  (abridged) We find that a disk can supply a forming planet with mass at an
essentially infinite rate ($\sim1$\mj/25 yr) so that a gap could form very
quickly. We show that mass accretion rates faster than $\sim10^{-4}$\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 $\sim10$ 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 $\sim3-6$. 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.
