ThreeDimensional Interaction between a Planet and an Isothermal Gaseous Disk. I. Corotation and Lindblad Torques and Planet Migration
Abstract
Gravitational interaction between a planet and a threedimensional isothermal gaseous disk is studied. In the present paper we mainly examine the torque on a planet and the resultant radial migration of the planet. A planet excites density waves at Lindblad and corotation resonances and experiences a negative torque by the density waves, which causes a rapid inward migration of the planet during its formation in a protoplanetary disk. We formulate the linear wave excitation in threedimensional isothermal disks and calculate the torques of Lindblad resonances and corotation resonances. For corotation resonances, a general torque formula is newly derived, which is also applicable to twodimensional disks. The new formula succeeds in reproducing numerical results on the corotation torques, which do not agree with the previously wellknown formula. The net torque of the inner and the outer Lindblad resonances (i.e., the differential Lindblad torque) is caused by asymmetry such as the radial pressure gradient and the scale height variation. In threedimensional disks, the differential Lindblad torques are generally smaller than those in twodimensional disks. Especially, the effect of a pressure gradient becomes weak. The scale height variation, which is a purely threedimensional effect, makes the differential Lindblad torque decrease. As a result, the migration time of a planet is obtained as of the order of 10^{6} yr for an Earthsize planet at 5 AU for a typical disk model, which is longer than the result of twodimensional calculation by the factor of 2 or 3. The reflected waves from disk edges, which are neglected in the torque calculation, can further weaken the diskplanet interaction.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 2002
 DOI:
 10.1086/324713
 Bibcode:
 2002ApJ...565.1257T
 Keywords:

 Stars: Planetary Systems: Formation;
 Stars: Planetary Systems: Protoplanetary Disks;
 Solar System: Formation;
 Waves