Disk Surface Density Transitions as Protoplanet Traps

Abstract

The tidal torque exerted by a protoplanetary disk with power-law surface density and temperature profiles onto anembedded protoplanetary embryois generally anegative quantity that leads to the embryoinward migration. Here we investigate how the tidal torque balance is affected at a disk surface density radial jump. The jump has two consequences:(1)Itaffects thedifferential Lindbladtorque.Inparticular,ifthediskismerelyemptyontheinnerside,the differential Lindblad torque almost amounts to the large negative outer Lindblad torque. (2) It affects the corotation torque, which is a quantity very sensitive to the local gradient of the disk surface density. In particular, if the disk is depleted on the inside and the jump occurs radially over a few pressure scale heights, the corotation torque is a positive quantity that ismuchlargerthan inapower-lawdisk.Weshow bymeans ofcustomized numerical simulations of low-massplanetsembedded inprotoplanetarynebulaewithasurfacedensity jump that thesecond effect isdominant; that is, that the corotation torque largely dominates the differential Lindblad torque on the edge of a central depletion, even a shallow one. Namely, a disk surface density jump of about 50% over 3–5 disk thicknesses suffices to cancel out the total torque. As a consequence, the type I migration of low-mass objects reaching the jump should be halted, and all these objects should be trapped there provided some amount of dissipation is present in the disk to prevent the corotation torque saturation. As dissipation is provided by turbulence, which induces a jitter of the planet semimajor axis, we investigate under which conditions the trapping process overcomes the trend of turbulence to induce stochastic migration across the disk. We show that a cavity with a large outer to inner surface density ratio efficiently traps embryos from 1 to 15 M� , at any radius up to 5 AU from the central object, in a disk that has same surface density profile as the minimum mass solar nebula (MMSN). Shallow surface density transitions require light disks to efficiently trap embryos. In the case of the MMSN, this could happen in the very central parts (r < 0:03 AU). We discusswhereinaprotoplanetarydiskonecanexpectasurfacedensityjump.Thiseffectcouldconstituteasolutionto the well-known problem that the buildup of the first protogiant solid core in a disk takes much longer than its type I migration toward the central object. Subject headings: accretion, accretion disks — hydrodynamics — methods: numerical — planetary systems: formation — planetary systems: protoplanetary disks