The magnetic coupling of planets and small bodies with a pulsar's wind

We investigate the electromagnetic interaction of a relativistic stellar wind with a planet or a smaller body in orbit around the star. This may be relevant to objects orbiting a pulsar, such as PSR B1257+12 and PSR B1620-26 that are expected to hold a planetary system, or to pulsars with suspected asteroids or comets. We extend the theory of Alfv\'en wings to relativistic winds. When the wind is relativistic albeit slower than the total Alfv\'en speed, a system of electric currents carried by a stationary Alfv\'enic structure is driven by the planet or by its surroundings. For an Earth-like planet around a "standard" one second pulsar, the associated current can reach the same magnitude as the Goldreich-Julian current that powers the pulsar's magnetosphere.