On the Interaction between Protoplanets and Protostellar Disks

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Abstract
The recent discovery of a planetary system around Ups And raises questions concerning the formation process of several planets in the Jupiter-mass range around a single host star. We consider numerically two scenarios involving the interaction of protoplanets with low-viscosity host disks. In the first case, a single protoplanet is assumed to have been formed already, and the development of a tidally induced gap in the disk is calculated. Beyond the outer boundary of the gap, a positive pressure gradient induces the disk gas to attain an azimuthal velocity that is larger than the Keplerian speed. The accumulation of small solid particles at the outer edge of this region provides a favorable location for the formation of an additional protoplanetary core with an orbital radius approximately twice that of the original protoplanet. In the second scenario, we assume that two protoplanets have formed simultaneously, one with twice the orbital radius of the other. Both clear gaps, and the ring of remaining disk material between the planets has a width only a few times the thickness of the disk. The density waves excited by planets on both sides of the ring propagate throughout the ring, and nonlocal dissipation of these waves leads to gas leakage from the ring edges into the gaps. After the ring is depleted, the separation between the planets tends to decline as a result of angular momentum exchange between them and the surrounding inner and outer disks. For a disk with moderate viscosity, the timescale for the planets to approach each other is less than the lifetime of the gas.