Context. White dwarfs are the last evolutionary stage for the majority of main-sequence stars. With nuclear burning having ceased, these stars are slowly cooling. There is observational evidence indicating that planetary remnants, and possibly even planets, orbit a considerable fraction of the known white dwarf population. These objects are interesting targets for transit observations due to their large planet-to-star radius ratio. Especially interesting is the possible outgassing from such objects and their eventual observational prospects.
Aims. Here, we investigate whether electromagnetic induction heating can drive additional volcanic outgassing from small planetary remnants orbiting white dwarfs. This mechanism can be important for such bodies in addition to tidal heating due to the extremely strong magnetic fields of some white dwarfs and close orbital distances of planets to their host stars.
Methods. We calculated the heating and related magmatic effects for a Moon-sized body around a magnetized white dwarf using an analytical model for induction heating and a numerical model for interior processes. We also calculated induction heating inside asteroid-sized bodies.
Results. We show that induction heating can melt the mantle of a Moon-sized object within a geologically short time and contribute to desiccation of small asteroids on extremely tight orbits. These findings can have important implications for the evolution of rocky bodies orbiting white dwarfs and the potential detection of their outgassing.
