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.

General relativistic calculations for white dwarfs

“…They indicated that the presence of high magnetic fields can give rise to white dwarfs of masses as high as 2.3 − 2.6M ⊙ with radii around 600 km. 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.…”

The fundamental plane of black hole activity for quiescent sources

“…Dong et al (2014)) found that both “outliers” of BH XRBs and bright AGNs follow a steeper fundamental plane of black hole activity. Coriat et al (2011) argued that the two fundamental planes are regulated by radiatively inefficient (e.g., ADAF) and radiatively efficient accretion processes (e.g., SSD + corona), respectively, if we assume the jet launching and radio radiation behave identically (see also, Deng et al 2020; Gao et al 2011a; Fu et al 2020; Li et al 2016; Zhu et al 2016; Wang et al 2020).…”

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“…The Fermi energy of electrons inside an NS can have a direct impact not only on the weak‐interactions processes but also on the electron degeneracy pressure counteracting gravity collapse of the star. These impacts will in turn change intrinsic (e.g., Gao et al ; Liu ; Zhu et al ) EoS, internal structure, and heat evolution, and even influence the whole properties of the star. Thus, more attention has been paid to the two parameters above due to their importance.…”