Paper: astro-ph/0511082
Date: Wed, 2 Nov 2005 17:35:28 GMT (294kb)

Title: On the width and shape of gaps in protoplanetary disks

Authors: A. Crida, A. Morbidelli, F. Masset

Comments: 22 pages, 13 figures, ICARUS, in press
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Although it is well known that a massive planet opens a gap in a
proto-planetary gaseous disk, there is no analytic description of the surface
density profile in and near the gap. The simplest approach, which is based upon
the balance between the torques due to the viscosity and the gravity of the
planet and assumes local damping, leads to gaps with overestimated width,
especially at low viscosity. Here, we take into account the fraction of the
gravity torque that is evacuated by pressure supported waves. With a novel
approach, which consists of following the fluid elements along their
trajectories, we show that the flux of angular momentum carried by the waves
corresponds to a pressure torque. The equilibrium profile of the disk is then
set by the balance between gravity, viscous and pressure torques. We check that
this balance is satisfied in numerical simulations, with a planet on a fixed
circular orbit. We then use a reference numerical simulation to get an ansatz
for the pressure torque, that yields gap profiles for any value of the disk
viscosity, pressure scale height and planet to primary mass ratio. Those are in
good agreement with profiles obtained in numerical simulations over a wide
range of parameters. Finally, we provide a gap opening criterion that
simultaneously involves the planet mass, the disk viscosity and the aspect
ratio.

\\ ( http://arXiv.org/abs/astro-ph/0511082 , 294kb)