ABSTRACT
Title of dissertation: CONNECTING MOLECULAR CLOUDS
TO CLUSTERED STAR FORMATION
USING INTERFEROMETRY
Arnab Dhabal
Doctor of Philosophy, 2018
Dissertation directed by: Professor Lee Mundy
Department of Astronomy
Stars are commonly formed in clusters in dense regions of interstellar medium
called molecular clouds. In this thesis, we improve our understanding of the physics
of star formation through multiple experiments involving interferometry. We use
CARMA observations of filaments in Serpens and Perseus molecular clouds to study
their morphology and kinematics using dense gas tracers. The observations are com-
pared against predictions from simulations to explain how filaments form and evolve
to form stars. Ammonia inversion transitions data is obtained from VLA observa-
tions of the NGC 1333 molecular cloud. From this data, we derive temperature,
structural and kinematic information about the gas participating in star formation
on scales from 2 parsec to 0.01 parsec, thereby connecting the large scale gas and
dust structure to individual protostellar envelopes.
These observations from ground-based arrays are complemented by the de-
velopment of the Balloon Experimental Twin Telescope for Infra-red Interferome-
try (BETTII). This pioneering instrument performs Michelson interferometry along
with Fourier Transform Spectroscopy, thereby providing sub-arcsecond angular reso-
lution and spectroscopic capabilities at far-infrared wavelengths 30−100 µm. Using
this capability, BETTII will study the dusty envelopes around protostars in clustered
star forming regions. The instrument development is a component of the thesis with
focus on the optics designing, evaluation and alignment for the completed and up-
coming flights. We discuss how the optical system mitigates the challenges of phase
control for such a balloon borne interferometer. Further, interferometric simulations
of BETTII observations are carried out to investigate how well these observations
can constrain the defining parameters of protostars.
CONNECTING MOLECULAR CLOUDS
TO CLUSTERED STAR FORMATION
USING INTERFEROMETRY
by
Arnab Dhabal
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2018
Advisory Committee:
Professor Lee Mundy, Chair/Advisor
Dr. Stephen Rinehart, Co-Advisor
Professor Andrew Harris
Dr. Marc Pound
Professor Eun-Suk Seo
©c Copyright by
Arnab Dhabal
2018

Acknowledgments
This thesis has been a great learning experience, and I am grateful to many
people without whose contributions this work would not have been possible. First
and foremost, I thank my two advisors Lee Mundy and Stephen Rinehart for guiding
me through this thesis. I learned a lot by following their examples. Even though
they are quite different from each other in their approach, they always had the
right advice for me whenever I needed it. They encouraged me to take on research
projects, gave me a lot of freedom in how I conducted the research and how I
paced myself. I thank Andrew Harris for being a great teacher and ensuring that
I broaden the scope of my thesis during the early years. I thank Marc Pound for
his guidance during the CARMA summer school, where I appreciated the power of
interferometry for the first time. I thank Eun-Suk Seo for accepting to serve on my
thesis committee.
I am grateful to the entire BETTII team. I feel privileged to have worked with
such a motivated group of people –Maxime Rizzo, Jordi Vila, Todd Veach, Roser
Juanola-Parramon, Dale Fixsen, Elmer Sharp, Steve Maher and Robert Silverberg.
Over the course of developing the instrument, I have shared lots of experiences with
them especially during the two flight campaigns. Maxime has been a great mentor,
and I loved having discussions with him on various technical aspects of BETTII and
interferometry in general. I also learned a lot from Dale, who lives in the Fourier
world, and often provided me glimpses into that wonderland. I thank Eric Mentzell
and Henry Sampler for guiding me in the fields of optics and metrology, both of
ii
which are crucial components of my thesis.
I thank Peter Teuben who was always there to sort out my ‘troubles’ with
the CARMA and VLA interferometric data. It has been a great experience working
with him –discussing ideas and implementing suggestions that shaped my thesis. I
have sought Shaye Storm’s help on several occasions (more so, since he graduated),
and he always had the answers ready for me. I thank him for his feedback as well
which helped improve the analysis I carried out for some of the interferometric data.
I also thank the other members of the LMA group for useful discussions on a variety
of topics related to star formation and molecular clouds.
I thank the UMD Astronomy departmental staff, in particular Eric McKenzie,
MaryAnn Phillips, Adrienne Newman and Susan Lehr, who were always there to
assist me. I thank my classmates, Drew and Qian for being great friends. I loved
those adventures with Qian especially during the first two years in College Park.
I am grateful to Vicki, Krista and Maggie for helping me get integrated into the
department and providing me with guidance all along. Friends outside the depart-
ment also played an important role in helping me unwind; thank you Saurabh, Amit,
Shweta, Swarnav, Arka, Apara, Mahashweta and Santanu.
My family has played a very important role in shaping who I am. I attribute
my inquisitive nature and analytical bent of mind to my father. From my mother,
I learned that family is more important than God. In my sister, I always had
the companion who unconditionally supported me. I take this opportunity to thank
them for always being by my side and making me capable of taking my own decisions
from a very early age.
iii
I thank my teachers and friends from my alma mater CBS who were like my
second family during my childhood. Many of them have left a lasting impression
on me. I still love going back to those days especially with Arpan and Aritra.
Another person who inspired me to become a scientist is late Prof. P. K. Chatterjee.
With him, Sunday mornings were fun times spent in doing various experiments and
hearing stories of the lives of different scientists across the world.
I thank my friends from IIT Kanpur with whom I developed wonderful memo-
ries over the 5 years I spent there. I would like to thank my wing-mates, particularly
Siddharth, Harshal, Laxmikant, Vishesh and Viresh. I thank my Physics mates Raz-
iman, Vivek, Siddhardh and Mani. Raziman was the one who taught me the first
steps in astronomy, in addition to being a great friend and experiment-partner. I
thank the entire Jugnu nano-satellite team, and Shantanu in particular for inculcat-
ing in me a team spirit for the first time. I am grateful to my advisors S. Dhamodaran
and M.K. Verma, with whom I worked on experimental physics projects. I gained
two of my closest friends during this period, Shubhayu and Diptarka. Thank you
both for being an important part of my life.
Finally, I am grateful to my life-partner Ayoti who makes everything worth
it. With you around, I always feel confident to take on challenges. The thesis work
would not have been possible without you by my side.
iv
Table of Contents
Acknowledgements v
List of Tables viii
List of Figures ix
List of Abbreviations xi
1 Introduction 1
1.1 Molecular Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Spectral lines as probes . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Filaments in Molecular Clouds . . . . . . . . . . . . . . . . . . 9
1.2 Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Long-baseline Interferometry . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Ground-based Interferometry: Radio Telescope Arrays . . . . 16
1.3.2 Air-borne Interferometry: Balloon Twin Telescope . . . . . . . 20
2 Morphology and Kinematics of Molecular Cloud Filaments 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 CARMA Observations of Perseus and Serpens . . . . . . . . . . . . . 26
2.3 Results: Moment Maps . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.1 Serpens South - NW Region . . . . . . . . . . . . . . . . . . . 38
2.4.2 Serpens South - E Region . . . . . . . . . . . . . . . . . . . . 40
2.4.3 Serpens Main - Cloud Center and E Filament . . . . . . . . . 43
2.4.4 Serpens Main - S Region . . . . . . . . . . . . . . . . . . . . . 45
2.4.5 NGC 1333 - SE Region . . . . . . . . . . . . . . . . . . . . . . 48
2.5 Filament Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5.1 Physical parameters of tracers . . . . . . . . . . . . . . . . . . 51
2.5.2 Filament Widths . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5.3 Multiple Structures . . . . . . . . . . . . . . . . . . . . . . . . 57
2.5.4 Absorption Features in HNC . . . . . . . . . . . . . . . . . . . 58
2.5.5 Filaments in relation to star formation . . . . . . . . . . . . . 60
2.6 Filament Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.6.1 Velocity gradients across filaments . . . . . . . . . . . . . . . . 63
2.6.1.1 Implications on filament formation mechanism . . . . 65
2.6.2 Velocity gradients along filaments . . . . . . . . . . . . . . . . 66
2.6.2.1 Core Mass Estimation . . . . . . . . . . . . . . . . . 67
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
v
3 Ammonia Mapping 72
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2 VLA Observations of Perseus . . . . . . . . . . . . . . . . . . . . . . 75
3.3 Combination of Interferometric and Single Dish Data . . . . . . . . . 76
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4.1 Ammonia (1,1) Results . . . . . . . . . . . . . . . . . . . . . . 85
3.4.2 Ammonia (2,2) Results . . . . . . . . . . . . . . . . . . . . . . 97
3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.1 Optical Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.2 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.5.3 Column Density . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.6.1 Cloud Morphology . . . . . . . . . . . . . . . . . . . . . . . . 112
3.6.2 Cloud Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.6.3 Filaments in NGC 1333 and their relation to Star Formation . 117
3.6.3.1 Filament formation by colliding turbulent cells . . . 117
3.6.3.2 Effect of Outflows on Filaments . . . . . . . . . . . . 119
3.6.3.3 Star Formation . . . . . . . . . . . . . . . . . . . . . 121
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4 The Balloon Experimental Twin Telescope for Infrared Interferometry 125
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.2 Studying Star Formation Using BETTII . . . . . . . . . . . . . . . . 126
4.3 Instrument Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.4 Engineering Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.5 BETTII: Looking Forward . . . . . . . . . . . . . . . . . . . . . . . . 134
5 BETTII Optics 136
5.1 Optical Layout and Design . . . . . . . . . . . . . . . . . . . . . . . . 136
5.2 Design Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.2.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.2.1.1 Aluminum Mirrors . . . . . . . . . . . . . . . . . . . 140
5.2.1.2 Dichroics and Filters . . . . . . . . . . . . . . . . . . 142
5.2.2 Heat Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.2.3 Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.3 Delay Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.3.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.3.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.3.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.3.4 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.4 Flight Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.5 Optics Re-design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
vi
6 Optics Alignment 163
6.1 Tolerancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.1.1 Simulations Using Optical Software . . . . . . . . . . . . . . . 165
6.1.2 Interferometric Visibility Analysis . . . . . . . . . . . . . . . . 166
6.2 Alignment Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2.1 Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2.1.1 Laser Tracker . . . . . . . . . . . . . . . . . . . . . . 170
6.2.1.2 Theodolites . . . . . . . . . . . . . . . . . . . . . . . 171
6.2.2 Telescope Assembly . . . . . . . . . . . . . . . . . . . . . . . . 173
6.2.3 Warm Delay Line and K-mirror . . . . . . . . . . . . . . . . . 177
6.2.4 Siderostats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.2.5 Far-infrared Optics . . . . . . . . . . . . . . . . . . . . . . . . 183
6.2.6 Relative Alignment of FIR, NIR and External Optics . . . . . 188
6.2.7 Control System Measurements . . . . . . . . . . . . . . . . . . 191
6.3 NIR Alignment Test and Results . . . . . . . . . . . . . . . . . . . . 193
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7 Interferometric Simulations 199
7.1 Mathematical Formalism . . . . . . . . . . . . . . . . . . . . . . . . . 200
7.2 Protostellar Physical Parameter Sensitivities . . . . . . . . . . . . . . 207
7.2.1 Hyperion Protostar Modeling . . . . . . . . . . . . . . . . . . 208
7.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.3 Dispersive Backend Simulations . . . . . . . . . . . . . . . . . . . . . 215
7.3.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
7.3.2 Simulations and Recovered Spectra . . . . . . . . . . . . . . . 217
7.4 Path to Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . 222
8 Conclusion 225
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Bibliography 253
vii
List of Tables
2.1 Summary of Observations . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Observed Molecular Lines . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Widths and gradient statistics of filamentary structures . . . . . . . . 40
3.1 Observed Molecular Lines . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Properties of the original and combined NGC 1333 images . . . . . . 79
5.1 Delay Line control and knowledge requirements . . . . . . . . . . . . 148
5.2 BETTII-2: SW and LW band specifications . . . . . . . . . . . . . . 161
6.1 Alignment Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
viii
List of Figures
1.1 Molecular Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Protostar Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Spectral Energy Distributions from Protostars . . . . . . . . . . . . . 11
1.5 Interferometry Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Baseline Coverage and PSF . . . . . . . . . . . . . . . . . . . . . . . 18
2.1 Herschel images and N +2H observations of CLASSy observed regions 25
2.2 Serpens South - NW region : Observation Results . . . . . . . . . . . 30
2.3 Serpens South - E region : Observation Results . . . . . . . . . . . . 31
2.4 Serpens Main - cloud center and E filament : Observation Results . . 31
2.5 Serpens Main - S region : Observation Results . . . . . . . . . . . . . 32
2.6 NGC 1333 - SE region : Observation Results . . . . . . . . . . . . . . 33
2.7 Serpens South - NW region : H13CN observation results . . . . . . . . 34
2.8 Serpens South - NW region : Analysis . . . . . . . . . . . . . . . . . 39
2.9 Serpens South - E region : Analysis . . . . . . . . . . . . . . . . . . . 41
2.10 Serpens Main - Cloud Center and E Filament : Analysis . . . . . . . 43
2.11 Serpens Main - S region : Analysis . . . . . . . . . . . . . . . . . . . 46
2.12 NGC 1333 - SE Region : Analysis . . . . . . . . . . . . . . . . . . . . 50
2.13 Filament Widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.14 Absorption Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.15 Schematic of filament cross-section to demonstrate velocity gradients
across them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.16 Filament schematic for core mass calculation . . . . . . . . . . . . . . 67
3.1 GBT and VLA visibilities . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2 Comparisons of combined map with only VLA map . . . . . . . . . . 81
3.3 Comparisons of combined map with GBT map . . . . . . . . . . . . . 82
3.4 Flux Comparisons for different weights . . . . . . . . . . . . . . . . . 83
3.5 Comparisons of combined maps using different weights . . . . . . . . 84
3.6 NH3 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.7 NH3 (1,1) Integrated Intensity map . . . . . . . . . . . . . . . . . . . 88
3.8 NH3 (1,1) main component peak intensity map . . . . . . . . . . . . . 90
3.9 NH3 (1,1) satellite components peak intensity map . . . . . . . . . . 91
3.10 NH3 (1,1) line-of-sight velocity map . . . . . . . . . . . . . . . . . . . 92
3.11 NH3 (1,1) velocity dispersion map . . . . . . . . . . . . . . . . . . . . 93
3.12 NH3 (2,2) intensity maps . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.13 NH3 (1,1) optical depth map . . . . . . . . . . . . . . . . . . . . . . . 101
3.14 NH3 (1,1) excitation temperature map . . . . . . . . . . . . . . . . . 104
3.15 NH3 rotational temperature map . . . . . . . . . . . . . . . . . . . . 105
3.16 NH3 kinetic temperature map . . . . . . . . . . . . . . . . . . . . . . 106
3.17 NH3 column density map . . . . . . . . . . . . . . . . . . . . . . . . . 111
ix
3.18 Comparison with N H+2 integrated intensity map and JCMT 850 µm
map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.19 Comparison with N +2H velocity map . . . . . . . . . . . . . . . . . . 115
4.1 BETTII Model and Image . . . . . . . . . . . . . . . . . . . . . . . . 127
4.2 Science Target: S140 . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.3 BETTII Launch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.1 BETTII Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.2 Telescope Assembly and Optics Bench . . . . . . . . . . . . . . . . . 141
5.3 Optics assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.4 Filter Transmission Curves . . . . . . . . . . . . . . . . . . . . . . . . 143
5.5 Delay Lines Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.6 Warm Delay Line results . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.7 Cold Delay Line results . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.8 Thermometry data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.9 Pendulation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.10 Warm Delay Line - Flight Operation . . . . . . . . . . . . . . . . . . 157
5.11 Cold Delay Line - Flight Operation . . . . . . . . . . . . . . . . . . . 158
5.12 BETTII-2 Internal Optics Changes . . . . . . . . . . . . . . . . . . . 159
5.13 New post beam-combiner optics . . . . . . . . . . . . . . . . . . . . . 160
6.1 Ray-trace Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.3 Alignment References . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.4 Telescope Assembly Flat Alignment . . . . . . . . . . . . . . . . . . . 175
6.5 Telescope Assembly Alignment using Theodolites . . . . . . . . . . . 176
6.6 K-Mirror and Warm Delay Line Assemblies Alignment . . . . . . . . 179
6.7 Siderostat Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.8 FIR Alignment Flowchart . . . . . . . . . . . . . . . . . . . . . . . . 184
6.9 Optics Bench Alignment . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.10 Star Camera Measurement . . . . . . . . . . . . . . . . . . . . . . . . 193
6.11 Star Transits across NIR Detector . . . . . . . . . . . . . . . . . . . . 195
7.1 Basic schematic of a two aperture interferometer . . . . . . . . . . . . 201
7.2 BETTII Interferometry Simulations . . . . . . . . . . . . . . . . . . . 206
7.3 BETTII observation simulation of 2 close point sources . . . . . . . . 207
7.4 Hyperion Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.5 Amplitude and Visibility variations with protostar orientation . . . . 211
7.6 Amplitude sensitivity of the BETTII bands to protostar inclination
angle and disk mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
7.7 Amplitude and Visibility sensitivity to Disk and Envelope masses . . 214
7.8 Dispersive Backend Simulation . . . . . . . . . . . . . . . . . . . . . . 219
7.9 Recovered Spectra from Simulations . . . . . . . . . . . . . . . . . . . 220
x
List of Abbreviations
ALMA Atacama Large Millimeter/submillimeter Array
BETTII Balloon Experimental Twin Telescope for Infra-red Interferometry
c2d cores to disks
CARMA Combined Array for Research in Millimeter-wave Astronomy
CASA Common Astronomy Software Applications
CCMG Compensated Control Moment Gyro
CHARA Center for High Angular Resolution Astronomy
CLASSy CARMA Large Area Star Formation Survey
CDL cold delay line
DEC Declination
ESA European Space Agency
EVLA Expanded Very Large Array
FIR far-infrared
FIRI Far Infrared Interferometer
FOV field of view
FTS Fourier Transform Spectroscopy
FWHM full width at half maximum
GBT Green Bank Telescope
GMC Giant Molecular Clouds
GSFC Goddard Space Flight Center
IF intermediate frequency
JCMT James Clark Maxwell Telescope
JWST James Webb Space Telescope
LO local oscillator
LOS line of sight
LTE Local Thermodynamic Equilibrium
LW long wavelength
MIRIAD Multichannel Image Reconstruction, Image Analysis and Display
MCE Multi-Channel Electronics
MEM Maximum Entropy Method
MHD magneto-hydrodynamic
MRO Magdalena Ridge Observatory Interferometer
NASA National Aeronautics and Space Administration
NEP noise-equivalent power
NIR near-infrared
NIST National Institute of Standards and Technology
NPOI Navy Precision Optical Interferometer
OPD optical path length difference
OVRO Owens Valley Radio Observatory
xi
PACS Photoconductor Array Camera and Spectrometer
PID proportionalintegralderivative
PMS pre-main sequence
PSF point spread function
RA Right Ascension
RMS root mean square
SED Spectral Energy Distribution
SHARP-IR Space High-Angular Resolution Probe for the InfraRed
SKA Square Kilometer Array
SNR signal-to-noise ratio
SMA Sub-millimeter Array
SOFIA Stratospheric Observatory for Infrared Astronomy
SPECS Submillimeter Probe of the Evolution of Cosmic Structure
SPIRIT Space Infrared Interferometric Telescope
SPIRE Spectral and Photometric Imaging Receiver
SW short wavelength
TES transition-edge sensor
VLA Very Large Array
VLBA Very Long Baseline Array
VLBI very-long-baseline Interferometry
VLTI Very large Telescope Interferometry
WDL warm delay line
YSO young stellar object
xii
Chapter 1
Introduction
Stars are commonly formed in dense regions of interstellar medium called
molecular clouds. The clouds typically have masses in the range 104 − 106 times
the solar mass (M) and sizes ranging from 10s to 100s of light years [1]. The
low temperatures (10 − 20 K) and high densities (n = 102 − 105 cm−3) of these
clouds containing molecular Hydrogen provide the ideal conditions in which stars
can form [2]. The molecular clouds are considered to have a hierarchical structure
with stellar clusters forming out of clumpy and filament-like gas distributions, and
individual stars (or binaries or small multiple systems) within the cluster forming
from gravitationally bound cores [3, 4]. In terms of the physical processes involved,
there is a competition between self-gravity trying to collapse a part of the molecular
cloud and various pressure forces like thermal pressure, turbulence and magnetic
fields supporting it from collapsing [5, 6]. The relative importance of each of the
these forces is debatable. Eventually, often triggered by shocks, the balance between
the forces is disturbed and gravitational collapse begins giving birth to a protostar.
Over the subsequent period in its evolution (∼ 100,000 years), the protostar
rapidly accumulates material from a surrounding envelope of rotating gas and dust.
This leads to the formation of an accretion disk through which matter is channeled
1
Figure 1.1: Herschel image of a molecular cloud about 450 light years away in the
constellation Taurus. The image shows the presence of filament like structures in
the molecular cloud. (Image credit: ESA)
onto the protostar. Coinciding with this accretion, to conserve angular momentum,
there is a steady outflow of material from the poles of the protostar driven by dense
collimated jets [7]. Gradually the circumstellar envelope disperses, and the protostar
enters its next evolutionary stage – a pre-main sequence (PMS) star. As the density
of the central part of the PMS star increases, its temperature rises to millions of
Kelvin. About 50 million years from the commencement of gravitational collapse,
the temperature reaches the fusion temperature of Hydrogen, which gets converted
to Helium, and the star enters the main-sequence.
1.1 Molecular Clouds
Molecular clouds contain most of the molecular Hydrogen gas within galaxies.
They are dense condensations in the more widely distributed interstellar medium
(comprised mainly of atomic gas). There are over 1000 identified clouds in the Milky
Way [8]. Of these, the local molecular clouds located within a distance of 500 pc like
2
Figure 1.2: Model of a protostar showing its structure consisting of a circumstellar
disk, an envelope and bipolar outflows. Image from Greene (2001) [2].
Orion, Taurus, Perseus, Serpens, Rho-Ophiucus and Lupus are of particular interest
in the study of star formation. They are present in a ring in the neighborhood of
the Sun and coincide with the Gould Belt, which is an area rich in star formation.
The typical age of the molecular clouds is 10 million years. Structures within
these clouds are transient in the context of astronomical timescales [9]. They are
formed by large scale gravitational instabilities in the Galactic gas layer due to
spiral shocks, swing-amplified spiral arms, expanding shells and other dynamical
structures that form by turbulence [10]. The cloud formation may be aided by col-
lisions and coalescence of smaller clouds [11]. When the column densities of the
accumulated material are high enough, the atomic gas gets shielded from the far
ultraviolet photons, and Hydrogen atoms can combine to form molecules without
getting dissociated. In addition to molecular Hydrogen, the clouds also contain He-
lium (0.1 by mole fraction), dust (1% by mass), CO (∼ 10−4 by mole fraction) and
3
traces of many other molecules. The relative abundances of various molecules indi-
cate that they are not in chemical equilibrium. The observed abundances resemble
predictions at an early stage of chemical processing [12].
1.1.1 Spectral lines as probes
Although H2 is the main component of these clouds, CO, the next most abun-
dant molecule is widely used as a probe to study the molecular clouds [13] because
CO molecules have a permanent dipole moment, unlike H2. Simple linear molecules
like CO have quantized rotational energy levels (denoted by the total angular mo-
mentum quantum number ‘J’). For linear molecules, the rotational energy at level
J is given by
h2
Erot = J(J + 1) (1.1)
8π2I
where h is the Planck’s constant and I is the moment of inertia of the molecule
about an axis perpendicular to the line joining the nuclei and passing through the
center of mass of the molecule. Transitions between these energy levels can be
associated with photon emission or absorption. Quantum-mechanical selection rules
for photons require ∆J = ±1. For CO, the frequency of this spectral line emission
is in multiples of 115 GHz which can be observed using mm-wavelength telescopes.
A limitation with some of the molecular transition emissions is related to their
absorption by the cloud. Depending on the abundance of a certain molecular species,
the emission from the interior of the cloud may get absorbed by the regions closer to
us in the line of sight, thereby reducing the observed emission. The optical depth τ
4
is a measure of this absorption, and it indicates whether the emission being observed
corresponds to the entire cloud (optically thin: τ  1), or just the outer layers of
the cloud closest to the observer (optically thick: τ & 1). If observations with a
certain molecular transition are not optically thin, less abundant isotopologues of
the same molecule can be used to probe the cloud. For example, 13CO and C18O
are often observed instead of CO to account for optical depth.
The emission also depends on the gas temperature and density. Molecules can
be excited into higher states by collisions in the gas and by ambient radiation. In
optically thin media where the photon escape probabilities are higher, the ambient
radiation is not as important as collisions in exciting the molecules. A minimum
temperature (∼ Erot/k where k is the Boltzmann constant) is required to excite
the molecules to a level having energy Erot. After getting excited to higher energy
states, the molecules transition back to the lower energy states via emission or
collisions downward. Thus based on Equation 1.1, higher temperatures are required
to populate the higher J levels and to have any detectable emission due to downward
transitions from these levels.
In addition to this minimum temperature requirement, there is also a minimum
density requirement at which the upper level of a transition begins to get significantly
populated. As a simple approximation, a level becomes significantly populated
when the rate of upward collisional transitions is equal to the rate of radiative
transitions downward. In the optically thin limit, this critical density can be defined
as Aul/γul [14]. Aul is the Einstein A coefficient in s
−1 which gives the rate of
spontaneous emission, and γul is the collision rate coefficient in cm
3 s−1 for the
5
downward transition at a given temperature. For CO J=1-0 transition, the critical
density is 1400 cm−3 at 25 K, and so this transition is a good probe for gas at
comparable densities [15]. Of the two factors on which the critical density depends,
Aul is proportional to the cube of the transition frequency and to the square of the
dipole moment of the molecule, while γul has a weak dependence on temperature.
Based on the frequency dependence of Aul, high frequency transitions (corresponding
to higher energy levels or molecules with lower values of moments of inertia) have
significantly higher values of critical density. It is important to note that this critical
density value is only an approximation, and at higher optical depths where radiative
trapping becomes important, it can lower the effective critical density. On the
other hand, for transitions at low frequencies (< 50 GHz), stimulated emission is
important, and this results in a higher effective critical density.
The molecular clouds are not uniformly dense over their characteristic sizes
of ∼ 50 pc. The gas is distributed into denser regions, such as clumps or fila-
ments (typical size scales of about 0.2 pc), which can have 1000 times the density
of the remaining cloud [17]. To probe the denser regions, we need to choose molec-
ular transitions that have a higher critical density. Molecules that have a higher
dipole moment have a greater Aul value and consequently a greater critical density.
Molecules such as CS, N H+, HCO+2 , HNC and HCN progressively probe higher
density regions from 104 cm−3 to 106 cm−3 for transitions in the 3 mm wavelength
range [18].
The molecules discussed so far are all linear molecules and so their rotational
energy levels are defined by a single quantum number. Nonlinear symmetric-top
6
Figure 1.3: Left: The CO molecule rotational energy levels below 100 K. The CO
molecule is linear and has a single quantum number J to describe the energy lev-
els. Spectral lines are associated with ∆J = ±1 transitions between these levels.
The frequencies corresponding to these transitions are indicated. Right: The NH3
molecule rotational energy levels below 100 K. Due to its pyramidal structure, it
requires two quantum numbers J and K to define its energy levels. Additionally the
K 6= 0 rotational levels are further split into two inversion levels (+ and −). The
notation used alongside the levels is J±K . Of the transitions indicated in the image,
the inversion transitions for (J,K) = (1,1) and for (2,2) are important to probe the
kinetic temperature of the gas. Images adapted from Mangum & Shirley (2015) [16]
7
molecules require an additional angular momentum quantum number K to define
their energy states. Relative intensities of the various possible transitions of such
molecules are good probes of the kinetic temperature of the emitting medium [19].
CH3CN and NH3 are examples of symmetric-top molecules. The NH3 molecule has
a further peculiarity due to its pyramidal structure in which the N atom can tunnel
through the plane formed by the 3 H atoms. This results in inversion splitting of
each (J,K) rotational level for K≥1 (see Figure 1.1.1). Transitions between these
split levels for different (J,K) energy levels all occur at similar frequencies near
24 GHz. So they trace similar densities, but since the relative populations of the
different (J,K) states are primarily determined by collisions, we can determine the
gas temperature using the population ratios. In NH3, the lower-most J level in each
K-ladder, i.e. the J=K states, are most populated due to radiative de-excitation.
With respect to the (1,1) level, the (2,2) (3,3,) and (4,4) energy levels are 41 K, 100
K and 176 K higher in terms of E/k. Since the level population of the bottom level
of each K-ladder [(2,2), (3,3), (4,4), etc] is determined primarily by collisions, and
hence approximately gas temperature, these lines are useful for different temperature
ranges. For gas temperatures comparable to, or down to factor of 3-4 less than the
level energy, a specific inversion transition is a good probe of the temperature. For
example, the (1,1) and (2,2) line is good for gas temperatures in the range of 8-50 K.
For higher temperatures, a range of 60-200 K, the (4,4) line is a good probe of the
temperature. The (4,4) line is not a practical probe of temperatures in the range of
8-50 K simply because the level populations are too low to be observable. In this
discussion, we have skipped the (3,3) level because it is the ortho species (K = 3n
8
where n is a non-negative integer), not the para species, and comparison between
species add the complication of the para to ortho abundance ratios.
1.1.2 Filaments in Molecular Clouds
Molecular clouds are generally turbulent, showing supersonic line widths and
complex magnetic fields which play crucial roles in the cloud dynamics. Supersonic
turbulence can result in the creation of over-dense flattened structures [3]. Driven
by turbulence over a wide range of scales, the clouds fragment into a network of
denser material. Some parts of the network achieve high enough mass per unit
length to become strongly self-gravitating. They contract into narrower filaments
and accrete material from the surrounding flattened structure. Herschel far infrared
images have demonstrated the prevalence of filamentary structure over a very wide
range of scales and trace those structures into areas of active star formation [20, 21].
Numerical hydrodynamic and MHD simulations of molecular clouds also point to
the importance of planar and filamentary structures which are created by collisions
of turbulent cells within the cloud [22, 23].
The filaments form the bridge between molecular clouds and protostars. It
is suggested that as these filaments become more massive, they fragment due to
gravitational instability leading to the formation of protostellar cores [24]. Although
it is inconclusive whether this scenario gives the complete picture, there is no doubt
that filaments play an important role in the birth of protostars. The morphologies
and kinematics of these filaments hold the key to many answers related to star
9
formation processes. In Chapters 2 and 3 of this thesis, we use dense gas observations
of filaments to investigate their formation in the molecular clouds and their role in
star formation.
1.2 Star Formation
The prestellar cores in the dense regions of the molecular clouds undergo grav-
itational collapse to form protostars. Until the star enters the main sequence, they
are called young stellar objects (YSOs). As the YSOs accumulate mass from the en-
velope of gas around it through an accretion disk, the central core and disk heats up
by the accretion shocks at their surface to temperatures above 2500 K [25] and emit
like a blackbody. This emission typically peaks in the optical wavelengths but they
get absorbed by the dust grains surrounding the core. The dust, which is mostly
composed of sub-micron graphite and silicate grains, then re-radiates at higher far
infrared (FIR) wavelengths which is observable (Figure 1.2). This results in infrared
emission from the dust accounting for ∼ 30% of the total observed luminosity of our
galaxy [26], even though the dust to gas ratio is only 1:100 by mass.
Over the course of its evolution, the protostar gradually loses the envelope as
the opening angle of the bipolar outflow cavity increases, clearing away the gas [28].
The inner disk progressively becomes visible, and accordingly the spectral energy
distribution (SED) of the YSOs evolve. The spectral index (α) of the SEDs in the
2 − 20 µm wavelength range is used to classify the evolutionary state of YSOs in
the following sequence: Class 0, Class I, Flat Spectrum, Class II and Class III [29]
10
Figure 1.4: Simulation results from Whitney et al. (2003) [27] showing Spectral
Energy Distributions (SEDs) from a Class 0 YSO viewed at different angles of
inclination (dark green: edge-on; pink: pole-on). The dotted line shows the typical
blackbody spectrum of the central source, which is absorbed by the dust in the
envelope and re-radiated at higher wavelengths to produce the resulting SEDs.
(having monotonically decreasing values of α). Class 0 and Class I YSOs have a
positive value of α, while Class II and III sources have a negative value of α. The
term protostar typically refers to Class 0/I YSOs.
There is another important property of the YSOs that affect their evolution
–they typically form in clusters. Approximately 60% of all stars are thought to
form in embedded, young stellar clusters with 100 or more stars [30]. There are
two factors associated with this clustering. First, the cores tend to form close to
one another within dense regions of molecular clouds, at median distance of 0.07 pc
[31]. Second, in many cases, the cores divide to form binary/multiple protostellar
sources. Approximately 65% of all protostars exist in binary/multiple systems that
share a single envelope [32].
11
In the context of clusters, it is important to understand the timescale and
source of the material being accreted onto the stars, because that determines the
predominant physical processes and the star formation rate. Currently multiple
theories exist attempting to explain this: Core Accretion, Competitive Accretion
and Collisional Mergers [33, 34]. To understand which of the three models is most
accurate, there is a requirement for resolving the emissions from these young stellar
objects (YSOs) to account for the mass distribution at different stages of evolution.
The transition from disk to envelope occurs somewhere in between 10s of AU to
1000s of AU from the protostellar core. ALMA, with its unprecedented resolution
and sensitivity will improve our understanding of these regions. However, average
temperatures in these regions, ranging from 50− 150 K [35, 36], result in consider-
able amounts of FIR emission from the dust. Thus ALMA can trace only part of
the Rayleigh-Jeans tail of the dust emission. To better constrain the protostellar
physical parameters and the accretion models, we need high resolution FIR obser-
vations. Since the atmospheric transmittance at these wavelengths is low, there is
a growing requirement for space-based FIR interferometry. Development of a pre-
cursor balloon experiment for spatio-spectral interferometry is studied in this thesis
from Chapters 4 to 7.
1.3 Long-baseline Interferometry
The angular resolution of single dish telescopes is limited by their diameters.
For a circular aperture of diameter D, at any wavelength λ, the smallest resolvable
12
Figure 1.5: Point Spread Functions corresponding to a single dish telescope (top)
and two apertures (bottom) showing the angular resolution limit in the two cases.
angular distance is proportional to λ/D based on the Airy diffraction pattern. A
single dish radio telescope of 100 m diameter like the Green Bank Telescope pro-
vides a resolution of 7500 AU for typical molecular cloud distances of 300 pc, at
a wavelength of 1 cm. At FIR wavelengths, space-based single aperture telescopes
like Herschel with an aperture diameter of 3.5 m provided comparable resolution
at 350 µm. In the study of star formation, imaging at higher resolution from the
optical to radio wavelengths is of utmost importance to probe the environment near
protostellar sources and constrain the masses participating in the star formation
process. Since it is not feasible to make extremely large apertures (of sizes 10 times
or more compared to the largest existing facilities), an alternative approach based
on interferometry is used to obtain high resolution images.
In the context of astronomy, interferometry involves collecting light from mul-
tiple apertures and combining them, thereby measuring the interference pattern
13
produced by pairs of apertures. The line joining a pair of apertures is called a
baseline vector B~ , which is generally normalized by the wavelength and defined in
a coordinate system (u, v) based on the four cardinal points on the earth’s surface.
Mathematically, B~/λ ≡ (u, v). Observations are carried out at multiple baselines.
The maximum baseline B sets the angular resolution, and is given by λ/2B (Figure
1.3.1). The observation output at each baseline is called visibility. It is the Fourier
transform of the spatial distribution T (x, y) of the brightness of the observed ob-
ject in the sky plane angular coordinates (x, y) (also defined based on the Earth’s
cardinal points). The visibility V is given by
∫ ∫
V(u, v) = T (x, y)e2πi(ux+vy)dxdy (1.2)
This is called the van Cittert-Zernike theorem. The measured visibility has an
amplitude and a phase, which depends on the source brightness and the difference
in the optical path length from the source to the pair of apertures. The phase gives
information about the source location, while the amplitude tells us how much flux
is present at a particular frequency. In principle, an inverse Fourier transform of the
visibilities can reproduce the sky map. However, in most interferometers, the base-
lines only sample a small part of the entire (u, v) plane. Thus a weighting function
is required along with the visibility function to obtain the high resolution sky map.
Even then, non-uniform u-v coverage presents various challenges in reproducing the
image plane and involve ‘aperture synthesis’. Even though the angular resolution of
an interferometer is of the same order as that of a single aperture of diameter equal
14
to the largest baseline, the sensitivity is determined by the size of the collectors.
So interferometers are significantly less sensitive than single apertures providing the
same angular resolution.
Interferometers were first used in astronomy to obtain angular diameters of
sources. The spacing between the two apertures in a Michelson interferometer was
increased and visibility amplitudes (fringe visibility) recorded until a minima was
obtained, from which the angular diameter was derived [37, 38]. With improve-
ments in technology, it became possible to measure both amplitude and phase of
the visibilities [39]. The number of apertures was increased and tracking antennas
were developed which increased the (u, v) plane coverage (as in the Cambridge One
Mile Telescope [40]). Spectral line capabilities were introduced in the Owens Valley
Radio Observatory (OVRO) in the 1960s [41]. The distance between apertures was
increased from 100s of meters to a few kilometers (for example, in the former Green
Bank Interferometer and the Very Large Array [42]) and eventually to hundreds of
kilometers with the advent of very-long-baseline interferometry (VLBI) [43]. The
combination of electromagnetic signals is more challenging in VLBI and requires
recording the signal with extremely precise atomic clocks. The Very Long Baseline
Array (VLBA) [44] which uses this technique has a maximum baseline of 8611 km.
The upcoming Square Kilometer Array (SKA) [45] which also has baselines of 3000
km, will have the added advantage of high sensitivity with its total collecting area
of approximately one square kilometer.
Gradually the techniques were extended to mm and sub-mm wavelengths in
the 1980s and 1990s. This led to development of arrays like SMA [46], CARMA
15
[47] and more recently ALMA [48]. Simultaneously, advancements were made in the
near infra-red (NIR) and optical wavelengths, which require more precise optics to
maintain the phase information at these smaller wavelengths. The closure phases
and bispectrum are more useful observables for obtaining the phase and amplitude
information at NIR/optical wavelengths[49]. The CHARA array [50], NPOI[51]
VLTI [52] and the under-development MROI [53] are all cutting edge in the field of
interferometry between 480 nm and 2.5 µm. Some of these facilities use variants of
interferometric techniques such as nulling interferometry and speckle interferometry
[54]. Now, NIR interferometry is set to be used in space in the form of non-redundant
aperture masking interferometry on JWST [55].
1.3.1 Ground-based Interferometry: Radio Telescope Arrays
Most radio arrays contain many telescopes/antennas ranging from 8 for SMA
to 66 for ALMA. Sometimes, they have dishes of different diameters, for better
sensitivity on all scales. A set of N antennas results in NC2 or N(N−1)/2 baselines.
On top of this, the tracking of the sources as the earth rotates, results in elliptical
arcs of baseline coverage in the (u, v) plane (see Figure 1.3). The arrays typically
have some fixed configurations in which they are used. They are moved around from
time to time to change configurations. The different configurations give different
ranges of spatial sensitivity and resolution.
The incoming radiation that is collected using each antenna is measured by
sensitive cryocooled receivers within its passband. The signals are mixed with a
16
local oscillator (LO) signal to convert to a lower frequency called the intermediate
frequency (IF). This allows amplification and digitization of the signal, before it is
transferred to the correlators (which could be located a large distance away). The
signals from the various pairs of antennas are combined in the correlators, thereby
producing the visibility amplitude and phase information [56]. In case of spectral
line observations, the passband of each receiver is divided into a number of channels
at the IF stage. For each channel, a separate correlator combines the signals from
the antenna pairs. This entire process is called heterodyne beam combination.
Calibration of the visibility measurements is very important in radio inter-
ferometry. The three main types of calibration are bandpass calibration, phase
calibration and amplitude calibration. Bandpass calibration corrects for variations
in the receiving system gain with frequency across the observing band. This is done
by observing a strong source with a known spectrum not having any spectral lines
at the beginning of each observing track. (Each track typically lasts a few hours.)
Phase calibration is done to compensate for the temporal variations of the phase of
the correlated signal on different baselines. The variations arise due to fluctuations
in the water vapor content of the atmosphere. Phase calibration involves observing
a strong source with a known spectrum and at a small angular distance from the
science target. This observation is carried out at regular intervals (about every 15
minutes) in an observing track. Finally, amplitude calibration involves observing a
source with a known flux once in an observing track to compensate for atmospheric
opacity. For a single pointing of an interferometric array, the field of view depends
on the diameter D of a single telescope and is proportional to λ/D. Sources more
17
Figure 1.6: u-v plane coverages and their corresponding ‘dirty beams’ (inverse
Fourier transforms of the respective u-v plane coverages). The dirty beams rep-
resent the effective PSF. The PSF improves with observations at greater number of
baselines. This can be done by using an array of apertures and/or with the help of
earth’s rotation. Images adapted from presentation by Andrea Isella (2011).
extended than the field of view can be observed using multiple pointing centers
forming a mosaic.
The next step where the visibilities are converted to an image involves aperture
synthesis [57]. The van Cittert-Zernike theorem multiplied with the afore-mentioned
weighting function W (u, v) can be inverse Fourier transformed to get the image
I ′(x, y). W (u, v) is 0 where the (u, v) plane is not sampled, and 1 or a fraction
18
where sampled depending on the weighting scheme (uniform, natural, robust etc.).
∫ ∫
I ′(x, y) = V(u, v)W (u, v)e−2πi(ux+vy)dxdy (1.3)
The image thus obtained is called the ‘dirty image’. The inverse Fourier transform
of the weighting function gives the ‘dirty beam’ B(x, y) (also called the synthesized
beam). ∫ ∫
B(x, y) = W (u, v)e−2πi(ux+vy)dxdy (1.4)
The dirty beam represents the point spread function (PSF) of an interferometric
observation. The dirty beam and image are so called because they contain negative
sidelobes caused by the gaps in the u-v coverage. The dirty image is the convolution
of the true image of the sky with the dirty beam, which needs to be deconvolved to
produce the ‘clean image’ I(x, y).
I ′(x, y) = B(x, y) ~ I(x, y) (1.5)
For this purpose, the dirty beam is fit to a 2D Gaussian function to obtain a ‘clean
beam’ not having the negative sidelobes. After this, different techniques are used
to carry out the deconvolution. One of the famous techniques, ‘CLEAN’ is an
iterative point source subtraction algorithm [58], while there are other techniques like
Maximum Entropy Method (MEM) that involve model fitting until a defined entropy
term is maximized [59]. Dedicated softwares have been developed to handle visibility
data and carry out the calibration, image synthesis, deconvolution and data analysis.
19
MIRIAD (Multichannel Image Reconstruction, Image Analysis and Display) and
CASA (Common Astronomy Software Applications) are two such popularly used
softwares that have been used in this thesis.
In this thesis, we use radio array data in Chapters 2 and 3 from CARMA
and VLA respectively. With CARMA, we map selected filaments in the molecular
clouds using rotational level transitions of optically thin dense gas tracers. With
the VLA, we observe inversion transitions of NH3 to map the NGC 1333 molecular
cloud. Both sets of data involve non-trivial image reconstruction techniques. We
will see in Chapter 3 that even the standard cleaning process cannot always get
rid of the negative sidelobes, and requires u-v coverage near the zero spacings. So
we develop a method to combine single dish images with interferometric data. The
spectral channel data not only maps the dense gas distribution, but also provides
kinematic information for the mapped regions.
1.3.2 Air-borne Interferometry: Balloon Twin Telescope
Far-infrared (FIR) astronomy is crucial for the study of star forming regions
[60]. Ground-based observations are not possible at wavelengths between 15 − 300
µm because the Earth’s atmosphere is effectively opaque at these wavelengths. By
operating above most or all of the Earth’s atmosphere, facilities such as Spitzer,
Herschel, and SOFIA [61] have opened new paths of discovery in the infrared. How-
ever, all of these facilities have been limited in spatial resolution by their aperture
size. The next big step towards higher resolution astronomy in the FIR wavelengths
20
is the development of a space-based interferometer [62, 63]. To provide high angular
resolution in the FIR, interferometric missions such as SPIRIT [64], SPECS [65] and
FIRI [66] have been studied, and a new concept (SHARP-IR [67]) is currently being
explored.
At FIR wavelengths, the challenges are different from those at higher wave-
lengths. Heterodyne detection as is carried out in radio interferometry has basic
limitations on sensitivity at lower wavelengths due to electronics. So the electro-
magnetic fields must be propagated by sensitive optics and interfered optically in
the pupil-plane or the image-plane [68]. Image-plane combination (Fizeau interfer-
ometry) involves multiplexing in the spatial domain and is thus limited in how many
fringes can be observed by the detector array. Thus to get even a modest spectral
resolution large focal plane arrays with many pixels are required, which do not yet
exist for the FIR wavelengths. This means that only pupil-plane combination of
light is feasible at the moment. Combining light beams optically has a limitation
on the number of apertures (and thereby baselines) that can be used. Standard
aperture synthesis techniques are not applicable for poor baseline coverage and it-
erative model fitting is required to derive the image plane data. Additionally, since
the light must be kept coherent within a fraction of a wavelength over long optical
paths, it requires very precise optics.
BETTII (Balloon Experimental Twin Telescope for Infrared Interferometry)
[69] and FITE (Far-Infrared Interferometric Telescope Experiment) [70] are the pi-
oneering experiments being developed to demonstrate long-baseline interferometry
above the earth’s atmosphere. Both these instruments have two apertures and the
21
limited number of baselines that they cover is due to earth’s rotation. Typically
these payloads are flown for less than 24 hours on high altitude balloons, although
their power systems and cryogenic systems may be upgraded to fly longer (∼ 40
days) in circumpolar orbits. Such an instrument also requires a very accurate point-
ing system, which is challenging for a payload suspended from a balloon [71].
The development of BETTII and its optical system is a chief component of this
thesis. BETTII does Fourier Transform Spectroscopy in addition to long-baseline
interferometry to perform spatially resolved spectroscopy in star forming regions.
In Chapters 4 and 5, we discuss the development of BETTII, its current status and
how its optical system is designed to maintain the wavefronts from the two arms
until combination. We discuss the detailed procedure for optics alignment for such
an interferometer in Chapter 6. Finally, in Chapter 7, we carry out simulations
to model the BETTII observations, and understand its sensitivity to protostellar
systems.
22
Chapter 2
Morphology and Kinematics of
Molecular Cloud Filaments
2.1 Introduction
The presence of filaments in molecular clouds has been well known for many
decades [72, 73, 74, 75]. Far infrared continuum images taken by Herschel demon-
strated the prevalence of filamentary structure over a wide range of scales [76, 77].
There is growing observational evidence that filaments play a fundamental role in
the star formation process by setting the initial conditions for core formation and
fragmentation, and defining the morphology of the material available for accretion
[78, 79, 80, 81, 82, 83]. Some cores within filaments evolve to harbor YSOs, the
properties of which depend on the filament physical characteristics [84, 85].
Filaments are also commonly present in numerical simulations of turbulent
molecular gas [22, 86, 87, 88, 89, 90, 91]. These filaments form at the interface
of converging flows in regions of supersonic turbulence. However the impacts of
self-gravity [92], turbulence [93] and magnetic fields [94] on filament formation and
structure are still under study. Filament morphologies, their widths, densities, ori-
entations with each other and with respect to local magnetic fields, can provide
23
important insights into the filament formation process. For example, the system-
atics of filament width could be related to the sonic scale of turbulence [95], ion-
neutral friction [96], or the presence of magnetic fields [97]. Maps using molecular
tracers with high angular resolution and/or high spectral resolution resolved some
filamentary structures further to multiple filaments [98, 99], which are also found in
simulations [92, 94, 100, 101].
The kinematics of filaments [102, 103] can be useful indicators of the evolu-
tionary processes involved in star formation. For example, velocity gradients along
filaments have been postulated either as mass infalls towards the clumps [104],
as projections of large-scale turbulence [105], or as convergence of multiple flows
[106, 107]. On the other hand, a velocity gradient perpendicular to the major axis
has been postulated as effects of filament rotation [108], or infall due to self-gravity
of gas compressed into a planar structures by supersonic turbulence [90, 100]. Su-
personic velocity dispersions are expected in the case of gravitationally accelerated
infalling material which enter the filaments through shocks at the boundaries [89].
This chapter presents high angular resolution maps of dense gas filaments
in three active star formation regions –Serpens Main, Serpens South, and NGC
1333 to study the detailed morphology and kinematics of five filaments. This study
derives from the CARMA Large Area Star Formation Survey (CLASSy), a CARMA
key project which imaged 800 square arcminutes of Perseus and Serpens Molecular
Clouds using the N +2H , HCN and HCO
+ J=1-0 lines [98, 105, 109]. These clouds
host a large number of young stars and protostars associated with hub-filament
type gas structures [110, 111], and are hence well-suited for studying the connection
24
Figure 2.1: Herschel 250 µm maps (Units: Jy beam−1) overlaid with N2H
+ inte-
grated intensity contours (green) from CLASSy observations of the Serpens South,
Serpens Main and NGC 1333 molecular clouds. The contours are at 3σ and 6σ,
where σ = 0.25, 0.7 and 0.4 Jy beam−1 km s−1 respectively for the three regions.
The circles mark the CLASSy-II mosaic pointing centers and indicate the regions
observed. The regions correspond to filaments that we name based on their loca-
tions with respect to the parent cloud cores. The Herschel beam is 18′′ in diameter
(shown in the bottom-right corner of each image).
between filaments and star formation. N2H
+ emission, which is a cold, dense gas
tracer [112], was found to closely follow the far-infrared filamentary structure in
high column density regions [98, 105, 109]. Figure 2.1 shows the N2H
+ emission
overlaid on the Herschel dust continuum emission at 250 µm. The N H+2 emission
also revealed distinctive velocity gradients in a number of filaments. The HCN and
HCO+ emission, on the other hand, were found to be poor tracers of filaments.
Storm et al. (2014) [109] proposed that these lines were optically thick, and in the
case of HCO+ affected by higher fractional abundances in lower density gas which
create an overlying absorption region.
25
To investigate whether the kinematics of filamentary structures are accurately
traced by the CLASSy N +2H observations, we selected 5 filaments from the CLASSy
regions to observe using optically thin dense gas tracers H13CO+ and H13CN. The
mapped regions are marked in Figure 2.1 by the white circles. These molecules
do not have the same chemistry as N +2H ; hence they serve as a test of whether
the observed kinematics is a bulk property of the material or if they arise from
chemical or excitation effects. We refer to the observations presented in this chapter
as CLASSy-II observations.
The layout of the chapter is as follows. In Section 2.2, we discuss how the
observations were carried out followed by the data calibration and reduction proce-
dure. We present the maps for the various tracers for all the regions in Section 2.3.
Section 2.4 deals with analyzing the individual regions and characterizing them. In
Sections 2.5 and 2.6, we report the trends in the morphology and kinematics of these
observed regions. We further discuss some of these results in context of the major
questions in filament formation and their relation to star formation.
2.2 CARMA Observations of Perseus and Serpens
The observations were made using the full CARMA array of 23 antennas in D
and E configurations, providing an angular resolution of 7′′. In CARMA 23-element
mode, the correlator has four bands. In addition to the 13C isotopologues of HCO+
and HCN, HNC was also available in the correlator setting as a third tracer. For
NGC 1333, N H+2 was observed instead of H
13CN. The fourth band was used to
26
Region Name Lines observed Hours observed No. of Synthesized
D E pointings Beam Size*
Serpens South - NW region H13CO+, HNC, H13CN 51.9 41 22 9.1” × 6.8”
Serpens South - E region H13CO+, HNC, H13CN 31.3 20.6 42 8.9” × 6.0”
Serpens Main - cloud center H13CO+, HNC, H13CN 18.6 43.6 30 8.4” × 7.1”
and E filament
Serpens Main - S region H13CO+, HNC, H13CN 24.1 19.4 45 9.5” × 6.4”
NGC 1333 - SE region H13CO+, HNC, N2H
+ 28.7 29 19 7.2” × 5.4”
*Final synthesized beam sizes obtained after Maximum Entropy deconvolution
Table 2.1: Summary of Observations
Lines Frequency ncr@10K Velocity
(GHz) (cm−3)a Resolutionb
(km/s)
H13CO+ J=1-0 86.75429 1.5 × 105 0.169
H13CN J=1-0 86.33986 2.0 × 106 0.170
HNC J=1-0 90.66357 2.8 × 105 0.162
N H+2 J=1-0 93.17370 1.4 × 105 0.158
a Critical densities (ncr) are calculated from the ratio of Einstein A coefficient values Aul and
collision rate coefficients γul. These values are obtained from the Leiden molecular database [15]
and are based on γul values from [113], [114] and [115].
b Calculated based on channel widths of 49 kHz.
Table 2.2: Observed Molecular Lines
observe the continuum at 90 GHz with a bandwidth of 500 MHz. The spectral line
bands were 7.7 MHz wide with 159 channels, providing a resolution of ∼ 0.16 km/s.
The summary of the observations are given in the Table 2.1, while the properties
of the molecular tracer transitions are given in Table 2.2. The observations were
carried out for a total of 308 hours over 61 tracks between August 2013 and February
2015.
Of the three molecular tracers, H13CO+ J=1-0 has the simplest spectrum: a
single line with no hyperfine components. H13CN J=1-0 has three isolated hyperfine
components. HNC J=1-0 [116] has hyperfine components within a range of 200 kHz
27
(0.66 km sec−1), which are barely resolved by our correlator channel width of 49 kHz;
the primary effect is to modestly increase the observed linewidth. For comparison,
N2H
+ J=1-0 has seven hyperfine components, of which three F1=1-1 lines are within
a range of 600 kHz, three F1=2-1 lines within 500 kHz, and one isolated F1=0-1 line.
Although all four molecules are dense gas tracers, H13CN has the highest critical
density ∼ 106 cm−3, while the other transitions have critical densities in the range
1.4− 2.8 ×105 cm−3 (see Table 2.2).
The flux calibrators for individual tracks were MWC349, Mars, Mercury and
Uranus, as available during observations. The phase calibrators were 3C84 and
3C111 for NGC 1333, and 1743-048 for all Serpens regions. Although a bandpass
calibrator was observed in all observation sessions, in many cases the phase calibra-
tors were also used for bandpass calibration.
The MIRIAD package [117] was used to process the visibility data. The autocor-
relation data from the 10 m antennas were used to make single-dish images. After
iterative flagging and calibration of the visibilities, the single dish maps were used
with the interferometric visibility data to generate the data-cubes using the MIRIAD
Maximum Entropy Method program mosmem. The combined deconvolution using
the single dish images helps in recovering the large-scale structure filtered out by
the interferometer [118]. The spectral channel RMS noise is in the range of 50−125
mJy/beam, while the continuum RMS noise is 0.4− 1.0 mJy/beam for the various
fields.
28
2.3 Results: Moment Maps
We generated integrated intensity (0th Moment) and velocity (1st Moment)
maps from the position-velocity data cubes using MIRIAD. We used only the channels
near the line centers containing the signal, and clipped the data at 2σ, based on the
RMS noise of each line map. For the first moment maps of N2H
+ and H13CN, line
fitting including the contribution of all the hyperfine components was carried out to
determine the velocity centroid.
We display the moment maps for H13CO+ and HNC and compare them with
the CLASSy N2H
+ maps in Figures 2.2, 2.3, 2.4, 2.5 and 2.6. The H13CN maps are
weak, having signal-to-noise ratio (SNR) of less than 4 along the filaments, which is
not sufficient to do kinematic analysis. We present the H13CN integrated intensity
map only for the Serpens South - NW region (Figure 2.7 left).
We find that the N H+2 emission corroborates well with the H
13CO+ emission,
both for the integrated intensity and velocity maps. Although the N +2H emission
intensity is more than 5 times brighter than the H13CO+ emission, the RMS noise
in the N H+2 maps are also greater. Depending on the SNR of the N H
+
2 maps in
comparison to the H13CO+ maps for a particular region, the relative extent of the
emission in the two species varies. For example, in the Serpens South regions, the
filaments are traced much more extensively in N2H
+, while in the Serpens Main
region, we detect more structure and trace the known structures over larger areas
in H13CO+.
The HNC emission traces most of the structures seen in N +2H and H
13CO+,
29
Figure 2.2: Integrated intensity maps (top row) and velocity centroid maps (bottom
row) for Serpens South - NW filament in the N2H
+, H13CO+ and HNC J=1-0 lines.
The integrated intensity map color bar values are given for H13CO+ in Jy beam−1
km s−1. The corresponding values for N H+2 and HNC maps are respectively 6.0 and
3.0 times the value for the H13CO+ maps. The velocity maps are all in units of km/s.
The N H+2 integrated intensity contours at (2,4,6) × σ (σ = 0.25 Jy beam−1 km s−1)
are overlaid on all the images. The synthesized beam is shown at the bottom-right
of each image.
30
Figure 2.3: Same as Fig. 2.2 for Serpens South - E region. The integrated intensity
maps are in units of 10.0, 1.0 and 4.0 Jy beam−1 km s−1 for N2H
+, H13CO+, and
HNC respectively. The N H+2 contours are at (5,10) × σ (σ = 0.25 Jy beam−1 km
s−1).
Figure 2.4: Same as Fig. 2.2 for Serpens Main - cloud center and E filament. The
integrated intensity maps are in units of 6.0, 1.0 and 3.0 Jy beam−1 km s−1 for
N H+, H13CO+2 , and HNC respectively. The N2H
+ contours are at (3,6,9) × σ (σ
= 0.7 Jy beam−1 km s−1).
31
Figure 2.5: Same as Fig. 2.2 for Serpens Main - S region. The integrated intensity
maps are in units of 5.0, 1.0 and 2.0 Jy beam−1 km s−1 for N H+, H13CO+2 , and
HNC respectively. The N2H
+ contours are at (3,6,9) × σ (σ = 0.7 Jy beam−1 km
s−1).
32
Figure 2.6: Same as Fig. 2.2 for NGC 1333 - SE region. The integrated intensity
maps are in units of 6.0, 1.0 and 4.0 Jy beam−1 km s−1 for N + 13 +2H , H CO , and
HNC respectively. The N +2H contours are at (1,3,5) × σ, where σ = 0.4 Jy beam−1
km s−1.
33
Figure 2.7: Left : Integrated intensity maps of Serpens South - NW filament using
H13CN J=1-0 transition line. The map is in units Jy beam−1 km s−1. The N +2H
integrated intensity contours are overlaid on the image as in Figure 2.2. The syn-
thesized beam is shown at the bottom-right of the image. The blue circle marks
the location where the spectra is taken for comparison with other molecules. Right :
H13CO+ (black, solid), HNC (brown, dashed) and H13CN (grey, dotted) J=1-0 spec-
tra taken at the location shown in the left figure. The peaks of H13CO+ and H13CN
coincide, but the HNC spectrum shows an absorption dip.
but the relative emission varies in different regions of the maps. HNC emission also
has greater SNR than the H13CO+ maps by a factor of 2 to 4. In the Serpens South -
NW region (Figure 2.2), it traces the NW part of the filament more than the central
part, while in the Serpens Main - cloud center and E filament (Figure 2.4), the HNC
emission is more extensive. In the NGC 1333 - SE region (Figure 2.6), HNC traces
the west side of the filament more than the east by a factor of two, although both
in H13CO+ and N2H
+, the relative emission of the two sides are comparable.
The HNC velocity maps are noticeably different from the corresponding H13CO+
and N H+2 maps for most of the regions. This is because its spectrum shows ab-
sorption dips at many locations along the filaments. This results in two peaks on
either side of the line center in H13CO+ and H13CN emission; the relative strengths
of the two HNC peaks depend on the velocity of the absorbing material in the line
34
of sight (see Figure 2.7 right). Since HNC is a main isotopic species with higher
abundance, it is not surprising that it shows absorption in the J=1-0 transition as
was previously found for HCN and HCO+ [98, 109]. However, there are some re-
gions especially near the Serpens Main cloud core, where the HNC spectrum does
not show absorption features. In these cases, there is a greater match in the moment
maps between the different tracers. The variations in the HNC spectra are further
discussed in Section 2.5.4.
2.4 Analysis
By themselves, the integrated intensity and velocity maps are insufficient to
understand the finer structure in many of the studied regions. The H13CO+ (J=1-
0) channel maps are best suited for analysis especially in fields containing multiple
sub-structures in close position or velocity proximity. This species is optically thin
and has an isolated spectral line (corresponding to the J=1-0 transition), while at
the same time it has sufficient SNR to detect the filaments. The complex hyper-
fine structures (in N H+2 and HNC) or absorption features (in HNC) of multiple
sub-structures can overlap, leading to degeneracy and challenges in disentangling
the contributions of the separate components. However, these species have greater
abundance than H13CO+ and hence they can easily map extensive areas.
To disentangle the structures, we compare individual channel maps in H13CO+,
and use position-velocity diagrams to check for emission continuity. In this section,
we present H13CO+ contour maps, averaged over 3-4 contiguous channels. These
35
contours are overlaid on Herschel column density maps obtained from the Gould
Belt Survey Archive [119, 120] to compare the individual structures with the dust
emission. We also use the isolated hyperfine component of N2H
+ in regions having
SNR > 2 to confirm our identification of the velocity-coherent structures. We use
other indicators such as variations in HNC absorption features and relative abun-
dances to further support the identifications of structures in complex regions.
Following the identification of velocity-coherent sub-structures, we determine
their extent using contours at half the peak emission for each channel. These con-
tours over multiple channels are stacked, and we establish the lengths of the major
and minor axes for the combined area within these stacked contours. The minor
axis gives a representative width value, while the major axis gives a minimum length
estimate (within the observed area). It is to be noted that this method only gives
a rough estimate of the extent of the individual structures. We use a more formal
method for determining the widths by Gaussian curve fitting of cuts in the inte-
grated intensity maps (discussed in details in Section 2.5.2), but it is applicable
only to filaments not having overlapping sub-structures.
Only the structures having aspect ratios greater than 4 (as in Lee et al. (2014)
[98]) and at least 0.25 pc long are considered in our velocity analyses. We identify 8
such ‘filamentary structures’ over the 5 regions by this method (see Table 2.3). All of
them are aligned with the filaments identified in Herschel maps, although some are
not resolved into multiple components in those low-resolution dust maps. Serpens
South NW is the least complex region having only one velocity coherent structure
along the Herschel filament. The Serpens South - E region, the Serpens Main - S
36
region and the NGC 1333 SE region each have two partially overlapping velocity
coherent structures. Other authors have noted similar structures in observations
and simulations and termed them as sub-filaments [93] or as fibers [99]. We refer
to them as sub-filaments or components and denote them by letters A and B. The
Serpens Main - Cloud center and E filament region also has overlapping structures
at the cloud center, but the Herschel filament east of the cloud does not have any
identifiable sub-structure.
Many of the filamentary structures show systematic variations in their ve-
locity. In non-overlapping filamentary structures, the local velocity gradients are
calculated directly from the Moment 1 maps. For the overlapping structures, we
trace the H13CO+ spectral peak over the extent of the filament, identifying the peak
corresponding to each structure. Their velocity gradients are calculated locally using
the H13CO+ spectral peak velocity difference in different parts of the same velocity
coherent structure. They are reported as gradients only if they satisfy the following
conditions: (i) the velocity monotonically changes in one spatial direction (generally
along the filament or perpendicular to it), (ii) the velocity difference is greater than
or equal to 0.2 km/s and (iii) the above conditions are satisfied for a distance of at
least 4 beam-widths along the filament. From the multiple local velocity gradient
values for each filamentary structure, we report the maximum, minimum and mean
gradients (see Table 2.3). The error in the gradient calculation can be estimated
from the velocity difference errors reported in the table. They are generally less
significant than the variation in the gradient values over a filamentary structure.
For our analyses, we use distances of 436 pc for the 4 Serpens regions [121],
37
and 300 pc for the Perseus region [122]. Both clouds have an average recessional
velocity of 7.5−8 km/s. Dust temperatures in these filaments range from 12 K to 15
K [123, 124]. We use the Spitzer catalog of YSOs [125] and identified point sources
in the Herschel 70 µm maps corresponding to the studied regions to compare their
locations with respect to the structures identified by us.
We also calculate the mean H13CO+ and H13CN velocity dispersions 〈σ〉 for the
two isolated filaments, where we can determine the value unambiguously by taking
statistics over a large part of the structu√re. The non-thermal velocity dispersion is
calculated using the expression 〈σ〉 = 〈σ〉2nt − kT/(µmH) where T is the kinetic
temperature and µmH is the mass of each molecule of the tracer (µ = 30 for H
13CO+
and 28 for H13CN and mH is the the atomic Hydrogen mass). At typical filament
temperatures of 12-15 K, the non-thermal dispersion is the main component of the
overall dispersion. We compare this to sound speeds cs ≈ 0.22-0.25 km/s at these
temperatures.
2.4.1 Serpens South - NW Region
Figure 2.8 (top) shows the H13CO+ contours of the Serpens South - NW region,
averaged over 4 channels. This region has no evident sub-structures, as can be
confirmed from the position-velocity diagram for a representative cut across the
filament. There is a velocity gradient of about 0.24 km/s over the 0.04 pc width
of the filament both in the H13CO+ and N2H
+ emission. This is seen all along the
0.4 pc length of the filament in the mapped area (Figure 2.2). The mean H13CO+
38
Figure 2.8: Top: Herschel column density map (1022 cm−2) with H13CO+ contours
overlaid on it for the Serpens South - NW region. The contours are at (2,4) × σ
(σ = 0.06 Jy/beam) for H13CO+ emission averaged over 4 channels between 7.24
km/s and 7.88 km/s. The black line corresponds to the cut for which the position-
velocity diagram is presented in the lower panel. The black stars denote the locations
of known Class 0/I YSOs. The yellow circle at the bottom-right represents the
resolution of the column density map, corresponding to the Herschel 500 µm beam.
Bottom: Position-velocity plot for a cut across the filament,showing a single velocity-
coherent component. The slope indicates the velocity gradient.
39
Filament Representative Gradient 〈∆v〉 Distance along ∇v (km s−1 pc−1)
(sub-filament) widtha (pc) Directionb (km/s) filamentc (pc) Min Max Mean
Serpens South - NW 0.06 across 0.24 ± 0.07 0.19 3.9 6.8 5.5
Serpens South - E (A) 0.08 across 0.22 ± 0.08 0.11 3.6 5.3 4.2
Serpens South - E (B) 0.04 -
across 0.54 ± 0.09 0.07 5.7 12.0 8.9
Serpens Main - E 0.04
along 1.06 ± 0.06 0.23 2.7 10.3 4.6
Serpens Main - S (A) 0.07 -
Serpens Main - S (B) 0.05 along 0.78 ± 0.15 0.29 1.2 5.0 2.6
NGC 1333 - SE (A) 0.05 -
NGC 1333 - SE (B) 0.03 across 0.30 ± 0.14 0.09 8.1 12.2 9.9
a The widths are calculated from the extent of contours in channel maps at half the peak
emission. All the values vary in a range of about 0.03 pc over the length of the filament.
b Only monotonically changing velocities ∆v > 0.2 km/s over a part of the filament > 4 beam
widths long are considered as gradients.
c Distance along filament spine over which gradient statistics are taken, both for perpendicular
and parallel gradients.
Table 2.3: Widths and gradient statistics of filamentary structures using H13CO+
maps
velocity dispersion for this filament (0.21 km/s) is transonic. There are no YSOs
identified along the filament, although there are multiple Class 0/I sources near the
filamentary hub at the south-eastern end of the studied region.
2.4.2 Serpens South - E Region
Figure 2.9 shows two sub-filaments in the Serpens South - E region running in
the east-west direction - a weaker sub-filament (A; red contours) which is wider and
a parallel narrow sub-filament (B; blue contours) having stronger emission. These
are easily separable in the position-velocity diagram (middle panel of Figure 2.9).
There is partial line-of-sight overlap between these two components. There is a large
line-of-sight velocity difference over the region. It varies between 6.6 km/s and 8.0
km/s according to the H13CO+ and N H+2 maps (see Figure 2.3). Sub-filament ‘A’
40
Figure 2.9: Upper-left : Herschel column density map (1022 cm−2) with H13CO+
contours overlaid on it for the Serpens South - E region. The red contours correspond
to emission averaged over 3 channels centered at 7.49 km/s, while the blue contours
correspond to emission averaged over 3 channels centered at 6.98 km/s. The red
and blue contours represent the two sub-filaments ‘A’ and ‘B’. The contours are
at (2,4,6) × σ (σ = 0.08 Jy/beam). The black line shows the cut for which the
position-velocity diagram is presented in the upper-right panel. The dark red and
orange circles are two regions where the H13CO+ spectrum is taken and presented
in the lower-right panel. The black and green stars denote the locations of known
Class 0/I and Flat spectrum YSOs respectively. The yellow circle represents the
resolution of the Herschel map. Upper-right : Position-velocity plot for a cut across
the filament showing the two velocity-coherent components. ‘A’ is wider and fainter
than ‘B’. Lower-left : N2H
+ integrated intensity map (Jy beam−1 km s−1) with
the H13CO+ contours corresponding to the two sub-structures overlaid on it. The
synthesized beam for the N2H
+ map is shown at the bottom-right. Lower-right :
H13CO+ spectrum at two locations marked by circles of the same color in the left-
most panel. This shows the velocity gradient which is present in the eastern half of
the filament, only in component ‘A’.
41
is more red-shifted and has a velocity gradient across it, while ‘B’ is blue-shifted and
has no consistent gradient across it. In the H13CO+ maps, because of low SNR, the
gradient could be determined only in the east part of ‘A’. The right panel of Figure
2.9 shows spectra at two representative locations across the filament. The gradient
is about 4.2 km s−1 pc−1.
The HNC emission has absorption features in sub-filament ‘A’ , but absorption
is absent or minimal in ‘B’. The sharp velocity and intensity gradients near the
brightest emission combined with the differences in the HNC absorption across the
two regions are also in support of the multiple structure interpretation. Two Class
0/I/Flat YSOs are identified in this region closer to the cloud center. Both are in
the region where the two sub-filaments overlap in the line-of-sight, and thus cannot
be associated with one or the other.
Using the N H+2 maps, Fernández-López et al. (2014) [105] could not distin-
guish between the two velocity coherent components and concluded a large velocity
gradient across a single filament structure. Even though the Moment 0 and velocity
maps of N2H
+ are similar to H13CO+ with the N2H
+ maps having a higher SNR
than H13CO+ (for this region), the hyperfine structure of N +2H prevents analysis
using position-velocity diagrams to distinguish the velocity coherent structures. The
gradient in the eastern part although visible in the N +2H maps as well, has a lesser
magnitude and opposite sense compared to the inaccurately identified gradient in
the central and western part, and was thus not reported in Fernández-López et al.
(2014)[105]. With the knowledge of the two-component structure using the H13CO+,
we find that the isolated hyperfine line of N H+2 (J=1-0, F=0-1) shows similar trends
42
Figure 2.10: Left : Herschel column density map (1022 cm−2) for Serpens Main
- cloud center and E filament, with H13CO+ contours overlaid on it for emission
averaged over channels centered at 8.68 km/s (red) and at 7.58 km/s (blue). The
contours are at (2,4,6) × σ (σ = 0.1 Jy/beam). The two sets of contours correspond
to the two sets of structures identified in the region. The green circle near the center
marks the location where the H13CO+ spectrum is taken and presented in the right-
most panel. The black and green stars denote the locations of known Class 0/I and
Flat spectrum YSOs respectively. The yellow circle represents the resolution of the
Herschel map. Middle: Same as the left panel for H13CO+ channels centered at
7.58 km/s (blue contours) and 6.57 km/s (violet contours). In spite of the large
velocity spread, these two components are part of the same structure. The two sets
of contours however indicate the flows towards a potential well in this region at the
center of the violet contours. The dashed black circle marks the intersection region
of the flows. Right : H13CO+ spectrum at the locations marked by the green circle in
the left and middle panels. This shows that there are two sets of velocity-coherent
structures separated by about 1.4 km/s.
as H13CO+, but by itself this line has much lesser SNR than H13CO+, and is too
weak to map the kinematics of the entire region.
2.4.3 Serpens Main - Cloud Center and E Filament
This is a complex region mapping the south-east part of the Serpens Main
hub, with emission extending in various directions. On comparing to the larger
scale structures in the region using Herschel maps, we see that only two parts of the
emission form long filaments, one in the east, and the other in the south. The east
filament is mapped completely in this region. The filament in the south is completely
43
mapped in the Serpens Main - S region (discussed in the following section).
In the cloud center region, there is a large range of line-of-sight velocities from
6 km/s to 9 km/s. Using H13CO+ channel maps, two sets of structures associated
with different velocities are identified within the hub (Figure 2.10 right). Of these,
the velocities above 8 km/s correspond to a separate velocity-coherent structure
(marked in red in the left panel of Figure 2.10) while another set of structures have
velocities in the range of 6 to 8 km/s. This second set includes a convergent point
at (α, δ) = (18:29:59.8, +1:13:00) where three flows seem to intersect from east,
south-east and north-west respectively (middle panel of Figure 2.10). We call them
flows because they have a velocity gradient, such that their ends closer to the hub
is highly blue-shifted, possibly indicating acceleration in a potential well. The HNC
spectrum has no absorption dips in the blue-shifted set of structures, but has very
strong dips in the red-shifted regions.
Of these flows, the one from the east is identified as a filament in our analysis.
Most of the filament is isolated from the other structures and so can be analyzed
from the moment maps. The filament has a velocity gradient of 1.1 km/s over its
length of 0.23 pc. The gradient vector is oriented along the filament close to the
hub (10.3 km s−1 pc−1), but its magnitude reduces by a factor of four 0.2 pc away
from the cloud center. Moving further from the hub, the gradient direction rotates
by about 90 degrees such that it is oriented almost across the filament near the
easternmost extreme. The mean velocity dispersion over this filament is 0.33 km/s,
which is marginally supersonic.
In the central hub, three point sources SMM1, SMM3 and SMM4 are identified
44
in the continuum map, but they are not closely associated with the multi-filament
intersection point. However, on comparing with the Spitzer YSO catalog [125], two
Class I/0 YSOs are identified within 5000 AU projected distance from this point.
Additionally, an outflow identified in previous CO maps [126] and the CLASSy
HCO+ map can be traced to be originating close to the filament intersecting region.
2.4.4 Serpens Main - S Region
The northern part of this region maps into part of the cloud center of Serpens
Main. In this upper part, two velocity components are identified at about 7.3 km/s
and 8.4 km/s respectively. The relatively blue-shifted component has a greater
spatial extent and does not show any absorption in the HNC spectrum compared
to the relatively red-shifted component.
This region also has two sub-structures along the filament, which originates
from the hub in the north (see Figure 2.11) and are more than 0.3 pc in length.
These velocity-coherent sub-filaments ‘A’ and ‘B’ are parallel to each other and
cross-over in the projected sky plane at (α, δ) = (18:29:59.5, +1:09:45), correspond-
ing to an emission peak in the integrated intensity maps (see Figure 2.5). The
position-velocity diagrams for cuts along the two sub-filaments reveal their velocity
distribution. Sub-filament ‘A’ has velocities in the range 8.2 − 8.7 km/s with no
evident gradients. Sub-filament ‘B’ has a velocity gradient along the filament such
that the line-of-sight velocities are 7.5 km/s at the south end of the filament, and
8.5 km/s close to the cloud center. As in the Serpens Main - E filament (discussed
45
Figure 2.11: Left : Herschel column density map (1022 cm−2) with H13CO+ contours
overlaid on it for the Serpens Main - S region. The red and blue contours corre-
spond to emission averaged over 3 channels centered at 8.66 km/s and 7.65 km/s
respectively. They represent the two sub-filaments ‘A’ and ‘B’. The contours are at
(2,4,6) × σ (σ = 0.1 Jy/beam). The channels in between 7.90 km/s and 8.42 km/s
have emission corresponding to both the sub-filaments and are inseparable in the
channel maps. The black solid and dashed lines correspond to the cuts along the
lengths of ‘A’ and ‘B’, for which the position-velocity diagrams are presented in the
middle panels. The black and green stars denote the locations of known Class 0/I
and Flat spectrum YSOs respectively. The yellow circle represents the resolution of
the Herschel map. Middle-top: Position-velocity plot for a cut along ‘A’ (solid line
in left panel), showing its velocity range from 8.2 to 8.7 km/s with no evident gradi-
ents. The left half of the image also shows the emission from sub-filament ‘B’ before
it crosses over and the separation of the components increase in the projected sky
plane. Middle-bottom: Position-velocity plot for a cut along ‘B’ (dashed line in left
panel), showing its velocity changing from 7.5 to 8.5 km/s. ‘B’ is weaker than ‘A’
and so there is substantial contribution from ‘A’ along the cut. Right : N H+2 inte-
grated intensity map (Jy beam−1 km s−1) with the H13CO+ contours corresponding
to the two sub-structures overlaid on it. The synthesized beam for the N2H
+ map
is shown at the bottom-right.
46
in the previous section), this sub-filament also indicates accelerated flow closer to
the cloud center. The gradient changes from 1.2 km s−1 pc−1 to 5.0 km s−1 pc−1,
going towards the cloud center.
The N2H
+ emission identifies both these sub-filaments, but does not trace the
lower half of ‘B’ because of insufficient SNR. In their kinematic analysis, Lee et
al. (2014) [98] used a single velocity component fit for most regions. They used
a two velocity component fit only in regions where there is a large velocity differ-
ence between the components (> 1 km/s) that could be resolved unambiguously.
They detected two sub-filaments using the integrated intensity maps since the sub-
filaments had well-defined ridges, spatially resolved by the CARMA beam. However
they used a single component fit to obtain the velocity maps because the velocity
difference between the components in the northern part is 6 0.5 km/s, and were
thus unable to capture the extent of the two components in the overlapping regions.
The velocity gradient observed across the filament in the lower half of the
H13CO+ first moment map (see Figure 2.5) is not a true gradient; it is an effect of
the overlapping sub-filaments. This case is similar to that observed by Beuther et
al. (2015) [80] in the dense filament IRDC 18223, and by Moeckel & Burkert (2015)
[92] in simulations.
South of the intersection points of ‘A’ and ‘B’, the spectrum corresponding
to emission from ‘A’ is wide, and at places divides into two peaks separated by
2-3 channels. In the HNC integrated intensity map, the width of ‘A’ is lesser than
in H13CO+, strengthening the case for an additional sub-structure in this region
possibly having different physical parameters. However, there is insufficient evidence
47
in our data to identify this sub-structure with certainty. Three Class 0/I/Flat YSOs
are identified along the length of the filament. Of them, one Flat spectrum YSO is
located close to the cross-over point of the sub-filaments.
2.4.5 NGC 1333 - SE Region
This region has a filament with two sub-structures running parallel to each
other from north-west to south-east. As shown in Figure 2.12, the eastern sub-
filament (A) has a velocity in the range 8.1 − 8.4 km/s with a fork towards the
south. The western sub-filament (B) has a velocity gradient across its 0.03 pc
width changing gradually from about 7.8 km/s to 7.5 km/s. As explained at the
beginning of this section, we measure the gradient using the spectral peak locations
corresponding to the same velocity-coherent structure. This is shown in the bottom-
right panel of Figure 2.12. In some sections of sub-filaments ‘A’, there is a small
gradient in the opposite sense compared to that for ‘B’.
The relative intensities of the two sub-filaments are comparable, both with
N2H
+ and H13CO+. However the HNC emission from the right sub-filament is
about 2 times brighter than the left. The difference in the HNC emission compared
to the other two tracers strengthens the interpretation that there are two distinct
sub-filaments having different physical parameters.
The four YSOs corresponding to the components of IRAS 4 are located in the
top-right part of the mapped region. They appear bright in the CLASSy-II contin-
uum (360 Jy/beam and 130 Jy/beam peak intensities respectively) maps. Neither
48
of the outflow axes from these protostars [127] are oriented along the filament in
this region. Stephens et al. (2017) [128] postulated that the lack of correlation be-
tween outflow axis directions and the filament orientations indicates that the angular
momentum axis of a protostar may be independent of the large-scale structure.
2.5 Filament Morphology
On comparing the CLASSy-II observations with the Herschel dust continuum
maps and the CLASSy N H+2 maps, we find that the structure traced by all the
maps are similar on the large scale. However on smaller scales (< 0.1 pc), the finer
structure of these filaments becomes evident in the CARMA maps. In many of
the regions we identify multiple sub-structures, instead of a single uniform filament
identified in the Herschel maps.
Using just the CLASSy N H+2 maps, it was argued that the finer structure
could be real or could alternatively be due to N H+2 abundance variations caused as
a result of N H+2 depletion by CO in less dense regions [129]. However, the similarity
between the structures traced by N H+2 and H
13CO+ at the CLASSy resolution
scale imply that the morphology and kinematics determined from these maps truly
represent the dense gas distribution and are unlikely to be arising from chemical
selectivity. There are some differences in the relative intensities of the structures
traced by HNC, which could be an effect of relative abundance, temperature, density
or a combination of them.
The different regions studied in this chapter indicate that despite the variety of
49
Figure 2.12: Upper-left : Herschel column density map (1022 cm−2) with H13CO+
contours overlaid on it for the NGC 1333 - SE region. The red and blue contours
correspond to emission averaged over 3 channels centered at 8.26 km/s and 7.42
km/s respectively. The red and blue contours represent the two sub-filaments ‘A’
and ‘B’, but not their true extent because the channels in between have emission
from both the components that are inseparable in the channel maps. The contours
are at (2,4,6) × σ (σ = 0.075 Jy/beam). The black line shows the cut for which
the position-velocity diagram is presented in the lower-left panel. The red, green
and blue circles are regions where the H13CO+ spectrum is taken and presented
in the lower-right panel. The black stars denote the locations of known Class 0/I
YSOs. The yellow circle represents the resolution of the Herschel map. Upper-right :
N + −1 −1 13 +2H integrated intensity map (Jy beam km s ) with the H CO contours
corresponding to the two sub-structures overlaid on it. The synthesized beam for
the N2H
+ map is shown at the bottom-right. Lower-left : Position-velocity plot for a
cut across the filament showing the two overlapping velocity-coherent components.
‘A’ has a fairly constant velocity, while ‘B’ has a velocity gradient across it. Lower-
right : H13CO+ spectrum at three locations marked by circles of the same color in
the left panel. The spectra indicate that there are two velocity components, the
relative intensities of which change as we move across the filament. This is also
associated with a shift in the spectral peak of ‘B’ by 0.33 km/s. This is how we
distinguish between the emission peaks corresponding to the two components and
appropriately determine their independent velocity gradients.
50
filament structure, there are many common features. In this sub-section, we discuss
the different aspects of filament morphologies and their implications. In some cases,
rigorous analysis is only possible for the well isolated filaments, i.e. for Serpens
South - NW filament and Serpens Main - E filament.
2.5.1 Physical parameters of tracers
Single transitions can be used to determine physical parameters like column
density in molecular clouds only if we assume thermalization. This assumption gives
a good estimate of the column density which is not very sensitive to the excitation
temperature variations. Thus if we assume that a single excitation temperature Tex
defines the level populations of a molecule, we can use the integrated intensity to
calculate the total column density of the molecular species in the optically thin limit
using the formula [130]
∑
2 ∫
thin thin Q 8πkν g e
−Ei/kTex ∞
i
N = Nu =g e−Eu/kTex hc3A g e−
T
E /kT b
dv (2.1)
u ex
u ul u −∞
where c, k and h are the speed of light constant, the Boltzmann constant and the
Planck constant respectively. The transition frequency is ν and Aul is the Einstein
A coefficient corresponding to the transition. Q is the partition function, which is
assumed to be a function of a single variable Tex. gi and Ei are respectively the
degeneracy and energy of the ith energy level. The subscripts u and l represent
the upper and lower levels of the transition respectively. The integral represents the
integrated line intensity with Tb as the observed brightness temperature in K and dv
51
as the channel width in km/s. Here we assume a unity beam filling factor. Further,
a correction factor of τ/(1− e−τ ) is needed if the transition is not optically thin (τ
 1). This opacity τ can be determined using the radiative transfer equation
hν( 1 )
Tb = −
1
[1− e−τ ] (2.2)
k ehν/kTex − 1 ehν/kTbg − 1
where Tbg is the background radiation 2.73 K.
Because of the limitations of the analysis and the presence of overlapping
structures in many regions further complicating the analysis, we present the results
only for the Serpens South - NW filament ridge in H13CO+ and N H+2 . The lower
limit of Tex for N2H
+ is estimated from the observed brightness temperature (∼ 6 K).
This Tex limit is also applicable to H
13CO+ since it has a critical density similar to
that of N +2H . For the upper limit of Tex, we use the maximum kinetic temperature
from the dust temperature maps. Based on this, we use representative Tex values
in the range 6-15 K. Using these equations and the assumed range of Tex values, we
obtained column densities of 0.9 − 1.1 × 1012 cm−2 for H13CO+ and 7.9 − 10.3 ×
1012 cm−2 for N2H
+ along the ridge of the isolated filament in Serpens South - NW
region. The column density values can be averaged over areas equal to the Herschel
beam size and compared to the H 22 −22 column densities of ∼ 2.0 × 10 cm (obtained
by fitting modified blackbody spectra to the Herschel maps at different wavelengths
[131, 132]) to get molecular abundances. By this method, we calculate abundances
of 2.7− 4.6 × 10−11 for H13CO+, and 2.2− 3.3 × 10−10 for N2H+.
We can also use the ‘large velocity gradient’ (LVG) approximation to get a
52
lower bound on the density of the region. Using the H13CO+ observed brightness
temperature and a maximum value of τ = 0.8 (from Equation 2.2) corresponding
to Tex = 6 K, we get a minimum gas density of 3.0 × 105 cm−3 along the Serpens
South - NW filament ridge. From the LVG model, we also obtain a minimum
H13CO+ column density of 0.9 × 1012 cm−2 corresponding to the mean brightness
temperature of 1.9 K. This estimate matches well with the analytically obtained
column density in the previous paragraph.
2.5.2 Filament Widths
Several publications from the Gould Belt survey argued that all filaments have
a similar width of about 0.1 pc [76, 133, 134], with a narrow distribution in width.
Other authors like Juvela et al. (2012) [135] and Hennemann et al. (2012) [136]
have however reported larger widths of about 0.3 pc, while Panopoulou et al. (2016)
[137] reported a lesser width of 0.06 ± 0.04 pc. Ysard et al. (2013) [138] reported
widths varying by a factor of 4, while Panopoulou et al. (2017)[139] concluded that
a single characteristic width of filaments is inconsistent with observations, and that
the narrow distribution is an averaging effect.
Earlier in Section 2.4, we reported the widths for the individual filamen-
tary structures. Here we use a more systematic approach to calculate the widths
of filaments using H13CO+ and dust column density maps and compare between
them. Since H13CO+ is optically thin, the integrated intensity map scales di-
rectly with the column density (Equation 2.1). Hydrogen column density maps
53
were obtained from the Herschel Gould Belt archive. We take parallel cuts across
the filaments at multiple points along its length, about 7′′ apart (comparable to
beam size), average over the cuts and fit a Gaussian to get the full-width at half-
maxim√um (FWHM). The deconvolved width, Wd, is obtained using the expression
W = (FWHM)2d − (HPBW )2 where HPBW is the half-power beam width for
the maps [119]. We use distance estimates mentioned in Section 2.4 to obtain the
filament widths in parsecs. We also fit a Gaussian to each individual cut in order
to obtain a range for the filament widths.
In many of the regions, the presence of overlapping sub-filaments prevents us
from determining their individual widths by this method, both in H13CO+ and dust
maps. We apply this method to isolated filaments (Serpens South - NW filament and
Serpens Main - E filament) and sections of filaments not having any overlapping sub-
structure. We use two-Gaussian fits for regions where partially overlapping parallel
sub-filaments have ridges separated by more than twice the beam size (see Figure
2.13 lower-right). The Serpens South - NW filament has a deconvolved FWHM
width of 0.059 ± 0.011 pc in H13CO+ and 0.083 ± 0.006 pc in dust, while the
corresponding values for Serpens Main - E filament are 0.043 ± 0.011 pc and 0.067
± 0.026 pc respectively. Our analysis shows that even in the isolated filaments,
H13CO+ maps do not have a smooth Gaussian profile (see Figure 2.13 lower-left).
The widths vary along the length of the filaments by up to a factor of two. In regions
where we could compare the dust and H13CO+ widths for isolated structures, we
found that the deconvolved widths are lesser in the H13CO+ maps than the dust
maps by a factor of about 1.5 (see Figure 2.13 top). Overall, we report filament
54
Figure 2.13: Filament width in different regions. The dark dots represent the nor-
malized average of the cuts over a filament section, which is fitted with one or
two Gaussians. The light color spread represents the range of normalized values
over a section of the filament. Top: Serpens South NW filament – Comparison
of filament widths in dust (blue) and H13CO+ (green). The dust map shows two
parallel filaments about 75′′ apart and is fitted with two Gaussians. The FWHM
of the filament mapped by us is 53±3′′ in dust and 29±5′′ in H13CO+. Lower-left :
Serpens Main E filament – Comparison of filament widths in two parts of the same
filament – FWHM 26±5′′ near cloud center (green) and 17±5′′ away from cloud cen-
ter (red). Closer to the cloud core, the intensity profile across the filament departs
from a Gaussian profile, even though we detect a single velocity-coherent component
throughout. Lower-right : Northern part of Serpens Main S filament – Two parallel
sub-filaments separated by about 25′′ with FWHM 23±8′′ and 19±7′′ respectively.
A 2-Gaussian fit is used since two velocity-coherent sub-filaments were identified
using the data cube.
55
deconvolved FWHM widths in the range 0.03 pc to 0.08 pc using H13CO+ which is
comparable to the N +2H widths for these filaments reported in Lee et al. (2014)[98]
and Fernández-López et al. (2016) [105]. Our width estimation from the channels
maps gives similar values, although there we estimated the widths of the overlapping
structures as well that could not be determined using the integrated intensity maps.
The CLASSy-II results show that the widths of the filaments in dense gas
tracers are on average significantly less than the Herschel filament widths. The
greater widths in the Herschel maps cannot be solely explained by the presence of
unresolved sub-structures, because we find this to hold true for isolated structures
as well. This could indicate that the dust emission is tracing material which is
intrinsically more extended than the distribution of dense gas in filaments. The
difference between the dust and the dense gas tracers could arise from the fact that
the dust primarily responds to the column density, while the dense gas tracers like
N H+ and H132 CO
+ respond to a combination of the physical density and the column
density of the tracer. While the column density and density are expected to be well
correlated for filaments with cylindrical cross-sections, this may not hold true in the
case of filaments having an elliptical cross-section. In such cases, it is possible that
the N +2H is preferably sampling the physically denser part of the filament which
may be narrower compared to the dust emission.
56
2.5.3 Multiple Structures
Except for the Serpens South - NW filament, all the remaining regions have
partially overlapping multiple structures in the line of sight. The regions in Serpens
Main have a line of sight velocity difference of as much as 1.4 km/s. Assuming
timescales comparable to the cloud free-fall times (∼ 1 Myr) for motion governed by
gravity (which also includes turbulence in a bound molecular cloud), these structures
should be separated by about 1.5 pc. This is comparable to the size of the molecular
clouds and is much larger than the filament widths. In this scenario, they are
unlikely to be arising from common formation mechanisms. Alternatively, if they
are assumed to be in closer physical proximity, then they have proportionately lesser
free-fall times, and therefore represent transient structures that may be forming from
or evolving into larger structures. This discussion does not take into account effects
of magnetic fields which can also affect the timescales.
These velocity-coherent structures are also distinct from each other in their
morphology, velocity gradients and HNC absorption characteristics. Many of the
sub-filaments are parallel to each other. Additionally in Serpens South - E region
and NGC 1333 - SE region, the parallel sub-filaments have a fairly constant velocity
difference of about 0.5 km/s at the nearer edge between the filaments. In both these
regions, there is a velocity gradient across one of the filaments.
Hacar et al. (2013) [99] also observed multiple velocity components in the
L1495/B213 filaments in Taurus. They identified shorter 0.5 pc coherent non-
interacting sub-filaments which have velocity separations of 0.5-1.0 km/s, similar
57
to what we observe. Tafalla & Hacar (2015) [140] proposed a ‘fray and fragment’
model to explain the multiple structures. This model starts with a wide filament
that fragments into sub-filaments, which then further fragment into cores. Hydro-
dynamic simulations of turbulent clouds by Moeckel & Burkert [92] and Smith et al.
(2016) [100] also showed the presence of multiple components in filaments. However
contrary to the ‘fray and fragment’ model, Smith et al. (2016) [100] proposed a ‘fray
and gather’ model, in which the sub-filaments are formed first and then gathered
together by large-scale motions within the cloud – initially by large scale turbulent
modes and afterwards gravitationally. Since the sub-filaments observed by us are
parallel, they are likely to be influenced by the same physical processes locally, but
the observations cannot distinguish between the two models discussed above.
2.5.4 Absorption Features in HNC
The HNC spectrum shows absorption features in many regions. These dips
result in the HNC spectrum having multiple peaks, and are identified as absorp-
tion features based on the peaks in the H13CO+ spectrum and the N +2H isolated
hyperfine spectrum. In many regions, the dips correspond to similar dips in HCO+
and HCN. In regions having multiple structure, we see that in some cases only one
structure has absorption dips, while in other cases emission from both structures
have absorption dips.
Absorption features with a higher blue-shifted peak and a lower red-shifted
peak are considered as a signature of radially symmetric infall into the filament core
58
Figure 2.14: H13CO+ (black, solid) and HNC (brown, dashed) spectra in various
regions – Upper-left : Example of single velocity component with HNC absorption
profile having higher blue-peak. This is found along the Serpens South - NW fil-
ament. Upper-right : Example of single velocity component with HNC absorption
profile having higher red-peak. This is observed in Serpens South - E region and in
sub-filament ‘B’ of Serpens Main - S region. Lower-left : Example of single velocity
component with no HNC absorption. This is observed in the Serpens Main cloud
center. Lower-right : Example of two velocity components one of which shows ab-
sorption in HNC, while the other does not. This is found in many regions in Serpens
Main and in NGC 1333 - SE region. Additionally there are regions having two or
more components, more than one of which show absorption (not shown in figure).
59
[141, 142]. We find that in the regions studied by us, there are absorption features
with both blue-asymmetry and red-asymmetry (see Figure 2.14). The generic infall
models are inadequate in explaining the velocity structure of the HNC lines.
Although self-absorption within the filament is likely, an alternate possibility
is absorption by lower density clouds surrounding the main filament that are in
the line-of-sight. This scenario is supported by the observation that the absorption
features in filaments are equally strong as we move from the center of the filament
to the edges. Self-absorption by filament material should decrease through lesser
optical depth regions near the edges of the filament.
2.5.5 Filaments in relation to star formation
Filaments are known to be closely associated with star forming regions, and
many YSOs and prestellar cores are identified along some filaments [78, 143]. On
comparing our regions with the Herschel 70µm detections and the Spitzer catalog
of YSOs [125], we find that two of the filaments harbor multiple YSOs along their
length, –the Serpens South - E filament (left panel of Figure 2.9) and the Serpens
Main - S filament (left panel of Figure 2.11). The YSOs in these filaments are
all Class 0/I/Flat sources indicating that they are associated with early stages of
star formation. Both these filaments have parallel sub-structures and it cannot
be determined whether some of the YSOs are associated with one sub-filament or
the other, since they appear in the overlapping regions. YSOs are also detected
at the filament intersection in the Serpens Main - S region and the filament-flow
60
intersection in the Serpens Main cloud center (left panel of 2.10), corroborating with
observations by Jiménez-Serra et al. (2014) [103] towards the IRDC G035.3900.33.
This suggests that the sub-filaments may be interacting with each other, and are
probably in close proximity even in the line-of-sight. We also find that all of the
regions have continuum sources close to the ends of the filaments near filamentary
hubs or cloud centers.
Different filaments can be at different stages of their star forming life [144], and
based on our observations it can be argued that only two of the five filaments studied
by us are currently actively star forming. The mass per unit length of filaments is
often used as an indicator of the evolutionary stage of filament accretion [134, 145,
146], with higher values indicating greater chances of gravitational fragmentation.
We can estimate the mass per unit length of the Herschel filaments by summing
over the pixels of the H2 column density map over the filament and subtracting
the background. On applying this method to the isolated filaments, we obtain an
average mass per unit length of 21.3 M/pc for Serpens South - NW filament and
16.9 M/pc for Serpens Main - E filament. The values are comparable to or lesser
than the critical mass per unit length of 20.9 M/pc, calculated for isothermal (T =
12.5 K) self-gravitating cylinders using the formula M 2L,crit = 2cs/G where cs is the
sonic speed in the cloud and G is the universal Gravitational constant [147]. This
is consistent with the observation that neither of these filaments have any Class 0/I
sources along their lengths. The Serpens South - E filament and the Serpens Main -
S filament, which have YSOs along their length, have mass per unit length values of
28.7 M/pc and 44.6 M/pc respectively, which are both greater than the critical
61
value. However the 36′′ column density map beam-size is insufficient to resolve the
contribution of individual sub-structures within the filament. In the NGC 1333 - SE
filament, the mass per unit length varies by a factor of 4; although its mean value
is super-critical, it does not have any YSOs along its length. So even though the
mass per unit length is a good indicator of the star formation stage for a filament,
it is not a conclusive discriminator.
2.6 Filament Kinematics
All the CLASSy-II regions have at least one filamentary structure with an
evident gradient in the line-of-sight velocity: – either across the filament or along
the filament or both. The complete list is given in Table 2.3. The filaments and
regions where we observe negligible velocity variations may still have gradients into
the plane of the sky.
The kinematics observed in N +2H match well with that in H
13CO+ for the non-
overlapping regions, and show similar trends in regions having multiple structures in
the line-of-sight. This is evident from the velocity maps in Section 2.3. However, the
hyperfine structure of N2H
+ limits its capability of distinguishing between multiple
structures and quantifying their kinematic features independently. N +2H velocity
maps had been generated using line-fitting of all the 7 hyperfine components, but
assuming a single velocity component for most locations on the map. In regions with
multiple velocity components, such a line-fitting produced a centroid velocity with
a large line-width. Velocity maps thus obtained were used previously to determine
62
the kinematics of the regions [98, 105], which in some cases give different results
from our H13CO+ analysis that allows for multiple components. Attempts to fit
for multiple velocity components in the N2H
+ spectra leads to erroneous degenerate
solutions, unless the components are > 1 km/s apart. For example, in Fernández-
López et al. (2014) [105] the Serpens South - E filament is reported to have a large
velocity gradient of 11.9 km s−1 pc−1 across the filament. However, the H13CO+
data cube reveals that this is an effect of multiple velocity-coherent components in
close proximity (see Figure 2.9), even though its velocity map matches well that of
N H+2 (see Figure 2.3). Only the eastern half of one of the sub-structures (‘A’) in
this filament has a gradient across it, but in the opposite sense to that reported in
Fernández-López et al. (2014) [105].
2.6.1 Velocity gradients across filaments
Four of the eight identified filamentary structures have velocity gradients per-
pendicular to their length in the range 3.6−12.2 km s−1 pc−1. They are determined
from the H13CO+ maps as discussed in Section 2.4. These gradients are unidi-
rectional in each filamentary structure but have variations in magnitude along the
filaments. The magnitudes correspond to crossing times of 1− 3 × 105 years. Such
gradients of smaller magnitude have been observed by Peretto et al. (2014) [148] as
well. Schneider et al. (2010) [102] also reported observations of gradients across a
filament in the Cygnus molecular cloud but it has a width of 1 pc, about 20 times
wider than the filaments observed by us. Further, the gradient across the Cygnus
63
Figure 2.15: Simplified schematic of two types of filament cross-sections – circular
and elliptical, indicating that gas accretion towards the filament core has differ-
ent kinematic signatures in the two cases. In the isotropic accretion case (left),
the centroid velocity remains constant for a cut across the filament. In the non-
axisymmetric case (right), depending on how the filament cross-section is oriented
with respect to the sky plane, it can result in a gradient in the centroid velocity
vs position plot. The blue-shifts and red-shifts are expected to be greater closer to
the filament core compared to the edges. This causes a change in the slope going
from the center to the edges, though it may not be evident in the observations since
the emission is also lesser in these parts. The plots are simplified and do not show
effects of velocity dispersion which is expected to increase the velocity spread near
the filament core in both cases.
filament changes direction at different positions along the length of the filament.
Out of the regions studied by us, in addition to the four filamentary structures
with gradients across their widths, we also identified line-of-sight velocity gradients
across the Serpens Main - S region, but it is arguably an effect of multiple juxtaposed
structures at different velocities.
64
2.6.1.1 Implications on filament formation mechanism
The velocity gradients across the filaments support the filament formation
model by Chen and Ostriker (private communication). According to the model,
the velocity gradient is a projection effect of the accreting material in a 2-D flow
within the dense layer created by colliding turbulent cells. The cartoon in Figure
2.15 illustrates this effect. In case of a non-axisymmetric cylinder in the sky plane,
we expect the observed centroid velocity to vary systematically for a cut across the
filament. This model also corroborates with Smith et al. (2016) [100], who report
that the filament cross-sections in their simulations are elongated instead of being
circular, and that the largest gradients appear perpendicular to the filament. The
absence of gradients across some of the filaments could be a result of close to face-on
viewing angle or a different formation mechanism. More observations are required
to establish the broad relevance of this model.
Alternate interpretations of the velocity gradient include filament rotation
[108] and multiple narrow filaments that are partially overlapping in the sky view-
ing plane [80]. To our knowledge, the first idea is not supported by numerical
simulations [100]. We have seen some evidence of parallel sub-filaments in a few
regions masquerading as a single filament with a large gradient if we only see their
velocity maps (as in Serpens South - E region and NGC 1333 - SE region). However
after disentangling their individual velocity distributions using the H13CO+ maps,
we see that one of the parallel sub-filaments has a velocity gradient across it in-
dependent of the other sub-filament (see Figure 2.12 lower-right). The observed
65
gradients across filaments (which are equally or more evident than gradients along
filaments) indicate that the local dynamical evolution of these filaments occur much
faster than the rate of flow of material along them.
2.6.2 Velocity gradients along filaments
Two filamentary structures in Serpens Main have velocity gradients along their
lengths of 2.6 and 4.6 km s−1 pc−1 in H13CO+ (Figures 2.4 and 2.11). They both
have one end close to the cloud core, and another end away from it. Additionally
there are distinct velocity gradients along multiple flows in the hub region (that are
not long enough to be classified as filamentary structures). As shown in Figure 2.10,
the flows intersect at the same point along with one of the filamentary structures.
The gradients are maximum closer to the cloud core increasing by a factor of ∼ 4
compared to the gradients near the other end of the filamentary structures. This
may indicate accelerated motions near regions of higher gravitational potential as
the structures fall into the potential well.
The different interpretations of this gradient discussed in Jiménez-Serra et al.
(2014) [103] include cloud rotation, unresolved sub-filament structures, accretion
along the filaments and global gravitational collapse. In the Serpens Main - South
region, although cloud rotation is unlikely based on the large scale kinematic signa-
tures of the region, the gradient could be caused by any of the other scenarios, or
due to projection effects. In the Serpens Main cloud center, the presence of multiple
converging structures with accelerated gradients along their lengths is suggestive
66
Figure 2.16: Simplified schematic of a filament at an inclination angle with respect
to the sky plane. The filament is assumed to be accelerating along its length due to
the gravitational field of a massive core at P. B is closer to the core and has a greater
velocity along the filament than A. In this configuration with the filament inclined
away from the observer, emission from B is more blue-shifted (or less red-shifted)
compared to emission from A.
of global gravitational collapse [149]. In this scenario, matter from large scales are
gathered to the center of a gravitational potential well, where multiple protostars
are formed. It is to be noted that material does not flow along the filaments (anal-
ogous to water flowing in a river), rather the entire filament moves down into the
potential well.
2.6.2.1 Core Mass Estimation
In the Serpens Main cloud center, we identify a filament intersection point
having the highest blue shift. We use velocities (vobs) at different distances (lobs)
from this point as a probe of the gravitational potential. The line-of-sight cloud
velocity (vcloud) of 8.15 km/s is subtracted from the observed line-of-sight velocities.
The velocity thus obtained is a projection of the velocity along the filament v in
the local frame of the cloud (see Figure 2.16). We obtain v assuming an inclination
angle i (positive when filament inclined away from observer), using the expression
67
vobs = vcloud − v sin i. The observed distance lobs is also a projection of the radial
distance r and they are related as lobs = r cos i. Assuming a steady state, using
energy conservation for a pair of points along the filament, we can write
(
2 − 2 1 − 1
)
v2 v1 = GM (2.3)
r2 r1
where G is the Gravitational Constant and M is the mass of the core. This can be
written in terms of the observables and the inclination angle as
( 1 1 )
(v − v 2cloud 2,obs) − (v 2 2cloud − v1,obs) = GM sin i cos i − (2.4)
l2,obs l1,obs
Using this equation, and measured sets of velocities at different distances from
the core for the different structures, we obtain consistent core mass values in the
range 30− 37 Mfor an inclination angle of i = 45◦. The mass varies by a factor of
about 1.5 if we assume an inclination angle range of 30− 60 degrees. Additionally,
because of uncertainties in the distance and velocity measurements, there can be up
to 50% error in mass estimates. On assuming a core region of 1′ angular diameter
and using the H2 column density map, we obtain a gas mass of 28 M. In addition,
there are three known protostars in this region, which add to the mass and result
in a combined mass comparable to that obtained by us from the velocity analysis.
As shown in the figure, from our interpretation, we can also make inferences about
the 3-D structure of the filaments –whether the filaments are inclined towards us or
away from us. For both these cases, the more blue-shifted (or less red-shifted) part
68
of the filament is expected to be closer to the observer than the less blue-shifted (or
more red-shifted) part.
2.7 Summary
We presented CARMA observations of H13CO+(1-0) and HNC(1-0) for five
regions in Serpens Main, Serpens South and NGC 1333 containing filaments. For
the four Serpens regions, we also obtained data on the H13CN(1-0) emission. The
observations have an angular resolution of ∼ 7′′ and a spectral resolution of 0.16
km/s. We studied the morphology and kinematics of these regions, comparing
them to existing maps of the dust continuum and N2H
+(1-0) emission. Our main
conclusions are summarized below.
• The emission distribution in the H13CO+ maps traces similar filamentary
structures as the N H+2 maps obtained by CLASSy, and correspond to the
same morphology and kinematics.
• In many regions, multiple velocity-coherent structures are present, identifi-
able by multiple peaks in the H13CO+ spectrum. H13CO+ is the only species
observed by us that allows us to unambiguously disentangle the overlapping
components.
• Some of these multiple structures are filament sub-structures that are roughly
aligned with each other even though they have velocity differences of 0.5 −
1.0 km/s between them. We identify 2 sub-structures each in 3 filaments,
69
while 2 filaments are each found to be comprised of a single velocity-coherent
component. We report statistics of these 8 filamentary structures.
• The mean width of these filamentary structures is 0.05 pc, but they vary in
the range of 0.03− 0.08 pc. Along the same filamentary structure, the width
can vary by a factor of 2. The widths of velocity-coherent filaments in the
dense gas tracers are a factor of 1.5 narrower than the Herschel widths.
• Four of the eight filamentary structures have significant velocity gradients
perpendicular to the filament length, with mean values in the range of 4− 10
km s−1 pc−1. This provides evidence for predictions from simulations, in which
filaments form via inflows within the dense layer created by colliding turbulent
cells.
• Two filamentary structures in Serpens Main have velocity gradients along their
lengths, which increase closer to the cloud core. This may indicate gravita-
tional inflow of filaments into the central core.
• Class 0/I/Flat YSOs are identified only along two of the filaments, and are
found to be preferably located at the overlapping regions of the filamentary
structures. This suggests that the sub-filaments are physically interacting with
each other, which possibly plays a role in star formation.
Overall, the observations support the presence of finer structures within the
Herschel filaments with systematic properties like alignment of sub-filaments and
presence of velocity gradients across them. These properties suggest a common
70
formation mechanism. Features like the large distribution of widths of filamentary
structures and the presence of YSOs only in some of the regions indicate their di-
versity. These can arise from local effects or could be dependent on the evolutionary
stage of the filaments.
71
Chapter 3
Ammonia Mapping
3.1 Introduction
Maps spanning large to small scales are fundamentally important to under-
stand star formation in molecular clouds. The relative importance of processes such
as turbulence, magnetic fields, gravity and chemical evolution vary at the different
scales, all contributing to the birth of a protostar. In addition, feedback from star
formation also affects the molecular cloud environment over a range of distances.
Large area gas and dust surveys of molecular clouds ranging from parsecs to about
1000 AU are required to get the complete picture of the formation and evolution of
dense structures that eventually form stars.
In going from the less dense regions of the clouds to denser filaments and on
to cores, a sharp transition from turbulent to thermal line widths has been observed
[150, 151, 152]. This suggests that dense cores may form as pressure-confined struc-
tures within filaments and evolve to gravitationally bound cores before undergoing
collapse to form a protostar. Observations at high angular resolution and over large
areas are required to understand the spatial variations of the velocity dispersion
and column density in these regions. Such observations can be compared against
72
theoretical predictions from turbulent star formation models [90] to verify and con-
strain them better. Magnetic fields within the cloud can affect core fragmentation
and collapse by providing pressure support [153]. By comparing kinematics of neu-
tral and ionic species in the gas [154], it is possible to determine the presence and
significance of magnetic fields. Radiation feedback from the embedded protostars
also play an important role in suppressing fragmentation of cores [155]. Numeri-
cal models show that protostellar outflows and wind from intermediate-mass stars
can drive turbulence in the molecular clouds [156, 157]. This is suggested based on
observations of cavities and shells in Perseus as well [158, 159]. Gas temperature
maps that are sensitive from large to small scales can establish the importance of
the feedback processes involved in star forming regions [160, 161].
In the previous chapter, we have seen how dense gas tracers like N H+2 and
H13CO+ can be used to map the high density gas in the clouds and understand the
filament structure and motions. In this chapter, we study the NGC 1333 region in
Perseus using high angular resolution Very Large Array (VLA) observations of NH3
inversion transitions. NH3 is an abundant molecule that traces gas of density greater
than 104 cm−3 [18] and is a late-depleter [162]. Nitrogen containing molecules like
NH3 and N
+
2H remain in gas phase longer than carbon and oxygen molecules such
as HCO+, HCN, and CO. Hence, it is particularly suitable to study cores [163]
and dense regions of the molecular clouds that are expected to participate in star
formation in the future. Most previous observations using NH3 involved small target
areas around cores. The Green Bank Ammonia Survey (GAS) [164] is the first large-
scale NH3 survey of all the major clouds in the Gould Belt. However the 32
′′ beam
73
is insufficient to resolve the cores. The VLA observations reported here make it
possible to probe the regions close to the cores at a resolution of 1025 AU and to
study how the emission is connected to the large scale emission over the molecular
cloud.
The NGC 1333 region in Perseus is a reflection nebula at a distance of 293
± 23 pc (based on the recently available Gaia observational data). It is known for
its active low-to-intermediate mass clustered star formation [165, 166]. There exists
a wealth of information for this region, which is rich in sub-mm cores[167], YSOs
[161, 168], outflows [169], Herbig Haro objects [170] and masers [171]. The Spitzer
cores to disks (c2d) [172, 173] legacy survey, the Herschel PACS and SPIRE images
[76], the James Clark Maxwell Telescope (JCMT) Gould Belt survey [174] and the
CARMA CLASSy observations [109, 175] all provide complementary data to track
the YSOs and put the VLA data in larger context.
Using the VLA NH3 (1,1) observations, we obtain line-of-sight velocities, ve-
locity dispersions and optical depth maps. On comparing with the CARMA N2H
+
maps and the dust maps, we establish the morphology and kinematics of the clouds.
The intensity ratio of the NH3 (1,1) and NH3 (2,2) lines are used to obtain the gas
temperatures of the entire region. We are also able to derive NH3 column density
maps, and using the N H+2 line temperatures can estimate the physical density of
the entire region. The gas temperature and column density maps can be compared
against the corresponding dust maps from Herschel data.
74
3.2 VLA Observations of Perseus
The K-band (18-26 GHz) observations were carried out using the VLA array
of 25-m antennas in D configuration providing a resolution of about 4′′. The NGC
1333 region is covered by 87 pointings to cover an area of 102 square arcminutes
They were observed in multiple sessions, with 8-12 minutes integration time on each
pointing. The observations were carried out from March to May 2013.
The correlator was set-up to observe the NH3 (1,1), NH3 (2,2), NH3 (3,3)
and NH3 (4,4) lines with a channel width of 3.9 kHz (corresponding to about 0.049
km/s). The maximum sub-band bandwidth of 4 MHz was not sufficient to cover
all the satellites of the Ammonia inversion transitions. So two partially overlapping
sub-bands were used for NH3 (1,1) and NH3 (2,2). The relative intensities of the
satellites are negligible for NH3 (3,3) and NH3 (4,4). So we used a single sub-band
for them covering only the main transition line. CC34S N=1-2, J=2-1, HNCO 1(0,1)-
0(0,0), H2O maser 6(1,6)-5(2,3), CCS N=1-2, J=2-1 and
15NH3 (1,1) lines were also
available to be observed in the same set-up (see Table 3.1). A channel width of
7.8 kHz was used for these observations to improve the signal-to-noise ratio (SNR),
anticipating their relatively low brightness temperatures. Two continuum bands of
width 128 MHz were also observed at 22.3 GHz and 23.9 GHz.
Flagging and calibration were carried out using the CASA EVLA pipeline.
J0336+3218, 3C84 and 3C147 were used as phase, bandpass and flux calibrators
respectively. The calibrated visibility data in the measurement sets was cleaned
using the CASA tclean routine. The synthesized beam over the channels has a
75
Molecular Species Transition Frequency Channel Frequency
(MHz) Width (kHz) Range (MHz)
NH ±3 (J,K) =(1,1)
+-(1,1)− 23694.4955 3.9 5.574
NH3 (J,K)
±=(2,2)+-(2,2)− 23722.6333 3.9 5.574
NH3 (J,K)
±=(3,3)+-(3,3)− 23870.1292 3.9 1.997
NH (J,K)±3 =(4,4)
+-(4,4)− 24139.4163 3.9 1.997
15NH3 (J,K)
±=(1,1)+-(1,1)− 22624.9295 7.8 1.997
HNCO J(Ka,Kc)=1(0,1)-0(0,0) 21981.5726 7.8 1.997
H2O J(Ka,Kc)=6(1,6)-5(2,3) 22235.0798 7.8 1.997
CCS N=1-2, J=2-1 22344.0308 7.8 1.997
CC34S N=1-2, J=2-1 21930.4860 7.8 1.997
Table 3.1: Observed Molecular Lines
median size of 3.76′′ × 3.34′′. For the NH3 lines, the mean value of the spectral
channel RMS noise is 6.8 mJy/beam at the native channel width. Channel binning
was carried out to improve the sensitivity and look for detections in the rarer species,
at the cost of velocity resolution. NH3 (1,1) and NH3 (2,2) were detected over large
areas in the observed regions. NH3 (3,3) was only detected at the outflows in the
NGC 1333 region. Six 22 GHz H2O masers were also detected. In the remaining
five molecular species transitions, no emission was detected above the noise.
3.3 Combination of Interferometric and Single Dish Data
The maps produced from the VLA data alone have strong negative sidelobes,
which is typical of maps produced from interferometric visibility data due to the
lack of small u-v spacings [176]. In our VLA data, the minimum u-v spacing is 25
m. Consequently, in many areas of the map the negative sidelobes corresponding
to strong emission elsewhere suppress the actual flux levels and spatial variations
even though the interferometer is sensitive to small scale structure. This issue can
76
be remedied by using complementary single dish observations [177]. The NGC 1333
region has been observed in NH3 (1,1), NH3 (2,2) and NH3 (3,3) with the Green
Bank Telescope (GBT) as part of the Green Bank Ammonia survey (GAS) [164] and
the data are publicly available. These data were combined with the high resolution
VLA maps to make the maps sensitive to large scale structure as well. In the rest of
the chapter, we only discuss the NH3 inversion transition observations in the NGC
1333 region.
The strategy described in Koda et al. (2011) [178] is adopted to combine the
interferometric and single dish data. This involves converting the single dish data
to visibilities to fill the inner part of the u-v plane, followed by weighting these
visibilities with respect to the interferometric visibilities. This combined visibility
dataset is inverse Fourier transformed and cleaned to produce the final image. There
are multiple ways to combine the data from single dish telescopes and interferom-
eters. Other methods involve combining the data in the image domain [179], or
further Fourier transforming the image domain data and then combining them [180]
(as is done in the CASA feather routine). Since inverse Fourier transforming the
visibilities to produce the interferometric image is a non-linear process, combining
them after this step leads of loss of information from the interferometric component.
Thus we combine the data in the visibility domain. This method involves a Fourier
transform too while generating the visibilities from the single dish image and can
lead to some loss of information on the large scale structure, but since we prioritize
the interferometric data, we use this method.
The GBT single dish maps have a spectral resolution of 5.7 kHz (∼ 0.07 km/s
77
Figure 3.1: Left : u-v plane showing the coverage of VLA observations (green) upto
150m, and the coverage of the visibilities generated from the GBT observations
(red). Middle: Comparison of the GBT (red) and VLA (green) visibility amplitudes.
Right : Matched weights of GBT (red) and VLA (green) visibilities after scaling.
at 23.7 GHz). We binned the channels by a factor of 2 to improve the SNR, while
having 5 channels to cover the typical FWHM linewidth of 0.7 km/s. The resulting
channel width is about 3 times the VLA channel width. A total of 400 channels
cover all the NH3 (1,1) and NH3 (2,2) hyperfine components. We converted the map
from K to Jy/beam using a factor of 0.69 taking into account the GBT beam size
of 31.8′′ × 31.8′′. The mean RMS of the resulting SD map is 0.059 Jy/beam.
After extracting the relevant region of the map, we generate fake visibility
data from the single dish data cubes using the tp2vis program [178]. This involves
sampling the GBT single dish map with the VLA pointings with a 25 m primary
beam (same as the VLA beam) and with u-v distances up to 100 m (equivalent to
the GBT diameter). The single dish visibilities are inverse Fourier transformed to
check how the resulting map compares with the input single dish map. The flux
levels are within 10% of original map, and there are no noticable differences in the
intensity distributions.
The weight densities (weights/GHz/pointing/arcmin2) of the single dish vis-
78
Images u-v range Channel Widtha Synthesized Beam Sensitivity
VLA 25 - 1000 m 3.9 kHz 3.76′′× 3.34′′ 0.007 Jy/beam
GBT 0 - 100 m 5.7 kHz 31.8′′× 31.8′′ 0.083 Jy/beam
Combined 0 - 1000 m 11.4 kHz 3.93′′× 3.41′′ 0.004 Jy/beam
a Native channel widths for VLA and GBT maps, and rebinned channel width for combined
map.
Table 3.2: Properties of the original and combined NGC 1333 images
ibilities are compared with that of the interferometric visibilities. Accordingly the
single dish weights are scaled to roughly match them (Figure 3.1). This ensures
that the sensitivities transition smoothly from the large scales to the smaller scales.
This combined set of visibilities is now used to generate the dirty map and cleaned
using the qac clean routine that uses the CASA tclean routine [181]. We use the
multiscale deconvolver with scales of 0′′, 4′′ and 12′′. The cleaning proceeds by a
set of major cycles transforming between visibility and image domains progressively
updating the model and residual images. Within each major cycle, an inner loop of
minor cycles cleans the map in the image domain. We needed to induce more major
cycles without cleaning too deep in the corresponding minor cycles to avoid picking
up the interferometric artifacts. So a ‘cycleniter’ parameter of 1000 was used. Based
on the noise RMS of 0.004 Jy/beam, we also use a ‘threshold’ parameter value of
0.02 Jy/beam, which decides the minimum target peak flux at the end of each minor
cycle for each channel. Typically, the channels containing signal are cleaned in 10-15
major cycles. In regions having strong emission, the flux remaining in the residuals
is less than 10% of the total flux.
The final maps thus obtained do not have negative sidelobes and show the
79
high resolution features, while being sensitive to the large scale structure. The syn-
thesized beam is 3.93′′ × 3.41′′. The flux values are compared to the interferometric
maps obtained from the VLA data alone in Figure 3.2. Typically the average flux in
regions of strong emission in the VLA maps is about 20% lesser than the correspond-
ing flux in the combined maps, but the local spatial variations of the flux are very
similar. The maps are also smoothed to the GBT beam size and compared to the
original GBT map (Figure 3.3). In this case, all fluxes match up to about 5%. Since
the NH3 (2,2) emission traces warmer gas, it is less extended, and consequently the
flux levels in the combined map are better matched with the interferometric map
fluxes than for NH3 (1,1).
The weighting parameter used prior to the visibility combination is critical in
the combined mapping. Assuming the GBT weighting parameter in the nominal
case to be 1, we use GBT weights in the range of 0.25 to 4 on a single channel
containing signal to obtain the corresponding dirty maps and study the progression
of the cleaning process in each of them. We used the same ‘cycleniter’ parameter
as before (1000), and set a threshold of 3 times the RMS noise in the dirty maps.
As shown in Figure 3.4, in the nominal case the total flux remains close to the
GBT flux (scaled for the beam area) throughout the cleaning cycles. For higher
(lower) than nominal GBT weights, the total flux in the dirty map is very high
(low), but with progressive iterations the final cleaned flux reaches closer to that of
the nominal weight case. Eventually they end up within a factor of 2 of the total
flux in the nominal case for a weight factor of 4. Most of the contribution to this
difference comes from the extent of the emission, which increases with increasing
80
Figure 3.2: Comparisons of combined VLA and GBT map (left) with only VLA
map (right) shown here for a single channel after cleaning. The small scale flux
variations are present in both, but the distinct negative sidelobes of the VLA only
map are absent in the combined map.
81
Figure 3.3: Comparisons of combined VLA and GBT map convolved to the GBT
beam size (left) with the original GBT map (right) for a single channel. The fluxes
match up with less than 5% variations in most regions.
82
Figure 3.4: Evolution of model flux, residual flux and total flux with major cy-
cles of cleaning iterations for a single channel sub-region containing signal for VLA
and GBT combined dirty maps. Top-left, top-right and bottom-left : Flux evolu-
tion for different weights of the GBT visibilities (0.25, 1 and 4 times the nominal
weights respectively) used while combining with the VLA visibilities. Bottom-right :
Comparison of the total flux evolution with cleaning for different weights of GBT
visibilities. The dotted line indicates the total flux in the corresponding GBT map
channel (scaled based on the beam size ratio). The total number of iterations is
different in each case because the threshold limit of 3σ (where σ is the RMS noise
of the combined dirty map) is reached after different number of major cycles.
GBT weights. The differences in regions of peak emission are lesser (< 10% for a
weight factor of 4). The model flux and residual flux also end up at different ratios
with respect to the total flux in the different cases. The beam areas only vary by
about 2% for a factor of 4 in the weights. We compare the outcomes of the final
cleaned channel maps for GBT weights 0.25 and 4 in Figure 3.5.
83
Figure 3.5: Comparisons of combined VLA and GBT maps for a single channel for
different weights of the GBT visibilities: 0.25 (left) and 4.0 (right) times the nominal
weight. The left image shows more of the interferometric artifacts, while in the right
image the emission is more extended and the total flux is overestimated by about a
factor of 2.
84
3.4 Results
The NH3 inversion transitions involve quantum tunneling of the N nuclei
through the plane of the H nuclei in the same rotational quantum state (J,K). How-
ever, the inversion transition has hyperfine components due to electric quadrupole
coupling (quantum number denoted by F1) and magnetic dipole coupling (quan-
tum number denoted by F)[16, 19]. In case of NH3 (1,1) there are 18 hyperfine
components that are bunched into 5 groups of 2, 3, 8, 3 and 2 lines based on the
F1 transition. Their theoretical relative intensities are 0.111, 0.139, 0.5, 0.139 and
0.111 respectively. Similarly, the NH3 (2,2) transition has 24 hyperfine components
also divided into 5 groups of 3, 3, 12, 3 and 3 lines, having relative intensities 0.05,
0.052, 0.796, 0.052 and 0.05 respectively. In both cases, the central line is the main
component, and the other four components are called satellite components.
3.4.1 Ammonia (1,1) Results
NH3 (1,1) main and satellite lines are detected over large areas in the NGC
1333 region. However, the relative intensities of the hyperfine components vary in
different regions from their theoretical relative intensities. We also note the presence
of clear multiple velocity-coherent components in the spectrum in multiple regions
(see Figure 3.6). Integrated intensity maps are generated from the position velocity
data cubes, by using channels near the line centers containing signal, and clipping
them at 3σ based on the RMS noise of each channel map. Figure 3.7 shows the
integrated intensity map for the main NH3 (1,1) component. We have roughly
85
Figure 3.6: Top row: NH3 (1,1) spectrum at the West region, where the relative
intensities of the satellite components are similar. The dotted line gives the spectral
fit, while the vertical lines on the x-axis indicate the relative frequencies and the
amplitudes of the 18 hyperfine components. Three of the satellite components are
resolved into two peaks because of the hyperfine components. Second row: NH3
(1,1) spectrum at an area in the SVS 13 region, where the intensities of the satellite
components deviate from the theoretical expectations. The inner satellites have
much lesser intensities compared to the outer ones. The dotted line indicates the
spectral fit. Third row: NH3 (1,1) spectrum at an area also in the SVS 13 region,
showing the presence of multiple velocity components. The difference in the line-
of-sight velocities is greater than 1 km/s. Bottom row: NH3 (2,2) spectrum at the
same area as the NH3 (1,1) spectrum in the top-most row.
86
divided the map into 11 regions based on their location in the map or the main
embedded protostellar source(s) in the region.
IRAS 4, IRAS 2 and SVS 13 are well known YSO systems, each of which has
been resolved into multiple sources [166], and are all located in the central cloud
core. There is a known Herbig-Haro object HH 12 in northern region, and it is
located at the apex of the two filaments (NW and NE filaments). To the west of the
HH 12 region, there is a region of modest emission, but no protostars are detected
in this region. There is a similar relatively quiescent area to the west of the IRAS
2 region. The IRAS 7 protostellar cluster region is located to the east of the NE
filament. Towards the south there is a narrow ‘u’ shaped filament connecting the
IRAS 2 and the IRAS 4 regions. At the bottom of the ‘u’ is a known Class 0 YSO
source – SK 1 [182]. There is another narrow short filament in this area extending
towards the south-west from the IRAS 2 region. The cloud core near IRAS 4 extends
to a wide filament in the south-east, which has been studied in the previous chapter
as part of the CLASSy-II regions.
Spectral line fitting is carried out to obtain the NH3 velocity structure of NGC
1333. Since we noted that the relative intensities of the satellites do not match
theoretical predictions in many areas, we allow the peak intensities for each of the
5 NH3 (1,1) components to vary. The magnetic dipole based hyperfine splitting
within each of the 5 groups also have spreads ranging between 11 kHz and 56 kHz.
As some of them are resolvable by our channel width of 11.4 kHz, we fit the spectra
to a model having all 18 hyperfine components. However, even though we vary the
relative intensities (an) of the 5 groups of hyperfine components (n = 1,2,3,4,5), we
87
Figure 3.7: NH3 (1,1) (main component) integrated intensity map for the NGC 1333
region. The map beam size is indicated at the bottom-right corner. The locations
of the known Class 0/I (red circles) and Flat (black circles) YSOs are marked.
The circles correspond to a diameter of roughly 5000 AU (about 5 times the map
resolution). The different regions discussed in the chapter are also indicated. They
are separated by dotted lines in regions of continuous emission.
88
assume that the relative intensities (wi) of the components (denoted by i) within
each of the 5 groups to be based on the theoretical values (as given in Table 15 of
Mangum & Shirley (2015) [16]). We assume a single line-of-sight velocity vlos and
a Gaussian line shape with a single dispersion value σv for all the 18 components.
Thus we fit the spectrum at each pixel as a function of velocity S(v) using the
following equation:
∑5 ∑ ( )v − vlos − c∆fi/f0
S(v) = an wi exp − (3.1)
2σ 2v
n=1 i
where c is the speed of light, ∆fi is the frequency offset of the hyperfine component
relative to the line center frequency f0 = 23.6944955 GHz. We solve for a1, a2,
a3, a4, a5, vlos and σv. We mask the pixels that have lesser than 4σ detections in
all channels. The pixels containing emission from outflows are identified by their
unusually wide Gaussian fits and omitted. The results are shown in figures 3.8, 3.9,
3.10 and 3.11. The intensity map distributions can be considered to be representative
of the brightness temperature distributions.
The peak intensity map for the main NH3 (1,1) component has a median value
of 30 mJy/beam. This corresponds to a brightness temperature of 4.9 K. The max-
imum brightness temperature goes up to as much as 20 K near the IRAS 2 sources.
The four satellite components a1, a2, a4 and a5 have median brightness tempera-
tures of 2.4 K, 2.0 K, 2.1 K and 2.1 K respectively. The ratios between the different
components are not consistent throughout the map, but typically indicate an optical
depth of greater than 1 for the main component, while the satellite components can
89
Figure 3.8: NH3 (1,1) main component peak intensity map for the NGC 1333 region.
90
Figure 3.9: NH3 (1,1) satellite components peak intensity map for the NGC 1333
region obtained by spectral fitting.
91
Figure 3.10: NGC 1333 line-of-sight velocity map from spectral fitting of NH3 (1,1).
92
Figure 3.11: NGC 1333 velocity dispersion map from spectral fitting of NH3 (1,1).
93
be considered to be optically thin.
On comparing the main component intensity map (Figure 3.8) to the inte-
grated intensity map (Figure 3.7), we find many differences in the maximum inten-
sity regions. The integrated intensity map has greater intensities near the Class 0/I
YSOs, but the peaks of the brightness temperatures are well distributed throughout,
including the filaments and regions having low integrated emission. This difference
is particularly evident in the south west quadrant of the map. The SK 1 region, the
West region and the southern part of the IRAS 2 region all have greater brightness
temperatures compared to the northern part of the IRAS 2 region. Yet, the IRAS
2 northern region has greater integrated intensities.
Correspondingly, we see in Figure 3.11 that the velocity dispersion is greater
in the regions containing the protostars (although they don’t always peak at the
YSO locations, but around them). They are particularly high near the boundaries
of the SVS 13 region going up to as much as 0.8 km/s compared to the nominal
values of about 0.3 km/s in the filaments. Some of the high dispersions correspond
to known locations of outflows as well.
In some regions, we see sharp boundaries in the dispersion map where areas
having different estimates of dispersion are adjacent to each other. They are caused
by the presence of multiple velocity components of comparable intensities. In such
cases, depending on the relative intensities, the spectral line fitting which fits for
a single component, may select one of the components or fits both of them to a
Gaussian with a greater width. These multiple velocity components also tend to be
located near the protostellar sources. In addition, the SE filament has a distinct
94
narrow region of higher dispersion as well. This is caused by the presence of the two
parallel velocity coherent sub-filaments partially overlapping in the line-of-sight [175]
(as discussed in the previous chapter). In the narrow region, the two components,
which have comparable intensity get fit by a Gaussian with a greater dispersion
value. These multiple velocity component spectra also affects the velocity map and
the intensity maps, but the effects are less drastic in those maps.
The intensities of the satellite components also show variations, even though
they have a good positive correlation of about 0.8 − 0.9 to each other and to the
main component. In the ideal case of no anomalies, the correlation is expected to
be 1. The F1=0-1 satellite component has greater mean intensities over most of
the regions than the other satellites, while the F1=2-1 and the F1=1-0 satellites
have relatively lesser mean intensities of all the satellites. The F1=1-0 emission
has lesser contrast between the strong emission regions and the surroundings. A
mechanism to explain the deviations from the theoretical relative intensities of the
satellites was suggested by Stutzki & Winnewisser (1985) [183]. In their paper, the
hyperfine anomalies are caused by selective trapping of infrared photons in the (J,K)
= (2,1) to (1,1) transition. They are generally associated with maser activity and
are postulated to be associated to star forming clumps of high density. A suggested
indicator of this effect involves the ratio of the intensities of the outer satellites or
the inner satellites. Typically TB(F1=1-0)/TB(F1=1-0) and TB(F1=2-1)/TB(F1=1-
2) are both expected to be less than one in the selective trapping based anomalous
regions [184].
We generated maps of these two intensity ratios O = TB(F1=1-0)/TB(F1=1-0)
95
and I = TB(F1=2-1)/TB(F1=1-2). The anomalous regions were defined to be ones
where O is less than 0.8 or greater than 1.2. By this definition, 55% of the unmasked
pixels are found to be anomalous. We found that the anomalous regions are spread
throughout, but are in lesser concentration in regions of high NH3 (1,1) integrated
intensity. The lower ratio (O < 0.8) regions comprise 67% of the anomalous pixels,
while the higher ratio regions (O > 1.2) are concentrated mainly near the IRAS
4 region. Also we found no correlation between O and I (Spearman correlation
coefficients between -0.1 and +0.1), even after selecting only the lower ratio anoma-
lous pixels. Thus the selective trapping mechanism fails to account for the relative
intensity anomalies in the NGC 1333 region.
The line-of-sight velocity map shows rich variation throughout the map with
values ranging from 6.25 km/s to 9.25 km/s. The velocity gradient in the SE filament
(discussed in the previous chapter), extends to the IRAS 4 region and further north
to the SVS 13 region. The west part of the SVS 13 region has velocities varying
monotonically by 2.0 km/s in the north-south direction. Similar large gradients are
present in the northern part of the HH 12 region (in the east-west direction), and
immediately to the west of the IRAS 4 sources. The IRAS 2 region also has a large
magnitude velocity gradient in the SE-NW direction, but it is not monotonic. Most
of these large gradients are caused by a combination of (a) multiple velocity-coherent
components with varying intensities across the field of view and (b) a gradient across
a single velocity-coherent component.
The NE filament has a single velocity coherent component in most of the
northern half and it has a gradient across it which changes direction once. Going
96
from east to west, the gradient changes from positive to negative near the ridge. In
the southern half, again there is a gradient across the filament which changes from
negative in the east to positive in the west, but this seems to be caused by multiple
velocity components in the line of sight. The velocity dispersion map of this region
shows sharp contrast region along the filament ridge. The NW filament, SK 1 region,
the West region and the IRAS 2 have relatively lesser variations of about 0.5 km/s.
The NW region has the least line-of-sight velocity variations among all fields.
3.4.2 Ammonia (2,2) Results
For the integrated intensity map of NH3 (2,2) (Figure 3.12 left), we used a
lower clip value of 2 times the RMS noise to cover a greater area of the map, that
would be useful for the analyses in the following section. The NH3 (2,2) detections
are spread over a relatively lesser area and they peak closer to the Class 0/I YSOs
compared to the NH3 (1,1) integrated intensity emission. An outflow (from IRAS
2A) between the IRAS 2 region and the West region has NH3 (2,2) emission but is
absent in the NH3 (1,1) map.
The satellite components of NH3 (2,2) have very low relative intensities and are
indistinguishable from the noise for most regions (see Figure 3.6 bottom panel). We
fit the central component of the NH3 (2,2) spectra with 12 hyperfine components,
using their theoretical weight ratios. We fixed the line-of-sight velocities from the
corresponding values of the NH3 (1,1) map to ensure fitting for the same velocity
component as in NH3 (1,1). In single component regions, solving for the line-of-
97
sight velocity gives the same result in both NH3 transitions, but this is not always
followed in regions having multiple components in the line of sight. So, we solved
for the velocity dispersion and a single peak intensity for the main NH3 (2,2) com-
ponent. The peak intensity map is shown in Figure 3.12 right. The median value
is 9 mJy/beam corresponding to a brightness temperature of 1.5 K. The maximum
brightness temperature is 7.5 K near the protostellar sources in the SVS 13 region.
For the (2,2) transition there is a better match between the integrated intensity
map and the peak intensity map. Only the IRAS 2 region shows a reversal in the
areas of maximum intensity for the two maps, i.e. in this region the areas having
greater NH3 (2,2) integrated intensity have lesser NH3 (2,2) velocity dispersions and
vice-versa.
3.5 Analysis
3.5.1 Optical Depth
The optical depths can be calculated using the ratios of the main and satellite
components of NH3 (1,1) assuming the hyperfine levels to be in local thermodynamic
equilibrium (LTE). In this approximation, the optical depth ratios of the main to
satellite components are equal to their respective theoretical intensity ratios (α).
The optical depth at any of the NH3 inversion transitions’ line center τm can be
calculated by solving for the equation [16]:
T (m) 1− e−τmR
= (3.2)
TR(s) 1− e−ατm
98
Figure 3.12: NH3 (2,2) integrated intensity map (left) and NH3 (2,2) main compo-
nent peak intensity map of the NGC 1333 region.
99
where TR(m) and TR(s) are the main and satellite component source radiation tem-
peratures. Their ratio is equal to the ratio of the respective relative intensities
am and as obtained from the spectral line fitting. For either of the outer satel-
lites of NH3 (1,1), the theoretical value of α is 2/9. For the inner satellites, α is
5/18. We calculated the optical depth for the main component separately using the
mean outer satellite intensities τm,outer and using the mean inner satellite intensities
τm,inner. The mean was taken to reduce the effect of the intensity anomalies, and
to get a better optical depth estimate by taking advantage of the same theoretical
α values. τm,outer was found to be systematically higher than τm,inner based on the
relative intensities. The variations in the intensity distribution get magnified in the
τm maps and using the mean of the two inner or the two outer satellites does not
nullify this effect. In some regions the intensity ratios are so skewed, that we get
non-physical values of τm, particularly for τm,inner. Due to these effects, over the
entire map area, the τm,inner and τm,outer only have a modest positive correlation of
about 0.31.
To obtain a representative τ(1,1,m) for NH3 (1,1), we use intensities of all the
four satellites after scaling up the outer satellite intensities by a factor of 5/4 (ratio
of theoretical intensities), and using a value of 5/18 for α in equation 3.2. The
optical depth map is shown in Figure 3.13. All the regions are fairly optically thick
(median value 2.1), with no particular identifiable distribution pattern. We use this
value of τ(1,1,m) for the next analysis steps.
100
Figure 3.13: NGC 1333 optical depth map at the NH3 (1,1) line center obtained
using the ratio of all the satellite components to the main component of NH3 (1,1)
(after appropriate scaling).
101
3.5.2 Temperatures
The level populations of the two quantum states (n+ and n−) involved in the
NH3 (1,1) inversion transition are related by an excitation temperature Tex in the
equation
n+ g+
= e−hν/kTex (3.3)
n− g−
where g+ and g− are the statistical weights of the two levels. The statistical weight
ratio is 1 for the inversion transitions of NH3. The transition frequency is ν. The
Boltzmann constant and the Planck constant are denoted by k and h respectively.
The sum of n+ and n− gives the total level population of the corresponding J=K
quantum state.
If we assume that a single value of Tex is applicable to all the hyperfine com-
ponents of the inversion transition, we can use the optical depth and the brightness
temperature Tb(1,1,m) of the main component of NH3 (1,1) to determine the NH3
(1,1) excitation temperatures Tex(1,1) by solving for the equation
( 1 )
T −τ(1,1,m)b(1,1,m) = [1− e ] (3.4)Jν(Tex)− Jν(Tbg)
where we have assumed a beam filling factor of 1. The (1,1) inversion transition fre-
quency is ν and Jν(T ) is the Rayleigh-Jeans equivalent temperature at a frequency
ν of a black body at temperature T . It is given by Jν(T ) = hν/[exp( hν )− 1]. Thek kT
background radiation temperature Tbg is 2.73 K. The resulting excitation tempera-
ture map is shown in Figure 3.14. The median Tex(1,1) value is 9.4 K and it increases
102
to a maximum of 20 K in the IRAS 2 region.
Similar to Tex, a rotational temperature Trot can be used to define the ratio of
the NH3 level populations for (J,K) = (1,1) and (2,2) (column densities N(1,1) and
N(2,2) respectively):
N(2,2) 5
= e−41.0/Trot (3.5)
N(1,1) 3
The factor 5/3 comes from the J-degeneracies and 41.0 K corresponds to the
energy difference between the (1,1) and the (2,2) levels. From this equation, it is
possible to derive Trot in terms of the NH3 (1,1) optical depth τ(1,1,m), the ratio of the
NH3 (1,1) and NH3 (2,2) main component intensities (TR(2,2,m)/TR(1,1,m)) and the
ratio of the NH3 (1,1) and NH3 (2,2) velocity dispersions (σv(2,2)/σv(1,1)) as follows
[185]:
{ [ }0.283σ ( )]
− − v(2,2)
TR(2,2,m)
Trot = 41.0 ln ln 1− (1− e−τ(1,1,m)) (3.6)
τ(1,1,m)σv(1,1) TR(1,1,m)
The rotational temperature can be used to solve for the kinetic temperature TK
in the following equation [186] based on statistical equilibrium and detailed balance
{ T ( )}K
Trot = TK 1 + ln 1 + 0.6e
−15.7/TK (3.7)
41.5
The rotational and kinetic temperature maps are shown in Figures 3.15 and
3.16 respectively. Both maps have very similar distributions. The median values of
Trot and TK are 13.0 K and 12.4 K respectively. Over the cloud core, there are many
regions of high temperature near the three main Class 0/I YSO groups. In addition,
103
Figure 3.14: NH3 (1,1) excitation temperature map of NGC 1333.
104
Figure 3.15: NGC 1333 rotational temperature map obtained from the NH3 (1,1)
and NH3 (2,2) maps.
105
Figure 3.16: NGC 1333 kinetic temperature map obtained from the rotational tem-
perature map. The Class 0/I/Flat YSOs are overlaid as in Figure 3.7. The contours
of the Herschel temperature map (in K) are overlaid. The contour levels are 11, 13,
15, 17, 19 and 21 K. The Herschel beam is shown at the top-right corner.
106
the west part of SVS 13 region has higher temperatures between 14 K and 17 K. At
the southern-west tip of this region, the temperature reaches 20 K. The northern
part of the NW filament near the HH 12 region also has higher temperatures of
16− 18 K compared to the other filaments.
Figure 3.16 also has the Herschel dust temperature map contours [187] overlaid
on them for comparison. Most of the filaments have temperatures between 11 K
and 13 K, lesser than the temperatures (∼ 14 K) in the less dense areas of the
cloud. The dust temperature values in the filaments and quiescent regions are in
fair agreement to the kinetic temperatures obtained for NH3 indicating that the
dust that is thermodynamically coupled to dense gas [188]. The dust temperatures
are however greater than the NH3 temperatures near the YSOs, with values greater
than 20 K near IRAS 4, IRAS 2 and SVS 13. The dust temperatures are also greater
than 16 K near IRAS 7 and HH 12. In these regions, the effective dust temperatures
are elevated because the line-of-sight dust emission is dominated by the contribution
from the warm regions near the protostars, unlike the NH3 which traces the entire
column of dense gas [189]. We also note that in regions closer to the YSOs, there
are greater temperature variations in the high resolution NH3 map than in the dust
map.
3.5.3 Column Density
To derive the column density of NH3 we first express the column density of
the upper level of the (1,1) inversion transition N(1,1),+ in terms of the optical depth
107
τ(1,1) and the excitation temperature Tex(1,1) using the following equation
∫
3hJ(J + 1) 1
N(1,1),+ = τ(1,1)dv (3.8)
8π3µ2K2 (ehν/kTex(1,1) − 1)
where the dipole moment of the NH3 molecule µ has a value of 1.468 Debye. Using
equation 3.3, the ratio of the column densities of the two inversion states in (1,1)
can be written as
N(1,1),+
= e−hν/kTex(1,1) (3.9)
N(1,1),−
where N(1,1),− is the column density of the lower energy level of NH3 (1,1). So the
total column density of the NH3 (1,1) is
N(1,1) = N(1,1),− +N
hν/kTex(1,1)
(1,1),+ = N(1,1),+(e + 1) (3.10)
Assuming a single rotational temperature Trot to define all the (J,K) level
populations, the total NH3 column density Ntot can be estimated from N(1,1) and
the rotational partition function Qrot using the following equation [185]:
N(1,1)Qrot
N = eE(1,1),+/kTrottot (3.11)
gJgKgI
where gJ and gK are the rotational degeneracies and gI is the spin degeneracy. For
NH3 (1,1) their values are 3, 2 and 0.25 respectively. E(1,1),+ is the energy of the
upper level in the NH3 (1,1) inversion transition. The value of E(1,1),+/k is 24.35 K
where k is the Boltzmann constant. This derivation includes both ortho and para
108
species of NH3.
By combining equations 3.8, 3.10 and 3.11, we get
∫
3hJ(J + 1) Q hν/kTex(1,1)rot e + 1
Ntot = e
E(1,1),+/kTrot τ(1,1)dv (3.12)
8π3µ2K2 gJg g ehν/kTK I ex(1,1) − 1
Since the optical depths for the different components of NH3 (1,1) are different, we
express the total optical depth in terms of the main component optical depth of NH3
(1,1) using a relative intensity factor Ri = 0.5. By using equation 3.4, we can express
this op∫tical depth in terms of the integrated intensity of the main component of NH3
(1,1) ( TR(1,1,m)dv). We use a correction factor of τ/(1−e−τ ) for the optically thick
case [130] which is applicable for most of the regions being analyzed.
3hJ(J + 1) Q ehν/kTex(1,1)rot E + 1N = e (1,1),+/kTrottot
8π3µ2K2 gJgKgI ehν[/kTe∫x(1,1) − 1 ]
T
× 1 R(1,1,m)
dv τ(1,1,m)
(3.13)
R J (T )− J (T ) 1− e−τ(1,1,m)i ν ex ν bg
The expression can be simplified to:
1.137/T ∫ex(1,1) τ
Ntot = 4.51×
1 + e (1,1,m)
1012 Q e24.35/Trotrot T dv cm
−2
1.517− e1.137/T R(1,1,m)ex(1,1) 1− e−τ(1,1,m)
∫ (3.14)
where TR(1,1,m)dv is in K km/s. The optical depths, excitation temperatures and
rotational temperatures were calculated in the previous section. To calculate the
109
partition function Qrot, we use the formula:
∑∑
Qrot = (2J + 1)g g e
−EJK/kTrot
K I (3.15)
J K
The K-degeneracy gK is 1 for K = 0 and 2 for K 6= 0. The nuclear spin degeneracy
value gI is 0.25 for K = 3n and 0.5 for K 6= 3n, where ‘n’ is a non-negative integer.
The energy levels EJK up to J=5 are available in Table 9 of Mangum & Shirley
(2015) [16] and are sufficient for our rotational energy temperature ranges.
The resulting column density map of NH3 is shown in Figure 3.17. The column
density values vary over two orders of magnitude, with a median value of 9.9 × 1014
cm−2. In the eastern part of the SVS 13 region, the NH3 column density is as high
as 5 × 1015 cm−2. This region coincides with the minimum dust temperatures (∼
10.5 K) as well as gas kinetic temperatures (∼ 10 K) in NGC 1333. The filaments
have lesser column density than the cloud center, with the NW filament having the
least column densities (mean value of 7 × 1014 cm−2). We overplot the dust column
density map contours (from Herschel) for comparison. The dust map traces the
same structures as the NH3 map (at the 36
′′ Herschel beam scale), including the
narrow filament in the SK 1 region. The typical values are 3 × 1022 cm−2 in the
filaments and goes up to 9 × 1022 cm−2 at the cloud cores. The only exception is
the region close to the IRAS 4 sources, where the dust column density is relatively
much higher compared to the NH3 column density in that region.
110
Figure 3.17: NH3 column density map for the NGC 1333 region. The Class 0/I/Flat
YSOs are overlaid as in Figure 3.7. The contours of the Herschel column density
map are overlaid. The contour levels are 1.5, 3, 6 and 12 in units of 1022 cm−2. The
Herschel beam is shown at the top-right corner.
111
3.6 Discussion
One important question that arises is how much of the different NH3 maps
show the true characteristics of the dense gas and the dust. In the previous section,
we have seen good correlation with the Herschel temperature and column density
maps, but that comparison was limited by the 10 times larger beam size of maps
compared to our VLA and GBT combined maps. In this section, the regions are
compared with the CLASSy-I N H+2 maps covering the entire NGC 1333 region
(Storm et. al. in prep.) and with the JCMT 850 µm dust emission map [174] from
the JCMT Gould Belt Survey.
3.6.1 Cloud Morphology
The CLASSy-I N2H
+ (J=1-0) maps at 93.173 GHz have a synthesized beam
size of 9.06′′× 7.58′′, a channel width of 195.2 kHz (0.63 km/s) and a sensitivity of
0.08 Jy/beam. Figure 3.18 (left) shows the integrated intensity map (color), with
the NH3 (1,1) integrated intensity contours overlaid on them. The two maps show
very good agreement on all scales. The N H+2 maps have slightly better SNR which
results in it having a greater extent especially near the filaments. The only region of
noticeable difference between the N +2H and NH3 (1,1) map is at the north-eastern
edge of the NW filament, which has relatively greater emission in N H+2 . This is
the same region where higher temperatures were calculated from the NH3 (1,1) and
NH3 (2,2) maps (see Section 3.5.2).
The JCMT Gould Belt survey observations also surveyed the Perseus region.
112
The map beam size is 15′′. A comparison with the NH3 integrated intensity map
(Figure 3.18 right) also shows good correlation except in the regions associated
with embedded YSOs, where the dust emission strongly increases due to increasing
column density and temperature on the small scale. On close comparison, we suspect
that the JCMT map is offset by about half the beam size in the south-west direction.
This is particularly evident in the NE filament, and the right arm of the narrow ‘u’
shaped filament in the SK 1 region. One clear fact from the JCMT comparison is
that the integrated intensity maps of NH3 and N H
+
2 are poor tracers of individual
YSOs. This is also clear from the NH3 column density map in Figure 3.17.
The high values in the NH3 temperature map have good correspondence with
the outflows of the region [169] observed using CO maps and Hα maps. The Herbig
Haro objects HH 7-11 are associated with the high temperatures in the northern
part of the SVS 13 region. The high temperature region in the HH 12 region and
the connected NE filament is identified in literature as a bow shock structure [190].
The western part of the SVS 13 region and the parts of the IRAS 2 region are heated
by the outflow from IRAS 2A.
3.6.2 Cloud Kinematics
To analyze the kinematics of N H+2 in comparison to NH3, spectral fitting was
carried out for all the 7 hyperfine components of N2H
+, with variable amplitudes
for the three F1 quantum number based groups of lines. The resulting line-of-sight
velocity map and its difference with the convolved and regridded NH3 velocities are
113
Figure 3.18: N2H
+ integrated intensity map (left) and JCMT (SCUBA) 850 µm
map (right) of the NGC 1333 region with NH3 (1,1) integrated intensity contours
overlaid on them. The contours are at 0.01, 0.02, 0.04 and 0.08 Jy beam−1 km s−1.
The beams of the two maps are shown at the bottom right.
114
Figure 3.19: Left: N2H
+ line-of-sight velocity map of NGC 1333 obtained from
spectral line fitting. The region names that are discussed in the chapter are marked
on this map. Right: Difference between the NH3 and N
+
2H velocity maps. NH3
(1,1) integrated intensity contours are overlaid on them as in Figure 3.18.
115
shown in Figure 3.19. The two maps are very well correlated in most regions to
within the error in the N2H
+ spectral fitting (based on the channel width of 0.63
km/s). The IRAS 4 region and the SVS 13 region have the greatest differences
between the two velocities. On investigating these regions with the F1=1-0 isolated
hyperfine component of N +2H (J=1-0), we found that this is caused by the presence
of multiple overlapping velocity-coherent components in these regions. In most cases,
the multiple components have similar relative intensities for both molecular species;
so the spectral fitting, which does a single velocity fit gives comparable line-of-sight
velocities. Two small regions (near SVS 13 on the east and near IRAS 4 on the
west) show greater than 1 km/s difference in the velocity values. Here the relative
intensities of the two velocity-coherent components in the two species are reversed,
resulting in one getting selected by N H+2 and another by NH3.
The results indicate that NH3 is tracing the same material as N2H
+ and the
dust, and that most features in the NH3 map can be expected in high resolution
maps of other similar dense gas tracers. Since a lot of these regions have multiple
velocity components, it is challenging to get a good estimate of each of these compo-
nents using complex molecular tracers like N2H
+ and NH3 both of which have many
hyperfine components. Attempts to fit for multiple velocity components resulted in
degenerate solutions, especially since the relative intensities of the hyperfine com-
ponents also vary from region to region. To get a good representation of all the
multiple velocity components, some of these regions (especially near the Class 0/I
YSOs) need to be observed with dense gas tracers like H13CO+. It is optically thin
in most regions and has no hyperfine splitting, thereby allowing easier identification
116
of the different velocity components. This would also allow better estimation of the
velocity dispersion of each component. A single component fit sometimes overesti-
mates the dispersion in the dynamic environment near protostars having multiple
velocity-coherent components.
3.6.3 Filaments in NGC 1333 and their relation to Star Formation
We identified 3 filaments in the NGC 1333 region (SE, NE and NW filaments)
and some narrower filaments in the SK 1 region. The FWHM values of the filaments
range from 0.015 pc in the SK 1 region to 0.05 pc in the NW filament. The cor-
responding deconvolved widths from the JCMT map after taking into account the
larger beam size, show that the filament widths in dust are greater by about 50%.
These results match with those for the CLASSy-II filaments.
3.6.3.1 Filament formation by colliding turbulent cells
The NH3 (1,1) map of the SE filament indicate the presence of two parallel sub-
structures as with the H13CO+ and N2H
+ observations. With the H13CO+ map, our
analysis (Section 2.4.5) showed that one of the two sub-structures has a significant
velocity gradient across it. With the large area high resolution NH3 (1,1) maps, we
can put this in perspective of the kinematics of the entire cloud. We note that in
the southern part of NGC 1333, there is a large region having line-of-sight velocities
around 6− 7 km/s, which is at least 1 km/s lesser than the adjacent regions in the
rest of cloud. We see a large velocity gradient all along the southern edges of the SE
filament, IRAS 4 region, the SVS 13 region and the IRAS 2 region. The gradient is
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as much as 2 km/s across 0.09 pc in the SVS 13 region. It continues into the IRAS
4 region and the SE filament, where the gradients are comparable (1 − 1.5 km/s
across 0.04 pc). The IRAS 2 region also shows a ridge of high velocity resulting in
a sharp gradient in the SE-NW direction. We propose that this could indicate that
a large-scale (∼ 0.5 pc) turbulent cell is moving towards the cloud center from the
south (in the projected sky plane). The collision between this cell with the cloud
could result in the formation of a layer of compressed gas.
The importance of supersonic turbulence in structure formation is well estab-
lished by hydrodynamic simulations (with or without magnetic fields) [88, 191, 192].
Generally driven by stellar winds and supernovae [193], these large-scale supersonic
flows generate locally planar shock layers of compressed gas and help in transferring
energy to smaller scales. In such shock layers created by colliding cells, dense struc-
tures can form seeded by turbulent velocity perturbations [23] or at the intersection
of shock fronts [192]. With increasing density, gravity starts becoming dominant
amplifying the initial anisotropies and resulting in filament formation.
There are additional observational evidences of this scenario. In the SE fila-
ment region studied with H13CO+ we identify a velocity gradient across the filament
in agreement with the model by Chen and Ostriker as discussed in Section 2.6.1.
In this scenario, the velocity gradient is a projection effect of accretion within the
dense layer created by colliding turbulent cells. Secondly, these regions along the
high velocity gradient ridge also have relatively high velocity dispersions (> 0.5
km/s) in the NH3 (1,1) map that is typical for shocked layers. Thirdly, we see many
protostars along the boundary of this proposed compressed gas layer. This region
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has the highest number of Class 0/I YSOs in the entire region studied by us. They
are divided into the multiple systems IRAS 2, IRAS 4 and SVS 13. The star for-
mation in this region could be triggered by gravitational instabilities in the dense
gas layer. Similar interpretations have been made for cloud-cloud collisions based
on observations [194, 195, 196], and is often reported in simulations [197, 198, 199].
We detect multiple parallel sub-structures in the SE and NE filaments, and
all along the proposed compressed gas layer. Similar observations of parallel sub-
structures in the Serpens filaments and in observations by other authors [80, 99]
indicate that this is an important feature related to filament formation. A common
formation mechanism like the ‘fray and gather’ model [100] has been proposed based
on hydrodynamic simulations of turbulent clouds. In this model, the sub-filaments
are formed first and gathered together by large scale motions of the cloud. Alter-
natively, it could be explained as multiple filaments forming in the dense gas layer
created by colliding turbulent cells, which on projecting in the sky plane can seem
parallel to each other. Another explanation involves formation of a wide filament
that fragments into multiple sub-filaments [140].
3.6.3.2 Effect of Outflows on Filaments
The NE filament and the NW filament are in regions known to be impacted
by outflows. Knee & Sandell (2000) [190] showed that the cavity between these
filaments is filled with high-velocity gas from several outflows. They identified HH
12 as the leading bow shock of a Class 0 source in the SVS 13 multiple system.
The region inbetween these filaments is clear of dust and gas, and many evolved
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YSOs and main sequence stars are present here. Past outflows from these sources
could have played an important role in the formation of the NE and NW filament by
clearing out the cloud. Quillen et al. (2005) [158] interpreted the two filaments as
the walls of ancient outflow cavities which are no longer actively driven. Outflows are
known to clear the gas surrounding forming stars, that eventually lead to disruption
of the cloud [200]. They could also gravitationally unbind the gas in the dense core
and stop the stellar mass accretion phase [201]. It is estimated that at the current
rate of energy ejection from the outflows in NGC 1333, the entire cloud will be
dispersed in 10 million years [190].
The NE filament shows major velocity variations along its length (∼ 0.7 km/s)
and across its width (∼ 0.5 km/s) with a ridge of maxima in the north and a ridge
of minima in the south. In addition to the evolved sources on the west of the NE
filament, the outflow from one of the IRAS 7 sources [170] can also contribute to the
morphology of the NE filament from the eastern side. We observe small sections of
parallel sub-structures (having different velocities) in the southern part of the NE
filament. The narrow ‘u’ shaped filament in the SK 1 region has been proposed to
be a dust shell by Lefloch et al. (1998) [202]. However, in the NH3 (1,1) velocity
dispersion map, we find that this filament has very low dispersion values (∼ 0.15
km/s), which is not expected in bow shocks. The cavity to its north could still have
been cleared out by outflows from one or more of the sources in the cloud core.
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3.6.3.3 Star Formation
We find that many of the Class 0/I YSOs are embedded in the cloud, but
not necessarily confined to the filaments. There is one Class 0/I source at the
southern tip of the NW filament, and another similar source SK 1 in the ‘u’ shaped
filament. Most of the remaining Class 0/I sources are present in the protostellar
multiple systems like IRAS 2, IRAS 4 and IRAS 7. Of these, seven of the sources are
present along the proposed high-velocity-gradient ridge identified in Section 3.6.3.1.
The compression of the gas to very high densities can make them gravitationally
supercritical and induce cores and protostars to form within them [93, 203].
There are a string of Flat YSOs in the less dense area north of the SVS 13
region. Along the NW filament, there is a sequence of 5 Class II YSOs. The
relatively evolved YSOs are spread throughout the cloud including the low density
regions. These evolved stars may have participated in clearing out some regions
of the cloud through outflows. The formation of the Class 0 YSO sources – VLA
42 in the HH 12 region and SK 1 have been proposed to be triggered by outflow
bow shocks by Sandell & Knee (2001) [204]. We do not find sufficient evidence for
the same in the case of SK 1, because of the low velocity dispersion values along
the proposed shock layer. However, in case of VLA 42, there is evidence of high
temperatures (> 16 K) and velocity dispersions (∼ 0.4 km/s) in this region over a
large area (compared to the VLA beam area). Bright Hα emission is also detected in
this region [205], which further supports the shock-triggered star formation scenario
for VLA 42. Thus outflows could be playing an important role in regulating star
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formation in NGC 1333.
3.7 Summary
In this chapter, NH3 observations are used to study the morphology, kinematics
and temperature of the entire NGC 1333 region at an angular resolution of 4 ′′. We
demonstrated the importance of high resolution large area maps that are sensitive
to structure at all the spatial scales. To attain this, VLA interferometric data was
combined with GBT single dish maps in the visibility domain. We have studied the
effects of the various parameters that are important in the joint deconvolution of
the visibility data.
For further analysis, we used data cubes corresponding to NH3 (1,1) and NH3
(2,2) inversion transitions, which have the maximum emission among all the ob-
served transitions. The final data cubes have a channel width of 11.4 kHz, a syn-
thesized beam of 3.93′′ × 3.41′′, and a sensitivity of 4 mJy/beam. We produced
the integrated intensity maps for both NH3 (1,1) and NH3 (2,2). Line fitting was
carried out taking into account all the hyperfine components of NH3 (1,1) to obtain
the peak intensity maps of the main and satellite components, the line-of-sight ve-
locity map and the dispersion map. For NH3 (2,2), we used a similar method on the
main component to obtain its peak intensity map and the dispersion map. We also
derived maps of the optical depth for the NH3 (1,1) main component, the rotational
temperature, the kinetic temperature and the column density of NH3.
Using these maps, we studied the distribution and properties of the dense gas
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in NGC 1333. Our main conclusions are summarized below.
• In regions near the cloud center and in some filaments, we observed multiple
velocity components in the cloud. Many of these components are parallel
to each other indicating that they could be affected by a common physical
process.
• In many regions, there are large deviations from theoretical expectations in
the relative intensities of the NH3 (1,1) main and satellite groups of hyperfine
components. The observed anomalies in the NGC 1333 region do not sup-
port the theory involving hyperfine selective trapping [183]. Although these
anomalies affect the optical depth map, the effects on the temperature maps
are negligible.
• We found very good correlation of the NH3 (1,1) maps with the morphology
and kinematics of the corresponding N2H
+ (J=1-0) maps. In regions away
from the protostellar sources, the dust maps from JCMT and Herschel also
match well with the NH3 (1,1) integrated intensity map. They all trace the
same material in these regions.
• The northern part of the region has many active outflows, which possibly
cleared out a cavity between two filaments.
• In the southern part of the map, based on the continuous large velocity gra-
dient pattern, the presence of Class 0/I YSOs along the region of the gradient
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and other kinematic signatures, we have argued that this is a region of com-
pressed gas formed by the collision of large-scale turbulent cells.
Overall, the NH3 observations of the entire NGC 1333 region are very rich
in information and have many clues about star formation in molecular clouds. We
have postulated theories to explain some of these observations. Further analysis of
the data needs to be carried out to study the regions around each of the protostars,
by investigating the relation between the various map features at all the scales.
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Chapter 4
The Balloon Experimental Twin
Telescope for Infrared
Interferometry
4.1 Introduction
Dense gas tracers are useful to study the dynamics and physical conditions
of the gas in molecular clouds participating in star formation. Although dust con-
tributes to a small fraction of the total mass compared to the gas mass, it plays a
very important role in the star formation process as well. Dust absorbs short wave-
lengths and radiates in the thermal infrared, thereby removing the gravitational
energy of collapsing clouds and allowing star formation to take place [206]. The
spectral energy distributions (SEDs) of these protostellar sources peak in the FIR
wavelengths. Since the stars generally form in clusters, we need to study the dust
emission at a high resolution to complete the star formation picture. The balloon-
borne interferometer BETTII has been developed to study this FIR emission from
star forming regions at a high angular resolution. BETTII was conceived as a tech-
nology demonstration and pathfinder mission for interferometry in space, while also
providing unique scientific capability [69, 207]. It is a 2-aperture interferometer
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designed to fly on a balloon at an altitude of 37 km.
BETTII has a baseline of 8 meters between its two 0.5 meter (projected) di-
ameter apertures (Fig. 4.1). It is a double-Fourier Michelson interferometer that
combines long-baseline interferometry with Fourier Transform Spectroscopy to cap-
ture both spatial and spectral information [208]. BETTII is expected to achieve
a spatial resolution of 0.5-1.0′′ and a spectral resolving power λ/∆λ of up to 100
in the FIR wavelengths (30 to 100 µm). Its ability to perform spatially resolved
spectroscopy will allow us to resolve protostellar clusters in molecular clouds into
multiple young stellar objects and measure their spectral energy distributions.
While the concept for BETTII builds heavily upon the foundations laid by
concepts for space-based interferometers (SPIRIT, SPECS etc.), it also builds off of
the tradition of NIR and optical ground-based interferometry (CHARA, VLTI etc.).
These systems, and their long-wavelength counterparts (VLA, ALMA etc.), have
demonstrated the scientific value of high angular resolution observations and have
addressed many of the fundamental technical challenges of long baseline interferom-
etry. BETTII will serve as a bridge between these facilities and future space-based
interferometers, needed to provide complementary data at wavelengths inaccessible
from the ground.
4.2 Studying Star Formation Using BETTII
BETTII has two science bands: 30-55 µm (short wavelength or SW Band) and
55-100 µm (long wavelength or LW Band). It is expected to have a sensitivity of 25
126
Figure 4.1: Left: BETTII Model and Right: BETTII at CSBF Fort Sumner.
Jy and 13 Jy in the SW and LW bands respectively to achieve a spectral signal-to-
noise ratio (SNR) of 5 in 10 minutes at a spectral resolution R = 10 [209]. BETTII is
designed to probe very luminous regions of embedded protostars in binaries, multiple
systems or clusters. At typical distances of 300 pc to star forming regions, BETTII’s
angular resolution translates to hundreds of AU. BETTII observations will allow
us to obtain the SEDs of the protostars in these multiple systems, and thereby
determine their individual temperature, mass and luminosity.
The BETTII observations will be able to test predictions from accretion mod-
els like Turbulent Core Collapse and Competitive Accretion. The main difference
between these two models is in the stage when accretion takes place. In Turbulent
Core Collapse model, the prestellar core already contains most of the mass that goes
into forming the protostar (or protostars in multiple systems). On the other hand,
in Competitive Accretion, multiple cores 1000s of AUs apart share a common mass
reservoir or envelope, from which the protostars accrete by competing gravitation-
ally. By resolving the emission in these protostellar systems, BETTII will be able
127
to determine the extent of the emission around the protostars. If the emission is
localized around individual protostars, then the Turbulent Core Collapse model is
more likely, and if the emission is more extended, Competitive Accretion would be
considered the favored mechanism. Thus the BETTII data will shed light on the
origins of the initial mass function of stars born in clusters because most of the mass
accretion occurs while the protostars are embedded in the dust.
In low multiplicity systems, BETTII can also reveal various physical properties
of each protostar such as the distribution of mass between the protostellar disk
and the envelope around it [210]. This is also critical to study the co-evolution
of protostellar cores embedded in molecular clouds. The spectroscopy provided
by BETTII will help detect broadband features due to water ice and silicate-rich
minerals.
The first science targets of BETTII are S140 (see Figure 4.2) and IRAS
20050+2720. S140 is a cluster of 5 identified sources separated by 5-15′′ [211]. The
sources have brightness values in the range 350 Jy to 2650 Jy at 37 µm and should
be easily detected by BETTII. Currently, their SED fluxes between 37 µm and
100 µm are estimates from super resolution fitting. Their FIR emission peaks are
expected to fall within BETTII’s wavelength range. The observations will resolve
the SEDs from the individual sources up to 100 µm. Notably, S140 is circumpolar
and is therefore observable at all flight times, and from a wide range of baseline
orientations.
The second source, IRAS 20050+2720 [212] is composed of 5 bright YSOs in
close proximity (∼ 5.5′′) that are unresolved in the FIR wavelengths. The BETTII
128
Figure 4.2: (a) Observed 37 µm image of S140 using SOFIA-FORCAST from Harvey
2012 [211]. BETTII’s angular resolution of 1′′ in the SW band is shown at the
bottom left in yellow. (b) The spectra of the five sources in S140 from the same
paper. Observations are available up to 37 µm. The flux values at 50 µm and
100µm for 3 of the sources are estimates. The SW and LW Bands of BETTII are
overlaid.
team acquired SOFIA-FORCAST data and constructed the SEDs of these sources
from 3 µm to 40 µm by combining this data with Spitzer-IRAC data [71]. BETTII
observations will provide the longer FIR wavelength information to complete the
SEDs and enable modeling of the dust emission and hence material distribution. It
will also allow us to resolve the core into individual FIR sources. This may include
sources that are not seen or unresolved at any other wavelength.
BETTII’s combination of wavelength coverage, spatial resolution, and spec-
troscopic capability will provide essential information on star formation that is not
available from any existing or planned facility. The data from BETTII will com-
plement ALMA and JWST observations by providing sensitivity to material in the
temperature range from 50− 150 K. Thus, it will break degeneracies between tem-
perature and column density distributions, thereby providing essential data for ra-
129
diative transfer models. This will shed new light on how protostars accrete dust and
gas in clustered regions, and how they evolve onto the main sequence.
4.3 Instrument Design
BETTII is designed around its optical system. It consists of a 8-meter long
truss that supports the light collecting and collimating optics on its two arms, and
a cryostat at its center for housing the remaining optics train and the detectors (see
Figure 4.1). Built around this carbon-fiber truss is an aluminum exoskeleton, which
supports all the electronics and most of the control system. The exoskeleton has
fixtures at the top for suspending the payload from the balloon. The entire payload
weighs about 1000 kg. At float altitudes of 37 km, the ambient temperature is
expected to be about 240 K.
The cryostat has an inner liquid 4He cooled volume at 4.2 K and an outer
liquid-N2 cooled volume at 77 K. The 4.2 K volume contains the optics that combines
the compressed beams from the two arms and focuses them to 4 science detectors.
The 77 K volume contains the optics for a tracking channel (1 − 2.5 µm). The
science channel detectors are transition edge sensor (TES) bolometer arrays [213].
There are 9x9 array elements, each of size 1 mm2, that are read out using a single
Multi-Channel Electronics (MCE) unit. There is a 3He+4He sorption refrigerator
for cooling the detectors to 300 mK. Before the science channel beams are combined,
the path lengths between them are systematically modulated using a delay line (cold
delay line or CDL). Each stroke of the delay line generates an interferogram (a plot
130
of intensity vs optical path length difference) on each of the detector array pixels.
These are the primary science outputs of BETTII containing the spectral and spatial
information of the source field. All electrical systems are slaved to a single master
clock, for synchronous controlling and data collection.
The pointing control system of BETTII uses 3 gyroscopes, 2 star cameras and
a near infra-red (NIR) tracking detector (H4RG) as sensors. Based on the target
pointing, it uses a Compensated Control Moment Gyro (CCMG) for controlling
azimuth pointing, rotation stages for controlling elevation, a warm delay line (WDL)
assembly for correcting for pendulating motions of the payload and tip-tilt mirrors
for finer pointing control. In addition, there is a momentum dump mechanism
to maintain the CCMG wheels close to its nominal position. The light-collecting
siderostats are mounted on the rotation stages, such that the surface normal is at
45 degrees with respect to the baseline vector and the pointing vector. The rotation
axes are aligned to the baseline. Thus, while the entire balloon payload rotates
for pointing to the target azimuth, the target elevation is achieved by rotating the
siderostats.
4.4 Engineering Flight
The development of BETTII started at NASA Goddard Space Flight Center
in 2011. Over the following five years, the payload was designed, constructed and
tested. In 2016, BETTII was ready for a flight to calibrate the payload and demon-
strate the functioning of each subsystem individually and in conjunction with the
131
Figure 4.3: BETTII during launch at Palestine, TX
others. In Fall 2016, a launch was attempted from the Columbia Scientific Bal-
loon Facility (CSBF) in Fort Sumner, NM. A morning launch with at least 4 hours
flight time after sunset or an evening launch was preferred so that the instrument
had more dark time effects of non-uniform solar heating are eliminated. However,
unsuitable weather conditions prevented launching in Fort Sumner.
Another flight campaign was planned in Palestine, TX in 2017. On June 8th
at 7.15pm, BETTII was successfully launched for its first Engineering Flight (Figure
4.3). During ascent, we monitored the temperatures of the various subsystems and
the truss using the communication system and ground station software. We switched
on heaters at different points on the truss based on the local temperature values.
Once BETTII reached float altitudes of 25 km and above (at 10pm), we tested
the different subsystems. Star camera solutions were obtained to determine the
pointing and propagated successfully using the gyroscopes. Closed-loop pointing
control was demonstrated using the momentum dump mechanism [214]. The delay
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lines were successfully operated in flight. The flight electronics and software were
validated. NIR images were obtained in the H4RG detector. We established that the
thermal performance over the flight duration was satisfactory, and that the truss
was structurally stable and thermally homogeneous meeting the requirements for
interferometry.
There were a few issues during flight. One was a cold leak in the cryostat
during rollout, that resulted in the Helium reservoir being empty by the time of
launch. This prevented an on-flight test of the 3He fridge and characterization of
the FIR arrays. Another issue was identified in the control system – communication
between the flight computer and the CCMG controller was lost due to a network
issue. This prevented us from testing the control system completely during flight.
However, even though these issues prevented us from carrying out some of the flight
tests, most of these systems had been tested on ground, and there was a clear path
to resolution of these issues. The only system that could have only been tested
on flight is the closed loop fine pointing. As an Engineering Flight, BETTII was
very successful. Based upon the flight results, the team was confident that BETTII
would be ready for its first Science Flight in Fall 2018.
After a 12-hour overnight flight, it was time to bring the payload back to
ground and at 8am the payload was released from the balloon. At this point a critical
anomaly occurred, which resulted in the payload separating from the parachute
leading to a free-fall from 41 km altitude to ground. The payload was almost
completely lost on crash-landing. A NASA post-flight investigation showed that this
problem occurred because the steel pin that attached the gondola to the payload had
133
snapped during parachute deployment. This happened due to poor material choice,
as the steel used for the purpose was strong but brittle at very cold temperatures.
The BETTII team’s review and the CSBF safety review failed to identify this issue
prior to flight. Only a small fraction of the flight hardware including some of the
optics inside the cryostat was deemed re-usable or refurbishable. The team managed
to recover all the flight data.
4.5 BETTII: Looking Forward
The team is currently rebuilding the payload (BETTII-2) to complete the tech-
nical and scientific objectives. The new model draws heavily from the old design,
but at the same time upgrading some aspects of the design to improve the per-
formance, facilitate easier testing and/or reduce costs and risks [215]. Titanium is
being used instead of carbon fiber to make the truss structure stronger and lighter.
The new rotator pin will also be made of titanium. A new exoskeleton has been
built. The instrument cryostat has been re-designed to increase the hold time to
more than 30 hours, and to simplify the integration and independent testing of the
optics and the cryogenic systems. It also allows future integration of a cryocooler,
needed for long-duration flights. A new power system has been designed and built.
It uses a single battery pack with a set of isolating DC-DC converters.
In addition to this, the optics system (discussed in details in the following
chapter) is also getting an upgrade. A dispersive backend has been included in
the design to improve the instrument sensitivity. The gratings and their location
134
in the optics train has been finalized, and the effects on the detector output has
been modeled. In addition, some modifications in the optics have been carried
out to reduce thermal loading on the ‘liquid 4He cooled’ volume, and to facilitate
interferometric testing of the FIR optics in the lab. The optics design modifications
are discussed in further detail in the final section of Chapter 5.
135
Chapter 5
BETTII Optics
5.1 Optical Layout and Design
A double-Fourier Michelson interferometer involves collecting light from mul-
tiple apertures (for spatial interferometry) and changing the delay between them
systematically (for spectral interferometry) before combining them in the pupil-
plane and focusing them on to detectors [208]. BETTII’s design comprises two
light collecting siderostats at the two ends of its 8-meter long truss structure. The
siderostats are elliptical in shape with a projected diameter (on sky) of 0.5 m. They
steer the light onto a telescope assembly on each arm that compresses the beam, re-
ducing its width by a factor of 20 (see Figure 5.1). The telescope assembly achieves
this with the help of an off-axis parabolic mirror (primary), a flat mirror, an ellipti-
cal mirror (secondary), and another small parabolic mirror (tertiary) –all mounted
on a trough structure attached to the truss.[216, 217]
After this, the optical design which is otherwise bilaterally symmetric for the
two arms, has its single asymmetric feature. Arm 1 has a delay line (warm delay
line or WDL) to compensate for the path length differences between the two arms
primarily due to pendulations of the balloon. Arm 2 has a 3-mirror arrangement to
136
Figure 5.1: (a) BETTII optics schematic. The dashed line separates the external
optics on the left and the internal optics (inside the cryostat) on the right. (b)
The ray trace from the apertures (siderostats) to the detector modeled using FRED
Optical Engineering software. Here the siderostats are pointing at an elevation of
90◦. The global reference frame is marked in red, and an example local reference
frame is shown in black for the +Y arm siderostat. (c) Zoomed in view of the
telescope assembly showing its 4 reflective components. (d) Zoomed in view of the
rays in the FIR bench.
137
rotate the beam by 180 degrees which ensures that they are aligned when combined
with the other beam. This is called the K-mirror assembly. The final mirrors in the
optical train of both the warm delay line and the K-mirror have a tip-tilt mechanism
to correct for pointing errors during tracking.
The two beams enter the cryostat at the center of the truss structure through
a polypropylene window. The beams are divided into two channels by a dichroic:
reflecting FIR for the science (>30 µm), and transmitting NIR (1.0− 2.5 µm) used
for tracking. The NIR beams are focused onto a H4RG detector array, which acts a
sensor for the control system involving the tip-tilt mirrors as actuators. (Earlier a
H1RG array was planned to be used for this purpose, and was used in an alignment
test discussed in the Chapter 6.) The FIR beams are guided on to a parabolic
mirror-spherical mirror assembly used to re-image the entrance pupil at a cold pupil,
thereby rejecting the thermal emission entering through the cryostat window. This
is followed by a cold delay line assembly, which systematically varies the optical
path difference between the two arms. The beams are combined using a 50-50
beam-combiner producing two output beams. The reflected part of each beam
combines with the transmitted part of the other. They further pass through a
dichroic, separating them into two science channels SW Band: 30− 55 µm and LW
Band: 55−100 µm, and focused on to 4 detector arrays (two frequency bands times
two beam-combiner outputs). The total field of view for the SW Band detectors
and the LW Band detectors are 2.0 and 2.5 sq. arcmins respectively.
In addition to the reflective optics and dichroics, there are filters and thermal
blockers at appropriate locations to prevent non-science frequencies from contami-
138
nating the output. The FIR optics are mounted on a bench and are in the 4.2 K
chamber, while the NIR optics are at 77 K within the cryostat. The entire opti-
cal system was designed using the Zemax OpticStudio software, and later analyzed
using the FRED Optical Engineering software.
5.2 Design Challenges
For an interferometric system, it is of utmost importance to maintain the
wavefronts of the beams from the two arms until combination, i.e. the phase in-
formation of the two beams should be preserved. Phase errors can arise due to a
variety of reasons: surface figure errors of the reflective surfaces, mirror misalign-
ment, temperature variations and differences between the two arms, pointing jitter,
pendulation and delay line errors. Of these, the path length difference errors are
zeroth-order phase errors, the tip-tilt errors of the beam-front are first-order phase
errors while the surface figure errors typically result in higher order phase errors.
The opto-mechanical design mitigates these at different levels – in fabrication, in
alignment, using active optics during flight, and using knowledge of error while post
processing.
First, all mirrors and their mounts (with the exception of the two tip-tilt
mirrors) are made of Aluminum-6061. The high thermal conductivity of aluminum
helps in attaining fast thermal equilibration and the fact that all the optics are made
of the same material allows homologous contraction of each assembly symmetrically
for the two arms during flight. The siderostats, the primary telescope mirrors and
139
the flats, which are the largest mirrors, have been light-weighted to reduce gravity
sag/ deformation and to provide greater surface area for heat dissipation. Heat
treatment of optics bench, mounts and all mirrors, have been carried out to prevent
distortion of optical surfaces caused by internal stress. Second, we have identified the
most critical mirrors for alignment in terms of translation and rotation errors. The
alignment plan takes into account the alignment of the mirrors within each assembly,
and all the assemblies with respect to each other. Alignment of the optics is covered
in details in Chapter 6. Third, the active optics include a delay line (Warm Delay
Line) to correct for pendulation, and a pair of tip-tilt mirrors for correcting residual
tip-tilt errors (first order phase errors). The delay lines use capacitive sensors for
distance measurement which provide knowledge of optical path differences up to
1 µm. This will be used in post-processing to re-interpret the detector outputs,
thereby forming our final level of phase error mitigation.
In addition to this, BETTII’s attitude control system also counters some of
the phase errors during flight. It provides a pointing stability of 1′′ over a timescale
of minutes and 0.1′′ over a timescale of 0.1 second.
5.2.1 Fabrication
5.2.1.1 Aluminum Mirrors
The large optics at the beginning of the optics train (siderostats, telescopic
primary mirrors and flats) were designed and fabricated in collaboration with North
Carolina State University (NCSU) [218]. The mirrors have been diamond turned
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Figure 5.2: (a) all-Aluminum Telescope Assembly: Primary, Flat, Secondary and
Tertiary mounted on a trough (b) Optics bench with only the FIR optics mounted.
[219] to meet our surface figure requirements of 300 nm RMS. This corresponds
to λ/100 at the shortest wavelength which reduces the spectral SNR by 0.1% only
[209]. For BETTII, the surface figure is more important than the surface roughness
because the former is required to maintain the phase across the entire beamfront and
affects the fringe visibility, while the latter reduces the throughput due to scattering.
The weight of each of the 520 mm diameter primary mirrors is only 5.7 kg. The
areal densities (mass/aperture area) of the large mirrors are relatively low and in the
range 6 − 10 kg m−2 thereby reducing gravity sag and the thermal time constant.
The design also involves kinematic Kelvin coupling and pre-deflected clamps to
decouple mounting structure deformations from the optical surface, thereby reducing
distortions. One dimension of the elliptical siderostats was too large (730 mm) to be
diamond turned at once. A multi-step diamond turning process was used identically
on the two siderostats, such that the optical path differences between the two arms
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Figure 5.3: Active Optics Assemblies: (a) K-mirror (b) Warm delay line (c) Cold
delay line. The final mirrors of the K-mirror and the warm delay line are mounted
on tip-tilt stages.
of the interferometer for every part of the beam remains the same.
The remaining Aluminum mirrors (34 in number) were fabricated by diamond
turning as well (at Nu-Tek Precision Optical Corp.). They have surface figures in
the range of 10− 30 nm RMS.
5.2.1.2 Dichroics and Filters
The filters, thermal blockers and dichroics have metal-mesh designs [220].
They were all fabricated at Cardiff University, with the exception of the NIR-FIR
beamsplitter. This beamsplitter has an inductive grid design of gold deposited on a
sapphire substrate [221]. For this purpose, the PMMA positive resist patterning was
carried out using an electron beam lithography system at NIST (National Institute
of Standards and Technology). The combined transmission from all these filters is
shown in Figure 5.4.
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Figure 5.4: Left: 50-50 Beam-splitter – metal-mesh design and Right: Combined
transmission curves for all the FIR filters in the optics train for each of the 4 science
channels. The vertical lines demarcate the proposed science bands. Based on the
filters designed, the LW Band extends beyond 100 µm wavelength, instead of the
originally proposed upper limit of 90 µm.
5.2.2 Heat Treatment
During flight, the optical bench will be at a temperature of 4.2 K, while the
optical alignment is carried out at room temperature of about 300 K. Heat treatment
was carried out to reduce internal stress and associated distortions of the Aluminum
optical bench, optical mounts and the cold volume mirrors (before the final cut
was made). The procedure used is called Uphill Quenching [222]. This involves
putting an object through alternate rapid heating and cooling cycles. The heating
was carried out in a heat chamber equipped with a fan until the air temperature
stabilized to the set value of 530 K, while the cooling was done by immersing the
pieces in liquid Nitrogen until bubbling stopped. The heat chamber temperature
was set to relatively high value to ensure a very fast rate of heating.
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5.2.3 Coating
After the internal optics were delivered, they were gold coated, to provide
oxidation protection and a very high reflectivity in our wavelength range. It was
decided that the large optics (the siderostats, primary mirrors and the flats) were
to be coated with SiO for abrasion protection since they are exposed to the open
environment during preparation for flight. It was found using a test piece that
the variation in coating from the edge to the center was 14 nm, well within the
acceptable limits for our experiment. The reflectivity in the 30 − 100 µm band
was measured to be 98%. Further all the non-optical surfaces are painted white for
thermal considerations. The paint has a low ratio of solar absorptivity to infra-red
emissivity (α/ε ∼ 0.3) , thereby assisting to attain thermal equilibrium faster.
5.3 Delay Lines
5.3.1 Requirements
To accomplish BETTII’s goals of spatially resolved spectroscopy, it requires
delay lines to (1) compensate for perturbations in the path length difference between
the two arms of BETTII, (2) sweep the delay across the detector array to cover delays
appropriate for each pixel in the field covered by the array, and (3) sweep the delay
over a range of +/- R wavelengths in order to measure source spectra with spectral
resolution R ≡ λ/∆λ. The strategy on BETTII is to utilize the cold delay line
(operating at 4.2 K) to sweep the zero path difference (ZPD) across the array field
144
of view to cover the required field of view and spectral resolution, and to track the
ZPD with the warm delay line (operating at 240 K) as the two beams enter the
cryostat. The ultimate quality of the spectra and astrometry is dependent on the
knowledge and control of the zero path difference (ZPD) and of the stage positions
of the two delay lines.
A balloon system can be considered to be a compound pendulum with pivots
at the point of attachment between balloon and ladder, and that between the ladder
and the gondola. Thus there are three main pendulating modes, two about these
attachment points, and one for the entire system. Based on these expected mode
periods and amplitudes [223], and taking into account corrections by BETTII’s
attitude control system, the warm delay line (WDL) is required to have a range of
5 mm (corresponding to 1′ amplitude), and a speed specification of ∼ 1 mm/s.
The cold delay line (CDL) should have a range large enough to ensure that
the edge pixel ZPD falls within it. The 2.5′ maximum FOV corresponds to 6 mm
in optical path difference (OPD). An additional 1 mm at either end ensures that
complete interferograms (R > 10) are produced even for the edge pixels, complying
with spectral resolution requirements. Hence we can accommodate the ZPD offsets
and spectral range, by setting the delay line OPD range at 8 mm. This OPD range
corresponds to ∼ 260 fringes in the shortest wavelength. Nyquist sampling of the
fringes requires a minimum 2 samples per fringe, corresponding to 520 measure-
ments. In practice, BETTII plans to over-sample the fringes by a factor of 2-4 in
order to achieve a better signal-to-noise ratio. The detector readout rate is fixed
at 400 Hz by detector noise and saturation considerations. Thus, the total time to
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scan across the field and back at a constant speed is 2.5 seconds for twice Nyquist
sampling, and 5 seconds for 4 times Nyquist sampling. We anticipate collecting
100-200 such scans in one track, over 10 minutes. It is to be noted that over the
integration and readout time for each pixel (2.5 ms), the OPD changes by ∼ 7.5
µm (at a minimum of 4 samples per fringe) because of the constant velocity motion
of the cold delay line and this reduces interference fringe amplitude by 10% for λ =
40 µm.
In addition to the range requirements, there are control requirements at dif-
ferent timescales. To analyze them, we express the total error in ZPD as
ε = εest + εWDL + εCDL + σCS,
where εest = actual ZPD offset minus estimated ZPD offset (unknown except
on calibrator),
εWDL = target position for WDL as given by the estimation - actual
position attained by WDL as reported by the capacitive sensors
(known),
εCDL = target position for CDL - actual position of CDL as reported by
the capacitive sensors (known),
σCS is the sum of the RMS measurement error in the two capacitive
sensors after filtering (measurable in lab).
Since errors and uncertainties are unavoidable in mechanical systems, it is
important to breakdown the requirements on control and knowledge of the path
146
length in order to achieve the science objectives. The first constraint is that of total
control error |ε| which should not be so large that the fringes of sources at the edge
of the FOV go outside the scan length of 8 mm. This translates to |ε| < 200 µm.
Although we keep the control requirement relaxed, the knowledge of position should
be at least as good as λ/15 in the shortest wavelength, so that we can reconstruct
accurate interferograms with minimal phase noise (1% loss of fringe amplitude at
the shortest wavelength) [209]. This is equivalent to σCS < 2 µm.
There is an additional set of control constraints based on the rate at which
the error is changing on different time scales. First, over the integration period of a
single data point, it is important for the fringe pattern to be coherent to within λ/20
(corresponding only at 5% loss of fringe amplitude at the shortest wavelength) [209].
At the shortest wavelength this is equivalent to σ < 1.5 µm in time scales of 2.5 ms,
where σ = σest + σWDL + σCDL, with the three terms being the standard deviations
of each of the respective errors as defined earlier. Second, over the period of a
single scan, the total ZPD error should not fluctuate to a level that the individual
data points in the scan do not sample well the fringe pattern of a source. The
fringe pattern length in delay space is given by the coherence length (λ2/∆λ). It is
expected to be 75 µm wide in the short wavelength band, and 180 µm wide in the
long wavelength band. The larger of the two values correspond to about 24 samples
or 60 ms scanning time. We set a more stringent condition that over time scales of
200 ms, the standard deviation error should not exceed the nominal distance between
two consecutive data points along the scan, i.e. σ < 7.5 µm. Third, as we move
from one scan to the next, if the uncertainty in ZPD error becomes comparable to
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Accuracy
Timescale Ensures
Requirement
Control:
Entire duration |ε| < 200 µm Fringes fall within the scan range for all
of measurement sources in the FOV
2.5 milliseconds σ < 1.5 µm Coherence over detector integration and
read-out time
0.2 seconds σ < 7.5 µm Uniform sequential sampling along a scan
10 minutes σest < 10 µm Effective stacking of interferograms
Knowledge:
Entire duration σCS < 2 µm Knowledge for reconstructing interferograms
of measurement
Table 5.1: Control and knowledge requirements at different timescales
the wavelength, the SNR won’t improve on stacking up the interferograms. Taking
a nominal value of λ/4, we get σest < 10 µm in time scales of 3s − 600s. These
accuracy constraints are summarized in Table 5.1 below. In shorter timescales,
the major contributor to error fluctuations are the delay line control errors and
vibrations from the instrument packages, while on the longer timescales, the major
contributor to error is drift in the ZPD relative to the estimation.
5.3.2 Design
Both the delay lines are designed to be controlled in a closed loop using capac-
itive sensors and voice coils as actuators.The warm delay line consists of 4 mirrors
arranged at 45 degrees to the incoming beam, two of which are fixed and two are
movable. The adjustable mirrors are connected to a support mounted on a low fric-
tion stage that can be moved back and forth using a voice coil actuator (VCA). The
148
Figure 5.5: Design of the warm delay line (left) and the cold delay line (right), with
the light path traced in red for Arm 1 and blue for Arm 2 of BETTII. The direction
of travel is shown by black arrows.
support has flat areas which are used as the target of a capacitive sensor to read
the distance. The sensor (Microsense Model 8800 with 2811 sensor) and the target
surface on the stage are both oriented at an angle of 66.4◦ to the direction of motion
to ensure that the 4 mm sensor range corresponds to a 10 mm movement range of
the stage. This movement range of the stage allows for a maximum range of 20 mm
for the optical path difference (OPD). To improve the linearity of the warm delay
line stage movement, an additional spring is used. It has a spring constant k = 60
N/m.
The cold delay line has 4 mirrors rotated at 45 degrees to the two incoming
beams coming from the two arms (see Figure 5.5). The four mirrors move as a single
unit simultaneously decreasing the optical path on one of the beams and increasing
it on the other, thereby achieving a 4-fold OPD between the two interfering beams.
A 2 mm stroke delay line produces the required OPD of 8 mm. The movable stage is
supported by titanium flexures, which results in very linear control. Two capacitive
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sensors (Microsense Model 4810 with 2821V Probe) are mounted on a central fixed
plate pointing to target plates on the movable stage on opposite directions. One of
the sensors is used in control, while the other gives an additional distance measure.
They are set to a range of 2.5 mm using on-board controls. Both the delay line
algorithms are implemented in National Instruments LabVIEWTM and run on a
FPGA-based Real Time Controller.
In theory, the two delay lines could have been combined into a single assem-
bly performing both tasks. However, this is challenging because the interferogram
generation requires smooth control over a small range, while the correction of pen-
dulation requires a larger range. Accordingly, it also gives us the freedom to operate
them at different control loop rates.
5.3.3 Calibration
A capacitive sensor measures distance using the inverse relation of capacitance
between two plates and the distance between them. This relation is perfect for ideal
parallel conductors having uniform surface charge distribution. However, based on
the particular geometry and design of the sensor targets in the delay lines, it was
required to map the relation between the actual distance and the Voltage measured
by the capacitive sensor. Two methods were used for doing the calibration, using
a distance-measuring interferometer and using a micrometer of least count 10 µm
and revolution of 0.5 mm. Repeated measurements in both directions of travel were
carried out at different speeds. By interpolation, we obtained sub-micron position
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Figure 5.6: Left: The control error of the warm delay line as it travels along a
representative sum of sinusoidals profile (depicting the pendulation modes). The
optical path length error has a RMS value of 38.2 µm. Right: The change of the
OPD error over the detector integration time (equivalent to each time-step). The
error changes at about 1.1 µm per time-step (RMS value).
accuracy over the capacitive sensor Voltage range of ±10 V. The measurements
established our knowledge of position of the delay lines, which will be critical to
control the optical path lengths and later reconstruct the interferograms.
5.3.4 Characterization
Open loop tests were carried out to characterize the op-amp and voice coil
actuator’s linearity and control parameters. While the warm delay line has non-
linearities due to stiction, the cold delay line is very linear over its range. The latter
is limited by non-linearities in the magnetic force between the actuator solenoid and
the core magnet which depends on the displacement of the coil with respect to the
core. Transfer functions were determined to find frequencies of instability.
During flight, the target position of the warm delay line is set by the resid-
ual cross-elevation errors determined by the tracking channel. We used a sum of
sinusoidals as the representative target position corresponding to the expected pen-
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Figure 5.7: Left: The sawtooth profile that the cold delay line travels along during
closed loop control, showing the control error, after it is multiplied by the factor of
4 to get the optical path length error of about 47.7 µm. Right: The change of the
OPD error over the detector integration time (equivalent to each time-step). If we
exclude the small turn-around time corresponding to < 5% of the entire travel time,
the error changes at about 0.4 µm per time-step.
dulating modes for characterizing the closed loop PID control of the warm delay line.
One such representative test result is shown in Figure 5.6. For the cold delay line,
the position target is a triangular waveform, for sweeping the ZPD systematically
(see Figure 5.7). We intend to remove as much error as possible by the closed loop
‘control’ during flight, but using the ‘knowledge’ of their position, which is 2 orders
of magnitude (∼ 1 µm) more accurate than the control (∼ 100 µm), we can improve
our outputs in post processing. The delay lines are characterized and calibrated,
and the errors are within our instrument specifications at the different time scales.
Cold tests were carried out for the warm delay line at 240 K, and for the cold
delay line within the cryostat. This is done to ensure that the delay lines perform
in flight and to further fine-tune the control parameters for flight environment.
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5.4 Flight Results
As discussed in Section 4.4, during the engineering flight of BETTII, we tested
the various subsystems. Thermometry data showed that each of the optics had uni-
form temperatures throughout flight. Figure 5.8 shows the thermometry data for the
two telescope assemblies. They thermalized around -55◦C at float. The temperature
differences between identical optical elements in the two arms were typically about
0.5◦C and less than 2◦C during the entire flight. The only deviation from pre-flight
predictions was that the bottom of the truss remained about 5◦C warmer than the
top of the truss (due to radiative coupling with the Earth). These deviations were
symmetric across the payload and are unlikely to affect the interferometric visibility.
Pointing solutions were obtained after ascent using the star camera images,
and propagated continuously using the three-axis gyroscopes. There were periods
of time as long as 20 minutes during flight when star camera solutions were not
available. However, the pointing solutions obtained by integrating the gyroscope
angular velocities corroborated with the new star camera solutions to within 20′′
[214].
The gyroscope X that measured the angular velocity along the direction per-
pendicular to the truss and the gravity vector gives information on the pendulation
modes of the gondola. During float, the RMS angular velocity was found to be
20′′/sec with a maximum of ± 175′′/sec.
Figure 5.9 shows the Fourier spectra from 3 × 106 datapoints collected over
1 hour at 100 Hz, and divided by the proper normalizing factors and the frequency
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Figure 5.8: Top: Temperature profiles at three points at the back of one of the
Telescope Assemblies during the engineering flight from Palestine, TX on 8th June,
2017. Bottom: Temperature profile comparison of the two Telescope Assemblies on
the two arms of the BETTII truss during float.
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Figure 5.9: The Fourier spectra of the Gyroscope X-axis angular velocity data,
normalized by the frequency and the data acquisition rate to obtain the pendulation
mode amplitudes. The modes can be identified by the peaks that appear in the log-
log plot in the frequency range 0.03− 0.7 Hz. The 3 main modes are marked by the
arrows.
to get the amplitude in arcsecs. The modes have time periods between 1.5 s to
30 s. The three main modes are at 1.8 s, 11 s and 25 s having amplitudes of 1.1
arcsec, 3.1 arcsec and 12.6 arcsec respectively. The major modes correspond to the
oscillations of the gondola about the two attachment points –between the balloon
and the flight ladder and between the flight ladder and the gondola, and oscillations
as a single unit along with the balloon. The sum of all the modes add up to about
2 mm of optical path length difference, well within the 20 mm range of the delay
line. We still need the warm delay line range to correct for possible errors in the
location of the zero path difference due to truss balancing errors and due to residual
path length errors from alignment (measurable on ground but not trivial to correct
mechanically).
During flight, an issue was identified with the control system. The Galil mi-
155
crocontroller used to control the CCMG reaction wheels successfully turned on.
Diagnostics received through a serial interface indicated that it was functioning
normally. However, it did not respond to commands issued through the primary
communication port (an Ethernet line). During laboratory testing, the microcon-
troller was programmed to automatically retrieve a dynamically assigned IP address
on startup through the local wireless network. During launch, the Galil was turned
off to avoid potential damage to the reaction wheels. When it was turned on dur-
ing ascent, the lack of a network led to no IP assignment. This prevented us from
spinning up the reaction wheels and limited our ability to point the gondola using
the momentum dump mechanism. With the momentum dump alone, we achieved
20′′ pointing accuracy, and verified the accuracy of the control system sensors, but
tracking a target and fine pointing was not possible [215].
Since BETTII did not get into the tracking mode, the cross-elevation errors
were unavailable to be used as a target for the warm delay line. Instead we tested
the delay line for about 40 minutes during flight by controlling it at a constant
position (see Figure 5.10). The error is less than 3 µm over the entire duration of
the test. We noted a mechanical jitter in the position of RMS 0.5 µm. These errors
are well within the delay line specifications discussed in Section 5.3.1 and validates
the opto-mechanical assembly for use in the flight environment.
We also operated the cold delay line during flight. However, since the cryostat
had a cold leak that re-opened during rollout prior to launch, the Helium boiled off
soon after launch. So the cold volume was not at 4.2 K, and it gradually thermalized
with the 77 K liquid N2 cooled chamber. The cold delay line was operated at this
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Figure 5.10: The position errors (blue dots) of the WDL stage while being controlled
at a constant position during flight. The control loop operates at 100 Hz, although
the position data is collected at 400 Hz. There is a jitter of about 0.4 µm RMS,
while the overall error is less than 3 µm over a period of > 30 minutes.
temperature. The full range test showed that there was a mechanical issue in part
of the delay line travel, closer to one edge, which introduced oscillations in the delay
line control. So we changed the range to operate over half the total range and
obtained reasonable results. The results are shown in Figure 5.11. The rms error
is 49.5 µm, similar to what we obtained from ground testing. The average rate of
change of error is slightly higher at about 1.1 µm/step. However, the PID gains were
not tuned for this experiment, since we were not operating at the nominal cryostat
temperature. Even though we control the delay line positions to errors comparable to
the wavelengths, the large scale errors occur over much longer timescales compared
to the detector integration time of 2.5 ms. Further, using the capacitive sensors
we have knowledge of these errors to an accuracy of 0.3 µm that is used in post-
processing while reconstructing the interferograms and co-adding them.
During the flight, the H4RG detector array was also operated for the first time
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Figure 5.11: Left: The sawtooth profile that the cold delay line was operated in
closed loop control during flight. The optical path length error (blue dots) has a
RMS value of 49.5 µm. Right: The change of the OPD error over the detector
integration time (equivalent to each time-step) is about 1.1 µm per time-step.
ever in a flight environment. More than 250,000 images were collected over the flight
duration. The data is being analyzed to characterize noise performance of the array
[224].
5.5 Optics Re-design
As discussed in the previous chapter, after the loss of the payload at the end
of the Engineering Flight, BETTII is being rebuilt as BETTII-2. Although most of
the optics remain the same as discussed in Section 5.1, some design changes have
been made in the internal optics. A dispersive backend has been included in the
optics train to improve the overall sensitivity, by reducing the fractional bandwidth
at each pixel of the detector, thereby reducing the effect of photon noise [225].
Later in Chapter 7, with the help of mathematical formalism and interferometric
simulations of BETTII observations, we explain how the dispersive element will
improve the sensitivity of the instrument. Here we discuss the grating design that
158
Figure 5.12: New internal optics model showing salient features. This may be
compared with Figure 5.1 (d).
disperses the light over the columns of the 9 × 9 TES detector arrays in both the
BETTII bands. Some other changes in the optical system to redistribute the thermal
loading and for ground testing of the FIR optics are also discussed here.
The optics was re-modeled in Zemax (as shown in Figure 5.12). The dispersive
element is required to be placed after the dichroic separating the two BETTII bands
at 55 µm. In the previous model, the dichroic separation was occurring in non-
collimated space. Modeling showed that placing a reflective grating between the
dichroic and the detector plane for all 4 outputs is able to disperse the sources along
the columns of the detector arrays (see Figure 5.13). A grating of 2.79 lines/mm
for the SW band linearly disperses the wavelengths 30 µm to 55 µm over 8 mm on
the square detector array of sides 9 mm. The first order diffraction requires a blaze
angle of 4.60◦ to maximize the efficiency of the waveband, producing a minimum
159
Figure 5.13: Post Beam-combiner optics for the two BETTII channels :SW (left)
and LW (right).
efficiency of 67% at the band extremes and a maximum efficiency of 80% at 40
µm. For the LW band, the grating spacing is 2.58 lines/mm and the blaze angle is
5.84◦. The minimum efficiency is 66% at the band extremes the maximum efficiency
is 89% at 70 µm. The non-linear effects of not being in the collimated space are
negligible for the small range of wavelengths involved here. The new SW and LW
band specifications are summarized in Table 5.2.
In addition to the dispersive backend, a few more changes are incorporated
in the new optics design. In the previous design, each of the two input beams first
entered a 4.2 K liquid He-cooled chamber of the cryostat, where a dichroic divided it
into a NIR part (for the tracking channel) and a FIR part (for the science channels).
The FIR part continued in the He-cooled chamber until the detectors, while the NIR
was relayed to a 77 K liquid N2 cooled chamber. This resulted in a heavy thermal
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Table 5.2: BETTII-2: SW and LW band specifications
SW band: 30− 55 µm LW band: 55− 100 µm
Plate scale 13.3′′/pixel 16.7′′/pixel
Focal length 15.45 m 12.40 m
f/number f/30.9 f/24.8
Field of View 2′× 2′ 2.5′× 2.5′
Linear Dispersion 3.125 µm/mm 5.625 µm/mm
loading on the He-cooled chamber. The current model houses the dichroic in the
liquid N2 cooled chamber, such that the compressed beam from the external optics
enters the 77 K chamber of the cryostat first (see Figure 5.12). The thermal blockers
present here will absorb the unwanted IR radiation, and will deposit less heat in the
more critical 4.2 K chamber housing the detectors. This will lead to longer cryogen
hold time and improved detector performance.
Another important modification also involves the entry of light onto the FIR
optics bench. Obtaining interferometric fringes in the laboratory using coherent
and collimated FIR light is valuable to test the performance of the instrument
prior to launch. In the previous model, the two input beams were at diametrically
opposite points of the cryostat. In such a case, feeding a coherent FIR beam into
both the arms was extremely challenging, because of the requirement of a beam
splitting and relaying assembly. The entire input assembly required to be in a cold
chamber (to eliminate thermal IR radiation). Further, this assembly would have
introduced additional sources of error that would have required disentangling from
the instrument errors to determine the instrument performance. The current design
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bypasses these problems by having two parallel and adjacent input beams into the
liquid He-cooled chamber. Thus, for laboratory testing, a collimated FIR beam of
diameter roughly 3 times that of the input beam can be used to generate coherent
inputs for both arms simultaneously through the FIR port (see Figure 5.12).
Some of the optics have been re-designed to ensure that there is only one
reflective surface per physical optical element. Mirrors like the double-sided focusing
parabola were challenging to align for both arms simultaneously because of the
presence of non-negligible tip-tilt errors of one reflective surface with respect to
the other. The new design avoids such mirrors. The detector planes have been
re-oriented to ensure that the detector packaging containing all the four detector
arrays has a regular cuboidal shape. Finally, several minor changes were made to
simplify manufacturing and integration. The modifications have been checked for
compatibility with the mechanical model, and are being implemented on BETTII-2.
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Chapter 6
Optics Alignment
In an interferometric system, it is important to account for two types of phase
errors: (i) optical path difference errors between the two arms of the interferome-
ter and (ii) wavefront errors across the beams. According to BETTII’s sensitivity
analysis [209], a phase error of λ/20 corresponds to a fringe contrast drop by 5%.
In the previous chapter, we discussed how some of these errors are reduced by using
appropriate optical design and fabrication techniques. We also discussed how the
optical path length errors can be handled by using the warm delay line. In this
chapter, we discuss the alignment of the optical system based on the requirements
of the interferometric system [226].
6.1 Tolerancing
The optics alignment process requires us to first build an error budget to set
tolerance requirements. We carry out alignment tolerancing based on effects of
misalignments on the interferometric output of BETTII. The effects of standard
optical aberrations are already taken into account in BETTII’s optical design [217].
We analyze the sensitivity of each optical element and certain optical assemblies on
the output at the detectors. One of the principal effects of phase errors is reduction
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of fringe contrast in the interferograms. For this purpose, we use a measure called
interferometric visibility (V), which is defined as V = (Imax−Imin)/(Imax+Imin). As
shown in Figure 6.1 right, Imax and Imin are respectively the maximum and minimum
intensities recorded at the science detectors by changing the delay between the arms.
The value of V is 1 for perfect constructive and destructive interference. We use
reduced visibility values as a measure for alignment sensitivities.
The impact of some alignment errors can be mitigated through adjustment
of other optical elements. This relaxes a few constraints on the individual mirrors,
which would otherwise have extremely challenging tolerance requirements. Exam-
ples of such errors are the linear phase gradients across the beam and collimation
errors. The linear phase variations are caused by angular errors of a reflective surface
with respect to their nominal values in collimated space, and they can be corrected
by introducing a compensating shift on another mirror in the optics train. The
tip-tilt mirrors may be used in flight for such corrections. However their limited
range is to be preferably used for correcting dynamic errors over the static align-
ment errors. The collimation errors are specific to the powered mirror assemblies,
where the relative distances between the mirrors may be re-adjusted to optimize for
the overall collimation at the output. Taking these into consideration allows us to
estimate an error budget, and use alignment techniques accordingly.
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Figure 6.1: (a) FRED simulation model of BETTII, with a single source split into
two for producing two coherent inputs. (b) The PSF at one of the SW detector
arrays (9 × 9 pixels) for a single source at the center of the FOV. (c) Interferogram
obtained at the central pixel of the same array by changing the delay. (d) and (e)
The same as (b) and (c) respectively at one of the LW detectors.
6.1.1 Simulations Using Optical Software
FRED is an optical ray-trace package by Photon Engineering that preserves
phase information with beam propagation. It is used to model the optical system of
BETTII. A monochromatic source of coherent light is defined and incident on the two
apertures (Figure 6.1) with the aid of a beam-splitter arrangement. The outputs are
obtained at the center of the field-of-view at the detector arrays. Further, the model
simulates the movement of the cold delay line, and thereby generates interferograms.
The loss in interferogram visibility as a function of rotation and translation errors
for each optical surface/assembly is recorded.
In our sensitivity analysis, we examine the translation errors from the nominal
positions along the principal axis normal of each optical element, and in the direction
transverse to it. We consider angular errors with respect to the optic surface normal.
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In most cases, the vertical angle error has the same effect as the horizontal angle
error. For the powered optics and assemblies, the rotation about the optic normal
(local ẑ axis) is also considered if their mounting allowed for this degree of freedom.
In addition, the effect of the rotation stage angular misalignments are considered
for the siderostats and the K-mirror assembly. The analysis for rotation stages is
carried out for multiple elevations, and involves a source at multiple positions within
the field of view to compare the effects.
The modeling takes into account the misalignment effects of optical assemblies
as a unit, wherever the mechanical design involves a common mounting structure as
with the delay line assemblies. Part of the analysis co-evolved with the alignment
procedure as misalignment correction options and alignment technique limitations
became apparent. We examine the extent to which it is possible to correct for some
of the wavefront errors while treating the optical system as a whole. This allows for
a more realistic estimate of the required alignment accuracy of the optical elements
and assemblies.
6.1.2 Interferometric Visibility Analysis
We use the misalignment error corresponding to an interferometric visibility
value of 0.98 (or a visibility loss of 0.02) in the more sensitive SW band as a bench-
mark to compare the sensitivities. The interferometric visibility is found to resemble
a sinc-squared function (Figure 6.2) for many of the misalignments, thereby indicat-
ing that the linear component of these phase errors is dominant. This implies that if
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Figure 6.2: Example plots of interferometric visibility loss for both BETTII bands
for the flat mirror in one of the telescope assemblies when it is translated along the
direction of its normal (left) and when the angle of its normal is changed (right).
misalignments of one of these elements are compensated by another to ensure beam
overlap, the visibility loss of the system will be minimal.
The siderostats, which are the farthest from the detectors, are the most sensi-
tive to angular errors. Even after correcting using the tip-tilt mirrors, its V = 0.98
point is at 2′ which uses 70% of the tip-tilt range. This means that we have to aim
for a few tenths of an arcminute error, so as to reduce the range of the tip-tilt used.
For the telescope assembly too, the angles are critical and require sub-arcminute
accuracy. The angular errors in this assembly can be partially corrected by the
tertiary mirror, while the collimation error is easiest to correct using the flat mirror.
This allows the secondary and tertiary mirrors to have > 2 mm errors along the
direction of the mirror normal, as long as the telescope flat translation is used to
correct for them to within 0.15 mm (for V = 0.98). This roughly corresponds to a
power of about +/- 0.015 diopters at the output of the telescope assembly.
Once the beam is compressed by the telescope assembly, the alignment re-
quirements are relatively less stringent. This section involves a large number of flats
which are used as relays. They all need to be accurate to within 6′ for V = 0.98 as
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long as the mirrors in the ensuing part of the relay corrects for that error. We have
to ensure that this is achieved for the FIR bench to NIR bench alignment as well as
the FIR to external optics alignment.
Table 6.1 summarizes these results corresponding to 98% interferometric visi-
bility for the individual optical elements and assemblies for the SW Band, with and
without correction. The correcting method, the alignment technique and achieved
alignment results are listed. The details of these are discussed in the following sec-
tion. The translation errors of some relay flat mirrors are not included in the list,
as their only effect on the output is in vignetting or an optical path difference error.
Vignetting effects are limited by oversizing the mirrors with respect to the beam and
so a 2% visibility loss corresponds to a translation error of a few millimeters, which
is easily met by the mirror-mount tolerances. On the other hand, optical path differ-
ences are mitigated by introducing an offset in the delay lines. Angular errors of the
warm delay line assembly and the horizontal angle error of the K-mirror assembly
also have no effect on the beam other than vignetting for extreme errors. Mirrors
in the optics train post beam-combination have no effect on the interferograms.
6.2 Alignment Procedure
The target of the alignment effort is to attain less than 2% visibility loss for
each individual optic misalignment by taking advantage of the appropriate compen-
satory mechanism. The alignment procedure involves aligning different assemblies
in the optics train with respect to a local reference frame, followed by associating
168
the assemblies to the global reference frame. To ensure that the control subsys-
tem points the payload in the desired target direction, the star camera orientation
and the axis of the three gyroscopes are also measured in the same global reference
frame.
The primary mirrors in the telescope assemblies have three tooling bosses that
were used to reference the figure of the diamond turned surface [218]. The tooling
holes for one of the primaries (+Y arm) are used to set up the global reference frame.
This means that all the optical elements and assemblies are aligned with respect to
that primary mirror. Of the optical sub-assemblies, the FIR bench has a set of
12 built-in alignment holes to get into its reference frame (Figure 6.3). The optics
outside the cryostat and the NIR optics are aligned in the +Y primary reference
frame directly, while the FIR optics are aligned in the reference frame set by the
FIR bench tooling holes. The relation between the two sets of alignment references
are used to align the FIR bench as an unit with respect to the external optics.
6.2.1 Instruments
For precise alignment of BETTII optics, we primarily use two types of metrol-
ogy equipment: (i) a laser tracker, which can measure the distance to retroreflectors
up to an accuracy of 20 µm and (ii) a set of theodolites, which can provide up to
0.1′′ accuracy angular measurements.
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6.2.1.1 Laser Tracker
We use a Leica Absolute Tracker AT 401 as our laser tracker in conjunction
with SpatialAnalyzer software by New River Kinematics. The laser tracker measures
the distance to a reflective target with the help of an absolute distance meter [227].
It also has 0.5′′ angular encoders to determine its pointing direction. We use 0.5
inch and 1.5 inch diameter spherically mounted retroreflectors (SMRs) on magnetic
nests at reference locations [228]. By setting up the laser tracker at a location and
measuring the distances to 3 or more SMR targets at known co-ordinates, we can
establish the reference frame in the software. The tracker can then be used to make
subsequent measurements in the same reference frame.
We use the laser tracker primarily for two types of measurements: (i) locations
of movable or fixed SMRs to define some geometry (points, plane, cylinder etc.) (ii)
direction cosines of flat reflective surfaces by a ‘direct-and-through’ method. The
latter involves measuring the distance to a SMR by pointing the tracker directly to
it, and also measuring the distance to the same SMR through its reflection on the
mirror surface. These two measurements along with the knowledge of the tracker
pointing directions are processed by the software to determine the reflective plane
angle to an accuracy of 5′′. [229]
We also make use of transfer reference points because the direct reference
points of the global coordinate system are often not simultaneously visible with the
target(s) to be measured. Sometimes, the original reference points may also get
obscured (by the cryostat in our case). For this purpose, we set up many more
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Figure 6.3: Left: Telescope assembly with tooling holes at the back, that are used
to set the global reference frame. Right: Alignment holes on optics bench. Spherical
reflectors are mounted on magnetic nests in some holes for use with theodolites.
SMR mounts at vantage points all around the BETTII truss. Their co-ordinates
in the global frame are established with the help of the tracker. This allows us
to move the tracker to a new location and put it into the same global reference
frame by measuring these transfer points. It is advisable to use as many transfer
points as possible beyond the bare minimum of three to reduce errors in the best-fit
transformation to get into the frame.
6.2.1.2 Theodolites
We use Leica Geosystems T-3000 theodolites that are small movable telescopes
with two angles of rotation, one vertical and another horizontal [230]. The vertical
angle corresponds to elevation which is measured with respect to the gravity vector,
while the horizontal angle corresponds to azimuth which has no absolute reference,
and only gives a relative measure. Before taking theodolite measurements, these are
171
leveled with reference to gravity. These theodolites also have a built-in collimated
light source in the shape of a cross. This is often used for sub-arcsecond accuracy
auto-collimation measurements involving reflection from a flat mirror. Most mea-
surements use multiple theodolites, with one designated as the primary that serves
as the azimuthal reference for additional theodolites.
Theodolites are extremely valuable for aligning BETTII, and are used in three
major ways:
• With spherical reflectors, for defining vectors in a reference frame: These
polished metallic spheres are mounted at the reference points with known co-
ordinates, such that a pair of these separated by a short distance define a
vector (preferably an axis) in the reference frame. We align a theodolite along
a vector by translating it horizontally and vertically, until the reflected spots
from the two spheres are exactly coincident at the center of the cross-hairs for
the same theodolite pointing. With this method, we consistently achieve 1-2′′
accuracy in aligning the theodolites with a vector.
• Collimation through flat reflecting assemblies: This is similar to auto-collimation,
except that separate theodolites are used as light source and detector, because
the input and output light vectors for the assembly are not co-linear. If the
two theodolites can be directly pointed to each other, one is used as the pri-
mary. If there is some obscuration, a third theodolite is placed at a convenient
location and acts as the primary. [231]
• Directed laser light source: The Leica DL2 laser diode source can be mounted
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on these theodolites as a stronger collimated light source at 655 nm wavelength.
This allows us to point the light source along a particular readout direction,
and visually trace the optical path with a screen, without having to use another
theodolite at the output. This method is easier to implement and allows us
to test the alignment of assemblies having powered mirrors in the optics train.
The angular accuracy that can be achieved by this method is of the order of
arc-minutes and is dependent on the optical arrangement, but it is sufficient
for many of the BETTII alignment requirements.
Based on the measured direction cosines of the reflective surfaces, we calcu-
late their vertical and horizontal angle errors compared with the modeled nominal
direction cosines. Most of the mirrors use three point mounts. We calculate the
shim thickness to be used at two of the points based on the angular errors and the
distance between the mount points. The minimum shim thickness of 1 mil (25 µm)
corresponds to 5′ for the small mirrors, and about 0.25′ for the large mirrors. These
angles are sufficient for most of our requirements. If we need finer angular adjust-
ments, we move the shims at a mounting point either towards the center of the
optic or towards the edge of the optic. For mirror translations along their normal
direction, the same amount of shims are added to all the mount points.
6.2.2 Telescope Assembly
Each of the telescope assemblies are mounted as a unit on the two arms of
the BETTII truss. The first step is to align the two primaries with respect to each
173
other. The laser tracker is used to get into the frame of one of the primaries with the
help of SMRs at its tooling bosses, while SMRs at the corresponding points of the
other primary mirror are measured. The direction cosines of the plane defined by
these three point measurements is compared against the nominals to determine the
angular error of the telescope. The rotation is also measured using the deviation of
the measured points from the nominals. The correction for the errors is distributed
between the two telescopes, to reduce translation offsets between the principal axes
of the primary mirrors and the siderostats. A measurement of the rotation stage spin
axes of the two siderostats by the movable SMR method (as described in Section
6.2.1.1) in the same reference frame is used as an additional check.
During the primary mirror manufacturing process, a 10 mm wide flat polished
rim was left around the figured area of the optic. This provides an additional
reference for the primary normal angle. Based on this, the angular errors of one
telescope assembly with respect to the other are additionally measured using three
theodolites. We use one theodolite to level the truss in pitch (about the baseline
vector), while two theodolites are pointed along a normal to the two primary rims.
The relative azimuth angles and elevation angles gives a direct and very accurate
measure of the angular errors. After correcting using shims, and measuring by both
methods, the telescope assemblies were found to have a residual error of about 1.1′
in angles and 1.7′ in rotation.
To characterize the collimation of the output beam of the individual telescope
assemblies and correct the errors as required, we use a camera focused to infinity
at the output of each telescope assembly. This is used to capture an inverted image
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Figure 6.4: Left: Checking the collimation of the telescope assembly using a camera
by setting its focus to infinity. The inverted image of the horizon through the
telescope assembly can be compared to the direct image of the horizon on the left.
Right: Model showing laser tracker set-up for telescope assembly flat mirror angle
measurement by direct-and-through method. The tooling holes at the back of the
primary (marked in red) are used as references. The triangle on the right marks the
location of the spherically mounted retroreflector (SMR).
of the horizon (> 3 km away) after light from it has traveled through the assem-
bly (Figure 6.4 left). Accordingly, the flat mirror is translated closer/farther from
the primary to understand the effects on the focus. It was determined that the
combination of the relative distances between the optical elements in each telescope
assembly amounted to the output beam having a power less than 0.02 diopters. This
corresponds to a visibility of 0.96 in SW band and 0.99 in the LW band.
This is followed by the angular alignment of the telescope mirrors. The laser
tracker is used for the alignment of the flat mirror, while the two smaller mirrors
(secondary and tertiary) are aligned with the help of a theodolite light source. SMRs
are used at the tooling bosses of each of the telescope assemblies. The laser tracker is
set-up to measure the flat mirror by direct-and-through method as shown in Figure
6.4 (right). The flat mirror is shimmed to within 0.5′ angular error in the reference
frames of the respective telescope assemblies.
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Figure 6.5: Model (top) and actual set-up (bottom) of the theodolites being used
for telescope assembly angular alignment: Theodolite 1 is pointing along the two
lower tooling holes behind the primary mirror (marked as red spots in left figure).
It also acts as the primary theodolite. Theodolite 2 is pointing along a normal
of the primary mirror’s flat rim. They are used for measurements to set up the
global reference frame for Theodolite 3 to point along the principal input axis of
the primary mirror. Light path from the third theodolite (shown in red) is used for
aligning the angles of the secondary and tertiary mirrors.
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Three theodolites are used to point a light source along the principal optical
axis of the telescope assembly (Figure 6.5). First, a theodolite is pointed along
the axis defined by the two lower tooling bosses to level the truss in pitch angle.
Another theodolite is used to point normally at the flat rim of the primary mirror.
The first theodolite gives the reference for the azimuth angle of the light source
(third theodolite), while the second theodolite measurement sets the elevation angle
of the light source using the angle of the rim-normal with respect to the optical axis
in the model. We translate the light source to ensure that the source is reflected
at the center of the primary mirror. The centering of the light on the tertiary
mirror is used as an indicator of angular misalignment of the secondary mirror,
which is shimmed accordingly. Assuming we can measure the centering to within
+/- 1 mm, this results in angular accuracy of about 20′ which is at the limit of our
requirements. The same method is used for aligning the tertiary mirror, where we
use the centering of the light on the tertiary mirror at the other telescope assembly.
An error of 1 mm in spot centering determination results in an angular accuracy of
3′ for the tertiary mirror.
6.2.3 Warm Delay Line and K-mirror
The warm delay line and K-mirror assemblies are first aligned as sub-assemblies
such that the combination of the mirrors match the angles in the model within 1′.
This is carried out with the aid of theodolites, making use of the parallelism of the
input beam and output beam through the sub-assemblies in the ideal case. Since
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the K-mirror assembly has an odd number of reflections, the exact incident angle is
important while matching the input and output vectors. This is unlike the warm
delay line assembly, which involves an even number of reflections, such that if the
input vector matches the output vector, it stays valid for a large range of incident
angles and is only limited by vignetting.
The K-mirror assembly is initially leveled with respect to gravity such that
the mirror normals are all perpendicular to the gravity vector. As shown in Figure
6.6 left, we use a pair of theodolites, the first as a source to reflect light off the first
mirror in the assembly and the second as the detector. This arrangement is used
to measure the incident angle of light on the first mirror. Now without moving the
assembly, the azimuth of the source theodolite is set such that light is incident along
the path as in the flight configuration. A third theodolite is used at the output to
measure the output angles of the light (azimuth and elevation). In this case, the
second theodolite doubles as the primary for referencing the azimuth angle. Based
on the errors, the second mirror in the assembly is adjusted in tip and tilt.
The warm delay line assembly alignment involves aligning the two movable
mirrors first and then aligning in conjunction with the two fixed mirrors. The re-
quirement is that the mirrors in each pair are aligned to be at 90◦ to each other. The
movable part is leveled with respect to gravity and aligned by using two theodolites
each pointing directly at the mirror normals to determine their elevation angles and
relative azimuth angles. After shimming them appropriately, we mount the movable
stage in the assembly. The assembly is leveled similarly to the K-mirror assembly.
A three theodolite set-up is used to inject light (theodolite 1) through the assembly,
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Figure 6.6: Alignment models of K-mirror assembly (left) and warm delay line
assembly (right) using 3 theodolites – T1 (input), T2 (primary) and T3 (output).
For the K-mirror assembly, T1 and T2 are additionally used to measure the angle
of incidence for the first mirror. The mirror numbers for each assembly represent
the sequence in which light is incident on them.
measure the output light angles (theodolite 3) while referring the azimuth angles to
another (theodolite 2).
Since both assemblies have a tip-tilt mirror, it is important to keep it powered
at the nominal central angle while carrying out the alignment. Also since the tip-
tilt axes may be arbitrarily rotated with respect to the principal optical axis, the
output vector directions are mapped for the entire range of tip-tilt voltages after
the alignment is completed.
Before mounting each of the two assemblies, the theodolites are again set-
up as described in the ‘Telescope Assembly’ section. The K-mirror assembly whose
alignment is more critical is mounted first on its rotating stage. The theodolite laser
source input is compressed through the telescope assembly and travels through the
K-mirror assembly. The light is recorded on a detector (without using any focusing
lens). As the stage is rotated, the effects of the movement of the spot on the detector
179
are noted. Based on the tip and tilt errors of the rotation stage, the spot center will
move along an elliptical path. We try to minimize this movement by correcting the
rotation stage angles. We were limited by the minimum shim thickness and could
correct the angle to about 2′.
Mounting the warm delay line is easier as it is not critical in incident angle.
Depending on the mounting errors it can cause a slight transverse shift of the output
beam with respect to the input beam. We use a set-up similar to the other arm
using theodolites and a detector to note the spot position before and after mounting
the assembly.
6.2.4 Siderostats
The siderostat alignment involves correcting for the angles of both the rotation
stages as well as the mirror mounting on the stages. Being at the extremes of the
arms, they also have very high angular sensitivity of less than 1′′ for 98% visibility.
This is unfeasible to achieve and requires correction using the tip-tilts because of the
dynamic nature of this error with elevation. However, the tip-tilts have a limited
range and a 0.5′ angular error in the siderostats corresponds to using about 15% of
the tip-tilt range. The truss structure around the siderostat and its height above the
ground limit its accessibility using a laser tracker. Measurements of the optic surface
is only possible for a small range of rotation angles, while measuring the rotation
stage axis by tracing its geometry using SMRs has errors of several arc-minutes. A
procedure involving mathematical formalism is adopted to simultaneously solve for
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Figure 6.7: Siderostat model at α = 0. The rotation stage reference frame is shown
here. The siderostat rotates about +z axis.
all the angular errors.
We introduce 4 error terms θhs, θvs, θhr, θvr. The first subscripts h and v stand
for horizontal and vertical angle errors respectively for the siderostat and rotation
stage individually which are denoted by the second subscripts s and r respectively.
These errors are in their respective reference frames. As described in section 2, the
vertical angle error is the error about +x and the horizontal error is about +y in
the same reference frame.
Starting with a vector A~ pointing along (0, 0, 1) to represent the siderostat
normal in its reference frame, we use rotation matrices to include the siderostat
error terms. As described in section 2, the vertical angle error is about +x and the
horizontal error is about +y in the same reference frame. We take the product of the
two rotation matrices. We perform a linearized Taylor expansion on each element
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of the resulting matrix and get
  cos θhs 0 sin θ hs
   1 0 0 1 0 θ
 0 1 0 
   hs     0 cos θvs − sin θ  ≈   (6.1)vs  0 1 −θvs
− sin θhs 0 cos θhs 0 sin θvs cos θvs −θhs θvs 1
The rotation stage reference frame has the +z axis along the rotation stage axis
towards the telescope assembly and the +y along the gravity vector (Figure 6.7).
To express the siderostat normal vector in the rotation stage reference frame, we
have to transform it by a rotation matrix of 45◦ about the common +x axis.
   1 0 0  1 0 θhs 0
~ ′ √ √A = 0 1/ 2 −1/ 2 0 1 −θ   (6.2)vs0√ √  
0 1/ 2 1/ 2 −θhs θvs 1 1
Each siderostat can be rotated from its stow position (α = 0) to an arbitrary
angle α about +z. We apply this rotation on the vector A~ ′ and further multiply it
by the rotation stage error terms, to get the following expression:
   1 0 θhr cosα − sinα 0
A~′′ =  ′ 0 1 −θ  A~ (6.3)vrsinα cosα 0
−θhr θvr 1 0 0 1
Since the errors are expected to be small, we discard the second and higher
order error terms. The direction cosines (l,m, n) can now be expressed in terms of
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the errors as:
  
 l 
     θ
   
 hs
 √1 sinα  cosα √1 sinα √1 0     2   2 2A~′′ = m ≈ −√1 cosα+sinα −√1 cosα 0 −√12 2 2 
θ  vs
 
θ hr
n √1 0 −√1 −√1 sinα −√1 cosα 
2 2 2 2 
θvr
(6.4)
We measure the direction cosines of the siderostat at multiple values of α using the
laser tracker by direct-and-through method. We refer all the measurements to the
global reference frame, and transform them to the rotation stage reference frame.
Using these numbers, we solve for the 4 error terms, and calculate the required
shim thicknesses for the rotation stage and the siderostats. For greater accuracy,
we carried out the measurement for ≥ 5 values of α, and achieved angular errors 6
0.5′.
6.2.5 Far-infrared Optics
The far infra-red optics bench has a large number of optical surfaces mounted
within a small volume[69]. The alignment requires near-perfect beam overlap be-
yond beam combination all the way to the detector, and it should stay so over the
entire range of the cold delay line. When this is satisfied for one output of the beam
combiner, ideally it should be satisfied for the other output as well. Following instal-
lation of all of the FIR optics, the positions and alignment are checked mechanically.
Optical alignment proceeds by first aligning two sub-assemblies: the double sided
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Figure 6.8: Flowchart showing alignment sequence of FIR optics.
parabolic mirror assembly and the cold delay line assembly while they are mounted
on the bench. These are followed by aligning the train of optics injecting light into
these individual sub-assemblies. After this, the entire optic path is traced by ob-
taining the light on the SW detectors and the LW detectors in turn. The flowchart
is shown in Figure 6.8.
The bench has an array of alignment holes on it used to get into its local
reference frame. The bench is laid flat and supported on its largest side by three
stands. We validated alignment in this non-flight orientation by establishing that
variations in alignment relative to the flight orientation were within instrument
measurement errors. Two theodolites are used to get into this reference frame by
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pointing along two orthogonal directions as defined by the array of holes (Figure
6.9). Using one of the theodolites as the primary, we use a third theodolite to inject
light along specific directions. The light travels through a 25 mm diameter pupil to
get the desired beam size.
To check the alignment of the sub-assembly involving a double-sided parabolic
mirror and two small spherical mirrors, we remove the four fold mirrors immediately
before and after the sub-assembly on the two arms. A theodolite source is injected
along the input direction on one arm, and another theodolite is used at the output
to compare the elevation and azimuth angles, which should match the input angles
when perfectly aligned. This procedure is repeated for the other arm.
All the reflective optics prior to this sub-assembly are now re-mounted. The
NIR-FIR dichroic is replaced by a surrogate flat mirror, and this test is repeated,
this time injecting light at the entry port of the bench. The output is obtained at
the same spot as before. Depending on the output angle measured, the fold mirror
prior to the sub-assembly on each arm is corrected for tip and tilt.
We check the cold delay line alignment, each arm at a time by a similar method,
with an additional check to ensure that the alignment holds when the delay line is
scanned. After aligning it for the nominal position at the center of its travel, we
found that the delay line output beam shifted by about 5′ close to the extremes of
its range. An additional brace was designed to reduce this angle variation over the
range of motion to 1′. The reflective optics between the two sub-assemblies are now
re-mounted and the test repeated by injecting light at the entry port. Accordingly,
the two pre-CDL fold mirrors are shimmed. We also ensure that there is minimal
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Figure 6.9: Alignment model of the FIR optics bench: Theodolites T1 and T2
are used to get into the FIR reference frame with the help of spherical reflectors
at machined alignment holes on bench. Theodolites T3 and T4 are brought into
the same reference frame, referencing azimuth measurement to T1 (primary) and
used to point source along input optical axis of the bench. (Inset) Photograph
of the alignment in progress, with the red circle showing the green cross from the
theodolite source projected onto the detector plane after traveling through the entire
FIR optics. The photo is taken from behind the empty detector plane.
vignetting at the two cold pupils on the bench.
Now we aim two laser mounted theodolites at the two opening ports of the
bench simultaneously, referring them to the local frame as before. The post-CDL
mirrors all the way up to the detector plane are mounted. The possible light paths
are shown in Figure 5.1 (a) and (d). The beam-combiner, although designed for
optimal performance in the FIR wavelengths, reflects and transmits visible light too,
thus producing outputs from both the theodolite sources on either side. The SW-LW
dichroic is not used at first to obtain light on the two LW detector planes. The post-
CDL fold mirrors are adjusted very precisely, until we get the best overlap between
186
the two combined beams over the entire light path between the beam combiner
and the detector plane. The final fold mirrors before the detectors are adjusted to
center the beam on the array. This same process is repeated for the SW section by
introducing a surrogate mirror at the SW-LW dichroic.
After the alignment is complete, all the thermal filters are mounted in place,
and the surrogate mirrors are replaced by the dichroics. In this alignment process,
the intermediate fold mirrors do not require critical alignment individually, but their
combined angular error matters; so each set of consecutive fold mirrors is precisely
aligned as a unit. Machining tolerance of the optics and their mounts (< 0.5 mm)
is sufficient to ensure that there is no beam vignetting. The compact all-aluminum
design of the optics bench and its mirrors are intended to ensure that the optics
bench contracts homologously, thereby not affecting the alignment [69, 216]. In the
future, we intend to carry out the end-to-end test for the optics bench in a 4.2 K
liquid He-cooled chamber to ensure that misalignments due to thermal deformations
are minimal. In addition, we also plan to perform an interferometry test. This is
made easier with the new optical design for the FIR bench (discussed in Section
5.5). For this purpose, we will use a FIR source as input for both the arms of the
optics bench and operate the cold delay line to obtain fringes on the detector as a
further test of the FIR alignment.
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6.2.6 Relative Alignment of FIR, NIR and External Optics
The far and near infrared optics are designed to be inside the cryostat. The
alignment of these parts must be linked to the external optics to complete the optics
train. Our alignment strategy for the cryostat involves the following steps:
1. Align the FIR optics bench to external optics using their respective alignment
references (with dewar shell removed)
2. Define external reference points outside the cryostat
3. Mount NIR optics and re-achieve previous alignment using cryostat references
4. Align NIR optics to external optics by tracing optical path using theodolite
light source
5. Complete cryostat assembly and re-achieve previous alignment using cryostat
references
First, we mount the optics bench on the Helium cold plate. This assembly is
then mounted on the truss with the help of its top plate, without the shell of the
cryostat. We use a laser tracker to measure retroreflector positions at the reference
hole array in the bench and at the tooling bosses of the +Y primary. After aligning
the open cryostat such that the nominal position of the retroreflectors match the
measured positions, we transfer this alignment information to retroreflectors on the
top plate. They remain accessible for measurements even when the cryostat is closed.
The cryostat is removed from the truss to close the cold volume and mount
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the NIR optics below the FIR optics. Before closing the cool volume, we mount the
cryostat once again on the truss. By using the top plate retroreflectors, we ensure
that the FIR and the external optics are aligned. Now the NIR section needs to be
aligned to the external optics. This is done by using the same theodolite set-up as in
the ‘Telescope Assembly’ section for both the arms referencing them all to the +Y
primary mirror. The collimated laser source along the principal optical axis travels
through the NIR optics train and focuses on the H1RG detector plane (which was
used for testing prior to using the H4RG array for flight). We note the position of
the spot on the plane, and accordingly align the NIR stage with respect to the FIR,
until the spots are centered on the two halves of the H1RG plane. This is done
visually without switching on the actual detectors.
The cryostat is removed once again to be closed up and for vacuum tests. It is
remounted and the top plate references used to check alignment for a final time. The
angles of the two telescope assemblies are also re-checked by pointing two theodolites
at the two primary rims, and comparing the azimuth-elevation measurements to that
before the cryostat was mounted. This ensures that the deformation on the truss is
minimal when the cryostat is mounted on it.
The results of the alignment techniques and the obtained accuracies (measured
or estimated) are listed in the Table 6.1. The errors for the large mirrors (siderostats
and telescope assemblies) were checked before and after shipment. The difference
in angle was a few arcseconds thereby validating the mechanical stability of the
design. Assuming that the angular and collimation errors are compensated, and that
there is no vignetting, the overall interferometric visibility of BETTII is dominated
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SW Band V=0.98 limit
Optical Correction by Alignment Achieved
Error in:
element/assembly without with (if applicable) method used accuracyB
correction correctionA
vertical angle 0.015′ 2′ tip-tilts in operation 0.26′
Siderostat Laser tracker and
horizontal angle 0.02′ 2′ tip-tilts in operation mathematical 0.26′
Siderostat rotation vertical angle 0.015′ 2′ tip-tilts in operation formalism to solve 0.53′
stage over 15◦-75◦ range horizontal angle 0.015′ 2′ tip-tilts in operation simultaneously 0.51′
′ tip-tilts inangle 0.03 3′ Reference points 1.1′
operation with laser tracker;
Telescope assembly
primary rim with
rotation about normal 12′ N.A. theodolite 1.7
′
Laser tracker -
angle 0.04′ 1′ ′direct and 1.0
Telescope assembly Flat through for angle;
translation along
0.035 mm 0.15 mm Flat translation camera image for 0.2 mm
normal to correct for focus
angle 1.5′ 20′ collimation; 20′
Telescope assembly Tertiary pitch and
Secondary translation along normal 0.04 mm > 2 mm 0.25 mm
translation along tangent 0.03 mm 0.35 mm yaw to correct for Theodolite laser 0.25 mm
angles
angle 0.35′ > 60′ source centering 3′
Telescope assembly
Tertiary translation along normal 0.06 mm > 2 mm 0.25 mm
translation along tangent 0.03 mm > 2 mm 0.25 mm
Warm delay line and
tip-tilts in Theodolite
K-mirror assembly - angle 0.4′ 60′ 1.0′
operation auto-collimation
individual mirrors
vertical angle 0.3′ 60′ tip-tilts in operation ′
K-mirror assembly Theodolite laser
2
rotation about axis 50′ * N.A. source centering; 5′
K-mirror rotation stage vertical angle 0.3′ 60′ tip-tilts in operation camera for spot 2′
over 15◦-75◦ range horizontal angle 0.3′ 60′ tip-tilts in operation movement 2′
All reflective surfaces
until beam combiner;
′ ′ subsequent fold Theodolite laserFIR bench, NIR stage angle 0.4 6 ** 5′
mirrors angles source centering
and external optics with
respect to each other
rotation about normal 25′ N.A. 5′
angle 2.5′ 6′ subsequent fold 5′
Double-sided parabola
translation along normal 0.03 mm 0.1 mm mirror angles Theodolite 0.1 mm
translation along tangent 0.3 mm N.A. auto-collimation 0.1 mm
translation along normal 0.07 mm N.A. 0.1 mm
Spherical mirror
translation along tangent 0.75 mm N.A. 0.1 mm
tip-tilts in Theodolite
Cold delay line assembly angle 0.4′ 60′ ** 1.0′
operation auto-collimation
angle 0.4′ 60′ ** tip-tilts in operation Theodolite laser 5′
Beam combiner
translation along normal 2.5 mm N.A. source centering 0.1 mm
A for linear phase error and afocus corrections if applicable; N.A. in list implies not applicable; for items that are
corrected by the tip-tilts, a more conservative tolerance is required to reduce the range of the tip-tilt used up
B If multiple error items refer to same element, the maximum error is reported here
* source at corner of FOV for maximum error
** limited by beam vignetting
Table 6.1: Summary of required and achieved alignment for optical elements and
assemblies. The alignment requirements that are barely met or not met are marked
in red.
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by the following errors: Telescope Assembly - Flat mirror angle and translation
along normal, Telescope Assembly - Secondary mirror angle and Spherical mirror
translation along normal. For some of these elements, the 98% visibility requirement
is barely met or not met. If we assume that the individual visibilities contribute
in the same sense, the overall visibility of the system is given by the product of
the individual visibilities. By this assumption, based on the attained alignment
accuracies we get an estimated overall visibility of V ∼ 0.75 in the SW Band. Since
some of the errors may compensate each other, the visibility is expected to be greater
than this minimum value. However this reduced visibility can limit the instrument
capability of determining the true size of extended sources. It will also reduce the
sensitivity to some of the protostellar parameters discussed in the following chapter.
The NIR Alignment test (Section 6.3) and interferometric tests that will be carried
out in the future (Section 6.2.5) are intended to ensure that even though some
individual tolerances are not met, the combined visibility of the system is improved.
An accurate measure of the overall visibility will be possible only upon obtaining
fringes from a calibration source during flight.
6.2.7 Control System Measurements
Even though the entire optics train is now aligned, to point to targets accu-
rately, we also need to know what the control system pointing is with respect to the
optics train pointing. The control system involves two main measuring devices: the
star cameras and the gyroscopes [232]. The star cameras provide pointing direc-
191
tion solutions every 5 seconds, while the gyroscopes propagate the pointing over the
period that a star camera solution is not available, allowing the pointing to be main-
tained to better than an arcsecond during that period. On the ground, sometimes
the gap between two star camera solutions is longer because of cloud coverage.
The star cameras consist of a camera, a focusing lens and a cylindrical baffle to
reduce stray light. Standard methods of measuring the star camera geometry using
retroreflectors did not provide the required accuracy for the pitch, yaw and roll
measurements. We use a novel technique to accurately measure the orientation of
each star camera. In this method, we use a laser tracker in the global reference frame
to point light at the star camera detector (Figure 6.10). We make a map of multiple
array locations on the star camera detector alongside the direction cosine readings
of the laser tracker. Interpolating the points within the detector plane, we get the
pointing direction cosines for the center of the array, which is used to calculate the
pitch and the yaw values to sub-arcsecond precision. We use the multiple pointings
to calculate how much the array pixel axes are rotated with respect to the pitch-yaw
axes. This gives the roll of the camera to an accuracy of about 10′.
The three gyroscopes are orthogonally attached to the inner sides of a hollow
box. A 0.5 inch SMR mounted on a hand-held probe is used to scan each of the
three planes. We get the laser tracker in the global reference frame and take mea-
surements of the retroreflector at multiple (25-30) points of each plane. By creating
three planes from these measured points, we generate the required orthogonality
information of the gyroscopes to an accuracy of 2′. This is used to get the angular
velocity measurements projected in the global reference frame. It is assumed that
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Figure 6.10: Model of star camera alignment using laser tracker, by directly pointing
a source at the star camera detector while in the global reference frame.
the gyroscopes axes are perpendicular to the corresponding sides of the hollow box
in which they are mounted to an angle lesser than the measurement accuracy. If
the three axes of the gyroscopes are pre-aligned in an unit having a known reference
surface, then the measurement is more reliable. Handheld retro-reflectors also have
greater manual errors especially for smaller surfaces. This error can be reduced
by measuring many points on the surface. Another method to reduce this error is
by mounting multiple small flat mirrors flush against the reference surfaces, and
measuring them by the direct-and-through method (described in Section 6.2.1.1).
6.3 NIR Alignment Test and Results
During the Fort Sumner flight campaign, we carried out some system level
testing from the ground by observing a few stars with the NIR H1RG detector.
This was a test for both a validation of the attitude estimation system and the
optics train, involving both the external optics and the NIR bench, when they
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work in conjunction. The star cameras and gyroscopes provided pointing solutions.
Unfortunately, ground wind speeds greater than 5 Knots made a full hang test
impractical: such a test would have allowed a star to be tracked in both azimuth
and elevation. Instead, with the payload resting on the ground, only the siderostat
rotation stages were used to track the stars in elevation. When the azimuth of
the stars matched that of the pointing, the stars transited across the NIR tracking
detector plane, along the cross-elevation axis (the axis perpendicular to the elevation
axis).
Here we report our observations of two stars which are bright in the near infra-
red: 30 Psc (Magnitude H = -0.25) and χ Aqr (Magnitude H = -0.06). Both stars
were close to their meridians, but rising slowly, at around 45 degrees elevation. A
45-degree elevation corresponds to the elevation cross-elevation axes being rotated
on the H1RG by 45 degrees with respect to the pixel axes. Since we were tracking
the elevation, this corresponds to the stars traversing along the cross-elevation axis,
i.e. diagonally across the detector (Figure 6.11). The sources crossed the field-of-
view in about 38 seconds. The two halves of the H1RG are expected to be mirror
images of each other for perfect alignment. In our case, there was a small overlap
between the two halves of the H1RG with the light from the right arm (K-mirror
side) reaching about a fifth of the left half (WDL side). This misalignment of about
1′ needs to be corrected by re-adjusting the NIR to external optics alignment.
The H1RG images had an integration time of about 3s, and they were captured
in intervals of 6-8 seconds. The difference of consecutive raw images was taken to re-
duce background effects and clearly identify the sources. The error analysis involved
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Figure 6.11: 30 Psc (left) and χ Aqr (right) transits across the 1024 × 1024 pixel
H1RG array. The left and right halves of the array correspond to the two arms
of BETTII. These images are obtained by taking differences of consecutive frames
obtained on the array 8 seconds apart. The bright (yellow) spots correspond to the
stars in the latter frame, while the dark (purple) spots correspond to them in the
previous frame. The white lines on the right figure indicate the transit direction
across the array which corresponds to the cross-elevation axis.
using the location of the star centroid in the array at an instant, its ‘Right Ascension-
Declination’(RA-Dec) coordinates, and the H1RG to sky coordinate transformation
equation to calculate the actual Azimuth-Elevation of the center of the H1RG half
under consideration. This is compared against the expected Azimuth-Elevation of
the pointing, calculated from the Telescope pointing RA-Dec estimates at the same
instant.
In the left arm (warm delay line arm), the elevation error was consistently
around 0.3′ for both the sources. The cross-elevation error was about 2′ for χ Aqr,
and around 0.3′ for 30 Psc. For the right arm (K-mirror arm), the elevation error was
around 2-2.5′ for both sources, while the cross-elevation errors were approximately
0.8′ for χ Aqr and 1.1′ for 30 Psc. The uncertainties in the error include centroid
195
pixel error of +/- 10 pixels, and timing error of +/- 1 seconds corresponding to about
0.1′ and 0.2′ in sky projected angle, respectively. The detector noise was higher in
the right arm, making centroid determination for the stars more challenging and
less reliable.
This test provided a combined error estimate of the star camera, gyroscopes,
the elevation tracking system, all the external optics, the NIR section of the optics
in the FIR bench, and the NIR optics. It was not possible to identify the errors
of individual sub-systems by this method. However, of the two observations, one
transit (χ Aqr) occurred while continuously getting star camera pointing solutions,
while in the other case (30 Psc) the gyroscopes were used to propagate the pointing
solutions for almost 40 minutes since the last star camera solution. So the first
results can be considered to be a measure of the misalignment between the star
camera and the optics system, while the second result when compared to the first
establishes the error of the gyroscope with respect to the optics.
Future efforts will involve carrying out further testing for sources at different
elevations so as to understand the effect of rotation stage variations. This error will
be challenging to counter other than by the tip-tilts during flight. However, errors
which are independent of the source elevation may be corrected by adjusting the
angles of some of the mirrors. For example, misalignments between the right arm
and the left arm may be corrected by angular adjustments of a fixed mirror in the
warm delay line; while misalignments between the actual and estimated pointing
solutions may be corrected by changing the measurement angles of the star camera
and/or gyroscopes. In particular, the measured roll of the star camera has a large
196
error margin, and it may be adjusted for better pointing accuracy.
A complete interferometric test of the instrument is only feasible during flight
while pointing at FIR targets. It is extremely challenging to create two coherent
sources 8 meters apart for testing on ground in a controlled environment. Addi-
tionally, the specifications of the optics will allow them to operate only in the FIR
wavelengths. As mentioned in Section 6.2.5, we intend to carry out interferometric
tests for the FIR optics bench on ground.
6.4 Summary
In this chapter, we have addressed the alignment challenges for a complex
interferometric system through a mixture of conventional and unconventional meth-
ods. In our analysis, we have connected each of the metrology requirements directly
with the fringe pattern outputs, and have investigated the possibility of correcting
them with the help of the rest of the optics. While we use conventional pieces of
metrology equipment like theodolites and a laser tracker, their applications are dif-
ferent based on the specific requirements of each optical element and assembly. One
of the unconventional approaches include extensively using both pieces of equipment
as a light source whose pointing direction can be measured or set in the global ref-
erence frame. This has two major advantages: (i) it allows for relaxed alignment
requirements (for example parts of the telescope assembly, relay flats), and (ii) it
results in very accurate measurements especially when the output light is obtained
on a detector that is read out electronically (for example star camera measurement,
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K-mirror rotation stage alignment).
Our approach also involves treating some of the systems as assemblies and
correcting for the combined effects of their errors (for example siderostats, telescope
assembly, cold delay line). In particular, the alignment of opto-mechanical parts like
the siderostat rotation stages was challenging because of the absence of any direct
optical references. Measuring the rotation axis direction cosines using retroreflectors
to trace the geometry had errors of several arc-minutes. Instead, we developed
mathematical formalism to determine the errors in these opto-mechanical parts to
a few arcseconds accuracy by measuring the optics that they move. We show that
the combination of these methods on BETTII can be used to achieve arc-minute
level pointing accuracy which can be further corrected because we can get exact
knowledge of the error by testing, and by understanding the sensitivity of each part
on the simulated output.
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Chapter 7
Interferometric Simulations
Mariotti & Ridgeway (1988) [208] showed how we can combine spectroscopy
along with spatial interferometry in the infra-red to gain a more complete picture of
star forming regions. BETTII is an implementation of this principle in the 30− 100
µm band. Each of the detectors in BETTII are 9 × 9 arrays, Nyquist sampling
the point spread function of the single telescopes. So in a sense each pixel is an
interferometer. Since it is a two-aperture interferometer, its baseline coverage is
very limited. Standard inversion techniques cannot be used in such cases. To have a
better understanding of the instrument’s performance, preferred observing strategies
and how to process the data to perform spatially resolved spectroscopy, simulating
it is of utmost importance.
In this chapter, we discuss the development of a simulator for BETTII. It takes
in (i) the sky map (ii) the specifications of the instrument and (iii) the location and
time, to compute the interferograms. We use the simulations to study the sensitivity
of the instrument to physical parameters of protostars like disk mass, envelope mass
and inclination angle. We also use the simulations to motivate a new optical design
for BETTII involving a dispersive backend.
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7.1 Mathematical Formalism
For most fixed ground-based interferometers, the baseline coverage for a par-
ticular pair of telescopes pointed at an arbitrary target in the sky is an arc of an
ellipse. In these cases, the projected baseline lengths can be less than the absolute
baseline distances. BETTII is designed such that the entire truss rotates around in
flight to an orientation that depends on the azimuth of the pointing center; while the
two siderostats on the two arms rotate according to the elevation angle to point at
the target. Since its baseline vector B~ is always perpendicular to the pointing center
ŝ0, the projected baseline as seen from the source is always equal to the absolute
baseline B. This means that the baseline coverage of BETTII for any of its targets
is an arc of a circle (and its negative counterpart). Further, this arc is limited based
on the latitude from where the observation is being done and the declination of the
source as well.
Let us assume a two element interferometer with a baseline vector B~ (from the
aperture center in arm 1 to that in arm 2) is pointing at a direction ŝo in the sky.
There is a point source i in the field of view in the direction ŝi. Plane electromagnetic
waves are coming from the source. The total electric field due to a point source at
a particular wavelength λ = 2π/k, after beam combination is given by the sum of
the electric fields in the two arms:
E~ (k) = E~a1(k) exp i(kx1 − ωt) + E~a2(k) exp i(kx2 − ωt) (7.1)
200
Figure 7.1: Basic schematic for a two-aperture double-Fourier interferometer pointed
at a direction ŝo with a source at ŝi. The Baseline vector isB~ . For BETTII,B~ ·ŝ0 = 0.
The instrument includes a delay line which systematically adds a delay of ∆z for
Fourier Transform Spectroscopy.
where E~a1(k) and E~a2(k) are the electric field amplitudes after the radiation passes
through arm 1 and 2 respectively, while x1 and x2 are the total optical distances
traveled by the incident optical radiation from the source until combination in the
corresponding arms. In an ideal instrument, we can assume that the electric field
E~0(k) entering the instrument from the two arms are affec√ted equally for each wave-
length until combination i.e. E~a1(k) = E~ ~a2(k) = E0(k) η(k), where η(k) is the
efficiency of each arm. This efficiency term largely depends on the transmissivity
and reflectivity curves of the optical filters, and the total integrated scatter from
each reflective surface. Additionally in the ideal instrument, the distances traveled
by the light wave in the two arms are different because of the source not being
perpendicular to the baseline, and because of the presence of delay lines in the
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instrument (Figure 7.1). The optical path difference (OPD) is given by
x1 − x2 = B~ · ŝi + ∆z (7.2)
where ∆z is the extra path traveled by beam 1 w.r.t beam 2, due to a delay line.
There can be an additional phase factor if the instrument does the beam combination
in the pupil plane (as opposed to combining them in the detector plane). The former
makes use of a beam-combiner/beam-splitter that has two outputs. The two incident
beams divide into two, a reflected and a transmitted beam. The reflected beam of
one incident beam combines with the transmitted beam of the other to produce the
two output beams, each having half the time-averaged total power. In one output,
there is a phase difference of +π/2 between the two combined beams, while in the
other the phase difference is −π/2 [68]. So the two outputs are exactly out-of-phase
at any instant. Thus, for BETTII which does pupil plane interferometry, the total
electric field after combination can be written as
√
E+ = E0(k) η(k) exp i(kx2 − ωt)[exp i(k(B~ · ŝi + ∆z) + π/2) + 1] (7.3a)
√
E− = E0(k) η(k) exp i(kx2 − ωt)[exp i(k(B~ · ŝi + ∆z)− π/2) + 1] (7.3b)
The post beam-combination intensities due to emission at multiple wave-
lengths can be calculated independently and integrated over the wavelength range.
The total power after combination is P+ = A
∗ ∗
0cE+ E+ and P− = A0cE− E−,
where the starred components are the complex conjugates of their corresponding
202
electric fields. A is the effective aperture area, 0 is the permittivity of free space
and c is the speed of light. For BETTII, A can be calculated using the effective
aperture diameter D = 0.5 m.
Let us consider only the + output after combination. On simplification,
P (i, k, B~ ,∆z) = 2A cE 20 0 (k)η(k)(1 + sin k(B~ · ŝi + ∆z))dk (7.4)
After re-writing the electric fields in terms of radiative flux F (k) =  cE 20 0 (k) and
adding over all sources (which are incoherent to each other), the total power becomes
∑∫
P (B~ ,∆z) = 2A Fi(k)η(k)(1 + sin k(B~ · ŝi + ∆z))dk (7.5)
i k
The combined beams are focused on to a detector by the use of focusing
mirrors, which results in a ‘jinc’ distribution of the intensity at the detector plane.
The intensity at a certain point P ≡ (xp, yp) on the detector plane due to a point
source centered at I ≡ (xi, yi) on the same plane may be written in terms of θ and
θi respectively. θi is the angle between ŝ0 and ŝi while θ is the angle between ŝ0 and
the equivalent pointing direction of P on the sky.
[ ]2
I(θ − 2J1(x)θi) = I0 (7.6)
x
Here x = kD sin(θ − θi) ≈ kD(θ − θi), J1 is the Bessel Function of the first kind,
and the central intensity I = PA /(λ20 p f
2), where Ap is the pupil area and f is
the focal length of the camera. It is to be noted that in BETTII, a compressed
203
beam is focused on to the camera. If we had defined D as the pupil diameter (after
compression) instead of effective aperture diameter, we should consequently use the
angle in the compressed beam, and not the angle in the sky for θ − θi.
Using the expression for power from the equation 7.5, we get
∑∫ [ ]
~ 2AAp 2J {k
D
1 (θ − θ 2P 2 i
)}
I( , B,∆z) = 2 Fi(k)η(k)(1 + sin k(B~ · ŝi + ∆z))dk
λ2f 2 D∑k2 ∫ [ k (θ − θ]i)4 i2Ap J1{kD (θ − θi)} 2
= 2 Fi(k)η(k)(1 + sin k(B~ · ŝi + ∆z))dk
πf 2 k (θ − θi)i
(7.7)
The values of θ and θi are derived using the elevation and cross elevation angles
from the pointing center ŝ0. For this, we use a parameter α defined as the ratio of
the angle on the sky to the corresponding distance on the detector array, both with
respect to the pointing center. The focal length of√the camera can be expressed in
terms of this parameter as f = 1/(αC), where C = A/Ap is the beam compression
factor between the incident beam diameter and the instrument pupil diameter. The
value of C is about 20 for BETTII. Using these relations, the intensity expression
may be re-written as
[ ]
2Aα2 ∑∫ J {kD~ 1 (θ − θ 2P 2 i)}I( , B,∆z) = Fi(k)η(k)(1 + sin k(B~ · ŝi + ∆z))dk
π k (θ − θi i)
(7.8)
A code was developed in C to implement this derived equation, given the
instrument parameters for BETTII for the two bands – short wavelength (SW: 30−
55 µm) and long wavelength (LW: 55− 100 µm). The code determines the baseline
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orientations and the detector array orientations with respect to the sky (in terms of
elevation and cross elevation angles) for a set of timeframes and geographic locations.
An input sky model is taken consisting of a set of point sources (independent or
together forming an extended structure) with a spectra being associated with each
source (fluxes in Jy). The code calculates the intensities (in W) for each pixel, for
each delay line location, and for each baseline orientation. An example simulation
output is shown in Figure 7.2, for a field of view (FOV) containing 4 point sources
arranged in a T. In Figure 7.3, we show how sources very close to each other can be
identified, even though they are not resolved by the BETTII aperture PSF in the
detector plane.
After generating the BETTII observations, the steps to obtain the sky map
from the observations is more complex. The procedure would typically involve
model fitting and is challenging to automate without inspecting the outputs at
every step. The general outline is given in Section 7.4. If there is a single source in
the interferogram, their spectra F (k) can be recovered by using the equation
∫ ∞
F (k) = 2 [I(z)− I0] sin (kz)dz (7.9)
−∞
where I(z) represent the interferogram intensities at a pixel, and I0 is the average of
the maximum and minimum intensities: (Imax + Imin)/2. This technique has been
used in Section 7.3 to compare the derived spectra for an instrument design variant.
205
Figure 7.2: Simulations for a simple field and spectra on BETTII detectors (LW
band) for two baselines (top and bottom). On the left is the 9 × 9 array with each
pixel showing the time averaged signal, while on the right side, the interferograms
(intensity vs optical path difference) on the central 9 pixels are shown. There are four
point sources in the FOV, marked as 1, 2, 3 and 4 each having some assumed spectra.
The corresponding fringe packets are marked on the interferograms. For a particular
baseline orientation, the fringe packets corresponding to each source always appear
at the same delay location irrespective of the pixel. For a different baseline rotation
of BETTII, the sky rotates with respect to the detector array and by a different
angle compared to the baseline rotation. Accordingly the interferograms have fringe
packets at different distances on the OPD axis.
206
Figure 7.3: Simulations for two point sources 4 ′′apart observed in the LW band.
The averaged intensity at the detector plane (left) does not distinguish between the
sources, but the presence on two fringe packets on the central pixel interferograms
(right) allows us to detect the two sources.
7.2 Protostellar Physical Parameter Sensitivities
One important objective of BETTII is to probe the structure of embedded pro-
tostars in binary and multiple systems. Thus we need to investigate the capability
of the instrument in determining the physical parameters of protostars such as the
distribution of the mass of material in protostellar disks and the envelope around
it. In this section, we simulate the BETTII observations of a hypothetical protostar
taking into account the instrument characteristics and limitations. Varying the in-
put model parameters that we use to define the dust emission from the protostar,
we produce sets of simulated outputs. By comparing these outputs with the hypo-
thetical observations, we explore how well the BETTII observations constrain the
defining parameters of the young stellar system.
207
7.2.1 Hyperion Protostar Modeling
We use the Hyperion [233] radiative transfer modeling code to produce the
high resolution spatio-spectral image cubes of protostars. The model includes many
parameters about the dimensions and the physical properties of the protostars. We
fixed some of these parameters, while allowing the others to vary, thereby generating
a grid of models. The parameters we fixed include the central luminosity at 30 L
(accounting for the modest sensitivity of BETTII), the disk outer radius at 100 AU,
the disk surface density exponent at -1, the envelope density power law exponent
at -1.5 and the outflow cavity opening angle at 10◦. We assumed a typical distance
of 400 pc to the protostar. Some of these parameters can be determined directly
from our observations, or with other instrument observations, or are considered less
important in the context of protostellar evolution. The parameters we varied include
the disk masses (ranging from 0.25− 5 × 10−3 M), envelope masses (ranging from
0.025 − 0.5 M), envelope radii (1000 − 7000 AU) and inclination angles from 0◦
to 90◦. These properties define the material that participates in the star formation
process and/or are useful to constrain star forming models. The masses are varied
on a logarithmic scale, while the radii and inclination angle are varied on a linear
scale.
The outputs were generated corresponding to both the SW and LW BETTII
bands. We oversampled the input images at a resolution of about 40 AU (∼ 4 times
the BETTII resolution at 30 µm for a distance of 400 pc). The images cover an
area of 15000 AU × 15000 AU (37.5′′ across). The typical flux is 35 Jy and 30 Jy
208
in the SW band and LW band respectively for a source of 0.001 M disk mass and
0.1 M envelope mass (given the luminosity of 30 L). Two sample image slices
are shown in Figure 7.4. The emission is more extended in the longer wavelengths
which correspond to the emission from lower dust temperatures.
Over the entire parameter space, the SEDs peak near the upper wavelength
of the SW band or the lower wavelength of the LW band. As the parameters
are varied, the position of the SED peak, and the slope on the two sides of the
peak changes. Accordingly the emission in the two BETTII bands change. For
example, with change in inclination angle from face-on (outflow axis pointed towards
the observer) to edge-on, the SEDs become steeper in the SW band and the peak
emission decreases. This results in the SW band emission decreasing by a significant
amount compared to the LW band emission. Similarly, as we increase the envelope
mass, the SED peaks shift from the upper part of the SW band to the lower part of
the LW band. The peaks also become higher, and so the emission increases in both
the bands, although the gain is more in the LW band. With increase in the disk
mass, the overall emission does not change much in either band, but the SEDs rise
more steeply in the SW band.
This grid of model datacubes are used as inputs for the BETTII interferometry
simulation code to generate outputs interferograms at the SW and LW bands of
BETTII. The interferograms are in units of 10−15 W, which can be compared against
√
the total noise-equivalent power (NEP) of 2 × 10−15 W/ Hz in the SW band and
√
1 × 10−15 W/ Hz in the LW band. The integration time per reading in a delay
line stroke of 2.5 s is 2.5 ms. The typical observation time of 10 minutes means 240
209
Figure 7.4: Dust embedded YSO image slices at 40 µm and 75 µm from the data
cube generated using Hyperion. The X-like structure in the images corresponds to
the outflow.
strokes or a nominal value of 0.6 s for the total integration time per interferogram
data-point. From the maxima (Imax) and minima (Imin) in the interferograms, we
obtain the amplitudes (Imax−Imin) and visibilities (defined as (Imax−Imin)/(Imax+
Imin)) for the entire grid of model protostars. They are measures of absolute and
relative fringe contrast respectively. We use these to study the sensitivity of the
observations to model parameters.
7.2.2 Results
The fringe amplitudes depend on the spatial distribution of the emission con-
volved with the point spread function (PSF) of the instrument apertures. For a
point source smaller than the interferometer resolution, the visibility is maximum.
For an extended source that is smaller than the beam size, the visibility reduces. We
note that the amplitudes are about a factor of 10 greater in the SW band compared
to the LW band for typical protostars. This is because the emission is greater and
less extended in the SW wavelengths than in the LW wavelengths.
210
Figure 7.5: Amplitude (left) and Visibility (right) variations in LW observations of
protostars with orientation changing from face-on(0◦) to edge-on(90◦). The different
curves correspond to protostars with different disk mass (DM in units of 10−3 M)
and envelope mass (EM in units of M) values.
The trends in the amplitudes and visibilities are found to depend on the com-
bination of the variable parameters. Both the BETTII bands are sensitive to in-
clination angle, but the sensitivity increases near edge-on orientations. The fringe
amplitude decreases going from face-on (0◦) to edge-on (90◦) orientation of pro-
tostars. In face-on orientation, the emission from the disk passes through lesser
column densities of dust and gas exterior to it. Thus its extent is limited, thereby
leading to higher fringe amplitudes, as opposed to in the edge-on case.
BETTII is more sensitive to inclination angles for high values of disk mass and
low values of envelope mass. This effect is more pronounced in the LW band than
in the SW band. In the LW band, the amplitude increases by a factor of 6.6 from
90◦ to 0◦, for a disk mass of 5 × 10−3 M and an envelope mass of 0.025 M, but
the factor reduces to 1.3 for a disk mass of 0.25 × 10−3 M and an envelope mass
of 0.5 M(see Figure 7.5). The inclination angle sensitivity has lesser dependence
211
on the envelope radius. On the other hand, the sensitivity to other parameters (like
disk and envelope mass) is greater for close to face-on angles.
The fringe amplitudes and visibilities are higher for greater disk masses, be-
cause the 100 AU disk is like a point source whose contribution increases with mass
as compared to the emission from the envelope. This effect reduces at edge-on angles
of viewing where the optical depth is much higher. For example, for face-on observ-
ing in the LW band, the amplitude increases by a factor of ∼ 3 and the visibility
by a factor of ∼ 2 for a factor of 20 increase in the disk mass of a YSO having a
fixed envelope mass of 0.1 M (see Figure 7.6). Although the recorded amplitude
and visibility are much higher in the SW band, the sensitivity to change in disk
mass is much lesser in the SW band for the same set of protostellar properties. This
difference between the two BETTII bands can be used to constrain the disk mass
and inclination angle in the protostellar model.
With greater envelope mass, the extended emission increases. This reduces
the fringe visibility. However the total emission increases with envelope mass as
well and it has a greater effect on the fringe amplitude. So for a factor of 20 increase
in envelope mass, the LW band visibility drops by 0.3, while the corresponding
amplitude increases by a factor of 2-3 (for an inclination angle of 60◦). This opposing
trend of visibility and amplitude can be used to break the degeneracy between the
protostellar disk mass and envelope mass from the observations (see Figure 7.6).
Since the typical envelope size is comparable to or larger than the beam size,
the effect of envelope radius in lowering the fringe amplitude is negligible. The
variation is less than 20% in the LW band and less than 5% in the SW band. In
212
Figure 7.6: A slice from the parameter space hypercube, showing the variation of
LW and SW amplitudes with inclination angle and disk mass for a fixed envelope
mass (0.1 M) protostar. The units are 10
−15 W. Both the BETTII bands are
sensitive to inclination angle, but only the LW Band also has a significant sensitivity
to disk mass. This will allow distinguishing between protostar incident angle and
disk mass.
this discussion, we have simplified some of the relationships. However, in specific
combinations of the parameters, we find low or non-monotonic variations of the
amplitude and/or visibility. They are less useful for our analyses, but should be
noted as limitations of the BETTII instrument in disentangling the parameters for
those combinations. As an example, for low disk masses, the visibility and the
amplitude almost remain constant with variations in inclination angle in the LW
band (see Figure 7.5). We can derive some information from the SW band if the
orientation is close to edge-on, or if the envelope mass is on the higher side. However,
in the parameter space of low envelope masses (< 0.1 M), low disk masses (< 5 ×
10−4 M) and orientation angles in the range 0
◦ to 60◦, the combined information
from the two BETTII bands is insufficient to determine the protostellar parameters
213
Figure 7.7: Amplitudes (in units are 10−15 W) and visibilities (unitless) variation
with envelope mass and disk mass properties of a protostar oriented at 60◦ inclina-
tion angle. The fringe visibility and amplitude sensitivity for envelope mass follow
distinctly different patterns. This can be used to break the degeneracy between
envelope mass and disk mass
due to inherent degeneracies.
Overall, the models show that BETTII will be sensitive to protostellar in-
clination angle, disk mass and envelope mass for protostars having luminosities
comparable to that used in the model (30 L) over most of the parameter space
studied by us. If the source is bright enough, we can use the LW band information,
which is more sensitive to changes in many of these parameters. The degeneracies
between the parameters can be broken by combining the amplitude and visibility
information from the two BETTII bands. The protostellar modeling combined with
the simulations pipeline also gives a platform to fit models to flight data when they
are available. The analysis discussed here only deals with a single point source,
but this is easily scalable to extend the analysis to multiple embedded sources with
varying properties.
214
7.3 Dispersive Backend Simulations
The most significant limitation for BETTII is its sensitivity; obtaining spectral
signal-to-noise ratio > 5 in < 10 minutes requires sources >13 Jy. One possible
way to improve the signal-to-noise ratio (SNR) for future BETTII flights is by
dispersing the spectra. This is implemented by using a dispersive element post
beam combination to spread out a polychromatic point source PSF on the detector
array, such that each pixel corresponds to a small fraction of the bandwidth. This
results in a broader envelope of the interferometric fringe pattern allowing more
fringes to be detected, and thereby improving the spectral SNR. In BETTII’s effort
to return to flight, this is a key addition to the existing optical design to improve
the overall sensitivity. The optical design to implement this is discussed in the final
section of Chapter 5. Here we discuss the concept to motivate this design change,
and demonstrate the improvement using simulations.
7.3.1 Concept
Rizzo et al. (2015) [209] studied the sensitivity of the BETTII instrument,
and the effects of intensity noise and phase noise. The intensity noise includes
source photon noise, background photon noise (from the sky, the optics and the
cryostat window) and detector noise (phonon, readout and Johnson noise). Of
these intensity noise sources, in the previous BETTII design, the main contributor
to the noise is the background photon noise. Compared to the LW band, the SW
band has greater thermal background noise contributions from the telescope and
215
the window assuming a nominal temperature of 230 K during flight. The photon
√
noise-equivalent power (NEP) is estimated to be 1.4 × 10−15 W/ Hz in the SW
√
band and 0.7 × 10−15 W/ Hz in the LW band compared to the detector NEP of
√
0.3 × 10−15 W/ Hz. Since the NEPs are added in quadrature, the contribution of
the detector noise is considerably less in both the bands - 4% and 15% in the SW
and LW bands respectively.
If we consider only intensity noise, for N discrete measurements of an inter-
ferogram with a step size of xi and a noise variance σ
2
i in the interferogram√domain,
the noise standard deviation in the spectral domain is given by σs = σixi N/2. In
the interferogram domain, the signal-to-noise ratio in unit time can be expressed as
SNRi ≡ I0/σi, where I0√is the peak intensity of the interferogram. In the photon
noise limited case, σi ≈ I0 + Ibkg where Ibkg is the background photon noise inten-
sity. If we assume that over the spectral bandwidth of interest ws, the mean spectral
intensity of the source is S and the mean spectral intensity of the background is
Sbkg, then the SNRi expression can be written as
Sws S √
SNRi = √ = √ ws (7.10)
Sws + Sbkgws S + Sbkg
In the spectral domain, we define [234] the signal-to-noise SNRs ≡ S/σs ,
which can be simplified as
√
S S 1 2 S
SNRs = = √ = √ (7.11)
σs σixi N/2 xi Nws S + Sbkg
216
Using the above relations, we can also derive a relation between the signal-to-noise
ratios in the two domains as
√
1 2
SNRs = SNRi (7.12)
wsxi N
√
This shows that even though SNRi is directly proportional to ws, SNRs is
√
inversely proportional to ws. In other words, on decreasing the spectral bandwidth,
even though the central fringe has lesser SNR, the fringe envelope is more extended
resulting in more number of fringes being detected over the noise. This is the concept
behind using a dispersive element in the BETTII optics train to improve the spectral
SNR. The concept has been studied previously by multiple authors [235, 236, 237].
A mathematical treatment including the effect of readout noise is given in Pritt et
al. (1997) [234].
7.3.2 Simulations and Recovered Spectra
The dispersive grating concept was implemented in the interferometric simula-
tion to compare the effects with that of the previous design and with the theoretical
results. Figures 7.8 and 7.9 show the results for a single point source with a model
spectra. The spectra includes a representative transmission function for the BET-
TII bands. The BETTII plate scale ensures Nyquist sampling of the point spread
function (PSF). We carried out the simulations for the source to be at the center of
the field of view (FOV) and used only the central pixel interferogram (having most
of the signal) in the non-dispersive case for the spectral analysis. The dispersive
217
grating spreads the signal along the columns, according to wavelength. In this case,
we used all the interferograms in the central column to recover the spectra. In both
cases, the photon noise was approximated as a normal distribution with a standard
√
deviation of I, where I is the signal intensity at the pixel and the OPD.
As is evident from Figure 7.9, for the dispersed case, the interferograms include
more detectable fringes and consequently the spectra has lesser noise compared to
the non-dispersed case. The absorption features in the spectra are identifiable in the
new design, but not in the previous design. Since grating dispersion is proportional
to wavelength and not wavenumber, there is a slight deviation from the theoretical
SNR improvement. The higher wavelengths have greater improvement in spectral
SNR than the lower wavelengths within a band.
In the previous section we showed that theoretically the spectral SNR can
improve by a factor equal to the square root of the fraction by which the bandwidth
is reduced. So if we disperse the signal corresponding to 1 pixel over 9 pixels in the
BETTII TES detectors, we should expect an improvement by a factor of 3. However,
there are some caveats to this. In the case of BETTII, since we are dominated by
background photon noise (and not source photon noise), we also have to reduce the
field of view (FOV) on the detector in order to gain from this design change. The
optics train has a focus inside the cryostat prior to the cold pupil for both arms of
BETTII. A slit can be introduced here perpendicular to the dispersion direction to
reduce the background noise. A slit of width 0.5 mm corresponds to about 40′′ on
the sky. This is covered by 3 pixels in the SW band, and 2.4 pixels in the LW band.
At any single baseline, BETTII would have a FOV of 120′′ × 40′′, although the
218
Figure 7.8: BETTII interferometry simulations for a point source at the center of the
field of view (FOV) with an assumed spectra in the SW band. The upper row shows
the results for the original BETTII design with no dispersive element, while the
lower row represents the results for the new design with a dispersive back-end. The
images on the left show the time-averaged and normalized intensity at each pixel of
the 9 × 9 SW detector array. The images on the right show the interferograms for
the 3 × 3 central pixels of the detector. In the case of the dispersed interferograms,
a diffractive element disperses the fringes along a column, such that each pixel
corresponds to a small fraction of the spectral range. This reduces the average
intensity of each pixel but the fringe packets are much wider. So even though the
SNR of the interferograms decrease, the total detected signal from the entire fringe
packet increases, resulting in a net increase in the spectral SNR.
219
Figure 7.9: Model input spectra and recovered spectra for SW band (left) and LW
band (right). The source is assumed to be in the center of the BETTII FOV. The
recovered spectra are shown for (i) interferograms with no noise, (ii), interferograms
with photon noise in the no dispersion case and (iii) interferogram with photon noise
in the dispersed case. In the non-dispersive case, only the central pixel interferogram
is used to extract the spectral information. In the dispersive case, the interferograms
for the central column of pixels (see Figure 7.8 lower-left panel) are used for obtaining
spectral information. The extracted spectra in the dispersive case have better SNR
than the non-dispersive case.
220
fringes will be dispersed over the entire column of pixel. However, as we observe at
different baselines (using earth’s rotation), the sky field will rotate with respect to
the slits. So we would have an effective FOV corresponding only to the central 40′′.
In each pixel of a column, we will still get the background photon noise contribution
from the 3 central pixels in the SW band (and√the 2.4 central pixels in the LW
band). So effectively the gain is by a factor of 9/3 = 1.7 in the SW band. The
corresponding gain in the LW band is 1.9.
Although the requirement of a slit reduces the total FOV, the SNR will improve
by having to use a smaller range of the cold delay line mechanism in order to cover
the FOV. In the previous design, the range was set by the LW band FOV of 2.5′
(See Section 5.3.1). With the FOV reduced by a factor of 3.75 in the LW band,
the effective cold delay line range requirement is reduced to 2.5 mm instead of 8
mm (after taking into account overheads at the turning points). With the range
reduced, the instrument would be spending more time at each point in the reduced
FOV by a factor of 3.2 over a fixed time period of observation. This will improve the
√
interferogram SNR and consequently the spectral SNR by another factor of 3.2 =
√
1.8 (SNRi ∝ time).
Another thing to consider is that with increasing dispersion, the recorded
intensities at each pixel reduces and the detector noise starts becoming as relevant
as the photon noise. This comparison between background noise and detector noise
is the limiting factor setting the optimal dispersion. In case of BETTII, the number
of pixels over which we can disperse the photons corresponding to a single pixel
before detector noise becomes comparable to photon noise is 22 pixels for the SW
221
band, and 6 pixels for the LW band. Accordingly, taking the slit width, delay line
range and detector noise into account and also using the efficiency estimates of the
diffractive grating (from Chapter 5), the new sensitivities of the two BETTII bands
are 11 Jy in the SW band and 6 Jy in the LW band (instead of 25 Jy and 13 Jy
respectively) to obtain a spectral SNR of 5. These values are determined for ‘normal
observing’, which consists of co-adding delay line scans in 10 minutes covering the
effective FOV, using a spectral resolution of R = 10 and a nominal OPD noise of 5
µm RMS.
The analysis from the interferograms shown here does not represent the actual
spectral extraction process, which would require iterative modeling. However, this
technique combined with preliminary astrometry can produce the starting model
for the iterations. The use of dispersion makes the disentanglement of multiple
sources more challenging. In a more complex field, the interferograms of two sources
may overlap, not only based on their projected distances along the baseline vector
and because of partially overlapping PSFs, but also based on the spectral energy
distributions of the individual sources. Information from multiple baselines obtained
through field rotation can be used to break these degeneracies.
7.4 Path to Image Reconstruction
Future work using these simulations involve incorporating the effects of real-
istic phase errors, intensity errors and filter effects to get interferograms that we
are likely to produce with the instrument [209]. The intensity noise consists of the
222
astronomical and thermal background noise, the photon noise from the source, and
the detector noise. These can be modeled with appropriate distributions. There are
additional error terms in the combining electric fields. The field amplitudes can vary
due to efficiency asymmetries between the two arms, including the beam-combiner.
Variations in the phase are caused by instrument limitations like pendulations, er-
rors in the delay lines, optics figure errors, non-homologous contraction during flight,
misalignments and pointing jitter. The phase error may be varying non-uniformly
over the combining beam area.
Phase errors due to the optical path length difference (OPD) errors can be
modeled by introducing a Gaussian distributed error on the OPD values (∆z) and
calculating the intensity at those OPD locations, but recording them on a linear
OPD scale. Alternatively, we can use the calibration results from the delay line to
introduce the OPD error. In the post-processing, we can then correct for them to
the error limit of the capacitive sensors, before co-adding them.
Because of the presence of filters in the bolometer array current detection
procedure, our readings at 400Hz won’t be instantaneous but a weighted integration
of the intensities over the time period between each reading. Even the readings on
each pixel, are an integration over its area. To model discretization and filtering
effects, we can produce very high resolution interferograms (both in terms of detector
plane coverage and OPD sampling). These are summed up over the appropriate pixel
areas and the delay spaces, taking into account filtering effects due to the detector
electronics and software.
Finally, one of the major uses of the simulations would be to devise a technique
223
to derive astrometric and spectroscopic information iteratively from the raw data.
This will involve co-adding the interferogram scans at each baseline and using them
to identify the individual point sources (or determine if they are extended). The
spectral component of each of the sources may be disentangled especially using
interferograms from baselines where the projected distance between the sources is
maximum. The location of the peaks of point sources in interferograms at different
baselines will provide astrometric information. For flight data, we can use this basic
spectral and astrometric analysis, combined with source models to re-simulate the
interferograms, and then iteratively produce a better spectral and astrometric map.
The simulations allow us to see the effects of co-adding multiple scans as the
sky rotates gradually on the detector. Accordingly, we will be able to fine tune
our observation strategies to set the duration of time spent on one target FOV
at a particular baseline orientation. We can also simulate the error effects due to
different cold delay line scan speeds, and accordingly set the optimal speed to be
used in flight.
224
Chapter 8
Conclusion
8.1 Summary
In this thesis, we have studied molecular clouds to understand their role in star
formation. CARMA interferometric observations of five filaments in the Serpens
and Perseus regions were carried out using dense gas tracers. These were used to
map the morphology and kinematics of the filaments. Of the molecular transitions
we observed, H13CO+ is the best tracer of the dense gas, and reveals multiple sub-
structures of the filaments in the line-of-sight. Most of the sub-structures are aligned
to each other indicating that they are affected by a common physical process. The
kinematics revealed that in most of the studied filaments and sub-structures, the
velocity gradients are more prominent across their widths than along their lengths.
We propose that this indicates filament formation via inflows within a dense layer
created by colliding turbulent cells.
We get further evidence of this for the NGC 1333 region, based on VLA
observations using NH3 as a tracer. From the NH3 (1,1) velocity map, we find
225
that the velocity gradient ridge extends in an arc across the entire southern part of
the cloud. This region is dotted with Class 0/I YSOs, that could have formed from
local overdensities in the compressed gas leading to gravitational instabilities. The
NH3 (1,1) velocity dispersion map also has relatively high values along this region,
thereby substantiating the shock layer argument.
The NH3 (1,1) and NH3 (2,2) VLA observations are further used to obtain
kinetic temperature and column density maps for the entire NGC 1333 region. The
high values in the kinetic temperature maps have a good correlation with the location
of the outflows. The outflows also play a role in filament formation by clearing out
the molecular clouds. By creating bow shocks and dense gas layers, they can also
contribute to star formation as in the apex of the NGC 1333 cloud structure.
We conclude that the NH3 (1,1), N
+
2H J=1-0 and H
13CO+ J=1-0 transitions
all trace the same material in these dense star forming regions. There is good
correlation with the sub-mm dust emission maps as well, especially in regions away
from the protostars. However, the filament widths determined using the dense gas
are lesser than their widths in dust. Additionally, the widths are found to be non-
uniform along the lengths of the filaments.
For both the CARMA and VLA observations, we combined the interferometric
data sets with single dish observations to obtain maps that are sensitive to both
small scale and large scale structure. This technique of combining the data in the
visibility domain and carrying out their joint deconvolution can be applied to other
data sets to get large area maps having high angular resolution.
To study regions of clustered star formation in the FIR wavelengths, we have
226
developed a balloon-borne interferometer BETTII. The instrument performs long-
baseline interferometry using two apertures 8 meters apart, and combines it with
Fourier Transform Spectroscopy. In this thesis, we discuss the design of its optics
system in the context of maintaining the phase information of the two beams until
combination. Delay line mechanisms used to maintain the optical path lengths of
the two arms of the interferometer are calibrated and characterized. This accounts
for one type of phase error. The other type of phase error is wavefront error. This
is mitigated by fabrication techniques and alignment procedures that are discussed
in details in the thesis.
For the alignment, we devise a method to determine the tolerance of each
optical element based on their effect on the fringe visibility at the detector. Novel
techniques are developed to meet these requirements involving the use of laser track-
ers and theodolites. We extend the techniques to measure the optics system pointing
and the relevant vectors of the control system in the same reference frame. We also
validate the alignment using NIR observations from the ground.
Finally, we investigate how effective BETTII will be in studying star forming
regions. We carry out interferometric simulations and determine that the fringe
amplitudes and visibilities can be used to determine protostellar parameters like
disk mass and envelope mass. The instrument sensitivity to variations in these
parameters however depend on the protostellar parameter space being probed. We
use the simulations to motivate a dispersive backend design for the BETTII optical
system, in order to improve the sensitivity of the instrument. This will allow BETTII
to carry out spatially resolved spectroscopy for fainter multiple systems of protostars.
227
8.2 Future Work
The CARMA and VLA interferometric observations call for further study of
other filaments using tracers like H13CO+ J=1-0 which is sensitive to dense gas,
is optically thin and has no hyperfine splitting. NH3 and N2H
+ has better SNR
than H13CO+; so they could be used to map large areas and identify the interesting
regions to be studied in details using H13CO+. More observations are required to
establish a census of the various kinematic signatures discussed in this thesis. Only
then can we be certain whether the observations match the simulations and how
important turbulent cell collision is in the context of filament formation.
The VLA datasets are very rich in information. Further studies can be car-
ried out using the existing data by focusing on smaller regions around each of the
protostars in the NGC 1333 region. Future work involving the analysis of the ve-
locity dispersions of the independent velocity-coherent components near the YSOs
and their connections to the large scale structure of the cloud would provide further
insights into the star formation process.
The similarity between the velocity maps of N H+2 and NH3 in the NGC 1333
region indicate that there is good ion-neutral coupling over most of the region. Thus
there is no clear evidence that the magnetic field is restricting the motion of the
ionic species. This suggests that the magnetic field may not be strong enough to
constrain turbulent motions. Further investigations need to be carried out to derive
quantifiable limitations on the magnetic fields in the region.
Future work on BETTII involves rebuilding the instrument based on the new
228
design upgrades. This includes fabricating the blazed diffraction grating to imple-
ment the new dispersive backend design for the optics system. The new optics design
will allow us to obtain fringes using the FIR optics bench in the laboratory. This
will be crucial to validate the alignment of the entire FIR optics train at cryogenic
temperatures. If required, relevant corrections or modifications can be carried out
on ground.
Based on the lessons learned from the first version of BETTII, the optics align-
ment plan should be laid out beforehand to identify potential locations for machined
references in the structure. This will be particularly useful to associate the reference
frames of the optics outside the cryostat with those inside it. The alignment strat-
egy also needs to be modified to account for the various design changes, especially
with the new star camera and gyroscope models.
The interferometric simulations need to be improved to take into account the
various forms of instrument error. The simulations give the platform to develop
the process of disentangling the BETTII data and obtaining the spatio-spectral
information. An iterative model fitting algorithm needs to be established for this
purpose. Based on the findings, we can develop a pipeline to process the data
from BETTII flights. Future work will also include studying various observation
strategies with BETTII, and investigating potential design changes for future space-
based long-baseline interferometers.
229
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