Chandrasekhar Hall

Gravitational waves from compact binary coalescences: Tests of General Relativity and Astrophysics

Shilpa Kastha

IMSc and Max Planck Institute for Gravitational Physics

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.
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). We argue
that the co-moving spatial distribution of DNS mergers leaves a unique imprint on the statistical
distribution of SNRs of the detected DNS mergers. Hence the SNR distribution of DNS mergers
can be used as a novel probe of their redshift evolution. We consider detections of DNS mergers
by CE and study the SNR distributions for different possible redshift evolution models of DNSs
and employ Anderson Darling p-value statistic to demonstrate the distinguishability between these
different models. We find that a few hundreds of DNS mergers in the CE era will allow us to
distinguish between different models of redshift evolution.