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

doi:10.1046/j.1365-8711.2003.06406.x

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Title:		Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs
Authors:		Bate, M. R.; Lubow, S. H.; Ogilvie, G. I.; Miller, K. A.
Affiliation:		AA(School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL), AB(Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA), AC(Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA), AD(Astronomy Department, University of Maryland, College Park, MD 20742, USA)
Publication:		Monthly Notice of the Royal Astronomical Society, Volume 341, Issue 1, pp. 213-229. (MNRAS Homepage)
Publication Date:		05/2003
Origin:		MNRAS
Astronomy Keywords:		accretion, accretion discs, hydrodynamics, planets and satellites: formation, planetary systems: formation, planetary systems: protoplanetary discs
DOI:		10.1046/j.1365-8711.2003.06406.x
Bibliographic Code:		2003MNRAS.341..213B

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 1 Earth mass (1 M_⊕) to 1 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_p>~ 0.1 M_J produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc mid-plane, 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 orbit of the planet. 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 time-scales for planets of mass less than 0.1 M_J, based on torques from disc material outside the Roche lobes of the planets, 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 the order of 10 M_J would undergo large migration, which makes formation and survival difficult.

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