Kilohertz Gravitational Waves from Binary Neutron Star Mergers: Full Spectrum Analyses and High-density Constraints on Neutron Star Matter

TL;DR

This work develops and validates a full-spectrum gravitational-wave analysis pipeline for binary neutron star mergers in the Einstein Telescope era, combining TEOBResumSPA for inspiral with NRPMw for postmerger to form TEOBResumSPA_ NRPMw. Through 20 mock injections, it demonstrates that Bayesian inference across the complete spectrum can tightly constrain the neutron-star equation of state, including the mass-radius relation and the high-density pressure-density curve, by leveraging quasiuniversal relations that connect $f_2$ to ${\rho_{ m max}^{\rm TOV}}$ and ${R_{ m max}^{\rm TOV}}$. The results show substantial gains in high-density EOS inference when incorporating postmerger information, with quantified improvements in ${M_{ m max}^{\rm TOV}}$, ${R_{ m max}^{\rm TOV}}$, and the $\ abla\Lambda(M)$ curve, compared to inspiral-only analyses; the study also clarifies how detector geometry (triangular vs two-L) and initial-frequency choices affect parameter estimation and sky localization. Finally, the work assesses the prospects for predicting prompt black-hole formation and demonstrates robust model selection capabilities for distinguishing pc from NS remnants, highlighting the PM signal’s crucial role in probing supranuclear matter.

Abstract

We demonstrate Bayesian analyses of the complete gravitational-wave spectrum of binary neutron star mergers events with the next-generation detector Einstein Telescope. Our mock analyses are performed for 20 different signals using the TEOBResumSPA_NRPMw waveform that models gravitational-waves from the inspiral to the postmerger phase. They are employed to validate a pipeline for neutron star's extreme matter constraints with prospective detections and under minimal hypotheses on the equation of state. The proposed analysis stack delivers inferences for the mass-radius curve, the mass dependence of the quadrupolar tidal polarizability parameter, the neutron star's maximum density, the maximum mass and the relative radius, and the pressure-density relation itself. We show that a single event at a signal-to-noise ratio close to the minimum threshold for postmerger detection is sufficient to tightly constrain all the above relations as well as quantities like the maximum mass (maximum density) to precision of ${\sim}6$% (${\sim}10$%) at 90% credibility level. We also revisit inferences of prompt black hole formation with full spectrum signals and find that the latter can be robustly identified, even when the postmerger is not detectable due to a low signal-to-noise ratio. New results on the impact of the initial signal frequency and of the detector configuration (triangular vs. two-L) on the source's parameters estimation are also reported. An improvement of approximately one order of magnitude in the precision of the chirp mass and mass ratio can be achieved by lowering the initial frequency from 20 Hz to 2 Hz. The two-L configuration shows instead significant improvements on the inference of the source declination, due to geographical separation of the two detectors.

Figures (15)

• Figure 1: Attachment between TEOBResumSPA and NRPMw for a gw template of nonspinning binary with $m_1=1.5~{\rm M_{\odot}}$, $m_2=1.4~{\rm M_{\odot}}$, $\Lambda_1=400$, $\Lambda_2=600$ and $D_L=40~{\rm Mpc}$. Since the model is defined in the frequency domain, we obtain $h_{22}(t)$ by performing an inverse fft of $h_{22}(f)$.
• Figure 2: Amplitude spectral density (ASD) of et in configuration D Hild:2010idHild:2011np (in black) and comparison with ASD of LIGO L1 detector, relative to GW170817 event LIGOScientific:2018mvr (in gray), to show the improvement in the detection of gw signals with xg detectors. The solid colored lines represent five exemplary bns waveform spectra with TEOBResumSPA_ NRPMw template for $\mathcal{M}=1.24~{\rm M_{\odot}}$, $q=1$, varying $\tilde{\Lambda}$ and $D_L$ as indicated in the legend.
• Figure 3: Relative precision on chirp mass (top) and mass ratio (bottom) with respect to the different initial frequencies for a nonspinning bns with $\mathcal{M} = 1.1976917{\rm M_{\odot}}$, $q = 1.5$, $\tilde{\Lambda} = 488$, at different luminosity distances. A lower initial frequency or a closer source leads to improved precision in both the chirp mass and the mass ratio estimations.
• Figure 4: Posterior distributions for reduced tidal parameter $\tilde{\Lambda}$ with respect to snr, varying the injected luminosity distances, for eight fiducial binaries. The initial frequency is kept fixed to $f_0 = 5~{\rm Hz}$. As the snr increases, i.e. the luminosity distance decreases, the width of the distribution of $\tilde{\Lambda}$ shrinks.
• Figure 5: Posterior distributions for reduced tidal parameter $\tilde{\Lambda}$ with respect to snr, varying the initial frequencies of the detection, for eight fiducial binaries. The luminosity distance is kept fixed to $D_L=40~{\rm Mpc}$. As the snr increases, i.e. the initial frequency decreases, the width of the distribution of $\tilde{\Lambda}$ shrinks. Two different configurations of et, triangular Hild:2010idHild:2011np in orange and two-L Branchesi:2023mws in blue, give comparable results.