Journal Article

A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag

S.-J. Paardekooper, C. Baruteau, A. Crida and W. Kley

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 401, issue 3, pages 1950-1964
Published in print January 2010 | ISSN: 0035-8711
Published online January 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2009.15782.x
A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag

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We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal effects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, using three independent numerical methods, and find good agreement.

Keywords: planets and satellites: formation; planetary systems: formation

Journal Article.  10635 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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