DISK-SATELLITE INTERACTIONS

DISK-SATELLITE INTERACTIONS

1980 October 1 | PETER GOLDREICH AND SCOTT TREMAINE
This paper investigates the angular momentum and energy transfer between a disk and a satellite orbiting the same central mass. The satellite's orbit, whether circular or eccentric, exerts torques on the disk at Lindblad and corotation resonances. Angular momentum is transported outward from the disk material inside the satellite's orbit to the satellite and from the satellite to the disk material outside its orbit. For a satellite with an eccentric orbit, torques are also exerted at corotation resonances. The angular momentum and energy transfer at Lindblad resonances tend to increase the satellite's orbit eccentricity, while at corotation resonances, it tends to decrease it. In a Keplerian disk, corotation resonances dominate and damp the eccentricity, but if the strongest corotation resonances saturate due to particle trapping, the eccentricity grows. The results are applied to the interaction between Jupiter and the protoplanetary disk. The angular momentum transfer is so rapid that substantial changes in both the disk structure and Jupiter's orbit must have occurred on a time scale of a few thousand years. The paper also presents an alternate derivation of the results based on a single close encounter between the satellite and each ring particle. The torque cutoff at Lindblad resonances is accurately computed, and additional features of disk-satellite interactions relevant to planetary rings are described. The paper concludes with a summary and guide to the most important equations. The results are applicable to various systems, including the rings of Saturn, Uranus, accretion disks in close binary systems, and protoplanetary nebulae.This paper investigates the angular momentum and energy transfer between a disk and a satellite orbiting the same central mass. The satellite's orbit, whether circular or eccentric, exerts torques on the disk at Lindblad and corotation resonances. Angular momentum is transported outward from the disk material inside the satellite's orbit to the satellite and from the satellite to the disk material outside its orbit. For a satellite with an eccentric orbit, torques are also exerted at corotation resonances. The angular momentum and energy transfer at Lindblad resonances tend to increase the satellite's orbit eccentricity, while at corotation resonances, it tends to decrease it. In a Keplerian disk, corotation resonances dominate and damp the eccentricity, but if the strongest corotation resonances saturate due to particle trapping, the eccentricity grows. The results are applied to the interaction between Jupiter and the protoplanetary disk. The angular momentum transfer is so rapid that substantial changes in both the disk structure and Jupiter's orbit must have occurred on a time scale of a few thousand years. The paper also presents an alternate derivation of the results based on a single close encounter between the satellite and each ring particle. The torque cutoff at Lindblad resonances is accurately computed, and additional features of disk-satellite interactions relevant to planetary rings are described. The paper concludes with a summary and guide to the most important equations. The results are applicable to various systems, including the rings of Saturn, Uranus, accretion disks in close binary systems, and protoplanetary nebulae.
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