structures above it merge together.
(15) “Contrast” is defined as the difference between the peak intensity of a leaf and the height of its closest branch in the dendrogram, divided by the 1-σ sensitivity of the data.
(16) The branching level in the dendrogram. For example, the base of the tree is level 0, so an isolated leaf that grows directly from the base is considered to be at level 0. A leaf that
grows from a branch one level above the base will be at level 1, etc.
75
0.0 0.1 0.2 0.3
0
5
10
15
size (pc)
N
HC Leaf
LC Leaf
Branch
0.5 0.6 0.7 0.8 0.9
filling factor
0
2
4
6
8
N
0.2 0.4 0.6 0.8 1.0
axis ratio
0
2
4
6
8
10
N
6.5 7.0 7.5 8.0
<vlsr> (km/s)
0
2
4
6
8
10
N
0.00 0.05 0.10 0.15 0.20 0.25
∆vlsr (km/s)
0
5
10
15
20
N
0.05 0.10 0.15 0.20 0.25 0.30
<σ> (km/s)
0
2
4
6
8
10
12
14
N
Figure 2.18: Histograms of dendrogram leaf and branch properties. High-contrast
(HC) leaves, above 6-σ contrast, are represented by green; low-contrast (LC)
leaves, below 6-σ contrast, are represented by blue; branches are represented by
white. See the text in Sections 2.6.3 and 2.6.4 for a discussion of trends seen in
these histograms.
2.7 A Connection Between Size-Linewidth Rela-
tions and Cloud Structure
This chapter presented the morphology and kinematics of the dense gas in Barnard 1,
along with a dendrogram analysis of the N2H+ emission. We conclude with an
analysis of the spatial and kinematic properties of dendrogram structures and what
they can tell us about the turbulent and physical nature of the Barnard 1 region.
A turbulent cloud will have scale-dependent spatial correlations of its veloc-
ity field that take on power law forms over a wide enough range of spatial scales
76
(McKee & Ostriker 2007). Size-linewidth relations are commonly used to probe
turbulence; there have been numerous studies of observed and simulated molecu-
lar clouds using a wide array of observational and statistical techniques, such as
correlation plots (Larson 1981; Solomon et al. 1987), structure function and auto-
correlation analysis (Miesch & Bally 1994; Ossenkopf & Mac Low 2002), principal
component analysis (Brunt & Mac Low 2004; Heyer & Brunt 2004), and dendro-
grams (Rosolowsky et al. 2008b), to name a few. The overall result is that most
galactic molecular clouds exhibit power-law scaling relations consistent with turbu-
lence in a compressible medium, where supersonic motions and overlapping shocks
are important (so-called “Burgers turbulence”). It is well accepted from these anal-
yses that molecular clouds are turbulent, but there are new insights that can be
gained by using size-linewidth relations derived from high angular resolution obser-
vations.
2.7.1 Total Linewidth of Dendrogram Structures
Our dendrogram analysis identified N2H+ structures in the Barnard 1 hierarchy as
either leaves or branches, and we evaluated the size and kinematic properties of those
objects in Section 2.6. Since the spatial scales of dendrogram structures in Barnard 1
range from ∼0.01–0.3 pc, we can utilize these structures to investigate the turbulent
properties of the cloud. Before discussing size-linewidth relations that use the full
angular resolution of our observations, it is useful to consider a relation that uses the
“total” linewidth of each dendrogram structure—this relation can be compared with
classical size-linewidth relations from Larson (1981) and Solomon et al. (1987), in
which the detailed kinematic variation within individual clouds was not resolved. We
calculated a total linewidth for each structure by summing all the spectra assigned
to it and fitting the velocity dispersion of the resulting spectrum (the σ, not FWHM,
77
of the line); for a visualization, see Figure 2.17, which shows the kinematic maps of
an example leaf and branch. In that figure, all the spectra within the red contour
of leaf 39, and all the spectra within the white contours of branch 42 (including
the leaf emission), are summed to calculate the total linewidths of those respective
structures.
Figure 2.19 shows plots of projected size versus total linewidth for all dendrogram
structures that have kinematic values listed in Table 2.5, excluding the objects
associated with the peculiar narrow filament in the ridge zone (leaves 0 and 1,
branch 50). We separate structures in the main core zone (MCZ) from structures in
the ridge and SW clumps zones (RSWZ) because the main core zone has a cluster of
protostars driving outflows. Keeping the zones separate allows us to see whether or
not they have different turbulent or physical properties. We also separately identify
the few structures surrounding compact continuum cores, since their non-thermal
gas motions are likely influenced by their central source.
The data in Figure 2.19 are scattered and could be fit by several functions.
However, there does appear to be variation of total linewidth with size in both zones,
with the linewidth varying more strongly with size in the MCZ. If we use a single
power-law fit, the MCZ correlation is best fit with a slope of 0.37 ± 0.08, and the
RSWZ correlation slope is 0.16 ± 0.06. The steeper slope in the MCZ could be due
to outflows adding energy to the turbulence at these scales. The best-fit slope from
the MCZ is consistent with the result (Larson 1981) that clouds ranging in size from
0.1 to 100 pc have a power-law slope of 0.38. However, we are probing the scaling
relation across much smaller spatial scales than has typically been done, and unlike
previous studies, we are using high-density molecular tracers that are sensitive to
non-thermal motions near the sonic scale of the cloud. Therefore, directly comparing
our results to studies that used larger scales and lower-density gas tracers, such as
78
12CO, should be considered with caution.
Main Core Zone
0.01 0.10 1.00
Projected Size (parsec)
0.1To
ta
l L
in
ew
id
th
 (k
m/
s)
0.37±0.08
Ridge+SW Zones
0.01 0.10 1.00
Projected Size (parsec)
0.1To
ta
l L
in
ew
id
th
 (k
m/
s)
0.16±0.06
Figure 2.19: Scaling relations between projected structure size and total linewidth
for the main core zone and the combined ridge and SW clumps zones. The
projected size for each dendrogram structure is defined as the geometric mean of
its best-fit major and minor axes. The majority of structures are labeled with
squares, while the three leaves toward the three strongest compact continuum
detections in main core zone are marked with triangles, along with the branch
directly surrounding the B1-c leaf. The solid line represents a single power-law fit
to the square points. The horizontal line represents the typical thermal speed for
H2 at gas kinetic temperatures near 11 K. The vertical line represents our spatial
resolution of ∼0.008 pc.
2.7.2 Resolved Linewidths of Dendrogram Structures
We have two kinematic measurements of leaves and branches in Table 2.5 that use
the full angular resolution of our dataset—they complement the total linewidth and
enable a different type of size-linewidth analysis. The first measurement is the Vlsr
variation, ∆Vlsr. For a leaf or branch of size L, ∆Vlsr(L) is computed by measuring
the rms variation of the (beam-scale) centroid velocity over the whole structure.
The second measurement is the mean non-thermal velocity dispersion, 〈σ〉nt. To
calculate 〈σ〉nt from 〈σ〉 in Table 2.5, we remove the thermal velocity dispersion,
σth, of 11 K N2H+ gas, which is the typical gas kinetic temperature across the entire
79
Barnard 1 region (Rosolowsky et al. 2008a): 〈σ〉nt =
√
〈σ〉2 − σ2th. Recall that 〈σ〉
for a structure is defined by averaging all the individual velocity dispersions over
the structure; each individual pointing captures the velocity dispersion along the
line-of-sight for a given beam-width.
Main Core Zone
0.01 0.10 1.00
Projected Size (parsec)
0.01
0.10
∆ 
V l
sr
 
(km
/s) 0.80±0.08
Main Core Zone
0.01 0.10 1.00
Projected Size (parsec)
0.01
0.10
<
σ
>
n
t 
(km
/s)
0.12±0.11
Ridge+SW Zones
0.01 0.10 1.00
Projected Size (parsec)
0.01
0.10
∆ 
V l
sr
 
(km
/s)
0.69±0.17
Ridge+SW Zones
0.01 0.10 1.00
Projected Size (parsec)
0.01
0.10
<
σ
>
n
t 
(km
/s)
0.04±0.07
Figure 2.20: Left : Scaling relations between projected structure size and Vlsr
variation (∆Vlsr) for the main core zone and the combined ridge and SW clumps
zones. Right : Scaling relations between projected structure size and mean non-
thermal velocity dispersion (〈σ〉nt) for the main core zone and the combined ridge
and SW clumps zones. The solid line represents a single power-law fit to the
square points. The horizontal line represents the typical thermal speed for H2
at gas kinetic temperatures near 11 K. The vertical line represents our spatial
resolution of ∼0.008 pc.
We compare the dependences of ∆Vlsr and 〈σ〉nt on projected structure size
80
in Figure 2.20. Size versus ∆Vlsr for the dendrogram structures in both zones is
plotted on the left; the data appears to follow a power-law relation. There is a steep
correlation in both regions, with power-law slopes of 0.80 ± 0.08 in the MCZ and
0.69 ± 0.17 in the RSWZ. The value of ∆Vlsr is very low for the smallest objects in
all zones, and rises to the sound speed for the largest objects in the MCZ. Size versus
〈σ〉nt is plotted on the right side Figure 2.20. There is a much flatter correlation
between size and 〈σ〉nt in both zones, with a power-law slope of 0.12 ± 0.11 in the
MCZ and 0.04 ± 0.07 in the RSWZ. The mean non-thermal velocity dispersions
are all sub-sonic to trans-sonic in the MCZ (though still superthermal). The two
structures with largest 〈σ〉nt are surrounding B1-b and B1-c; it is likely that the
non-thermal motions of the gas around them is boosted by rotation and/or outflows
and is not purely turbulent. The 〈σ〉nt are all sub-sonic in the RSWZ.
Why are the dependences of 〈σ〉nt and ∆Vlsr on projected structure size so dif-
ferent? In the following section, we set up a theoretical framework that can explain
this disparity in terms of differences between a structure’s projected size and its
depth into the plane of the sky.
2.7.3 Inferring Cloud Depth from Resolved Size-Linewidth
Relations
In this section, we assume that the observed non-thermal gas motions in our den-
drogram structures are generated by isotropic, three-dimensional turbulence. In the
previous section, we noted a few structures surrounding compact continuum cores
that likely have non-thermal gas motions due to the influence of their central source;
we exclude them from this analysis.
The total turbulent linewidth of a structure is most strongly influenced by the
largest scale an observation encompasses, under the assumptions that the gas we
81
observe is isotropically turbulent, and optically thin with uniform excitation condi-
tions. If the structure is wider across the plane of the sky than it is deep into the sky,
then its turbulent linewidth will be most strongly influenced by its projected size.
But if the structure is deeper into the sky than in either of the projected directions,
then its turbulent linewidth will be most strongly influenced by its depth.
For a structure that is many resolution elements across (the case for all of our
dendrogram structures), ∆Vlsr and 〈σ〉nt probe turbulence in different ways from
the total linewidth. The value of Vlsr on any given line-of-sight is a measure of the
mean motion of gas along that line-of-sight, which varies from one line-of-sight to
another line-of-sight as a consequence of turbulence. The Vlsr variation, ∆Vlsr, is
expected to increase with the projected scale of a structure if turbulence increases
with scale, as is the case for the observed and simulated turbulent power spectra in
molecular clouds. For any given line-of-sight, the turbulent contribution to 〈σ〉 will
be set by the larger of the beam size and the structure depth. Since our beam size is
very small (∼0.008 pc), we expect that the linewidth along individual lines-of-sight
will be dominated by structure depth, and thus 〈σ〉nt for a structure will depend
primarily on the mean (unseen) depth of that structure into the sky. Statistically,
along many lines-of-sight for a resolved structure, the comparison of linewidths set
by the projected size of the structure (∆Vlsr) to linewidths set by the depth of the
structure (〈σ〉nt) should allow an estimation of the structure depth.
We can use a mathematical framework to explain how we can compare ∆Vlsr to
〈σ〉nt to learn about the typical depth of gas structures. In the full three dimensional
turbulence, line-of-sight turbulent velocities (vz,turb) can be written as
vz,turb(x, y, z) =
∑
kx,ky ,kz
vp(kx, ky, kz) exp[i(kxx+ kyy + kzz)], (2.4)
where vp(kx, ky, kz) is the turbulent velocity power spectrum, kx = (2pi/Lx)nx, ky =
(2pi/Ly)ny, and kz = (2pi/Lz)nz. Lx is the size of an observed structure in the x
82
direction, and nx is the number of full waves of a given turbulent velocity component
that fit in the x-direction (the same is true for the y and z components in these
equations). If the turbulent motions are Gaussian and isotropic, then vp(kx, ky, kz)
is drawn from a normal distribution whose standard deviation depends only on
the magnitude of the k-vector, |k| =
√
k2x + k2y + k2z . We assign the z direction as
the line-of-sight, so that in Equation 2.4, vz,turb(x, y, z) is the z-component of the
turbulence, and there are other independent components in the x and y directions.
In this framework, the total linewidth of a structure is the sum of components
with non-zero kx, ky, or kz. The resolved linewidths (∆Vlsr and 〈σ〉nt) are explained
below with the aid of Figure 2.21.
The observed centroid velocity at a resolved projected position in the structure,
Vlsr(x, y), is the sum of components in Equation 2.4 that have kz=0. The Vlsr de-
pendence on spatial scale via vp(kx, ky; kz = 0) is assumed to depend statistically
only on |k| if the turbulence is isotropic. Therefore, Vlsr(x,y) has the same statistical
dependence on |k| =
√
k2x + k2y (which we can measure) that the underlying turbu-
lent velocity, vz,turb(x, y, z), has on |k| =
√
k2x + k2y + k2z (which we cannot measure).
The Vlsr(x,y) variation, ∆Vlsr, which is the standard deviation of Vlsr(x, y) over all
resolved positions in a structure, will scale with the (x, y)-size of the structure ac-
cording to the turbulent scaling relation of the cloud (see Dickman & Kleiner (1985)
for a discussion of spatial correlation properties of centroid velocity fields). To vi-
sualize this, we consider the structure on the left-side of Figure 2.21. We call the
full 4-cell structure, structure A, and any contiguous 2-cell substructure within it,
structure B. Structure A is wider than structure B in the (x, y) directions on the sky,
so the minimum, non-zero kx and ky must be smaller in structure A than structure
B. Assuming vp has a (statistical) inverse power-law dependence on |k|, this implies
higher power in structure A, with a greater contribution to the Vlsr variation across
83
the (x, y) face of structure A compared to structure B.
The non-thermal velocity dispersion at each resolved position in a structure,
σnt(x, y), is obtained from the sum of turbulent components with all possible kx and
ky, and non-zero kz, along each line-of-sight. For a given (x, y), the total line-of-sight
velocity is a sum: vz(z) = vz,turb(z) + vth(z), where vth is the thermal component of
the velocity. The mean value of vth(z) is zero, and the mean value of vz,turb(z) is Vlsr.
Thus, assuming that vz,turb(z) and vth(z) are uncorrelated, for a given line-of-sight,
the square of the total velocity dispersion, σ2(x, y), is:
σ2(x, y) = 〈v2z〉 − V2lsr = 〈v2z,turb〉 − V2lsr + 〈v2th〉+ 2〈vz,turb〉〈vth〉. (2.5)
The last term in Equation 2.5 is zero because the mean value of vth(z) is zero.
The second-to-last term in Equation 2.5 is equivalent to the square of the thermal
velocity dispersion, σ2th; σ2 − σ2th is equal to the non-thermal component of the
velocity variance, σ2nt, which means that the first two terms Equation 2.5 contribute
to the non-thermal velocity dispersion. The combination of the first two terms is
〈|
∑
kx,ky ;kz 6=0
vp(kx, ky, kz) exp(ik · x)|2〉, (2.6)
where the summation includes combinations with all kx, ky, and with all kz except
kz = 0; k is the wavenumber vector, and x is the spatial vector. This shows that the
mean non-thermal velocity dispersion for our structures, 〈σ〉nt, defined as the mean
of σnt(x, y) at each resolved position, will scale with the z-depth of the structure
according to the turbulent scaling relation of the cloud. Along any given line-of-
sight, a larger Lz implies that the minimum nonzero kz = 2pi/Lz is smaller, such that
the contribution to Equation 2.6 would be larger (under the assumption that vp(k)
statistically increases with decreasing |k|). To visualize this, we can consider the
structure on the right-side of Figure 2.21. We call the full 4-cell structure, structure
A, and any contiguous 2-cell substructure within it, structure B. Structure A extends
84
deeper into the sky than structure B, so the minimum, non-zero kz in structure A
is smaller than the minimum, non-zero kz in structure B. This implies higher power
in structure A, with a larger contribution to σnt(x, y) in structure A compared to
structure B.
Based on the arguments above, the scaling relation between Vlsr variation and
projected size, l, (∆Vlsr ∝ lq) should have the same power-law dependence as the
scaling relation between mean non-thermal velocity dispersion and depth, d, into
the sky (〈σ〉nt ∝ dq) if the turbulence is isotropic and we are observing all the gas
along each line-of-sight. But we saw in Figure 2.20 that the dependences of ∆Vlsr
and σnt on projected structure size are very different. The simplest explanation of
this difference is that the projected size of an object need not be the same as its
line-of-sight depth into the sky. The size axis in Figure 2.20 (right) is an estimate
based on the geometric mean of the projected size. If every object, no matter its
projected size, has the same depth, then we should measure a similar non-thermal
velocity dispersion for those objects. Therefore, we interpret the shallow dependence
of 〈σ〉nt with size as an indication that our collection of dendrogram structures have
similar depths.
85
Figure 2.21: One-dimensional cartoons explaining our interpretation of the kinematics
of spatially resolved dendrogram structures in the framework of isotropic turbulence. The
spatial dimension of each structure is represented by four square cells, each one unit by one
unit in area. The colored vectors in each figure represent turbulent velocity components
along the line-of-sight (blue = blue-shifted velocity component, red = red-shifted velocity
component). The length of the velocity vectors are not to scale, but are simply used to
show that there is larger velocity power on the larger scales, and vice-versa. (a): We
are looking across the resolved major axis (x-direction) of this filament, and down the
minor axis (z-direction; line-of-sight). The Vlsr of the filament at each resolved L=1 cell
is determined by the velocity of all vectors influencing the gas in that cell with kz = 0.
Since all vectors have kz = 0, for example, the left-most cell has Vlsr contributions from
a small red vector, a medium blue vector, and a large red vector, while the right-most
cell has Vlsr contributions from a small blue vector, a medium red vector, and a large red
vector. The Vlsr variation (∆Vlsr) across the four resolved cells is the standard deviation
of the Vlsr in each L=1 cell. If this structure were half as wide, then ∆Vlsr would
decrease because each cell would only have contributions from a small and a medium
vector. The non-thermal velocity dispersion along each resolved line-of-sight (σnt) is zero
because there are no kz 6= 0 vectors along the line of sight of each cell. The total velocity
dispersion is a combination of vector components with k 6= 0, which is determined by
small and medium vectors across x-direction. (b): We are looking down the major axis
of this filament (z-direction; line-of-sight), through the single resolved spatial element in
the x-direction. The Vlsr of the filament is determined by the velocity of the large vector
because it is the only vector with kz = 0; oscillations of the small and medium vectors
average each other out along the line-of-sight, and they do not contribute to the Vlsr. The
Vlsr variation (∆Vlsr) is zero because there is only one resolved Vlsr value for this object.
The non-thermal velocity dispersion (σnt) along the single line-of-sight is determined by
the small and medium vectors, since both have kz 6= 0. If this structure were half as
deep, then σnt would decrease because it would be determined by the small vectors alone.
The total velocity dispersion is a combination of vector components with k 6= 0, which is
determined by small and medium vectors along the z-direction in this case; it equals σnt
since there is only one resolved line-of-sight.
86
To illustrate these effects, we created a numerical realization of a three-dimensional,
isotropic turbulent power spectrum, with power spectrum scaling v2 ∝ k−4. Using
an arbitrary length scale, L, the position-position-position box had x, y, z dimen-
sions of L×L×2L, where L corresponds to 512 pixels. We used this realization along
with three sub-boxes with different Lz to demonstrate how 〈σ〉nt and ∆Vlsr depend
on structure depth for a single turbulent realization. The original box had dimen-
sions of L×L×2L (the “double depth” box), the first sub-box was L×L×L (the “full
depth” box), the second was L×L×L/2 (the “half depth” box), and the third was
L×L×L/4 (the “quarter depth” box). For each of these sub-boxes (with uniform
density), we created PPV cubes and then processed them similarly to the observa-
tions. The end products were centroid velocity and velocity dispersion maps across
the L×L x, y surface of each numerical box. We segmented each L×L surface into
equally sized square regions with side L, L/2, L/4, L/8, and calculated ∆Vlsr and
〈σ〉nt within each segment to show how they scale with size. The results for each box
are shown in Figure 2.22. Evidently, 〈σ〉nt has no dependence on size, while ∆Vlsr
increases with size, similar to the behavior seen in the observations in Figure 2.20.
The size where ∆Vlsr crosses 〈σ〉nt corresponds well with the depth of the numerical
cube.
If turbulence in the observed region has similar behavior to that in the isotropic
turbulent realization, then we can use the correlation of Vlsr variation with size to
estimate the depths of the Barnard 1 structures. For this correlation, we know the
projected size is directly related to ∆Vlsr, so there is no size ambiguity as there is in
the correlation between projected size and 〈σ〉nt. To estimate the typical depth of the
cloud, we can find the size scale at which the best-fit line for ∆Vlsr versus projected
size is equal to the best-fit line for 〈σ〉nt versus projected size. This corresponds to
∼0.11 pc for the MCZ, and ∼0.18 pc for the RSWZ. Under the assumption that
87
Double Depth 
0.1 1.0
Size (L)
0.1
1.0
Li
ne
w
id
th
∆Vlsr
<σ>nt
L~2.0
Full Depth 
0.1 1.0
Size (L)
0.1
1.0
Li
ne
w
id
th
∆Vlsr
<σ>nt
L~1.0
Half Depth 
0.1 1.0
Size (L)
0.1
1.0
Li
ne
w
id
th
<σ>nt
∆Vlsr
L~0.5
Quarter Depth 
0.1 1.0
Size (L)
0.1
1.0
Li
ne
w
id
th
<σ>nt
∆Vlsr
L~0.25
Figure 2.22: Size-linewidth relations from a numerical realization of an isotropic
turbulent power spectrum. The four plots represent results from four different
boxes taken from the realization: the “double depth” box is twice as deep as
it is wide (L×L×2L), the “full depth” box is cubic (L×L×L), the “half depth”
box is half as deep as it is wide (L×L×L/2), etc. The vertical axis represents
the two linewidths we discussed in text: 〈σ〉nt and ∆Vlsr (in arbitrary units).
The horizontal axis represents the size-scale we sampled across the face of the
box when calculating the linewidths: a size-scale of 1 represents sampling across
the full L×L scale, a size-scale of 0.5 represents sampling across smaller-scale
L/2×L/2 segments, etc. There are several things to notice in these panels: 1)
〈σ〉nt is independent of size, and its magnitude decreases by
√
2 as the box depth
is halved from panel to panel, 2) ∆Vlsr increases with increasing size, 3) The
magnitude of 〈σ〉nt and ∆Vlsr cross near the size that represents the depth of the
box.
turbulence is isotropic, this implies that Barnard 1 is on the order of 0.1–0.2 pc deep,
comparable to the largest projected width (∼0.2–0.3 pc) of individual structures.
Since the largest-scale dust structure in Barnard 1 extends over 1 pc on the sky,
the overall region may be more flattened than spherical at the largest scales. Nu-
merical simulations over the past 15 years have consistently shown that high-density
88
sheets and filaments are a generic result of strongly supersonic turbulence with pa-
rameters comparable to those in observed clouds (e.g., reviews by Elmegreen & Scalo
2004; Mac Low & Klessen 2004; McKee & Ostriker 2007). But measuring the depth
of an individual structure in a molecular cloud is a difficult task. Comparison to
realizations of turbulence suggests that the high angular resolution, large area ob-
servations from CLASSy allow us to estimate the physical depths of individual
structures in molecular clouds, thus providing new observational insight into the
true nature of those clouds3. Our observational result suggests that Barnard 1 is
an over-dense region within the larger Perseus Molecular Cloud that could have
formed a sheet-like geometry from supersonic turbulence. Lee et al. (2014) present
the same size-linewidth relations using CLASSy observations of Serpens Main, and
find similar behavior. We will compare the results from all our CLASSy regions in
an upcoming cross-comparison paper.
2.8 Summary of Barnard 1 Results
We presented the CLASSy project overview with a focus on Barnard 1. CLASSy
spectrally imaged over 800 total square arcminutes of the Perseus and Serpens
Molecular Clouds at 7′′ angular resolution.
1. We spectrally imaged N2H+, HCN, and HCO+ (J = 1 → 0) emission across
150 square arcminutes of Barnard 1. The final data products are position-
position-velocity cubes with full line emission recovery obtained through joint
3We emphasize, however, that it is important to confirm the behavior seen in simple, isotropic
turbulent realizations with fully-realistic turbulent simulations of clouds. For best comparison to
observations, it will be valuable to create synthetic PPV data cubes via radiative transfer modeling,
rather than assuming uniform excitation and optically thin conditions.
89
deconvolution with single-dish observations. The velocity resolution of the
data is ∼0.16 km s−1.
2. Four compact continuum sources were detected at >5-σ at 3 mm, all in the
main core zone. B1-c, B1-b South, and B1-b North were previously known; we
report a new detection of compact emission towards the Per-emb 30 continuum
source.
3. The N2H+ (J = 1 → 0) gas morphology closely matches dust continuum
observations of Herschel, while HCN and HCO+ (J = 1 → 0) emissions are
weaker throughout most of the field and show less correlation with the long
wavelength dust emission. HCN and HCO+ also well-trace outflows in the
main core zone.
4. Spectral line fitting of the molecular line data shows that the Barnard 1 main
core is much more kinematically complex than the filaments and clumps that
extend to its southeast; these filaments and clumps are characterized by more
uniform centroid velocities and lower velocity dispersions.
5. We used dendrograms to identify N2H+ gas structures in Barnard 1. The
motivation for using dendrograms instead of a more traditional clumpfinding
algorithm was the need to analyze the morphological and kinematic structure
of dense gas across the wide range of spatial scales captured in our CLASSy
data. We found that dendrograms are better able to quantify that range of
spatial scales. We created a new, non-binary adaptation to the standard,
binary dendrogram algorithm to ensure that the dendrograms represent the
true hierarchy of the emission within the noise limits of real data, and that
tree statistics can be used to quantify that hierarchy.
90
6. The non-binary dendrogram of Barnard 1 contains 41 leaves and 13 branches.
We calculated three simple tree statistics using the dendrogram: the maximum
branching level, the mean path length, and the mean branching ratio. The
tree structure representing the dense gas around the main core is the most
complex, with four hierarchy levels and the highest contrast leaves. The tree
statistics give insight into the type and amount of fragmentation a region has
undergone, and will be used to compare the hierarchical complexity of the
different CLASSy regions.
7. We characterized the spatial properties of the dendrogram structures and de-
rived structure sizes ranging from ∼0.01 to 0.34 pc. The high angular resolu-
tion data reveal a variety of irregular shapes, showing that star-forming gas is
not composed of well ordered spheroids and filaments on the smallest scales.
We also characterized the kinematic properties of the structures and found
that, in general, branches have larger Vlsr variation, but similar mean velocity
dispersion, compared to the leaves. The gas surrounding the most massive
compact continuum cores have the largest velocity dispersions in the entire
region.
8. Using the spatial and kinematic properties of the dendrogram leaves and
branches, we estimated the depth of the Barnard 1 cloud to be ∼0.1–0.2 pc.
This estimate was made by comparing two size-linewidth relations: one using
the mean non-thermal velocity dispersion of the dendrogram objects, which is
sensitive to the depth of the cloud, and the other using the Vlsr variation of the
objects, which is sensitive to the projected size of the cloud. The mean non-
thermal velocity dispersion varied very little with structure size, while the Vlsr
variation varied steeply with size. We interpreted this as an indication that
91
Barnard 1 is more flattened than spherical on the largest scales. This method
is a powerful tool for observationally probing the structure of molecular clouds
into the plane of the sky.
92
Chapter 3
Analysis of the Young L1451
Region Within Perseus
Abstract
We present spectral line images of HCO+, HCN, and N2H+ (J = 1 → 0), and a con-
tinuum image at 3 mm, toward the L1451 region in the Perseus Molecular Cloud.
These observations are part of the CARMA Large Area Star Formation Survey,
which also imaged the Barnard 1 and NGC 1333 regions in Perseus. L1451 is the
region of the survey with the lowest level of star formation activity; it contains no
confirmed protostars, only a first hydrostatic core candidate source. All three dense
gas tracer molecules are detected throughout the 150 square arcminute region, with
HCO+ the most spatially widespread. We detect molecular emission toward 90% of
the area above N(H2) column densities of 1.9×1021 cm−2, where column densities are
derived from Herschel observations. Our non-binary dendrogram algorithm reveals
complex hierarchical structure in all three molecular lines, with similar trends of
hierarchical fragmentation based on a comparison of tree statistics. Gas surround-
ing the candidate first hydrostatic core, L1451-mm, and other previously detected
93
single-dish continuum clumps show similar tree statistics, providing evidence that
different sub-regions of L1451 are fragmenting on the pathway to forming young
stars. Spectral line fitting reveals that HCO+ has the broadest velocity dispersion,
near 0.3 km s−1 on average, compared to ∼0.15 km s−1 for the other molecules. A
virial analysis using Herschel -derived column densities and CLASSy-derived kine-
matics shows that the most centrally-condensed dust structures are likely in virial
equilibrium when considering effects including density stratification within a core,
external confining pressure, and the systematic underestimation of column densities
from fitting Herschel SEDs with a single-temperature component model. An anal-
ysis of N2H+ emission from L1451-mm and a newly identified centrally condensed
feature, called L1451-west, shows that L1451-west is younger than L1451-mm, but
more centrally condensed than a typical prestellar core, suggesting it could be an-
other first hydrostatic core candidate. We determined the typical depth of molecular
emission from L1451 structures to be ∼0.4 pc and 0.1 pc for HCO+, and HCN and
N2H+, respectively; the comparison of these typical depths to the projected size of
the largest dense gas features suggests that the dense gas in the L1451 region is
not significantly flattened at the parsec-scales, and that the main features are more
ellipsoidal than filamentary. These overall results point to L1451 being a young
region that is forming its first generation of stars.
3.1 Introduction
The star formation process in a molecular cloud starts well before protostars are
detectable at infrared wavelengths. In general, it begins with the formation of the
molecular cloud that may span tens of parsecs (Evans 1999; Elmegreen & Scalo
2004; McKee & Ostriker 2007); it continues as structure and density enhancements
94
are created by the interaction of turbulence, gravity, and magnetic fields at parsec
scales (McKee & Ostriker 2007; Crutcher 2012), and it progresses until prestellar
core collapse occurs at 0.01–0.1 pc scales (di Francesco et al. 2007; Bergin & Tafalla
2007). Once a first generation of protostars is formed within those dense cores,
the young stars can feed energy back into the cloud and impact subsequent star
formation that may occur (Nakamura & Li 2007; Carroll et al. 2009; Nakamura & Li
2014). A full understanding of how turbulence, gravity, and magnetic fields control
the star formation process requires observations that span cloud to core spatial scales
at these distinct evolutionary stages.
An individual molecular cloud can be a great testbed for studying the star for-
mation process across space and time if it is sufficiently close to get better than
0.1 pc resolution, and if it contains regions with distinct evolutionary stages. The
Perseus Molecular Cloud is a nearby example of such a cloud. At a distance of
235 pc (Hirota et al. 2008, 2011), Perseus has several regions of clustered star for-
mation that have been observed as part of large Spitzer, Herschel, and JCMT sur-
veys. The regions with infrared detections of young stellar objects (YSOs) span a
range of evolutionary epochs based on YSO statistics from the c2d Legacy project
(Jørgensen et al. 2008; Evans et al. 2009). The IC 348 region has 121 YSOs, with
9.1% being Class I or younger; the NGC 1333 region has 102 YSOs, with 34% being
Class I or younger; the Barnard 1 region had 9 YSOs, with 89% being Class I or
younger; and, the L1448 region has five YSOs, with 100% being Class I or younger.
Regions without current protostellar activity also exist within Perseus. The B1-E
region may be forming a first generation of dense cores (Sadavoy et al. 2012), and
the L1451 region has a single detection of a compact continuum core, which is a
candidate first hydrostatic core (FHSC) (Pineda et al. 2011).
The CARMA Large Area Star Formation Survey (CLASSy) observed the dense
95
gas in three evolutionary distinct regions within Perseus (Storm et al. 2014) and
two regions within Serpens (Lee et al. 2014; Ferna´ndez-Lo´pez et al. 2014) with high
angular and velocity resolution. From early to late stages of evolution (based on the
ratio of Class II and older to Class I and younger YSOs), the Perseus regions are:
L1451, Barnard 1, and NGC 1333. The observations enable a high resolution study
of the structure and kinematics of star forming material at different epochs. The
youngest region, L1451, probes conditions during the origin of clumps and stars; the
more evolved Barnard 1 region probes conditions when a relatively small number
of protostars are formed, and the active NGC 1333 region probes conditions when
dozens of clustered protostars are driving outflows back into the cloud. Details of
CLASSy, along with an analysis of Barnard 1, can be found in Chapter 2.
This chapter focuses on the L1451 region. L1451 is located ∼5.5 pc to the south-
west of NGC 1333 (see Figure 1.3). The region has been surveyed at a number of
wavelengths. It contains no Spitzer -identified YSOs at IRAC or MIPS wavelengths
(Jørgensen et al. 2008). Hatchell et al. (2005) and Kirk et al. (2006) did not identify
any cores in their JCMT SCUBA 850 µm survey. There are four 1.1 mm sources
identified in the Bolocam Survey (Enoch et al. 2006) that are classified as “starless”
cores in Enoch et al. (2008): PerBolo 1, 2, 4, and 6. Pineda et al. (2011) showed
that PerBolo 2 is not a starless core, but likely a core with an embedded YSO or a
FHSC.
The Bolocam cores within L1451 are colder and less dense than the average
Bolocam cores within Perseus. The visual extinction (Av) of the four Bolocam
sources ranges from 8 to 11 magnitudes, while the mean and median Av for all
Perseus sources are 24.6 and 12, respectively (Enoch et al. 2006). The mean particle
density of the L1451 Bolocam sources ranges from 0.9×105 to 1.5×105 cm−3, which
is lower than the mean density for all Perseus sources of 3.2×105 (Enoch et al. 2008).
96
The kinetic temperature of gas within the L1451 cores ranges from 9.1 to 10.3 K,
which is lower than the mean for all Perseus cores of 11.0 (Rosolowsky et al. 2008a).
These statistics indicate that the dense cores forming within L1451 are, on av-
erage, a little colder and less dense than other star forming regions within Perseus,
supporting the YSO statistics suggesting it is at an earlier evolutionary epoch than
Barnard 1 and NGC 1333. The main science goals of our large-area, high-resolution,
spectral line observations of this young region are: 1) to determine whether com-
plex, hierarchical structure formation exists before the onset of star formation, as
predicted by theories of turbulence-driven star formation, 2) to better understand
how natal cloud material fragments on the pathway to star formation, by quan-
tifying the hierarchical similarities and differences between different sub-regions of
L1451, 3) to estimate the boundedness of the dense structures in young star forming
regions, and 4) to potentially discover new young cores.
The chapter is organized as follows. Section 3.2 provides an overview of CLASSy
observations of L1451. Properties of the L1451-mm continuum detection are in
Section 3.3. Section 3.4 presents the dense gas morphology using integrated intensity
and channel maps, and Section 3.5 presents the dense gas kinematic results from
spectral line fitting. A dendrogram analysis of the HCO+, HCN, and N2H+ data
cubes is in Section 3.6. Section 3.7 shows how we calculate column density, dust
temperature, and extinction maps using Herschel data, along with a dendrogram
analysis of the extinction map. Section 3.8 uses the spectral line data in combination
with the continuum data to assess the properties of structures in L1451, along with
the typical depth of molecular emission from the region. We summarize our key
findings in Section 3.9.
97
Table 3.1. Observation Summary
Array Dates Total Hours Flux Cal. Gain Cal. Mean Flux (Jy)
DZ October 2012 25 Uranus 3C84/3C111 18.6/2.6
February - June 2013 50 Uranus 3C84/3C111 19.5/3.5
EZ August - September 2012 25 Uranus 3C84/3C111 18.0/2.8
July - August 2013 50 Uranus 3C84/3C111 17.5/4.2
3.2 Observations
The details of CLASSy observations, calibration, and mapping are found in Chap-
ter 2 (Section 2.2); specifics related to L1451 are summarized here. We mosaicked a
total area of ∼150 square arcminutes in CARMA23 mode. The mosaic was made up
of two adjacent rectangles, containing a total of 673 individual pointings with 31′′
spacing in a hexagonal grid (see Figure 3.1). The reference position of the mosaic
is at the center of the eastern rectangle: α=03h25m17s, δ=30◦21′23′′(J2000). The
L1451-mm core (Pineda et al. 2011) is within the eastern rectangle. The region was
observed for 150 total hours, evenly split between the DZ and EZ configurations,
which provide projected baselines from about 1–40 kλ and 1–30 kλ, respectively. See
Table 3.1 for a summary of observing dates, and calibrators. The mapped region
covers roughly 1.1 pc by 0.6 pc with about 1700 AU (0.008 pc) spatial resolution.
The correlator setup is summarized in Table 3.2. N2H+, HCO+, and HCN J =
1 → 0 were simultaneously observed in 8 MHz bands, providing a velocity resolution
of 0.16 km s−1. We also used a 500 MHz band for continuum observations and
calibration. Data were inspected and calibrated using MIRIAD (Multichannel Image
Reconstruction, Image Analysis and Display; Sault et al. 1995). 3C84 was observed
every 16 minutes for gain calibration; 3C111 was used for gain calibration when
3C84 transited above 80 degrees elevation. Uranus was observed for absolute flux
calibration. The flux of 3C84 varied between 16 and 21 Jy over the observing
98
Figure 3.1: A Herschel image of the 250 µm emission (yellow is brighter emission,
red is fainter emission) from L1451 with the CLASSy mosaic pointing centers over-
laid as white points. The spacing of the pointing centers is 31′′, and our total area
coverage is ∼150 square arcminutes. The locations of 1.1 mm Bolocam sources
(Enoch et al. 2006) and the L1451-mm compact continuum core (Pineda et al.
2011) are marked with black squares and a black star, respectively.
Table 3.2. Correlator Setup Summary
Line Rest Freq. No. Chan. Chan. Width Vel. Coverage Vel. Resolution Chan. RMS Synth. Beama
(GHz) (MHz) (km s−1) (km s−1) (Jy beam−1)
N2H+ 93.173704b 159 0.049 24.82 0.157 0.14 8.6′′ × 6.8′′
Continuum 92.7947 47 10.4 1547 33.6 0.0013 9.2′′ × 6.6′′
HCO+ 89.188518 159 0.049 25.92 0.164 0.12 8.8′′ × 7.1′′
HCN 88.631847c 159 0.049 26.10 0.165 0.12 8.9′′ × 7.2′′
Note. — aIn principle, the synthesized beam is slightly different for each pointing center. Miriad calculates a
synthesized beam for the full mosaic based on all of the pointings. bThe rest frequency of the band was set to the
weighted mean frequency of the center three hyperfine components. cThe rest frequency of the band was set to
the frequency of the center hyperfine component. See http://splatalogue.net for frequencies of the HCN and N2H+
hyperfine components.
period, while 3C111 varied between 2.6 and 4.5 Jy. The uncertainty in absolute flux
calibration is about 10%. We will only report statistical uncertainties when quoting
errors in measured values throughout the chapter.
To create spectral-line images which fully recover emission at all spatial scales,
CARMA observed in single-dish mode during tracks with stable atmospheric opac-
99
ity. The OFF position for L1451 was 3.5′ west and 13.7′ south of the mosaic reference
position. The single-dish data from the 10.4-m dishes was calibrated in MIRIAD
using the sinbad, sinpoly, varmaps, and imstack commands. The antenna tem-
perature rms in the final single-dish cubes was ∼0.02 K for all three molecules.
The spectral-line interferometric and single-dish data were combined with mosmem,
a maximum entropy joint deconvolution algorithm in MIRIAD. The noise levels and
synthesized beams for the final data cubes are given in Table 3.2. The rms noise in
these lines correspond to brightness temperature rms of 0.34 K for N2H+ and 0.30 K
for HCO+ and HCN.
We created a 3 mm continuum map with the interferometric data from the
500 MHz window. The rms in the continuum map is ∼1.3 mJy beam−1 with a
synthesized beam of 9.2′′ × 6.6′′. Single-dish continuum data can not be acquired
at CARMA.
3.3 Continuum Results
We detected no compact continuum sources above the 5-σ level. One source was
detected above 3-σ that could be confirmed with other observations; L1451-mm
(Pineda et al. 2011) is detected at 4-σ with 5.2 mJy beam−1. Figure 3.2 shows
the 3 mm continuum image toward L1451-mm. The position, peak brightness, and
lower-limit mass for our detection were calculated following the prescription de-
scribed in Section 2.3 and are listed in Table 3.3. The position and peak brightness
agree with 3 mm measurements from Pineda et al. (2011). Our image shows a pos-
sible secondary peak to the north of the brightest emission. However, this secondary
peak is only within the 2–3 σ contours, and does not appear in the higher sensitiv-
ity observations of Pineda et al. (2011). Pineda et al. (2011) detected a low-velocity
100
Table 3.3. Observed Properties of Continuum Detections
Source Position Pk. Bright. Mass
Name (h:m:s, d:′:′′) (mJy beam−1) (M⊙)
(1) (2) (3) (4)
L1451-mm 03:25:10.38, +30:23:55.9 5.2 ± 1.3 0.10 ± 0.03
Note. — (3) Peak brightness, (4) Lower-limit mass using the peak brightness and
assumptions outlined in Section 2.3.
CO (J = 2 → 1) outflow in this area; we do not detect any HCN or HCO+ outflow
emission near this source.
Figure 3.2: The single continuum detection in our field. The synthesized beam is
9.2′′ × 6.6′′, and the 1-σ sensitivity is 1.3 mJy beam−1. The contour levels are 2,
3 times 1-σ; no negative contours are present.
3.4 Morphology of Dense Molecular Gas
3.4.1 Integrated Intensity Emission
Figure 3.3 shows integrated intensity maps for HCO+, HCN, and N2H+ J = 1 → 0
(∼7.5′′ angular resolution), along with a Herschel 250 µm image (18.1′′ angular res-
olution) for a visual comparison between the dense gas and dust emission. The line
maps were integrated over all channels with identifiable emission. HCO+ emission
101
was integrated from 5.316 to 3.018 km s−1. HCN emission was integrated over all
three hyperfine components from 9.945 to 7.962 km s−1, 5.154 to 2.841 km s−1,
and −2.115 to −3.932 km s−1. N2H+ emission was integrated over all seven hy-
perfine components over velocity ranges from 11.542 to 8.714 km s−1, 5.729 to
2.744 km s−1, and −3.383 to −4.639 km s−1. The rms of the maps are 0.08, 0.13,
and 0.16 Jy beam−1 km s−1 for HCO+, HCN, and N2H+, respectively.
The locations of the four Bolocam 1.1 mm sources (Enoch et al. 2006) and the
one compact continuum core in L1451 are marked on each image of Figure 3.3. Four
of the five sources are located near peaks of dense gas and dust emission. Kirk et al.
(2006) showed possible evidence for dense cores being preferentially offset from the
peak of their parent core due to the B0.5 V star, 40 Per, triggering star formation
and sculpting Perseus material (Walawender et al. 2004; Kirk et al. 2006); we do
not see evidence for this with our high-resolution observations.
While the molecules and dust are tracing similar features around those sources,
the exact morphological details vary. Below, we describe the qualitative emission
features, and refer to the colored rectangles in Figure 3.3 for reference.
All tracers show a curved structure surrounding L1451-mm and the two nearby
Bolocam sources (see red rectangle in Figure 3.3), with a peak of integrated emission
at the location of L1451-mm. The southwestern edge of the curved structure has a
stream of emission that extends further to the southwest (see dark blue rectangle in
upper left panel of Figure 3.3), which can be seen in all the maps, though it extends
furthest in the HCO+, HCN, and dust maps. The two other Bolocam sources to
the far east of L1451-mm are surrounded by significant molecular gas structure (see
green rectangle in lower left panel). The HCO+ emission has the largest extent of
strong emission in this region.
The integrated emission in the three lines is less similar across the western half
102
of L1451 compared to the eastern half. There is a strong, condensed N2H+ source
(see orange rectangle in lower right panel) that does not appear in the HCN or
HCO+ maps, but that does correspond to a peak of emission in the dust map (see
Section 3.8.3 for more details on this source). The strongest HCO+ feature in the
western half of the map has a weaker counterpart in the HCN map (see purple
rectangle), which appears even weaker in N2H+. Finally, there is HCO+ emission to
the northwest of the curved structure (see cyan rectangle) that closely mimics dust
emission in that region; this emission is weakly detected in HCN, but not in N2H+.
Figure 3.3: Integrated intensity maps of HCO+, HCN, and N2H+, (J = 1 → 0)
emission toward L1451, along with a Herschel 250 µm map of the region. The
four Bolocam 1.1 mm sources in this region are marked with “x” symbols, and
the L1451-mm compact continuum core is marked with an asterisk. Colored
rectangles show the locations of qualitative features discussed in Section 3.4.1.
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3.4.2 Channel Emission
Figures 3.4, 3.5, and 3.6 show channel maps of HCO+, HCN, and N2H+ respectively,
highlighting the bulk of the emission1, which occurs from ∼4.9 to 3.5 km s−1. In
general, it is clear from the maps that strong HCO+ emission is more widespread
compared to HCN emission, and particularly N2H+ emission (as was also evident
in Figure 3.3). We labeled qualitative features in the HCO+ channel maps, from
A through I, in the order that they appear in velocity space (with eastern sources
being labeled before western sources). We then placed those same labels on the
HCN and N2H+ maps to aid a qualitative comparison of dense gas features, given
below2.
We detect no HCN or HCO+ outflow emission in any channels, which suggests
that L1451 is a young region with little to no protostellar activity. The strongest
emission in the field is near the L1451-mm core; the peak brightness temperature for
a single channel in a single synthesized beam is: 6.9 K, 6.3 K, and 3.9 K for HCO+
(2.47 Jy beam−1 to K conversion factor), HCN (2.46 Jy beam−1 to K conversion
factor), and N2H+ (2.42 Jy beam−1 to K conversion factor), respectively.
Features A and C
Features A and C in the eastern half of the map are traced with all molecules,
with varying strength. Feature A appears strongly in the first HCO+ channel in
Figure 3.4, faintly in the first HCN channel in Figure 3.5, and not until the third
N2H+ channel in Figure 3.6. Even when it finally appears in the N2H+ channel, the
1These figures do not show some of the highest and lowest velocity channels with emission;
those channels can be viewed by downloading the publically available data cubes.
2The condensed structure labeled J in Figure 3.6 only appears in the N2H+ maps, so the J
label is excluded from the HCO+ and HCN maps.
104
emission is much more concentrated than what we observe in HCO+ and HCN. This
concentration is likely because the N2H+ (J = 1 → 0) line traces higher-density,
colder material compared to HCO+ and HCN (J = 1 → 0) lines. A 1.1 mm Bolocam
core is located within Feature A, and corresponds with a peak in the N2H+ emission.
Feature A moves from northeast to southwest as the first few channels progress from
higher to lower velocity, and Feature C then appears to its southwest. Features A
and C are possibly part of the same larger-scale structure, which will be explored
in the next section when we analyze the kinematics of this region. Like Feature A,
Feature C is more concentrated in N2H+, and contains a 1.1 mm Bolocam source at
an N2H+ peak of emission.
Figure 3.7 shows HCO+ and HCN spectra from three locations across Feature
A, along with an integrated intensity view of HCO+. The purpose of this figure is to
demonstrate the complexity of HCO+ and HCN emission in many parts of L1451.
Location 1 shows a ∼6-σ dip between two peaks of HCO+ emission. This could be a
detection of a two component system, a signature of self-absorption, or a signature
of infall. The HCN spectrum at this location shows a similar dip in the two higher-
velocity hyperfine components, but no dip in the lowest-velocity component—this
makes a two-component system unlikely. This feature is likely not due to infall,
which predicts a stronger blue peak (Evans 1999), since the red peak is stronger.
Double-peaked spectra from self-absorption can be due to several effects including:
a foreground screen of lower-density HCO+, infall of material onto a dense core, and
the spherical expansion of material (Zhou et al. 1993). The dotted line in each panel
of Figure 3.7 indicates the N2H+ centroid velocity from our spectral line fitting in
Section 3.5. The N2H+ spectra at these locations do not show evidence of double
peaks. The best-fit centroid velocity of N2H+ at location 1 is 4.57 km s−1, which
is between the two HCO+ and HCN peaks, thereby adding support to the case for
105
self-absorption at this location. Observations of optically thin tracers of HCO+ and
HCN species are needed to more definitively understand the emission.
The HCN spectrum at location 2 has all hyperfine components at a similar
intensity—this is either a sign that part of the two higher opacity hyperfine com-
ponents have been absorbed away, thereby matching the intensity of the lowest
opacity hyperfine component, or that the line is optically thick and all components
are saturated to the same intensity. The HCO+ spectrum at location 2 has a weak,
single-channel dip between two peaks of emission, which hints at self-absorption be-
ing the more likely cause of the matching HCN intensities at this location. Location
3 has a single-component HCO+ spectrum, and a single-component HCN spectrum
with hyperfine intensity ratios closer to the expected local thermodynamic equilib-
rium values, showing that spectra can vary on the scale of ∼30′′ when observations
have high angular and velocity resolution.
Feature B
Feature B contains the L1451-mm compact continuum source. It appears strongly
in all molecules, though it contains a prominent ridge of emission in the 4.82 km s−1
channel of HCO+ and HCN that does not appear in the closest N2H+ channel.
Figure 3.8 shows an integrated intensity map of HCO+ with HCO+ and HCN
spectra from a location in the eastern and western half of this feature. The HCO+
spectrum from location 1 shows a double-peaked spectrum with a single-channel dip.
The center hyperfine component of the HCN spectrum shows a remarkably similar
shape to the HCO+ spectrum, with a single-channel dip between two channels of
significant emission. The full HCN spectrum shows a single-channel dip in the two
higher-velocity hyperfine components, but not the lower-velocity component. It also
shows similar component strengths for all three hyperfine lines. The N2H+ spectrum
106
at location 1 has no evidence of a second component along the line-of-sight. The
N2H+ centroid velocity is 4.12 km s−1 (plotted as dotted line in Figure 3.8), closer to
the HCO+ dip near 4.0 km s−1 than the HCO+ peaks at 3.87 and 4.30 km s−1. All
of this suggests that the dip in the HCO+ and HCN spectra is from self-absorption.
The HCO+ and HCN spectra from location 2 show a two-peak structure, where
the bluer component is significantly stronger than the redder component. This fea-
ture appears in all HCN hyperfine components, unlike all the other spectra we looked
at above. The N2H+ spectrum at location 2 does not show two components. The
N2H+ centroid velocity is 4.32 km s−1, closer to the HCO+ dip near 4.45 km s−1 than
the HCO+ peaks at 4.14 and 4.75 km s−1. These results are consistent with infall
models, and suggest that the gas in this region may be undergoing collapse. This
would require that the HCO+ line and all three HCN hyperfine lines are optically
thick. Similar spectra are seen at and around the peak of integrated emission nearest
to location 2, as well as at the other two peaks of integrated emission to the north-
east of location 2, suggesting that these could be young cores undergoing infall. As
mentioned above, observations with optically thin tracers toward these sub-regions
of L1451 are needed for a more complete understanding of the gas dynamics.
Features D Through J
Features D, E, F, G, H, and I are all identified based on the HCO+ channel emission.
N2H+ only shows faint emission in two channels for Feature G, while HCN emission
appears weakly toward all features seen with HCO+. The descriptions below are
based on HCO+.
Feature D appears to the west of Features A and C, and to the south of Feature
B, in the 4.66 and 4.50 km s−1 channels as an elliptical feature not connected to
larger-scale structure. Feature E appears as a prominent, round emission feature
107
in the 4.50 km s−1 channel, with more extended emission in channels surrounding
the 4.50 km s−1 peak of emission. Feature F is emission that starts just to the
northwest of Feature B in the 4.17 km s−1 channel, peaks in the 4.0 and 3.83 km s−1
channels, and then appears to get fainter while extending to the southwest in chan-
nel 3.67 km s−1, while then brightening at the extended southwestern edge in the
3.51 km s−1 channel. Feature G emission peaks in the 3.83 km s−1 channel, and
appears as a stream of emission to the east of Feature D. Feature H is a streamer to
the southwest of Feature B and the south of Feature F, which first appears in the
3.83 km s−1 channel. It persists in both the 3.67 and 3.51 km s−1 channels shown
in Figure 3.4, and more faintly extends into two bluer channels not shown in the
figure. Feature I first appears in the 3.51 km s−1 channel, brightens in the two bluer
channels not shown in the figure, and is not detectable at velocities lower than that.
Feature J, referred to as L1451-west in the rest of the chapter, is relatively round
emission that only appears in the N2H+ data. It first appears in the 4.79 km s−1
channel of Figure 3.6, and extends across a total of four channels per hyperfine
component (the structure can be seen repeating for another hyperfine component,
starting in the 3.84 km s−1 channel). We discuss details of the structure and kine-
matics of L1451-west in Section 3.8.3.
108
Figure 3.4: Ten HCO+ channels maps. The rms in each channel is 0.12 Jy beam−1,
and the color intensity ranges from 0.12–1.3 Jy beam−1. The red crosses represent
the locations of the L1451-mm compact continuum core and the Bolocam sources.
Features discussed in the text are identified with a letter in the first channel they
appear.
109
Figure 3.5: Similar to Figure 3.4, but for HCN. The rms in each channel is
0.12 Jy beam−1, and the color intensity ranges from 0.12–0.9 Jy beam−1. Feature
labels from Figure 3.4 are overplotted in the same locations for aid in comparing
the emission across molecules.
110
Figure 3.6: Similar to Figure 3.4, but for N2H+. The rms in each channel map is
0.14 Jy beam−1, and the color intensity ranges from 0.14–0.9 Jy beam−1. Feature
labels from Figure 3.4 are overplotted in the same locations for aid in comparing
the emission across molecules. Feature J (also referred to as L1451-west) only
appears in N2H+, so it is only labeled in this figure.
111
Figure 3.7: Example HCO+ and HCN spectra from three locations within Fea-
ture A (integrated intensity in greyscale on left), highlighting the varying spectra
seen in CLASSy data toward L1451. Spectra are averaged over one synthesized
beam at each location, and the HCO+ spectra are shifted by 1 Jy beam−1 for
visualization. The dashed line represents the centroid velocity of N2H+ emission
at each location.
Figure 3.8: Example HCO+ and HCN spectra from two locations within Fea-
ture B. Spectra are averaged over one beam at each location, and the HCO+
spectra are shifted by 1 Jy beam−1 for visualization. The dashed line represents
the centroid velocity of N2H+ emission at each location.
112
3.5 Kinematics of Dense Molecular Gas
We fitted the molecular line emission with gaussians as described in Chapter 2
(Section 2.5), and present the centroid velocity and line-of-sight velocity dispersion
maps here. The N2H+ line was simple to fit relative to the other lines; there is
only one velocity component along each line-of-sight and there is no sign of self-
absorption. Examples of HCN and HCO+ spectra with double peaks, which could
be interpreted as self-absorption or two components along the line-of-sight, were
shown in Figures 3.7 and 3.8. Since we cannot determine which of these scenarios is
correct without H13CN and H13CO+ observations at each cloud location, and since
the available evidence points towards self-absorption being the dominant factor,
we fit the HCN and HCO+ lines with a single component across the entire field.
Modeling the self-absorption across so many spectra is beyond the scope of this
chapter. About 3% of HCO+ spectra could be fit with two peaks separated by
three or more channels, while about 0.2% could be fit with two peaks separated by
five or more channels. By extrapolating self-absorbed spectra to a single peak, and
measuring the full width at half of that peak, we estimate that the velocity dispersion
is overestimated by ∼10% toward these locations. Therefore, double-peaks have a
relatively small overall impact on the results presented in this chapter.
There are no outflows affecting the line profiles. A low-velocity outflow from
L1451-mm was previously detected in CO (J = 2 → 1) by Pineda et al. (2011),
but we do not detect any outflow signature in our HCN or HCO+ (J = 1 → 0)
observations.
In Figure 3.9, we plot the fitted centroid velocity and velocity dispersion where:
1) the integrated intensity is greater than or equal to four times the rms of the
integrated intensity map, and 2) the peak signal-to-noise of the spectrum is greater
113
than five. We will use these kinematic maps in the following section in order to
interpret the hierarchical and turbulent nature of the cloud. Here we list some
broad features of interest pertaining to the maps:
1. HCO+ has systematically larger line-of-sight velocity dispersion compared to
HCN and N2H+, even if we account for an overestimation of velocity disper-
sion due to fitting self-absorbed spectra. Mean velocity dispersions across
the maps are 0.29±0.10, 0.16±0.07, 0.12±0.04 km s−1, for HCO+, HCN, and
N2H+, respectively. If we assume that the typical temperature in this region
is 10 K based on ammonia observations of Bolocam cores (Rosolowsky et al.
2008a), then the isothermal sound speed of the gas would be 0.20 km s−1.
The N2H+ velocity dispersions are subsonic everywhere, the HCN are sub-
sonic most places, and the HCO+ are transsonic to supersonic most places.
Note that even though N2H+ and HCN are subsonic in many areas of L1451,
they are not exhibiting purely thermal velocity dispersions, which would be
∼0.05 km s−1 for 10 K gas.
The J = 1 → 0 line of HCO+ trace densities about an order of magnitude lower
than that of HCN and N2H+ (see Shirley 2015, and Chapter 1). Therefore,
we are likely observing the trend from supersonic to subsonic gas motions as
gas goes from the larger, less-dense scales traced by HCO+ to the smaller,
more-dense scales traced by HCN and N2H+. This is expected in a turbulent
medium, where velocity dispersion scales proportionally with size (as is the
case for observations of an optically-thin turbulent gas; McKee & Ostriker
2007).
2. All three molecules are tracing gas with centroid velocities ranging from ∼3.8–
4.7 km s−1. However, the HCO+ gas extends to lower velocities, due to the gas
114
in the feature H streamer, which appears in the HCN maps, but is not strong
enough to provide reliable kinematic measurements. HCO+ also extends to
higher velocities, due to gas from the northeast part of feature A, which is
noticeable in the first channel of Figure 3.4.
3. The HCO+ centroid velocities for features A and C show a clear gradient from
northeast to southwest. It is possible that this is a large, rotating piece of
dense gas, which is fragmenting into denser components (e.g., the Bolocam
1 mm sources). It is also possible that the redshifted northeast section and
the blueshifted southwest section represent independent components in the
turbulent medium, or that they are merely projected along the same line of
sight. Observations of optically thin tracers, and tracers of lower-density,
larger-scale material are needed to help distinguish between these scenarios.
4. The gas in the eastern half of feature B shows an axial velocity gradient.
It is most blueshifted at the southeastern end near the L1451-mm core, and
becomes increasingly redshifted further away to the northwest. The gas im-
mediately surrounding the L1451-mm compact continuum core has a centroid
velocity pattern that is consistent with rotation (Pineda et al. 2011), and has
velocity dispersions that increase toward the core center. L1451-west shows
similar N2H+ kinematic features, and we compare these two sources in detail
in Section 3.8.3.
5. Our measurements of N2H+ centroid velocity and velocity dispersion towards
L1451-mm agree well with the results in Pineda et al. (2011), in terms of
absolute values measured and gradients across the source.
115
Figure 3.9: Kinematics of dense gas in L1451. Left: Centroid velocity maps of
HCO+, HCN, and N2H+ (J = 1 → 0) emission, from top to bottom. Right:
Line-of-sight velocity dispersion maps of HCO+, HCN, and N2H+ (J = 1 → 0)
emission, from top to bottom. We masked these maps to visualize only statistically
robust kinematic results (see Section 3.5 text). The color scales are the same
across molecules.
3.6 Dendrogram Analysis of Molecular Emission
3.6.1 The Non-binary Dendrograms
We qualitatively described the dense gas morphology of L1451 in Section 3.4. Here
we quantitatively identify dense gas structures in all three molecular tracers, and
study the hierarchical nature of L1451 with the non-binary dendrogram algorithm
described in Chapter 2 and Appendix B.
116
A dendrogram algorithm identifies emission peaks in a dataset, and keeps track of
how those peaks merge together at lower emission levels. This method of identifying
and tracking emission structures is advantageous compared to a watershed object-
identification algorithm, such as CLUMPFIND (Williams et al. 1994), when the
science goals include understanding how the morphology and kinematics of star-
forming gas connects from large to small scales. A full discussion of the most widely
used dendrogram algorithm can be found in Rosolowsky et al. (2008b); details of
dendrograms and our non-binary version of the dendrogram algorithm are found in
the Appendix A and B, along with a comparison with the results from using a more
standard clump-finding algorithm on our CLASSy data.
We ran our non-binary dendrogram algorithm on the HCO+ emission, the emis-
sion from the strongest HCN hyperfine line, and the emission from the strongest
N2H+ hyperfine line. For other CLASSy regions, we limited our analysis to N2H+
emission because the HCO+ and HCN lines were complicated by protostellar out-
flows and severe self-absorption effects. We also ran the algorithm on the isolated
N2H+ hyperfine component in the other CLASSy regions because the stronger hy-
perfine components come in clusters of three and were not resolved in every location.
The N2H+ hyperfine components in L1451 are resolved in all locations, letting us
use the strongest component for our dendrogram analysis. A caveat is that some
bluer emission from the higher-velocity, adjacent hyperfine component, and some
redder emission from the lower-velocity, adjacent hyperfine component appear in
the channels of the strongest component. Since there was no blending of hyperfine
emission at the same location within the cloud, we masked the emission from the
adjacent hyperfine components in the individual channels of the strongest hyper-
fine component in which they appeared. As an example, L1451-west (Feature J)
appears in much bluer channels compared to Feature A, so L1451-west from the
117
higher-velocity, adjacent hyperfine component also appears in the reddest channel
of the strongest hyperfine component that shows Feature A. For this example, we
simply masked out L1451-west from this red channel of the strongest component.
We ran the algorithm with similar parameters used for the Barnard 1 analysis
described in Chapter 2, while following the prescription for comparing data cubes
with different noise levels presented in Appendix C. As in Chapter 2 (Section 2.6.1),
we masked the channel emission of each PPV cube, only keeping pixels ≥4-σ along
with adjacent pixels of at least 2.5-σ, where σ is the rms level of the data cube. For
the minpixel noise-suppression parameter, we again required at least three synthe-
sized beam areas of pixels for a leaf to be considered real. Appendix C shows that
using uniform minheight and stepsize allows a proper comparison of dendrogram
properties that is independent of noise-level differences between data cubes. There-
fore, the minheight noise-suppression parameter required a local maximum to peak
at least 2-σn above the intensity where it merges with another local maximum for
it to be considered a leaf, where σn is the rms level of the noisiest data cube (N2H+
at ∼0.14 Jy beam−1, in this case). The stepsize parameter allowed branching at
integer values of 1-σn.
Figures 3.10, 3.11, and 3.12 show HCO+, HCN, and N2H+ non-binary dendro-
grams for L1451, respectively. The vertical axis of the dendrograms represents the
intensity range of the pixels belonging to a leaf or branch. The horizontal axis is
arranged with the major features identified in Figures 3.4–3.6 progressing from east-
to-west; we label certain branches that are associated with major features, and we
provide the numeric label for structures referred to in the upcoming discussion. The
isolated leaves are presented in numerical order. The horizontal dotted line in each
dendrogram represents an intensity cut at 2.5-σn that aids in cross-comparison of
dendrogram statistics (see Appendix C), and is discussed in Section 3.6.3.
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The HCO+ dendrogram contains the largest number of structures, with 86 leaves
and 27 branches. The HCN dendrogram contains 33 leaves and 13 branches, while
the N2H+ dendrogram only contains 16 leaves and 6 branches. Leaves that peak
at least 6-σn in intensity above the branch they merge directly into are colored
green in Figures 3.13–3.15, and referred to as high-contrast leaves3. The strongest
leaf for every molecule is at or near the location of L1451-mm in Feature B: Leaf
66 is the strongest structure in the HCO+ dendrogram, with a peak intensity of
2.78 Jy beam−1, leaf 30 is the strongest structure in the HCN dendrogram, with a
peak intensity of 2.58 Jy beam−1, and leaf 10 is the strongest structure in the N2H+
dendrogram, with a peak intensity of 1.62 Jy beam−1.
3.6.2 Dendrogram Spatial and Kinematics Properties
The leaves and branches of each dendrogram represent molecular structures. We
fit for the spatial properties of each structure, as we did in Chapter 2, using the
regionprops program in MATLAB. This program fits an ellipse to the integrated
intensity footprint of each dendrogram structure to determine its RA centroid, DEC
centroid, major axis, minor axis, and position angle. Columns 2–6 in Tables 3.4–3.6
list the spatial properties of each structure. To quantify the shape of each structure,
we use the axis ratio and filling factor of the fit (Columns 7 and 8 of Tables 3.4–3.6).
We lastly define the structure size (Column 9 of Tables 3.4–3.6) as the geometric
mean of the major and minor axes, assuming a distance of 235 pc when converting
to parsec units.
Histograms of the size, filling factor, and axis ratio for all leaves and branches
are plotted in the top rows of Figures 3.13–3.15. All HCO+ and HCN leaves are
3We will use the definition of high-contrast leaves, first introduced in Chapter 2, as a way of
comparing the properties of strong leaves across CLASSy clouds in future papers.
119
Figure 3.10: The HCO+ non-binary dendrogram for L1451. The vertical axis rep-
resents the Jy beam−1 intensity for a given location within the gas hierarchy. The
horizontal axis is ordered so that features identified in Section 3.4 are generally
ordered from east to west. Leaves and branches discussed in the text are labeled
with their numerical identifier, and branches associated with major features from
Section 3.4 are marked with the feature letter. The leaves colored green peak
at least 6-σn above their first merge level. The horizontal dotted line represents
the 2.5-σn intensity cut above which we calculate tree statistics when comparing
different dendrograms.
smaller than 0.11 pc, while all N2H+ leaves are smaller than 0.06 pc. HCO+ branches
are the largest of all molecules, peaking at 0.46 pc, while HCN branches peak at
0.24 pc, and N2H+ branches peak at 0.17 pc. This is expected since HCO+ shows
the most widespread emission in the channel and integrated emission maps. The
filling factor for all molecular structures is between 0.45 and 0.95. The structures
with filling factor closest to one are leaves, indicating that leaves are more likely
to be elliptically shaped objects while branches are more likely to be irregularly
shaped objects. The axis ratio for all structures is between 0.19 and 0.95, showing
that there is a distribution from elongated to round structures, without differences
between leaves and branches. There are no obvious differences between the high-
120
Figure 3.11: Same as Figure 3.10, but for the HCN non-binary dendrogram.
Figure 3.12: Same as Figure 3.10, but for the N2H+ non-binary dendrogram.
contrast leaves and the rest of the leaves.
We use the integrated intensity footprints of the dendrogram structures in com-
bination with the centroid velocity and velocity dispersion maps to determine kine-
matic properties of leaves and branches. The four properties present in Tables 3.4–
3.6 are: mean and rms centroid velocity (〈Vlsr〉 and ∆Vlsr, respectively), and mean
and rms velocity dispersion (〈σ〉 and ∆σ, respectively). We illustrated how to derive
121
these properties for leaves and branches in Chapter 2 (Section 2.6 and Figure 2.17).
Histograms of 〈Vlsr〉, ∆Vlsr, and 〈σ〉 are plotted in the bottom rows of Fig-
ures 3.13–3.15. HCO+ traces larger variation in 〈Vlsr〉 compared to HCN and N2H+.
We attribute this to HCO+ being sensitive to more widespread emission away from
the densest regions of L1451, and therefore tracing more widespread centroid ve-
locities relative to the systemic velocity of the most spatially compact gas. For all
molecules, ∆Vlsr of the leaves generally extends from low to moderate velocities,
while it is distributed from moderate to high velocities for the branches. This indi-
cates a trend where ∆Vlsr is generally lower for smaller structures than larger struc-
tures. This trend was also seen for Barnard 1 gas structures, and we discussed ex-
planations in Chapter 2 (Section 2.6.4); the primary reason was the scale-dependent
nature of turbulence, which causes gas parcels separated by smaller distances to
have smaller rms velocity differences between them (McKee & Ostriker 2007).
The distribution of 〈σ〉 is similar for leaves and branches, with neither distri-
bution showing a preference to peak at high or low velocities. This trend was also
seen in Chapter 2 for Barnard 1, indicating that 〈σ〉 does not strongly depend on
the projected size of a structure. The peak 〈σ〉 for HCO+ is higher compared to
HCN and N2H+: 0.42 km s−1, 0.18, and 0.13 km s−1, respectively. Since HCO+
traces effective excitation densities of an order of magnitude lower than HCN and
N2H+ (Shirley 2015), we are likely observing emission from lower-density gas that is
more extended along the line-of-sight. This could increase the line-of-sight velocity
dispersions, which are expected to scale with cloud depth in a turbulent medium
(McKee & Ostriker 2007). We note that although the HCO+ velocity dispersion
measurements are likely inflated by ∼10% in regions with double-peaked spectra,
this is not a large enough effect to produce the difference between HCO+ and the
other molecules. There are no obvious differences in these kinematic properties
122
between the high-contrast leaves and the rest of the leaves.
3.6.3 Tree Statistics
The dendrograms in Figures 3.10–3.12 show an apparently wide variety of hierarchi-
cal complexity between molecular tracers, and between sub-regions of L1451. In this
section, we quantify the hierarchical nature of the gas with tree statistics that were
introduced and explained in Chapter 2 so that the complexity between molecules
and sub-regions can be quantitatively compared. Specifically, we calculate the max-
imum branching level, mean path length, and mean branching ratio of the entire
L1451 region for each molecule in a uniform way that accounts for differences in
the noise-level of each data cube (see Appendix C). We then calculate those same
statistics for individual features within each dendrogram.
The path length, defined only for leaves, is the number of branching levels it
takes to go from a leaf to the tree base. The branching ratio, defined only for
branches, is the number of structures a branch splits into immediately above it in
the dendrogram. We will be linking these tree statistics to cloud fragmentation in the
discussion to follow. A more evolved region with a lot of hierarchical fragmentation
will have a higher maximum branching level and larger mean path length than a
young region that is starting to form overdensities and fragment. The branching
ratio of a very hierarchical region will be smaller than a region fragmenting into
many substructures in a single step. This is likely an overly simplistic view, since
the molecular emission, and in turn, the dendrograms and tree statistics, can also
be affected by projection effects and line opacity. We briefly discussed these effects
in Chapter 2; since they are extremely difficult to accurately model over such a large
area, we use the simple view that hierarchy comes from fragmentation4.
4Although a few regions within L1451 show double-peaked HCO+ spectra, which we attribute
123
The PPV cubes of all three molecules have slightly different noise levels, and we
created the dendrograms by following the Appendix C discussion of how dendrogram
structure and statistics depend on noise. Based on Appendix C, to compare the tree
statistics of dendrograms derived from maps with different noise levels, we only count
leaves and branches above a 2.5-σn intensity cut, where σn is the rms of the noisiest
data cube. The N2H+ PPV cube has the highest noise level, at ∼0.14 Jy beam−1,
so the cut for each dendrogram is at ∼0.35 Jy beam−1, and is represented as the
horizontal dotted line in Figures 3.10–3.12. Only leaves that peak at least 2-σn
above the cut are still considered in these statistics—all other leaves are marked
with an “x” in the dendrogram. A branch below the cut is discounted, but if the
leaf directly above it is more than 2-σn above the cut, then the leaf is counted as a
leaf with a branching level of zero (e.g., leaf 64 in Figure 3.10). This comparison of
tree statistics ensures that we can analyze the fragmentation of molecular emission
independent of noise-level differences.
The tree statistics for the entire L1451 region are reported in the first section of
Table 3.7. The mean branching ratios are 3.8, 3.3, and 3.0 for HCO+, HCN, and
N2H+, respectively. We interpret this to mean that each molecule is tracing physical
structures that are fragmenting in a hierarchically similar way (e.g., a structure is
most likely to fragment into about three to four sub-structures). The mean path
length of HCO+ is 1.0 level longer than that of HCN and N2H+, and the maximum
branching level of HCO+ is two more than that of HCN and three more than that
primarily to self-absorption, the dendrogram algorithm rarely splits structures containing such
spectral features in two. We searched the dendrogram structure cube and data cube by eye, and
determined that only leaves 15 and 47 are likely split due to self-absorption. This has the effect
of reducing the branching ratio of branch 93 from three to two, has no effect on the maximum
branching level, and minimally impacts the other average tree statistics. Therefore, we do not
consider the HCO+ dendrogram to be contaminated by self-absorption.
124
of N2H+. This trend in fragmentation levels is likely due to the ability of each
tracer to detect material at different spatial scales and physical densities. As the
effective excitation density of the tracer goes down from N2H+ to HCN to HCO+, our
observations are more sensitive to more widespread emission, which means we are
sensitive to more levels of fragmentation extending from the higher-density leaves
(detectable with all tracers) to the lowest detectable branches (most detectable
with HCO+). Therefore, even though the dendrograms in Figures 3.10–3.12 look
very different, a comparison of their tree statistics using a uniform noise-level cut,
along with an understanding of what each molecule is tracing, produces a consistent
picture of how L1451 is hierarchically fragmenting from parsec-scales into much
smaller-scale structures.
Features A, B, and C are the only features with any hierarchical complexity in
the N2H+ dendrogram, and are the ones with the most branching steps in the HCN
and HCO+ dendrograms. They are also the most likely sites for current and future
star formation, since they account for emission surrounding the only continuum
source detections in the field: Feature B surrounds L1451-mm, and Features A and
C surround Bolocam 1 mm sources. Because of this, we next compare the tree
statistics of these sub-regions in Table 3.7, along with a comparison to any other
sub-region with hierarchical complexity (labeled as “others” in Table 3.7), using
the original dendrograms of each molecular tracer. We do not use a noise-level cut
because we are comparing different sub-regions of the same data cube. The sections
of the dendrograms corresponding to individual features are marked in Figures 3.10–
3.12 with letter identifiers, and we only consider structures above those identifiers
in this comparison. For example, in the HCO+ dendrogram, Feature A and C
merge together at the branch labeled “A+C,” but we consider the statistics of the
individual features only above labels “A” and “C”.
125
There is a trend of decreasing maximum branching level and mean path length
from Feature B to A to C and then to the other remaining features. Feature A and
B are more similar to one another than either is to the remaining other features,
indicating that the gas in both features has fragmented a similar amount relative
to the rest of the complex structure in the L1451 field. The mean path length
and maximum branching level of Feature C bridge the gap between the maximum
fragmentation amount seen in Feature A and B and the minimum fragmentation
amount seen in the remaining other features.
We interpret the similarity in hierarchical branching levels between Features A
and B to mean that these subregions have progressed to a similar stage along the
evolutionary track of cloud fragmentation. We know a young star or first core
(L1451-mm) is forming within Feature B at or near the location of the maximum
intensity (leaf 66, 30, and 10 for HCO+, HCN, and N2H+, respectively). For Feature
A, PerBolo 6 is at or near the location of maximum intensity in Feature A (leaf 15,
7, and 6 for HCO+, HCN, and N2H+, respectively). We argue that with Feature A
and B showing very similar tree statistics, Feature B having a confirmed compact
continuum detection at its hierarchical peak, and Feature A having a single-dish
continuum detection at its hierarchical peak, that a star is likely to form within
Feature A. This argument can be extended to Feature C being the next most likely
place for current or future star formation, followed by the even less fragmented
features. Follow-up observations of the single-dish cores and other column density
enhancements in these features will be useful for testing this expectation. The mean
branching ratios between all features are similar for all molecules, indicating that all
structures are fragmenting into a similar number of sub-structures at each branching
step, regardless how far a feature is along its evolution toward forming stars.
126
Table 3.4. HCO+ Dendrogram Leaf and Branch Properties
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈 σ 〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Leaves
0 03:24:41.3 +30:26:06.4 33.0 6.4 98.3 0.19 0.67 0.017 ... ... ... ... 0.88 2.4 1
1 03:24:39.5 +30:26:02.9 19.7 11.7 99.1 0.60 0.73 0.017 ... ... ... ... 1.10 4.0 1
2 03:25:31.2 +30:22:13.1 33.1 19.8 138.7 0.60 0.86 0.029 5.03(2) 0.07(1) 0.16(2) 0.07(1) 1.39 3.9 3
3 03:25:19.6 +30:23:38.3 36.0 17.8 62.1 0.49 0.58 0.029 ... ... ... ... 0.61 2.1 0
4 03:24:49.5 +30:26:05.1 31.2 20.4 109.1 0.65 0.50 0.029 ... ... ... ... 0.72 2.9 0
5 03:24:28.7 +30:26:13.6 94.0 23.5 86.7 0.25 0.86 0.054 ... ... ... ... 1.28 6.8 0
6 03:24:48.5 +30:26:22.2 20.6 8.1 103.8 0.39 0.81 0.015 ... ... ... ... 0.85 3.8 0
7 03:24:35.5 +30:21:47.8 30.7 15.7 160.2 0.51 0.78 0.025 4.08(6) 0.13(5) 0.26(7) 0.16(6) 0.81 2.4 2
8 03:25:15.7 +30:22:34.7 31.9 14.7 92.3 0.46 0.71 0.025 4.77(1) 0.04(1) 0.24(1) 0.04(1) 1.17 2.4 3
9 03:24:52.7 +30:23:59.2 33.1 22.9 95.1 0.69 0.81 0.031 4.77(4) 0.10(3) 0.22(4) 0.12(3) 0.99 2.6 3
10 03:24:54.4 +30:24:13.2 40.1 10.8 130.4 0.27 0.75 0.024 ... ... ... ... 0.96 2.4 3
11 03:24:36.7 +30:25:25.5 26.8 10.9 159.7 0.41 0.64 0.019 ... ... ... ... 0.74 2.1 1
12 03:25:35.5 +30:20:44.9 47.6 27.3 134.2 0.57 0.48 0.041 ... ... ... ... 0.62 2.2 0
13 03:25:31.6 +30:21:34.6 18.1 14.7 105.5 0.81 0.86 0.019 4.72(2) 0.04(2) 0.21(2) 0.04(2) 1.29 2.2 4
14 03:25:01.2 +30:21:13.7 140.5 65.4 139.4 0.47 0.62 0.109 4.63(2) 0.09(2) 0.21(2) 0.07(1) 0.99 4.8 0
15 03:25:26.1 +30:21:54.4 56.7 42.0 134.6 0.74 0.71 0.056 4.55(1) 0.05(1) 0.30(1) 0.05(1) 2.12 6.0 5
16 03:25:31.1 +30:22:56.5 117.4 53.9 121.4 0.46 0.75 0.091 4.76(1) 0.06(0) 0.17(0) 0.04(0) 1.74 7.4 2
17 03:24:55.8 +30:24:31.8 22.8 13.1 81.8 0.57 0.86 0.020 4.46(3) 0.06(2) 0.41(1) 0.03(1) 1.09 3.3 3
18 03:24:33.9 +30:25:25.8 83.2 41.1 78.3 0.49 0.52 0.067 ... ... ... ... 1.30 6.0 1
19 03:24:23.9 +30:26:05.6 19.9 13.0 67.9 0.65 0.64 0.018 ... ... ... ... 0.79 3.4 0
20 03:24:25.3 +30:26:11.1 22.3 16.5 42.6 0.74 0.57 0.022 ... ... ... ... 0.85 3.8 0
21 03:25:24.8 +30:20:47.6 37.9 26.3 60.9 0.70 0.85 0.036 4.45(1) 0.06(1) 0.28(1) 0.03(1) 1.98 3.1 6
22 03:25:23.3 +30:21:16.3 61.8 28.6 82.9 0.46 0.76 0.048 4.52(1) 0.05(1) 0.28(0) 0.03(0) 2.05 3.5 6
23 03:24:33.4 +30:21:51.4 16.5 11.8 77.1 0.71 0.95 0.016 ... ... ... ... 0.91 2.0 3
24 03:25:33.2 +30:22:00.4 16.7 10.0 12.9 0.60 0.79 0.015 ... ... ... ... 1.01 2.3 2
25 03:24:32.9 +30:22:23.2 45.8 40.6 107.3 0.89 0.80 0.049 4.55(2) 0.08(1) 0.24(2) 0.08(1) 1.51 6.2 3
26 03:24:28.1 +30:22:23.4 21.4 14.5 122.1 0.68 0.70 0.020 ... ... ... ... 0.80 2.3 2
27 03:24:55.0 +30:22:45.3 16.4 13.5 174.7 0.82 0.87 0.017 ... ... ... ... 0.78 2.2 2
28 03:24:47.4 +30:23:56.4 25.1 12.6 83.8 0.50 0.81 0.020 ... ... ... ... 0.92 2.2 3
29 03:25:04.3 +30:25:07.5 24.6 18.8 104.6 0.77 0.78 0.025 4.40(2) 0.06(2) 0.33(2) 0.05(1) 1.83 4.5 4
30 03:25:16.3 +30:18:43.7 30.0 9.1 107.0 0.30 0.83 0.019 4.30(1) 0.03(1) 0.28(2) 0.04(1) 1.85 2.1 5
31 03:25:25.2 +30:18:48.8 26.6 13.5 161.9 0.51 0.68 0.022 ... ... ... ... 0.71 2.8 0
32 03:25:11.4 +30:18:58.2 32.8 11.4 101.8 0.35 0.73 0.022 4.35(3) 0.07(2) 0.24(3) 0.07(2) 1.44 2.3 4
33 03:25:10.9 +30:19:44.6 29.0 17.5 52.5 0.60 0.66 0.026 4.19(2) 0.07(2) 0.35(1) 0.04(1) 1.26 2.0 3
34 03:25:16.4 +30:19:45.1 25.9 23.8 4.4 0.92 0.92 0.028 4.28(1) 0.05(1) 0.27(1) 0.05(1) 1.64 3.6 4
35 03:25:07.6 +30:21:15.2 55.4 40.0 58.9 0.72 0.65 0.054 ... ... ... ... 0.63 2.3 0
36 03:24:13.5 +30:21:11.5 29.7 9.4 41.8 0.32 0.64 0.019 ... ... ... ... 0.71 2.8 0
37 03:24:22.8 +30:21:53.0 98.6 42.2 85.8 0.43 0.64 0.074 4.32(2) 0.06(1) 0.30(3) 0.07(2) 1.00 3.7 2
38 03:25:12.9 +30:22:16.9 46.8 18.8 67.8 0.40 0.81 0.034 4.55(2) 0.08(1) 0.24(1) 0.04(1) 1.38 3.9 3
39 03:24:34.1 +30:23:38.8 52.1 17.6 79.0 0.34 0.60 0.034 ... ... ... ... 0.63 2.1 1
40 03:24:58.9 +30:24:29.8 20.8 14.7 100.0 0.70 0.87 0.020 4.44(1) 0.02(1) 0.25(1) 0.03(1) 1.51 2.2 4
41 03:25:22.3 +30:16:09.9 26.5 18.8 116.1 0.71 0.69 0.025 ... ... ... ... 0.72 2.9 0
42 03:25:18.2 +30:18:47.6 21.6 12.1 83.3 0.56 0.74 0.018 4.21(3) 0.07(3) 0.32(1) 0.02(1) 1.84 2.0 5
43 03:24:51.8 +30:19:51.7 17.2 9.4 129.5 0.55 0.89 0.014 ... ... ... ... 0.65 2.4 0
44 03:24:20.8 +30:21:04.1 17.2 8.8 34.5 0.51 0.84 0.014 ... ... ... ... 0.67 2.4 1
45 03:24:36.6 +30:21:25.7 27.3 11.5 82.8 0.42 0.78 0.020 4.18(1) 0.03(1) 0.15(2) 0.04(1) 1.33 2.9 4
46 03:25:15.9 +30:21:50.6 71.0 42.4 69.2 0.60 0.66 0.063 4.34(2) 0.10(1) 0.25(1) 0.05(1) 1.24 3.9 2
47 03:25:25.2 +30:21:50.4 60.2 19.5 66.7 0.32 0.74 0.039 4.46(1) 0.05(1) 0.34(1) 0.03(0) 1.96 4.9 5
127
Table 3.4 (cont’d)
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈 σ 〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
48 03:24:30.1 +30:23:20.9 86.6 20.9 112.2 0.24 0.47 0.048 4.15(5) 0.14(4) 0.28(5) 0.13(3) 0.96 2.4 3
49 03:24:26.7 +30:23:51.0 13.7 11.3 76.9 0.82 0.83 0.014 ... ... ... ... 0.81 2.3 2
50 03:25:00.5 +30:23:55.9 37.4 30.2 42.0 0.81 0.88 0.038 4.20(1) 0.05(1) 0.17(1) 0.06(1) 2.58 5.6 6
51 03:25:06.7 +30:24:19.6 19.2 13.2 115.2 0.69 0.91 0.018 4.12(1) 0.02(1) 0.25(1) 0.03(1) 2.02 2.7 5
52 03:25:04.3 +30:24:43.1 28.5 17.2 156.4 0.60 0.78 0.025 4.28(2) 0.05(1) 0.27(1) 0.04(1) 2.33 2.9 7
53 03:25:08.9 +30:24:35.9 42.9 19.9 147.7 0.46 0.65 0.033 4.14(1) 0.04(1) 0.19(1) 0.02(1) 2.40 4.4 6
54 03:25:02.5 +30:24:36.9 17.2 16.0 178.1 0.93 0.89 0.019 4.39(2) 0.04(1) 0.30(1) 0.03(1) 2.22 2.2 7
55 03:24:40.4 +30:25:00.0 28.1 18.3 35.7 0.65 0.72 0.026 ... ... ... ... 0.71 2.8 0
56 03:24:25.1 +30:25:03.9 24.5 18.4 74.5 0.75 0.70 0.024 ... ... ... ... 0.65 2.4 0
57 03:24:22.0 +30:22:20.8 34.6 16.8 76.4 0.48 0.68 0.027 ... ... ... ... 0.77 2.1 2
58 03:25:03.9 +30:24:08.4 39.9 22.9 74.2 0.57 0.62 0.034 4.14(1) 0.03(1) 0.24(1) 0.02(0) 2.22 3.1 6
59 03:24:32.1 +30:24:11.2 24.2 12.6 147.2 0.52 0.76 0.020 ... ... ... ... 0.65 2.4 0
60 03:24:53.2 +30:24:48.7 82.0 60.1 117.8 0.73 0.73 0.080 3.99(1) 0.08(1) 0.19(1) 0.07(1) 1.61 6.9 3
61 03:24:47.2 +30:25:28.6 19.9 10.6 50.9 0.53 0.76 0.017 ... ... ... ... 0.66 2.4 0
62 03:25:05.8 +30:16:38.0 16.4 13.4 42.1 0.81 0.81 0.017 ... ... ... ... 0.61 2.1 0
63 03:25:05.7 +30:19:44.2 34.0 14.0 135.1 0.41 0.62 0.025 ... ... ... ... 0.75 2.5 1
64 03:24:43.5 +30:21:38.6 63.3 23.5 79.1 0.37 0.52 0.044 ... ... ... ... 0.66 2.3 1
65 03:24:36.6 +30:22:06.6 92.5 37.6 156.8 0.41 0.62 0.067 3.86(1) 0.09(1) 0.19(1) 0.06(1) 1.87 6.7 4
66 03:25:10.3 +30:23:49.1 19.1 13.1 176.4 0.69 0.79 0.018 3.84(1) 0.02(1) 0.18(1) 0.03(1) 2.78 3.0 7
67 03:24:38.4 +30:23:55.8 19.6 18.3 25.7 0.93 0.86 0.022 ... ... ... ... 0.90 3.0 2
68 03:25:09.7 +30:24:04.5 25.9 11.5 100.4 0.45 0.71 0.020 3.88(1) 0.02(1) 0.17(1) 0.02(1) 2.77 2.9 7
69 03:24:50.6 +30:25:32.0 21.1 12.2 134.6 0.58 0.85 0.018 ... ... ... ... 1.06 3.1 3
70 03:25:24.7 +30:16:00.1 35.5 14.3 108.0 0.40 0.83 0.026 ... ... ... ... 0.87 3.9 0
71 03:24:56.9 +30:16:09.8 31.3 19.5 173.1 0.62 0.45 0.028 ... ... ... ... 0.73 2.9 0
72 03:25:23.9 +30:16:33.6 49.5 31.7 7.7 0.64 0.58 0.045 ... ... ... ... 0.63 2.3 0
73 03:24:50.5 +30:22:48.1 42.9 26.0 78.5 0.61 0.60 0.038 3.71(2) 0.06(1) 0.16(1) 0.05(1) 1.51 4.2 4
74 03:24:18.4 +30:26:02.3 18.8 12.9 179.1 0.69 0.66 0.018 ... ... ... ... 0.80 3.4 0
75 03:25:09.0 +30:17:32.7 26.7 18.5 84.3 0.69 0.65 0.025 ... ... ... ... 0.83 2.1 2
76 03:25:05.4 +30:17:42.7 26.4 17.5 51.8 0.66 0.72 0.025 ... ... ... ... 0.86 2.2 2
77 03:25:05.1 +30:18:31.4 94.4 41.7 76.3 0.44 0.66 0.071 ... ... ... ... 0.78 2.7 1
78 03:25:05.3 +30:19:04.0 37.8 29.0 135.8 0.77 0.56 0.038 ... ... ... ... 0.60 2.1 0
79 03:24:47.3 +30:22:48.2 32.1 22.6 136.4 0.70 0.84 0.031 3.61(1) 0.03(1) 0.17(1) 0.03(1) 1.51 4.2 4
80 03:24:45.6 +30:23:51.5 74.6 62.8 104.7 0.84 0.76 0.078 3.53(2) 0.11(1) 0.18(1) 0.09(1) 1.30 5.8 2
81 03:25:14.7 +30:17:32.2 21.8 13.8 7.6 0.63 0.77 0.020 ... ... ... ... 0.67 2.5 0
82 03:24:26.3 +30:23:26.4 17.6 13.7 122.4 0.78 0.80 0.018 ... ... ... ... 0.62 2.2 0
83 03:24:31.9 +30:23:38.8 39.6 16.6 144.4 0.42 0.72 0.029 3.41(2) 0.07(1) 0.19(2) 0.06(1) 1.21 3.1 3
84 03:25:16.2 +30:17:51.8 18.0 10.4 103.0 0.58 0.89 0.016 ... ... ... ... 0.61 2.1 0
85 03:24:32.9 +30:23:15.7 19.0 10.1 80.2 0.53 0.85 0.016 3.34(8) 0.16(6) 0.22(9) 0.17(7) 1.09 2.3 3
Branches
86 03:25:09.8 +30:23:52.9 47.6 42.9 118.3 0.90 0.73 0.051 3.89(1) 0.06(1) 0.19(1) 0.03(0) 2.35 ... 6
87 03:25:03.4 +30:24:39.6 50.3 38.0 54.4 0.75 0.65 0.050 4.32(2) 0.07(1) 0.29(1) 0.04(1) 1.91 ... 6
88 03:25:02.7 +30:24:17.9 110.8 59.8 49.9 0.54 0.68 0.093 4.20(2) 0.10(1) 0.26(1) 0.05(1) 1.77 ... 5
89 03:25:09.3 +30:24:03.8 89.4 53.3 161.4 0.60 0.65 0.079 4.03(2) 0.11(2) 0.21(1) 0.03(1) 1.77 ... 5
90 03:25:05.0 +30:24:13.9 186.3 102.2 93.1 0.55 0.75 0.157 4.18(1) 0.16(1) 0.24(0) 0.04(0) 1.62 ... 4
91 03:25:23.9 +30:21:03.6 90.0 64.9 112.9 0.72 0.80 0.087 4.48(1) 0.07(1) 0.29(1) 0.04(0) 1.54 ... 5
92 03:25:16.4 +30:19:02.3 119.7 48.7 112.1 0.41 0.76 0.087 4.23(1) 0.10(1) 0.28(1) 0.07(1) 1.54 ... 4
93 03:25:24.1 +30:21:21.4 151.6 111.6 57.7 0.74 0.81 0.148 4.48(1) 0.15(1) 0.29(0) 0.06(0) 1.26 ... 4
94 03:25:04.4 +30:24:09.9 215.8 132.0 97.1 0.61 0.80 0.192 4.27(2) 0.21(1) 0.24(0) 0.06(0) 1.19 ... 3
95 03:25:15.9 +30:19:06.8 134.7 81.6 104.8 0.61 0.68 0.119 4.18(2) 0.12(1) 0.30(1) 0.08(1) 1.11 ... 3
128
Table 3.4 (cont’d)
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈 σ 〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
96 03:25:24.5 +30:21:22.5 182.1 120.7 70.4 0.66 0.82 0.169 4.57(2) 0.19(1) 0.29(1) 0.07(1) 0.97 ... 3
97 03:25:14.6 +30:19:17.8 192.1 105.2 116.2 0.55 0.77 0.162 4.12(1) 0.11(1) 0.34(1) 0.08(0) 0.97 ... 2
98 03:24:50.0 +30:22:51.2 137.1 46.5 80.4 0.34 0.59 0.091 3.76(2) 0.12(1) 0.21(1) 0.09(1) 0.90 ... 3
99 03:24:36.5 +30:21:57.1 110.9 58.5 165.0 0.53 0.76 0.092 4.07(2) 0.13(2) 0.24(2) 0.10(1) 0.90 ... 3
100 03:25:24.8 +30:21:24.4 210.0 136.1 68.4 0.65 0.78 0.193 4.58(2) 0.22(2) 0.29(1) 0.09(1) 0.82 ... 2
101 03:25:14.4 +30:22:24.0 100.0 30.1 70.9 0.30 0.74 0.063 4.70(3) 0.11(2) 0.22(2) 0.08(1) 0.82 ... 2
102 03:24:32.2 +30:23:34.1 67.4 29.3 147.4 0.43 0.79 0.051 ... ... ... ... 0.76 ... 2
103 03:25:21.1 +30:20:58.9 451.6 252.0 51.7 0.56 0.79 0.384 4.60(6) 0.25(4) 0.24(2) 0.10(2) 0.68 ... 1
104 03:24:59.0 +30:23:59.2 387.5 181.2 80.4 0.47 0.62 0.302 3.79(7) 0.25(5) 0.23(4) 0.14(3) 0.61 ... 2
105 03:24:34.3 +30:22:19.7 199.4 78.4 135.2 0.39 0.71 0.142 ... ... ... ... 0.61 ... 2
106 03:25:07.7 +30:17:42.2 107.0 48.3 91.2 0.45 0.58 0.082 ... ... ... ... 0.53 ... 1
107 03:24:40.2 +30:26:01.8 67.0 29.9 58.9 0.45 0.59 0.051 ... ... ... ... 0.53 ... 0
108 03:24:30.5 +30:22:29.5 321.6 195.3 84.3 0.61 0.60 0.286 ... ... ... ... 0.47 ... 1
109 03:24:56.7 +30:23:50.0 422.3 208.9 80.5 0.49 0.74 0.338 ... ... ... ... 0.47 ... 1
110 03:24:34.7 +30:25:24.6 103.5 54.5 91.0 0.53 0.49 0.086 ... ... ... ... 0.43 ... 0
111 03:25:19.3 +30:20:38.4 528.3 268.5 50.4 0.51 0.81 0.429 ... ... ... ... 0.39 ... 0
112 03:24:46.8 +30:23:17.4 775.1 211.0 77.8 0.27 0.66 0.461 ... ... ... ... 0.32 ... 0
Note. — (2)–(6) The position, major axis, minor axis, and position angle were determined from regionprops in MATLAB. We do not report formal uncertainties
of these values since the spatial properties of irregularly shaped objects is dependent on the chosen method.
(7) Axis ratio, defined as the ratio of the minor axis to the major axis.
(8) Filling factor, defined as the area of the leaf or branch inscribed within the fitted ellipse, divided by the area of the fitted ellipse.
(9) Size, defined as the geometric mean of the major and minor axes, for an assumed distance of 235 pc.
(10) The weighted mean Vlsr of all fitted values within a leaf or branch. Weights are determined from the statistical uncertainties reported by the IDL MPFIT
program. The error in the mean is reported in parentheses as the uncertainty in the last digit. It was computed as the standard error of the mean, ∆Vlsr/
√
N ,
where ∆Vlsr is the value in column 11 and N is the number of beams’ worth of pixels within a given object. We report kinematic properties only for objects that
have at least three synthesized beams’ worth of kinematic pixels.
(11) The weighted standard deviation of all fitted Vlsr values within a leaf or branch. The error was computed as the standard error of the standard deviation,
∆Vlsr/
√
2(N − 1), assuming the sample of beams was drawn from a larger sample with a Gaussian velocity distribution.
(12) The weighted mean velocity dispersion of all fitted values within a leaf or branch. The error was computed as the standard error of the mean, ∆σ/
√
N .
(13) The weighted standard deviation of all fitted velocity dispersion values within a leaf or branch. The error was computed as the standard error of the standard
deviation, ∆σ/
√
2(N − 1).
(14) For a leaf, this is the peak intensity measured in a single channel of our 2-channel binned dataset used in the dendrogram analysis. For a branch, this is the
intensity level where the leaves above it merge together.
(15) “Contrast” is defined as the difference between the peak intensity of a leaf and the height of its closest branch in the dendrogram, divided by the 1-σ
sensitivity of the data.
(16) The branching level in the dendrogram. For example, the base of the tree is level 0, so an isolated leaf that grows directly from the base is considered to be
at level 0. A leaf that grows from a branch one level above the base will be at level 1, etc.
129
Table 3.5. HCN Dendrogram Leaf and Branch Properties
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈 σ 〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Leaves
0 03:25:31.1 +30:22:16.0 39.5 20.1 149.3 0.51 0.71 0.032 ... ... ... ... 0.70 2.5 1
1 03:25:02.2 +30:21:05.5 17.1 14.1 110.1 0.83 0.90 0.018 ... ... ... ... 0.63 2.3 0
2 03:25:02.8 +30:24:49.4 25.0 17.2 135.3 0.69 0.70 0.024 4.31(4) 0.10(3) 0.12(2) 0.06(2) 0.86 2.1 1
3 03:24:32.3 +30:25:16.6 26.6 17.3 95.6 0.65 0.73 0.024 ... ... ... ... 0.69 2.7 0
4 03:24:27.2 +30:26:21.3 20.3 10.6 137.4 0.52 0.83 0.017 ... ... ... ... 0.91 4.3 0
5 03:25:24.1 +30:21:03.2 71.4 41.7 162.3 0.58 0.59 0.062 4.49(1) 0.05(1) 0.13(1) 0.03(0) 1.29 3.5 4
6 03:25:25.4 +30:21:45.4 27.1 19.7 82.7 0.73 0.86 0.026 4.56(2) 0.06(1) 0.15(1) 0.04(1) 1.30 3.6 4
7 03:25:26.3 +30:22:10.6 37.0 20.7 112.3 0.56 0.80 0.031 4.60(2) 0.06(1) 0.13(1) 0.06(1) 1.51 6.0 3
8 03:25:31.6 +30:22:59.0 53.1 29.1 101.8 0.55 0.72 0.045 4.73(1) 0.04(1) 0.11(1) 0.04(1) 0.89 2.7 2
9 03:25:28.4 +30:23:09.9 46.9 26.4 18.9 0.56 0.57 0.040 ... ... ... ... 0.68 2.3 1
10 03:25:11.8 +30:19:01.5 45.7 24.1 36.6 0.53 0.65 0.038 4.42(2) 0.08(2) 0.10(2) 0.07(1) 0.86 2.1 2
11 03:25:15.0 +30:22:22.2 125.9 44.1 85.4 0.35 0.68 0.085 4.68(3) 0.07(2) 0.13(1) 0.04(1) 0.87 4.0 0
12 03:25:32.5 +30:22:25.3 30.0 17.4 143.5 0.58 0.67 0.026 ... ... ... ... 0.87 2.6 2
13 03:25:04.3 +30:25:10.1 35.0 13.0 93.5 0.37 0.86 0.024 4.31(2) 0.05(1) 0.13(1) 0.03(1) 0.99 3.0 1
14 03:25:16.7 +30:19:48.3 45.9 35.9 102.7 0.78 0.77 0.046 4.33(1) 0.05(1) 0.13(1) 0.04(1) 1.14 5.0 1
15 03:25:06.8 +30:24:24.7 27.7 19.7 112.1 0.71 0.83 0.027 4.15(2) 0.06(1) 0.12(1) 0.02(0) 1.31 3.2 2
16 03:25:17.9 +30:18:54.4 90.7 41.7 101.4 0.46 0.65 0.070 4.06(2) 0.12(1) 0.12(1) 0.07(1) 1.12 3.9 2
17 03:25:27.2 +30:21:27.7 29.4 15.1 83.2 0.51 0.80 0.024 4.42(1) 0.03(1) 0.07(2) 0.05(2) 0.81 2.2 2
18 03:24:29.3 +30:23:27.6 112.3 29.2 119.0 0.26 0.60 0.065 ... ... ... ... 0.74 3.1 0
19 03:25:00.9 +30:23:59.9 25.5 25.2 62.7 0.99 0.85 0.029 4.17(1) 0.04(1) 0.12(1) 0.03(1) 1.57 4.0 3
20 03:25:02.5 +30:24:43.2 56.3 23.7 13.9 0.42 0.65 0.042 4.24(1) 0.05(1) 0.10(1) 0.04(1) 1.80 4.6 4
21 03:25:04.4 +30:24:42.6 19.7 17.6 0.2 0.90 0.81 0.021 4.21(2) 0.06(2) 0.13(2) 0.04(1) 1.46 2.2 4
22 03:24:40.8 +30:25:03.4 29.0 17.6 87.6 0.61 0.58 0.026 ... ... ... ... 0.60 2.1 0
23 03:25:11.3 +30:19:47.2 32.0 14.0 59.3 0.44 0.80 0.024 ... ... ... ... 0.74 2.2 1
24 03:25:08.9 +30:24:40.1 31.6 12.7 128.3 0.40 0.93 0.023 4.08(1) 0.03(1) 0.10(1) 0.03(1) 2.12 6.8 3
25 03:24:53.6 +30:24:49.0 69.6 37.0 83.9 0.53 0.69 0.058 ... ... ... ... 0.71 2.9 0
26 03:24:38.3 +30:23:54.9 37.6 22.7 22.6 0.60 0.71 0.033 ... ... ... ... 0.66 2.6 0
27 03:24:50.8 +30:22:51.8 77.4 29.7 71.1 0.38 0.54 0.055 ... ... ... ... 0.80 3.0 1
28 03:24:34.9 +30:22:10.8 122.5 88.2 136.7 0.72 0.66 0.118 3.97(7) 0.18(5) 0.18(4) 0.09(3) 0.75 3.2 0
29 03:24:46.4 +30:22:47.3 64.3 33.9 95.8 0.53 0.52 0.053 ... ... ... ... 0.69 2.3 1
30 03:25:09.9 +30:23:57.1 53.6 35.5 137.5 0.66 0.81 0.050 3.83(1) 0.07(1) 0.09(0) 0.02(0) 2.58 10.0 3
31 03:24:46.2 +30:23:58.9 23.4 9.5 110.0 0.41 0.85 0.017 ... ... ... ... 0.69 2.7 0
32 03:24:32.3 +30:23:33.2 68.2 30.8 142.8 0.45 0.72 0.052 ... ... ... ... 0.70 2.8 0
Branches
33 03:25:03.0 +30:24:41.8 58.4 46.1 37.9 0.79 0.67 0.059 4.30(2) 0.08(2) 0.15(1) 0.05(1) 1.14 ... 3
34 03:25:09.5 +30:24:03.4 92.4 47.2 158.3 0.51 0.78 0.075 4.00(2) 0.10(1) 0.11(0) 0.03(0) 1.14 ... 2
35 03:25:02.7 +30:24:32.7 112.1 44.4 37.4 0.40 0.68 0.080 4.28(2) 0.11(2) 0.15(1) 0.05(1) 0.99 ... 2
36 03:25:05.6 +30:24:16.7 180.1 100.9 103.4 0.56 0.75 0.154 4.17(1) 0.14(1) 0.12(1) 0.06(0) 0.85 ... 1
37 03:25:24.6 +30:21:11.0 98.8 64.4 21.4 0.65 0.65 0.091 4.50(1) 0.06(1) 0.14(1) 0.04(0) 0.78 ... 3
38 03:25:24.5 +30:21:22.5 139.4 85.0 26.9 0.61 0.70 0.124 4.56(2) 0.15(2) 0.09(1) 0.07(1) 0.64 ... 2
39 03:25:16.0 +30:18:58.4 163.4 65.0 95.7 0.40 0.64 0.117 4.12(4) 0.15(3) 0.10(2) 0.07(1) 0.56 ... 1
40 03:25:04.9 +30:24:08.9 201.4 141.8 101.7 0.70 0.77 0.193 4.31(5) 0.17(4) 0.13(2) 0.05(1) 0.56 ... 0
41 03:25:31.9 +30:22:47.4 86.1 60.1 117.7 0.70 0.62 0.082 ... ... ... ... 0.50 ... 1
42 03:25:24.2 +30:21:22.2 168.6 120.2 44.7 0.71 0.66 0.162 ... ... ... ... 0.50 ... 1
43 03:25:15.3 +30:19:14.6 187.4 113.6 110.7 0.61 0.72 0.166 ... ... ... ... 0.42 ... 0
44 03:24:48.4 +30:22:50.0 150.6 55.3 86.5 0.37 0.57 0.104 ... ... ... ... 0.36 ... 0
45 03:25:25.3 +30:21:43.3 278.2 156.8 58.0 0.56 0.62 0.238 ... ... ... ... 0.35 ... 0
Note. — Same at Table 3.4.
130
Table 3.6. N2H+ Dendrogram Leaf and Branch Properties
No. RA DEC Maj. Axis Min. Axis PA Axis Filling Size 〈Vlsr〉 ∆Vlsr 〈 σ 〉 ∆σ Pk. Int. Contrast Level
(h:m:s) (◦:′:′′) (′′) (′′) (◦) Ratio Factor (pc) (km s−1) (km s−1) (km s−1) (km s−1) (Jy beam−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Leaves
0 03:25:30.8 +30:21:27.9 38.2 25.2 97.4 0.66 0.58 0.035 ... ... ... ... 0.69 2.1 1
1 03:25:32.9 +30:21:59.9 18.0 12.1 73.7 0.67 0.83 0.017 ... ... ... ... 0.97 3.0 2
2 03:25:30.9 +30:22:12.7 40.2 23.1 58.8 0.57 0.61 0.035 ... ... ... ... 1.02 3.4 2
3 03:25:14.7 +30:22:28.0 33.1 21.0 89.9 0.64 0.84 0.030 ... ... ... ... 0.83 3.2 0
4 03:25:31.3 +30:22:53.2 28.1 13.1 88.0 0.47 0.83 0.022 ... ... ... ... 0.83 2.1 2
5 03:25:23.5 +30:21:12.8 33.8 18.5 51.9 0.55 0.68 0.028 4.54(1) 0.03(1) 0.10(1) 0.01(0) 1.01 2.3 3
6 03:25:26.0 +30:21:44.0 51.1 36.0 30.7 0.70 0.66 0.049 4.57(1) 0.04(1) 0.13(1) 0.03(1) 1.25 4.0 3
7 03:25:03.9 +30:25:00.3 36.8 19.6 89.7 0.53 0.68 0.031 4.45(1) 0.03(1) 0.09(1) 0.02(0) 1.40 3.5 1
8 03:25:16.1 +30:19:47.4 35.7 28.9 54.8 0.81 0.68 0.037 ... ... ... ... 0.89 3.7 0
9 03:24:55.8 +30:23:23.3 19.3 11.6 61.8 0.60 0.77 0.017 ... ... ... ... 0.66 2.1 0
10 03:25:07.3 +30:24:32.1 38.5 21.1 96.6 0.55 0.71 0.032 4.24(1) 0.03(1) 0.08(0) 0.01(0) 1.62 3.0 2
11 03:25:18.3 +30:19:00.4 16.7 10.9 62.7 0.65 0.68 0.015 ... ... ... ... 1.00 2.1 1
12 03:24:36.7 +30:22:42.4 36.4 28.9 114.2 0.79 0.67 0.037 ... ... ... ... 0.75 2.7 0
13 03:25:09.3 +30:23:53.3 59.5 17.0 113.1 0.29 0.66 0.036 4.03(2) 0.08(1) 0.10(1) 0.03(0) 1.55 2.5 2
14 03:25:20.1 +30:18:51.6 36.6 18.0 123.7 0.49 0.81 0.029 3.93(1) 0.04(1) 0.12(0) 0.01(0) 1.13 3.0 1
15 03:24:26.3 +30:23:33.7 60.4 44.6 12.1 0.74 0.78 0.059 3.86(1) 0.06(1) 0.11(0) 0.03(0) 1.51 7.9 0
Branches
16 03:25:08.5 +30:24:11.8 101.3 38.3 136.7 0.38 0.71 0.071 4.11(2) 0.12(1) 0.10(0) 0.02(0) 1.18 ... 1
17 03:25:04.8 +30:24:18.4 196.1 108.9 95.0 0.56 0.62 0.166 4.26(2) 0.17(1) 0.11(0) 0.03(0) 0.90 ... 0
18 03:25:17.7 +30:18:54.8 141.7 42.6 101.8 0.30 0.65 0.088 4.08(2) 0.07(2) 0.13(1) 0.04(1) 0.69 ... 0
19 03:25:25.6 +30:21:34.2 96.5 65.4 41.1 0.68 0.62 0.091 4.58(1) 0.04(1) 0.10(1) 0.02(0) 0.67 ... 2
20 03:25:27.2 +30:21:45.9 200.6 100.1 53.0 0.50 0.56 0.161 ... ... ... ... 0.53 ... 1
21 03:25:27.2 +30:21:44.0 204.3 105.2 54.6 0.51 0.58 0.167 ... ... ... ... 0.38 ... 0
Note. — Same as Table 3.4.
131
Table 3.7. Tree Statistics
Line (Sub-region) Total No.a Max Levelb Mean PLc Mean BRd
Comparison Across Tracerse
HCO+ 113 6 2.3 3.8
HCN 46 4 1.3 3.3
N2H+ 22 3 1.3 3.0
Comparison of Sub-Regionsf
HCO+ (A) 10 6 4.8 2.3
HCO+ (B) 16 7 5.9 2.5
HCO+ (C) 8 5 4.2 2.3
HCO+ (others) 9 4 3.7 2.0
HCN (A) 13 4 2.4 2.4
HCN (B) 13 4 2.6 2.4
HCN (C) 6 2 1.5 2.5
HCN (others) 6 1 1.0 2.0
N2H+ (A) 9 3 2.2 2.7
N2H+ (B) 5 2 1.7 2.0
N2H+ (C) 3 1 1.0 2.0
N2H+ (others) NA NA NA NA
Note. — a Total number of leaves and branches. b Maximum
branching level. c Mean path length. dMean branching ratio. e Using
method to compare dendrograms from data with different noise levels.
f Using original dendrograms.
132
0.0 0.1 0.2 0.3 0.4 0.5
0
10
20
30
40
size (pc)
N
HC Leaf
LC Leaf
Branch
0.4 0.5 0.6 0.7 0.8 0.9 1.0
filling factor
0
2
4
6
8
10
12
N
0.2 0.4 0.6 0.8 1.0
axis ratio
0
5
10
15
N
3.5 4.0 4.5 5.0
<vlsr> (km/s)
0
1
2
3
4
5
6
N
0.0 0.1 0.2 0.3
∆vlsr (km/s)
0
5
10
15
N
0.1 0.2 0.3 0.4 0.5
<σ> (km/s)
0
2
4
6
8
10
N
Figure 3.13: Histograms of HCO+ dendrogram leaf and branch properties. High-
contrast (HC) leaves, above 6-σn contrast, are represented by green; low-contrast
(LC) leaves, below 6-σn contrast, are represented by blue; branches are repre-
sented by white. See the text in Section 3.6.2 for a discussion of trends seen in
these histograms.
0.0 0.1 0.2 0.3 0.4 0.5
0
5
10
15
size (pc)
N
HC Leaf
LC Leaf
Branch
0.4 0.5 0.6 0.7 0.8 0.9 1.0
filling factor
0
1
2
3
4
5
6
N
0.2 0.4 0.6 0.8 1.0
axis ratio
0
2
4
6
8
N
3.5 4.0 4.5 5.0
<vlsr> (km/s)
0
1
2
3
4
5
6
N
0.0 0.1 0.2 0.3
∆vlsr (km/s)
0
2
4
6
8
N
0.1 0.2 0.3 0.4 0.5
<σ> (km/s)
0
2
4
6
8
10
12
N
Figure 3.14: Same as Figure 3.13, but for HCN.
133
0.0 0.1 0.2 0.3 0.4 0.5
0
2
4
6
8
10
12
size (pc)
N
HC Leaf
LC Leaf
Branch
0.4 0.5 0.6 0.7 0.8 0.9 1.0
filling factor
0
1
2
3
4
N
0.2 0.4 0.6 0.8 1.0
axis ratio
0
1
2
3
4
5
N
3.5 4.0 4.5 5.0
<vlsr> (km/s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
N
0.0 0.1 0.2 0.3
∆vlsr (km/s)
0
1
2
3
4
5
6
N
0.1 0.2 0.3 0.4 0.5
<σ> (km/s)
0
1
2
3
4
5
6
7
N
Figure 3.15: Same as Figure 3.13, but for N2H+.
3.7 Dust in L1451
The CLASSy observations provide excellent measurements of gas structure and kine-
matics, but are less reliable for column density or mass information due to large
uncertainties in relative abundance and opacity of the molecular emission. For this,
we turned to Herschel observations.
3.7.1 L1451 Column Density and Temperature
We used Herschel 160, 250, 350, and 500 µm observations of L1451 to derive the col-
umn density and temperature of the dust. The Herschel images were corrected for
the zero-level offset based on a comparison with Planck and DIRBE/IRAS data
(Meisner & Finkbeiner 2015). The images were convolved to the angular reso-
lution of the Herschel 500 µm band (∼36′′) using the convolution kernels from
Aniano et al. (2011), and were regridded to a common pixel size of 10′′. The fit-
ting was performed on a pixel-by-pixel basis with a modified blackbody spectrum
134
of Iν = κνB(ν, T )Σ, where κν is the dust mass opacity coefficient at frequency ν,
B(ν, T ) is the Planck function at temperature T, and Σ = µmpN(H2) is the gas
mass column density for a mean molecular weight of µ = 2.8 (e.g. Kauffmann et al.
2008) assuming a gas-to-dust ratio of 100:1. We assume κν = 0.1 × (ν/1012 Hz)β
cm2 g−1 (Beckwith & Sargent 1991), and β = 1.7.
The resulting column density and temperature maps are shown in Figures 3.16
and 3.17, respectively. We validated our SED fitting procedure by comparing our de-
rived optical depth to that of the Planck Collaboration et al. (2014) model. Specif-
ically, we re-ran our SED fits after smoothing the Herschel input maps to match
the Planck Collaboration et al. (2014) resolution of 5′, and found that our derived
300 µm optical depth agrees with that of the Planck -based model to within 5% on av-
erage. The mean column density of L1451 that is enclosed within the 2.0×1021 cm−2
contour in Figure 3.16 (the white contour that encircles all of the high column den-
sity regions) is 3.7×1021 cm−2 with a standard deviation of 1.7×1021 cm−2. The peak
column density of 1.2×1022 cm−2 occurs at the location of the Bolocam source, Per-
Bolo 4. The mean temperature within the 15.0 K contour of Figure 3.17 is 14.0 K,
with a standard deviation of 0.7 K. A minimum temperature of 11.9 K occurs at
the location of L1451-mm.
We have independent temperature measurements toward the four Bolocam sources
in the field from Rosolowsky et al. (2008a) ammonia observations. Those tempera-
tures are ∼2–3.5 K lower than we find by fitting the Herschel SEDs. Our results,
and those from Planck Collaboration et al. (2014) that we compared to, assume
emission from a single cloud layer. However, there will always be a warmer layer of
foreground and background material surrounding a dense, cold star-forming region.
This warmer cloud component can drive the fitted temperature up and fitted column
density down when only doing a single component fit. To estimate the systematic
135
Figure 3.16: Column density map of L1451 derived from Herschel 160, 250, 350,
and 500 µm data. The white contours corresponds to N(H2)=[0.8, 2.0, 4.0, 6.0,
8.0, 10.0]×1021 cm−2. The measured column densities toward the densest regions
are likely systematically underestimated by half from the true values; see the
discussion in the text.
Figure 3.17: Temperature map of L1451 derived from Herschel 160, 250, 350,
and 500 µm data. The black contours represent 12 to 15 K, in 0.5 K increments.
The red contour represents a column density of 2.0×1021 cm−2, for comparison to
Figure 3.16. The temperatures toward the densest regions are likely overestimated
by a few Kelvin; see text for discussion.
overestimation of temperatures and underestimation of column densities toward the
densest regions of clouds, we created a simple radiative transfer model with a cold
layer at 9 K (representing L1451) between two warmer layers at 17 K (representing
foreground and background cloud material). If the warm layers have AV of 0.4,
then the temperature in cold layer regions with AV & 2 is overestimated by ∼2.5–
5.5 K when using a single component fit (e.g., 12 K instead of 9 K). This matches
136
the differences between our temperatures and the temperatures from the ammonia
data. Furthermore, measured column density values of a cold, dense region are pre-
dicted to be half of the true values in regions where the warm layers have AV of
0.4 and the cold layer has AV & 2. If the lower-resolution Herschel beam is not
filled in regions of cold, dense gas, then this could further bias temperatures to be
too warm, and column densities to be too low. In Section 3.8, we will discuss how
these systematic uncertainties can affect our energy balance results. An upcoming
paper will present a detailed comparison of single-layer and two-layer SED fitting
across Perseus, showing the improvement that is achieved for cold, dense regions
when considering the hot, diffuse component along the line-of-sight (Lee et al., in
preparation).
3.7.2 Dendrogram Analysis of Dust
The column density results in the previous section are angular resolution limited
compared to our CLASSy maps, so it is not possible to estimate the mass within
the smallest molecular structures we identified using the dendrogram analysis in
Section 3.6. Therefore, we take the approach of first defining structures based on
the dust data, and then using the kinematic information within those structures to
explore energy balance. A virial analysis is presented in Section 3.8.
We converted the NH2 column density map to an extinction map using a con-
version factor of NH2/AV = (1/2) × 1.87 × 1021 cm−2 mag−1 (Draine 2003). We
then ran our non-binary dendrogram algorithm on the extinction map to define dust
structures in the field. We used an rms and branching step of 0.2 Av, and required
that local maxima peak at least 0.4 Av above the merge level to be considered a
real leaf. The algorithm identified 8 leaves and 6 branches in the region where we
have molecular line data.
137
Table 3.8. Dust Structure Properties
No. RA DEC Size 〈T〉 〈NH2 〉 Mtot σtot,HCN σtot,N2H+
(h:m:s) (◦:′:′′) (pc) (K) (1021 cm−2) (solar) (km s−1) (km s−1)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Leaves
0 03:25:13.3 +30:19:05.8 0.23 13.6 5.1 5.1 0.39 0.34
1 03:25:00.2 +30:21:22.1 0.08 14.4 2.8 0.2 0.41 ...
2 03:25:27.2 +30:21:43.6 0.17 13.2 5.0 3.1 0.29 0.27
3 03:24:35.5 +30:22:09.5 0.07 13.6 4.4 0.4 0.34 0.37
4 03:24:47.0 +30:23:11.2 0.14 13.9 4.0 1.4 0.54 ...
5 03:24:26.8 +30:22:47.7 0.17 13.9 4.6 2.0 0.44 0.28
6a 03:25:08.7 +30:24:09.5 0.07 12.2 7.2 0.5 0.25 0.25
7 03:25:01.5 +30:24:27.9 0.07 12.7 6.4 0.5 0.28 0.26
Branches
8 03:25:01.5 +30:24:12.9 0.21 13.7 4.1 3.0 0.33 0.33
9 03:25:17.8 +30:20:07.0 0.41 14.2 3.1 13.1 0.47 0.44
10 03:24:29.2 +30:22:26.8 0.27 14.2 3.6 4.5 0.45 0.35
11 03:24:54.2 +30:23:38.9 0.33 14.1 3.3 6.2 0.39 0.34
12 03:24:43.1 +30:23:04.4 0.46 14.3 3.1 12.4 0.43 0.39
13 03:25:17.1 +30:19:52.8 0.51 14.3 3.0 14.9 0.50 0.47
Note. — (4) Geometric mean of major and minor axis fit to structure (used as diameter
of structure). (5) Weighted mean temperature within structure. (6) Weighted mean column
density of H2 within structure. (7) Total mass within structure. (8) HCN velocity disper-
sion calculated from integrated spectrum across structure. (9) N2H+ velocity dispersion
calculated from integrated spectrum across structure. a L1451-mm is located within this
structure.
The extinction map, with dendrogram-identified structures, is shown in Fig-
ure 3.18. Properties of the dendrogram structures are listed in Table 3.8, including
their coordinate, size, weighted mean temperature and column density, and total
mass. The mean temperature and column density, and total mass of each structure
considers all of the emission interior to the structure (e.g., branch 9 includes emis-
sion from branch 9 and leaves 0 and 2). To calculate the total mass within each
structure, we first converted the column density at each pixel to a solar mass unit
as:
M(α, δ) = µH2mHNH2(α, δ)A, (3.1)
where µH2 is the molecular weight per hydrogen molecule (2.8), mH is the mass of
a hydrogen atom, NH2(α, δ) is the column density at a pixel location, and A is the
pixel area. As before, the assumed distance is 235 pc. We then totaled the mass
enclosed within each structure. The mass of leaves ranges from 0.2 to 5.1 M⊙, and
the mass enclosed within branches ranges from 3.0 to 15.9 M⊙. The mass interior to
the yellow and purple contour in Figure 3.18 is 14.9 M⊙ and 12.4 M⊙, respectively.
138
Figure 3.18: Visual extinction map of L1451 (greyscale), as derived from the
column density map in Figure 3.16. The solid black contour represents Av=2,
and the mean extinction within that contour is 3.8 mag with a 1.8 mag standard
deviation. Dendrogram-derived dust structure boundaries are shown with colored
contours. The peak extinction is ∼13 mag within structure 0.
139
3.8 Understanding Star Formation in L1451
We selected L1451 as a CLASSy region because of its very low star formation activ-
ity. There are no confirmed protostar detections, and only one confirmed compact
continuum core. This is very different from the other CLASSy regions, which have
many protostars and outflows. We wanted to use L1451 to study cloud structure
and kinematics in the densest regions of clouds before star formation activity feeds
back into the cloud.
We now explore the following questions. What column density threshold are we
capturing with our spectral line observations, and do dendrogram-identified struc-
tures trace actual column density features that can inform structure formation in
a young cloud? If so, will any structures go on to form stars? We address these
questions in this section by exploring the correspondence between molecular line and
continuum emission, with a virial analysis of L1451 structures, and by describing
the similarities and differences between L1451-mm and L1451-west. We conclude
with an analysis of the three-dimensional morphology of L1451 on the largest scales.
3.8.1 Connecting molecular structures to physical cloud struc-
tures
L1451 is the one CLASSy region with strong, widespread HCO+ and HCN that
is not affected by outflows and severe self-absorption. This enabled a dendrogram
analysis of all three molecules, instead of just N2H+, and lets us compare the iden-
tified molecular structures to the column density structure of L1451. Figures 3.19
and 3.20 have the dendrogram footprints of the lowest-level branches, and all the
leaves, respectively, overplotted on column density derived from Herschel data. We
combined the footprints of all the contoured emission in Figures 3.19 and 3.20 to
140
create a mask for the column density map for determining how well the molecular
emission captures material at different column densities.
Figure 3.19: Dendrogram lowest-level branch footprints for all molecules, over-
plotted on the column density from Figure 3.16 that was regridded to match the
CLASSy pixel scale (beams for column density (36′′) and molecular (7′′) maps are
in the lower right). Red = HCO+, blue = HCN, and orange = N2H+. We label
each branch with its number corresponding to most Tables 3.4–3.6.
Figure 3.20: Dendrogram leaf footprints for all molecules, overplotted on the
column density from Figure 3.16 that was regridded to match the CLASSy pixel
scale (beams for column density (36′′) and molecular (7′′) maps are in the lower
right). Red = HCO+, blue = HCN, and orange = N2H+. We label a few examples
where leaves where emission from all tracers coincides with numbers corresponding
to Tables 3.4–3.6.
A threshold for star formation above Av∼8, or an H2 column density of 7.5× 1021 cm−2,
has been postulated based on the distribution of prestellar cores and protostars
141
within the densest regions of molecular clouds (Andre´ et al. 2014, and references
therein). Figure 3.21 shows cumulative distribution functions for column density
where we detect dense gas and where we do not detect dense gas. Only 0.002%
of dust regions without a molecular gas detection are above the threshold column
density if we take our derived column densities as correct. If our measured col-
umn densities are uniformly underestimated by half from the true values, as was
discussed in Section 3.7.1, still only 1% of dust regions without a molecular gas
detection are above the threshold column density. 90% of the regions where we de-
tect molecules are at column densities above 1.9 × 1021 cm−2, with a maximum of
1.3 × 1022 cm−2, and minimum of 8.9 × 1020 cm−2. 90% of the regions where we do
not detect molecules are below 2.4 × 1021 cm−2, with a maximum of 7.8 × 1021 cm−2,
and minimum of 3.6 × 1020 cm−2. This shows that spectral line observations using
our suite of dense-gas tracer molecules is a great probe of the star forming mate-
rial in young regions above the threshold for star formation and down to column
densities of a few × 1021 cm−2.
We demonstrated that the branches in Figure 3.19 are fragmenting to form the
leaves in Figure 3.20 in a similar hierarchical fashion for each molecule (see Sec-
tion 3.6.3). This consistent fragmentation story between molecules, combined with
the result of molecular emission capturing most of the cloud material near and
above threshold of star formation, shows that the dendrogram-identified molecular
fragmentation is tracing physical structure, accounting for some biases due to chem-
istry and extinction. This provides observational evidence that structure formation
precedes star formation in molecular clouds, which supports turbulence-driven star
formation theories that predict the turbulence cascade from large-scale flows leads
to the formation of complex morphological structure in clouds before the onset of
star formation (Klessen & Hennebelle 2010, and reference therein). Other theories
142
0 2.0•1021 4.0•1021 6.0•1021 8.0•1021 1.0•1022 1.2•1022 1.4•1022
N(H2) (cm-2)
0.0
0.2
0.4
0.6
0.8
1.0
CD
F
detect gas
do not detect gas
Figure 3.21: Cumulative distribution functions for the areas of the L1451 column
density map where we have detected molecular emission (solid curve), and the
areas where we have not detected molecular emission (dashed curve). The solid
vertical line marks the column density threshold for star formation (Andre´ et al.
2014, and references therein), while the dashed-dotted vertical line represents that
threshold if our measured column densities are underestimated by half from the
true column densities.
for the production of cloud structure consider internally-driven turbulence from pro-
tostellar feedback; protostars can inject energy and momentum back into molecular
clouds to impact cloud structure and dynamics (Carroll et al. 2009; Federrath et al.
2014; Nakamura & Li 2014). Our result helps to disentangle externally and inter-
nally driven structure, which it is important for demonstrating an observational
case of complex, hierarchical cloud structure existing at an epoch before internal
feedback can impact the natal cloud environment.
3.8.2 Energy balance of structures
We next use a virial analysis to assess whether structures in L1451 are gravitation-
ally bound and on the pathway to star formation. We know one star is currently
forming in L1451, based on the detection of compact 3 mm emission at L1451-
mm. Showing that other gas and dust structures in the field are gravitationally
143
bound would add support to L1451 being a region at the onset of star formation.
For the virial analysis, we use the dust results in combination with the molecular
data. In Section 3.7, we derived column densities and temperatures across L1451
at the angular resolution of the longest wavelength Herschel band (36′′). We also
found dendrogram-identified dust structures in the extinction map. In this section,
we use that information for dust leaves, along with CLASSy kinematic data from
Section 3.5, to assess the energy balance of structures in L1451.
The virial theorem is useful for describing the energy balance of structures. There
are several approaches for applying the virial theorem to molecular cloud observa-
tions in the literature (e.g., Larson 1981; Bertoldi & McKee 1992; McKee & Zweibel
1992; Ballesteros-Paredes 2006; Kauffmann et al. 2013). We follow the formalism
of McKee & Zweibel (1992), who derive a time-averaged Eulerian form of the virial
theorem that contains surface pressure terms for both thermal and turbulent pres-
sure. Equation (4.15) of McKee & Zweibel (1992) writes the virial theorem as
1
2 I¨cl = 3(P¯cl − cprPic)Vcl +M+W (3.2)
where I¨cl is the second-derivative of the moment of inertia of the cloud of interest, P¯cl
is the mean total pressure in the cloud (including thermal and turbulent pressure),
Pic is the total pressure in the intercloud medium (intercloud medium being the
gas and dust between discrete clouds), cpr is a dimensionless factor of order unity
(expected to be 0.5 . cpr . 1.0) that accounts for the surface pressure of the
intercloud medium on the cloud being at lower pressure than the average intercloud
pressure, Vcl is the total cloud volume, M is the net magnetic energy of the cloud,
and W is the gravitational potential energy of the cloud.
A steady-state cloud in virial equilibrium will have I¨cl = 0. We ignore M since
there are not adequate magnetic field data to assess its magnitude. What remains is
a balance of two confining terms and one dispersive term, all which can be estimated
144
using our observational data. The confining terms are the gravitational potential
energy of the cloud and the pressure term from the intercloud medium on the surface
of the cloud. The dispersive term is the mean total pressure in the cloud. A
structure is said to satisfy the virial theorem if the confining and dispersive terms
are equal. The virial expression in Equation 3.2 can technically be satisfied for a
source without any self-gravity if it is contained only by external pressure balancing
internal pressure. Thus, it is important to note that satisfying the virial theorem in
Equation 3.2 does not automatically mean a structure is gravitationally bound.
The confining term of surface pressure is often ignored in the literature. In this
case, the widely used virial parameter, α, is defined for a spherical source by only
considering gravitational potential energy and internal kinetic energy:
α = 51−
2k
5
1− k3
Rclσ2cl
GMcl
(3.3)
where Rcl and Mcl are the cloud radius and total cloud mass, respectively; σcl
is the one-dimension velocity dispersion of cloud gas, and k is the exponent of
the density distribution within the cloud. For a source with a uniform density
distribution (ρ(r) ∝ r−k, with k = 0), the virial parameter becomes the widely
used: 5Rclσ2cl/GMcl. A cloud is said to satisfy the virial theorem if α = 1, and is
bound if α . 2 (Kauffmann et al. 2013). McKee & Zweibel (1992) discuss how the
effects of external confining-pressure, non-uniform cloud density, and magnetic fields
all tend to compensate each other, making this balance of gravitational potential
energy and total internal pressure most important.
Although the external confining-pressure term is traditionally ignored, it can
be important for young star forming regions (Lada et al. 2008; Seo et al. 2015).
Therefore, we will discuss the magnitude of this extra energy term to determine if
L1451 structures satisfy the virial theorem with the addition of external confining
pressure. Finally, it should be noted that this approach assumes an isolated spherical
145
cloud with no tidal gravitational field from sources of gravity other than the cloud.
Since all of the identified structures are nearby other structures and embedded
within larger structures, the tidal forces may be non-negligible. One approach which
includes these effects is to compute the total gravitational potential from the column
density map (e.g., using the GRID-core algorithm from Gong & Ostriker 2011); that
analysis is beyond the scope of this work and will be explored in the future.
For the traditional virial parameter in Equation 3.3, Rcl, is half of the size
reported in Column 4 of Table 3.8, and Mcl is reported in Column 7 of Table 3.8.
The σcl of each structure includes thermal and non-thermal support against collapse.
The thermal component of the velocity dispersion was calculated as:
σth =
√
kT
µmH
, (3.4)
where T is the mean temperature of the dust within the structure, µ is the mean
molecular weight (2.33), and mH is the hydrogen atomic mass. The non-thermal
component of the velocity dispersion was calculated for each molecular tracer sepa-
rately, as:
σnth,tracer =
√
σ2obs,tracer − σ2th,tracer (3.5)
where σ2obs,tracer is the observed velocity dispersion of the molecular emission within
the structure, and σth,tracer is the thermal velocity dispersion of the molecule at the
mean temperature found within the structure:
σth,tracer =
√
kT
µtracermH
. (3.6)
We determined σ2obs,tracer by masking the CLASSy data cubes of N2H+ and HCN
using the boundaries of each dust structure, generating an integrated spectrum for
each molecule, and fitting for the velocity dispersion of that integrated spectrum.
The final σtotal,tracer value was then calculated as:
σcl,tracer =
√
σ2th + σ2nth,tracer (3.7)
146
Table 3.9. Virial Parameters
N2H+ HCN
k=0 k=2 k=0 k=2
No. No Pext Pext No Pext Pext No Pext Pext No Pext Pext
(1) (2) (3) (4) (5) (6) (7) (8) (9)
0 3.0 1.4 1.8 0.8 4.0 2.1 2.4 1.3
1 ... ... ... ... 28.5 20.0 17.1 12.0
2 2.3 0.9 1.4 0.5 2.8 1.2 1.7 0.7
3 15.3 12.0 9.2 7.2 13.0 7.5 7.8 4.5
4 ... ... ... ... 17.5 13.5 10.5 8.1
5 3.8 0.5 2.2 0.3 9.3 3.7 5.6 2.2
6a 4.4 2.9 2.6 1.7 4.5 3.0 2.7 1.8
7 6.2 3.5 3.7 2.1 6.8 4.1 4.1 2.5
Note. — (1) No. from Table 3.8. (2) Virial parameter calculated using Equa-
tion 3.3 with the N2H+ velocity dispersion and k = 0. (3) Virial parameter
calculated using Equation 3.8 with the N2H+ velocity dispersion and k = 0. (4)
Virial parameter calculated using Equation 3.3 with the N2H+ velocity dispersion
and k = 2. (5) Virial parameter calculated using Equation 3.8 with the N2H+
velocity dispersion and k = 2. (6-9) Same as Columns 2–5, but using HCN for
the velocity dispersion. a L1451-mm is located within this structure.
and is reported in Columns 8 and 9 of Table 3.8 for HCN and N2H+, respectively. We
do not analyze the HCO+ in this analysis because it has significantly larger velocity
dispersion than the other molecules, likely because it is tracing more extended,
lower-density emission compared to HCN and N2H+ (see Section 3.5).
Columns 2 and 6 of Table 3.9 list the virial parameters of dust leaves when
using N2H+ and HCN to determine the velocity dispersion, respectively, under the
assumption of uniform density and ignoring surface pressure. Structures 1, 3, and
4 have α > 10 when considering the N2H+ or HCN velocity dispersion. These
structures have the weakest dense gas emission from HCN and N2H+ of leaves in
the field, so it is sensible that they appear to be the least bound. Considering the
N2H+ velocity dispersion, the other structures have virial parameters between 2.3
and 6.2. This range of virial parameters suggests that none of the structures are
147
bound. But does this mean that L1451 will not form stars? Since we know a star
is forming at L1451-mm, and since there are centrally condensed structures in the
dust and molecular line maps (in Features A, B, C, and J), it is likely that some of
the structures are at least marginally bound.
The coefficient in the virial theorem used in Equation 3.3 assumes a density
profile of ρ(r) ∝ r−k, with k = 0, representing a constant density structure. If a
structure is centrally condensed, an exponent of k = 2 leads to a lower coefficient
that produces a factor of 1.67 decrease in the virial parameter (MacLaren et al.
1988): 3Rclσ2cl/GMcl. Columns 4 and 8 of Table 3.9 report values for k = 2 to
highlight this point. Now considering the N2H+ velocity dispersion, the structures
discussed above have virial parameters dropping from 2.3 < α < 6.2 to 1.4 < α < 3.7.
Structures 0 and 2 are at least marginally gravitationally bound with α < 2; they
appear in the Herschel maps as centrally condensed dust structures with Bolocam
cores within them.
Two major sources of systematic uncertainty in the measured virial parame-
ters, regardless of density profile, are the column density and temperature values
derived from the Herschel SED fitting in Section 3.7.1. We discussed how using a
single temperature model (ignoring the warmer foreground and background com-
ponent surrounding the colder L1451 region) for fitting the Herschel SEDs leads
to estimated column densities that are about half of the true column densities and
estimated temperatures that are ∼2.5–5 K higher than true temperatures. If the
measured column densities are half of the true column densities, this directly leads
to an α overestimate by a factor of 2. The temperature overestimate systematically
increases the thermal component of the internal velocity dispersion of each structure,
thereby increasing the dispersive term used to calculate α. The temperature error
is less significant than the column density error, but still contributes a ∼7% system-
148
atic increase in the virial parameter if the temperature is overestimated by 2.5 K.
Work has been done on the galactic scale to estimate dust mass underestimation
due to spatial resolution and temperature mixing in Herschel data; Galliano et al.
(2011) found that Herschel -derived dust masses can be ∼30% underestimated in
the Large Magellanic Cloud (LMC). Our observations have much higher spatial res-
olution than observations of the LMC, but the warm-cold temperature contrast in
local clouds like L1451 may be more extreme than on galactic scales, explaining our
larger correction factor. If the values in Table 3.9 are reduced by a factor of two,
then more dust leaves would appear to be in virial equilibrium.
The virial analysis from Equation 3.3 ignores the surface pressure term of Equa-
tion 3.2, 3cprPicVcl, which can be important for young star forming regions. If a
structure is not bound according to the balance of gravitational potential energy
and internal kinetic energy, it may still satisfy the virial theorem if the surface pres-
sure is enough to confine the structure in the presence of its internal energy. As we
noted above, confinement by surface pressure can satisfy the virial theorem, but it
does not mean a structure is gravitationally bound—the structure may form a star
in the future if it collapses, it may remain a persistent structure, or it may disperse
if the external pressure decreases.
We calculated the energy from surface pressure that is exerted on each dendro-
gram structure from the dendrogram structure immediately surrounding it (e.g.,
branch 9 adding confining pressure to leaves 0 and 2). The cpr term is considered
unity to assess the maximum possible confining pressure. The Pic term is calculated
as ρbranchσ2branch, where ρbranch is the density of the confining structure (measured
from the mean column density and size of the confining structure), and σbranch is
the quadrature sum of thermal and non-thermal velocity dispersion of the gas in the
149
confining structure. The modified virial parameter is then:
α = 51−
2k
5
1− k3
Rcl(Mclσ2cl − ρbranchσ2branchVcl)
GM2cl
. (3.8)
Columns 3, 5, 7, and 9 in Table 3.9 consider external confining pressure for the
different molecular tracers and density profiles. As an example, the virial parameter
of structure 0 is reduced by about a factor of two when considering external confin-
ing pressure. This means that the external confining energy from the surrounding
branch on the dust leaf is about 50% the internal energy of the dust leaf. Since
the gravitational potential energy of the dust leaf is comparable to the energy from
external confining pressure, this structure is likely confined by a combination of
self-gravity and external pressure. Overall, with the addition of this confining term,
for a k = 2 density profile, the majority of the sources have virial parameters of
α . 2. If we then consider the column density underestimation discussed above, the
values would be reduced even further. We will explore these results in more detail
in upcoming work.
Considering external pressure, the uncertainties in the density profile, and the
uncertainties in column density of the structures, most of the dust structures in
L1451 appear on the threshold of satisfying the virial theorem, and at least two
structures (0, 2) appear to be gravitationally bound as long as their density profile
is not uniform.
It is clear that even with the improved data from telescopes like CARMA and
Herschel, uncertainties still make it difficult to find a definite result with this type of
analysis. Therefore, we conclude that although the traditional virial analysis, which
only considers the balance of internal kinetic energy to gravitational potential energy,
suggests that most L1451 leaves are not bound, considerations of surface pressure,
density profiles, and column density underestimation suggest that several of the dust
structures satisfy the virial theorem and may be at the precipice of star formation. In
150
particular, structures 0, 2, 5, 6, and 7 are all candidates for being bound. All of these
structures appear centrally condensed: structure 0 contains Per Bolo 4, structure 2
contains Per Bolo 6, structure 5 contains L1451-west, structure 6 contains L1451-
mm, and structure 7 is a leaf adjacent to L1451-mm. This supports these structures
(or at least the central parts of these structures) being bound.
We will extend this type of virial analysis in upcoming work and will compare
virial parameters across CLASSy regions. This way, even if there are systematic
and statistical uncertainties, all structures will have been observed and analyzed in
the same way, making a relative comparison of virial parameters across clouds at
different stages of evolution possible.
3.8.3 Closer Look at L1451-mm and L1451-west
In this section, we explore the properties of the two centrally condensed, roughly
spherical cores in L1451. One is L1451-mm, which we know is a compact object
containing a YSO or a FHSC (Pineda et al. 2011). The other is L1451-west, which
has been discovered with these observations. We summarize the morphology and
kinematics of L1451-mm below, and then describe the properties of L1451-west and
how they compare to L1451-mm.
The top row of Figure 3.22 shows molecular and continuum features of L1451-
mm. L1451-mm is the only confirmed compact continuum core in L1451, and all
molecules trace strong emission near, and surrounding its location. N2H+ shows a
peak of integrated emission at the location of L1451-mm, while HCN and HCO+
show peaks that are slightly offset. The surrounding emission is more concentrated
for N2H+, and more widespread for HCN and HCO+. The N2H+ centroid velocity
field shows a gradient across the core, which Pineda et al. (2011) modeled as a
rotating and infalling envelope using slightly higher angular resolution data (5′′); we
151
measure a gradient of about 6 km s−1 pc−1 through the peak of integrated emission
at a position angle of 120 deg east of north (see white line in the top row panels of
Figure 3.22). The velocity dispersion field is narrowest around the edges of the core
with minima ∼0.07 km s−1, and it shows an increase toward the core location, with
a peak ∼0.2 km s−1. See Pineda et al. (2011) for detailed discussion and modeling
of the possibility that L1451-mm is a dense core with a central YSO and disk, or a
dense core with a central FHSC.
Figure 3.22: The top and bottom rows show properties of L1451-mm and L1451-
west, respectively. From left-to-right, the panels are: N2H+, HCN, and HCO+
integrated intensity (Jy beam−1 km s−1), N2H+ centroid velocity (km s−1), and
N2H+ velocity dispersion (km s−1). The kinematic maps of each source are
on the same color scale. The velocity dispersion is expressed as Gaussian σ
(FWHM/2.355 in km s−1). The green 0.0039 mJy beam−1 contour represents
our L1451-mm compact continuum detection. The red contours are used to ac-
centuate specific features in the greyscale maps. The white lines represent the
direction of the measured velocity gradient through each source.
The bottom row of Figure 3.22 shows molecular and continuum features of L1451-
west. The N2H+ integrated intensity map does not have a single peak of integrated
emission at the center of the structure. Instead, there are two peaks in the southern
half of the source ∼2.5 Jy beam−1 km s−1, and one peak in the northern half of the
source ∼2.4 Jy beam−1 km s−1 (the red contours in the bottom-left panel of Fig-
ure 3.22 represent 1.1–2.5 Jy beam−1 km s−1 in 0.2 Jy beam−1 km s−1 increments).
152
The source is considerably weaker in HCN, and not detected in HCO+. This is
an indication that this might be a very cold, dense region of L1451, where CO is
depleted. If CO is frozen out onto dust grains, then it is not able to destroy N2H+,
leading to an increased abundance of N2H+. Likewise, if CO is frozen out, it is not
available to create HCO+ through collisions with H3+ (Prasad & Huntress 1980).
Our temperature map in Figure 3.17 does not suggest that dust around L1451-west
is significantly colder than L1451-mm, but the systematic uncertainties in that tem-
perature map discussed in Section 3.7.1 leave room for lower temperatures than we
derived.
The N2H+ centroid velocity field of L1451-west shows a relatively complex struc-
ture compared with L1451-mm, with higher velocity emission in the southern and
northeastern sections of the core, and lower velocity emission toward the center and
west of the core. Since the higher velocity emission at both ends of the source is
bridged with intermediate velocity emission along the eastern edge, we consider the
simplest case to be the source rotating in a northwest-southeast direction, marked
by the white line in the bottom row panels. We measure a velocity gradient of
∼2.5 km s−1 pc−1 along that direction.
The velocity dispersion field of L1451-west is narrowest around the edges of the
core with minima ∼0.07 km s−1, and it peaks near ∼0.2 km s−1 at the location
of lowest velocity emission in the central part of the source. The axis of rotation
that we chose intersects this peak of velocity dispersion and runs between the three
peaks of N2H+ integrated emission, as seen in the bottom-left panel. It is possible
that infall is producing the increased velocity dispersion. Infall would broaden the
molecular emission toward the core center, with the blue shifted emission being
brighter than the redshifted emission if the N2H+ emission is optically thick. This
could explain why the peak of velocity dispersion is at the location with the bluest
153
centroid velocity. The signal-to-noise of the detectable HCN spectra are too low
to look for evidence of infall motions, so this needs to be followed up with deeper
observations of optically thick and thin lines.
There is no compact continuum emission detected in data toward L1451-west.
The 3-σ flux density limit for a point source (.3′′ = 700 AU) in our observations
is 3.9 mJy, corresponding to a mass limit of 0.08 M⊙ for the conversion from mJy
to M⊙ discussed in Chapter 2 (Section 2.3). We use the location of peak velocity
dispersion as a proxy for the location of a compact continuum core, if it exists; this
peak is offset from the peak in the Herschel -derived column density map by about
16′′.
We estimated the size, physical density, total mass, and virial mass of L1451-mm
and L1451-west for a more detailed comparison. To determine the size, we used the
MIRIAD imfit routine to fit a two-dimensional gaussian to the N2H+ integrated
intensity map. The geometric mean of the major and minor axes are 37′′ and 32′′
for L1451-mm and L1451-west, respectively. To determine the maximum physical
density, we took the peak column density of each source within the fitted gaussian,
and assumed their depth was the same extent as their geometric mean across the
plane of the sky. For both sources, the physical density is 7–8× 104 cm−3 in the 7′′
beam. This density is sensible, considering that we observe N2H+, HCN (J = 1 → 0)
in L1451, which are molecular transitions with effective excitation densities on the
order of 105 cm−3.
To estimate the total mass associated with each source, we summed the Herschel -
determined mass within the two-dimensional gaussian. L1451-mm and L1451-west
have a total mass of ∼0.25 and ∼0.16 M⊙, respectively. To estimate the virial
mass from the sizes measured above and the masses listed here, we calculated the
velocity dispersion of N2H+ within each two-dimensional gaussian as described in
154
Section 3.8.2, and used Equation 3.3 with k = 2 to account for these objects be-
ing approximated as centrally condensed spheres instead of uniform-density spheres.
L1451-mm and L1451-west have a virial mass of ∼0.70 and ∼0.59 M⊙, respectively.
Although this would imply that the material in these sources is not gravitationally
bound, we know that a young star is forming in L1451-mm. Considering the sys-
tematic uncertainties discussed in the previous section, along with uncertainties in
κν and our choice of β = 1.7, the mass of these sources could be double what we
measure here—in that case, the ratio of virial mass to total mass comes closer to
one, indicating structures that are consistent with being gravitationally bound.
We also compared the mass within 4200 AU (18′′ at d=235 pc) to the intrinsic
radius at 70% of peak intensity, following the analysis of starless cores presented in
Kauffmann et al. (2008). We measured the mass using the Herschel data, and got
0.22 and 0.23 for L1451-mm and L1451-west, respectively. We measured the radius
using the N2H+ integrated intensity, since the dust data is not as well resolved
to derive accurate radius measurements. L1451-mm measured 7′′, and L1451-west
measured 12′′ at 70% of the peak intensity. Compared to the sample of starless
cores in Kauffmann et al. (2008), L1451-mm is more compact than starless, while
L1451-west is at the upper limit of compactness seen in starless objects.
All of these observational results point to L1451-west being similar to, but
slightly less evolved than, L1451-mm, yet more evolved than a prestellar core. Deep
continuum and spectral line observations will be needed to determine the true nature
of these sources. But these two cores are the best evidence that L1451 is a region
that is just starting to form its first stars. L1451-mm was the target of an ALMA
Cycle 1 project that was observing a sample of five FHSC candidates, and we put
in an ALMA Cycle 3 proposal to observe L1451-west. These new observations will
build on the results presented here and in Pineda et al. (2011).
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3.8.4 Depth of L1451 Structures: A Non-Filamentary Re-
gion
Comparing the projected size of cloud structure to its depth along the line-of-sight
gives a better understanding of the three-dimensional geometry of a region where
stars are forming (e.g., a region that is primarily planar/sheet-like versus one that
is more spherical). We described a statistical method to estimate the typical line-
of-sight depth of cloud structures in Chapter 2 (Sections 2.7.2 and 2.7.3). The
method uses the spatial and kinematic properties of dendrogram objects presented in
Tables 3.4–3.6. It assumes that the Vlsr variation (∆Vlsr; Column 11) of a structure
scales with its projected size (Column 9) in a turbulent medium. It also assumes that
the mean non-thermal velocity dispersion (〈σ〉nt) of a dendrogram structure scales
with its depth along the line-of-sight in a turbulent medium. We calculate 〈σ〉nt
for each structure in all three molecular tracers by subtracting the thermal velocity
dispersion of 10 K gas of the given tracer from the value reported in Column 12
of Tables 3.4–3.6: 〈σ〉nt =
√
〈σ〉2 − σ2th. With those assumptions, we create two
size-linewidth relations using all the dendrogram structures (one with projected
size versus 〈σ〉nt, and the other with projected size versus ∆Vlsr), and take the
spatial scale where they cross as the typical depth of the region. See Chapter 2
(Section 2.7.3) for the theoretical framework and numerical results that justify this
method.
We used the method in previous papers to argue that the typical depth of the
N2H+ emission in the CLASSy Barnard 1 and Serpens Main regions was 0.1–0.2 pc
(see Section 2.7.3 and Lee et al. (2014)). Figure 3.23 shows the size-linewidth rela-
tions for each molecule. As in the analysis of Barnard 1 in Chapter 2 and Serpens
Main in (Lee et al. 2014), the projected size-∆Vlsr for each molecule has a positive
156
slope (which is expected for a turbulent medium), while the projected size-〈σ〉nt
relationship has a flatter slope (which is expected if all structures have a similar
depth along the line-of-sight, independent of their projected size). The best-fit lines
to the relations cross at a size-scale 0.11 and 0.10 pc for N2H+ and HCN, respec-
tively, indicating that those molecules are tracing structures ∼0.1 pc in depth. The
HCO+ fits cross near 0.40 pc, indicating that it is tracing structures with larger
line-of-sight depths compared to the other molecules. This is consistent with HCO+
detecting larger-scale, lower density gas than the other molecules.
HCO+
0.01 0.10
Projected Size (parsec)
0.01
0.10
Li
ne
w
id
th
 (k
m/
s)
0.02±0.04
0.50±0.07
HCN
0.01 0.10
Projected Size (parsec)
0.01
0.10
Li
ne
w
id
th
 (k
m/
s)
0.12±0.08
0.60±0.10
N2H+
0.01 0.10
Projected Size (parsec)
0.01
0.10
Li
ne
w
id
th
 (k
m/
s)
0.10±0.11
0.77±0.21
Figure 3.23: Scaling relations between projected structure size and Vlsr variation
(∆Vlsr; solid squares), and projected structure size and mean non-thermal veloc-
ity dispersion (〈σ〉nt; open diamonds), for each molecule. The solid lines represent
single power-law fits to the data points. The horizontal line represents the typ-
ical thermal speed for H2 at gas kinetic temperatures near 11 K. The vertical
dashed line represents our spatial resolution of ∼0.008 pc. The vertical solid line
represents the spatial scale where the power-law fits intersect.
These results show that the N2H+ emission in L1451 has similar depth as it does
in Barnard 1 and Serpens Main. However, there are differences between L1451 and
the other regions that lead us to different conclusions about the large-scale structure
of L1451. In Chapter 2 (Section 2.7.3), we said that the depth of Barnard 1 (0.1–
0.2 pc) is comparable to the largest size of individual N2H+ dendrogram structures
identified from the isolated N2H+ hyperfine component (0.2–0.3 pc). But we followed
up by discussing how the Barnard 1 has contiguous N2H+ structure at parsec-scales
157
when considering the full N2H+ emission instead of just the isolated hyperfine com-
ponent. We used the estimated 0.1–0.2 pc depth and observed parsec projected size
of Barnard 1 to conclude that the region is flattened at the largest scales with fila-
mentary substructure (such as the B1 Ridge) forming within the large-scale sheet.
A similar argument was made for Serpens Main in (Lee et al. 2014).
In projection, the full N2H+ emission, sub-millimeter continuum emission, and
other molecular emission from L1451 region does not appear to have contiguous
structure across parsec scales like the other CLASSy regions. Instead, the emission
is concentrated in a few major features, sub-parsec in size, that were identified in
Section 3.4. Because of this, we argue that the L1451 is not a flattened, sheet-like
region of dense gas and dust at parsec-scales with connected substructure. It appears
more like a loose collection of dense concentrations that are ∼0.2 pc projected on
the sky and ∼0.1 pc deep.
The physical density of the regions of L1451 with N2H+ emission can be es-
timated from the cloud depth and column density. For a 0.1 pc depth of N2H+
emission and a mean N(H2) of 6 × 1021 cm−2 measured from the Herschel data, the
derived physical density is 2 × 104 cm−3 in the regions of L1451 with N2H+ emission.
This is lower than the ∼105 cm−3 estimate for the physical density needed to excite
N2H+ (J = 1 → 0) to ∼1 K, which was discussed in Chapter 1. This is not an in-
consistency, since it is possible to excite N2H+ at a range of physical densities, where
the range depends on the molecular column density (and thus relative abundance
of N2H+ to H2), the gas kinetic temperature, and the linewidth of emission. Using
the RADEX program (van der Tak et al. 2007), we find that N2H+ (J = 1 → 0)
can reach 1 K brightness temperatures with a physical density of 2.7 × 104 cm−3
if the gas kinetic temperature is 12 K, the molecular column density of N2H+ is
6 × 1012 cm−2, and the linewidth of emission is 0.3 km s−1. This physical density is
158
essentially the same as derived from our depth and column density measurements.
We can compare the typical depth of the molecular emission to the projected
size of the largest-scale structures of each molecule in Figure 3.19 to infer the three-
dimensional morphology of the individual molecular structures. The projected size
of N2H+ structure 21 (lowest level branch of Features A) is ∼0.17 pc, structure 18
(lowest level branch of Features C) is ∼0.09 pc, and structure 17 (lowest level branch
of Features B) is ∼0.17 pc. For a typical N2H+ depth of 0.11 pc, these structures
have axis ratios of 1.5:1 and 0.8:1, with a mean of 1.3:1. The projected size of HCN
structure 45 (lowest level branch of Feature A) is ∼0.24 pc, structure 43 (lowest
level branch of Feature C) is ∼0.17 pc, and structure 40 (lowest level branch of
Feature B) is ∼0.19 pc. For a typical HCN depth of 0.10 pc, these structures have
axis ratios between 2.4:1 and 1.7:1, with a mean axis ratio of 2.0:1. The projected
size of HCO+ structure 111 (lowest level branch connecting Features A and C) is
∼0.43 pc, and structure 112 (lowest level branch connecting Features B, H, F, G, E,
and I) is ∼0.46 pc. For our derived typical HCO+ depth of 0.40 pc, these structures
have axis ratios of 1.1:1 and 1.2:1.
With axis ratios between 0.8:1 and 2.4:1 for individual structures that do not
connect at larger scales, these results support the L1451 region being composed of
discrete, high-density structures that are approximated as ellipsoids. In addition to
not having contiguous, flattened structure at parsec scales like the other CLASSy
regions, none of the large-scale structures of L1451 appear to have clear filamen-
tary substructure like was the case in the other CLASSy regions. These results
differentiate L1451 in a way beyond the lack of protostars and outflows.
We take these results as an indication that not everything in a molecular cloud is
filamentary, or required to be filamentary, for star formation to begin. This pushes
against the universality of filamentary cloud structure that has taken a hold in
159
the past few years (Andre´ et al. 2014). The Herschel Gould Belt Survey team has
suggested a paradigm for star formation where complex networks of filaments, with
filaments lengths from∼1 pc up to tens of parsecs, are formed within clouds, followed
by prestellar core formation that occurs due to fragmentation of the highest column
density filaments (Andre´ et al. 2010). However, the L1451 region within Perseus is
markedly not filamentary in Herschel and CLASSy data, with relatively ellipsoidal
dust and gas structures a few tenths of parsecs across found within the parsec-scale
region, and yet it is still beginning to form stars. Where does L1451 stand in the
paradigm mentioned above and why are we drawing a different conclusion from the
Herschel Gould Belt team?
The major differences between CLASSy and the Herschel Gould Belt Survey are
with spatial area coverage, angular resolution, and density sensitivity. The Herschel
survey has covered approximately 145 square degrees spanning a dozen molecu-
lar clouds, compared to the smaller CLASSy area coverage of about 800 square
arcminutes (0.22 square degrees) encompassing five regions within two molecular
clouds. The Herschel survey can map cloud column density and temperature struc-
ture with 36′′ angular resolution, compared to CLASSy that can map the denser
gas (n > 104 cm−3 and N(H2) > few × 1021 cm−2) structure and kinematics with
7′′ angular resolution.
Overall, the differences mentioned above mean that the Herschel Gould Belt Sur-
vey has captured a relatively macroscopic view of star formation across molecular
cloud complex scales throughout the Gould Belt, while CLASSy has captured a rel-
atively in-depth view of the dense gas in five parsec-scale regions of star formation.
The Herschel view of the entire Perseus Molecular Cloud is undoubtedly filamentary
on the macroscopic scale of several parsecs, with many filaments being well-traced by
Herschel continuum images. In the western half of Perseus, NGC 1333, Barnard 1,
160
and L1448 are the most active sites of star formation and have filamentary structure
that appears strong in the Herschel bands; there are also weaker emission filamen-
tary regions detected by Herschel between these active sites. However, we have seen
that some parts of Perseus, such as L1451, are not filamentary, and those exceptions
need to be accounted for in any global picture of star formation.
The morphology of Herschel continuum structure and CLASSy N2H+ structure
are remarkably similar where both have detectable emission, and L1451 appears non-
filamentary in both datasets. It is highly likely that many other non-filamentary
regions within “macroscopically filamentary” clouds can be identified and studied as
interesting sights of star formation. L1451 was chosen to be one of the five CLASSy
regions because it appeared to have different properties from the more well-studied
regions within Perseus and Serpens, and it is important that these parts of clouds
do not get ignored.
If L1451 is not a flattened, sheet-like region at parsec-scales (unlike other CLASSy
regions), if it does not have filamentary structure (unlike other CLASSy regions),
and if it has less active star formation than other CLASSy regions, then it is natu-
ral to question what caused these differences. A cloud complex, like Perseus, that
spans tens of parsecs will have different turbulent energies in different parts of the
cloud. Simulations of turbulence-driven star formation with supersonic turbulence
(e.g., Federrath & Klessen 2012) show that star formation within several-parsec scale
clouds is clustered in regions where material has been compressed to high densities,
leaving voids of star formation in other parts of the cloud. The L1451 region of
Perseus may not have been as compressed as strongly by supersonic turbulence to
form an overdense sheet-like structure at parsec-scales like may have happened sev-
eral parsecs away near the cloud regions that became Barnard 1 and NGC 1333.
Without a comparable push to high-density that other more active regions of Perseus
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got, the L1451 region could have been predisposed to forming fewer stars.
3.9 Summary of L1451 Results
We presented observations and analysis of the L1451 region of the CARMA Large
Area Star Formation Survey. We summarize the key findings below.
1. Only one compact continuum source is detected at 3 mm, down to a 3-σ limit
of 3.9 mJy beam−1 (0.08 M⊙ limit) in a 9.2′′ × 6.6′′ beam. The detected source
is L1451-mm, which has previously been identified as a FHSC candidate.
2. We detect widespread HCO+, HCN, and N2H+ (J = 1 → 0) emission in
L1451. The HCO+ emission covers the largest area of the cloud, which we
attribute to HCO+ tracing lower-density material than the other molecules.
HCN emission morphology is nearly identical to HCO+, although it is weaker
and less spatially extended in most regions. The N2H+ emission has the small-
est spatial extent, with morphology that differs from the other molecules at the
smallest scales; N2H+ traces denser, colder material than the other molecules,
as supported by comparison to Herschel.
3. We derived column density and temperature maps from Herschel observations
at 160, 250, 350, and 500 µm. The values were derived using modified black-
body spectrum fits to the data, and column densities agree to within 5% of
Planck results when compared at the same angular resolution. The tempera-
tures toward the densest regions are ∼2–3 K warmer than kinetic temperatures
derived from single-pointing ammonia observations toward dense cores. We
attribute this difference to a limitation of using a single-component fit when
modeling SEDs from cold, dense regions of molecular clouds. A simple two-
layer model shows that having warm, 17 K foreground emission in front of
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cold, 9 K cloud emission, can cause temperatures to be overestimated by a
few K, and column densities to be underestimated by half from the true value.
We use the single-component values in the analysis of this chapter, and discuss
how the uncertainties effect the subsequent virial analysis. We will present a
detailed comparison of single- and double-component fits using all CLASSy
regions in a future paper.
4. The structure of the star-forming material in L1451 that is traced by the sum
of all our molecular emission is very similar to column density structure that
we derived from Herschel observations. All of the cloud locations that are
above the Av∼8 threshold for star formation are detected, and 90% of the
molecular emission is at column densities above 1.9 × 1021 cm−2. This shows
that high-resolution observations of this suite of spectral lines over large areas
of molecular clouds are an excellent probe of the structure and kinematics of
star forming material in young regions.
5. We use our non-binary dendrogram algorithm to identify dense gas structures
in the HCO+, HCN, and N2H+ data cubes. Slight differences in the noise-
level of each data cube are accounted for to ensure a uniform comparison of
tree statistics. The HCO+ dendrogram has the largest number of leaves and
branches. A comparison of tree statistics shows that all tracers are identifying
structures that are fragmenting in a similar way, even though we detect more
HCO+ branching levels compared to than HCN or N2H+; the increase in levels
is likely due to HCO+ being more sensitive to widespread emission from lower-
density regions of the cloud. We show that tree statistics of the gas structure
surrounding L1451-mm (a confirmed young protostar or FHSC) is very similar
to that of the gas surrounding Per Bolo 6 (a single-dish continuum detection),
163
and argue this is an indication that star formation is proceeding in a similar
fashion in both regions, with Per Bolo 6 a likely site of future star formation.
6. All molecules trace gas at similar systemic velocities, but the velocity disper-
sion of the HCO+ emission is significantly larger than that of HCN or N2H+:
mean dispersions are 0.29, 0.16, and 0.12 km s−1, respectively. This is likely
due to HCO+ tracing lower-density gas at larger scales than the other two
molecules; in a turbulent medium, there is more power on larger scales, which
will produce larger velocity dispersions.
7. A traditional virial analysis, comparing the kinetic and gravitational potential
energy of dense structures assuming uniform density profiles, resulted in virial
parameters of all structures being near or above two. We discussed how the
virial parameter can be overestimated by about a factor of two from the sys-
tematic underestimation of column densities from our Herschel SED fitting,
by assuming uniform density instead of stratified density profiles for the dust
structures, or by neglecting the effects of external confining pressure. Sev-
eral structures in L1451 satisfy the virial theorem when considering one, or a
combination of these effects. We will explore these effects in more detail in
upcoming works that do a uniform comparison of structures in all CLASSy
regions.
8. We detect two strong, centrally condensed N2H+ structures: L1451-mm, and a
newly identified source that we label L1451-west. L1451-mm was characterized
by Pineda et al. (2011) as a FHSC candidate or young protostar. Our data
shows that L1451-west is similar to, but likely younger than L1451-mm. It has
strong emission from N2H+ but is depleted in HCO+, unlike L1451-mm which
has strong emission from both molecules; this could indicate that L1451-west
164
is colder than L1451-mm. It is less centrally condensed than L1451-mm, but
more centrally condensed that the typical prestellar core; this indicates that
L1451-west is at an evolutionary state between the prestellar core phase and
the FHSC or early protostellar phase of L1451-mm. Follow-up observations
will determine if L1451-west is a viable FHSC candidate.
9. We used our size-linewidth analysis presented in Chapter 2 to show that the
dense gas in L1451 is not flattened at the largest scales like the Barnard 1 and
Serpens Main CLASSy regions studied in previous chapters and papers, and
that its dense gas structures are more ellipsoidal than filamentary. Typical
inferred line-of-sight depths for HCO+ structures are 0.40 pc with projected
sizes ∼0.45 pc, and typical HCN and N2H+ line-of-sight depths are 0.10 pc
with projected sizes of ∼0.20 to 0.14 pc, respectively. This suggests that
sheet-like geometry at parsec-scales with filamentary substructure is not a
prerequisite for star formation, but that the lack of a sheet-like geometry
may be an explanation for why L1451 has formed fewer stars than the other
CLASSy regions.
10. Overall, these observations support turbulent star formation theories that ar-
gue that externally driven turbulence can create complex, hierarchical struc-
ture in molecular clouds (regardless of whether that structure is filamentary),
without internal feedback from protostars. The molecular emission from L1451
shows a lot of complex structure, even though there is very little existing star
formation in the region. We cannot say that individual structures within
L1451 are definitively gravitationally bound based on our virial analysis, but
that several structures are consistent with satisfying the virial theorem within
the uncertainties in the data; we also know at least one star is forming in the
165
region. This supports external supersonic turbulence being the driver of the
first structure within the densest regions of molecular cloud complexes; those
structures then become the dense, fertile grounds for the future formation of
stars.
166
Chapter 4
Comparing CLASSy Regions to
Understand Pathways to Star
Formation
Abstract
We present a comparison of the dense gas emission, hierarchical complexity, and
young stellar content of all five regions from the CARMA Large Area Star Forma-
tion Survey. The goals are to compare fragmentation properties of dense gas at
different stages of evolution, and how, if at all, the young stellar content of those
regions is linked to that fragmentation. We construct a non-binary dendrogram
from the integrated intensity map of each region, using a uniform set of algorithm
parameters to ensure a proper cross-comparison of region properties. The more
evolved regions, including Serpens Main, Serpens South, and NGC 1333, show more
levels of fragmentation in their dendrograms relative to Barnard 1, while the least
evolved L1451 region shows little hierarchical complexity in this uniform compari-
167
son. Despite the differences in hierarchical depth between the regions, all regions
have a similar mean branching ratio; this shows that fragmentation is similar across
all stages of star formation. We find that the Class 0 sources in each region are
primarily located within dendrogram leaves, which represent the peaks of the dense
gas hierarchy in each region. This shows that the youngest protostars tend to form
where gas has become the most hierarchically complex. The more evolved Class II
sources are preferentially found further from leaves. This shows that more evolved
protostars migrate away from their natal core as they accrete cloud material, or that
they may consume or disperse their natal core.
4.1 Introduction
A branching hierarchy is a general term for a system that contains objects with at
least two direct subordinates. One example of a branching hierarchy is in academia,
where a professor may have two postdoctoral subordinates, and each postdoctoral
scientist may have three graduate and undergraduate student subordinates. Obser-
vations have shown that the structure of the molecular ISM is a branching hierarchy,
which begins on the largest scale with molecular clouds, extends down in scale to
many clumps (overdensities within clouds), then to multiple cores (regions within
clumps where individual or multiple protostars may form), and then finally to pro-
tostars (Williams et al. 2000). This is a conceptual view of the hierarchical nature
of star formation, illustrated in Figure 4.1, which highlights the fact that smaller,
denser structures are born within larger, less dense structures. This is predicated
on an ordered relationship between clouds, cores, clumps, and stars, as is generally
accepted in the scientific community. However, observational limitations of clouds
(poor angular resolution, limited area coverage, limited types of dust and gas trac-
168
ers) have not allowed a detailed assessment of the linkage through molecular cloud
branching hierarchies to stars that are born with the clouds.
Figure 4.1: Left: A cartoon molecular cloud, where the blue emission is from the
large-scale cloud, the orange emission is from clumps forming within the cloud,
the red emission is from cores that fragmented from the clumps, and the yellow
star represents a protostar forming within a core. Right: A cartoon dendrogram
representation of the cloud on the left. The cloud represents the parent structure
that all substructures higher in the tree form from. The cloud fragments into
three clumps, and one clump fragments further into two cores. One core forms a
protostar, which sits at the top of the cartoon hierarchy.
In this chapter, we use our CLASSy data and catalogs of stellar content in each
region to assess the importance of fine-scale hierarchical fragmentation in the star
formation process. We do not classify structures in terms of clouds, clumps, and
cores—we instead map the full hierarchical nature of the regions from cloud-to-core
scales, quantify the hierarchies using tree statistics, and quantify the relationship
between the hierarchy and stellar content by comparing the spatial distribution
of stars and cloud structures. It is possible that parsec-scale regions of dense gas
fragment in a similar hierarchical fashion in most regions of clustered star formation,
with youngest stars always being found at hierarchical peaks of volume and column
density. Alternatively, clouds may fragment in a hierarchically similar way, but with
young stars forming in relatively random locations relative to hierarchical peaks.
Another possibility is that fragmentation and young star location differs from cloud-
to-cloud.
169
CLASSy data are able to address the relationship between hierarchical dense
gas structure and current star formation. We observed N2H+ (J = 1 → 0) with
high angular resolution (∼7′′) across five large regions with diverse star formation
properties. By having this sample of diverse regions within the Perseus and Serpens
clouds, we can explore the similarities and differences of dense gas fragmentation at
different evolutionary stages and environments. We can also explore whether the
stellar content is closely associated with peaks1—does star formation care about
the fine-scale hierarchical structure of dense gas? As a reminder, we discussed in
Chapter 1 (Section 1.5) how N2H+ is a tracer of high density, cold gas, which means
we are tracing cloud regions that are viable locations for star formation. In the
discussions that follow, we will assume that high (low) integrated intensity means
high (low) dense gas column density.
The following is a breakdown of this chapter. In Section 4.2, we present the
N2H+ integrated intensity maps of each region, and demonstrate that relative N2H+
integrated intensity is a good proxy for relative dense gas column density. The
young stellar content of each region is summarized in Section 4.3, using Spitzer
catalogs and Herschel observations for YSO identification. We use our non-binary
dendrogram algorithm in Section 4.4 to assess the hierarchy of each N2H+ integrated
intensity map in a uniform way, accounting for differences in region distance and
noise-level. Section 4.5 compares the tree statistics of each region to determine
the relative hierarchical complexity and fragmentation properties of each CLASSy
region. Section 4.6 connects YSOs to dendrogram-identified structures to determine
if hierarchical structure formation is linked to the formation of young stars. We
summarize key findings in Section 4.7.
1We are tracing gas denser than ∼105 cm−3 with observations of N2H+ (J = 1 → 0), but we
are not able to distinguish between column density and density peaks with just one observed line.
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4.2 Integrated Intensity Maps Across Regions
Figure 4.2 shows all CLASSy regions with the same N2H+ (J = 1 → 0) integrated in-
tensity color-scale. Serpens Main, Serpens South, and NGC 1333 have the strongest
emission, peaking at ∼22, 21, and 16 Jy beam−1 km s−1, respectively. Barnard 1
has weaker emission peaking at ∼11 Jy beam−1 km s−1. L1451 has the weakest
emission, peaking at ∼3 Jy beam−1 km s−1. This trend of integrated intensity
shows that the two Serpens regions and NGC 1333 have the largest concentration of
relatively high dense gas column density amongst the CLASSy regions, with L1451
having the lowest dense gas column density.
Figure 4.2: N2H+ integrated intensity maps (Jy beam−1 km s−1) for all five
CLASSy regions on the same intensity scale.
To support the view of relative integrated intensity as a proxy for relative dense
gas column density, we can first compare the Herschel -based column density map of
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L1451 presented in Chapter 3 and that of Barnard 1 seen in Figure 4.3 (provided by
K. Lee, priv. communication) to the N2H+ emission; Herschel -based maps for the
other CLASSy regions have not been made yet. We know from Chapter 3 that 90%
of our detected molecular emission in L1451 is at N(H2) above a few × 1021 cm−2,
peaking at 1.3 × 1022 cm−2. With the so-called threshold for star formation at
7.5 × 1021 cm−2 (Andre´ et al. 2014, and references therein), these column densities
show that L1451 has some sub-regions with gas above the threshold. The column
density map for Barnard 1 peaks at around 8 × 1022 cm−2, with nearly the entire
ridge structure having column densities above the L1451 maximum, and above the
threshold for star formation. This shows that Barnard 1 has much higher column
density than L1451, which agrees with what we were inferring from the comparison
of N2H+ integrated intensity between the regions. Note that the area-weighted
surface density (as defined in Leroy et al. 2013) of Barnard 1 and L1451 are about
105 and 65 M⊙ pc−2, respectively, above N(H2) ≃ 1.4 ×1021 cm−2. Heiderman et al.
(2010) report the mean surface gas density of the entire Perseus Molecular Cloud
as 90 ± 33 M⊙ pc−2, indicating that Barnard 1 and L1451 are above and below the
mean surface density of the cloud, respectively.
For a quantitative comparison of integrated intensity and dense gas column den-
sity maps, we convolved the integrated intensity of Barnard 1 and L1451 to the
Herschel angular resolution (36′′) and matched the pixel scale of the two maps. Fig-
ure 4.4 shows a general trend of increasing N2H+ integrated intensity with increasing
column density (for Herschel) in both regions. The lack of a perfect correlation is
not concerning since measured continuum column density and N2H+ integrated in-
tensity respond differently to changes in density and temperature—regions with the
same column density but different density or temperature can have different N2H+
emission properties (see discussion in Chapter 1, Section 1.5). Also, different N2H+
172
Figure 4.3: Column density maps for Barnard 1 (left) and L1451 (right) derived
from Herschel SED fitting (see Chapter 3 for discussion of method). The maps
are on the same color scale, from 1.0 × 1020 cm−2 to 4.0 × 1022 cm−2. The inner
contour represents the threshold for star formation at 7.5 × 1021 cm−2, and the
outer contour represents half that value. In Chapter 3, we discussed how our
measured column densities are likely half of the true values towards lines of sight
with AV > 2.
abundances across a single region can lead to differences in N2H+ emission strength
within that region that are independent of H2 column density.
1 10 100
Integrated Intensity (Jy/bm km/s)
1021
1022
1023
N
(H
2) 
(cm
-
2 )
L1451
Barnard 1
Figure 4.4: Pixel-by-pixel comparison of N2H+ integrated intensity and Herschel -
derived column density for Barnard 1 and L1451. The original integrated intensity
maps were convolved to match the angular resolution of the column density maps,
and then regridded to the same pixel scale. Each point represents one beam.
173
4.3 YSO Statistics Across Regions
Table 4.1 summarizes the YSO statistics in each CLASSy region, listing Class II,
Flat, and Class I YSOs from the Spitzer c2d Legacy Project (Evans et al. 2009, and
references therein). The classifications are based on the SED spectral indices, α.
The spectral index classification from c2d follows the convention from Greene et al.
1994, where Class II is -1.6 ≤ α < -0.3, Flat is -0.3 ≤ α < 0.3, and Class I is α ≥ 0.3.
Class III sources commonly have weak infrared excesses. Therefore, the Class III
numbers from Spitzer surveys are extremely incomplete, which has been confirmed
by X-ray surveys of molecular clouds (Winston et al. 2010). We will not consider
Class III sources in our analysis. The lifetime of the Class I and Flat phases is about
0.5 Myr each, while the Class II phase is observed to last for ∼2 Myr (Evans et al.
2009).
The Class 0 stage was not recognized by c2d as a separate Class, since it requires
a proper understanding of longer wavelength emission and viewing angle to help
determine whether a source is Class 0 or Class I. For our analysis, we complemented
the c2d sample in each region with sources visible in Herschel 70 or 100 µm images
that were not classified as YSOs by c2d. We classify any source identifiable at 70
and/or 100 µm, but not at 24 µm or shorter wavelengths, as a Class 0 source. Sources
identified at 70 and/or 100 µm, and also detected at 24 µm or shorter wavelengths
are added to the Class I category; these sources may not have been classified as YSOs
by c2d due to saturation, or incomplete SEDs. Appendix D contains a complete
listing of new YSOs for each CLASSy region. Herschel -identified Class I sources not
classified by Spitzer are arbitrarily given 3 > α > 4 to distinguish them from the
highest-α Spitzer Class I YSOs. Herschel -identified Class 0 sources are arbitrarily
given α > 5 to distinguish them from the other YSOs.
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Our mapped regions of Serpens Main, Serpens South, and NGC 1333 have the
largest number of YSOs within them (between 69 and 89 sources), followed by
Barnard 1 (with 16 sources), and then L1451 with no confirmed YSO detections
from Spitzer or Herschel. We classify L1451-mm as a Class 0-like YSO for the
purposes of this analysis since we know it has a slow CO (J = 2 → 1) outflow
(Pineda et al. 2011) that must be driven by a protostellar source or first hydrostatic
core. Even though we do not use a similar criteria for finding more Class 0-like YSOs
in the other CLASSy regions, such a criteria would have a relatively minor impact
on the YSO statistics of those other regions, while it is the difference between zero
and one YSO for L1451.
The ratio of (Class 0 + I)-to-(Flat + Class II) sources in Table 4.1 is 0.57, 0.60,
0.85, 2.2, and 1-to-0 for NGC 1333, Serpens Main, Serpens South, Barnard 1, and
L1451, respectively. Evans et al. (2009) utilizes a similar ratio as a youth indicator
for star forming regions: higher values are younger. This sets the order of evolution
in the discussion in the following sections, with NGC 1333 and Serpens Main being
the most evolved regions, followed by Serpens South, Barnard 1, and finally L1451.
4.4 N2H+ Dendrograms Across Regions
A goal of this chapter is to compare the hierarchical complexity, and its link to
star formation, across the five regions. To uniformly compare the dendrograms
of different regions, it is important to define the algorithm parameters used for
dendrogram creation so they account for differences in distance and the noise-level
of each region. Appendix C has details and examples for each of these considerations,
and we already had an example of comparing dendrograms from data cubes with
different noise levels in Chapter 3 (Section 3.6.1).
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Table 4.1. YSO Statistics in CLASSy Regions
Region Class II Flat Class I Class I Class 0
(c2d) (c2d) (c2d) (Herschel) (Herschel)
Serpens Main 30 13 21 1 4
Serpens South 33 15 20 20 1
NGC 1333 40 14 23 8 0
Barnard 1 4 1 8 1 2
L1451 0 0 0 0 1a
Note. — Source statistics are only counting sources in our
mapped region. The Class II, Flat, and I (c2d) sources are based
on the Spitzer c2d catalogs (Evans et al. 2009). Class I (Her-
schel) sources are those identified by eye in Herschel 70 or 100 µm
maps that have a corresponding Spitzer 24 µm detection. Class
0 (Herschel) sources are those identified by eye in Herschel 70 or
100 µm maps that do not have a corresponding Spitzer 24 µm
detection. aThis represents L1451-mm, which is not detected by
either Spitzer or Herschel, but which has a CO (J = 2 → 1)
outflow detection (Pineda et al. 2011).
We ran our non-binary dendrogram algorithm on the N2H+ integrated intensity
maps of all CLASSy regions shown in Figure 4.2. The emission of each input map is
masked down to the 2.5-σ level, where σ is the rms of each individual map. We ac-
count for differences in distance by contouring the data in units of Jy beam−1 km s−1
(conserved with distance), and ensuring that the minpixel parameter for each re-
gion corresponds to the same spatial area instead of the same angular area. The
squared ratio of distances between Serpens and Perseus is 3.12, so we require a
minimum of 4 and 12.5 beams worth of pixels for Serpens and Perseus structures
to be considered leaves, respectively. We account for differences in noise level by
setting the minheight parameter to be 2-σn, where σn is the rms of the noisiest
integrated intensity map, by setting the stepsize parameter to be 1-σn, and by
calculating tree statistics of each dendrogram above a cut at 2.5-σn. The Serpens
Main map has the largest integrated intensity rms, at 0.30 Jy beam−1 km s−1. There-
fore, the absolute values of parameters are: minheight of 0.60 Jy beam−1 km s−1,
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stepsize of 0.30 Jy beam−1 km s−1, and a cut for calculating tree statistics at
0.75 Jy beam−1 km s−1.
By contouring the data and defining noise-suppression parameters in absolute
units of integrated intensity units, the hierarchical structure derived for every region
is based on a uniform set of physical properties that can be linked to star forma-
tion; integrated intensity units are a proxy for dense gas column density, which we
demonstrated in Section 4.2. This is instead of contouring the data and setting
noise-suppression parameters in terms of the noise-level of each individual map.
That would lead to regions branching at different step sizes and having different
requirements for what it takes to be considered a true leaf, and it would make a
uniform comparison between regions impractical (demonstrated in Appendix C).
Figures 4.5–4.9 show the resulting non-binary dendrograms for each region. The
vertical axis of all the dendrograms represents integrated intensity and the relative
heights of the axes are to scale. Serpens South has the most structures (75), which
is about 60% more than the region with the next most structures. This is likely due
to a combination of Serpens South having the largest mapped area of all CLASSy
regions, and having significant amount of dense gas at high column densities. We
observed all of the strongest emitting areas in each selected region (guided by existing
lower-resolution maps of cool dust or other molecular tracers), so it is not the case
that we merely missed parts of Serpens Main or NGC 1333, but rather that Serpens
South has dense gas that covers the largest area on the sky. L1451 has the fewest
structures, all branching from the tree base with no hierarchical complexity, with a
mapping area that matches Barnard 1 and Serpens Main. This indicates that there
is not as much high-density material to form many identifiable structures in this
young region when contouring the data in a uniform way between regions. Note
from Chapter 3 that L1451 does have hierarchical structure when analyzed with
177
different branching step and leaf requirements—this is discussed in more detail in
the next section, where we use tree statistics for a comparison of the dense gas
hierarchies in each region.
Figure 4.5: Non-binary dendrogram of N2H+ integrated intensity in Serpens Main.
The vertical axis represents the Jy beam−1 km s−1 integrated intensity for a given
location within the gas hierarchy. The horizontal axis has no physical meaning.
The horizontal dotted line represents the noise limit for emission used in the
dendrogram analysis (2.5-σn, where σn=0.30 Jy beam−1 km s−1).
4.5 Statistical Comparison of Hierarchies
Table 4.2 lists region-averaged tree statistics for all five non-binary dendrograms. All
statistics are calculated only using structures above the horizontal dotted line in Fig-
ures 4.5–4.9. The dotted line represents the noise limit for emission used in the anal-
ysis of Serpens Main, which is our noisiest map (2.5-σn = 0.75 Jy beam−1 km s−1).
178
Figure 4.6: Same as Figure 4.5, but for Serpens South. The dotted line represents
the noise limit used for Serpens Main, since Serpens Main had the largest noise
limit of all five regions. Leaves that do not peak at least 0.60 Jy beam−1 km s−1
above the dotted line are marked with an “x” and not included in the calculation
of tree statistics.
Figure 4.7: Same as Figure 4.6, but for NGC 1333.
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Figure 4.8: Same as Figure 4.6, but for Barnard 1. Branch 22 is below the noise
limit of the noisiest map, and is not included in the calculation of tree statistics.
Leaves 1 and 2 become leaves at branch level 0 instead of branch level 1.
Figure 4.9: Same as Figure 4.5, but for L1451.
For regions less noisy than Serpens Main, we do not want to analyze any structures
that would not be identifiable in Serpens Main. Therefore, all leaves must peak at
least 0.60 Jy beam−1 km s−1 above the dotted line to be counted, and any branch
that is below the dotted line is discounted, with its leaves then considered to be
sprouting directly from the tree base.
The two Serpens regions have the highest maximum branching level of 11, fol-
lowed by NGC 1333 at 8, Barnard 1 at 4, and L1451 at 0. The mean path length
shows a similar trend, with the two Serpens regions on top, followed by NGC 1333
at about a half level lower on average, then Barnard 1 at about three levels lower
on average, and L1451 with a 0 level average. This indicates that the dense gas in
the two Serpens regions has fragmented to the most levels, with NGC 1333 not far
behind. NGC 1333 and the two Serpens regions were classified as the most evolved
regions in Section 4.3 based on their YSO statistics—the ratio of young-to-old pro-
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Table 4.2. Tree Statistics
Region Total No.a Max Levelb Mean PLc Mean BRd
Serpens Main 46 11 4.5 3.1
Serpens South 75 11 4.3 3.6
NGC 1333 37 8 3.8 2.6
Barnard 1 18 4 1.5 2.8
L1451 4 0 0 NA
Note. — a Total number of leaves and branches. b Maximum
branching level. c Mean path length. dMean branching ratio.
tostars are from 0.57 to 0.85 for the three regions. Barnard 1 is a much younger
region, with a ratio of young-to-old protostars of 2.2. The maximum branching level
and mean path length of Barnard 1 are much lower than the more evolved regions.
This suggests that the number of branching levels is correlated with the evolution
and range of dense gas column density in a region. This makes sense—if all regions
start with a base-level of weak emission early in their evolution, the regions that have
evolved to have the stronger emission on top of that base will have likely fragmented
in more steps along their evolution to reach those strong emission peaks. L1451,
which has the weakest emission of all regions, and only one Class 0-like source, has
yet to fragment in appreciable amounts relative to the other regions.
Even though the regions show a large diversity in levels of fragmentation, the
mean branching ratios for each region are similar. All regions, except for L1451, have
a mean branching ratio between 2.6 and 3.6, meaning that each branch structure
fragments into ∼3 sub-structures as the hierarchy is built. This similarity is inter-
esting, since the regions differ in their integrated intensity and protostellar outflow
properties. In terms of protostellar outflows, the N2H+ emission from NGC 1333
and Serpens Main regions is overlapping with numerous outflows that we detect in
HCO+ and HCN. However, Serpens South has outflows primarily concentrated in
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its central “hub” region, and Barnard 1 has a few outflows in its main core zone.
This shows that the average dense gas fragmentation properties of a region is not
strongly correlated with the stellar feedback in a region; regions that are dominated
by outflows (e.g., NGC 1333 and Serpens Main) have similar fragmentation to re-
gions where outflows are limited to a small percentage of the dense gas area (e.g.,
Barnard 1 and Serpens South). We cannot distinguish between structure formed
from protostellar feedback induced fragmentation or original cloud fragmentation,
but if some fragmentation near outflows was triggered by the protostellar feedback,
then this could mean the initial fragmentation of dense gas in a region before the first
generation of star formation is similar to subsequent fragmentation that is triggered
from protostellar feedback.
What about L1451? We do not present a mean branching ratio for L1451, since
it only has leaves sprouting from the tree base, and lacks hierarchical structure.
Although L1451 appears simple in this comparison of integrated intensity maps
contoured at the same levels, that does not mean L1451 is fragmenting with no
hierarchically complexity. Star formation is set by physical processes, and is linked
to high volume and column density regions of clouds. L1451 has lower amount of
high density gas compared to other CLASSy regions, so it is has not yet evolved
to the point where it can efficiently form stars. Even so, we know from Chapter 3
that there is detectable hierarchical structure in the HCO+, HCN, and N2H+ PPV
cubes, and we calculated mean branching ratios for all molecules ∼3–4. This means
that cloud fragmentation starts before a region has reached high enough densities
to efficiently forms stars. This fragmentation is likely seeded from initial supersonic
turbulence present in the cloud. Since the L1451 analysis in Chapter 3 revealed
mean branching ratios similar to those found in this chapter for the more evolved
regions, it shows that the hierarchical nature of the initial cloud fragmentation from
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the cascade of large-scale turbulence is similar to the fragmentation that occurs once
material has enough time to reach higher densities to collapse to form stars.
Putting this all together, it appears that dense gas fragments in a similar hi-
erarchical fashion from the first stage of fragmentation that we see in the L1451
PPV cubes, to the second stage of fragmentation that occurs when densities are
high enough to start forming stars, to the potential third stage of fragmentation
that may occurs when protostellar feedback injects additional energy into the cloud.
The main difference between a region like L1451 and a region like NGC 1333 is not
how the gas is fragmenting, but how much high density material has formed, and
how many distinct fragmentation levels have formed.
4.6 Linking Stellar Content to Hierarchies
The previous section showed how the dense gas in all five CLASSy regions is frag-
menting in a hierarchically similar way, even though each region is at a different
evolutionary stage in terms of amount of dense gas, type of YSOs, and number of
branching levels. Here we explore the connection between N2H+ hierarchy and the
young stars in the four CLASSy regions with Spitzer and Herschel YSO detections
to determine if star formation is correlated with the fine-scale hierarchical structure
of dense gas.
Figures 4.10–4.13 show the location of YSOs, color-coded by spectral index, over-
plotted on a greyscale representation of the N2H+ dendrogram-identified structures
for Serpens Main, Serpens South, NGC 1333, and Barnard 1, respectively. The
darker grey structures are leaves, while the surrounding, lighter grey structures are
the branches.
The dendrogram leaves represent peaks of the emission hierarchy, and can be
183
considered the regions with highest dense gas column density in the region. A few
things are apparent by eye. First, it appears that many YSOs do not reside within
the boundaries of leaves, and many leaves have no associated YSOs. We quantify
those statements in Tables 4.3 and 4.4, respectively. Barnard 1 has 50% of its YSOs
within leaves, with 88% of those sources being Class I or 0. The more evolved
regions have between 25 and 31% of their YSOs overlapping leaf boundaries, and
about 75% of those sources being Class I or 0. This shows that if a YSO is found
to be within a leaf, it is likely to be a younger YSO. It also shows that the less
evolved Barnard 1 region is the most likely to have a YSOs found within a leaves;
this makes sense since it has the largest percentage of Class 0 and I sources.
Looking at the leaf-YSO connection the other way, all regions have a relatively
similar percentage of leaves containing YSOs, with the Serpens regions at 28–29%,
and the Perseus regions at 35–40%. Barnard 1 does not have a larger percentage
of leaves with YSOs relative to the other regions, while it did have the largest
percentage of YSOs found within leaves relative to other regions by about 50%.
This is not contradictory, since a region can have many density peaks with no
stars forming in them—those peaks can either be on the verge of star formation, or
density enhancements that will never form stars. The fact that two Serpens regions
and the two Perseus regions have nearly identical percentages of leaves with YSOs
could indicate an inherent “leaf efficiency” for a cloud, where leaves have certain
efficiency-to-date for turning mass into stars; Serpens regions may be producing stars
from density enhancements at a leaf efficiency of about 38%, while Perseus regions
are doing so at a leaf efficiency of about 29%. The rest of the leaves might form
stars later in the life of the cloud, or fail to produce stars before getting disrupted
and dispersed.
The second apparent property of Figures 4.10–4.13 is that Class II sources are
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Table 4.3. YSOs Found Within Leaves
Region YSOs in Leaves(% of Total) Class II(L0) Flat(L0) Class I(L0) Class 0(L0)
(1) (2) (3) (4) (L5) (6)
Serpens Main 22(31%) 4(1) 1(1) 14(0) 3(0)
Serpens South 22(25%) 3(2) 3(0) 15(0) 1(0)
NGC 1333 24(29%) 4(0) 2(1) 18(2) 0(0)
Barnard 1 8(50%) 1(1) 0(0) 5(1) 2(0)
Note. — (2) Number of YSOs that are found within the boundary of a leaf, and the percentage
of the total number of YSOs this represents in parenthesis. (3–6) Number of the YSOs that
around found within the boundary of a leaf that are of this Class. The number in parentheses
is the number of YSOs of this Class that are at branching level 0.
Table 4.4. Leaves With YSOs
Region Leaves with YSOs(% of Total) No. Leaves at L0 (Class of YSOs)
(1) (2) (3)
Serpens Main 9(28%) 1 (F/II)
Serpens South 16(29%) 2 (II, II)
NGC 1333 10(40%) 2 (F/I, I)
Barnard 1 6(35%) 2 (I, II)
Note. — (2) Number of leaves that have a YSO within their boundaries, and
the percentage of the total number of leaves this represents in parenthesis. (3) The
number of leaves that have a YSO that are at branching level 0, along with the Class
of YSOs that are found within those leaves.
less preferentially found near dendrogram leaves, compared with younger sources.
To quantify this relationship between YSO location and dendrogram leaves, we
calculate the distance between each YSO and the centroid position of the nearest
dendrogram leaf, and plot the results as a function of classification in Figure 4.14. A
zero arcsecond separation means a YSO resides within a leaf boundary. All regions
have Class II sources distributed near and far from leaves. However, about 75%
of the Class II sources are separated from their nearest leaf by more than 10,000
AU (∼43′′ for Perseus and 25′′ for Serpens) in all regions: 3/4 in Barnard 1, 30/40
in NGC 1333, 24/33 in Serpens South, and 22/30 in Serpens Main. For Serpens
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Main, no Flat or Class I sources are found more than 50′′ from a leaf, while about a
dozen Class II sources are found at 50 and 200′′ separation. Above zero separation,
Barnard 1 shows the most consistent trend of decreasing YSO-leaf separation with
increasing α. Serpens South and NGC 1333 are different from the other regions,
with many Class I and Flat sources found at larger separations than seen in other
regions.
What might these trends mean? Having Class II YSOs generally distributed
further from hierarchy peaks than less evolved sources could be an indication that
some protostars are migrating away from their natal core, or dispersing/consuming
their natal core. The Class I and Flat phases last about 0.5 Myr each, and the
Class II lifetime is ∼2 Myr (Evans et al. 2009). Protostars can move with velocities
up to ∼0.1 km s−1 relative to their natal core (Walsh et al. 2004; Ayliffe et al. 2007),
so we can make a conservative estimate for how far a new Class II source may have
moved from its natal core in 1 Myr, if we ignore the Class 0 stage. If a star is
formed with a 0.1 km s−1 velocity relative to its natal core, it can move 0.1 pc
per 1 Myr, which would put it about 50′′ and 80′′ from its original position in
Serpens and Perseus, respectively. This could explain the wide distribution of Class
II separations with hierarchy peaks—some protostars may remain within their natal
core, while others might have small relative velocities that take them outside of the
core by the time they reach the Class II stage, and others still might have depleted
or dispersed their natal core.
One interesting cluster of YSOs that may have dispersed or depleted the dense
gas from a natal core is found in the southeastern part of Serpens South. This cluster
rivals the cluster in the Serpens South “hub” region, with four Class I, three Flat,
and five Class II YSOs. However, unlike the hub, this region is void of significant
N2H+, HCO+, or HCN emission. Since we are not seeing HCN or HCO+, which
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would remain in gas phase if this region were too warm for N2H+ emission, it is likely
that the dense gas has been dispersed or consumed. It is possible that the Class I
sources are actually Flat or Class II sources viewed at an angle causing their SEDs
to have larger spectral indices indicative of younger sources. This uncertainty in
YSO classification could explain why there are Class I and Flat sources distributed
as much as Class II sources in Serpens South and NGC 1333.
In Figure 4.14, all regions show a wide distribution of classes at zero arcsecond
separation from leaves, from Class II to Class 0. However, it is always the case that
the majority of the sources at zero separation are less evolved, as we saw in Table 4.3
and the discussion above. This relates to the discussion of migration above—the
younger sources with zero separation were likely born within those leaves, and the
more evolved sources with zero separation may have been born with zero relative
velocity to the core. It appears that Class 0 YSOs are only found near N2H+
hierarchical peaks. The one Class 0 source in Serpens South, the two Class 0 sources
in Barnard 1, and three of the four Class 0 sources in Serpens Main are found at
zero separation. The only Class 0 source not within a leaf boundary is in Serpens
Main, and it is less than 10,000 AU from the nearest leaf centroid. We interpret
this trend to mean that regions form their first generation of protostars embedded
in dense gas hierarchical peaks.
It is apparent from Figures 4.10–4.13 that even the YSOs that lie within leaf
boundaries are not always located at the leaf center. We counted any YSO within
leaf boundaries as having “zero” separation from the leaf in Figure 4.14, but if we
calculate the distance of those YSOs from the centroid position of the leaves, only
∼30% of YSOs are within 10′′ of the leaf centroid. What could this mean? A
gravitationally collapsing spheroid or ellipsoid would naturally form a star at its
center, not off to one side. We saw in Chapters 2 and 3 that dendrogram structures
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are not perfectly uniform spheroids or ellipsoids, so this suggests that irregularly-
shaped leaves containing YSOs could be fragmenting at even small scales and higher
densities to form one or multiple stars at positions off-center from the N2H+ leaf
centroid.
In addition to analyzing the separation of YSOs from leaves, we classified the
branching level at each YSO location, and plot the spectral index as a function of
branching level in Figure 4.15. In these plots, level “-1” refers to YSOs that are
located at a position with no dense gas. To complement Figure 4.15, Tables 4.3
and 4.4 show how many YSOs in leaves are at level zero, and how many leaves with
YSOs are at level zero, respectively.
The Class II sources are distributed across branching levels for the two Serpens
regions and NGC 1333, similar to how they were distributed over a wide range of
separations in Figure 4.14. Serpens Main shows a weak trend of increasing hierarchy
level with decreasing evolutionary stage, with all Classes being represented at high
levels, but only evolved sources being represented at low levels. Serpens South and
NGC 1333 show the full range of Classes across all levels of the hierarchy. However,
Barnard 1 has all Class II sources at level zero or “-1” and shows a trend of increasing
hierarchy level with decreasing evolutionary stage.
It appears that Class 0 YSOs are only found in hierarchically complex regions;
no sources are found at level 0 or “-1”. A small number of Class I sources are found
at level 0 (one out of five in Barnard 1, two out of 18 in NGC 1333), while the wide
majority are found at higher levels. This means that in the regions of clustered star
formation, hierarchically fragmented dense gas is more likely to the birthplace of a
young YSO, compared to isolated clumps of dense gas.
The overall results from this analysis, including all regions, is that: 1) not all
hierarchical peaks of dense gas are associated with young stellar content, and not
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all young stellar content is found in hierarchical peaks, 2) most Class 0 YSOs are
forming at the location of hierarchical peaks, while more evolved YSOs can be
distributed anywhere in a cloud, and 3) star formation is most efficient in locations
of rich hierarchy.
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Figure 4.10: Serpens Main dendrogram structures (greyscale) with overplotted lo-
cations of YSOs. The different greyscale levels correspond to the distinct numeric
identifier associated with each dendrogram leaf and branch; leaves have lower
numbers and appear as darker grey structures and branches have higher numbers
and appear as lighter grey structures. YSOs are colored by evolutionary state,
with Class II, Flat, and Class I sources from Spitzer c2d being blue, green, and
magenta crosses, respectively. Sources not identified by c2d as YSOs, but with
Spitzer 24 µm and either Herschel 70 or 100 µm detections, are classified as Class
I sources and marked with red crosses. Sources not identified by c2d as YSOs, and
with no Spitzer 24 µm and either Herschel 70 or 100 µm detections, are classified
as Class 0 sources and marked with red Xs. Class III sources identified by c2d
are no shown here, for reasons explained in the text.
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Figure 4.11: Same as Figure 4.10, but for Serpens South.
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Figure 4.12: Same as Figure 4.10, but for NGC 1333.
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Figure 4.13: Same as Figure 4.10, but for Barnard 1.
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Serpens Main
0 50 100 150 200
separation (arcsec)
-2
0
2
4
6
a
lp
ha
Serpens South
0 50 100 150 200
separation (arcsec)
-2
0
2
4
6
a
lp
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NGC 1333
0 50 100 150 200
separation (arcsec)
-2
0
2
4
6
a
lp
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Barnard 1
0 50 100 150 200
separation (arcsec)
-2
0
2
4
6
a
lp
ha
Figure 4.14: YSO classification (represented by the spectral index, α), as a func-
tion of minimum separation between a YSO and its nearest leaf. If a YSO overlaps
with any portion of a leaf, the separation is considered zero; otherwise, the sep-
aration is the minimum distance between a YSO and the centroid position of
the nearest leaf. The horizontal lines mark the separation between Classes dis-
cussed in the text. L1451 is not represented because it contains no Spitzer or
Herschel -identified YSOs.
4.7 Summary
We presented a uniform comparison of N2H+ integrated intensity maps using our
non-binary dendrogram algorithm, and compared dendrogram-identified structures
to the young stellar content in each region. We summarize key findings below.
1. Molecular clouds are known to have hierarchical structure. The high angular-
resolution and large-area of CLASSy observations allow a study of the fine-
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Serpens Main
0 2 4 6 8 10 12
dendrogram level
-2
0
2
4
6
a
lp
ha
Serpens South
0 2 4 6 8 10 12
dendrogram level
-2
0
2
4
6
a
lp
ha
NGC 1333
0 2 4 6 8
dendrogram level
-2
0
2
4
6
a
lp
ha
Barnard 1
-1 0 1 2 3 4 5
dendrogram level
-2
0
2
4
6
a
lp
ha
Figure 4.15: YSO classification (represented by the spectral index, α), as a func-
tion of dendrogram branching level. The branching level of a YSO is the branch-
ing level of the leaf or branch at the position of the YSO. A “-1” level means
the YSO is located at a position that does not overlap with any dense gas den-
drogram structure. The horizontal lines mark the separation between Classes
discussed in the text. L1451 is not represented because it contains no Spitzer or
Herschel -identified YSOs.
scale hierarchical structure of dense gas in clouds from the parsec to the
∼0.01 pc scale. We use N2H+ integrated intensity as a proxy for dense gas
column density in CLASSy regions, and use our non-binary dendrogram algo-
rithm to determine the hierarchical structure of each region in a uniform way
to allow us to compare regions.
2. Serpens Main and Serpens South have the largest peak integrated intensities,
followed by NGC 1333, Barnard 1, and finally L1451. The non-binary dendro-
grams of all regions, except for L1451, show complex structure when analyzed
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uniformly. Serpens South has the most leaves and branches, due to having the
largest area of high-density gas.
3. A comparison of tree statistics across regions show that the more evolved
regions with higher integrated intensity are fragmenting to more levels than
the less evolved regions. However, the mean branching ratio of all dendrograms
is similar, meaning that the dense gas is fragmenting in a similar way in each
region; each parent fragments into ∼3 sub-structures on average. Even though
L1451 shows no hierarchical structure in this uniform comparison of integrated
intensity maps, we know from Chapter 3 that the HCO+, HCN, and N2H+
emission shows hierarchical structure, with a mean branching ratio ∼3. This
shows that fragmentation is similar during all stages of star formation, from
the initial fragmentation in a region like L1451 that is just beginning to form
density enhancements, to the later fragmentation in a region like NGC 1333
that has gathered gas and dust to high densities and is efficiently forming
stars.
4. We compare the dense gas hierarchy to the young stellar content of Serpens
Main, Serpens South, NGC 1333, and Barnard 1, ignoring L1451 since it has
only one Class 0-like source (L1451-mm). We find that most Class 0 sources
are forming within leaves, and at branching levels high in the dendrogram, sug-
gesting that the youngest stars preferentially form within hierarchical peaks of
dense gas within clouds. Class II sources are distributed throughout the region,
mostly away from hierarchical peaks. This trend could be due to migration if
a YSO is born with a non-negligible velocity relative to its natal core, or due
to the YSO consuming or dispersing its natal core. Not all dendrogram leaves
have a YSO forming within them, and not all YSOs are found within den-
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drogram leaves. The two Serpens regions have embedded YSOs within ∼29%
of leaves, and the two Perseus regions have embedded YSOs within ∼38% of
leaves, suggesting a distinct efficiency-to-date for leaves in each cloud.
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Chapter 5
Key Findings, Summary, and
Future Work
5.1 Key Findings of Thesis
I highlight six important outcomes of this thesis below. A more complete summary
of the thesis is given in Section 5.2.
1. I developed a non-binary dendrogram algorithm that calculates the hierarchi-
cal structure of an emission map or position-position-velocity cube within the
noise limits of the data. The non-binary algorithm is an improvement over
the standard dendrogram algorithm, which forces binary branching structure,
because it permits a quantitative and more physically meaningful assessment
of the hierarchical properties of molecular clouds using tree statistics.
2. I showed that a proper comparison of dendrograms for star-forming regions
that are observed with different noise-levels and that are at different distances
requires using algorithm parameters that are based on absolute, physical units,
rather than based on the sensitivity or angular resolution of an individual
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dataset.
3. The non-binary dendrograms of all CLASSy regions reveal hierarchical frag-
mentation. The mean branching ratio tree statistic is ∼3 for all regions, mean-
ing that, on average, larger structures fragment into about three smaller sub-
structures during the earlier stages of star formation before protostars have
formed, as well as during the later stages of star formation when regions con-
tain feedback from protostars. The identified structures tend to be irregularly
shaped, implying that forming cores grow in non-spherically symmetric envi-
ronments.
4. The areas within Barnard 1 and L1451 with the strongest emission and the
most hierarchical levels contain the majority of embedded Class 0/I YSOs and
prestellar sources in those regions. A uniform comparison of N2H+ emission
and tree statistics across all CLASSy regions shows a similar trend, with the
more evolved regions having fragmented to the most hierarchical levels and
having the strongest N2H+ integrated intensity (proxy for dense gas column
density). A spatial analysis of the dendrogram structures and young stellar
content shows that the youngest protostars are preferentially found near hi-
erarchical peaks of dense gas emission located at high branching levels in the
dendrogram. This shows that regions with large clusters of star-forming cores
must have first accumulated enough dense gas column density to fragment to
many distinct hierarchy levels.
5. Our high-angular resolution, large-area spectral line observations allowed us
to create two size-linewidth relations sensitive to two distinct spatial proper-
ties of CLASSy regions: the depth of the gas structures in the region, and
the projected size of the gas structures in the region. We developed a frame-
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work to estimate the typical line-of-sight depth of the dense gas using these
relations. We found that the more evolved CLASSy regions are sheet-like at
parsec scales, with N2H+ depths ∼0.15 pc, and with filamentary substructure
within the sheet that is commonly found in numerical simulations of super-
sonic turbulence. We found that the dense gas in the L1451 region is better
characterized as a collection of distinct ellipsoidal structures than a contigu-
ous region of flattened gas and dust. It is possible that L1451 is the least
evolutionary advanced region in terms of star formation because it was not
compressed to high enough densities to efficiently fragment into many bound
cores.
6. There is an extraordinary correspondence in L1451 between the observed cu-
mulative emission from the HCO+, HCN, and N2H+ (J = 1 → 0) transitions
and the H2 column density derived from Herschel continuum observations.
The differences in the observed emission structure and kinematics between
individual molecules can be understood based on their chemical and excita-
tion properties, and the combination of molecules captures the kinematics of
star-forming material that could not be traced with continuum observations.
The HCO+ and HCN (J = 1 → 0) emission in the more evolved CLASSy
regions suffered from self-absorption effects and were better at tracing dense
gas outflows from protostars than the global structure and kinematics of cloud
material. Future studies of these more evolved star formation regions should
use different molecular transitions to complement N2H+ (J = 1 → 0) to build
a more complete picture of the dense gas in these regions.
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5.2 Summary of Thesis
This thesis presented the methodology and results from CLASSy, which used CARMA
to spectrally image dense gas in nearby molecular clouds with an unprecedented
combination of area coverage, angular resolution, and velocity resolution. CLASSy
observed N2H+, HCO+, and HCN (J = 1 → 0) emission across five evolutionar-
ily distinct regions within the Perseus and Serpens Molecular Clouds: NGC 1333,
Barnard 1, L1451, Serpens Main, and Serpens South. These observations capture
the structure and kinematics of star-forming regions from cloud-to-core scales. When
combined with catalogs of young stellar content and maps of continuum emission,
they provide the most complete picture to-date of how dense gas in nearby molecular
clouds fragments on the pathway to core and star formation.
5.2.1 CLASSy Observations
We presented details of CLASSy observations and mapping in Chapter 2. Obser-
vations were done in compact CARMA array configurations using the 23-element
mode, providing a synthesized beam ∼7-8′′ and improved sensitivity to larger struc-
tures compared to the standard 15-element observing mode. The largest-scale
structure—up to 1–2 pc—of each region was captured with large-area mosaics uti-
lizing the combination of interferometric and single-dish data from CARMA. We
used a newly developed “continuous integration” technique to improve on-source
efficiency for large mosaics; for example, the Barnard 1 mosaic was composed of
743 individual pointings, and on-source efficiency reached about 48%. The final
molecular line data cubes were made by jointly deconvolving the interferometric
and single-dish data cubes. The typical rms was ∼0.13 Jy beam−1 per 0.16 km s−1
channel. We also obtained interferometric-only λ=3 mm continuum observations of
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each cloud region down to a sensitivity of ∼1.3 mJy beam−1.
5.2.2 The Barnard 1 and L1451 Regions
The two younger CLASSy regions in Perseus, Barnard 1 and L1451, were analyzed
in Chapters 2 and 3, respectively. These regions provide a look at cloud conditions
before feedback from existing star formation has a chance to significantly influence
cloud structure, such as what is happening in the more evolved NGC 1333 and
Serpens Main regions, and to a lesser extent the Serpens South region. Serpens
Main was analyzed in detail in Lee et al. (2014), and an analysis of Serpens South
filaments is in Ferna´ndez-Lo´pez et al. (2014).
Barnard 1 is more evolved than L1451, based on the identification of over a dozen
YSOs by Spitzer and Herschel in Barnard 1 compared to only one Class 0-like pro-
tostar identified in L1451 based on millimeter detections of compact continuum
emission and a slow molecular outflow (Pineda et al. 2011). This was supported
by the CLASSy λ=3 mm continuum observations that detected four compact con-
tinuum sources in Barnard 1 above 5-σ, compared to no sources in L1451 above
that limit. Three of the Barnard 1 detections were from the known B1-c, B1-bN,
and B1-bS sources, while one was a new detection toward the Per-emb 30 λ=1 mm
continuum source (Enoch et al. 2009). In L1451, we did detect weak emission above
3-σ (0.08 M⊙ limit) towards L1451-mm, which is a candidate first hydrostatic core
(Pineda et al. 2011).
All three molecules were detected in each region, with the N2H+ morphology
most closely matching the morphology of cold dust observed by Herschel in both
cases. In Barnard 1, the strongest HCO+ and HCN emission was associated with
protostellar outflows in the main core, while the non-outflow emission was relatively
weak compared to N2H+ (possibly due to self-absorption from low-density gas along
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the line-of-sight). In L1451, no HCO+ or HCN outflows were detected, but the bulk
emission from those lines was stronger than was seen in Barnard 1. An orderly
progression of N2H+ to HCN to HCO+ emission was seen from the most compact to
the most widespread spatial scales. This progression is expected since HCO+ traces
about an order of magnitude lower densities than HCN and N2H+, and the N2H+
abundance should be highest in the coldest, densest regions of the cloud.
We developed a new non-binary dendrogram algorithm to quantitatively analyze
the dense gas structure in each cloud region. We discussed the benefits of dendro-
gram over clump-finding algorithms in Chapter 2 and Appendix A—dendrograms
trace cloud structure from large-to-small scales instead of forcing emission into dis-
tinct clumps that may not have physical meaning. The benefits of our non-binary
algorithm were also discussed in Chapter 2 and Appendix B—allowing dendrogram
structure to branch into more than two sub-structures allows for the quantifica-
tion of hierarchical complexity with tree statistics, and lets us present the actual
observable emission hierarchy within the noise limits of the data.
The non-binary dendrogram algorithm was applied to the N2H+ position-position-
velocity (PPV) cube of Barnard 1. Tree statistics showed that the main core of
Barnard 1 is the most hierarchically complex, with the largest maximum branch-
ing level and mean path length. Since the main core is the location of current
star formation in Barnard 1, this suggested that star formation is correlated with
hierarchical complexity of the dense gas.
For L1451, we created non-binary dendrograms for all three molecules in PPV
space since the HCO+ and HCN emission was not impacted by outflows or significant
self-absorption features as they were in the more evolved CLASSy regions. This al-
lowed us to compare tree statistics between subregions as well as between molecules.
All three dendrograms showed hierarchical complexity, with the gas the most hier-
203
archically complex around L1451-mm. This is an indication, as seen in Barnard 1,
that star formation occurs in regions that have achieved high hierarchical complex-
ity. L1451-mm is the only detected source of current star formation in the region.
Other continuum condensations were detected at λ=1 mm by Enoch et al. (2006).
The tree statistics of the gas surrounding these condensations is very similar to the
gas surrounding L1451-mm, which we argue means that the condensations are likely
sites of very early stages of star formation.
The dendrogram of each molecule observed in L1451 showed a similar mean
branching ratio, which tracks how many substructures each structure breaks into,
indicating that each molecule is tracing physical structures fragmenting in a hier-
archically similar way. The HCO+ dendrogram had the largest mean path length
and maximum branching level, followed by HCN, and then by N2H+. Since all
molecules peak near the same high-intensity structures (e.g., near the gas surround-
ing the bright L1451-mm core), the difference in branching level was attributed to
the varying sensitivity to low-intensity levels of fragmentation—HCO+ is able to
detect low-density, more extended emission than the other molecules, so we are able
to identify additional low-intensity branching levels not seen in the other molecules.
We interpreted the complex hierarchical nature of L1451 as supportive of turbulent
star formation theories that argue that externally driven turbulence can create the
first complex, hierarchical structure in molecular cloud regions. Those early struc-
tures are the seeds that form the over-dense, fertile grounds for the formations of
the first generation of stars.
In addition to quantifying the structure of the cloud emission, we fit the spectral
lines in each region to determine the kinematic properties of the dense gas. In
L1451, the mean velocity dispersion of HCO+, HCN, and N2H+ was 0.29, 0.16,
and 0.12 km s−1, respectively, meaning that the HCO+ was tracing trans-sonic to
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supersonic gas in most areas, while the other molecules were tracing mostly sonic-
to-subsonic motions. The N2H+ emission in Barnard 1 subregions with no young
stars had subsonic velocity dispersions, while the gas in the main core reached up
to 0.5 km s−1.
We measured the spatial and kinematic properties of each dendrogram struc-
ture to understand how larger branches may differ from smaller leaves. The spatial
measurements revealed that leaves and branches are irregularly shaped structures,
showing that star-forming gas does not fragment into orderly spheroidal or ellip-
soidal structures on the pathway to star formation. The kinematic measurements
showed that branches (larger structures) tend to have larger rms variation of their
velocity compared to leaves (smaller structures)—this can be understood based on
the scale-dependent nature of turbulence, where gas separated by larger distances
will have larger rms velocity differences between them. However, we found that
the distribution of mean line-of-sight velocity dispersion was similar for branches
and leaves. Since the line-of-sight velocity dispersion is sensitive to the line-of-sight
depth of emission in a turbulent medium, we interpreted this to mean that the depth
of emission was not closely linked to the projected size of a dendrogram structure.
We constructed two size-linewidth relations using the spatial and kinematic prop-
erties of dendrogram-identified structures discussed above, and used them to esti-
mate the typical depth of molecular emission from each region. The assumption for
this analysis was that observed non-thermal gas motions are generated by isotropic,
three-dimensional turbulence in the cloud. For each region, and each molecule, the
first relation showed that rms variation in centroid velocity increased with projected
structure size. The second relation showed that non-thermal line-of-sight velocity
dispersion varied weakly with projected structure size. We showed, using a theo-
retical framework and support from numerical realizations of turbulence, that the
205
projected structure size where the two size-linewidth relations cross gives an estimate
for the typical line-of-sight depth of emission.
We determined that the typical depth of Barnard 1 N2H+ structures are∼0.15 pc.
Compared to the parsec-scale size of Barnard 1 projected on the sky, this indicated
that the parsec-scale region is flattened at largest scales, and that the flattened gas
is fragmenting hierarchically as it forms stars in the Barnard 1 main core. A similar
result was found in an analysis of the Serpens Main region (Lee et al. 2014). These
results are consistent with numerical simulations that show high-density sheets and
filaments being generic results of supersonic turbulence.
Using this method, all three molecules for L1451 appear to be tracing line-of-
sight depths that are similar to the projected sizes of individual molecular features
that are not contiguous across the parsec-scale of the entire region. This suggests
that the dense gas in L1451 is more ellipsoidal than flattened at largest scales.
Since L1451 does not appear to have filamentary structure in projection, this shows
that not every star-forming region in a molecular cloud needs to be flattened and
filamentary for star formation to proceed. However, it is possible that L1451’s status
as the least-active CLASSy region is linked to the fact that it is the only one without
flattened, large-scale, high-density structure and filamentary substructure. A lack
of flattened, high-density structure could indicate that this region of Perseus has
not been strongly compressed by turbulent flows to create a sheet-like geometry and
strong density enhancement needed to bring gas to high enough density and column
density to efficiently form stars.
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5.2.3 A Closer Look At L1451
L1451 was the first CLASSy region where we used Herschel data to construct column
density and temperature maps, which allowed us to quantify how well our dense
gas observations captured material above the threshold for star formation, and to
estimate the gravitational boundedness of structures in this young region. Katherine
Lee and Aaron Meisner led the construction of the column density and temperature
maps by fitting modified blackbody curves to Herschel SEDs, and found that our
derived column densities matched Planck results to within 5% when smoothed to
matching angular resolutions. One major systematic uncertainty came from using a
single-temperature fit for modeling the SEDs from cold, dense regions—comparing
our results to a simple two-layer model with a warm and cold component showed
that single-component fits can underestimate column densities in cold regions by
a factor of two. This result will be presented in detail in future work, and the
remainder of the thesis analysis took the uncertainty into account.
We found that 90% of the total molecular emission detected in L1451 overlapped
with regions above H2 column densities of 1.9×1021 cm−2. With the threshold
for star formation near densities of 7.5×1021 cm−2, this shows that the suite of
molecular lines observed by CLASSy captures the gas structure and kinematics of
young regions within clouds.
The non-binary dendrogram algorithm was applied to the column density map to
identify dust structures. A virial analysis of those structures, using the column den-
sity information from Herschel and the CLASSy kinematic data, showed that many
structures are near the critical value for satisfying the virial theorem. However, sev-
eral uncertainties of a factor of two limit conclusive interpretations of gravitational
boundedness.
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Although the conclusiveness of the virial results was limited, it is known that
a star is currently forming within L1451-mm. L1451-mm is a candidate FHSC
Pineda et al. (2011) and appeared in the molecular maps as a strongly centrally
condensed feature. We detected another strong, centrally condensed N2H+ structure
in the west of L1451, and we named this new source L1451-west. L1451-west is likely
colder than L1451-mm, because it has N2H+ emission but lacks detectable HCO+
emission. We estimated that L1451-west is less centrally condensed than L1451-mm,
but more so than the typical prestellar core, making it another potential candidate
FHSC.
5.2.4 Comparing All CLASSy Regions
In Chapter 4, we compared the N2H+ emission, hierarchical structure, and young
stellar content of all five CLASSy regions to understand how gas is fragmenting at
different evolutionary stages in clouds, and if the protostars are connected to that
fragmentation.
We applied our non-binary dendrogram algorithm to each N2H+ integrated in-
tensity map in a uniform way across regions, accounting for differences in map noise
and cloud distance that are further explored in Appendix C. All regions, except for
L1451, showed complex hierarchical structure with the uniform comparison. Tree
statistics showed that the more evolved regions with stronger integrated intensity
fragmented to more branching levels than the less evolved regions with weaker inte-
grated intensity. This simply means that as a region evolves to higher intensities (or
dense gas column densities), the gas fragments along the evolutionary path to form
more distinct hierarchy levels. All regions, except for L1451, had a mean branching
ratio ∼3 in this uniform comparison, which showed that even though more evolved
regions may fragment to more levels, the type of fragmentation at each stage of
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evolution is similar. Although L1451 lacked hierarchical complexity in the uniform
comparison between regions, we noted that the region did have hierarchical struc-
ture in Chapter 3, with mean branching ratios ∼3 for each molecular dendrogram,
supporting this idea of similar fragmentation from early to late stages of evolution.
Finally, we compared the hierarchical structures to the YSOs identified in each
region from Spitzer and Herschel observations—this analysis excluded L1451 since
its one candidate YSO was identified only at millimeter wavelengths. Not all hier-
archical gas peaks contained a YSO, and not all YSOs were found at hierarchical
peaks. We showed that the youngest YSOs are preferentially located within leaves
high in the emission hierarchy, while the most evolved Class II YSOs are more evenly
distributed throughout regions. This indicates that star formation in these dense
regions is most likely to occur once a very dense, hierarchically complex subregion
has been created.
5.3 Looking Forward
CLASSy made an important step toward mapping large areas of star formation with
high angular and velocity resolution. There are many paths to continue moving this
type of mapping forward. We highlight a few here.
The new W-band (∼85–115 GHz) receiver, ARGUS, on the GBT will provide
an exciting opportunity for studying dense gas across a larger sample of clouds
than was feasible with CARMA. GBT and ARGUS will open the door to efficiently
mapping molecular gas in nearby clouds with sub-core angular resolution (∼7′′ an-
gular resolution, which corresponds to ∼0.004, 0.008, and 0.02 pc at the distances
of Taurus, Perseus, and Orion, respectively). CLASSy demonstrated the potential
use of mapping large areas of molecular clouds with enough angular resolution to
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see below core scales and with enough velocity resolution to resolve below the sonic
scale of the dense gas. We discovered complex hierarchical structure, and evidence
that many overall regions are sheet-like at parsec scales. These discoveries war-
rant follow-up observations of N2H+ (J = 1 → 0) in other nearby clouds to create
a statistical study of the properties of their densest regions and cores; this large,
sensitive observational dataset can then be used to constrain theoretical models of
filament, core, and star formation in turbulent molecular clouds. GBT and ARGUS
will achieve similar spectral line sensitivity to our CLASSy data with a factor of 30
less integration time, and it can be used to build on CLASSy results.
One limitation of CLASSy is that we are only sensitive to densities ∼104−6 cm−3
with N2H+, HCO+, and HCN J = 1 → 0. A more complete analysis of clouds will
include high-resolution maps of different CO isotopologues to probe the structure
and kinematics of the lower-density gas that contains the bulk of the cloud mass and
large-scale turbulent energy. The CarmaOrion project (PI: John Carpenter) started
this work, using CARMA to map one square degree of the Orion Molecular Cloud.
We also need to extend to even higher densities and smaller scales to understand
if the identified N2H+ leaves are fragmenting further. ALMA can be used for very
high angular resolution observations of the densest gas and dust within dense cores,
which can then be connected to the larger scales detected by CARMA and GBT.
With this combination of data, we will be able to investigate the influence of the
host cluster on properties of the gas and dust at smaller scales and higher physical
densities, by tracing mass flow from the large-scale cluster onto the cores, and then
mass accretion from cores onto protostars. With ALMA’s ability to resolve disks,
we can also study how larger-scale dense gas relates to disk orientation, velocity
field, and angular momentum.
210
Appendix A
Differences Between
Clump-finding and Dendrograms
for CLASSy Data
We use the Cloudprops algorithm (Rosolowsky & Leroy 2006) and an IDL dendro-
gram algorithm (Rosolowsky et al. 2008b) to identify N2H+ emission structures in
our CLASSy data cubes. The goal is to compare clump-finding and dendrogram
object identification methods when applied to nearby star forming regions observed
with high angular resolution. Both algorithms analyze the emission in position-
position-velocity cube to segment the emission into structures. Figure A.1 shows
Cloudprops (top) and dendrogram (bottom) contours for identified structures, over-
plotted on two N2H+ velocity channels around the B1-b continuum cores. The
common color contours represent the same structures in the left and right pan-
els. There are clearly major differences in the number and shapes of the identified
structures between the two methods.
We find that the Cloudprops algorithm forces emission into small-scale clumps,
211
Figure A.1: Two N2H+ channel maps of the B1-b region for a comparison of Cloudprops
(top) and dendrogram (bottom) object identification results. Each Cloudprops and den-
drogram object is contoured with a unique color—this particular region is broken up into
nine distinct Cloudprops objects, and three dendrogram objects. Cloudprops tends to put
all emission into smaller-scale, independent clumps, while dendrograms identifies peaks
of emission as leaves (green and blue contours in the online version), and then identifies
lower intensity contour(s) that surround them as branches (cyan contour in the online
version). We argue that the dendrogram approach is the more appropriate one for high
angular resolution studies of nearby molecular clouds, since it captures the hierarchical
nature of the gas emission across the wide range of spatial scales that exists in those
regions.
even when the data does not show clear regions with strong intensity enhancements.
When visually inspecting the emission channels in Figure A.1, there is no physical
reason to think that the plateau of emission west of the B1-b cores is made up on
several, independent clumps of dense gas that are separated with orderly borders.
The technical reason for the clumpy breakdown is that Cloudprops first locates the
highest level, local closed isocontours. Next, the algorithm steps down in intensity
dividing the lower intensity emission between the stronger peaks according to a
nearest-neighbor algorithm. This division of lower intensity emission across a fairly
uniform emission plateau leads to the arbitrary borders seen in the top row of
Figure A.1. Cloudprops and other clump-finding algorithms work best for sparse
212
fields that have resolved separations between objects—identifying giant molecular
clouds in an extragalactic source is one example of where they work well. But
attempting to decompose nearby, well-resolved, molecular gas emission into many
small clumps with fairly straight borders does not have good physical motivation.
Similar conclusions were found in Goodman et al. (2009), where the authors showed
that CLUMPFIND (Williams et al. 1994) makes artificial attempts to fill in the
structure between meaningful clumps.
Instead of partitioning all of the emission into individual clumps according to
a nearest-neighbor scheme, it makes more physical sense to interpret it as lower
intensity structure surrounding the peaks within it. For example, the peaks could
represent gas that fragmented from the lower intensity emission surrounding them.
This scenario considers that small-scale features can form from existing large-scales
features, and is a hierarchical way of thinking about the data. If we accept that
molecular clouds are hierarchical, then this is a more physical way to interpret the
emission, and it requires an algorithm that can track the emission structure as a
function of contour level intensity—a dendrogram algorithm does just that.
How does a dendrogram algorithm work? We quickly review the basic dendro-
gram procedure using a one-dimensional emission profile seen in Figure A.2 (from
Rosolowsky et al. 2008b). (See that paper for more discussion of this example and
the extension to two- and three-dimensions.) A one-dimensional, horizontal contour
can be started at the absolute maximum of the emission profile and stepped down-
ward to the base of emission. During this process, the peaks and merge levels of
the three local maxima are identified and represented in a dendrogram (seen inset
within the emission profile and repeated on the right with labels).
A dendrogram is composed of leaves and branches. In our example, the three
leaves of the dendrogram correspond to the three local maxima in the emission profile
213
Figure A.2: This figure is taken from Rosolowsky et al. (2008b). The left image shows
a one-dimensional, three-peak emission profile with the dendrogram representation as an
inset. The dendrogram is reproduced on the right with the tree features labeled (the labels
differ slightly from Rosolowsky et al. (2008b) to accommodate the naming conventions
used in this thesis). The dendrogram is formed by keeping track of the emission structure
as a function of intensity level. For example, contouring the emission profile at the I1 level
produces a single object, while contouring at I2 produces two objects—the Icrit contour
represents the level where the two strongest peaks in the emission profile merge together.
In the dendrogram, this contour level is represented by a horizontal line connecting the
two strongest leaves into the branch. Readers should see the original paper for a detailed
discussion on dendrograms in all three dimensions.
that do not break up into any substructure. The peak intensity of a leaf represents
the peak intensity of its corresponding local maximum, while the lowest intensity of
a leaf represents the intensity where the corresponding local maximum merges with
another local maximum. The two branches of the dendrogram correspond to lower-
intensity emission that breaks up into substructure at higher intensities. The upper
branch represents the lower-intensity emission that seeds the two strongest leaves,
and the lower branch represents even lower-intensity emission that encompasses
all of the emission peaks. The peak intensity of a branch represents the intensity
where the leaves above it merge together, while the lowest intensity of a branch
represents the intensity where it merges with another leaf or branch (the case of the
left branch) or where it reaches the lowest measured intensity (the case of the lower
branch). This algorithm can be extended from one-dimension to two- and three-
dimensions to operate on position-position or position-position-velocity datasets.
214
All of our object identification for CLASSy clouds was done in three-dimensions,
even if we occasionally represent the identified objects as two-dimensional contours
for visualization simplicity.
Going back to our example in Figure A.1, the dendrogram identified objects in
the two N2H+ channels are shown on the bottom row of the figure. Two peaks of
emission (leaves) are identified with isolated contours (green and blue contours),
and then get joined at a lower intensity level within a larger scale contour (a branch
shown as the cyan contour).
To summarize, the dendrogram identification method is more appropriate for
our data and science goals. Our data capture small-scale dense gas structures due
to the high-angular resolution of the interferometer, and they capture large-scale
dense gas features because of the large-area mosaicing and full emission reconstruc-
tion with single-dish data. Our science goals involve studying how small-scale gas
features connect to the large-scale cloud features. The dendrogram approach lets us
investigate the physical and kinematic properties of the dense gas across the wide
range of spatial scales probed by our CLASSy data in a way that purely small-scale,
clumpfind-like segmentation would not allow.
215
Appendix B
A New Non-binary Dendrogram
Procedure
The standard dendrogram algorithm forms a purely binary tree – thinking about a
tree growing from the base upward, every branch terminates in either two leaves, a
leaf and a branch, or two branches. A single branch is not allowed to directly sprout
three leaves, even if the leaves merge into the branch at exactly the same level. In this
three leaf example, two of the leaves would get merged into a branch, and then that
branch would merge with the remaining leaf into another branch. We refer to this
as “phantom branching” because an artificial branch was introduced only to enforce
a binary merger requirement, as opposed to being motivated by the true nature of
the data being modeled. This makes interpreting the true hierarchical nature of
the data difficult, and makes a quantitative assessment of the dendrogram using
tree statistics impossible (see Houlahan & Scalo (1992) for the use of tree statistics
to interpret the hierarchical nature of emission). Going back to our example, we
set out to allow all three leaves to merge into a single branch—we set out to allow
non-binary mergers.
216
Non-binary dendrograms are useful for two reasons: 1) they provide a collection
of branches that respect the noise inherent in real data, and 2) they allow the user
to quantitatively compare the hierarchical complexity of different emission regions,
and correlate that complexity with properties of those regions (e.g., star formation
efficiency, column density, etc.).
The three-leaf example we used to motivate non-binary dendrograms is artificial;
it is extremely unlikely for a real dataset to have three leaves merging at exactly the
same intensity. Typical behavior seen in real data sets may have two leaves merge
into a branch at the 1.0 Jy beam−1 level, and then merge with a third leaf into
another branch at the 0.98 Jy beam−1 level. Our key argument is that these three
leaves should merge into a single branch, if the sensitivity of the dataset is lower
than the branching difference. For example, the sensitivity of our Barnard 1 dataset
is 0.13 Jy beam−1, and the standard dendrogram algorithm produces branching in
increments less than 0.13 Jy beam−1 to ensure binary mergers—this produces a
collection of branches that is not meaningful within the noise limits of the data, and
limits the quantitative interpretation of the hierarchy. Our new method alleviates
the binary merger requirement and allows branches to sprout an unrestricted amount
of leaves and/or branches.
The key technical differences between our new non-binary method and the stan-
dard method are: 1) we restrict branching to intensity steps equal to integer values
of at least the 1-σ sensitivity of the data, instead of allowing branching at infinitely
small intensity steps, 2) we have an algorithm that can cluster more than two ob-
jects into a single group, instead of being restricted to clustering two objects at a
time. Another way to think about the difference is that the standard dendrogram
code yields the one emission hierarchy that represents the one realization of the
noise applied to the true emission being observed. Our modified dendrogram code
217
instead represents an observable emission hierarchy within the noise limits of the
data.
Figure B.1: Cartoon example of the difference between the standard dendrogram al-
gorithm, and our new non-binary algorithm. The standard algorithm (red tree in the
online version) forces binary mergers of dendrogram leaves and branches—the left and
center peaks are first merged into a branch at the Icrit,1 contour level, and that branch is
then merged with the right peak at the Icrit,2 contour level. Since the two merger levels
are separated by less than the 1-sigma sensitivity of the data, we argue that the branch
between Icrit,1 and Icrit,2 is not motivated by the data, but by the requirement of binary
mergers. Our new non-binary algorithm (cyan in the online version) merges all three
peaks at the highest merger level, and assigns the remaining emission between Icrit,1 and
Icrit,2 to a single branch. This represents an observable emission hierarchy within the
noise limits of the data.
A cartoon example of the difference is shown in Figure B.1. The cartoon shows
a one-dimensional intensity profile, where the intensity axis is quoted in terms of
the sigma sensitivity units of the data. Under the standard algorithm (red tree),
the two leftmost peaks merge together at the level of the first saddle point (Icrit,1,
which represents an intensity level of 5-sigma) into a branch. The algorithm then
merges that first branch with the rightmost peak at the level of the second saddle
point (Icrit,2, which is less than 1-sigma lower than Icrit,1) into a second branch. Our
algorithm (cyan tree) merges all three peaks into a single branch at the 5-sigma level
since the two saddle points are separated by less than the 1-sigma sensitivity of the
data.
218
Our algorithm comes with one obvious caveat. The resulting dendrogram de-
pends on the discrete contouring of the data (which occurs in 1-σ steps in the
example above and in Chapter 2); if branching levels are shifted slightly higher or
lower, then the dendrogram can change. For example, consider a dataset in Kelvin
units (for visual simplicity), with 0.10 K sensitivity, two leaves that peak at 4.00 K
and merge together at 1.00 K, and a third leaf that peaks at 3.00 K and merges
with the other leaves at 0.98 K. If the data is being contoured in 1-σ steps, our
algorithm would set 1-σ branching levels in 0.10 K steps starting from the 4.00 K
peak, which means that 1.00 K is an available merge level. All three leaves would
be merged into a single branch at 1.00 K using our non-binary algorithm. But if the
peak intensity is 3.98 K instead of 4.00 K, then 1.00 K is not an available branching
level anymore—but 1.08 K and 0.98 K are. For that case, the two strongest leaves
would merge at 1.08 K, and then merge with the third leaf at 0.98 K. This simple
example shows how our dendrograms, and the tree statistics derived from them, can
be slightly altered by shifts in the discrete contouring of the data. We went from a
dendrogram with one branching level, a branching ratio of three, and a mean path
length of one, to a dendrogram with to two branching levels, a mean branching ratio
of two, and a mean path length of 1.66.
This caveat produces only small changes in the dendrogram and tree statistics
when tested on the actual Barnard 1 data presented in Chapter 2, Section 2.6. We
shifted the 1-σ branching levels by 0.33-σ; compared to the results presented in
Section 2.6.2, the mean branching ratio changed from 3.9 to 3.8, and the mean path
length and maximum branching level were unchanged. We argue that the benefits
of this new non-binary algorithm outweigh this caveat, particularly when science
goals include: 1) correlating the physical properties of several star forming regions
with differences in dendrogram structure (by comparing tree statistics of different
219
regions, which is not possible with the standard algorithm), and 2) comparing the
structure and kinematics of large-scale and small-scale structures within a single
region (by comparing the spatial and kinematic properties of leaves and branches,
which is more difficult for the end-user if the branch list is contaminated by phantom
branching from the standard algorithm).
220
Appendix C
How to Compare Non-Binary
Dendrograms of Different Regions
We need to be able to compare the dendrograms of different clouds that were ob-
served with different noise levels and that are at different distances. In Chapter 2, we
analyzed a single non-binary dendrogram for the PPV cube of the isolated hyperfine
component of N2H+ in Barnard 1, which is the simplest case of one cloud distance
and one noise level. In Chapter 3, we analyzed the non-binary dendrograms for the
PPV cubes of the strongest hyperfine components of N2H+ and HCN, and the single
component of HCO+ in L1451; there was a noise difference of 15% between those
cubes, so this was a slightly more complex scenario. In Chapter 4, we analyzed
the non-binary dendrograms for integrated intensity maps of each CLASSy region,
which have different distances (Serpens at 415 pc, and Perseus at 235 pc), and dif-
ferent noise levels (e.g., Serpens Main at 0.30 Jy beam−1 km s−1 and Barnard 1 at
0.17 Jy beam−1 km s−1); this is the most complex scenario.
The goal of this section is to establish how we can compare dendrogram structure
and statistics between clouds that have significantly different observational noise-
221
levels and that are located at different distances. We will argue in this appendix
that the key is to construct the dendrograms using physically meaningful units for
the algorithm parameters first introduced in Chapter 2 (Section 2.6.1), including
the parameters for: 1) the minimum height for a local maximum to peak above
the level where it merges with adjacent local maxima to be considered a real leaf
(minheight), 2) the minimum area covered by a leaf for it to be considered real
(minpixel), and 3) the minimum allowed branching step height between adjacent
levels in the dendrogram (stepsize).
C.1 Noise Dependence of Dendrogram Structure
and Statistics
The goal of this section is to demonstrate a method for comparing regions with
different noise levels. We want to ensure that lowering the noise-level of a map will
not significantly change the dendrogram structure or tree statistics derived from the
emission.
To illustrate the problem, we start by imagining a scenario where we observe a
cloud for one hour, and make a map. We then observe it again for nine hours, and
make a second map that has the noise reduced by a factor of three compared to the
first map. We would then run our dendrogram algorithm on these two maps and
see if and how the structure and statistics change.
Although we do not have maps of the same cloud with different noise, an easy
way to mimic this scenario with existing data is to use the hyperfine components
in the N2H+ PPV cube. The N2H+ (J = 1 → 0) transition is split into seven
resolvable hyperfine components, which have the same velocity dispersion and exci-
tation condition but different peak intensity. We can integrate over different com-
222
binations of hyperfine components to create moment maps with different signal-to-
noise ratio (SNR). Signal is proportional to the number of channels with emission,
N, and is dependent on the strength of the emission in each channel. Integrat-
ing over only the lowest-velocity component will give lower signal than integrat-
ing over all velocity components. Integrating over the lowest-velocity component
will give slightly lower noise (σLV ) in emission-free regions compared to integrat-
ing over all of the velocity components, since noise scales as
√
Nσ, where N is the
number of channels, and σ is the noise in a single channel. For a real example,
the noise levels of the Barnard 1 lowest-velocity and full-velocity component maps
are 0.09 and 0.15 Jy beam−1 km s−1, respectively, with peak signals of 1.8 and
11.4 Jy beam−1 km s−1, respectively—the peak SNR are then 20 and 76, respec-
tively.
The questions we want to answer hinge on what happens to dendrogram struc-
ture and statistics when we reduce the noise in a map while keeping the signal the
same. In the paragraph above, we created two maps with different SNR, but the
difference came from different noise levels and even more disparate peak signals. To
turn these into maps with similar peak signal and different noise, we first normalize
the full-velocity component map to the low-velocity component map at locations
where the low-velocity component map has emission greater than 6-σLV ; this en-
sures that the regions with strong emission have matching signal (e.g., a pixel at
11.4 Jy beam−1 km s−1 in the full-velocity component map with a corresponding
pixel at 1.8 Jy beam−1 km s−1 in the low-velocity component map will be reduced
by a factor of 6.3 in the normalized map). In weaker regions (less than 6-σLV in the
low-velocity component map), we scale the full-velocity component map down by a
factor of 7, which is the mean normalization factor in regions of strong signal. We
then calculate the rms of the normalized full-velocity component map, σNFV , which
223
is 0.03 Jy beam−1 km s−1 compared to σLV = 0.09 Jy beam−1 km s−1. The result
is a new map with similar signal to the low-velocity component map but with three
times lower noise; this is the scenario we want to test our dendrogram algorithm on.
We ran our non-binary dendrogram algorithm on the Barnard 1 versions of these
two maps in two different ways. First, we allowed each dendrogram to have a
stepsize and minheight based on the rms of each map: stepsize = 1-σNFV
and minheight = 2-σNFV for the normalized full-velocity component map, and
stepsize = 1-σLV and minheight = 2-σLV for the lowest-velocity component map.
Second, we forced each dendrogram to have the same stepsize and minheight
based on the noisier map: stepsize = 1-σLV and minheight = 2-σLV for both maps.
Using absolute units across maps as in this second case could be beneficial because
absolute units are linked with physical properties of a cloud, while noise units are
linked with the properties of the observations. For example, if a study wants to
link fragmentation properties of column density structure in different clouds to the
properties of star formation in those clouds, it would be more sensible to define an
absolute unit, such as a minimum mass or column density that is always the same
across clouds, for branching and leaf identification, rather than a noise unit, such
as 1-σ, which can be different for different clouds.
For the first case, where we allowed the stepsize and minheight parameters
to be based on the noise-level of the individual map, the resulting dendrogram-
identified structures for the two Barnard 1 maps are shown in Figure C.1, and the
dendrograms are shown in Figures C.2. Two of the strongest peaks in the region are
similarly identified in both maps (structures 9 and 11 in the low-velocity component
map are 27 and 31 in the full-velocity component map). However, some leaves break
up into multiple structures when lowering the noise of the map and also lowering the
absolute threshold for creating a leaf and a branching step (structure 6 in the low-
224
velocity component map becomes structures 22, 23, 25, and 28 in the full-velocity
component map).
Figure C.1: Structures identified by our non-binary dendrogram algorithm from
the integrated intensity map made from the lowest-velocity hyperfine component
(left) and a scaled-down map made using all velocity components (right). The
dendrogram algorithm parameters are listed in the figure, and are based on the
noise level of the individual maps. Structures are labeled with numbers that
correspond to leaves and branches in Figure C.2.
This shows that the hierarchical structure of two maps of the same region that
have different noise can significantly change if minheight and stepsize are kept in
terms of the sensitivity of each individual map. This makes sense if we consider an
extreme limit of very low noise maps that may soon be produced by ALMA. If the
noise in a map is extremely reduced, structures peaking 2-σ above a merger level with
other structures would likely not represent physically relevant features, but small-
scale variations on top of physical meaningful features. In this case of extremely
low noise, it would make more sense to define a physically relevant minimum unit
for studying structure, such as a minimum mass.
For the second case, we used the values of the noisier map for stepsize and
minheight for the construction of both dendrograms. That meant that each dendro-
gram could branch in 0.09 Jy beam−1 steps, and leaves needed to be 0.18 Jy beam−1
225
Figure C.2: Non-binary dendrograms from the integrated intensity map made
from the lowest-velocity hyperfine component (left) and a scaled-down map made
from using all velocity components (right) using the dendrogram algorithm pa-
rameters listed in the figure.
above their merge level to be considered real—these were our minimum physically
relevant units to study structure across these two maps with different noise. The
resulting dendrogram-identified structures for the two Barnard 1 maps are shown
in Figure C.3, and the dendrograms are shown in Figure C.4. The main take-
away from these figures is that lowering the noise but keeping the same absolute
units for studying structure results in very similar dendrograms. A large-scale, low-
intensity branch (structure 16 in the full-velocity component map) is added around
smaller-scale, higher-intensity structures found in the noisier map, and some leaves
that branched directly from the tree base in the low-velocity component map now
branch from one level up due to the addition of the large-scale, low-intensity branch
(e.g., leaf 8 becomes leaf 7). The strongest peaks in the region are similarly identi-
fied in both maps (structures 6, 9, and 11 in the low-velocity component map are
6, 8, 10 in the full-velocity component map); lowering the noise did not cause these
structures to break up. This provides evidence that if the noise in a map is lowered,
226
and the stepsize and minheight parameters are kept constant, the hierarchical
structure will not significantly change—you mainly add lower-intensity branching
structure to connect parts of the emission hierarchy not previously connected.
Figure C.3: Structures identified by our non-binary dendrogram algorithm from
the integrated intensity map made from the lowest-velocity hyperfine component
(left) and a scaled-down map made from using all velocity components (right).
The dendrogram algorithm parameters are listed in the figure, and are the same
for each map. Structures are labeled with numbers that correspond to leaves and
branches in Figure C.4.
Another important test is how the tree statistics change between the dendro-
grams. We calculate the tree statistics of the low-velocity component map in both
cases as described in Chapter 2, and list the statistics as insets of Figures C.2
and Figure C.4. To properly compare statistics between the two maps, we need
to only consider the dendrogram structures in the full-velocity component map
above the mask level applied to the low-velocity component map. The dendro-
gram of the lowest-velocity component map has a minimum integrated intensity of
0.21 Jy beam−1 km s−1 (set by the 2.5-σLV mask limit to the data input to the
dendrogram algorithm). Since the full-velocity component map extends to lower
emission levels set by a 2.5-σNFV mask limit, we calculate the statistics for that
dendrogram above a cut corresponding to the same 2.5-σLV limit of the low-velocity
227
Figure C.4: Non-binary dendrograms from the integrated intensity map made
from the lowest-velocity hyperfine component (left) and a scaled-down map made
from using all velocity components (right) using uniform dendrogram algorithm
parameters listed in the figure for each map.
component map (the cut is represented in Figures C.2 and C.4 by the horizontal
dashed line). This means that leaves from the full-velocity component map must
peak 2-σNFV or 2-σLV above the noisier mask level to be considered real, for the
first and second case, respectively. The leaves that do not meet this requirement are
marked with an “x” in Figures C.2 and C.4. Any branch below this noisier mask
level is removed, and structures above it are lowered one level.
For the first case, where we set stepsize and minheight based on the noise-
level of the individual map, the lower-noise dendrogram has a maximum branching
level three levels higher than the higher-noise dendrogram, a mean path length
about half a level larger than the higher-noise dendrogram, and a mean branching
ratio 0.6 higher than the higher-noise dendrogram. The differences in maximum
branching level and mean path length can be explained by the lower-noise map
having a lower absolute threshold for what can be considered a leaf compared to the
higher-noise map (minheight of 0.06 Jy beam−1 km s−1 vs. 0.18 Jy beam−1 km s−1),
228
and allowing branching steps at smaller absolute units compared to the higher-noise
map (stepsize of 0.03 Jy beam−1 km s−1 vs. 0.09 Jy beam−1 km s−1); when it is
easier to break emission into leaves and to define new branching levels, there will be
more hierarchical structure in the dendrogram.
For the second case, where we set stepsize and minheight based on a minimum
relevant Jy beam−1 km s−1 amount, the mean path lengths agree to a tenth of a
level, the mean branching ratios are identical, and the maximum branching levels
differ by only one level. This demonstrates how tree structure can be defined so that
lowering the noise of a map will not alter the calculated tree statistics significantly.
When comparing different clouds with different noise-levels, it will be important to
use a minimum relevant amount so that the emission in each cloud has the same
absolute threshold for what can be considered a leaf and what can be considered a
significant branching step.
In conclusion, the dendrograms of clouds observed with different noise can be
uniformly compared if the comparison uses absolute units for the dendrogram con-
touring and leaf requirements instead of units based on the noise-level of each indi-
vidual map, and if the comparison of tree statistics only analyzes structures above
the intensity level set by the noisiest map.
C.2 Comparing Regions at Different Distances
In comparing clouds at different distances, there are two effects to consider: 1) a
fixed angular resolution covers a different spatial scale at different distances, and 2)
the emission measurement unit could depend on distance.
CLASSy can resolve slightly smaller spatial structures in Perseus (d=235 pc)
than it can in Serpens (d=415 pc) with its uniform angular resolution, but doing
229
so would create an imbalance in the comparison of tree statistics across clouds.
To account for this, we ensure that we match the minimum spatial size that a
dendrogram leaf can be in each region using the minpixel parameter.
To account for the second effect, if a physical measurement of each cloud, such as
mass, is not available, then using a measured value conserved with distance, such as
specific intensity, is a good option. Specific intensity, Iν , is a fundamental property
of radiation that describes how much energy is passing through a detector of some
area, per time interval, per frequency interval, per observed solid angle on a source.
It is written as
Iν =
dE
dAdtdνdΩ , (C.1)
with units of erg s−1 cm−2 Hz−1 Sr−1. Iν is conserved for non-cosmological distances
where the frequency of radiation is not changing. This is because if you move a
source to a greater distance, d, its flux density (erg s−1 cm−2 Hz−1) will decrease by
1/d2, while its solid angle as perceived by the observer will also decrease by a factor
of 1/d2. For a fixed telescope beam and a uniform, extended source, another way
of thinking about this conservation is that as the source moves twice as far away,
the collected flux density decreases by a factor of four, but the telescope beam is
covering four times more physical area of emission.
Interferometric data are in units of Jy beam−1, which are analogous to Iν , and
which are conserved with distance for a uniform, extended source. The flux density
(in units of Janskys) at a given position in a uniform, extended cloud will decrease
with the square of the distance, while a fixed beam area will cover a spatial area
that increases by the square of the distance.
In summary, we ensure a proper comparison of hierarchical structure for cloud
regions at different distances by using a matching minimum spatial area requirement
for leaves and constructing our dendrograms in Jy beam−1 or Jy beam−1 km s−1
230
units.
C.3 Summary
In astronomy, we are constantly comparing objects at different distances that have
been observed with different noise properties. To understand the state of star for-
mation in each cloud, it is most insightful to analyze cloud structure using physical
and spatial units, such as mass or column density and parsecs, since star formation
is controlled by physical processes that act on collections of mass at different spatial
scales. At a certain scale, very small pieces of cloud mass, or very low columns
of material, will have no effect on the global star formation picture of a cloud, so
getting more sensitive and high-resolution observations will have no impact on the
overall picture of fragmentation. If future observations become sensitive to such
small variations in a cloud, an analysis using a uniform set of physical units can
restrict dendrogram branching to meaningful quantities of mass or column density
that can be related to the physics controlling the star formation and compared across
clouds.
Since we do not have access to reliable, high-resolution maps in physical units
such as column density, we contour the data in the conserved units of Jy beam−1 (for
PPV cubes) or Jy beam−1 km s−1 (for integrated intensity maps) in this thesis1. We
then use a uniform set of physical units for dendrogram algorithm parameters when
comparing the hierarchical structure of cubes or maps with different noise levels or
distances so that the resulting hierarchies can be properly compared.
1We discuss how intensity measurements of dense gas tracers can be used as a proxy for dense
gas column density in Chapter 1.
231
Appendix D
Herschel-identified YSOs
232
Table D.1. Non-c2d YSOs Identified with Herschel
Region RA DEC Detections
(1) (2) (3) (4)
NGC 1333 52.2313 31.2432 24, 70, 100 µm
NGC 1333 52.2525 31.1996 24, 70, 100 µm
NGC 1333 52.2553 31.2595 24, 70, 100 µm
NGC 1333 52.2561 31.3392 24, 70, 100 µm
NGC 1333 52.2653 31.2673 24, 70, 100 µm
NGC 1333 52.2831 31.3641 24, 70, 100 µm
NGC 1333 52.2951 31.3658 24, 70, 100 µm
NGC 1333 52.3065 31.2323 24, 70, 100 µm
Barnard 1 53.3187 31.1136 24, 70, 100 µm
Barnard 1 53.3381 31.1282 100 µm
Barnard 1 53.3391 31.1230 100 µm
Serpens Main 277.4534 1.2822 70, 100 µm
Serpens Main 277.4899 1.2346 24, 70, 100 µm
Serpens Main 277.4956 1.2221 70, 100 µm
Serpens Main 277.5017 1.1955 100 µm
Serpens Main 277.5078 1.2525 100 µm
Serpens South 277.5056 -2.1741 24, 70, 100 µm
Serpens South 277.5727 -2.1671 24, 70, 100 µm
Serpens South 277.5657 -2.1221 24, 70, 100 µm
Serpens South 277.5517 -2.1150 24, 70, 100 µm
Serpens South 277.5521 -2.1075 100 µm
Serpens South 277.5026 -2.1171 24, 70, 100 µm
Serpens South 277.4861 -2.0975 24, 70, 100 µm
Serpens South 277.5121 -2.0700 24, 70, 100 µm
Serpens South 277.5051 -2.0297 24, 70, 100 µm
Serpens South 277.5026 -2.0140 24, 70, 100 µm
Serpens South 277.4981 -2.0195 24, 70, 100 µm
Serpens South 277.4961 -2.0240 24, 70, 100 µm
Serpens South 277.4936 -1.9614 24, 70, 100 µm
Serpens South 277.4711 -1.9684 24, 70, 100 µm
Serpens South 277.4680 -1.9629 24, 70, 100 µm
Serpens South 277.4668 -1.9599 24, 70, 100 µm
Serpens South 277.4248 -1.8331 24, 70, 100 µm
Serpens South 277.4243 -1.8376 24, 70, 100 µm
Serpens South 277.4032 -1.8606 24, 70, 100 µm
Serpens South 277.5151 -2.0751 24, 70, 100 µm
Serpens South 277.5151 -2.0832 24, 70, 100 µm
Note. — (1) CLASSy region. (2,3) J2000
RA and DEC position of source, determined by
eye. (4) Bands in which the source was detected,
among Spitzer 24 µm and Herschel 70 and 100 µm
bands.
233
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