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arXiv · 2608.05794

How Loud Must a Neutron-Star Merger Be to Reveal Its Equation of State?

Sk Md Adil Imam
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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, $\Delta\log Z = A\,\mathrm{SNR}^{n}$ with $n \simeq 1.74$--$1.95$, where the EOS contrast and binary properties determine only the prefactor $A$. This behavior follows from an Occam-factor argument, yielding $\Delta\log Z \propto (\Delta\tilde{\Lambda}\,\mathrm{SNR})^{2}$. 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.

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Sk Md Adil Imam. 2026-08-06. How Loud Must a Neutron-Star Merger Be to Reveal Its Equation of State?. https://arxiv.org/abs/2608.05794

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