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On the Early Evolution of Forming Jovian Planets. I. Initial Conditions, Systematics, and Qualitative Comparisons to Theory

We analyze the formation and migration of an already formed proto-Jovian companion embedded in a circumstellar disk. We use two-dimensional (r,θ) hydrodynamic simulations using a piecewise parabolic method code to model the evolutionary period in which the companion makes its transition from type I migration to type II migration. The results of our simulations show that spiral waves extending several wavelengths inward and outward from the planet are generated by the gravitational torque of the planet on the disk. Their effect on the planet causes it to migrate inward toward the star, and their effect on the disk causes it to form a deep (low surface density) gap near the planet. We study the sensitivity of the planet's migration rate to the planet's mass and to the disk's mass. Until a transition to slower type II migration, the migration rate of the planet is of order 1 AU per 103 yr and varies by less than a factor of 2 with a factor of 20 change in planet mass, but it depends near linearly on the disk mass. Although the disk is stable to self-gravitating disk perturbations (Toomre Q > 5 everywhere), implying that the effects of gravity should be insignificant, migration is faster by a factor of 2 or more when disk self-gravity is suppressed. Migration is equally sensitive to the disk's mass distribution within 1-2 Hill radii of the planet, as demonstrated by our simulations' sensitivity to the planet's assumed gravitational softening parameter, which also crudely models the effect of the disk's extent into the third (z) dimension. Deep gaps form within ~500 yr after the beginning of the simulations, but migration can continue much longer: the formation of a deep gap and the onset of type II migration are not equivalent. The gap is several AU in width and displays very nearly the M proportionality predicted by theory. Beginning from an initially unperturbed 0.05 M☉ disk, planets of mass Mpl > 0.3MJ can open a gap that is deep and wide enough to complete the transition to slower type II migration. Lower mass objects continue to migrate rapidly for the duration of the simulation, eventually impacting the inner boundary of our grid. This transition mass is much larger than that predicted as the "Shiva mass" discussed in Ward & Hahn, making the survival of forming planets even more precarious than they would predict.