Back to Search Start Over

Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs

Authors :
Matthew R. Bate
S. H. Lubow
Gordon I. Ogilvie
K.A. Miller
Source :
Monthly Notices of the Royal Astronomical Society. 341:213-229
Publication Year :
2003
Publisher :
Oxford University Press (OUP), 2003.

Abstract

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from one Earth mass (1 M$_e$) to one Jupiter mass (1 M$_J$) by using the ZEUS hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses $M \gsim 0.1$ M$_J$ produce significant perturbations in the disc's surface density. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc midplane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the planet's orbit. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M$_J$ and is highly efficient, occurring at the local viscous rate. The migration timescales for planets of mass less than 0.1 M$_J$, based on torques from disc material outside the planets' Roche lobes, are in excellent agreement with the linear theory of Type I (non-gap) migration for three-dimensional discs. The transition from Type I to Type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M$_J$ with little migration. Planets with final masses of order 10 M$_J$ would undergo large migration, which makes formation and survival difficult.<br />Comment: Accepted by MNRAS, 18 pages, 13 figures (6 degraded resolution). Paper with high-resolution figures available at http://www.astro.ex.ac.uk/people/mbate/

Details

ISSN :
13652966 and 00358711
Volume :
341
Database :
OpenAIRE
Journal :
Monthly Notices of the Royal Astronomical Society
Accession number :
edsair.doi.dedup.....919fe21ad6d9ce1a6561d514556d7628
Full Text :
https://doi.org/10.1046/j.1365-8711.2003.06406.x