Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view

In recent years a number of white dwarfs has been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (~ 10^{14} G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the energy density of matter) the number of Landau levels is restricted to one or two. We analyse the equation of states for magnetized electron degenerate gas analytically and attempt to understand the conditions in which transitions from the zero-th Landau level to first Landau level occur. We also find the effect of the strong magnetic field on the star collapsing to a white dwarf, and the mass-radius relation of the resulting star. We obtain an interesting theoretical result that it is possible to have white dwarfs with mass more than the mass set by Chandrasekhar limit.

💡 Research Summary

The paper addresses the intriguing possibility that white dwarfs (WDs) possessing extremely strong interior magnetic fields—potentially as high as 10¹⁴ gauss—can exceed the classical Chandrasekhar mass limit of ≈1.44 M☉. The authors begin by noting recent observations of surface magnetic fields in the range 10⁸–10⁹ G for several WDs, and argue that the magnetic field in the stellar core is likely amplified by flux conservation, reaching values orders of magnitude larger than the surface field.

The core of the analysis lies in the modification of the equation of state (EOS) for a relativistic, completely degenerate electron gas when Landau quantization becomes important. In a magnetic field B, the transverse motion of electrons is quantized into discrete Landau levels, with energy \