The frames above are part of a movie (mpeg format, 3.2Mb)
that illustrates how planets
of different masses interact with the gaseous protoplanetary disk. In the animation,
the mass of a planet on a fixed circular orbit grows exponentially in time from an
initial mass of 3 Earth masses to a final mass of 10
Jupiter masses. Meanwhile, the response of a viscous protoplanetary disk is calculated
using a high resolution 2D hydrodynamic simulation, and displayed in an almost
corotating frame. The actual simulation ran for more than 600 orbits (far too
many to display in an inertial frame), so the disk response to each mass planet is
almost in a steady state. Three distinct stages can be identified:
(1) Low mass planets: For the lowest mass planets, the gravitational interaction
between the planet and the gas disk is relatively weak. The planet excites a trailing
spiral wave in the disk, and experiences a gravitational torque from the resulting
perturbation to the disk surface density. In a real disk, this loss of angular momentum
would cause the planet's orbit to decay, a process known as Type I orbital migration.
This doesn't happen in the movie because the orbit is artifically kept fixed (and
anyway the time scale of the simulation is too short for significant migration). The
surface density profile of the disk (shown as function of radius in the inset graph)
is not significantly modified by the presence of the planet at this stage.
(2) Gap opening: As the planet mass grows, the strength of the resonant
interaction with the gas disk increases. The exchange of angular momentum repels
gas away from near the planet's orbit, creating an annular gap where the
disk surface density is lower than it would be in the absence of the planet. At first,
as shown in the middle frame above, the gap is only partially evacuated of gas. The
details of how the remaining gas in the coorbital region interacts with the planet
in this regime remain unclear.
(3) Type II migration: Once the planet's mass is high enough (above a Jupiter
mass for the particular parameters of this simulation), its gravitational interaction
with the disk succeeds in forming a deep, clean gap. Some gas continues to overflow
the gap edges and is captured within the Hill sphere of the planet, adding to the
planet mass. The rate of mass growth due to accretion across gaps decreases as the
planet grows, at least if the orbital eccentricity remains small. The overall
exchange of angular momentum between the planet and disk is now governed by
the viscous evolution of the disk, and the planet is expected to migrate in the
same sense as the disk gas (usually inward at small radii) while maintaining
its position within a gap.
For more details see Planetary migration, a
review for STScI's 2005 May Symposium "A Decade Of Extrasolar Planets Around Normal Stars".