ar X iv : a st ro - p h / 99 08 14 7 v 1 1 3 A ug 1 99 9 Towards Understanding Jovian Planet Migration

We present 2D hydrodynamic simulations of circumstellar disks around protostars using a 'Piecewise Parabolic Method' (PPM) code. We include a point mass embedded within the disk and follow the migration of that point mass through the disk. Companions with masses Mc > ∼ 0.5M J can open a gap in the disk sufficient to halt rapid migration through the disk. Lower mass companions open gaps, but migration continues because sufficient disk mass remains close to the disk to exert large tidal torques. We find that the torques which dominate the migration of low mass planets originate within a radial region within 1–2 Hill radii of the planet's orbit radius, a distance smaller than the thickness of the disk. We conclude that a very high resolution 3D treatment will be required to adequately describe the planet's migration. 1 Initial conditions The PPM code and initial conditions are very similar to those presented in Nelson et al. 1998. We begin with a one M ⊙ pro-tostar fixed to the origin of our coordinate system. We assume that a disk of mass M D = 0.05M ⊙ is contained between the inner and outer grid boundaries at 0.5 AU and 20 AU and that the disk is self gravitating. A second point mass (the 'planet') is set in a circular orbit at a radius 5.2 AU away from the pro-tostar and is free to migrate through the disk in response to gravitational forces. No other forces act on the planet and it does not accrete mass from the disk. In different simulations, we investigate migration rates of different planet masses. The disk mass is distributed on a 128×224 cylindrical (r, φ) grid with a surface density given by a power law, Σ(r) = Σ 1 (1AU /r) p , where Σ 1 is determined from the assumed disk mass and p = 3/2. We assume an initial temperature profile with a similar power law, T (r) = T 1 (1AU /r) q , where the temperature at 1 AU is T 1 = 250 K and q = 1/2. These initial conditions produce a radial profile for which the minimum Toomre Q (of ∼ 5) is found near the outer disk edge. The profile exhibits a steep increase in the inner regions due to the increased effects of pressure on the orbital characteristics there. A single component isothermal gas equation of state is …