Constraining the Neutron-Star Equation of State via Short Gamma-Ray Burst X-ray Afterglows

TL;DR

This paper addresses constraining the neutron-star EOS by leveraging short gamma-ray burst X-ray internal plateaus as signatures of supramassive magnetar collapse to a black hole. It combines magnetar multipolar spin-down modeling with Kerr black-hole energy extraction to link the pre-collapse NS spin state and the post-collapse energy budget to an EOS-dependent critical mass $M_{ m crit}(\

Abstract

Recent observations from NICER in X-rays and LIGO/Virgo in gravitational waves have provided critical constraints on the mass, radius, and tidal deformability of neutron stars, imposing stringent limits on the equation of state (EOS) and the behavior of ultra-dense matter. However, several key parameters influencing the EOS, such as the maximum mass of neutron stars, spin-down rates, and the potential role of exotic matter in their cores, remain subject of ongoing debate. Here we present a new approach to constraining the EOS by analyzing the X-ray afterglows of some short gamma-ray bursts, focusing on "the internal plateau" phase and its abrupt decay, which reflect the spin-down and possible collapse of a supra-massive neutron star into a black hole. By linking critical neutron star masses with black hole formation criteria and the observational data from Swift's BAT and XRT instruments with compact object models, we explore three representative EOSs that range from "soft" to "stiff". Our result supports a maximum mass for neutron stars of approximately 2.39 solar masses at the threshold of black hole formation. This conclusion holds under assumptions of magnetar-powered X-ray plateaus, constant radiative efficiency, isotropic emission, and full Kerr black hole energy extraction; deviations could influence the inferred results. Our results demonstrate the critical role of neutron star/black hole physics in probing dense nuclear matter and provide a novel framework for exploring extreme astrophysical environments.

Figures (3)

• Figure 1: Schematic (not from simulation): The merger of two neutron stars (NSs) is a leading model for SGRBs. If the remnant's mass is low enough, it may become a SMNS through secular spin-down. The X-ray plateau phase in SGRBs suggests magnetic spin-down from a rapidly rotating, highly magnetized SMNS. The collapse of this SMNS into a BH likely causes the steep decline in X-ray flux observed at the plateau's end.
• Figure 2: A: NS spin-down energy as the primary energy source of the GRB afterglow. Initial spin period (P$_0$) and magnetic field components, are detailed in Table \ref{['table:List']}. The plot is presented on a logarithmic scale, and the residuals are expressed relative to the model-predicted luminosity: $\text{Residual} = \frac{\text{Observed Luminosity} - \text{Model-Predicted Luminosity}}{\text{Model-Predicted Luminosity}}$.
• Figure 3: The GM1 EOS, representing an intermediate stiffness, provides the best fit to observational data by minimizing the absolute difference $\Delta P = \bigl|\,P_{\rm NS}(t_{\rm co}) - P_{\rm BH}(t_{\rm co})\bigr|,$ where $P_{\rm NS}(t_{\rm co})$ is the spin period of the neutron star at collapse (from multipolar spin‑down) and $P_{\rm BH}(t_{\rm co})$ is the black‑hole spin period inferred from post‑plateau energy (see Section \ref{['sec:methods']}). GM1 yields the smallest average $\Delta P$, with only a marginal difference from TM1 ($M_{\rm max}=2.2\,M_\odot$), as indicated by $\Delta\langle\Delta P\rangle\sim10\%$. This corresponds to $M_{\rm crit}\approx2.3\pm0.1\,M_\odot$. The uncertainty on $M_{\rm crit}$ shrinks with broader temporal coverage, and when only the highest‑quality light curves are used, the best‑fit value shifts to $M_{\rm crit}\approx2.4\,M_\odot$ with noticeably smaller error bars.