Nearly model-independent constraints on dense matter equation of state in a Bayesian approach

We apply Bayesian approach to construct a large number of minimally constrained equations of state (EOSs) and study their correlations with a few selected properties of a neutron star (NS). Our set of minimal constraints includes a few basic properties of saturated nuclear matter and low-density pure neutron matter EOS which is obtained from a precise next-to-next-to-next-to-leading-order (N$^{3}$LO) calculation in chiral effective field theory. The tidal deformability and radius of NS with mass $1-2 M_\odot$ are found to be strongly correlated with the pressure of $\beta$-equilibrated matter at densities higher than the saturation density ($\rho_0 = 0.16$ fm$^{-3}$) in a nearly model-independent manner. These correlations are employed to parametrize the pressure for $\beta$-equilibrated matter, around 2$\rho_0$, as a function of neutron star mass and the corresponding tidal deformability. The maximum mass of neutron star is also found to be strongly correlated with the pressure of $\beta$-equilibrated matter at densities $\sim 4.5\rho_0$.