Other
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p31a1520l&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P31A-1520
Other
[6296] Planetary Sciences: Solar System Objects / Extra-Solar Planets
Scientific paper
Tidal interactions occurring between a forming planet and its parent proto-planetary disk are likely to have profound implications on the orbital evolution of planets and planetary systems. The torques resulting from tidal interactions depend on the planet mass and on several disk properties. We focus on planets that do not induce large perturbations in the disk, but also consider planets that open density gaps. We calculate torques and torque density distributions. We determine a formula for the torque exerted on the planet by a viscous and locally isothermal disk. The turbulent viscosity of the disk is characterized by an α -prescription and varies in the range from α ˜ 0.0005 to α ˜ 0.05. The expression that we derive is based on 3D non-linear hydrodynamical calculations and includes the contributions from both Lindblad and corotation resonances. The formula gives the dependence of the torque on the radial gradients of surface density and temperature in the proximity of the planet. Both gradients contribute to inward migration when they are negative. Positive and relatively large gradients appear necessary to result in outward migration. It has been proposed that disk regions in which there are rapid radial variations in density and/or temperature, e.g., because of opacity transitions or because of shadowing effects, represent locations where planets may become trapped. If variations occur over several disk scale-heights, our results suggest that substantially slowing or stopping planet migration by means of large negative gradients is difficult and appears unlikely for a disk that is locally isothermal. The synthesis of semi-major axis distributions of extrasolar planets requires solving for the disk evolution as well as for the tidal interaction occurring between the planet(s) and the disk in a self-consistent manner. These calculations involve time scales equal to typical disk lifetimes, i.e., millions of years, and length scales of hundreds of AU. Therefore, they generally need to rely on vertically and azimuthally averaged, 1D models. The evolution of the disk in this case is described by an equation that contains radial distributions of torques. We provide a formula for the calculation of torque density distributions, based on 3D non-linear hydrodynamical calculations, which can be used in long-term evolution studies of planets embedded in locally isothermal disks. This formula represents an improvement over expressions derived from the impulse approximation, which have been used so far. Moreover, this formula can also be applied to disks that have mildly varying radial gradients and to planets that open gaps. We use this formalism to study migration scenarios of super-Earths in viscously evolving and photo-evaporating disks, starting from conditions that may be appropriate for a minimum-mass solar-type nebula. Results indicate that the final outcome is highly sensitive on the adopted initial conditions.
D'Angelo Gennaro
Lubow Stephen H.
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