Compact binary populations in globular clusters and prospects for gravitational wave detection [Elektronische Ressource] / presented by Jonathan Michael Blake Downing

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Dissertationsubmitted to theCombined Faculties for the Natural Sciences and forMathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byM.Sc. Physics Jonathan Michael Blake Downingborn in Halifax, Nova Scotia, CanadaOral examination: 18 November, 2009Compact Binary Populations in GlobularClusters and Prospects for GravitationalWave DetectionReferees: Prof. Dr. Rainer SpurzemProf. Dr. Ralf KlessenvAbstractThe inspiral and merger of compact binary stars will be major detection events for in-terferometric gravitational wave observatories. These observatories operate most effectivelyby comparing their output to template waveforms. In order to make these templates thephysical parameters of the source population must be understood. Compact binaries in thegalactic field have been investigated using population synthesis models but in dense stellarenvironments interactions can alter the binary population and may enhance the mergerrate.I study compact binaries in star clusters using a Monte Carlo model for the dynamics.I find that the black hole population interacts strongly, leading to an enhancement in boththe number of black hole binaries and the black hole binary merger rate. Due to the highinteraction rate the majority of black hole binaries are ejected and thus the mergers occurin the galactic field.

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Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for
Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
M.Sc. Physics Jonathan Michael Blake Downing
born in Halifax, Nova Scotia, Canada
Oral examination: 18 November, 2009Compact Binary Populations in Globular
Clusters and Prospects for Gravitational
Wave Detection
Referees: Prof. Dr. Rainer Spurzem
Prof. Dr. Ralf Klessenv
Abstract
The inspiral and merger of compact binary stars will be major detection events for in-
terferometric gravitational wave observatories. These observatories operate most effectively
by comparing their output to template waveforms. In order to make these templates the
physical parameters of the source population must be understood. Compact binaries in the
galactic field have been investigated using population synthesis models but in dense stellar
environments interactions can alter the binary population and may enhance the merger
rate.
I study compact binaries in star clusters using a Monte Carlo model for the dynamics.
I find that the black hole population interacts strongly, leading to an enhancement in both
the number of black hole binaries and the black hole binary merger rate. Due to the high
interaction rate the majority of black hole binaries are ejected and thus the mergers occur
in the galactic field. I find a promising rate of 1− 100 detections per year for the next
generation of ground-based gravitational wave detectors and two possible sources for space-
based detectors, both highly eccentric. I conclude that star clusters must be taken into
account in order to predict accurate event rates for gravitational wave detectors.
Zusammenfassung
Als wichtigste Zielobjekte fu¨r interferometrische Gravitationswellen-Detektoren werden
umeinander spiralende und verschmelzende kompakte Doppelsternsysteme angesehen. Die
Detektoren arbeiten am effektivsten durch Vergleichen der Beobachtung mit einer Schablone
aus der erwarteten Wellenform. Um die Schablonen zu erstellen mu¨ssen die physikalis-
chen Parameter der Quellenpopulationen verstanden werden. In der Galaxie k¨onnen kom-
pakte Doppelsternsysteme mithilfe von Populationssynthese-Modellen untersucht werden,
wohingegen in dichten Sterngebieten stellare Wechselwirkungen die Verteilung der Doppel-
Systeme beeinflussen und die Kollisionsrate anheben k¨onnen.
Ich erforsche kompakte Doppelsternsysteme in Kugelsternhaufen unter der Verwendung
eines Monte-Carlo-Modells fu¨r die Dynamik. Diese Studien zeigen, dass die Population
der schwarzen L¨ocher stark interagiert, wodurch sich sowohl die Anzahl der Paare von
schwarzen L¨ochern als auch deren Verschmelzungsrate erh¨oht. Die Mehrheit dieser Doppel-
systeme wird aus dem Kugelsternhaufen geschleudert, um endgu¨ltig im galaktischen Feld
zu verschmelzen. Fu¨r die erdgebundenen Gravitationswellen-Detektoren der n¨achsten Gen-
eration erwarte ich eine vielversprechende Rate von 1− 100 detektierten Ereignissen pro
Jahr sowie zwei m¨ogliche Quellen fu¨r weltraum-basierte Messungen, jeweils mit Bahnen
hoher Exzentrizit¨at. Daher schließe ich, dass Sternhaufen mit in Betracht gezogen werden
mu¨ssen, um genaue Ereignisraten fu¨r Gravitationswellen-Detektoren vorherzusagen.vii
Dedication
To my mother with many thanks for her unconditional love and support over so many
years. She has had confidence in me as a person and not just as an academic when I have
had none in myself. Without her I would never have made it this far.
We live life forwards but understand it backwards.
Søren KierkegaardContents
1 Introduction 1
1.1 Interferometric Gravitational Wave Detectors . . . . . . . . . . . . . . . . . 2
1.2 Compact Binaries as Gravitational Wave Sources . . . . . . . . . . . . . . . 4
1.3 Basic Concepts in Star Cluster Dynamics . . . . . . . . . . . . . . . . . . . 5
1.3.1 Evolution of the Phase Space Distribution . . . . . . . . . . . . . . . 5
1.3.2 The Relaxation Time . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.3 Mass Segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.4 The Gravothermal Catastrophe . . . . . . . . . . . . . . . . . . . . . 8
1.3.5 Few-Body Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.6 Escape Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 The Formation of Compact Binaries 11
2.1 The Evolution of Isolated Binaries . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 The Formation of Compact Binaries in Star Clusters . . . . . . . . . . . . . 18
2.2.1 Single-Single Interactions . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Binary-Single Interactions . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.3 Binary-Binary Interactions . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Current Results for Compact Binaries . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Population Synthesis in the Galactic Field . . . . . . . . . . . . . . . 22
2.3.2 Binaries in Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 The Relativistic Evolution of Compact Binaries 25
3.1 The Linearised Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Power Generation by Gravitational Waves . . . . . . . . . . . . . . . . . . . 27
3.3 Radiated Power as a Function of Harmonic . . . . . . . . . . . . . . . . . . 32
4 The Monte Carlo Code 35
4.1 The Monte Carlo Approximation . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 The Structure of a Monte Carlo Timestep . . . . . . . . . . . . . . . . . . . 36
4.2.1 The Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.2 The Timestep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.3 Additional Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.4 Relaxation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.5 New Positions and New Potential . . . . . . . . . . . . . . . . . . . . 41
4.2.6 New Velocities in the New Potential . . . . . . . . . . . . . . . . . . 41
4.3 Few Body Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ixx CONTENTS
4.3.1 3-Body Binary Formation . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.2 Binary-Single Interactions . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.3 Binary-Binary Interactions . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Stellar Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5 Tidal Escape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5 Initial Conditions 51
6 Compact Binaries Within Star Clusters 55
7 The Escapers 69
7.1 Escaper Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.2 Mergers due to Gravitational Radiation . . . . . . . . . . . . . . . . . . . . 75
7.3 Other Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8 Prospects for Gravitational Wave Detection 81
8.1 Ground-Based Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.2 Space-Based Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
9 Million-Body Simulations 89
9.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
9.2 Population Statistics Within the Clusters . . . . . . . . . . . . . . . . . . . 90
9.3 Escapers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9.4 Detection Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
10 Discussion and Outlook 111
10.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
10.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.2.1 Direct Integration of Few-Body Encounters . . . . . . . . . . . . . . 114
10.2.2 Relativistic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.2.3 Direct N-Body Simulations . . . . . . . . . . . . . . . . . . . . . . . 118
10.2.4 Further Analysis of the Simulations . . . . . . . . . . . . . . . . . . 121
10.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Bibliography 125