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, EF(e), 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 gn, the electron Landau level stability coefficient is introduced. According to the requirement that gn decreases with increasing the magnetic field intensity B, the magnetic field index β in the expression of EF(e) must be positive. By introducing the Dirac-δ function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to EF(e) in a superhigh magnetic field (SMF). This solution has a low magnetic field index of β=1/6, compared with the previous one, and works when ρ≥107g cm−3 and Bcr≪B≤1017 Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density ne, 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 B increases, more and more electrons will occupy higher Landau levels, though gn decreases with the Landau level number n. The enhanced ne 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.
