Stellar irradiated discs and implications on migration of embedded planets

III. Viscosity transitions

¹ Lund ObservatoryDepartment of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden
e-mail: bert@astro.lu.se
² Laboratoire Lagrange, UMR 7293, Université Nice Sophia-Antipolis/CNRS/Observatoire de la Côte d’Azur, 06300 Nice, France
³ Southwest Research Institute, Department of Space Studies, 1050 Walnut Street, Suite 300, Boulder, CO 80302, USA

Received: 16 April 2014
Accepted: 31 July 2014

Abstract

Context. The migration strength and direction of embedded low-mass planets depends on the disc structure. In discs with an efficient radiative transport, the migration can be directed outwards for planets with more than 3–5 Earth masses. This is due to the entropy-driven corotation torque, a process that extends the lifetimes of growing planetary embryos. However, smaller mass planets are still migrating inwards and might be lost to the central star.

Aims. We investigate the influence on the disc structure caused by a jump in the α parameter of the viscosity to model a dead-zone structure in the disc. We focus on Ṁ discs, which have a constant net mass flux. Using the resulting disc structure, we investigate the consequences for the formation of planetesimals and determine the regions of outward migration for proto-planets.

Methods. We performed numerical hydrosimulations of Ṁ discs in the r − z-plane. We used 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 was studied by using torque formulae.

Results. Viscosity transitions inside the disc create transitions in density that stop inward migration for small planets through the so-called “planet trap” mechanism. This mechanism also works for planets down to M_P > 0.5 M_Earth, while in radiative discs with no viscosity transition the lowest mass with which inward migration can be avoided is 3–5 Earth masses. Additionally, the viscosity transitions change the pressure gradient in the disc, which facilitates planetesimal formation via the streaming instability. However, a very steep transition in viscosity is needed to achieve in a pressure bump in the disc.

Conclusions. The transition in viscosity facilitates planetesimal formation and can stop the migration of small-mass planets (M_P > 0.5 M_Earth), but still does not halt inward migration of smaller planets and planetesimals that are affected by gas drag. A very steep, probably unrealistic viscosity gradient is needed to trap planets of smaller masses and halt gas-drag-driven planetesimal migration at a pressure bump.