The Magnetohydrodynamic Stability of White Dwarfs and Neutron Stars

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Abstract
Vandakurov has recently suggested that, as a degenerate gas has an equation of state in which the pressure is essentially a function of density alone, an arbitrarily weak destabilizing magnetic field may lead to the occurrence of convection in superdense stars. It is pointed out here that, when thermal corrections to the equation of state are included, instability is unlikely to occur throughout a large region of such a star unless the magnetic pressure exceeds the thermal correction to the ideal degenerate pressure. In the case of white dwarfs it appears that the necessary magnetic fields for instability are several orders of magnitude stronger than those which are generally believed to exist in the stars. In contrast, it seems possible that strong enough magnetic fields to cause instability could be present in neutron stars and the problem appears to be worthy of more detailed study. The calculations have been performed assuming that the stellar material is a fluid. The possibility of crystallization in white dwarf interiors strengthens the view that magnetohydrodynamic instabilities are unlikely to be important. In a neutron star, the magnetic field may only be strongly coupled to the electrons and protons. If this is so, the probability of the occurrence of instability is affected only slightly but the character of the instability is changed.

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