Planet–Disk Interactions

Tides come from the fact that different parts of a system do not fall in exactly the same way in a non-uniform gravity field. In the case of a protoplanetary disk perturbed by an orbiting, prograde protoplanet, the protoplanet tides raise a wake in the disk which causes the orbital elements of the planet to change over time. The most spectacular result of this process is a change in the protoplanet's semi-major axis, which can decrease by orders of magnitude on timescales shorter than the disk lifetime. This drift in the semi-major axis is called planetary migration, and is the most important aspect of planet–disk interactions. In this chapter, we first describe how the planet and disk exchange angular momentum and energy at the Lindblad and corotation resonances. Next we review the various types of planetary migration that have so far been contemplated: type I migration, which corresponds to low-mass planets (less than a few Earth masses) triggering a linear disk response; type II migration, which corresponds to massive planets (typically at least one Jupiter mass) that open up a gap in the disk; “runaway” or type III migration, which corresponds to sub-giant planets that orbit in massive disks; and stochastic or diffusive migration, which is the migration mode of low- or intermediate-mass planets embedded in turbulent disks. Third, we discuss questions linked to the planet eccentricity, in particular how the eccentricity is affected by the planet–disk interaction. Fourth, we discuss the various numerical schemes that have been used to describe planet–disk interactions. We discuss their strengths and weaknesses, and list the results that numerical simulations have achieved over the past decade.