On the Early Evolution of Forming Jovian Planets II: Analysis of Accretion and Gravitational Torques

Abstract

(abridged) We find that a disk can supply a forming planet with mass at an essentially infinite rate ($\sim 1$\mj/25 yr) so that a gap could form very quickly. We show that mass accretion rates faster than $\sim 10^{-4}$\mj/yr are not physically reasonable in the limit of either a thin, circumplanetary disk or of a spherical envelope. Planet growth and ultimately survival are therefore limited to the planet's ability to accept additional matter, not by the disk in which it resides. We find that common analytic torque approximations predict values that are a factor $\sim 10$ larger than those obtained from the simulations. Accounting for the disk's vertical structure (crudely modeled through a gravitational softening parameter), small shifts in resonance positions due to pressure gradients, to disk self gravity and to inclusion of non-WKB terms in the analysis (Artymowicz 1993) reduce the difference to a factor $\sim 3-6$. Torques from the corotation resonances that are positive in sign contribute 20-30% or more of the net torque on the planet. The assumption of linearity underlying theoretical analyses is recovered in the simulations with planets with masses below 0.5\mj, but the assumption that interactions occur only at the resonances is more difficult to support. The detailed shape of the disk's response varies from pattern to pattern, making its true position less clear. We speculate that the finite width allows for overlap and mixing between resonances and may be responsible for the remainder of the differences between torques from theory and simulation, but whether accounting for such overlap in a theory will improve the agreement with the simulations is not clear.

arXiv comment52 pages including 20 figures. also available at http://www.maths.ed.ac.uk/~andy/publications.html

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