On the tidal interaction between protostellar disks and companions

Formation of protoplanets and binary stars in a protostellar disk modifies the structure of the disk. Through tidal interactions, energy and angular momentum are transferred between the disk and protostellar or protoplanetary companion. We summarize recent progress in theoretical investigations of the disk-companion tidal interaction. We show that low-mass protoplanets excite density waves at their Lindblad resonances and that these waves are likely to be dissipated locally. When a protoplanet acquires sufficient mass, its tidal torque induces the formation of a gap in the vicinity of its orbit. Gap formation leads to the termination of protoplanetary growth by accretion. For proto-Jupiter to attain its present mass, we require that (1) the primordial solar nebula is heated by viscous dissipation; (2) the viscous evolution time scale of the nebula is comparable to the age of typical T Tauri stars with circumstellar disks; and (3) the mass distribution in the nebula is comparable to that estimated from a minimum-mass nebula model.