Eccentricity Evolution of Extrasolar Planetary Systems due to the Depletion of Nascent Protostellar Disks

Many extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets’ mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But prior to their depletion, self gravity of the planets’ nascent disks, dominates the precession eigenfrequencies. We examine here the initial evolution of young planets’ eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets’ relative phase of periapse is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets’ orbits pass through a secular resonance, their mean eccentricities undergo quantitative changes. For applications, we analyze the evolution of planetary eccentricities of Upsilon Andromedae and HD168443 system during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets’ eccentricity ratio. However, the relatively large amplitude of the planets’ eccentricity cannot be excited if all the planets had small initial eccentricities. Our analysis UCO/Lick Observatory, University of California, Santa Cruz, CA 95064, U.S.A. Present address: Space Science Division, MS 245-3, NASA Ames Research Center, Moffett Field, CA 94035-1000, U.S.A. Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo 1528551, Japan