Gravitational waves from oscillating accretion tori: Comparison between different approaches

TL;DR

This paper compares gravitational waveforms from oscillating accretion tori computed via the quadrupole formula and gauge-invariant metric perturbation theory, revealing conditions for their agreement and limitations.

Contribution

It introduces a relativistic modification of the quadrupole formula and assesses its accuracy against perturbative methods for accretion disk gravitational waves.

Findings

No excitation of black hole quasi-normal modes in stable disks

Relativistic quadrupole formula agrees well with perturbative results when back-scattering is negligible

Quadrupole formula errors are around 10% when back-scattering effects are significant

Abstract

Quasi-periodic oscillations of high density thick accretion disks orbiting a Schwarzschild black hole have been recently addressed as interesting sources of gravitational waves. The aim of this paper is to compare the gravitational waveforms emitted from these sources when computed using (variations of) the standard quadrupole formula and gauge-invariant metric perturbation theory. To this goal we evolve representative disk models using an existing general relativistic hydrodynamics code which has been previously employed in investigations of such astrophysical systems. Two are the main results of this work: First, for stable and marginally stable disks, no excitation of the black hole quasi-normal modes is found. Secondly, we provide a simple, relativistic modification of the Newtonian quadrupole formula which, in certain regimes, yields excellent agreement with the perturbative approach. This holds true as long as back-scattering of GWs is negligible. Otherwise, any functional form of the quadrupole formula yields systematic errors of the order of 10%.