Mass-radius relation for strongly magnetized white dwarfs with anisotropy

In this work the effect of anisotropic pressure that is produced in magnetized white dwarfs due to its magnetic field is investigated. For simplicity, we transacted with the anisotropic pressure and the radial pressure on an equal footing in order to recover the covariance form of the hydrodynamical and Lane-Emden equations. The equation of state of degenerate electrons in strong magnetic field, that takes a polytropic form in ultra-relativistic regime for a system containing one occupied Landau level, is used to calculate a new mass-radius relation of the magnetized white dwarf. Results show that the mass of the star increases with anisotropy and the upper limit mass is disappeared. Also the radius of the star decreases with increasing the strength of the magnetic field or the internal energy of the star at the same mass. Our results may explain recent observations of a peculiar type Ia supernova, that has an extraordinary higher luminosities and lower kinetic energy, which suggests that their progenitor mass lie in the range 2.1-2.8M⊙. This mass range is much higher than the famous Chandrasekhar mass limit.