Density curvature, skewness, and kurtosis of the nuclear symmetry energy and their impact on the compactness and tidal deformability of neutron stars

We investigate the influence of the density curvature, skewness, kurtosis, and the higher order isoscalar and isovector coefficients of the density and isospin dependence of the equations of state (EOSs) of nuclear matter (NM) to the structure properties of neutron stars (NSs). We consider nuclear EOSs derived from the semi-realistic M3Y nucleon-nucleon interaction, which describes NM of increasing stiffness, characterized by isoscalar incompressibility ${K}_{0}=150\ensuremath{-}330\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. We find that increasing ${K}_{0}$ and the fourth-order skewness coefficient ${Q}_{4}$, and decreasing the negativity of the isoscalar ${Q}_{0}$ and kurtosis ${H}_{0}$ coefficients and that of the isovector ${K}_{4}, {I}_{2}, {G}_{2}$, and ${K}_{\ensuremath{\tau}4}$ coefficients, increases the estimated NS radius, its tidal deformability, tidal Love number of the NS ($M\ensuremath{\ge}{\text{M}}_{\ensuremath{\bigodot}}$), and the speed of sound (${v}_{s}$) through the center of the NS ($\ensuremath{\le}$ 1.4 ${\text{M}}_{\ensuremath{\bigodot}}$), as well as the maximum mass ${M}_{\mathrm{max}}$ (NS) predicted based on a given EOS, and its corresponding maximum compactness and surface redshift ${z}_{\text{surf}}$ (${M}_{\mathrm{max}}$), but this indicates less compactness and ${z}_{\text{surf}}$ of a given NS, and less minimum tidal Love number ${k}_{2,\mathrm{min}}$ (${M}_{\mathrm{max}}$) and tidal deformability ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{min}}$ (${M}_{\mathrm{max}}$). Meanwhile, increasing the ${I}_{0}, {G}_{0}, {Q}_{2}, {K}_{6}, {H}_{2}$, and ${K}_{\ensuremath{\tau}6}$ (decreasing the negativity of the ${K}_{2}$ and ${K}_{\ensuremath{\tau}2}$) coefficients inverts the behavior of the NS quantities with ${K}_{0}$ and with the aforementioned coefficients. The values of the mentioned coefficients are estimated based on combined constraints from the observed NS masses, the causality condition on ${v}_{s}$, the threshold proton fraction needed for a direct Urca process, and those given on the NM pressure from matter flow data. The values of the isoscalar (quadratic isovector) incompressibility, skewness, and kurtosis coefficients anticipated from these combined constraints are ${K}_{0}=260\ifmmode\pm\else\textpm\fi{}20\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ (${K}_{2}=\ensuremath{-}28\ifmmode\pm\else\textpm\fi{}4\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$), ${Q}_{0}=\ensuremath{-}361\ifmmode\pm\else\textpm\fi{}127\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ (${Q}_{2}=403\ifmmode\pm\else\textpm\fi{}23\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$), and ${I}_{0}=992\ifmmode\pm\else\textpm\fi{}402\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ (${I}_{2}=\ensuremath{-}4849\ifmmode\pm\else\textpm\fi{}49\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$), and the isobaric isospin-asymmetry coefficients of incompressibility are estimated to be ${K}_{\ensuremath{\tau}2}=\ensuremath{-}248\ifmmode\pm\else\textpm\fi{}33\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}, \ensuremath{-}46\ensuremath{\le}\phantom{\rule{4pt}{0ex}}{K}_{\ensuremath{\tau}4}$ (MeV) $\ensuremath{\le}$ 34, and ${K}_{\ensuremath{\tau}6}=\ensuremath{-}38\ifmmode\pm\else\textpm\fi{}6\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$.