Strongly magnetized cold electron degenerate gas: Mass-radius relation
  of the magnetized white dwarf
  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
non-magnetic 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 2.3-2.6M_Sun,
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 2.4-2.8M_Sun, as their most likely progenitors.
Interestingly our results seem to lie within the observational limits.
