Retention of Long-period Gas Giant Planets: Understanding Type II Migration

It was originally conceived that after protoplanets have acquired sufficient mass to open deep gaps in their natal protoplanetary disks, they cut off the global disk gas flow in their vicinity and their type II migration is coupled to the viscous evolution of the disk (Lin & Papaloizou 1986). Their mass growth is quenched around the thermal mass while they undergo substantial migration on the disk’s evolution timescale.

However, more recent numerical simulations indicate that gas giants’ migrations are not solely determined by the viscous diffusion of their natal disks since the gaps are never totally depleted and the viscous flow is never completely cut off by them. Kanagawa+ (2015, 2018) concluded a new paradigm of Type II migration, where the minimum gap density in the gap can be analytically expressed, and the migration torque is analogous to the Type I migration. This theory relies on the assumption that the gap is relatively shallow and wide such that most of contributing Lindblad resonances are merely “uniformly-dropped” to the bottom of the gap.

In Chen et al. (2020), we carried out a series of hydrodynamic simulations combined with analytic studies to examine different paradigms of Type II migration. We found the deep gap profiles induced by Jupiter-mass planets modify the location of Lindblad resonances in a complicated manner. High-order Lindblad torques closer to the planet are weakened by the gas depletion in the gap, while low-order Lindblad torques near the gap edges might preserve their magnitudes. When the gap is shallow, low-order torques from the gap edges is negligible compared to the sum of all other torques in the bottom, therefore the “uniform-drop” approximation is valid; When the gap is deep, however, the low-order torques from the gap edges dominate the total torques since the gap density their is larger by 2 or 3 orders of magnitude. The original asymmetry between inner and outer Lindblad torques (driving a planet on inward migration) arises from the fact that the inner resonances are farther from the planet than the corresponding outer resonances and have smaller influence, but for Jupiter-mass planet surrounded by deep gaps, higher surface density of the gas at distance farther from the planet makes up for this loss and might produce smaller inward total torques for certain surface density slopes, which slows down inward migration or even drives the planet on an outward migration unpredicted by analytical theories.