A magnetic mechanism for halting inward protoplanet migration: I. Necessary conditions and angular momentum transfer timescales

Abstract

A magnetic torque associated with the magnetic field linking a giant, gaseous protoplanet to its host pre-main-sequence star can halt inward protoplanet migration. This torque results from a toroidal magnetic field generated from the star’s poloidal (dipole) field by the twisting differential motion between the star’s rotation and the protoplanet’s revolution. Outside the corotation radius, where a protoplanet orbits slower than its host star spins, this torque transfers angular momentum from the star to the protoplanet, halting inward migration. Necessary conditions for angular momentum transfer include the requirement that the Alfven speed vA in the region magnetically linking a protoplanet to its host star exceeds the protoplanet’s orbital speed vK. In addition, the timescale for Ohmic dissipation τD must exceed the protoplanet’s orbital period P to ensure that the protoplanet is magnetically coupled to its host star. For a Jupiter-mass protoplanet orbiting a solar-mass pre-main-sequence star, vA>vK and τD>P only when the migrating protoplanet approaches within about 0.1 AU of its host star, primarily because of the rapid drop in the strength of the magnetic field with increasing distance from the central star. Because of this restricted reach, inwardly migrating gaseous protoplanets can be expected to “pile up” very close to their central stars, as is indeed observed for extrasolar planets. The characteristic timescale required for a magnetic torque to transfer angular momentum outward from a more rapidly spinning central star to a magnetically coupled protoplanet is found to be comparable to planet-forming disk lifetimes and protoplanet migration timescales.