Tight bound on neutron-star radius with quasiperiodic oscillations in short gamma-ray bursts

TL;DR

The paper links kilohertz QPOs observed in two short GRBs to postmerger HMNS oscillation modes, exploiting NR-derived quasiuniversal relations between postmerger frequencies and premerger parameters to perform Bayesian inference of redshift, chirp mass, and binary tidal deformability. From these posteriors, source-frame frequencies are reconstructed and mapped to NS radii via a quasiuniversal radius relation, yielding a tight constraint on the radius of a 1.4 solar-mass NS: $R_{1.4}=12.48^{+0.41}_{-0.40}$ km. This approach provides a novel, EOS-tightly constrained pathway to utilize GRB QPOs as probes of neutron-star matter, while acknowledging uncertainties in the QPO origin and the need for future multimessenger observations to validate the framework. The results are compatible with GW170817/NICER constraints and illustrate the potential of QPOs to complement traditional EOS inferences.

Abstract

Quasiperiodic oscillations (QPOs) have been recently discovered in the short gamma-ray bursts (GRBs) 910711 and 931101B. Their frequencies are consistent with those of the quasiradial and quadrupolar oscillations of binary neutron star merger remnants, as obtained in numerical relativity simulations. These simulations reveal quasiuniversal relations between the remnant oscillation frequencies and the tidal coupling constant of the binaries. Under the assumption that the observed QPOs are due to these postmerger oscillations, we use the frequency-tide relations in a Bayesian framework to infer the source redshift, as well as the chirp mass and the binary tidal deformability of the binary neutron star progenitors for GRBs 910711 and 931101B. We further use this inference to estimate bounds on the mass-radius relation for neutron stars. By combining the estimates from the two GRBs, we find a 68\% credible range $R_{1.4}=12.48^{+0.41}_{-0.40}$~km for the radius of a neutron star with mass $M=1.4$~M$_\odot$, which is one of the tightest bounds to date.

Figures (5)

• Figure 1: Top: $\ell=m=2$ waveform mode ($h_{22}$) for the postmerger GW signal (left) and the maximum rest-mass density for the postmerger remnant normalized by the maximum stable central density for a nonrotating star with that EOS (${\bar{\rho}}_{\rm max}\equiv\rho_{\rm max}/\rho_{\rm TOV}$) (right) from the merger of two NSs of mass $1.35$ M$_{\odot}$ described by the piecewise polytropic approximation to the SLy EOS 2009PhRvD..79l4032R. The vertical dashed lines indicate the merger time $t_{\rm merger}$ and final time $t_{\rm final}$ within which we perform the Fourier transform. Middle: Power spectral density (PSD) of $h_{22}$ (left) and ${\bar{\rho}}_{\rm max}$ (right) between $t_{\rm merger}$ and $t_{\rm final}$. The vertical dashed lines indicate the peak frequencies in the spectra, $f_{2}$ (left) and $f_{0}$ (right), while the dotted lines in the left panel shows the beat frequencies $f_{2}\pm f_{0}$. Bottom: Spectrogram for $h_{22}$ (left) and ${\bar{\rho}}_{\rm max}$ (right). Note that the frequencies are approximately constant during the time span of the analysis and $f_{0}$$\rightarrow$$\sim 0$ as $t$$\rightarrow$$\sim t_{\rm final}$ as expected since the remnant collapses to a black hole.
• Figure 2: Quasiuniversal relations ${\bar{f}}_{2}(\tilde{\Lambda})$ and $f_{02}(\tilde{\Lambda})$. We show the EOS variation (left, see the different colors) and mass-ratio ($q$) variation (right, see the colorbar) of these relations. The solid lines are the best fits for these relations (using the fitting function in Eq. \ref{['Qfit']}) and the dashed lines represent the $1\sigma$ ($68.3\%$) credible regions. We also show the relative residuals $(Q_{i}-Q^{\rm fit}_{i})/Q^{\rm fit}_{i}$, where $Q$$\in$$\{$${\bar{f}}_{2}$, $f_{02}$$\}$, for these relations and the corresponding 1$\sigma$ credible regions.
• Figure 3: Results for the parameter estimation using the observed QPOs (see Table \ref{['tab1']}) in GRBs 910711 (left) and 931101B (right), and the quasiuniversal relations ${\bar{f}}_{2}(\tilde{\Lambda})$ and $f_{02}(\tilde{\Lambda})$ (see Fig. \ref{['fig2']}). Off-Diagonal: 2D marginalized posterior probability distributions for $(\tilde{\Lambda},\mathcal{M})$, $(\mathcal{M},z)$, and $(z,\tilde{\Lambda})$. The three different color tones represent the 1$\sigma$ (68.3$\%$), 2$\sigma$ (95.4$\%$), and 3$\sigma$ (99.7$\%$) credible regions from dark to light. Diagonal: 1D marginalized posterior probability distributions (solid) as well as prior (dotted) for $\tilde{\Lambda}$, $\mathcal{M}$, and $z$. The dashed lines represent the median and the $\pm1\sigma$ values.
• Figure 4: Left: Posterior probability distributions for the radius of a 1.4 M$_{\odot}$ NS for GRB 910711, GRB 931101B, and both. The dashed lines represent the median and the $\pm1\sigma$ values. Right: Credible regions (1$\sigma$ and 2$\sigma$) on the mass-radius plane from the constraint for both GRBs. We also show the mass-radius curves for the EOSs used in the NR simulations, and the credible regions for the mass-radius measurements obtained from GW observations for GW170817 2018PhRvL.121p1101A, using parameterized EOS inference, and X-ray observations for PSR J0030+0451 ( e.g., 2019ApJ...887L..24M) and PSR J0740+6620 ( e.g., 2021ApJ...918L..28M).
• Figure 5: Mass-radius posterior distributions for the individual stars in the BNS systems which, according to our interpretation, produced the GRBs 910711 and 931101B. We show the 1$\sigma$, 2$\sigma$, and 3$\sigma$ credible regions (from dark to light) for the primary (blue) and secondary (red) stars. We also show the marginalized distributions for mass and radius in the top and right panels, where the dashed lines indicate the median and $\pm1\sigma$ values. We report the numerical results explicitly in the top right. The mass-radius curves for the EOSs are the same as in Fig. \ref{['fig4']}.