How Loud Must a Neutron-Star Merger Be to Reveal Its Equation of State?
Sk Md Adil Imam
Abstract
The tidal response of neutron stars during binary inspiral encodes the equation of state (EOS) of dense matter in the gravitational-wave signal. Quantifying the signal-to-noise ratio (SNR) required to distinguish competing EOS models with third-generation detectors is therefore essential. We perform Bayesian nested-sampling parameter estimation on simulated binary neutron star signals observed by an Einstein Telescope plus two Cosmic Explorer detector network and compute the evidence difference between correct- and incorrect-EOS recovery models over a broad range of SNR. Across two tidal-deformability contrasts, a swap of the true and recovery EOS, and two binary mass points, we find a common scaling, Δ Z = A\,SNRn with n 1.74--1.95, where the EOS contrast and binary properties determine only the prefactor A. This behavior follows from an Occam-factor argument, yielding Δ Z (ΔΛ\,SNR)2. Calibrating this relation on three configurations predicts, before the run, the SNR required for decisive EOS discrimination in the fourth to within 0.3\%. These results establish a quantitative framework for assessing the EOS-discrimination reach of third-generation gravitational-wave detector networks.