Inspiralling compact objects with generic deformations

TL;DR

This paper analyzes how generic, nonaxisymmetric mass quadrupole moments affect the orbital dynamics and gravitational wave signals of inspiraling compact binaries, providing analytic solutions and potential observational constraints.

Contribution

It introduces analytic solutions for binary precession and orbital dynamics with generic quadrupole deformations, and computes gravitational wave phase and amplitude corrections at leading post-Newtonian order.

Findings

Phase differences > 0.1 radians for quadrupole parameters > 10^{-3}

Amplitude modulations at -0.5PN order with 3.25PN SUA correction

Constraints on multipolar deformations are feasible with current detectors

Abstract

Self-gravitating bodies can have an arbitrarily complex shape, which implies a much richer multipolar structure than that of a black hole in General Relativity. With this motivation, we study the corrections to the dynamics of a binary system due to generic, nonaxisymmetric mass quadrupole moments to leading post-Newtonian (PN) order. Utilizing the method of osculating orbits and a multiple scale analysis, we find analytic solutions to the precession and orbital dynamics of a (generically eccentric) binary in terms of the dimensionless modulus parameters $\epsilon_{m}$, corresponding to axial $m=1$ and polar $m=2$ corrections from oblateness/prolateness. The solutions to the precession dynamics are exact for $0 \le \epsilon_{2} < 1$, and perturbative in $\epsilon_{1} \ll 1$. We further compute the leading order corrections to the gravitational wave amplitude and phase for a quasi-circular binary due to mass quadrupole effects. Making use of the stationary phase approximation and shifted uniform asymptotics (SUA), the corrections to the phase enter at relative 2PN order, while the amplitude modulations enter at -0.5PN order with a SUA amplitude correction at 3.25PN order, relative 2PN order to the leading order SUA correction. By investigating the dephasing due to generic quadrupole moments, we find that a phase difference $\gtrsim 0.1$~radians is achievable for $\epsilon_{m} \gtrsim 10^{-3}$, which suggests that constraints with current and future ground-based gravitational wave detectors are possible. Our results can be implemented in parameter estimation studies to constrain generic multipolar deformations of the Kerr geometry and of neutron stars.