Relativistic Feynman-Metropolis-Teller Equation of State for White Dwarfs in presence of Magnetic Field

Abstract

The relativistic Feynman-Metropolis-Teller treatment of compressed atoms is extended to treat magnetized matter. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy which varies insignificantly with the magnetic field. In the relativistic treatment the limiting configuration is reached when the Wigner-Seitz cell radius equals the radius of the nucleus with a maximum value of the electron Fermi energy which can not be attained in presence of magnetic field due to the effect of Landau quantization of electrons within the Wigner-Seitz cell. This treatment is implemented to develop the Equation of State for magnetized White Dwarf stars in presence of Coulomb screening. The mass-radius relations for magnetized White Dwarfs are obtained by solving the general relativistic hydrostatic equilibrium equations using Schwarzschild metric description suitable for non rotating and slowly rotating stars. The explicit effects of the magnetic energy density and pressure contributed by a density-dependent magnetic field are included to find the stable configurations of magnetized Super-Chandrasekhar White Dwarfs.