Termination of Planetary Accretion Due to Gap Formation

The process of gap formation by a growing planetary embryo embedded in a planetesimal disk is considered. It is shown that there exists a single parameter characterizing this process, which represents the competition between the gravitational influence of the embryo and planetesimal-planetesimal scattering. For realistic assumptions about the properties of the planetesimal disk and the planetary embryo, a gap is opened long before the embryo can accrete all the bodies within its region of influence. The implication of this result is that the embryo slows its growth considerably and, thus, large bodies formed during the coagulation stage should be less massive than is usually assumed. For conditions expected at 1 AU in the solar protoplanetary disk, gap formation is expected to occur around bodies of mass ≲10 24 g. The effect of protoplanetary radial migration is also discussed.