Reinvestigation of the electron fraction and electron Fermi energy of neutron star

Abstract

In this work, we reinvestigate the electron fraction $Y_e$ and electron Fermi energy $E_F(e)$ of neutron stars, based on our previous work of Li et al.(2016), in which we firstly deduced a special solution to $E_F(e)$, and then obtained several useful analytical formulae for $Y_{\mathrm{e}}$ and matter density $\rho$ within classical models and the relativistic mean field(RMF) theory using numerically fitting. The advantages of this work include the following aspects:(1) The linear functions are substituted for the nonlinear exponential functions used in the previous work. This method may be more simple, and closer to realistic equation of state\,(EoS) of a neutron star(NS), because there are linear or quasi-linear relationships between number fractions of leptons and matter density, which can be seen by solving NS EoS; (2)we introduce a dimensionless variable $\varrho$\,($\varrho =\rho /{\rho }_0$, ${\rho }_0$ is the standard saturated nuclear density), which greatly reduces the scope of the fitting coefficients;(3)we present numerical errors including absolute and relative deviations between the data and fit. By numerically simulating, we have obtained several analytical formulae for $Y_e$ and $\rho$ for both APR98 and RMF models. Combining these analytical formulae with the special solution, we can calculate the value of $E_{\mathrm{F}}(e)$ for any given matter density. Since $Y_e$ and $E_F(e)$ are important in assessing cooling rate of a NS and the possibility of kaon/pion condensation in the NS interior, this study could be useful in the future study on the thermal evolution of a NS.

arXiv comment3 figures, 3 tables , and We welcome any comment you might have about the content, To be published in Astron. Nachr

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