Improved torque formula for low and intermediate mass planetary migration
arXiv:1707.08988 · doi:10.1093/mnras/stx1946
Abstract
The migration of planets on nearly circular, non-inclined orbits in protoplanetary discs is entirely described by the disc's torque. This torque is a complex function of the disc parameters, and essentially amounts to the sum of two components: the Lindblad torque and the corotation torque. Known torque formulae do not reproduce accurately the torque actually experienced in numerical simulations by low- and intermediate- mass planets in radiative discs. One of the main reasons for this inaccuracy is that these formulae have been worked out in two-dimensional analyses. Here we revisit the torque formula and update many of its dimensionless coefficients by means of tailored, three- dimensional numerical simulations. In particular, we derive the dependence of the Lindblad torque on the temperature gradient, the dependence of the corotation torque on the radial entropy gradient (and work out a suitable expression of this gradient in a three-dimensional disc). We also work out the dependence of the corotation torque on the radial temperature gradient, overlooked so far. Corotation torques are known to scale very steeply with the width of the horseshoe region. We extend the expression of this width to the domain of intermediate mass planets, so that our updated torque formula remains valid for planets up to typically several tens of Earth masses, provided these relatively massive planets do not significantly deplete their coorbital region. Our torque expression can be applied to low- and intermediate-mass planets in optically thick protoplanetary discs, as well as protomoons embedded in circumplanetary discs.
14 pages,9 figures, accepted for publication in MNRAS
References in corpus (9)
- A comparative study of disc-planet interaction
- On the corotation torque in a radiatively inefficient disk
- Mass Estimates of a Giant Planet in a Protoplanetary Disk from the Gap Structures
- On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration
- On disc protoplanet interactions in a non-barotropic disc with thermal diffusion
- Hot super-Earths and giant planet cores from different migration histories
- Saturated torque formula for planetary migration in viscous disks with thermal diffusion: recipe for protoplanet population synthesis
- On the width and shape of the corotation region for low-mass planets
- Planetary Torque in 3D Isentropic Disks