Bayesian Inference of High-density Nuclear Symmetry Energy from Radii of Canonical Neutron Stars

The radius $R_{1.4}$ of neutron stars (NSs) with a mass of 1.4 M$_{\odot}$ has been extracted consistently in many recent studies in the literature. Using representative $R_{1.4}$ data, we infer high-density nuclear symmetry energy $E_{\rm{sym}}(\rho)$ and the associated nucleon specific energy $E_0(\rho)$ in symmetric nuclear matter (SNM) within a Bayesian statistical approach using an explicitly isospin-dependent parametric Equation of State (EOS) for nucleonic matter. We found that: (1) The available astrophysical data can already improve significantly our current knowledge about the EOS in the density range of $\rho_0-2.5\rho_0$. In particular, the symmetry energy at twice the saturation density $\rho_0$ of nuclear matter is determined to be $E_{\mathrm{sym}}(2\rho_0)$ =39.2$_{-8.2}^{+12.1}$ MeV at 68\% confidence level. (2) A precise measurement of the $R_{1.4}$ alone with a 4\% 1$\sigma$ statistical error but no systematic error will not improve much the constraints on the EOS of dense neutron-rich nucleonic matter compared to what we extracted from using the available radius data. (3) The $R_{1.4}$ radius data and other general conditions, such as the observed NS maximum mass and causality condition introduce strong correlations for the high-order EOS parameters. Consequently, the high-density behavior of $E_{\rm{sym}}(\rho)$ inferred depends strongly on how the high-density SNM EOS $E_0(\rho)$ is parameterized, and vice versa. (4) The value of the observed maximum NS mass and whether it is used as a sharp cut-off for the minimum maximum mass or through a Gaussian distribution affect significantly the lower boundaries of both the $E_0(\rho)$ and $E_{\rm{sym}}(\rho)$ only at densities higher than about $2.5\rho_0$.