Numerically fitting the electron Fermi energy and the electron fraction in a neutron star

Abstract

Based on the basic definition of the Fermi energy of degenerate and relativistic electrons, we obtain a special solution to the electron Fermi energy, [Formula: see text], and express [Formula: see text] as a function of the electron fraction, [Formula: see text], and matter density, [Formula: see text]. We obtain several useful analytical formula for [Formula: see text] and [Formula: see text] within classical models and the work of Dutra et al. (2014) (Type-2) in relativistic mean-field theory are obtained using numerically fitting. When describing the mean-field Lagrangian, density, we adopt the TMA parameter set, which is remarkably consistent with the updated astrophysical observations of neutron stars (NSs). Due to the importance of the density dependence of the symmetry energy, [Formula: see text], in nuclear astrophysics, a brief discussion on [Formula: see text] and its slop is presented. Combining these fitting formula with boundary conditions for different density regions, we can evaluate the value of [Formula: see text] in any given matter density, and obtain a schematic diagram of [Formula: see text] as a continuous function of [Formula: see text]. Compared with previous studies on the electron Fermi energy in other studies models, our methods of calculating [Formula: see text] are more simple and convenient, and can be universally suitable for the relativistic electron regions in the circumstances of common neutron stars. We have deduced a general expression of [Formula: see text] and [Formula: see text], which could be used to indirectly test whether one equation of state of a NS is correct in our future studies on neutron star matter properties. Since URCA reactions are expected in the center of a massive star due to high-value electron Fermi energy and electron fraction, this study could be useful in the future studies on the NS thermal evolution.

General relativistic calculations for white dwarfs

“…It is interesting to mention that Gao et al (2013) and Zhu et al (2016) made a great deal of deliberations in this direction, particularly in the study of how the Fermi energy and the electron degeneracy pressure change in a neutron star due to the presence of a strong magnetic field. Gao et al (2013) and Li et al (2016) indicated that in the presence of a strong magnetic field the electron degeneracy pressure increases with strength of the magnetic field. This is because the pressure is proportional to E 4 F and the Fermi energy E F increases with the strength of the magnetic field.…”

The Dipole Magnetic Field and Spin-down Evolutions of the High Braking Index Pulsar PSR J1640–4631

“…As we know, the maximum NS mass predicted by EOSs is model dependent (e.g., Dutra et al 2014;Li et al 2016;Xia et al 2016;Xia & Zhou 2017;Zhou et al 2017). The largest sample of measured NS masses available for analysis is publicly accessible online at http://www.stellarcollapse.org/ and has been updated by J. Lattimer.…”

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

“…Our previous work (Li et al ) (“Li16” in short) was devoted to considering the electron Fermi energy and an associated value of the electron number fraction as functions of the matter density ρ within different layers of NS's crust and core of a common NS with B ≪ B cr (Li et al ; Gao et al ). Since the main purpose of this paper is to reinvestigate Y e and E F ( e ) inside an NS by revising Li16, it is necessary to briefly review Li16, which is provided below.…”