The Critical Mass for Protoplanets Revisited: Massive Envelopes through Convection

Abstract

According to the nucleated instability hypothesis giant planets form by accreting planetesimals onto a core. As the core's gravity increases, gas from the solar nebula is attracted and the protogiant planet approaches a "critical" mass. Previous investigations found the values of the critical core and envelope masses to be insensitive to the outer boundary conditions. This is a consequence of the radiative stratification of their outer envelopes. This article shows that (a) some of the outer envelopes of published critical mass protoplanets are close to convective instability; (b) they become convectively unstable for properties of proposed solar nebula models. (c) The critical core and envelope masses for protoplanets with convective outer envelopes depend on the outer boundary conditions. (d) Critical mass protogiant planets with solar composition envelopes and "interstellar" dust opacities may have masses up to 60 earth masses (12 in the core). (e) Along a sequence with increasing solar nebula density the critical mass models become increasingly convective and justify (f) an analytical model for fully convective protogiant planets which explicitly shows the dependence of the critical mass on the outer boundary conditions.I propose two classes of protogiant planets: (1) a class with radiative outer envelopes and a constant Mcore/Mtot ratio at the critical mass and (2) a class with convective outer envelopes having a wide range (5-48 earth masses for the parameter range explored in this article) of critical envelope masses. The main difference of this new class to the fully convective models of F. Perri and A. G. W. Cameron (1974, Icarus 22, 416-425) lies in the opacity gap, where the stratification always remains radiative.