ABSTRACT Title of dissertation: THE SEARCH FOR COINCIDENT GAMMA-RAY EMISSION FROM FAST RADIO BURSTS WITH THE HAWC OBSERVATORY Elijah Job Willox, Doctor of Philosophy, 2024 Dissertation directed by: Professor Jordan A. Goodman Department of Physics In 2007 a new class of radio transients was discovered, coming from outside of our galaxy with high fluence emitted in the radio band on millisecond timescales. These bursts of radio waves emitted within an order of magnitude of the power of the least bright gamma- ray bursts. These fast radio bursts (FRBs) have since become the target of many searches across radio observatories and multiwavelength follow-up campaigns, but their origin re- mains unknown. In order to understand more about these fascinating events, continued multiwavelength follow-ups are necessary to provide a more complete picture. The High Altitude Water Cherenkov (HAWC) observatory is a very-high-energy gamma-ray detector covering the range of 100 GeV to 300 TeV that is well suited to the detection of transient phenomena due its high live-time and wide field of view, and in particular for a follow- up search on FRBs to determine possible very high energy gamma-ray coincidences. The search for gamma-ray signals from FRBs consists of two searches: first is a persistent source search to identify if FRB emission ever comes from TeV gamma-ray emitting galax- ies, and a transient search centered on the reported burst time and location. The results of the FRB search within the HAWC data sets the most constraining limits on the widest population of FRBs ever searched in the VHE band. THE SEARCH FOR COINCIDENT GAMMA-RAY EMISSION FROM FAST RADIO BURSTS WITH THE HAWC OBSERVATORY by Elijah Job Willox 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 2024 Advisory Committee: Professor Jordan A. Goodman, Chair/Advisor Dr. Andrew Smith Professor Gregory Sullivan Professor Brian Clark Professor M. Coleman Miller © Copyright by Elijah Job Willox 2024 Dedication As it was written For the one who is everything. ii Acknowledgments Those of you who read this part know words come to me much better written than spoken. I want to express my gratitude firstly to my wife and best friend Kendyl, who has been with me from the beginning. You have always encouraged me to achieve my dreams, and I know I couldn’t have done it without you. Your support from applications, the hard classes, to your encouragement as I write this thesis make everything possible. Norm and Karen, you both have always supported me and welcomed me into your family without hesitation, and the joy you’ve brought and support given has meant so much to me. And Jo Anne, I will always appreciate the Power that you gave me from the very beginning have made every difference in getting me to this point. A deep and sincere thank you to Jordan, who agreed to bring me into the HAWC group and has advised me and given invaluable perspective and history on astrophysics, the University of Maryland, and so much more. To Andy for pushing me to do the best analysis and taking me ”under the hood” of how our science happens, and how a computer really works. The graduate students and post-docs who answered all my questions, Colas, Israel, Kristi and Chad. Thank you all for the help. I also wouldn’t be here if it weren’t for all of the great science and other teachers I had along the way. Ms. Vassar from Riverton Elementary inspired me to follow this path from a young age, and Mr. Sames at Lincoln Middle pressed me to keep learning past what my grade said I should be. Dr. Wittmann, my undergraduate advisor, is the reason I am at Maryland and taught me so much about what research is supposed to be, how to answer big questions, and communicate my thoughts effectively. Finally, thank you to Calvin for teaching me patience, making me get outside, and realizing that any dog can learn new tricks, if you spend the time to teach them. And thank you to Eleanor, for being the best support dog a person could ask for, you are always there in my shadow and make every day happy. iii Table of Contents Dedication ii Acknowledgements iii List of Figures vii List of Tables xii List of Acronyms & Abbreviations xiii 1 Introduction 1 1.1 FRBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Origin of VHE Gamma Rays . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 Gamma-Ray Transients . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Detecting Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2 Extensive Air Showers . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . 12 1.3.3 Water Cherenkov Detectors . . . . . . . . . . . . . . . . . . . . . . 13 1.3.4 Imaging Atmospheric Cherenkov Telescopes . . . . . . . . . . . . 14 1.4 The Landscape of Gamma Ray detections . . . . . . . . . . . . . . . . . . 14 1.4.1 Multi-Wavelength Astronomy . . . . . . . . . . . . . . . . . . . . 16 1.5 A Brief History of FRBs . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.1 FRB Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.2 Dispersion Measure . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2 The HAWC Observatory 26 2.1 The HAWC Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.1 The HAWC Detector Tank Units . . . . . . . . . . . . . . . . . . . 28 iv 2.1.2 Signal Processing and Calibration . . . . . . . . . . . . . . . . . . 29 2.2 HAWC Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2.1 XCDF Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.2 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 Reconstruction: Data Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3.1 Event Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3.2 Core and Angle Reconstruction . . . . . . . . . . . . . . . . . . . . 38 2.3.3 Gamma/ Hadron Classification . . . . . . . . . . . . . . . . . . . . 41 2.3.4 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3.5 The Summarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4 HAWCProd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.5 Post-Reconstruction Data Processing: Data Level 3 . . . . . . . . . . . . . 45 2.5.1 The HAWC Binning Scheme . . . . . . . . . . . . . . . . . . . . . 45 2.5.2 Data ”Chunks” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.5.3 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.5.4 Air Shower Alignment . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.7 Map Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.7.1 Counts Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.7.2 Detector Response Files . . . . . . . . . . . . . . . . . . . . . . . 51 2.7.3 Direct Integration and Other Background Methods . . . . . . . . . 52 2.7.4 Significance Maps . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.8 Transient Observations with HAWC . . . . . . . . . . . . . . . . . . . . . 54 2.8.1 Online Transient Searches . . . . . . . . . . . . . . . . . . . . . . 55 3 Transient Searches with the HAWC Observatory 58 3.1 Likelihood Analysis with the HAWC Observatory . . . . . . . . . . . . . . 59 3.1.1 Trials Factor and the ”Look Elsewhere” Effect . . . . . . . . . . . . 60 3.2 ZEBRA Transient Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.1 Feldman Cousins Upper Bounds . . . . . . . . . . . . . . . . . . . 64 3.2.2 Extragalactic Background Light Attenuation . . . . . . . . . . . . . 64 3.3 Transient Gamma-Ray Source Searches with HAWC . . . . . . . . . . . . 66 3.3.1 The HAWC sensitivity to Short Duration Transients . . . . . . . . . 68 3.3.2 Online Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.4 Application to FRBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4 Fast Radio Bursts and the Search for Coincident TeV Gamma-Ray Emission 74 4.1 The Search for Gamma Rays Coincident with FRBs . . . . . . . . . . . . . 75 4.1.1 The Case for VHE Emission from FRB Sources . . . . . . . . . . . 75 4.1.2 Source Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.3 Methods for the Steady-State Search for VHE Emission from FRB Hosts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 v 4.1.4 Transient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 Results of the Search for Gamma-Ray Signals from FRB Sources . . . . . . 83 4.2.1 Results of the Persistent Source Search . . . . . . . . . . . . . . . . 84 4.2.2 Transient Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5 Conclusions and Future Work 97 5.1 Future FRB Searches with HAWC . . . . . . . . . . . . . . . . . . . . . . 100 A FRB Locations, Times, and Implied Redshifts 101 B Steady State Flux Values at FRB Locations 109 C Transient Search FRB Sources and their Fluxes 116 Bibliography 154 vi List of Figures 1.1 The crab nebula composite image from five different observatories, the Very Large Array (radio), Spitzer space telescope (infrared), Hubble space telescope (Optical), XMM-Newton (Ultraviolet), and Chandra Observatory(X- ray) [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 A schematic diagram for the direct detection of gamma rays. The pho- ton passes through the anti-coincidence shield then interacts with a pair production medium with scintillators that allow gammas to pair produce positron/electron pairs. Finally the pairs are tracked through the medium and the base of the detector acts as a calorimeter to determine the energy deposited by the gamma ray. . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 The number of particles participating in a gamma-ray EAS as a function of the depth travelled from the first interaction of the primary particle. The optical depth of the HAWC observatory is at an optical depth of 637 g/cm2 [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 An air shower particle entering the top of a HAWC tank at faster than the speed of light in water, producing Cherenkov light that is detected by the PMTs at the bottom of the water volume. . . . . . . . . . . . . . . . . . . 13 1.5 Diagram of an IACT capturing an image of air Cherenkov light from a 1 TeV photon. The camera in the focus of the telescope registers an ellipse of light elongated along the direction of the shower and the total intensity measured is used to reconstruct the shower energy [22]. . . . . . . . . . . . 15 1.6 The sensitivity of instruments covering a wide range of the gamma-ray ob- servation energy to a point source for varying levels of exposure. IACTs report sensitivity to point source with 50 hours of exposure, while HAWC reports the sensitivity for 5 years of observation, and LHAASO is reported for 1 year. e-Astrogram, CTA-South, and HiSCORE are in varying stages of development and not active at the time of writing. Repoduced from [23]. 16 1.7 Multiwavelength SED of Mrk 421 which shows a ”double humped” emis- sion feature, emitting strongly in the X-ray band, falling off as energy in- creases, but rising again in the VHE gamma-ray band. From [24]. . . . . . . 17 vii 1.8 Data from the Swift satellite showing X-ray components from BAT and XRT tools onboard, as well as X-ray satellites NICER and MAXI (top panel. The data show a decay with time that is closely matched by data from the optical instruments aboard the Swift observatory. From [26]. . . . 18 1.9 The all-sky distribution of FRBs, overlain on the LAB HI Survey taken from FRBSTATS.org [29]. Each circle represents an FRB with the color representing the measured DM of the burst, which can be taken as a proxy measurement of the distance to the source. . . . . . . . . . . . . . . . . . . 21 1.10 A single beam of the Parkes detection of the Lormier burst showing how the dispersed signal sweeps across radio wavelengths in this beam of the Parkes detector (bottom). And the intensity, shown here summed over all channels and de-dispersed in time, which saturated the detector (top). Reproduced from [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.11 Waterfall plot showing the intensity measured for FRB20180801A by the CHIME/FRB detector, after de-dispersing the signal in time. Top: Intensity curve over time in milliseconds. Right: intensity over frequency band cov- ered by CHIME/FRB. Center: ”waterfall” plot showing relative intensity in frequency and time space in a 2D histogram. Reproduced from [27]. . . . . 23 2.1 The HAWC detector looking southwest at the Sierra Negra with the Large Millimeter Telescope visible at the top. . . . . . . . . . . . . . . . . . . . . 27 2.2 A schematic diagram illustrating how a PMT amplifies a signal through a chain of dynodes which multiply the original photon signal by a factor of 10 at every stage [33]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 A HAWC main array tank showing the distribution of the 4 PMTs in the water volume, a person for scale, and traces of Cherenkov light originating from an incoming shower particle. . . . . . . . . . . . . . . . . . . . . . . 30 2.4 Installation of PMTs with photo taken from the hatch. . . . . . . . . . . . 30 2.5 An 8 inch PMT like one used in HAWC detector for the A, B and D PMTs. This is a Hamamatsu R5912 8” PMT with attached base that seals the elec- tronics inside from the water that it will be submerged in during data taking. Photo credit Dr. Kristi Engel . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6 Plot showing Low ToT for PMT signals. . . . . . . . . . . . . . . . . . . . 33 2.7 Plot showing high ToT for PMT signals. . . . . . . . . . . . . . . . . . . . 33 2.8 The angular resolution of gamma-ray showers in HAWC simulation recon- structed with the pass 5 algorithms (solid lines) as a function of fraction of PMTs hit. The previous results are shown in faded lines for the ”pass 4” set of reconstruction algorithms, which does not include the MPF or high zenith improvements. The resolution is shown for three different zenith bands to show how angular resolution depends on the zenith angle of the primary particle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 viii 2.9 A high energy gamma ray event on the HAWC detector. The star represents the core of the shower and the red line extending from the star represents the angular direction of the shower arrival. The large red circle is a 40 m circles centered on the core position, and the small red circle is the largest hit in terms of PEs outside of the the 40 m circle used for calculating CxPE. Keep in mind the circle drawn is only an approximation, since the algorithm does all calculations in the shower plane. . . . . . . . . . . . . . . . . . . . 42 2.10 Left: The hits contained in a high-energy gamma-ray shower as a function of radial distance showing a fit to a lateral NKG function. Right: The same distribution shown for a cosmic ray shower. . . . . . . . . . . . . . . . . . 42 2.11 Reconstructed Energy vs. True energy for the two energy reconstruction algorithms used in HAWC analysis. Left: energy comparison for the NN algorithm, 93.9% correlation. Right: energy comparison for GP algorithm, 93.1% correlation. Reproduced from [38]. . . . . . . . . . . . . . . . . . . 43 2.12 The fHit binning scheme used in HAWC to separate the data grouping EASs with similar responses, shown here for crab nebula data for each bin as a function of true energy. . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.13 A muon from an EAS generated by CORSIKA simulation enters the top of a HAWC tank model implemented in GEANT, and the particle emits Cherenkov light (green tracks) which can be detected by the PMTs at the base of the tank. The number of particles is scaled down by a factor of approximately 1000 for illustrative purposes. The quantum efficiency of the PMT is also included in GEANT so that the simulated files have in- formation on the charge level of the hit on the PMT from the Cherenkov photon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.14 The all sky HAWC map for events greater than 56 TeV in reconstructed energy. Significance is calculated for every pixel in the skymap based on the number of signal events and the detector response function defined for the set of cuts that was applied. This map assumes a -2.5 index power law as the spectrum and searched for 0.5 degree extented emission. . . . . . . . 54 2.15 The measured significance of a sliding time window search given a small signal over a consistent background similar to what is seen in HAWC. The blue line shows how a non-overlapping time search can report artificially low significance when the maximum flux occurs on the edge of a time bin. For progressively increasing amounts of overlap it becomes clearer which timeframe contains the maximum flux measurement. Reproduced from [46]. 56 ix 3.1 A representation of the method implemented in ZTS for finding flux bounds using the FC method [51]. The horizontal axis is the measured flux by the instrument, and the vertical axis is the true flux from the source for arbitrary units scaled to the significance of detection. A measured flux at 4, shown with the blue dashed line, has a 95% confidence interval on the flux between 2 and 4 (the red dashed lines). For lower measured significances however, the lower bound goes to negative infinity and the calculated flux error becomes the upper limit on the flux calculated from the measurement. Reproduced from [46] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2 The attenuation function (e−τ ) for gamma rays for different redshift values across the energy range of GeV to TeV according to the model described in [53]. The model from that paper, and used in this analysis is the solid line and based on the WMAP5 survey with a fiducial model, the blue line is the model based on a fixed assumption and the WMAP5. The red lines are from a previous paper on this topic, Dominguez 2011. Figure reproduced from [53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.3 The sensitivity to GRBs for the HAWC observatory compared to several bright high-energy GRBs for different zentith angles of the burst. The like- lihood of HAWC detecting a GRB depends heavily on the affect of EBL on the detected emission. This sensitivity does not reflect recent improvements to HAWC sensitivity at lower energy. Reproduced from [46]. . . . . . . . . 69 3.4 The sensitivity of HAWC to a GRB compared with the lightcurve of GRB190114C detected by MAGIC. The MAGIC detection was made around 100 s follow- ing the T0 of the GRB, meaning this emission is from the afterglow, and the HAWC sensitivity places this burst in the detectable range for a 10 s search that begins at T0 and above a zenith angle of 30 degrees. The HAWC sen- sitivity is shown for 4 different zenith angles, showing a dependence of the sensitivity on the height of the GRB at the time of the burst in the HAWC data. Figure from Dr. Martinez-Castellanos, 2020, for the HAWC Collab- oration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.5 GRB search online with tiling of the entire sky. There is overlap in the 2.1x2.1 degree square tiles and in the time window of the search. Shown here are the spatial bins which contain counts for the time interval shown. Higher counts correlates with higher significance. If any trial of this search raises above the alert level a more detailed analysis will automatically follow- up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.1 In the AGN scenario for generating FRBs with VHE gamma-ray counter- parts, the AGN generates an electron/positron wind which interacts with a highly magnetized environment remaining after the supernova a massive magnetar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 x 4.2 Artist rendition of a binary NS merger. Two orbiting NS spiral in towards expelled matter in a halo around them. The moment of collision results in a GRB represented by the jet seen coming out perpendicular to the plane of the orbit of the two objects. Reproduced from [63]. . . . . . . . . . . . . . 78 4.3 The 1 sigma flux upper limits, calculated using the method described in [51], compared to the implied redshift of the FRB event calculated using the MacQuart relation from [31]. . . . . . . . . . . . . . . . . . . . . . . . 85 4.4 A visualization of the HAWC data around the FRB210328A in the transient search. The top color bands represent TS from the 5 s search, and the bot- tom band is for the 1 s search. The color bar shows the TS of the individual trials. The maximum significance for this FRB occurs at 435.5 s after T0 for the 1 s search with a TS value of 13.7, not rising to the level of detection even before trials factors are considered. . . . . . . . . . . . . . . . . . . . 86 4.5 The distribution of TS values for FRB20210327C for the 1 s search (top) and 5 s search (bottom). The data values are the live trials taken from the HAWC data and the background distribution is a combination of 10 simulations of the FRB search window with identical search parameters. . . 87 4.6 The all-sample TS distribution for the FRBs in this study for 1 s (left) and 5 s (right) searches compared to the combination of all background trials. All distributions follow a log-linear decrease as TS increases. No individual trials rose to the level of significant detection, and the bulk behavior does not show evidence for enhance emission above the background expectation for trials taken at these locations for the given duration searched. . . . . . . 88 4.7 HAWC flux upper limits for the 1 s and 5 s search, taken as the least con- straining trial from each FRB searched plotted against the radio flux. All energy-flux values are compared in erg cm−2. . . . . . . . . . . . . . . . . 93 xi List of Tables 2.1 Data levels as defined by the CTAO group in [34] . . . . . . . . . . . . . . 34 3.1 Parameter Choices for the FRB search. . . . . . . . . . . . . . . . . . . . . 72 4.1 Steps of the FRB source selection and the number remaining after taking consecutive cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2 The proportion of trials over 9 TS value for all FRBs tested and compared to the simulated background only model of these trials. Each FRB was simulated 10 times to increase statistics in the background. . . . . . . . . . 88 4.3 Flux upper limits from the HAWC measurement compared to the radio flux reported by CHIME/FRB in their first catalog [27]. . . . . . . . . . . . . . 92 xii Acronyms & Abbreviations High-Altitude Water Cherenkov High-Altitude Water Cherenkov [Observatory] ADC analog-to-digital converter AGN Active Galactic Nuclei ASKAP Australian Square Kilometer Array Pathfinder CHIME/FRB Canadian Hydrogen Intensity Mapping Experiment/ Fast Radio Burst CMB Cosmic Microwave Background COM center of mass CORSIKA COsmic Ray SImulations for KAscade CTA Cherenkov Telescope Array DAQ data acquisition system Dec Declination DRF detector response function EAS extensive air shower EBL Extragalactic Background Light FEB Front-End Board fHit fraction of PMTs hit FAST Five-hundred-meter Aperture Spherical Telescope FRB Fast Radio Burst GBM [Fermi] Gamma-ray Burst Monitor GBT Green Bank Telescope xiii GCN Galactic Coordinates Network GeV giga electron volt GRB Gamma-Ray Burst GTC GPS Timing and Control GW Gravitational Wave HAWC High-Altitude Water Cherenkov HE high-energy HEALPix Hierarchical Equal Area isoLatitude Pixelation [of a sphere] H.E.S.S. High-Energy Stereoscopic System HQE High Quantum Efficiency IACT Imaging Atmospheric Cherenkov Telescope IC Inverse Compton INTEGRAL INTErnational Gamma-Ray Astrophysics Laboratory IR Infrared [electromagnetic radiation] ISM Intestellar Medium K-S Kolmogorov-Smirnov keV kilo electron volt LAT [Fermi] Large Area Telescope LDF lateral distribution function LE low-energy LED light-emitting diode LHAASO Large High Altitude Air Shower Observatory LIGO Laser Interferometer Gravitational-wave Observatory MAGIC Major Atmospheric Gamma Imaging Cherenkov ME medium-energy xiv MeV mega electron volt MPF Multi-Plane Fitter NKG Nishimura-Kamata-Greisen NS Neutron Star p-value Poisson probability PBH Primordial Black Hole PDF probability density function pe photoelectron PeV peta-electronvolt PINC Parameter for Identifying Nuclear Cosmic rays PMT Photomultiplier Tube PSF point-spread function PWN Pulsar Wind Nebula RA Right Ascension SBC Single Board Computer SED Spectral Energy Distribution SFCF Super Fast Core Fitter SNR Supernova Remnant SSC synchrotron self-Compton SWGO Southern Wide-field Gamma-ray Observatory TDC Time-to-Digital Converter TeV tera electron volt ToT time-over-threshold TS test statistic UHE ultra-high-energy xv UMD University of Maryland, College Park UNAM Universidad Nacional Autónoma de México UTMOST Upgrade Monlongo Observatory Synthesis Telescope UV Ultraviolet [electromagnetic radiation] VERITAS Very Energetic Radiation Imaging Telescope Array System VHE very-high-energy WCD water Cherenkov detector ZEBRA ZEnith Band Response Analysis xvi Chapter 1: Introduction Photons reach the Earth and are observed from the farthest depths of the universe across twenty orders of magnitude in energy. Ranging from the longest wavelength ra- dio waves to the immensely energetic gamma rays, which are now measured past 1 peta- electronvolt (PeV). Utilizing various observation techniques astronomers can observe the same source through a wide swathe of the electromagnetic spectrum giving a clear picture of astrophysical sources and extreme astrophysical environments. Observation of sources across a wide range of the spectrum, called multi-wavelength astronomy, provides insights on the physical environment of sources that a single energy band cannot provide. Through detailed study of the spectrum and time-dependent behavior, multi-wavelength efforts pro- vide new information on the source(s) in question. Multi-wavelength and multi-messenger astronomy has been used successfully to understand the Gravitational Wave (GW)/Gamma- Ray Burst (GRB) coincidence, and in understanding GRBs across a wide range of wave- lengths, and also in the understanding of Active Galactic Nuclei (AGN). Gamma rays, defined as photons with energies greater than 100 keV are the category of the highest en- ergy photons detected. Gamma-ray astronomy is the way we observe the most energetic phenomena in the universe and gives a targeted view of the most extreme physical envi- ronments ever observed. Gamma rays come to earth from a range of sources including persistent, variable and transient phenomena. Due to the fact that gamma rays have now been detected over 10 orders of magnitude it is necessary to subdivide this category further because detection techniques and source classes change as you move higher in energy. For 1 this study we focus on very-high-energy (VHE) gamma rays, defined as photons over 100 GeV. In particular the High-Altitude Water Cherenkov (HAWC) which collects gamma rays between 50 GeV and more than 300 TeV, is used for its wide field of view and consistent livetime over 90 % for observing sources. This thesis will present the results of a search for emission coming from a class of extragalactic transient sources of radio waves called Fast Radio Bursts (FRBs). FRBs are extremely bright bursts of radio waves, observed to have isotropic energy equivalent of more than 1043 erg s−1, only a few orders of magnitude from the low energy range of a GRB which have been detected as low as 1045 erg s−1. These bursts emit this energy in bursts on the order of milliseconds. The cause of these events is still unknown, and theories to explain them rely on multiwavelength observation. Applying the lessons learned from years of multi-wavelength astrophysics and specific tools developed for the detection of GRBs with the HAWC Observatory, this study searches for persistent emission from the FRB locations as well as transient gamma-ray activity centered on FRB event times and locations. A detailed description of the HAWC detector, reconstruction pipeline and data products is in Chapter 2. The background of transient searches relevant to this study and previous work that informed the choices made in the FRB study is in Chapter 3. The details of the searches and their results are in Chapter 4. Finally, the conclusion of this study and future work is discussed in Chapter 5. 1.1 FRBs In 2007 an archival search of radio data from the Parkes telescope looking for radio pulsar pulses discovered a burst that was inconsistent with previously known astrophysi- cal radio bursts [1]. The inconsistency with previous radio bursts was the high dispersion measure which implied an extragalctic distance, paired with high fluence which saturated 2 the radio detector at the peak of the burst. (Dispersion measure will be discussed in detail later in this thesis.) The ”Lorimer Burst” as it was called opened the field of study of FRBs, with more bursts found including the discovery of four other high-dispersion bursts within the Parkes dataset [1, 2]. Taking the Thornton 2013 [2] result as inspiration for further study, FRBs continued to be detected by radio observatories including Arecibo [3], Green Bank Telescope (GBT) [4], the Australian Square Kilometer Array Pathfinder (ASKAP) [5], and the Upgrade Monlongo Observatory Synthesis Telescope (UTMOST) [6], between 2013 and 2018. The implication of extremely bright radio bursts coming from such large distances is that these bursts approach the power of some of the most intense astrophysi- cal phenomena ever observed, perhaps approaching the power of GRBs and supernovae at least within a few orders of magnitude [7]. In 2018 a dedicated instrument for the observation of FRBs, the Canadian Hydrogen Intensity Mapping Experiment/ Fast Ra- dio Burst (CHIME/FRB), began observing the northern sky and increased the number of observed FRBs by a factor of two within a year [8]. Now the number of FRBs has in- creased to over 900 [9]. Despite the increased observations of FRBs, their origin remains unknown. In order to understand these events better we can make observations at as many other wavelengths is possible and provide critical information on the mechanism or mecha- nisms which produce these exciting events. In the VHE range, this study expands on work from MAGIC [10], VERITAS [11], Fermi-LAT and GBM, and Swift [12] which have all used data to provide limits on VHE emission from FRBs. This work will contribute to the study of FRBs by looking for coincident emission in VHE gamma rays with the HAWC ob- servatory. The HAWC observatory is a wide field of view gamma-ray observatory meaning that it has continuous daily observations on all of the sources in its field of view, making it a valuable addition to the measurements taken by IACTs which must be pointed at a source. 3 1.2 Gamma-Ray Astronomy The electromagnetic spectrum is one window to observing the universe, and at the high- est energy end of this spectrum are gamma rays, defined as photons with energy greater than 100 keV. Gamma rays have been observed to come from several types of sources as seen in the 3HWC and 4FGL catalogs from the HAWC and Fermi collaborations respectively [13, 14]. However, in order to discus high energy gamma rays one must first understand the beginnings of cosmic ray astrophysics. Cosmic rays are high energy particles of atomic origin, being electrons, protons or heavier nuclei that constantly bombard the Earth. The origin of high energy astrophysics had a beginning with the detection of cosmic rays in the early 1900s. Victor Hess detected an excess of radiation determined to be originating from cosmic rays by balloon experiments in 1911-1913 [15]. Gamma rays also are constantly reaching the Earth across all energies, and the same techniques which capture cosmic rays will also pick up gamma rays. Gamma rays provide a more targeted probe of astrophysical phenomena when compared to cosmic rays because cosmic rays are deflected by magnetic fields since they are charged particles. Photons are not deflected along their path to an observatory and therefore can be used to point back directly to their source. The difficulty comes then from the relatively smaller flux when compared to cosmic rays. Techniques for detecting gamma rays and separating that signal from the cosmic ray background will be discussed below and in Chapter 2. 1.2.1 Origin of VHE Gamma Rays Gamma rays are produced at the energy range detected by HAWC only by a few known processes. The first of these is neutral pion decay. Pions are particles that are produced by collisions of high energy atomic nuclei, mostly protons as they are the most abundant but can also result from collisions of heavier nuclei. These collisions produce charged and 4 neutral pions, the neutral pions decay into gamma rays on very short time scales (10−16s) dominantly radiating two photons (eq. 1.1). π 0 −→ 2γ (1.1) The energy of the outgoing gamma rays depends on the initial momentum of the pion, which is a product of the momentum of the colliding nuclei. This decay process is a major contributor to the gamma ray emission above 1 GeV. The other major production mechanism to produce TeV gamma rays is Inverse Comp- ton (IC) scattering. As the name implies, IC is a related interaction to Compton scattering, the process by which high energy photons scatter off of charged particles, usually elec- trons. IC is thus the process by which a photon gains energy after a collision with a high energy electron. Where this analysis is concerned, the focus of this process is the scattering of Cosmic Microwave Background (CMB) and Infrared [electromagnetic radiation] (IR) background photons off of a highly energetic electron population with the relationship, Ee ≈ 17.2( Eγ 1TeV )0.5TeV (1.2) as expressed in [16]. This process allows a very direct measurement of electron energy if the other processes can be eliminated, and is a major source of the TeV photons de- tected by HAWC. A related process which produces VHE photons is synchrotron self- Compton (SSC) where photons produced by synchrotron emission can IC scatter within the population of photon produced by the same process. 5 1.2.2 Environments The radiative processes detailed above can only take place in certain extreme envi- ronments and produce gamma rays detectable by the HAWC observatory. As reported in the 3HWC catalog paper ([13]) the majority of sources are Supernova Remnants (SNRs), Pulsar Wind Nebula (PWN), or pulsar halos. Figure 1.1 shows the most well observed TeV gamma-ray source, the Crab nebula as a composite image from five different obser- vatories, illustrating the detail that can be gained by making multiple measurements of the same source. These sources are persistent meaning the flux is completely or nearly emitting gamma rays according to a consistent spectrum at all times and continued obser- vation provides more significance proportional to the square root of time. In addition to the persistent TeV gamma-ray sources are two prominent AGN, the Markarians 421, and 501 which are transient. In addition to these two, HAWC now detects three other AGN and publications are in preparation at the time of this thesis. These sources go through flaring periods where they will emit very brightly in TeV gamma rays for periods of days at a time. Detailed studies of many of these sources have been publish by the HAWC collaboration showing Spectral Energy Distributions (SEDs) and attempting to understand what emission mechanism produces the observed emission. 1.2.3 Gamma-Ray Transients In addition to all confirmed gamma-ray sources observed by HAWC, there are transient sources as well. Transient gamma-ray phenomena remain an intriguing field of study be- cause their nature doesn’t allow for persistent observation, and their observability is related to the sky coverage of instruments across the spectrum. Not all environments that produce high-energy gamma rays produce them at a persistent level over time. Transients and variable sources have been detected at all energies in the 6 Figure 1.1: The crab nebula composite image from five different observatories, the Very Large Array (radio), Spitzer space telescope (infrared), Hubble space telescope (Optical), XMM-Newton (Ultraviolet), and Chandra Observatory(X-ray) [17]. gamma-ray band with durations varying from very long to very short. Variable gamma-ray sources include AGN flares, GRBs and binary systems [18]. GRBs have been an exciting field of astrophysical study for the past 50 years since their initial discovery by the Vela satellites [19]. Transients such as bright GRBs have been observed in the photon energy range of keV up to past a TeV. The number of detected GRBs continues to grow and studies of this phenomenon aim to provide new insights into a class of accelerators of particles at immense energies coming from extreme astrophysical environments. GRBs have even been detected up to 13 TeV by the Large High Altitude Air Shower Observatory (LHAASO) [20]. In order to study the exciting physics taking place in the VHE regime measurements are needed that requires observatories designed specifically for the task of detecting highly energetic photons. 7 1.3 Detecting Gamma Rays The detection of VHE gamma rays poses an interesting challenge that requires different technology than optical astronomy. High energy gamma rays do not penetrate deeply in the atmosphere due to scattering of the photons off of nuclei in the atmosphere, interacting via pair production in about the first 4 percent of the atmosphere above the HAWC detector, about 37 g cm−2 of depth. This process is described in detail in 1.3.2. The techniques to detect VHE and ultra-high-energy (UHE) gamma rays are direct detection via satellite, and the ground based detector types water Cherenkov detector (WCD) and IACT, all described below. The major limiting factor on the detection of VHE gamma rays is the consistent and overwhelming background of cosmic rays which come from all directions at all times due to magnetic scattering in the interstellar medium and locally from the solar and geologic magnetic fields. The rate of cosmic rays is 104 more than gamma rays above 100 GeV, and can interact with the same detectors in the same energy regime, but because cosmic rays have distinct physical properties it is possible to build background reduction into your experiment through hardware, software, or a combination of the two. 1.3.1 Direct Detection Above the atmosphere it is possible to observe gamma rays directly up to over 1 TeV, limited only by the effective area allowed by a satellite in orbit [14]. This necessitates the use of satellites above the atmosphere and requires a technology which can capture the gamma rays and convert them into particles which can be tracked for direction and measured for energy. One such technique, which is used on the Fermi-LAT experiment is the pair-production detection. This technique takes advantage of the pair-production process where a gamma ray will enter the field of an atomic nucleus and make an electron- positron pair which can be detected and tracked by various methods. As an example the 8 Figure 1.2: A schematic diagram for the direct detection of gamma rays. The photon passes through the anti-coincidence shield then interacts with a pair production medium with scintillators that allow gammas to pair produce positron/electron pairs. Finally the pairs are tracked through the medium and the base of the detector acts as a calorimeter to determine the energy deposited by the gamma ray. Fermi-LAT detector is comprised of three systems, a tracker compartment of silicon strip detectors, a system of Cs-Id calorimeters and an anti-coincidence layer of plastic scintillator tiles to reject the background of charged particles. A schematic of this type of satellite can be seen in figure 1.2. The inclusion the anti-coincidence layer on the detector leads to excellent CR back- ground rejection, the tracker component allows reconstruction of the initial photon direc- tion, and the calorimeter captures the energy deposited by the photon. This direct detection technique works to provide a picture of the gamma ray sky up to a few hundred GeV. Above this number the event rate is too low to measure flux consistently due to small effective area of a satellite. 9 1.3.2 Extensive Air Showers Once we are in the regime where there is no longer the flux level required to use a satellite for direct detection, a ground based technology becomes necessary, and with that constraint a new process is necessary for the detection of gamma rays. When high en- ergy gamma rays interact with the atmosphere, a cascade of particles is initiated called an extensive air shower (EAS). Starting with the single photon or cosmic ray incident on the atmosphere, a chain reaction of particle interactions such as IC, Compton scattering, and pair production initiate a shower of particles, which produce further high-energy gamma rays and the process continues in a chain reaction, increasing the number of particles in the EAS, up to a maximum value called shower max. Shower max depends on the initial energy of the photon (or CR for hadronically induced showers) and a figure showing the number of particles as function of depth from the first interaction of a gamma ray can be seen in figure 1.3. An EAS resulting from the interaction of a gamma ray is characteristically different from that of a CR. This is due to the particle interactions that occur in the cascade of particles from the different progenitors. A gamma ray interacts in the atmosphere by pair production, that is, γV HE −→ e−+ e+ (1.3) where a VHE photon interacts with an atomic nucleus and produces an electron-positron pair. Now that we have charged particles travelling with momentum that was carried by the photon, bremsstrahlung produces more gamma rays, which can pair produce and so on. This process continues until the energy of the photons is low enough that ionization absorp- tion of atoms starts to dominate over the pair-production likelihood at shower max. It is also possible that photons in the atmosphere can produce electrons via Compton scattering, 10 Figure 1.3: The number of particles participating in a gamma-ray EAS as a function of the depth travelled from the first interaction of the primary particle. The optical depth of the HAWC observa- tory is at an optical depth of 637 g/cm2 [21]. but at the energy range of HAWC, pair production is the dominant process. A CR induced shower is not so simply modeled however, as a proton-proton colli- sion can produce pions, which decay further into gamma rays (for neutral pions), or neu- trinos and muons (for charged pions). Pions have lifetimes prior to decay that are long enough to interact with other nuclei in the atmosphere which creates even more pions. The non-photon CR interactions in the atmosphere create distinctly different shower shapes to gamma rays which allows WCDs to reliably separate gamma rays in their data. The de- tails of how the HAWC software distinguishes between these two EAS types is outlined in section 2.3.3. 11 1.3.2.1 Cherenkov Radiation One of the most important processes in the detection of astrophysical high-energy gamma rays is the Cherenkov process. The speed light travels is dependent on the medium through which it is moving, so when a charged particle travels through medium faster than the speed of light in that medium that particle radiates energy via Cherenkov radiation. The radiation occurs along a specific angle related to the speed of the particle and the index of refraction in the medium of travel (equation 1.4). cosθ = 1 βn (1.4) Where β ≡ v/c is the fraction of the speed of light in vacuum that the particle is travelling, and n is the index of refraction. The angle achieves a minimum value when the speed of the particle approaches the speed of light in a vacuum. For air n ≈ 1.0003 and in water n = 1.33 which gives values of θmax of ≈ 1.4◦ and 41.25◦ respectively. In order to detect EAS for gamma rays the detector needs to collect information about the secondary particles resulting from the primary interaction and the resulting cascade. Two primary techniques have been devised and successfully implemented across several generations of observatories. These two techniques are water Cherenkov detectors (WCDs), which use a volume (or volumes) of water to produce Cherenkov radiation off of the EAS particles which reach the ground, and imaging atmospheric Cherenkov telescopes (IACTs) which collect the Cherenkov light directly from EAS particles in the atmosphere, which due to the narrow Cherenkov cone for particles in air allows for excellent angular recon- struction of EASs. 12 Figure 1.4: An air shower particle entering the top of a HAWC tank at faster than the speed of light in water, producing Cherenkov light that is detected by the PMTs at the bottom of the water volume. 1.3.3 Water Cherenkov Detectors Water Cherenkov detectors (WCDs) collect energy from EAS’s using the water Cherenkov process. Similar to Cherenkov radiation in air, when a particle enters a volume of water moving faster than the speed of light in water the particle loses energy emitting Cherenkov light in the visible band that can be detected by photo-sensors. This is the technique utilized by the HAWC Observatory and in figure 1.4 a diagram is shown of a shower particle en- tering the top of a single HAWC tank. The particle is shown emitting Cherenkov radiation that is detected by 4 PMTs at the bottom of the tank. WCDs derive air shower properties by collecting the Cherenkov light in a volume of water with precise timing and energy resolution, and can then reconstruct the EAS by understanding of simulation and detector response. A full description of the HAWC detector is given in Chapter 2. 13 1.3.4 Imaging Atmospheric Cherenkov Telescopes The other widely used technique for detection VHE EAS’s is imaging atmospheric Cherenkov telescopes (IACTs), which use the radiation from the Cherenkov process with gamma-rays interacting in air, detected by parabolic telescopes with collection area at the focus. Current IACTs include Major Atmospheric Gamma Imaging Cherenkov (MAGIC), Very Energetic Radiation Imaging Telescope Array System (VERITAS), and High-Energy Stereoscopic System (H.E.S.S.), while Cherenkov Telescope Array (CTA) is under con- struction and has begun taking data. Figue 1.5 shows a schematic of how IACTs collect light from EAS’s [22]. The narrow opening angle of the air Cherenkov process allows for reconstruction of events from highly energetic gamma ray showers with very precise angu- lar resolution on the order of 0.1◦. The draw back of this technique is the limited field of view only observing a patch of the sky a few degrees in radius at any one time, requiring many nights of observation to obtain extended exposure on a single source. IACTs observe only during moonless nights with clear weather, meaning that IACTs operate with typical 10 to 15% live-time. 1.4 The Landscape of Gamma Ray detections Using all of these various techniques there is excellent sky coverage of the range from 20 MeV up to 1 PeV in photon energy (figure 1.6). Fermi-LAT measures gamma rays directly and can observe the whole sky every two orbits. The IACTs VERITAS, HESS, and MAGIC, as well as CTA which is still under construction, observe an instantaneous field of view of around 4◦ and take measurements 10-15% of the time. The EASs HAWC and LHAASO both observe with a greater than 90% duty cycle and can observe events out to 45◦ off of zenith. 14 Figure 1.5: Diagram of an IACT capturing an image of air Cherenkov light from a 1 TeV photon. The camera in the focus of the telescope registers an ellipse of light elongated along the direction of the shower and the total intensity measured is used to reconstruct the shower energy [22]. 15 Figure 1.6: The sensitivity of instruments covering a wide range of the gamma-ray observation energy to a point source for varying levels of exposure. IACTs report sensitivity to point source with 50 hours of exposure, while HAWC reports the sensitivity for 5 years of observation, and LHAASO is reported for 1 year. e-Astrogram, CTA-South, and HiSCORE are in varying stages of development and not active at the time of writing. Repoduced from [23]. The different types of experiments all provide a different view of the gamma-ray sky, in addition to seeing different energy ranges. The balance of live-time with angular coverage, and angular resolution make a complimentary observation space for the very-high-energy sky. Complete coverage over the energy range allows the distinction of radiative processes in high energy environments including persistent sources and transients. We can look at a source’s spectral energy distribution (SED) to differentiate between different processes to generate the gamma rays that are detected. 1.4.1 Multi-Wavelength Astronomy The benefits of multi-wavelength astronomy have been proven out over multiple appli- cations, including in extragalctic astrophysics. Here we can consider two cases, AGN and GRBs, which are relevant to any search for gamma rays coming from extragalactic sources. 16 Figure 1.7: Multiwavelength SED of Mrk 421 which shows a ”double humped” emission feature, emitting strongly in the X-ray band, falling off as energy increases, but rising again in the VHE gamma-ray band. From [24]. A greater distance to a source requires greater emitted power to cover the distances of the intergalactic space. AGN and GRBs are believed to be the result of beaming accelerators pointed at the Earth where boosting effects increase the energy observed. AGN are strong emitters of energy from the central regions of galaxies. Multiwavelength campaigns on the particularly strong AGN Markarian (Mrk) 421 proved the existence of a ”double humped” SED that included a peak in the emission in X-ray and another peak in high-energy gamma rays (figure 1.7) [24]. Multiwavelength studies also showed a correlation between the X- ray and gamma-ray emission, meaning the process to generate both must be happening concurrently [25]. Another powerful example of the utility of MW astronomy is the field of GRB studies. The brightest ever observed GRB, GRB221009A, was seen by a multitude of experiments at all wavelengths and continuously followed up for an extended period of time. From the Swift reporting of that GRB we see how x-ray and optical brightness decay on the same timescale in figure 1.8 [26]. 17 Figure 1.8: Data from the Swift satellite showing X-ray components from BAT and XRT tools onboard, as well as X-ray satellites NICER and MAXI (top panel. The data show a decay with time that is closely matched by data from the optical instruments aboard the Swift observatory. From [26]. 18 This burst was also detected by LHAASO, their detection of GRB221009A was the first detection of a GRB by a WCD, and opens the path for even more in depth study of the high energy component of GRBs [20]. The LHAASO result supports emission from that GRB extending past 10 TeV, a result that was not previously expected but is made possible by multi-wavelength astrophysics. This would also have been detected by HAWC, had it occured on the other side of the Earth. 1.5 A Brief History of FRBs The phenomenon of FRBs has been extensively studied since 2007 with the publication of the Lorimer burst, found in an archival search of data from the Parkes Radio Telescope, now known as FRB010724 [1]. This event was found during a search for radio pulsars, but this burst was unlike known radio pulsar events due to its dispersion measure (DM) which is greater than what was expected possible from galactic or nearby sources [7]. The distance implied by the dispersion, combined with the brightness of the signal caught the attention of astronomers because the energy being emitted in such a short period of time was unusual and hinted at a new type of progenitor for these events. After this initial discovery several other experiments began looking for similar events to identify the commonality of FRBs in radio data. The signature that distinguished these events was the intensity of the signal being much greater than previously detected for events with such high dispersion measure. 1.5.1 FRB Detection Follow up studies of Parkes data published in 2013 found several more FRBs with sim- ilarly high DM signals and high fluence [2]. This confirmed the existence of a new class of radio transients and other radio instruments followed up with their own data greatly expanding the number of detected FRBs that were published between 2014 and 2018 com- 19 prising the first phase of detection and reporting of FRB events. Instruments that detected FRBs in this time were the Green Bank Telescope (GBT), Arecibo, UTMOST and ASKAP, as well as continued searches with Parkes [7]. During this period the number of FRBs grew at the rate of tens per year, leading to a population of 50 or so in 2018. This hinted that the phenomenon was fairly common in terms of all-sky rate, given that radio telescopes that had made detections have relatively small instantaneous fields of view of at most a few square degrees [7]. The potential for discovery of these new transient sources inspired the construction of a new generation of radio observatories including the Canadian Hydrogen Intensity Mapping Experiment (CHIME) with a dedicated analysis pipeline for FRB detec- tion (CHIME/FRB). CHIME/FRB was designed to be much better suited to FRB detection by a greatly increased instantaneous field of view and time resolution that allows precise temporal accuracy for FRB events. These improvements in the ability of observers to find FRBs ushered in a new era of FRB detection [8]. In 2021 CHIME/FRB released its first catalog of events containing 536 FRBs in just over a year between July 2018 and July 2019 [27]. This great expansion in the number of FRBs allowed never before possible population studies of these events and expanded the possibilities for follow-ups from other observa- tories across all wavelengths of the spectrum. As of writing, the number of known FRB events is 934, 678 from apparent one-off bursts with the rest coming from 18 repeating FRB sources [9]. All FRBs have been attributed to extragalactic sources, with the notable exception of FRB-like activity from the galactic source SGR1935+2154 and possible other magnetar flares [28]. The all-sky distribution of FRBs, overlaid on the hydrogen intensity map from the LAB survey, can be seen in figure 1.9. FRBs appear in radio data as a highly dispersed, very bright signal across the radio band observed by a given detector. For example we can see in the Lorimer burst (FRB010724) how the Parkes data measured a bright flash starting in frequency around 1500 MHz and over the course of 300 ms the peak signal swept down to around 1300 MHz, with the 20 Figure 1.9: The all-sky distribution of FRBs, overlain on the LAB HI Survey taken from FRB- STATS.org [29]. Each circle represents an FRB with the color representing the measured DM of the burst, which can be taken as a proxy measurement of the distance to the source. majority of the power of the burst occurring in a central peak of a few ms (figure 1.10). We can also see in figure 1.10 that this signal saturated the detector for several milliseconds implying a very bright burst for that telescope. The peak of the emission takes place over a few ms time window which can saturate a radio telescope which was not designed to detect such high fluence signals. This was one of the leading drivers behind the next generation of FRB detectors including CHIME/FRB. As we can see in figure 1.11 that the newer instrument designed with FRB detection as a primary science goal detects FRBs with full measurement of the peak flux without satu- ration and provide detailed timing, frequency, and fluence measurements for hundreds of FRBs. 21 Figure 1.10: A single beam of the Parkes detection of the Lormier burst showing how the dispersed signal sweeps across radio wavelengths in this beam of the Parkes detector (bottom). And the inten- sity, shown here summed over all channels and de-dispersed in time, which saturated the detector (top). Reproduced from [1]. 1.5.2 Dispersion Measure Dispersion Measure is a frequency dependent delay in signal coming from extragalactic radio sources. The cause of this delay is a free charge density in the intervening medium between the source and the detector. A simplified expression is equation 1.5 when ne is the column density of free electrons between the source and the detector. DM = ∫ observer source ne(r)dr (1.5) In the case of extragalactic radio astronomy, the dispersion is caused by the free electron population along the path of emission, which can have three parts, DMMW which is the contribution from the Milky Way galaxy along the line of sight to the object, DMSource which is the dispersion coming from near the emitting radio source, and DMIGM which is 22 Figure 1.11: Waterfall plot showing the intensity measured for FRB20180801A by the CHIME/FRB detector, after de-dispersing the signal in time. Top: Intensity curve over time in milliseconds. Right: intensity over frequency band covered by CHIME/FRB. Center: ”waterfall” plot showing relative intensity in frequency and time space in a 2D histogram. Reproduced from [27]. 23 the contribution to DM from the intergalactic medium 1.6. DM = DMMW +DMSource +DMIGM (1.6) When observing FRBs this quantity is calculated by measuring the time difference be- tween two different frequencies detected (eq. 1.7) [30]. ∆Tν1−ν2 = e2 2πmec DM(ν−2 1 −ν −2 2 ) ≈ 4.149[GHz2 ·pc−1 · cm3 ·ms]DM(ν−2 1 −ν −2 2 ) (1.7) Of course this equation can be easily made into integral form for radio observatories with multiple frequencies measured simultaneously over a certain range, and calculated using standard regression and minimization techniques. Taking figure 1.10 as an example, the delay can be seen between the arrival time of the different wavelengths, and therefore the DM can be solved for by knowing the ∆T from observation, or by integrating a fit of arrival time as a function of ν using the same formula. Dispersion measure is key to understanding the possibility for GeV-TeV gamma-ray detec- tion because distance is an extreme limiting factor when it comes to detecting sources at cosmological distances; however, knowing the DM well, and with current understanding of the free electron population in the intergalactic medium (IGM), then we have a reasonable proxy measurement of the distance to an FRB even if the exact source galaxy is not known. For small redshifts less than z = 0.5 there is a reasonable approximation that the DM of an FRB is linearly correlated with the redshift z according to equation 1.8 [31]. This is called the Macquart relation and was confirmed with reasonable uncertainty after the pub- lication of the first CHIME/FRB catalog [27] particularly in the space of FRBs studied in this thesis. 24 z ≈ DM/850 (1.8) Where the units of DM are pc ·cm−3. This relation is what is used as a proxy measure- ment of the distance to the object when considering the effect of EBL attenuation on the HAWC measurement in gamma rays. As discussed in section 1.1 FRBs are an interesting and still not well understood phe- nomenon of high energy and frequently occurring in terms of all-sky rate. This implies that a multiwavelength campaign to observe these events will provide a more complete picture of what these sources may be, and provide for the construction of theories that align with the data that experiments across the photon spectrum can provide. There are theories that predict high energy emission and there have been follow-up studies at IACT and satellite observatories [10–12, 31]. A wide population study from a wide field of view instrument such as HAWC contributes strongly to the allowable space for those theories to be possible at the highest energies ever searched for coincident VHE gamma-ray emission from FRB sources. In addition to building upon the work done by these other VHE experiments, it is imperative for HAWC to look for these sources because they are still of unknown origin. The lack of detection of these sources in the intervening energies between radio and VHE gamma rays does not discourage the continued study of FRBs in the HAWC energy range. The study of FRBs in the HAWC dataset will be placed in the context of existing theories for coincident emission in the radio and VHE gamma rays, but unexpected behavior cannot be so easily classified into a set of theories. The history of physics is full of examples of unexpected measurements leading to new discoveries, including orphan flares seen only at TeV energies with no low energy component [32]. The HAWC contribution to FRBs will constitute the largest set of FRB sources ever search at such high energies, and will contribute new constraints on the possible explanation of these fascinating events. 25 Chapter 2: The HAWC Observatory The High-Altitude Water Cherenkov Observatory (HAWC) is a water Cherenkov gamma- ray detector in the state of Puebla, Mexico, located between the dormant Vulcan Sierra Ne- gra and the Pico de Orizaba (Figure 2.1. HAWC is at a latitude of 19◦ N and an altitude of 4100 m above sea level. The site was selected for its altitude and area of land which could be made flat enough for a water Cherenkov detector comprised of water tanks over a land area of 22,000 m2. The site consists of 300 main array tanks on that 22,000 m2 footprint and 345 outrigger tanks extending the area to about 100,000 m2 filled with purified water and instrumented with photo-multiplier tubes (PMTs). The detector records hit times and charge levels from particles which produce Cherenkov light in water coming from EASs, storing these data for later reconstruction and analysis. The HAWC observatory has been operating with greater than 90% livetime since November 21, 2014, and has taken more than 2800 days of data, monitoring two-thirds of the sky every 24 hours. This section will detail the HAWC detector, the data collected, and the process these data go through to produce meaningful products used in HAWC science. 2.1 The HAWC Detector The HAWC main detector consists of 295 instrumented and 5 water storage corrugated steel tanks that are 5 m high and 7.3 m diameter which comprise the main array [21]. The footprint of the main array tanks is 22,000 m2. Each tank contains a bladder for holding 26 Figure 2.1: The HAWC detector looking southwest at the Sierra Negra with the Large Millimeter Telescope visible at the top. 27 180 kL of purified water and is instrumented with 4 photo-multiplier (PMT) tubes, three 8 inch Hamamatsu R5912 PMTs and one high quantum efficiency (HQE) 10 inch R7081 PMT. The PMTs are powered with high voltage on the order 1500 V, and selected from the group of PMTs to have similar gain to the other tubes in the same tank. The HV is supplied on the the same cable which returns the PMT signals which are picked off by a capacitor circuit and read in on the front-end-boards (FEBs). PMT signals are associated with a GPS time supplied by a White Rabbit (WR) system which is accurate to the sub-nanosecond level. More details about the WR system can be found in [21]. 2.1.1 The HAWC Detector Tank Units Each tank, as stated above, consists of 4 PMTs arranged in an equilateral triangle of the 8” PMTs with the HQE 10” PMT at the center. The smaller PMTs are labeled A (abajo meaning below), B(Bolshevik meaning left), and D(derecha meaning right), with the center PMT having the label C (centro), named thus to identify the location of each PMT within a tank relative to the access hatch on the top of the tank. That is, A is below the opening hatch, B is to the left, D to the right, and C in the center of the tank. A photo taken during the installation of the PMTs into a tank, taken from the hatch position can be seen in figure 2.4. PMTs collect light by a photoelectric reaction with a coating on the interior of a glass vacuum chamber which is a photocathode material. The material has a high cross-section to photon interactions which displace photo-electrons. There is a voltage difference between the photocathode and the dynode in the center of the vacuum chamber which accelerates the photoelectrons towards a dynode. Inside the dynode side of the PMT is the multiplier portion of the unit where electrons after being accelerated in the electric field bombard a chain of dynodes which multiplies the electron count by a factor over 10 stages of multiplication before being output as a current which is handled by custom PMT 28 Figure 2.2: A schematic diagram illustrating how a PMT amplifies a signal through a chain of dynodes which multiply the original photon signal by a factor of 10 at every stage [33]. boards before signals are sent back to the counting house to be processed. In figure 2.2 you can see a schematic of the amplification of signals in a PMT. PMT specifications can be read in [21] and in the Hamamatsu product pages for the two types of PMTs used [33]. High voltage (HV) is supplied from a central counting house by a Weiner HV crate over RG-59 coaxial cable. While all A, B and D PMTs are the same model, there will always be slightly different gain values for signals so PMTs were tested for their signal gains before deployment, and PMTs with similar gain values were grouped together to give more uniformity to the signal collection across all of the instrumented tanks[21]. The HV is supplied on the coaxial cables such that the photo-cathode is at ground voltage. A PMT like the ones used in the HAWC detector can be seen in figure 2.5. 2.1.2 Signal Processing and Calibration Signals that are detected on the PMTs are run along the HV cables described above and are read in on a capacitor pick-off circuit designed for HAWC in the front-end electronics housed in the counting house [21]. The picked-off signals are amplified and shaped with a 75 ns time constant. Charge information is extracted and digitized from the width of the PMT pulses, a property made possible by the PMT base designed for WCD data taking. The time over threshold (ToT) is saved for a low and high threshold corresponding to 1/4 - 29 Figure 2.3: A HAWC main array tank showing the distribution of the 4 PMTs in the water volume, a person for scale, and traces of Cherenkov light originating from an incoming shower particle. Figure 2.4: Installation of PMTs with photo taken from the hatch. 30 Figure 2.5: An 8 inch PMT like one used in HAWC detector for the A, B and D PMTs. This is a Hamamatsu R5912 8” PMT with attached base that seals the electronics inside from the water that it will be submerged in during data taking. Photo credit Dr. Kristi Engel 31 1/2 of a PE and 3 - 4 PE respectively [21]. The analog-to-digital converter (ADC) takes the time of each crossing of a threshold, meaning small PMT signals will have 2 edges, and large signals will have 4 edges. The ToT for both thresholds allows the calculation of the total integrated charge in a PMT signal. In order to combine the information from around 1200 PMTs, a calibration system was constructed so that time offsets could be removed and time over threshold could be converted into the logarithm of the charge level. The calibration is performed by a laser system which illuminates a tank through a fiber optic cable with precise timing and amplitude. The laser emits green (532 nm) light over a width of less than 1 ns. It is important to consider that real EAS’ are typically wider in time on the order of 10 ns, and is considered in the systematic uncertainty of the HAWC detector. The laser light is distributed to all tanks through a filter and splitter system which is capable of varying the PE level sent to each tank from a fraction of a PE to 1000 PEs [21]. The front-end boards (FEBs) take signals from the PMTs and record the ToT for a low threshold and a high threshold voltage. The calibration system which is fully described in [21]. Because of the choice of front-end board described earlier and in [21], these two ToT measurements allow a direct calculation of charge incident on the PMT. Times for PMT signals are provided by a time to digital converter (TDC). This conversion is possible due to the HAWC calibration system which uses fiber optic cable and a laser timing system to return the hit delays between tanks. A sample PMT signal is shown in figures 2.6 and 2.7. In each case a signal activates a PMT and goes either above the low threshold, or both the low and high threshold. The two thresholds provide a way to discriminate between a large hit, and two smaller hits that are close in time. When a large hit is incident on a PMT, there is a rapid rise time in the signal meaning that the low threshold and high threshold are crossed in rapid succession. The time between these two crossings is very consistent for large hits, and shorter than the time that is typical for two separate, smaller hits. For a full description of this process see the HAWC Main Detector Paper [21]. 32 Figure 2.6: Plot showing Low ToT for PMT signals. Figure 2.7: Plot showing high ToT for PMT signals. 2.2 HAWC Data For the purposes of this thesis it is helpful to discuss data in terms of data levels used widely in NASA and ESA earth observing data, and adapted for astrophysical data by the CTA collaboration [34]. For ease of reading we most closely follow the table 1 from [34]. The idea of data levels (DLs) helps to organize the data processing steps and help in multiwavelength studies with making accurate comparisons of data sets from different ex- periments. Data processing levels range from 0 – being the raw unprocessed data measured by an experiment – to DL5 – fully processed data collated into outputs with parameters calculated from measurements and applying models to the data. In order to get meaningful results, we apply a trigger condition to the DL0 data, re- quiring that we have more than 28 PMT hits in an 150 ns window. The trigger happens in the software and conducted within the site computers. The trigger allows the organization of data into events, and reduces the size of the data that will be reconstructed. This 150 ns window is wider than a typical air shower in terms of the time that it takes to prop- agate across the array, but this allows a reasonable reduction in the data so that we can 33 Table 2.1: Data levels as defined by the CTAO group in [34] 34 begin applying cuts and calculate shower parameters. This is the ”trig” data and is con- sidered DL1 according to Figure 2.1 because detector hits have been separated into events, but have not yet calculated anything related to the physical properties of the air showers. That process takes place in two different ways. First is the online reconstruction which is a simplified version of our analysis which takes place in real time in order to send and respond to real-time alerts from the astrophysics community, including Galactic Coordi- nates Network (GCN) circulars, ATels and GW events. The second reconstruction is a full offline reconstruction of the triggered events, and involves data quality cuts in addition to calculations of air shower properties, including shower direction and energy. The offline reconstruction is managed jointly between the University of Maryland (UMD) and the Na- tion Autonomous University of Mexico (UNAM). During my graduate career I was the US manager for the offline reconstruction, alongside Dr. Jose-Andres Garcia-Gonzalez who managed the process at UNAM. Raw data and triggered data files are transferred to UNAM and then synced to UMD so that two copies of the data are kept separately, then the re- construction is managed by a custom daemon which balances the computing load between the computing centers at each location capable of reconstructing 10 days of data in 1 day. The size of the HAWC data set means that a complete re-reconstruction or ”pass” of the data takes on the order of 8 months of near complete computer resource utilization, and therefore must managed efficiently and carefully. This means I checked the data passed automated quality checks, and issues were addressed such as corruption of a reconstructed file as a result of temporary power outages or other interruptions to the reconstruction. In the event of an interruption I was responsible for checking and restarting the reconstruction process. 35 2.2.1 XCDF Format HAWC utilizes a data format which was designed for this data called the eXpressly Compacted Data Format (XCDF). XCDF compresses data by storing values as a data struc- ture with one field being the order of magnitude, one field for precision, and another field to store the value with leading and ending zeroes removed. This greatly reduces the storage size and calculation time for very large and very small numbers which are typical in astro- physical parameters. With the XCDF format there are also many utilities which allow ease of use for checking the bulk properties of the data such as number of events, minimum and maximum values for each field, etc. To learn more about XCDF read [35]. 2.2.2 Data Collection Data level 1, characterized as ”triggered” data, contains information of PMT hit times and amplitudes organized into events by a trigger condition. The trigger condition for HAWC is 28 PMT hits in a 150 ns window. When the trigger condition is met, all of the hits in a -150 ns to +450 ns window is grouped into a triggered event. During normal data taking, triggered data is organized into ”runs” and ”subruns” where a subrun is a 125 s period of continuous data taking with information organized into triggers, and a 24 hour period of continuous data taking is grouped into a run. Runs can be interrupted by power loss at the experiment, or lightning which temporarily alters the rates to an extreme value outside of what the data acquisition system (DAQ) system can handle. If there is an interruption to the data taking the run is stopped automatically and a new one will start automatically when the detector returns to a stable state. Data is initially stored at the site, as well as a reconstructed copy which is created at the site and is described below. The data is then moved in tranches to the computing center at UNAM, and synced to the center at UMD. 36 2.3 Reconstruction: Data Level 2 Now that the data is organized into events at the trigger level, with hit times and am- plitudes the next step is to determine the direction, energy and particle type. This is done by event reconstruction which which applies knowledge of air showers from Monte Carlo (MC) simulations of events on the HAWC detector. All of the HAWC software is kept in a git repository hosted on gitlab.com, including the main executable for reconstruction called ”offline-reconstructor” which is a C++ based custom chain of modules which take triggered data as input and calculates shower properties including shower angle on the detector, and primary particle energy. Changes to the code are reviewed by software experts in the col- laboration, called ”maintainers”, and I served as a maintainer for the HAWC Observatory for the past three years at the time of writing. This section will cover the modules used in the calculation of shower information. 2.3.1 Event Cleaning The HAWC data set is challenged by many backgrounds so it is necessary before cal- culating shower parameters to remove PMT hits that are not a usable portion of any EAS event. First, PMT hits which have negative calculated PE’s because those data are non- physical hits, and more that 10000 PE’s because this hits are not well characterized by simulation. At this point the trigger window is also narrowed to a time window of 150 ns before the trigger time, to 400 ns after the trigger time. Because of the speed of light it is known that particles coming outside of this window are extremely unlikely to originate from the triggered event, even if the trigger time is not precisely associated with the central arrival time of the EAS. It is also important to remove small hits defined as likely originat- ing from hit sizes of less than 1 PE which is done by taking the time-over-threshold (ToT) of the hits to be above a value which is taken from simulation to cut out a majority of the 37 less than 1 PE hits. All of this taken together is the first step in cleaning the data into coherent showers and allows the reconstruction to progress to a method for event improvement called the ”multi- plane fitter” (MPF). The MPF as the name suggests finds a primary shower plane which contains the majority of hits in a trigger window by using a likelihood method to associate hits into up to three shower planes in one trigger window. This solves the problem of late time particles, namely muons which are consistently incident on the detector at all times unassociated with any shower, with high charge being improperly weighted into a shower fit and causing a small percentage of events to mis-reconstructed in the wrong direction and with poor representation of shower energy. Unlike the name would suggest however, this MPF does not pass multiple shower planes to the next steps of reconstruction, and only passes the plane with the most hits to the next steps in the chain. 2.3.2 Core and Angle Reconstruction After cleaning, the data is now organized into showers with reasonably measured hits within a physically allowable time window with far out of time hits removed. The prop- erties of these events can now be measured according to the modules in the offline recon- structor which takes place as follows. First, a center of mass (COM) fit to the shower core is used to give a more reasonable seed to further modules. The COM is defined as a charge weighted fit to the hits in the plane of the detector. This fit by definition will have a core fit inside the area of the main array, but improves the computation time of the next steps by moving the core from the center of the array to a place which is closer to the most likely core location. The next step is a second core fit called the ”Super/Stupid Fast Core Fitter” (SFCF) which takes hit locations and magnitudes into account to find a better guess for the core, taking the COM fit as a seed. Now that the shower has much better core local- 38 ization, the first angle fit is preformed. This fit takes a Gaussian shape for the arrival time distribution of hits in a shower which is dependent on radius from the core of the shower and size of the hit in PEs. This fit goes through five iterations of finding the best fit arrival direction in local zenith and azimuth, cutting out of time hits from the fit, and fitting again with progressively stricter cuts. Now that the event has been assigned a first pass core and angle fit, the event is given a full likelihood calculation to find the best-fit core location based on a lookup table derived from simulated showers. Using the tables and the informa- tion from the showers, a likelihood surface is drawn and the maximum likelihood location is found using the ROOT Minuit minimizer which is widely used in physics applications [36]. The minization takes the shape of the lateral distribution function for gamma-ray showers which is known to follow a Nishimura-Kamata-Greisen (NKG) function [37]. The full calculation cannot be executed in reconstruction time and so a lookup table is used for shower properties of distance and hit time relative to the plane of the shower. This like- lihood method gives the final core location used in the rest of reconstruction. Next in the chain is the final angle reconstruction, which is done by the same Gaussian plane method as before, but now with a better core location to rotate around. Five more iterations through that fit give the final direction for the event. The overall angular resolution, and how this is an improvement over previous reconstruction algorithms is seen in figure 2.8. In the next iteration of HAWC reconstruction the final angle fit will be performed with a maximum likelihood calculation that I developed with help from Dr. Andrew Smith and Dr. Tom Weisgarber. This method will account for the spread in time of shower particles arriving asymmetrically, as opposed to the assumed Gaussian distribution used now, to find the shower angle which maximizes the likelihood of particles belonging to a given air shower. The new fitter will also account for the differences in response between the two types of main array PMTs, and allow for the inclusion of outrigger tanks as well. This new fitter is not used in this analysis and therefore will not be discussed further in this work. 39 Figure 2.8: The angular resolution of gamma-ray showers in HAWC simulation reconstructed with the pass 5 algorithms (solid lines) as a function of fraction of PMTs hit. The previous results are shown in faded lines for the ”pass 4” set of reconstruction algorithms, which does not include the MPF or high zenith improvements. The resolution is shown for three different zenith bands to show how angular resolution depends on the zenith angle of the primary particle. 40 2.3.3 Gamma/ Hadron Classification Now that the shower geometric properties of core location and arrival direction have been determined, the next step is identifying physical properties of the primary particle. The most important for gamma-ray observation is the classification of gamma-ray induced events. To determine the primary particle type the offline-reconstructor uses three main al- gorithms based on two different concepts of separating gamma-ray induced showers from cosmic ray ones. The first calculated property of the shower used for gamma-hadron sep- aration is called ”compactness” based off of a calculated parameter called CxPE, which measures the largest hit in terms of total charge outside of a radius of 40 m from the shower core as measured in the plane of the shower (as opposed to the plane of the detector). Com- pactness then, is the number of hits in the shower divided by the value of CxPE, meaning more gamma-like showers have higher compactness values. Figure 2.9 shows how the largest hit is found outside of the 40 m radius circle surrounding the reconstructed shower core. This method takes advantage of the fact discussed in 1.3.2.1 that hadronic showers contain more muons, and interact in the atmosphere with larger transverse momentum. The result is that hadronically induced showers deposit large amounts of energy further from the core when compared to gamma-ray induced showers. We take advantage of the fact that gamma-ray induced showers are more compact, meaning that there is less shower charge deposited far from the shower core. The next to be calculated is a parameter called the ”Parameter for Identifying Nuclear Cosmic rays” (PINC or PINCness) which is a fit to a modified NKG function which is the proposed shape of charge distribution radially from a gamma-ray shower core. Gamma-ray showers fit this function much better than hadronic showers due to the asymmetry of hadronic showers (Figure 2.10). Lastly, we use a χ2 fit to a modified NKG function which captures the fit of gamma rays to the most probable shape of the lateral distribution and thus is called the ”LDFChi2” parameter. 41 Figure 2.9: A high energy gamma ray event on the HAWC detector. The star represents the core of the shower and the red line extending from the star represents the angular direction of the shower arrival. The large red circle is a 40 m circles centered on the core position, and the small red circle is the largest hit in terms of PEs outside of the the 40 m circle used for calculating CxPE. Keep in mind the circle drawn is only an approximation, since the algorithm does all calculations in the shower plane. Figure 2.10: Left: The hits contained in a high-energy gamma-ray shower as a function of radial distance showing a fit to a lateral NKG function. Right: The same distribution shown for a cosmic ray shower. 42 Figure 2.11: Reconstructed Energy vs. True energy for the two energy reconstruction algorithms used in HAWC analysis. Left: energy comparison for the NN algorithm, 93.9% correlation. Right: energy comparison for GP algorithm, 93.1% correlation. Reproduced from [38]. 2.3.4 Energy Reconstruction The last event property that needs to be determined is the energy of the primary particle which initiated the shower. HAWC uses two independently derived energy estimators. The first method is the ”neural net” (NN) which takes advantage of the machine learning strategy of the same name, with input parameters of total charge in annuli surrounding the shower core. The level of charge in each annulus surrounding the shower core allows the NN algorithm to estimate the energy after being trained on MC simulation of gamma rays accross the HAWC energy range [38]. The second is the ”Ground Parameter” (GP) which calculates the energy based on a fit to a modified version of the NKG function. 2.3.5 The Summarizer Once of the modules have completed the object storing all of the reconstructed param- eters populates a reconstructed data file in the XCDF format. This happens in another module called the summarizer, which takes all of the calculated and trigger parameters for all of the events. The events stored in this way are then taken as input to the map making tools. Returning again to 2.1 we see that the data now has been reconstructed and shower parameters have been calculated so this is DL3. 43 2.4 HAWCProd Taking data at a rate of 25 kHz with greater than 90% livetime means that HAWC must reconstruct an immense number of events before scientific meaning can be extracted. The raw data rate tanslates to aproximately 500 MB/s of information coming from the PMTs. After triggering we reduce down to approximately 22 MB/s, meaning in a year HAWC col- lects 500 TB per year. For the most recent pass through the HAWC data, ”pass 5”, the total reconstruction required more than 10,000,000 core-hours of CPU, which was accomplished in 8 months running full time at two computing centers. To aid in the reconstruction effort, a custom job manager program was created called HAWC Production or ”HAWCProd” which manages the production of reconstructed data on two computing clusters taken from the Ice Cube collaboration tool for the same purpose, IceProd [39]. Sharing the workload between physically separated resource centers effectively doubles the amount of comput- ing power available to reconstruct events. HAWCProd works by taking runs, which are 24 hour segments of continuous data, and creating a task to reconstruct all of the subrun files belonging to that run. The tasks will be assigned to one computing cluster depend- ing on the availability of resources, and as tasks finish to allocate tasks. This reduces the need for human intervention in the reconstruction of shower events and only requires some- one to initiate a reconstruction, check on it occasionally, and restart the small number of jobs which fail out of the reconstruction chain. In addition to reconstructing the data, the HAWCProd system checks data against the quality monitoring database (QMDB) for any runs or subruns which may not pass all the criteria for good data. This is one way in which the offline reconstruction is different from the online reconstruction. 44 2.5 Post-Reconstruction Data Processing: Data Level 3 After reconstruction we have a set of DL2 data, ie. events with calculated parameters organized on a per-event basis, including parameters on the likelihood of an event being a gamma ray, its energy, and originating direction in the sky. This results in approximately 500 TB of data per year of operation, meaning that at the time of writing the HAWC reconstructed dataset is nearly 10 PB of data. In order to quickly generate meaningful science results from this dataset it needs to be reduced in size and cleaned of events which are not going to be used in any analysis. Thus creating a DL3 set according to figure 2.1. In addition to reducing the data size, DL3 requires creating a set of detector response files that assist in taking the processed list of events and extracting meaningful science products such as spectra and sky-maps. 2.5.1 The HAWC Binning Scheme In order to characterize the HAWC detector response to showers it helps to bin the data into bins which have a similar response such as characteristic values of the gamma-hadron separators described in section 2.3.3. To this end the HAWC data is divided into fractional hit (fHit) bins defined on the value of the number of PMTs participating in a shower divided by the total number of available PMTs at the time of the shower. The first bin edge is set at the detector threshold for detecting an air shower, and the subsequent bin edges are calculated to establish bins which contain half as many showers as the bin previous. As expected the bin number is correlated with energy since a higher energy photon will generate more particles participating in an air shower detected by HAWC (figure 2.12). 45 Figure 2.12: The fHit binning scheme used in HAWC to separate the data grouping EASs with similar responses, shown here for crab nebula data for each bin as a function of true energy. 2.5.2 Data ”Chunks” Because HAWC operates continuously, observing two-thirds of sky daily for more than 2500 days, it is necessary to break up the sky-map making into more manageable chunks of data. Thus HAWC separates the reconstructed data files into ”chunks” which have at least enough data to calculate a reasonable background from a process called direct integration see [40]. This chunk is a subset of the data that must have at least 2 hours of data and is capped at 48 hours. Doing this separates the data into manageable chunks for analysis. To ensure that direct integration is meaningful for background calculation the data in each chunk must be continuous, that is having no breaks longer than 2 minutes. The data within a chunk must also be reliable and reflect that the data came from a stable period of data taking. On top of the checks which occur during the data taking which ensure this, it is also imposed at this step that the standard deviation of the median zenith angle distribution be less than 0.075 radians. This is a good stability check due to the fact that the distribution of air showers in local coordinates is centered on zenith by symmetry. If this distribution is 46 significantly altered by some environmental or experimental instability then the data is not considered good. The result is a list of reconstructed files grouped into chunks with known stability and continuity of data that allows the further steps of map making to continue. This step removes only a small amount of the data size by removing files with very few events, or files with instability caused by power interruptions or high electric field events (lightning). 2.5.3 Data Reduction A new challenge that arose with the continued operation of HAWC was the speed at which maps could be fully remade over the length the experiments’ livetime. To address this issue a new data reduction scheme was implemented to reduce the size of the recon- structed data before the map making stage. The scheme consists of three major parts. The first step is the retention of so-called heart-beat events, which keeps the first and last events in a file and at least one event every 0.1 s so that the most common analysis package used with HAWC data, 3ML, can accurately calculate the livetime of maps made from this dataset. Secondly, all XCDF fields that are not used in the map making step are stripped from the reconstructed files saving space in memory from removing unused data points. The last step is a removal of all events that won’t be used in the map making. This is ac- complished by taking all cut files from the different types of analysis that will be performed on the data and taking the least restrictive cut of every field. The result is a reduction of the full data set by a factor of 10 in data size and also combines files so that the map maker only needs to read 30 files per chunk of data instead of one file per subrun which is about 1400 files per chunk of data. 47 2.5.4 Air Shower Alignment After reduction, an alignment to events is applied to correct for various biases that are understood to exist in the HAWC reconstruction. First is a correction to the tilt of the array found as a survey error after the completion of the offline reconstruction. Next is a set of systematic fixes for a few small order errors in the alignment. The final alignment is a fine tuning to the Crab nebula position which improves the overall pointing accuracy of the experiment. I performed this process for all of the HAWC data which is required before any analysis can be done with the most recent dataset. 2.6 Simulation In addition to the data taken by the HAWC observatory, a set of simulated showers are generated for gamma rays and cosmic rays to allow evaluation of the detector perfor- mance and response to EASs. The simulation chain begins with air showers simulated from first interaction in the atmosphere with COsmic Ray SImulations for KAscade (CORSIKA) [41]. CORSIKA showers were generated taking into account the latitude and altitude of the HAWC site, and initially generated using QGSJet-II and Fluka interaction models available with CORSIKA, though other interaction models have been used in subsequent simulations [41]. CORSIKA tracks the development of EASs from first interaction producing a list of particles with location, energy and momentum. The next step is to let these particles inter- act with the HAWC detector, which is done in a software called GEANT-4 (or GEANT). GEANT takes the particle information from CORSIKA, and a detailed detector layout in- cluding spatial layout of tanks and PMTs and material information for the entire experi- ment. GEANT simulation tracks the particles from an EAS through the WCD tanks to the PMTs and uses PMT quantum efficiency to generate the signal size that would be measured 48 in the real world [42]. In figure 2.13 a shower particle from CORSIKA simulation enters the top of a HAWC tanks and begins to emit Cherenkov photons, which are transported to the PMTs according the GEANT particle propagation simulation, including the produced Cherenkov photons, through water and detected by the PMTs at the bottom of the tank. To determine the response of the HAWC detector to the interactions generated in the GEANT stage and how the measurements are treated during data acquisition (DAQ), the next step in the chain is called the data-acquisition simulation or DAQSIM. DAQSIM allows for the simulated hits in the detector from a shower to go through a simulated DAQ process taking into account the processes which effect real signals before being stored in the data files. At the end of this process the result is an XCDF file similar to that for reconstructed data, but with added fields for the known properties of the simulated showers such as the originating particle type, as well as core location, angle of incidence, and primary particle energy. This allows for studies of the efficacy of the algorithms applied to data reconstruc- tion. For analysis of gamma rays it is important to understand how gamma-ray EAS behave when interacting with the HAWC detector especially when considering angular resolution, and gamma-hadron efficiency. 2.7 Map Making Reconstructed data contains event information for all potential gamma-ray events de- tected by HAWC at data level 2. To move to data level 4 we can apply what we know about events to assign a significance of detection at all points in the sky. The map making pro- cess occurs in multiple stages, first creating counts maps of signal events and background as determined by data cuts and stored as fits maps as is standard in astrophysics. Based on our understanding of our background and instrument response we calculate the signifi- cance of each pixel in the sky map. Pixelation of the skymap is made following the healpix 49 Figure 2.13: A muon from an EAS generated by CORSIKA simulation enters the top of a HAWC tank model implemented in GEANT, and the particle emits Cherenkov light (green tracks) which can be detected by the PMTs at the base of the tank. The number of particles is scaled down by a factor of approximately 1000 for illustrative purposes. The quantum efficiency of the PMT is also included in GEANT so that the simulated files have information on the charge level of the hit on the PMT from the Cherenkov photon. 50 convention which makes equal area pixels for all sky regions while minimizing distortion from spherical projection [43]. Additionally, HAWC stores all of its maps in Flexible Im- age Transport System (FITS) format which has been the standard in astronomy since the 1980’s, to read more about this data format, see the definitions set out by the Internation Astronomical Union (IAU) [44]. 2.7.1 Counts Maps The first step in map making is to take our DL2 reconstructed data and fill a FITS map with our signal events, separated out by established gamma-hadron cuts, and simultane- ously fill a second column of the FITS map with background events. The data maps then are two histograms stored together, one histogram being signal events over the sky, and another filled with background even