Gravitational waves from compact binary coalescences: Tests of General Relativity and Astrophysics By SHILPA KASTHA PHYS10201404001 The Institute of Mathematical Sciences, Chennai A thesis submitted to the Board of Studies in Physical Sciences In partial fulfillment of requirements For the Degree of DOCTOR OF PHILOSOPHY of HOMI BHABHA NATIONAL INSTITUTE August, 2019 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at Homi Bhabha National Institute (HBNI) and is deposited in the Library to be made available to borrowers under rules of the HBNI. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the Competent Authority of HBNI when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. Shilpa Kastha DECLARATION I, hereby declare that the investigation presented in the thesis has been carried out by me. The work is original and has not been submitted earlier as a whole or in part for a degree / diploma at this or any other Institution / University. Shilpa Kastha 5 LIST OF PUBLICATIONS ARISING FROM THE THESIS 1. Testing the multipole structure of compact binaries using gravitational wave observa- tions Shilpa Kastha , Anuradha Gupta, K G Arun, B S Sathyaprakash and Chris Van Den Broeck Physical Review D. 98, 124033 (2018) arXiv:1809.10465 [gr-qc] 2. Testing the multipole structure and conservative dynamics of compact binaries using gravitational wave observations: The spinning case Shilpa Kastha , Anuradha Gupta, K G Arun, B S Sathyaprakash and Chris Van Den Broeck Physical Review D. 100, 044007 (2019) arXiv:1905.07277 [gr-qc] 3. Imprints of the redshift evolution of double neutron star merger rate on the signal to noise ratio distribution Shilpa Kastha, M. Saleem and K G Arun Communicated arXiv:1801.05942v2 [gr-qc] 4. Linear momentum flux from inspiralling compact binaries in quasi-elliptical orbits at second post-Newtonian order Shilpa Kastha , Chandra Kant Mishra, K G Arun In preparation Shilpa Kastha 6 WORKSHOPS ATTENDED AND POSTER PRESENTED 1. 7 - 10 August 2018 : Physics and Astrophysics at the eXtreme, IUCAA, Pune, India . 2. 5 - 9 February 2018 : XXXVI Meeting of Astronomical Society of India (ASI 2018) , Osmania University, Hyderabad, India. 3. 18 - 20 May 2017 : 29th meeting of IAGRG., IIT Guwahati, Asam, India. Poster : Gravitational recoil of eccentric compact binaries 4. 18 - 20 May 2016 : The Future of Gravitational Wave Astronomy (FGWA 2016), Inter- national Centre for Theoretical Sciences, Bangalore, India. 5. 10 - 13 May 2016 : XXXIV Meeting of Astronomical Society of India (ASI 2016), Uni- versity of Kashmir, Srinagar, India. Poster : Tracking the merger rate density evolution of double Neutron star binaries. 6. 14 - 18 December 2015 : 8th International Conference on Gravitation and Cosmology (ICGC 2015), ISER Mohali, India. Poster : Probing the inhomogeneity in the spatial distribution of Double Neutron Star mergers Through Gravitational wave observations 7 SEMINARS PRESENTED 1. Testing The Multipole Structure Of Compact Binaries Using Gravitational Wave Obser- vations 22nd International Conference on General Relativity and Gravitation, 13th Edoardo Amaldi Conference on Gravitational Waves, 2019 at Valencia, Spain. 2. Testing the multipolar structure of compact binary spacetimes XXXVI Meeting of Astronomical Society of India, 2018 at Osmania University, India. 3. Testing Post-Newtonian multipole structure of general relativity Seminar at the Institute of Gravitation & Cosmos, Penn State, USA (2017) 4. Probing Inhomogeneity in the Spatial distribution of double neutron star binaries using Gravitational-Wave Observations The Future of Gravitational Wave Astronomy, ICTS-TIFR, Bangalore, India (2016). To my loved ones.. 9 ACKNOWLEDGEMENTS Completing PhD and writing the dissertation is a long and challenging journey– and it is certainly not done singlehandedly. In all these years many people have helped me in shaping up my aca- demic career. It was hardly possible for me to complete my PhD thesis without their support, encouragement and love. Firstly, I would like to express my heartfelt gratitude to my co-supervisor, Prof. K G Arun for his patience, constant support and encouragement through out my PhD. I have been immensely benefited from all the discussions and debates we used to have. I have been extremely lucky to have a supervisor who cared so much about my work, and who responded to my questions and queries so promptly. His careful editing contributed enormously to the production of this thesis. I am grateful to Dr. Manjari Bagchi and Prof. Ghanashyam Date for their willingness to be my joint supervisors. I would like to thank them for encouraging my research and for allowing me to grow as a researcher. I would like to thank all my doctoral committee members, Prof. Bal- achandran Sathiapalan, Prof. Shrihari Gopalakrishna, Prof. Venkata Suryanarayana Nemani and Prof. Sibasish Ghosh for the useful discussions and comments during all the doctoral committee meetings. I would like to extend my gratitude to my collaborators, Prof. B S Sathyaprakash, Prof. Chris Van Den Broeck, Dr. Chandra Kant Mishra, Dr. Anuradha Gupta, Dr. M Saleem for all their suggestions. I remember enjoying all the long discussion sessions with Prof. Sathyaparaksh, while visiting PennState, which has given me a broader perspective about the gravitational wave research. I would also like to thank Astrorel group of The International Centre for Theoretical Sciences for all the group meetings and journal clubs which has broaden my understanding of the field. My sincere thank to Prof. Sanjit Mitra and Dr. Anirban Ain for introducing me to the field. I would like to express my sincere gratitude to Chennai Mathematical Institute for providing me all the facilities in perusing my research. Thanks to all my group members, Krishnendu, Sayantani, Anjali, Aneesh for tolerating me and being a part of my journey during these years. 10 I sincerely acknowledge IMSc computing facilities. Thanks to all IMSc. official staffs, canteen workers, security persons for providing such a research-friendly environment and a pleasant stay at IMSc. Special thanks to R. Indra, Vasan, Jahir for their generous responses and the friendly behavior. I must thank to all the F6 members, perhaps the craziest people I have ever met, Trisha di, Upayan da, Anish da, Aritra da for all the outings, night parties, endless Addas. And offcourse, a special thanks to Taushif da and Rana for the weekend biriyanis. Thanks a ton to Jahanur Hoque, Rusa di and Pinaki da for being always beside me during the happy and the hard moments to push me and motivate me. I owe thanks to Arghya. You were always around at times when I thought that it is impossible to continue and helped me to keep things in perspective. Finally, I acknowledge the people who mean a lot to me, my parents. Thank you, baba, for guiding me all these years and being always there with me. Thank you, Ma, for the selfless love, care, pain and sacrifice you did to shape my life. Although you hardly understood what I researched on, you were willing to support any decision I made. Words would never say how grateful I am to both of you. SUMMARY The first two observation runs of advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo interferometers have led to the detections of gravitational waves (GWs) from ten binary black hole (BBH) mergers and a binary neutron star (BNS) merger. Among other things, GWs from these compact binary mergers can be used to probe the behavior of gravity in highly non-linear and dynamical regime and gain insights about the astrophysics associated with the formation of these binaries. In this thesis, we explore the dynamics of the compact binary system within the post-Newtonian (PN) framework in the context of GW astronomy and develop tests of general relativity (GR) in the strong field regime. We propose a new model-independent test of GR by parametrizing the gravitational waveform in terms of the multipole moments of the compact binary using the PN framework. We derive the parametrized multipolar GW phase evolution for compact binaries (CBs) in quasi-circular orbit including spin effects in the inspiral dynamics at 3.5PN order and deviations to the PN coefficients in the 3.5PN conserved energy. We assume that the companion spins are either aligned or anti- aligned with respect to the orbital angular momentum and compute spin-orbit corrections that are accurate up to the next-to-next-to-leading order (3.5PN order) and the quadratic-in-spin effects up to 3PN order in the GW flux and the PN phase. We find that third generation detector such as Cosmic Explorer (CE) and space based Laser Interferometer Space Antenna (LISA) mission have the similar ability and can measure the first 4 leading order multipole coefficients with reasonable accuracies. Asymmetric emission of GWs from a compact binary can lead to a flux of linear momentum from the system. As a result, depending on the system configuration, the center of mass (CM) of a binary system recoils. In this thesis we compute 2PN accurate LMF from various mass and current type multipole moments for an inspiralling, non-spinning compact binary system in quasi-elliptical orbit. 2PN Quasi-Keplarian representation (QKR) of the parametric solution to the PN equation of motion is employed to obtain the LMF at 2PN. 12 We also propose a new method to track the redshift evolution of the double neutron star mergers. Proposed third generation detectors such as CE will have the sensitivity to observe double neutron star (DNS) mergers up to a redshift of ∼ 5 with good signal to noise ratios (SNRs).