Journal Article

On the width and shape of the corotation region for low-mass planets

S.-J. Paardekooper and J. C. B. Papaloizou

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 394, issue 4, pages 2297-2309
Published in print April 2009 | ISSN: 0035-8711
Published online April 2009 | e-ISSN: 1365-2966 | DOI:
On the width and shape of the corotation region for low-mass planets

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We study the coorbital flow for embedded, low-mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high-resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, xs, which in the limit of zero softening is given by xs/rp= 1.68(q/h)1/2, where q is the planet to central star mass ratio, h is the disc aspect ratio and rp is the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero-softening limit. Thus, the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of approximately a pressure scaleheight H can affect xs, even though for low-mass planets xsH. The effect is to distort streamlines and reduce xs through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which xs becomes comparable to H.

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

Journal Article.  8792 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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