Magnetospheric Truncation, Tidal Inspiral, and the Creation of Short-period and Ultra-short-period Planets

Sub-Neptunes around FGKM dwarfs are evenly distributed in log orbital period down to ∼10 days, but dwindle in number at shorter periods. Both the break at ∼10 days and the slope of the occurrence rate down to ∼1 day can be attributed to the truncation of protoplanetary disks by their host star magnetospheres at corotation. We demonstrate this by deriving planet occurrence rate profiles from empirical distributions of pre-main-sequence stellar rotation periods. Observed profiles are better reproduced when planets are distributed randomly in disks—as might be expected if planets formed in situ—rather than piled up near disk edges, as would be the case if they migrated in by disk torques. Planets can be brought from disk edges to ultra-short (<1 day) periods by asynchronous equilibrium tides raised on their stars. Tidal migration can account for how ultra-short-period planets are more widely spaced than their longer-period counterparts. Our picture provides a starting point for understanding why the sub-Neptune population drops at ∼10 days regardless of whether the host star is of type FGK or early M. We predict planet occurrence rates around A stars to also break at short periods, but at ∼1 day instead of ∼10 days because A stars rotate faster than stars with lower masses (this prediction presumes that the planetesimal building blocks of planets can drift inside the dust sublimation radius).