Astrophysical assumptions and equation of state framework have larger impact on equation of state inference than individual neutron star observations

TL;DR

This paper tackles how implicit astrophysical priors and the choice of nuclear equation-of-state (EoS) parameterization affect inferences drawn from neutron-star observations. Using a hierarchical Bayesian framework and a HyperPipe-enabled sampling approach, it combines galactic pulsars, NICER mass-radius constraints, and GW170817 within two simple EoS representations (Γ-spectral and Υ-spectral) and explicit NS population models. It demonstrates that population priors, particularly for GW sources, can shift the inferred radius R1.4 by about 0.5 km and qualitatively alter the mass-radius relation, far exceeding the ~0.1 km shift from adding individual observations. The work further shows that the Υ-spectral parameterization can imply a phase-transition-like feature near densities around 10^14.5 g cm^-3, and that including auxiliary data like the HESS source yields only modest changes, underscoring the predominance of population and model choices in current EOS inferences and the need for systematic handling of these factors in multi-messenger analyses.

Abstract

The wide range of nuclear densities achieved in neutron stars makes them probes of dense nuclear behavior in the form of the nuclear equation of state (EoS). Studying neutron stars both in isolation, with X-ray measurements and pulse profiling, and in dynamic events, such as neutron star mergers, have provided insight into these high nuclear densities. Though nominally congruent, here we highlight impact of implicit assumptions embedded in joint analysis of these messengers and their systematic impact on EoS inference. We show that astrophysical assumptions and EoS framework can have a larger effect on inferred EoS than individual contemporary neutron star observations. Performing a proof-of-concept demonstration using the chronologically first few observational constraints, after the application of 5 to 6 observational constraints, additional observations provided diminishing returns and modified the inferred EoS by shifting the radius of a 1.4 $\unit{M_\odot}$ NS by $\sim$ 0.1 km. By contrast, astrophysical priors, specifically the spin and mass ratio motivated by astrophysical source population uncertainties, and EoS framework tend to impact EoS inference much more substantially by shifting the 1.4 $\unit{M_\odot}$ NS radius by $\sim$ 0.5 km and by modifying shape of inferred mass-radius relationship. The inferred EoS depends strongly on the adopted choice of spectral parameterizations: when we employ a framework which explicitly enforces causality, we find a strong phase-transition-like feature at $\sim 10^{14.5}$ g cm$^{-3}$.

Figures (19)

• Figure 1: Methodology Mass-Radius likelihoods evaluated for sample cold nuclear EoSs. The pulsar constraints used for the likelihoods are shown in the background in various colors. Darker colors of the M-R curves indicate higher $\log$ likelihood for each EoS. The EoS with the lowest likelihood is represented with a dashed curve. The red and purple patches are the posterior samples from NICER pulse profile of PSR-J0030 and the HESS-J1731 respectively. The horizontal color bands are mass constraints of J0740, J0348, J1614.
• Figure 2: Priors Pressure $p$ versus energy density $\rho$ for cold nuclear matter prior utilized. The shaded region shows the 100% credible interval implied by our fiducial prior on the $\Gamma$-spectral model (blue) and $\Upsilon$-spectral model (orange). Also shown are several fiducial equations of state in dashed and dotted curves, for reference. Top panel: Pressure-Density priors for the causal and regular spectral representations along with five fiducial EoSs. The interval shown encompasses all draws from our prior (here, shown for $10^4$ samples). Bottom panel: Mass-Radius prior range for the EoSs in the above range. The grey shaded regions indicate various constraints on single-stable NS; 'BH limit' is where the Schwarzchild radius is larger than the NS radius, 'Buchdahl limit' is the range where an NS would need infinite pressure PhysRev.116.1027, and 'Causality limit' is obtained by finding the maximally compact (M/R) solution for Mass-Radius in the limiting physical range of pressure-density 2012ARNPS..62..485L.
• Figure 3: Marginal likelihood for symmetry energy: scatterplot of the symmetry energy likelihood evaluated for many $\Gamma$-spectral EoS realizations, versus the corresponding $R_{1.4}, M_{max}$ evaluated for the same EoS realizations. Roughly speaking and within the context of this model family, this symmetry energy constraint favors smaller radii at each fixed $M_{max}$.
• Figure 4: Top panel: Likelihood ${\cal Z}$ versus $R_{1.4}$ deduced by comparing realizations of the $\Gamma$ spectral EoS family to the NICER mass-radius constraints of J0030 (blue) and HESS J1731 (orange) Bottom panel: Likelihood ${\cal L}$ versus $M_{max}$. The blue solid, black dashed, and orange dash-dotted lines show Eq. (\ref{['eq:L_mmax']}), evaluated for each known pulsar mass. The dark-red points show a direct evaluation using realizations of the $\Gamma$ spectral EoS family to the pulsar J0348, for expediency using lalsuite rather than RePrimAnd to evaluate $M_{max}$ for each EoS. The dotted green line shows the hypothesized lower bound on the maximum mass implied by prompt collapse to a black hole; see Section \ref{['sec:sub:ext']} for discussion.
• Figure 5: EoS inference from galactic pulsars and symmetry energy, $\Gamma$-spectral family: Marginal posterior distribution for the combined inference of observations PSRs J0030, J0348, J0740, J1614, and applying the PREX symmetry energy constraint. Top-left panel: Distribution of $\Gamma$-spectral hyperparameters. Color scale shows the marginal likelihood, with red indicating the largest values and the solid contour shows the 90% credible interval, while one-dimensional histograms show a one-dimensional marginal distribution. Top-right panel: 90% credible interval of pressure versus density, evaluated at each density. Bottom panel: 90% credible interval for radius evaluated at each NS mass, rendered as mass versus radius. In the figures in the top-right and bottom the 98% interval of the region covered by the initial samples supplied to HyperPipe is also shown.