Inferring Neutron Star Nuclear Properties from Gravitational-Wave and Gamma-Ray Burst Observations

Technical Summary: Inferring Neutron Star Nuclear Properties from Gravitational-Wave and Gamma-Ray Burst Observations

Problem Statement
Recent observations of long-duration gamma-ray bursts (lGRBs) accompanied by kilonova emission (e.g., GRB 211211A, GRB 230307A) challenge the traditional paradigm that lGRBs arise solely from massive star collapse. If these events originate from binary neutron star (BNS) or neutron star–black hole (NSBH) mergers, a critical question arises: what physical property governs the duration of the burst? Theoretical models suggest that the total mass of the merger determines the lifetime of the merger remnant. Lighter mergers may form long-lived neutron star (NS) remnants that power short GRBs (sGRBs), while heavier mergers result in short-lived remnants that collapse into black holes (BHs), potentially powering lGRBs via massive accretion disks. However, the specific mass thresholds separating these outcomes and their relationship to fundamental nuclear properties, specifically the Tolman-Oppenheimer-Volkoff (TOV) mass ($M_{\text{TOV}}$), remain observationally unconstrained.

Methodology
The authors develop a Bayesian framework to infer characteristic mass scales by comparing gravitational-wave (GW) merger rates from the LIGO-Virgo-KAGRA (LVK) collaboration with the observed rates of sGRBs and kilonova-associated lGRBs.

1. Characteristic Mass Definitions: The study parameterizes three critical total mass thresholds relative to the TOV mass ($M_{\text{TOV}}$):

   • $M_{\text{VL}} = k_1 M_{\text{TOV}}$: The boundary between very long-lived and long-lived remnants.
   • $M_{\text{LS}} = k_2 M_{\text{TOV}}$: The boundary between long-lived and short-lived remnants. Mergers with $M_{\text{VL}} < M_{\text{tot}} \le M_{\text{LS}}$ are hypothesized to produce sGRBs.
   • $M_{\text{PC}} = k_3 M_{\text{TOV}}$: The boundary between short-lived remnants and prompt collapse. Mergers with $M_{\text{LS}} < M_{\text{tot}} \le M_{\text{PC}}$ are hypothesized to produce lGRBs. Mergers with $M_{\text{tot}} > M_{\text{PC}}$ undergo prompt collapse; lGRBs are produced only if the mass ratio ($q$) allows for sufficient disk formation ($1.2 \le q \le 3$ for BNS, $q \le 3$ for NSBH).

2. Data Sources:

   • GW Rates: The LVK GWTC-4 catalog (Abac et al. 2025a) and the FullPop-4.0 population model (Abac et al. 2025b) provide local merger rates as a function of component masses.
   • GRB Rates: Intrinsic rates for sGRBs ($R_{\text{sGRB}}$) and the rate ratio $\eta = R_{\text{lGRB}}/R_{\text{sGRB}}$ are treated as observational constraints with significant uncertainties, modeled via normal distributions.

3. Inference: Using Bayes' theorem, the authors infer the posterior distributions for the parameter set $\vec{\Theta} = (k_1, k_2, k_3, M_{\text{TOV}})$. The likelihood function compares the predicted GW-induced GRB rates (derived from the mass thresholds) against the observed GRB rates. Priors for $M_{\text{TOV}}$ and the NS radius at TOV mass ($R_{\text{TOV}}$) are drawn from Legred et al. (2021), conditioned on pulsar and GW observations.

Key Results

• Characteristic Mass Ratio ($k_2$): The analysis yields a median value of $k_2 = 1.36^{+0.08}_{-0.09}$ (68% confidence interval), with $k_2 > 1.24$ at 90% confidence. This indicates that the transition from long-lived to short-lived remnants occurs at approximately $1.36 M_{\text{TOV}}$.
• Implication for Remnant Lifetimes: The high value of $k_2$ suggests that massive neutron stars can survive for extended periods (hundreds of milliseconds) after merger before collapsing, rather than collapsing immediately.
• Correlations: The study identifies a strong correlation between $k_2$ and $k_3$, and an anti-correlation between $k_2$ and $M_{\text{TOV}}$. This anti-correlation allows constraints on the characteristic mass ratio $k_2$ to be directly mapped to upper limits on the TOV mass.
• Robustness: The inference of $k_2$ remains robust across a wide range of assumed sGRB rates ($30$ to $2000 \text{ Gpc}^{-3}\text{yr}^{-1}$) and rate ratios ($\eta$ from $0.01$ to $3$). Variations in mass ratio thresholds ($q_{\text{low}}$ and $q_{\text{high}}$) and the inclusion/exclusion of the $M_{\text{VL}}$ boundary have minimal impact on the inferred $k_2$.

Significance and Claims
The paper establishes a novel, independent method for constraining the neutron star equation of state (EoS) by linking GW merger populations to GRB durations. By identifying a characteristic mass scale ($1.36 M_{\text{TOV}}$) that separates sGRB and lGRB progenitors, the authors provide a direct observational constraint on the maximum mass of neutron stars.

The authors note that their findings are consistent with numerical relativity simulations (e.g., Perna et al. 2025) which predict a transition between $1.3$ and $1.4 M_{\text{TOV}}$. They emphasize that while current results are robust against observational uncertainties, future improvements in GW and GRB rate measurements, particularly joint detections of GRBs with GW events, will tighten the correlation between characteristic masses and $M_{\text{TOV}}$, potentially reducing the uncertainty on the TOV mass to $\sim 0.1 M_{\odot}$. This approach complements existing techniques and offers a pathway to place tighter limits on the NS EoS.