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.

💡 Research Summary

The paper investigates how a strong, uniform, static magnetic field modifies the equation of state (EOS) of a relativistic, completely degenerate electron gas at zero temperature, and consequently how this altered EOS affects the mass‑radius relation of a white dwarf composed of such matter. In the presence of a magnetic field, the transverse motion of electrons is quantized into Landau levels, while motion parallel to the field remains continuous. This quantization changes the density of states and therefore the pressure‑density relationship. The authors restrict their analysis to the extreme cases where only one, two, or three Landau levels are occupied. These cases correspond to magnetic field strengths so high (of order 10⁹ Tesla) that the spacing between Landau levels exceeds the electron Fermi energy, ensuring that higher levels remain empty.

The electron energy spectrum is taken as

Eₙ(p_z)=√