Inference of Neutron Star Mass Distributions and the Equation of State from Multi-messenger Observations

TL;DR

The paper develops a hierarchical Bayesian framework to jointly infer neutron star mass distributions across three astrophysical populations (DNS, NS-WD, LMXB) and the dense-matter equation of state (EoS) by combining multi-messenger observations, including GW events GW170817 and GW190425, EM mass-radius constraints, and direct NS mass measurements. It employs two high-density EoS parametrizations (a low-density core with either a piecewise polytrope or a fixed high-density sound speed) and models population masses with skewed normal distributions while handling measurement errors with asymmetric normals. A key finding is that the inferred maximum NS mass lies roughly in the range of 2.0–2.5 solar masses, with the posterior depending on the chosen EoS prior and whether M_max is treated as a parameter with a flat prior, which can shift the peak toward higher values. The analysis reveals distinct, population-dependent NS mass distributions and demonstrates the significant influence of EoS priors on both mass distributions and radii constraints when incorporating multi-messenger data, highlighting the need to account for prior choices in such inferences.

Abstract

We construct a combined model to incorporate neutron star (NS) mass measurements with electromagnetic mass-radius constraints and gravitational-wave observations using Bayesian inference. We use different mass distributions for three populations depending on the companion stars: double neutron stars, NS - white dwarfs, and low-mass X-ray binaries (LMXB). To observe the effects of different parametrizations, we use two equation of state (EoS) models: a piecewise polytrope and a fixed sound-speed model at high densities in combination with a low-density EoS. Our results show that the mass distributions of these NS populations are distinct and sensitive to the EoS prior choices. In addition, we show for the first time that using a uniform prior on the observable NS maximum mass, rather than a nuisance parameter in the unknown high-density EoS, shifts the posterior maximum mass to larger values. For polytropic EoSs, the maximum mass posterior changes from $M_\mathrm{max}=2.09_{-0.07}^{+0.18} M_\odot$ to $2.15_{-0.10}^{+0.19} M_\odot$ at 90% confidence level. This change in prior also impacts the shape of the mass distribution for NSs in LMXB, shifting the posterior for the population mean from $1.51_{-0.13}^{+0.13} M_\odot$ to $1.62_{-0.12}^{+0.15} M_\odot$ at 68% confidence level.

Figures (6)

• Figure 1: EoS models with $68\%$ (purple) and $95\%$ (orange) confidence levels. The color map shows locally normalized densities.
• Figure 2: Mass-radius curves for the corresponding EoS in figure \ref{['fig:eos']}, with $68\%$ (purple) and $95\%$ (orange) confidence levels. The color map shows locally normalized densities.
• Figure 3: The posterior distributions of the NS maximum mass. The modes are reported at the peaks and the means ($\mu_{\rm max}$ of $M_\mathrm{max}$) are given in the inset.
• Figure 4: Tidal deformability as a function of NS mass for each model, with $68\%$ (purple) and $95\%$ (orange) confidence levels. The color map shows locally normalized densities.
• Figure 5: The normalized mass distributions of NS populations (row-wise), grouped by the EoS models (column-wise). The contour lines represent $68\%$ (purple) and $95\%$ (orange) confidence levels. The statistics are reported in table \ref{['tab:dist']}.