Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerically Fitting The Electron Fermi Energy and The Electron Fraction
  in A Neutron Star   Based on the basic definition of Fermi energy of degenerate and relativistic
electrons, we obtain a special solution to electron Fermi energy, $E_{\rm
F}(e)$, and express $E_{\rm F}(e)$ as a function of electron fraction, $Y_{e}$,
and matter density, $\rho$. Several useful analytical formulae for $Y_{e}$ and
$\rho$ 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 with the updated astrophysical observations
of neutron stars. Due to the importance of the density dependence of the
symmetry energy, $S$, in nuclear astrophysics, a brief discussion on the
symmetry parameters $S_v$ and $L$ (the slope of $S$) is presented. Combining
these fit formulae with boundary conditions for different density regions, we
can evaluate the value of $E_{\rm F}(e)$ in any given matter density, and
obtain a schematic diagram of $E_{\rm F}(e)$ as a continuous function of
$\rho$. Compared with previous study on the electron Fermi energy in other
models, our methods of calculating $E_{\rm F}(e)$ 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 $E_{\rm F}(e)$ and $n_{e}$, which could be used to indirectly
test whether one EoS 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.

20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
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The categories of this paper are: nucl-ex
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg