Migration of massive planets in accreting disks

Massive planets that open a gap in the accretion disk are believed to migrate with exactly the viscous speed of the disk, a regime termed type II migration. Population synthesis models indicate that standard type II migration is too rapid to be in agreement with the observations. We study the migration of massive planets between $2\times10^{-4}$ and $2\times10^{-3} M_\odot$ corresponding to 0.2 to 2 Jupiter masses $M_J$. in order to estimate the migration rate in comparison to type II migration. We follow the evolution of planets embedded in two-dimensional, locally isothermal disks with non-zero mass accretion which is explicitly modelled using suitable in- and outflow boundary conditions to ensure a specific accretion rate. After a certain relaxation time we release the planet and measure its migration through the disk and the dependence on parameters such as viscosity, accretion rate and planet mass. We study accreting and non-accretion planets. The inferred migration rate of the planet is determined entirely by the disk torques acting on it and is completely independent of the viscous inflow velocity, so there is no classical type II migration regime. Depending on the local disk mass the migration rate can be faster or slower than type II migration. From the torques and the accretion rate profile in the disk we see that the gap formed by the planet does not separate the inner from the outer disk as necessary for type II migration, rather gas crosses the gap or is accreted onto the planet.