Z. F. Gao

The effects of intense magnetic fields on Landau levels in a neutron star

In this paper, an approximate method of calculating the Fermi energy of electrons (EF(e)) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: EF(e) is related to density ρ, the mean electron number per baryon Ye and magnetic field strength B.

PRESSURE OF DEGENERATE AND RELATIVISTIC ELECTRONS IN A SUPERHIGH MAGNETIC FIELD

Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons, P-e, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynamic (QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows: P-e is related to the magnetic field B, matter density rho, and electron fraction Y-e; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of electrons in a superhigh magnetic field; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star (NS) due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star.

Numerical simulation of the electron capture process in a magnetar interior

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy E (E>Q, Q is the threshold energy of inverse β-decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient q and the effective electron capture rate Γeff. By using Γeff, the values of LX and Lν are calculated, where LX and Lν are the average neutrino luminosity of AXPs and the average X-ray luminosity of AXPs LX, respectively. The complete process of electron capture inside a magnetar is simulated numerically.

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

Based on the basic definition of the Fermi energy of degenerate and relativistic electrons, we obtain a special solution to the electron Fermi energy, EF(e), and express EF(e) as a function of the electron fraction, Ye, and matter density, ρ. We obtain several useful analytical formula for Ye and ρ 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, J, in nuclear astrophysics, a brief discussion on J and its slop is presented. Combining these fitting formula with boundary conditions for different density regions, we can evaluate the value of EF(e) in any given matter density, and obtain a schematic diagram of EF(e) as a continuous function of ρ. Compared with previous studies on the electron Fermi energy in other studies models, our methods of calculating EF(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 EF(e) and ne, 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.

Could the low-braking-index pulsar PSR J1734-3333 evolve into a magnetar?: GAO et al.

The low braking-index pulsar PSR J1734

Modified Fermi energy of electrons in a superhigh magnetic field

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Reinvestigation of the electron fraction and electron Fermi energy of neutron star: GAO et al

3333 could be born with superhigh internal magnetic fields

The relationship of electron Fermi energy with strong magnetic fields

B_{\rm in}\sim10^{15}-10^{16}

The surface and inner temperatures of magnetars

G, and undergo a supercritical accretion soon after its formation in a supernova explosion. The buried multipole magnetic fields will merger into a dipole magnetic field. Since the magnetic flow transfers from the core to the crust of the pulsar, its surface dipole field grows quickly at a power-law form assumed until it saturates at the level of internal dipole field. The increase in surface dipole magnetic field results in the observed low braking index of

Constraining the braking indices of magnetars

n=0.9(2)