Impact of the $(\ell=2,m=0)$ spherical harmonic mode with memory on parameter estimation for ground-based detectors

TL;DR

This paper evaluates how including the $( ext{l}=2, ext{m}=0)$ spherical harmonic mode with memory in waveform models improves parameter estimation accuracy for future ground-based gravitational wave detectors, especially in reducing biases.

Contribution

It introduces a waveform model incorporating the $(2,0)$ mode with memory and assesses its impact on parameter estimation for advanced detectors.

Findings

Including the mode reduces biases in spin parameter estimates.

The mode helps mitigate the distance-inclination degeneracy.

Impact varies between edge-on and face-on orientations.

Abstract

We recently presented an efficient and accurate waveform model for the $(2,0)$ spherical harmonic mode including both the displacement memory contribution and the ringdown oscillations for aligned-spin binary black holes in quasi-circular orbits. The model we developed is constructed in time domain and implemented within the computationally efficient IMRPhenomTHM waveform model. In this article, we employ it to perform in-depth parameter estimation studies for future ground-based detectors, specifically considering LIGO A$^{\#}$, Cosmic Explorer, and the Einstein Telescope, combining them in different detector networks. While previous studies have reviewed the impact of the memory contribution in parameter estimation, we assess the effect of incorporating the complete mode in the analysis on the posterior estimation of source parameters, performing zero-noise injections of high signal-to-noise ratio signals. We investigate the impact of this mode on the distance-inclination degeneracy and compare its impact in edge-on and face-on configurations. We find that including this mode helps mitigate biases in the estimation of individual spin components, which may otherwise arise when the mode is neglected.