Bayesian reconstruction of nuclear matter parameters from the equation of state of neutron star matter

The nuclear matter parameters (NMPs), those underlie in the construction of the equation of state (EoS) of neutron star matter, are not directly accessible. A Bayesian approach is applied to reconstruct the posterior distributions of NMPs from the EoS of neutron star matter. The constraints on lower-order parameters as imposed by the finite nuclei observables are incorporated through appropriately chosen prior distributions. The calculations are performed with two sets of pseudo data on the EoS whose true models are known. The median values of second- or higher-order NMPs show sizable deviations from their true values, and associated uncertainties are also larger. The sources of these uncertainties are identified as (i) the correlations among various NMPs and (ii) leeway in the EoS of symmetric nuclear matter, symmetry energy, and neutron-proton asymmetry which propagates into the posterior distributions of the NMPs.

Figure 1

Corner plots for marginalized posterior distributions of the NMPs which appear in the expansion of the EoS for the symmetric nuclear matter (top) and those in the density-dependent symmetry energy (bottom). The results are obtained for the model M1 with the prior set P2. One-dimensional posterior distributions (light blue) plotted along the diagonal plots are also compared with the corresponding prior distributions (light green). The vertical lines indicate the 68% confidence interval of the NMPs. The confidence ellipses for two-dimensional posterior distributions are plotted with $1\sigma , 2\sigma$, and $3\sigma$ confidence intervals.

Figure 2

Same as Fig. 1, but for model M2.

Figure 3

The EoS for symmetric nuclear matter (top) and the symmetry energy (bottom) as a function of density obtained within 95% confidence interval from the posterior distributions of nuclear matter parameters for models M1 and M2 for the prior set P2. The pseudodata for M1 and M2 are shown by triangles and squares, respectively.

Figure 4

Corner plots for the marginalized posterior distributions of nuclear matter parameters (in MeV) obtained from the EoS for the neutron star matter for the model M1 with prior set P2. The prior distributions (light green) are also plotted for the comparison.

Figure 5

Same as Fig. 4, but for the model M2.

Figure 6

Plots of 68% and 95% confidence intervals for the EoS for neutron star matter (top), the symmetric nuclear matter (middle), and the symmetry energy (bottom) as a function of scaled density for model M2 with prior set P2. The results are obtained from the posterior distributions of the NMPs which are reconstructed from the pseudodata for the EoS of neutron star matter( triangles). The spread in $\varepsilon (\rho ,0)$ and $J\left(\rho \right)$ are consistent with those for $\varepsilon (\rho ,\delta )$.

Figure 7

Plots of confidence ellipses with $1\sigma$ interval for the EoS for symmetric nuclear matter (top) and asymmetry parameter (bottom) as a function of symmetry energy at densities $\rho =4{\rho }_0$ and $6{\rho }_0$. The symbol tilde denotes that the corresponding quantity is obtained with respect to its median value.