The Interplay of Symmetry Energy Uncertainties, Nonlinear $\sigma-\delta$ Coupling, and Dark Matter in Neutron Star Macroscopic Properties
The poorly constrained density dependence of the nuclear symmetry energy introduces significant uncertainties in the equation of state (EOS) of dense nuclear matter and, consequently, in neutron-star properties. We systematically investigate how uncertainties in the symmetry energy $E_{\rm sym}$ and its slope $L$ at saturation density $n_0$ affect NS properties within the relativistic mean-field (RMF) framework, including the effects of nonlinear $\sigma$-$\delta$ coupling and possible admixture of dark matter(DM) . For fixed $E_{\rm sym}(n_0)$ and $L(n_0)$, we find that the $\sigma$-$\delta$ coupling with $g_{\sigma\delta}=-0.004$ induces an abnormal softening of the EOS, which simultaneously increasing the maximum NS mass and reducing the stellar radius and tidal deformability. A similar behavior is found in the presence of DM with Fermi momentum $k_F^{\rm DM}=50~\mathrm{MeV}$ at $E_{\rm sym}(n_0)=36~\mathrm{MeV}$. In this case, the RMF EOS satisfies the tidal-deformability constraint from GW170817. We further find that the surface curvature of NSs is strongly correlated with the stiffness of $E_{\rm sym}$, with softer symmetry energy corresponding to larger surface curvature. Our results also indicate that the behavior of $E_{\rm sym}$ around $n_0$ is mainly governed by isoscalar rather than isovector parameters.