PROSPECTS FOR OBSERVING DYNAMICALLY FORMED BINARY BLACK HOLES IN THE LOCAL UNIVERSE WITH GRAVITATIONAL WAVES by DONGMING JIN Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT ARLINGTON May 2018 Copyright c by Dongming Jin 2018 All Rights Reserved Abstract PROSPECTS FOR OBSERVING DYNAMICALLY FORMED BINARY BLACK HOLES IN THE LOCAL UNIVERSE WITH GRAVITATIONAL WAVES Dongming Jin, Ph.D. The University of Texas at Arlington, 2018 Supervising Professor: Matthew Benacquista The dynamical evolution of globular clusters is expected to produce stellar-mass binary black holes with higher total mass than found in the field population of binary black holes. Such systems are identified as gravitational wave sources with the recent detections made by advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO). We use the Monte Carlo code MOCCA to simulate the generation of binary black holes from globular clusters. These compact binary systems are found to be ejected quickly from the host globular clusters. Thereafter, they evolve independently due to the emission of gravitational radiation. We model the population of globular clusters for galaxies out to 30 Mpc and present the statistics of the results. At the end, we discuss here the prospects for detecting dynamically formed binary black holes at extragalactic distances using space-borne gravitational wave detectors. iii Table of Contents Abstract . iii List of Illustrations . vii List of Tables . ix Chapter 1 Introduction . .1 1.1 Background . .1 1.2 Motivation . .5 1.2.1 Cosmological Overview . .5 1.2.2 Objective . 10 1.3 Chapter Overview . 12 Chapter 2 Populating The Local Universe . 14 2.1 Galaxy Abundances . 14 2.1.1 Local Galaxies . 14 2.1.2 Astrometry . 17 2.2 Globular Cluster Population Models . 23 2.2.1 Number of Globular Clusters per Galaxy . 23 2.2.2 Dynamical Mass Model . 28 2.2.3 Globular Cluster Specific Number Model . 36 2.3 Modeling Globular Cluster Populations . 41 2.3.1 Bandpass Conversion . 42 2.3.2 All Sky Globular Cluster Distribution . 44 Chapter 3 Globular Clusters . 46 3.1 Characteristics of GCs . 47 iv 3.2 Stellar evolution in GCs . 51 3.2.1 Hertzsprung-Russell Diagram . 52 3.2.2 Evolutionary Track of a Sun-like Star . 53 3.2.3 Stellar Evolution Equations . 57 3.2.4 Evolutionary Timescales . 62 3.3 Stellar Dynamics of GCs . 63 3.3.1 Dynamical Timescales . 63 3.3.2 GC Structure . 67 3.3.3 GC evolution . 69 3.4 External Environment . 75 Chapter 4 Simulating Globular Clusters . 77 4.1 Monte Carlo Method . 77 4.1.1 Fokker-Planck Equation . 77 4.1.2 Monte Carlo Codes . 78 4.2 MOCCA . 81 4.2.1 Stellar Evolution Code . 87 4.2.2 The Fewbody Code . 90 4.2.3 External Environment . 95 4.3 Sampling Globular Clusters . 97 4.3.1 General Setup . 98 4.3.2 Variations of Parameters . 100 4.3.3 Age Spread . 103 Chapter 5 General Relativity and GW Astronomy . 105 5.1 Gravitational-Wave Astronomy . 105 5.1.1 The First Detection . 105 5.1.2 General Relativity and GWs . 107 v 5.2 BBH GW Astronomy . 111 5.2.1 Schwarzschild Black Hole . 112 5.2.2 BBH Formations . 116 5.2.3 Relativistic Evolutions . 122 5.2.4 GWs from BBHs . 125 5.3 Gravitational Wave Detectors . 128 Chapter 6 Prospective Detection . 131 6.1 Merger Event Rate . 131 6.1.1 GC Simulations . 131 6.1.2 Dynamically Formed BBHs . 133 6.1.3 Relativistic Evolutions . 135 6.2 Prospects for GW Astrometry . 137 6.2.1 Detector Response for LISA . 139 6.2.2 Localization of BBHs . 142 6.3 Conclusion . 146 References . 149 vi List of Illustrations Figure 2-1 Spatial distribution of galaxies in the GWGC . 15 Figure 2-2 GWGC galaxies near 30 Mpc . 22 Figure 2-3 Spatial distribution of galaxies in the Harris catalog . 25 Figure 2-4 Completeness of the Harris catalog . 26 Figure 2-5 Visualization of the missing data in GWGC. 26 Figure 2-6 K-Magnitude vs V-Magnitude for galaxies in the Harris catalog 27 Figure 2-7 Correlations in GC properties . 32 Figure 2-8 NGC and log MGC with dynamical mass models . 33 Figure 2-9 NGC and log MGC with V/K-Magnitude . 34 Figure 2-10 NGC dynamical mass models . 35 Figure 2-11 NGC luminosity models . 36 Figure 2-12 GC SN model . 37 Figure 2-13 GC SN model with error bar . 39 Figure 2-14 LOWESS regression with GC SN model . 41 Figure 2-15 Missing data in the Harris catalog . 42 Figure 2-16 B-Magnitude vs V-Magnitude . 43 Figure 2-17 B-Magnitude vs color index . 44 Figure 2-18 All-sky projection of galaxies in local universe . 45 Figure 3-1 Star clusters . 49 Figure 3-2 Evolutionary track of a Sun-like star . 52 Figure 3-3 Evolutionary tracks for stars in different masses . 56 vii Figure 4-1 Call chart of data routine in MOCCA . 82 Figure 4-2 Call chart of scale0 routine in MOCCA . 83 Figure 4-3 Call chart of relaxt routine in MOCCA . 84 Figure 4-4 Call chart of MOCCA . 86 Figure 4-5 Caller chart for mass-loss in MOCCA . 88 Figure 4-6 Caller chart for SSE code in MOCCA . 89 Figure 4-7 Call chart for Fewbody code in MOCCA . 91 Figure 4-8 Caller chart for binary formation in MOCCA . 92 Figure 4-9 Age spread of galactic GCs . 104 Figure 5-1 GW polarizations . 110 Figure 5-2 BBHs detected by LIGO . 112 Figure 5-3 Outcome of binary-single interaction . 121 Figure 6-1 GC population distribution from GC SN model . 132 Figure 6-2 GC model variations . 133 Figure 6-3 Snapshot of the 324 base models at a Hubble time . 133 Figure 6-4 BBH orbital periods at ejection . 134 Figure 6-5 Coordinate system for a precessing binary . 135 Figure 6-6 Chip mass distribution . 136 Figure 6-7 Spatial distribution of the BBH mergers . 137 Figure 6-8 BBH orbital frequency distribution . 138 Figure 6-9 Expected GW signal from a single BBH . 142 Figure 6-10 GW signal spectrum for LISA . 143 Figure 6-11 Localized BBHs . 146 viii List of Tables Table 2-1 Duplicated galaxy entries in GWGC. 23 Table 2-2 Feature importances of GC properties. 31 Table 4-1 Comparison of the two mass-loss models . 89 Table 4-2 Parameters of the general setup . 98 Table 4-3 Parameter space of GC models . 100 Table 6-1 One sample of the BBH in the database . 142 Table 6-2 Localizable BBHs . 145 ix CHAPTER 1 Introduction 1.1 Background On September 14th 2015, a special data flow was recorded by the advanced Laser Interferometer Gravitational wave Observatory (aLIGO). aLIGO is a large ex- perimental facility designed to detect gravitational waves with two sites, located in Hanford, WA and Livingston, LA. Each site has two perpendicular arms to monitor the tiny changes between the 4 km long space, waiting for some special patterns that have been expected for over fifty years. This is the largest and most ambitious project ever funded by the National Science Foundation. More than 1200 scholars from 18 different countries have been working together since 1997 for this moment (Abbott et al., 2016b). On February 11th 2016, a press conference was organized to announce that gravitational waves, which were predicted based on Albert Einstein's theory of general relativity over a hundred years ago, had been directly detected. The detection also cleared another widespread doubt about the existence of the most compact binary system, made up of two black holes (BHs). BHs are named for the region of spacetime that exhibits such strong gravitational effects that nothing, not even light, can escape from inside. No existing method could directly observe these objects so they remained a theoretical hypothesis from general relativity. Observations have reported high- energy electromagnetic radiation and fast-moving celestial bodies that can only be explained by the unprecedented gravitational field generated by BHs. Those indirect measurements are limited in revealing the nature of such objects other than the 1 dynamical aspects. The lasting mystery of the physics behind, together with the non-detection of gravitational waves, increased the doubt Einstein himself once held. As Copi puts in his Introduction to Logic, \In some circumstances it can be safely assumed that if a certain event had occurred, evidence of.