EDP Sciences
Free access
Issue
A&A
Volume 387, Number 2, May IV 2002
Page(s) 605 - 623
Section Formation and evolution of planetary systems
DOI http://dx.doi.org/10.1051/0004-6361:20020240


A&A 387, 605-623 (2002)
DOI: 10.1051/0004-6361:20020240

The co-orbital corotation torque in a viscous disk: Numerical simulations

F. S. Masset

Service d'Astrophysique, L'Orme des Merisiers, CE-Saclay, 91191 Gif-sur-Yvette Cedex, France

(Received 26 September 2001 / Accepted 5 February 2002)

Abstract
The torque felt by a non-accreting protoplanet on a circular orbit embedded in a uniform surface density protoplanetary disk is analyzed by means of time-dependent numerical simulations. Varying the viscosity enables one to disentangle the Lindblad torque (which is independent of viscosity) from the corotation torque, which saturates at low viscosity and is unsaturated at high viscosity. The dependence of the corotation torque upon the viscosity and upon the width of the librating zone is compared with previous analytical expressions, and shown to be in agreement with those. The effect of the potential smoothing respectively on the Lindblad torque and on the corotation torque is investigated, and the question of whether 3D effects and their impact on the total torque sign and magnitude can be modeled by an adequate smoothing prescription in a 2D simulation is addressed. As a side result, this study shows that the total torque acting on a Neptune-sized protoplanet is positive in a sufficiently thin, viscous disk ( $H/r \ga 4$%, $\alpha \ga 10^{-2}$), but the inward migration time of smaller bodies is still very short, making it unlikely that they reach the torque reversal mass before having migrated all the way to the central object.


Key words: stars: planetary systems: formation -- stars: planetary systems: protoplanetary disks -- stars: planetary systems -- hydrodynamics -- methods: numerical




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