Springer Theses. Recognizing Outstanding Ph.D. Research

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1 Springer Theses Recognizing Outstanding Ph.D. Research

2 Aims and Scope The series Springer Theses brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria They must be written in good English. The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. The work reported in the thesis must represent a significant scientific advance. If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder. They must have been examined and passed during the 12 months prior to nomination. Each thesis should include a foreword by the supervisor outlining the significance of its content. The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. More information about this series at

3 Carl-Johan Haster Globular Cluster Binaries and Gravitational Wave Parameter Estimation Challenges and Efficient Solutions Doctoral Thesis accepted by the University of Birmingham, UK 123

4 Author Dr. Carl-Johan Haster Canadian Institute for Theoretical Astrophysics Toronto, ON Canada Supervisor Prof. Ilya Mandel University of Birmingham Birmingham UK ISSN ISSN (electronic) Springer Theses ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

5 Supervisor s Foreword This is an extremely exciting time in astrophysics as the first direct detections of gravitational waves were made by the Laser Interferometer Gravitational-wave Observatory (LIGO) in late 2015, in the beginning of the final year of Carl-Johan Haster s Ph.D. work. We have already learned a lot from the very first detections: stellar-mass binary black holes exist; they merge within the age of the Universe; they can be more massive than some of us anticipated. And there s a lot more to learn, as LIGO and other detectors grow in sensitivity, and a whole population of observed merging compact binary sources can teach us about binary astrophysics and strong-field gravity. At lower frequencies, pulsar timing arrays and the space-borne detector LISA, whose technology readiness was recently successfully tested by the Pathfinder mission, hold the promise of exploring wider and more massive binaries. Carl s work, as described in this thesis, can serve as an introduction to some of the specific challenges and successes in this rapidly growing field. During the course of his Ph.D. work at the University of Birmingham, UK, Carl has worked on the astrophysics of gravitational-wave sources, including modelling of dynamical formation channels, and on the data analysis of signals, which requires sophisticated statistical techniques to extract signals from the noise and infer the source parameters from the gravitational-wave signature. Binary black holes may be formed dynamically in dense stellar environments, such as globular clusters. Carl has contributed to globular cluster simulations that demonstrated that this dynamical population could be competitive with the rate of coalescing binary black holes from the isolated binary evolution channel. This thesis includes a chapter on the impact of intermediate-mass black holes, weighing in at around 100 solar masses, on globular cluster evolution. Carl was able to use very high accuracy N-body simulations to evolve the cluster all the way through to the merger of a binary consisting of an intermediate-mass and a stellar-mass black hole following a sequence of three-body interactions that gradually hardened the binary. This demonstrates that previously predicted inspirals of stellar-mass compact objects into few-hundred-solar mass intermediate-mass black holes can indeed be a source for gravitational-wave observations. v

6 vi Supervisor s Foreword Such intermediate-mass-ratio inspirals are particularly exciting because they have the potential of precisely probing both globular cluster dynamics and General Relativity in the strong-field regime. Carl led the first systematic effort to explore the feasibility of inference on gravitational-wave signals from such sources. Among other results, this work demonstrated that the gravitational-wave signature carried enough information, even for limited signal-to-noise-ratio detections, to measure the larger body s mass with sufficient accuracy to confirm the existence of intermediate-mass black holes. Bayesian inference methods for gravitational-wave parameter estimation are computationally expensive. Carl led a project on comparing these methods against faster but suboptimal techniques in order to establish the expected accuracy of astrophysical inference that will be possible with advanced detector data. This work, described in the final pre-conclusion chapter of this thesis, has demonstrated that the faith of the community in some of the previously proposed techniques was misplaced. More importantly, it proposed a very efficient and arbitrarily accurate new parameter estimation method for parameter spaces of limited dimensionality. Carl is now continuing to make contributions to gravitational-wave astrophysics as a postdoctoral fellow at the Canadian Institute for Theoretical Astrophysics. In the meantime, his work as described in this thesis provides a reference for some of the important issues facing gravitational-wave astronomy. Birmingham, UK January 2017 Prof. Ilya Mandel

7 Abstract Following the first detection of gravitational waves from a binary coalescence the study of the formation and evolution of these gravitational-wave sources and the recovery and analysis of any detected event will be crucial for the newly realised field of observational gravitational-wave astrophysics. This thesis covers a wide range of these topics including simulating the dense environments where compact binaries are likely to form, focusing on binaries containing an intermediate-mass black hole (IMBH). It is shown that such binaries do form, are able to merge within a: 100 Myr simulation, and that the careful treatment of the orbital evolution (including post-newtonian effects) implemented here was crucial for correctly describing the binary evolution. The latter part of the thesis covers the analysis of the gravitational waves emitted by such a binary, and shows it is possible to identify the IMBH with high confidence, together with most other parameters of the binary, despite the short-duration signals and assumed uncertainties in the available waveform models. Finally a method for rapid parameter estimation of gravitational-wave sources is presented and shown to recover source parameters with comparable accuracy using only a small fraction: 0.1% of the computational resources required by conventional methods. vii

8 Acknowledgements It is my sincere pleasure to thank the following people: Min bror Erik, mamma Kerstin och pappa Lars-Olof, utan ert stöd och hjälp hade jag aldrig vågat tro att detta hade varit möjligt. My supervisors Ilya Mandel and Alberto Vecchio for their mentorship, support and endless patience; Christopher Berry, Walter Del Pozzo, Will Farr, John Veitch, Alberto Sesana and David Stops for providing both interesting discussions and answers to my many questions. Fabio Antonini, Katie Breivik, Sourav Chatterjee, Ben Farr, Vicky Kalogera, Tyson Littenberg, Fred Rasio and Carl Rodriguez for making my months in Chicago both fun, interesting and memorable. All my friends in the ASR group at Birmingham, especially Jim Barrett, Charlotte Bond, Daniel Brown, Mark Burke, Chris Collins, Sam Cooper, Sebastian Gaebel, Anna Green, Kat Grover, Maggie Lieu, Hannah Middleton, Chiara Mingarelli, Sarah Mulroy, Trevor Sidery, Rory Smith, Simon Stevenson, Daniel Töyrä, Alejandro Vigna-Gómez and Serena Vinciguerra for years of fun and adventures; The members of the CBC group, and specifically the Parameter Estimation subgroup, for all their help. I would also like to thank Alberto Sesana and Jonathan Gair for their great skill and patience as the examiners for my Ph.D. viva. Several of the chapters in this thesis were the result of collaborations and benefited from discussions with several people. Chapter 2 was based on work done in collaboration with Fabio Antonini, Ilya Mandel and Vicky Kalogera [1], and benefited from discussions with Sourav Chatterjee, Jonathan Gair, James Guillochon, Fred Rasio and Alberto Sesana. Chapter 3 was based on work done in collaboration with Zhilu Wang, Christopher Berry, Simon Stevenson, John Veitch and Ilya Mandel [3] and benefited from discussions with Michael Pürrer, Tom Callister and Tom Dent. Chapter 4 was based on work done in collaboration with Ilya Mandel and Will M. Farr [2], and benefited from discussions with Christopher Berry, Walter Del Pozzo, Alberto Vecchio, John Veitch, Richard O Shaughnessy and Chris Pankow. My work has been supported by a studentship from the University of Birmingham and the Center for Interdisciplinary Exploration in Astrophysics at Northwestern University. ix

9 x Acknowledgements References 1. Haster, C.-J., Antonini, F., Kalogera, V., Mandel, I. (2016a). N-body dynamics of intermediate mass-ratio inspirals. In preparation. 2. Haster, C.-J., Mandel, I., Farr, W. M. (2015). Efficient method for measuring the parameters encoded in a gravitational-wave signal. Classical and Quantum Gravity, 32(23):235017, Haster, C.-J., Wang, Z., Berry, C. P. L., Stevenson, S., Veitch, J., Mandel, I. (2016b). Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes. MNRAS, 457, ,

10 Contents 1 Introduction Formation and Evolution of Compact Binaries Binary Formation from Stellar Evolution in the Galactic Field Dynamical Binary Formation in Dense Stellar Environments Gravitational Wave Sources General Relativity Modelling Compact Binary Coalescenses Gravitational Wave Data Analysis Searches for CBC Sources Parameter Estimation Structure of Thesis Chapter Chapter Chapter References N-Body Dynamics of Intermediate Mass Ratio Inspirals Introduction Simulations Results Discussion Conclusion References xi

11 xii Contents 3 Inference on Gravitational Waves from Coalescences of Stellar-Mass Compact Objects and Intermediate-Mass Black Holes Introduction Study Design Sources and Sensitivity Parameter Estimation Key Results Effects of Cosmology on Inferring the Presence of an IMBH Discussion Impact of Low-Frequency Sensitivity Uncertainty Versus Signal-to-Noise Ratio Systematics Summary References Efficient Method for Measuring the Parameters Encoded in a Gravitational-Wave Signal Introduction Binary Coalescence Model Bayesian Inference Stochastic Sampling Chapter Organisation Discretizing the Credible Regions Cumulative Posterior on a Grid Grid Placement Key Results Comparison with Alternative Methods: Which Approximations Are Warranted? Cumulative Likelihood Iso-Match Contours and the Linear Signal Approximation Comparasion Conclusions and Future Directions References Conclusion... 91