Abstract
We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.
Highlights
Low-mass planets, embedded in circumstellar gas discs, are subject to orbital migration (Goldreich & Tremaine 1979, 1980) through disc tides
We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc
Recent work has indicated that the situation may be different if the disc’s thermodynamics is taken into account properly (Paardekooper & Mellema 2006a; Kley & Crida 2008; Kley et al 2009), in which case outward migration is possible
Summary
Low-mass planets, embedded in circumstellar gas discs, are subject to orbital migration (Goldreich & Tremaine 1979, 1980) through disc tides. Apart from possibly keeping the corotation torque unsaturated, diffusion of heat and momentum can in the limit of high diffusion, act to reduce the non-linearity of the torque It was already noted in Masset (2002) that there exists a cut-off for the isothermal horseshoe drag at high viscosity.
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