Impact of neglecting center-of-mass acceleration in parameter estimation of stellar-mass black holes

TL;DR

This paper investigates how neglecting the center-of-mass acceleration caused by a tertiary body can bias parameter estimation of stellar-mass black hole binaries in future gravitational wave detectors, emphasizing the importance of including this effect.

Contribution

It demonstrates the potential systematic biases in binary parameter estimation due to unaccounted CoM acceleration and provides bounds for constraining this acceleration with next-generation detectors.

Findings

Unaccounted CoM acceleration can bias chirp mass and mass ratio estimates.

Asymmetric binaries are more affected by neglecting CoM acceleration.

Next-generation detectors can constrain CoM acceleration parameters effectively.

Abstract

A tertiary body near a coalescing binary can imprint its influence on the gravitational waves (GWs) emitted by that binary in the form of center-of-mass (CoM) acceleration. An example of such a scenario is a binary black hole (BBH) merging near a supermassive black hole, which is touted to occur frequently. The limited low-frequency sensitivity of current GW detectors makes it challenging to detect these effects, as the associated waveform phase remains elusive. However, next-generation (3G) detectors such as Cosmic Explorer (CE) and Einstein Telescope (ET), with improved sensitivity at lower frequencies, are expected to be capable of capturing such signatures. In our study, we focus on the stellar-mass BBHs and explore the parameter space where the CoM acceleration will play a dominant role affecting parameter inference of the binary. We demonstrate that an unaccounted CoM acceleration of a low-mass binary with a total mass of $5\, \rm{M}_{\odot} $ can lead to significant systematic biases, exceeding statistical errors in the estimation of the chirp mass and symmetric mass ratio when the CoM parameter $\alpha$ is as small as $\sim 10^{-9}$ and $10^{-10}$ $\rm{s}^{-1}$ for CE and ET, respectively. We also find that asymmetric binaries are more susceptible to systematic bias when CoM acceleration is neglected. When the effect of CoM acceleration is included in the GW phase, then $\alpha = 10^{-7} \rm s^{-1}$ can be constrained with a bound of $10^{-9} (10^{-11})\, \rm s^{-1}$ for CE (ET). Our study thus highlights the crucial implications of considering the presence of a tertiary body in the GW emitted by a stellar-mass BBH when observed in 3G detectors.