Modified Fermi energy of electrons in a superhigh magnetic field

Abstract

In this paper, we investigate the electron Landau level stability and its influence on the electron Fermi energy, [Formula: see text], in the circumstance of magnetars, which are powered by magnetic field energy. In a magnetar, the Landau levels of degenerate and relativistic electrons are strongly quantized. A new quantity [Formula: see text], the electron Landau level stability coefficient is introduced. According to the requirement that [Formula: see text] decreases with increasing the magnetic field intensity [Formula: see text], the magnetic field index [Formula: see text] in the expression of [Formula: see text] must be positive. By introducing the Dirac-[Formula: see text] function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to [Formula: see text] in a superhigh magnetic field (SMF). This solution has a low magnetic field index of [Formula: see text], compared with the previous one, and works when [Formula: see text] and [Formula: see text] Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density [Formula: see text], and decrease the maximum of electron Landau level number, which results in a redistribution of electrons. According to Pauli exclusion principle, the degenerate electrons will fill quantum states from the lowest Landau level to the highest Landau level. As [Formula: see text] increases, more and more electrons will occupy higher Landau levels, though [Formula: see text] decreases with the Landau level number [Formula: see text]. The enhanced [Formula: see text] in a SMF means an increase in the electron Fermi energy and an increase in the electron degeneracy pressure. The results are expected to facilitate the study of the weak-interaction processes inside neutron stars and the magnetic-thermal evolution mechanism for magnetars.