Bayesian inference of dense matter EOS encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars

TL;DR

This paper uses Bayesian inference with observational data to characterize the dense matter equation of state in neutron stars, revealing a likely first-order hadron-quark phase transition and a significant quark matter fraction in typical neutron stars.

Contribution

It introduces a Bayesian framework combining multiple observational data sets to constrain the dense matter EOS and the properties of the hadron-quark phase transition in neutron stars.

Findings

Most probable transition density is 1.6 times nuclear saturation density.

Quark matter fraction in a 1.4 solar mass neutron star peaks around 90%.

Quark matter speed of sound squared is likely close to the causal limit.

Abstract

[Purpose:] We infer the posterior probability distribution functions (PDFs) and correlations of nine parameters characterizing the EOS of dense neutron-rich matter encapsulating a first-order hadron-quark phase transition from the radius data of canonical NSs reported by LIGO/VIRGO, NICER and Chandra Collaborations. We also infer the quark matter (QM) mass fraction and its radius in a 1.4 M$_{\odot}$ NS and predict their values in more massive NSs. [Method:] Meta-modelings are used to generate both hadronic and QM EOSs in the Markov-Chain Monte Carlo sampling process within the Bayesian statistical framework. An explicitly isospin-dependent parametric EOS for the $npe\mu$ matter in NSs at $\beta$ equilibrium is connected through the Maxwell construction to the QM EOS described by the constant speed of sound (CSS) model of Alford, Han and Prakash. [Results:] (1) The most probable values of the hadron-quark transition density $\rho_t/\rho_0$ and the relative energy density jump there $\De\ep/\ep_t$ are $\rho_t/\rho_0=1.6^{+1.2}_{-0.4}$ and $\De\ep/\ep_t=0.4^{+0.20}_{-0.15}$ at 68\% confidence level, respectively. The corresponding probability distribution of QM fraction in a 1.4 M$_{\odot}$ NS peaks around 0.9 in a 10 km sphere. Strongly correlated to the PDFs of $\rho_t$ and $\De\ep/\ep_t$, the PDF of the QM speed of sound squared $\cQMsq/c^2$ peaks at $0.95^{+0.05}_{-0.35}$, and the total probability of being less than 1/3 is very small. (2) The correlations between PDFs of hadronic and QM EOS parameters are very weak. [Conclusions:] The available astrophysical data considered together with all known EOS constraints from theories and terrestrial nuclear experiments prefer the formation of a large volume of QM even in canonical NSs.