Mass–radius relation and dynamical stability of strongly magnetized white dwarfs in anisotropic configuration using Bowers and Liang model

Abstract This paper concerned with the effect of anisotropic pressure in the mass–radius relation and dynamical stability for strongly magnetized white dwarfs using Bowers and Liang model. Strongly magnetized white dwarfs is hot topic where it is believed that it can be a progenitor for some peculiar type Ia supernovae that was observed recently. In order to get the equation of state we assumed that the internal magnetic field strength of the star is constant and strong enough to oblige the electrons to occupy the first Landau level. We dealt with the problem by using both relativistic and non-relativistic equilibrium equations. In non-relativistic formalism, the mass–radius relation of the star was investigated and it is found that the dynamical stability of the star does not depend on the radius but on the mass of the star. In relativistic formalism, it is found that the radius of the star decreases in comparison with non-relativistic case. Also the maximum mass limit of the star does not exceeds the non-relativistic one in isotropic case. Unfortunately, in both cases the predicted internal magnetic field of the star always exceeds the magnetic field strength that needed for the stability. This leads to weaken the stability of the star and making the star deviates from the spherical configuration to oblate spheroidal shape. Thus according to this model the magnetic white dwarfs configurations are unstable and unbound.