Self-gravitating Newtonian models of fermions with anisotropy and cutoff energy in their distribution function

Abstract

Systems of self-gravitating fermions constitute a topic of great interest in astrophysics, due to the wide field of applications. In this paper, we consider the gravitational equilibrium of spherically symmetric Newtonian models of collisionless semidegenerate fermions. We construct numerical solutions by taking into account the effects of the anisotropy in the distribution function and considering the prevalence of tangential velocity. In this way, our models generalize the solutions obtained for isotropic Fermi-Dirac statistics. We also extend the analysis to equilibrium configurations in the classical regime and in the fully degenerate limit, recovering, for different levels of anisotropy, hollow equilibrium configurations obtained in Maxwellian regime. Moreover, in the limit of full degeneracy, we find a direct expression relating the anisotropy with the mass of the particles composing the system.