Growing and moving low-mass planets in non-isothermal disks

¹ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: S.Paardekooper@damtp.cam.ac.uk
² Leiden Observatory, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands
³ Stockholm Observatory, AlbaNova University Center, Stockholm University, 106 91 Stockholm, Sweden e-mail: garrelt@astro.su.se

Received: 31 August 2007
Accepted: 21 November 2007

Abstract

Aims.We study the interaction of a low-mass planet with a protoplanetary disk with a realistic treatment of the energy balance by doing radiation-hydrodynamical simulations. We look at accretion and migration rates and compare them to isothermal studies.

Methods.We used a three-dimensional version of the hydrodynamical method RODEO, together with radiative transport in the flux-limited diffusion approach.

Results.The accretion rate, as well as the torque on the planet, depend critically on the ability of the disk to cool efficiently. For densities appropriate to 5 AU in the solar nebula, the accretion rate drops by more than an order of magnitude compared to isothermal models, while at the same time the torque on the planet is positive, indicating outward migration. It is necessary to lower the density by a factor of 2 to recover inward migration and more than 2 orders of magnitude to recover the usual type I migration. The torque appears to be proportional to the radial entropy gradient in the unperturbed disk. These findings are critical for the survival of protoplanets, and they should ultimately find their way into population synthesis models.