Bayesian Survey of the Dense Matter Equation of State built upon Skyrme effective interactions

Mikhail V. Beznogov, Adriana R. Raduta

Published 2023-08-29Version 1

The equation of state (EOS) is a key ingredient for understanding the structure and composition of neutron stars (NSs). Observation of several pulsars with masses $\approx$ 2 Msun, inference of tidal deformabilities from gravitational waves signals in binary neutron stars mergers and joint mass and radius estimates of two millisecond pulsars contributed to better constraining the behavior of NS EOS beyond the nuclear saturation density. We aim to build families of EOSs subjected to various minimal sets of constraints and identify the role some of these constraints play. We also aim to establish correlations between properties of nuclear matter (NM) and properties of NSs. The non-relativistic mean field theory of NM and the standard Skyrme parametrization of the nucleonic effective interactions are used to generate, within a Bayesian framework, models of EOSs. The constraints we pose come from empirical parameters of NM, ab initio calculations of pure neutron matter (PNM) and the 2 Msun lower limit on the maximum NS mass. EOSs also have to be causal. A purely nucleonic composition is hypothesized. EOSs are generated and investigated for five sets of constraints. Marginalized posteriors of the effective interaction's parameters; empirical parameters of NM; selected global properties of NSs are plotted and analyzed. Correlations among parameters in the isoscalar and isovector channels as well as with NS properties are studied. EOSs of NM and NSs are very sensitive to the set of constraints, including whether correlations among the values that the energy per nucleon in PNM takes at different densities are accounted for. In each of the five sets that we have generated there is a significant number of models that comply at 50\% credible region with joint mass and radius constraints from PSR J0030+045 and J0740+6620, while a tension exists with similar data from the NS in HESS J1731--34.