Environmental effects in stellar mass gravitational wave sources II: Joint detections of eccentricity and phase shifts in binary sub-populations

TL;DR

This paper shows that eccentric gravitational wave signals significantly improve the detection of environmental effects, with potential SNR boosts up to 10^5, especially in high-eccentricity binary populations observed by future detectors.

Contribution

It introduces a method to enhance environmental effect detection in eccentric GW signals and analyzes their impact on future GW observatories.

Findings

Eccentricity increases detectability of environmental effects in GW signals.

SNR enhancements can reach up to 10^5 for high-eccentricity sources.

Environmental effects are likely common in merging binaries observed by future detectors.

Abstract

We demonstrate that the properties of eccentric gravitational wave (GW) signals enhance the detectability of GW phase shifts caused by environmental effects (EEs): The signal-to-noise ratio (SNR) of EEs can be boosted by up to $\ell_{\rm max}^{1 - n}$ with respect to corresponding circular signals, where $\ell_{\rm max}$ is the highest modeled eccentric GW harmonic and $n$ is the frequency scaling of the GW dephasing prescription associated to the EE. We investigate the impact on a population level, adopting plausible eccentricity distributions for binary sources observed by LIGO/Virgo/Kagra (A+ and A\# sensitivities), as well as Cosmic Explorer (CE) and the Einstein Telescope (ET). For sources in the high eccentricity tail of a distribution ($e \gtrsim 0.2$ at 10 Hz), phase shifts can systematically be up to $\ell_{\rm max}^{1 - n}$ times smaller than in a corresponding circular signal and still be detectable. For typical EEs, such as Roemer delays and gas drag, this effect amounts to SNR enhancements that range from $10^2$ up to $10^5$. For CE and ET, our analysis shows that EEs will be an ubiquitous feature in the eccentric tail of merging binaries, regardless of the specific details of the formation channel. Additionally, we find that the joint analysis of eccentricity and phase shift is already plausible in current catalogs if a fraction of binaries merge in AGN migration traps.