The University of Chicago Astronomy and Cosmology

THE UNIVERSITY OF CHICAGO ASTRONOMY AND COSMOLOGY WITH GRAVITATIONAL WAVES A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ASTRONOMY & ASTROPHYSICS BY MAYA FISHBACH CHICAGO, ILLINOIS AUGUST 2020 Copyright c 2020 by Maya Fishbach All Rights Reserved לאמא ואבא To my parents TABLE OF CONTENTS LIST OF FIGURES . vii ACKNOWLEDGMENTS . xv ABSTRACT . xvi 1 INTRODUCTION . 1 2 ARE LIGO'S BLACK HOLES MADE FROM SMALLER BLACK HOLES? . 5 2.1 Abstract . .6 2.2 Introduction . .7 2.3 Methods . 10 2.3.1 Hierarchical Merger Spin Distribution . 10 2.3.2 Mixture Model Analysis . 14 2.4 Results . 20 2.5 Conclusion . 24 3 WHERE ARE LIGO'S BIG BLACK HOLES? . 25 3.1 Abstract . 26 3.2 Introduction . 27 3.3 Sensitive volume . 31 3.4 Fitting the Mass Distribution . 34 3.5 Results . 38 3.5.1 Non-detection of heavy BBHs . 38 3.5.2 Bayesian evidence in favor of mass gap . 40 3.5.3 Joint power law{maximum mass fit . 43 3.6 Discussion . 47 3.6.1 Effect of Redshift Evolution . 47 3.6.2 Distribution of mass ratios . 48 3.6.3 Extending to non-power-law mass distributions . 49 3.6.4 Are there BBHs beyond the gap? . 49 3.7 Conclusion . 50 4 DOES THE BLACK HOLE MERGER RATE EVOLVE WITH REDSHIFT? . 52 4.1 Abstract . 53 4.2 Introduction . 54 4.3 Detected redshift distribution . 55 4.4 Joint Mass-redshift Model . 58 4.4.1 Redshift Model A . 59 4.4.2 Redshift Model B . 61 4.5 Fitting the Mass-redshift Distribution . 64 4.5.1 LIGO-Virgo detections . 67 iv 4.5.2 Future detections . 73 4.6 Discussion . 78 4.7 Conclusion . 81 5 PICKY PARTNERS: THE PAIRING OF COMPONENT MASSES IN BINARY BLACK HOLE MERGERS . 83 5.1 Abstract . 84 5.2 Introduction . 85 5.3 Mass Distribution Models . 88 5.4 Methods . 91 5.5 Results . 95 5.5.1 LVC Model . 95 5.5.2 Random Pairing . 95 5.5.3 Mass Ratio Dependent Pairing . 97 5.5.4 Total Mass Dependent Pairing . 98 5.5.5 Comparison of Pairing Functions . 100 5.5.6 Posterior predictive distributions . 100 5.6 Simulations . 105 5.6.1 Method for Simulating Detections . 105 5.6.2 Simulation Results . 106 5.7 Conclusion . 108 6 THE MOST MASSIVE BINARY BLACK HOLE DETECTIONS AND THE IDEN- TIFICATION OF POPULATION OUTLIERS . 111 6.1 Abstract . 112 6.2 Introduction . 113 6.3 Population Prior on Individual Events . 115 6.4 Evaluating tension between model and data . 118 6.4.1 Definitions and assumptions . 119 6.4.2 Application to the O1+O2 population . 121 6.5 Non-parametric Constraints on the Rate of Mass-Gap Mergers . 130 6.6 Conclusion . 133 6.7 Additional Analysis Details . 134 6.7.1 Mock observations . 134 6.7.2 Binned histogram likelihood . 138 7 A STANDARD SIREN MEASUREMENT OF THE HUBBLE CONSTANT FROM GW170817 WITHOUT THE ELECTROMAGNETIC COUNTERPART . 141 7.1 Abstract . 143 7.2 Introduction . 144 7.3 Methods . 146 7.4 Galaxy catalogs . 151 7.5 Source Localization and Distance . 155 7.6 Results . 158 v 7.7 Conclusion . 161 7.8 Additional Analysis Details . 162 7.8.1 Statistical H0 likelihood . 162 7.8.2 GW170817-like events . 165 REFERENCES . 167 vi LIST OF FIGURES 2.1 Probability distribution for the dimensionless spin magnitude for each generation of BHs formed through hierarchical mergers. Unless labeled otherwise, the first generation is nonspinning (a = 0) and all mergers take place between equal mass BHs (q = 1). For each generation, the spin directions are as- sumed to be isotropically distributed. Note the rapid convergence to a universal distribution (turquoise solid line). The dotted orange line shows the second- generation distribution for the case where the first generation has near-maximal (a = 0:99) spins. The initially nonspinning (a = 0) and initially near-maximally spinning (a = 0:99) cases are indistinguishable by the fourth generation, converg- ing on the universal distribution. 11 2.2 Converged spin distributions (fourth generation) of hierarchically formed BHs, where in one scenario the BHs always merge with equal mass (q = 1) and in the other scenario the BHs always merge with mass ratio q = 0:7. Changing the spin of the first generation leads to indistinguishable distributions. 13 2.3 Posterior probability density functions on the parameter fu for 3 simulated populations of BHs that have not formed hierarchically (the true fu = 1). The populations of BHs all have spin magnitudes drawn from a uniform [0; 1] distribution, but differ in the uncertainty on their measured spins magnitudes. We approximate spin measurements as truncated Gaussians and vary σa1, σa2 between populations. We note that 10 detections may be sufficient to rule out a pure hierarchical merger model. 18 2.4 Posterior probability density functions on the parameter fu for 3 simulated populations with different values of fu (given by the dashed lines). The simulated BH populations with fu = 0 (turquoise) and fu = 1 (sky blue) each consist of 200 BBH events, while the simulated BH population with fu = 0:5 (orange) consists of 400 BBH events. We assume that for all events the spin magnitude measurements p(a1 di), p(a2 di) are truncated Gaussians with standard deviations σ = 0:66. The shadedj regionsj denote 90% credible intervals. 19 2.5 Probability density function of the spin magnitude of a final BH formed through a \cluster catastrophe" of a fixed number of BHs, compared to the universal hierarchical merger distribution. Initially the N BHs are of equal mass and spin magnitudes drawn uniformly on [0; 1], and they merge with each other in randomly selected pairs (with isotropic spin directions) until they have all merged into a single final BH. 22 3.1 Sensitive redshifted spacetime volume, VT , of the LIGO detectors in O1 and O2 as a function of BBH total mass, Mtot, and mass ratio, q, calculated under the semi-analytic approximation described in the text for one year of observation. 2:2 We find that VT m over the range 10 M Mtot 100 M ......... 30 / 1 ≤ ≤ vii 3.2 Ratio VT low= VT high of the expected number of\low" mass to \high" mass BBHh i detectionsh i from an underlying population with power law slope α (solid curves). The blue and orange curves define low mass BBHs to have m1 < 50 M , while the green curve defines low mass as m1 < 40 M . The blue and green curves conservatively assume that the mass distribution and detector sensitivity extend only up to a total BBH mass of 100 M , while the orange curve assumes that the BBH population and sensitivity extend up to total masses of 200 M . The dashed (dotted) horizontal line corresponds to values of the ratio VT low= VT high for which the probability of detecting no high mass BBHs and tenh (four)i h lowi mass BBHs is less than 5%. VT ratios below this line correspond to values of α that lie to the left of the vertical colored dashed lines. With enough low mass BBH detections, shallow power law slopes (small positive values of α) become inconsistent with the existence of high mass BBHs. 39 3.3 Inferred likelihood for the power law slope of the mass distribution, α, calculated for 120 mock observations from a Mmax = 41 M , α = 2:35 population (dashed and dotted curves) and the first four BBH detections (solid curves). The blue and orange curves correspond to the canonical LVC analysis in which the maximum mass of the BBH mass distribution is set to Mmax = 95 M , while the pink and green curves correspond to a fixed maximum mass at Mmax = 41 M . Neglecting to account for a high mass cutoff biases the power law inference to steep slopes. The solid black line at α = 2:35 is.

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