Abstract
We consider the impact of electromagnetic induction and Ohmic heating on a
conducting planetary object that orbits a magnetic star. Power dissipated as
heat saps orbital energy. If this heat is trapped by an insulating crust or
mantle, interior temperatures increase substantially. We provide a quantitative
description of this behavior and discuss the astrophysical scenarios in which
it might occur. Magnetic fields around some main-sequence stars and white
dwarfs are strong enough to cause the decay of close-in orbits of asteroids and
dwarf planets, drawing them through the Roche limit on Myr time scales. We
confirm that Ohmic heating around neutron stars is driven by the rotation of
the stellar magnetic dipole, not orbital dynamics. In any case, heating can
raise interior temperatures of asteroids or dwarf planets on close-in orbits to
well above liquidus. Hot material escaping to the surface may lead to volcanic
ejections that can obscure the host star (as in the light curve of KIC 8462852)
and pollute its atmosphere (as observed with metal-rich white dwarfs). We
speculate that mixing of a volatile-rich mantle or crust with material from an
induction-heated core may lead to an explosion that could destroy the asteroid
prior to tidal break-up.
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