Abstract
Super-massive white dwarf (WD) stars in the mass range 2.4 - 2.8 solar masses are believed to be the progenitors of “super-luminous” Type Ia supernovae according to a hypothesis proposed by some researchers. They theorize such a higher mass of the WD due to the presence of a very strong magnetic field inside it. We revisit their first work on magnetic WDs (MWDs) and present our theoretical results that are very different from theirs. The main reason for this difference is in the use of the equation of state (EoS) to make stellar models of MWDs. An electron gas in a magnetic field is Landau quantized and hence, the resulting EoS becomes non-polytropic. By constructing models of MWDs using such an EoS, we highlight that a strong magnetic field inside a WD would make the star super-massive. We have found that our stellar models do indeed fall in the mass range given above. Moreover, we are also able to address an observational finding that the mean mass of MWDs are almost double that of non-magnetic WDs. Magnetic field changes the momentum-space of the electrons which in turn changes their density of states (DOS), and that in turn changes the EoS of matter inside the star. By correlating the magnetic DOS with the non-polytropic EoS, we were also able to find a physical reason behind our theoretical result of super-massive WDs with strong magnetic fields. In order to construct these models, we have considered different equations of state with at most three Landau levels occupied and have plotted our results as mass-radius relations for a particular chosen value of maximum Fermi energy. Our results also show that a multiple Landau-level system of electrons leads to such an EoS that gives multiple branches in the mass-radius relations, and that the super-massive MWDs are obtained when the Landau-level occupancy is limited to just one level. Finally, our theoretical results can be explained solely on the basis of quantum and statistical mechanics that warrant no assumptions regarding stars.
Highlights
Several observations of “peculiar” Type Ia supernovae: SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc seem to indicate that their progenitor stars might be super-massive white dwarf (WD) with masses in the range 2.4 - 2.8 solar masses (M )
Magnetic field changes the momentumspace of the electrons which in turn changes their density of states (DOS), and that in turn changes the equation of state (EoS) of matter inside the star
We have established a crucial correlation between the DOS and the non-polytropic EoS of a cold, relativistic, degenerate electron gas in a magnetic field which is required to understand the possibility of having super-massive WD stars with strong magnetic fields inside them
Summary
Several observations of “peculiar” Type Ia supernovae: SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc seem to indicate that their progenitor stars might be super-massive WDs with masses in the range 2.4 - 2.8 solar masses (M ). We address the possibility of having super-massive WDs, having very strong, static and uniform magnetic field throughout, that violate the Chandrasekhar limit We do this by making stellar models of MWDs from a “non-polytropic” EoS and find that our theoretical results do concur with the observations. Each point on the plot implicitly represents a value of the Fermi energy EF , and the entire plot is generated by varying EF from EF = mc to EF = EFmax to ensure that the electron gas is relativistic throughout the star, except possibly for a very thin outer crust, which does not affect the main results of our work. The above equation can be re-written as dP dρ dρ dr
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