Analyzing the dense matter equation of states in the light of the compact object HESS J1731-347

The recent mass ($0.77{\ifmmode\pm\else\textpm\fi{}}_{0.17}^{0.20}{M}_{\ensuremath{\bigodot}}$) and radius ($10.4{\ifmmode\pm\else\textpm\fi{}}_{0.78}^{0.86}\text{ }\text{ }\mathrm{km}$) measurement of HESS J1731-347 made it one of the most fascinating object if it is indeed a neutron star. In this work, we examine the current status of the dense matter equation of states in the context of this compact object being a neutron star. We use three sets of equation of states corresponding to the three classes---neutron stars, strange stars, and hybrid stars and perform Bayesian model selection on them. Our results show that for hadronic models, the equation of state is preferred to be stiff at the intermediate densities. This makes the Brueckner-Hartree-Fock approximation and models based on effective interactions deviate from current astrophysical observations on the inclusion of HESS J1731-347. Furthermore, for the strange star family, the equation of states composed of three flavor quarks prefers relatively smaller bag parameters. Analyzing the hybrid family of equation of states consisting of a first-order phase transition revealed preferences for early first-order phase transition. Comparing all the preferred equations of state among each family, it was found that the current astrophysical constraints prefer the hybrid equation of states the most.