Influence of viscosity and the adiabatic index on planetary migration

¹ Institut für Astronomie & Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: bertram.bitsch@oca.eu
² Dep. Cassiopée, University of Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, 06304 Nice, France
³ University of Florida, Department of Astronomy, 211 Bryant Space Science Center, Gainesville, FL 32611, USA

Received: 20 November 2011
Accepted: 28 November 2012

Abstract

Context. The strength and direction of migration of low mass embedded planets depends on the disk’s thermodynamic state. It has been shown that in active disks, where the internal dissipation is balanced by radiative transport, migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index.

Aims. In this paper we investigate the influence of different viscosity prescriptions (α-type and constant) and adiabatic indices on disk structures. We then determine how this affects the migration rate of planets embedded in such disks.

Methods. We perform three-dimensional numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20 M_Earth planets is studied.

Results. Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. Hence, in these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration.

Conclusions. For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20-M_Earth planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing protoplanetary cores.