On the origin of the sub-Jovian desert in the orbital-period--planetary-mass plane

Abstract

Transit and radial velocity observations indicate a dearth of sub-Jupiter--mass planets on short-period orbits, outlined roughly by two oppositely sloped lines in the period--mass plane. We interpret this feature in terms of high-eccentricity migration of planets that arrive in the vicinity of the Roche limit, where their orbits are tidally circularized, long after the dispersal of their natal disk. We demonstrate that the two distinct segments of the boundary are a direct consequence of the different slopes of the empirical mass--radius relation for small and large planets, and show that this relation also fixes the mass coordinate of the intersection point. The period coordinate of this point, as well as the detailed shape of the lower boundary, can be reproduced with a plausible choice of a key parameter in the underlying migration model. The detailed shape of the upper boundary, on the other hand, is determined by the post-circularization tidal exchange of angular momentum with the star and can be reproduced with a stellar tidal quality factor \(Q^\prime_*\sim10^6\).