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Aims. We investigate the evaporation of close-by pulsar companions, such as planets, asteroids, and white dwarfs, by induction heating.
Methods. Assuming that the outflow energy is dominated by a Poynting flux (or pulsar wave) at the location of the companions, we calculate their evaporation timescales, by applying the Mie theory.
Results. Depending on the size of the companion compared to the incident electromagnetic wavelength, the heating regime varies and can lead to a total evaporation of the companion. In particular, we find that inductive heating is mostly inefficient for small pulsar companions, although it is generally considered the dominant process.
Conclusions. Small objects like asteroids can survive induction heating for 10⁴yr at distances as small as 1R_☉ from the neutron star. For degenerate companions, induction heating cannot lead to evaporation and another source of heating (likely by kinetic energy of the pulsar wind) has to be considered. It was recently proposed that bodies orbiting pulsars are the cause of fast radio bursts; the present results explain how those bodies can survive in the pulsar's highly energetic environment.