Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf

Abstract

We consider a relativistic, degenerate electron gas at zero temperature under the influence of a strong, uniform, static magnetic field, neglecting any form of interactions. Since the density of states for the electrons changes due to the presence of the magnetic field (which gives rise to Landau quantization), the corresponding equation of state also gets modified. In order to investigate the effect of very strong magnetic field, we focus only on systems in which a maximum of either one, two, or three Landau level(s) is/are occupied. This is important since, if a very large number of Landau levels are filled, it implies a very low magnetic field strength which yields back Chandrasekhar's celebrated nonmagnetic results. The maximum number of occupied Landau levels is fixed by the correct choice of two parameters, namely, the magnetic field strength and the maximum Fermi energy of the system. We study the equations of state of these one-level, two-level, and three-level systems and compare them by taking three different maximum Fermi energies. We also find the effect of the strong magnetic field on the mass-radius relation of the underlying star composed of the gas stated above. We obtain an exciting result that it is possible to have an electron-degenerate static star, namely, magnetized white dwarfs, with a mass significantly greater than the Chandrasekhar limit in the range $2.3--2.6{M}_{\ensuremath{\bigodot}}$, provided it has an appropriate magnetic field strength and central density. In fact, recent observations of peculiar type Ia supernovae---SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg---seem to suggest super-Chandrasekhar-mass white dwarfs with masses up to $2.4--2.8{M}_{\ensuremath{\bigodot}}$ as their most likely progenitors. Interestingly, our results seem to lie within these observational limits.