Stellar irradiated discs and implications on migration of embedded planets

II. Accreting-discs

University of Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Laboratoire Lagrange, BP4229, 06304 Nice Cedex 4, France
e-mail: bertram.bitsch@oca.eu

Received: 7 November 2013
Accepted: 3 January 2014

Abstract

Context. The strength and direction of migration of embedded low mass planets depends on the disc’s structure. It has been shown that, in discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos.

Aims. In this paper we investigate the influence of a constant Ṁ-flux through the disc, as well as the influence of the disc’s metallicity on the disc’s thermodynamics. We focus on Ṁ discs, which have a net mass flux through them. Utilizing the resulting disc structure, we determine the regions of outward migration in the disc.

Methods. We perform numerical hydrosimulations of Ṁ discs with viscous heating, radiative cooling and stellar irradiation in 2D in the r-z-plane. We use the explicit/implicit hydrodynamical code FARGOCA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets is studied by using torque formulae.

Results. For a disc of gas surface density Σ_G and viscosity ν, we find that the discs thermal structure depends on the product Σ_Gν and the amount of heavy elements, while the migration of planets additionally to the mentioned quantities, depends on the amount of viscosity ν itself. As a result of this, the disc structure can not be approximated by simple power laws. During the lifetime of the disc, the structure of the disc changes significantly in a non-linear way in the inner parts. In the late stages of the discs evolution (characterised by low Ṁ), outward migration is only possible if the metallicity of the disc is high. For low metallicity, planets would migrate inwards and could potentially be lost to the star.

Conclusions. The presented disc structures and migration maps have important consequences on the formation of planets, as they can give hints on the different formation mechanisms for different types of planets as a function of metallicity.