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H. Tanaka (Southwest Research Institute, Tokyo Institute of Technology), W. R. Ward (Southwest Research Institute)
Tidal interaction between a planet and a nebular disk is thought to cause a rapid inward migration of the planet (i.e., the type I migration). In most studies of disk-planet interaction, however, the density waves excited by a planet are assumed to propagate away and to dissipate completely. If the waves reflect at the disk edges and return to the planet, the torque exerted on planet significantly decreases. Thus, in order to fix the migration speed of planets, it is necessary to clarify the damping rate of waves during their propagation and at the disk edges.
In the present work, we performed three-dimensional linear calculations of wave propagation in a isothermal nebular disk. As initial waves, we adopted two-dimensional modes in which the velocity perturbation does not depend on the z-axis, since planets excite such waves. It is found that, as the waves propagate, the velocity perturbation becomes dependent on the z-axis due to the changes in the disk scale height. The dependence is quite different between waves propagating inward and those propagating outward. In the inward waves, the velocity becomes so large at the disk surfaces that shock waves would be formed. The waves propagating outward, on the other hand, oscillate mainly near the mid-plain of the disk and their amplitude does not increase so much compared to the inward waves. This result indicates that the inward waves may dissipate more strongly during their propagation than the outward waves. This asymmetric dissipation mechanism of the density waves could possibly decrease the migration speed of planets in the solar nebula.