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Tidal Evolution of Close-in Extra-solar Planets

Wednesday, December 19, 2007
Brian
Jackson (LPL, U of AZ)

The distribution of eccentricities e of extra-solar planets with semi-major axes a > 0.2 AU is very uniform, and values for e are relatively large, averaging 0.3 and broadly distributed up to near 1. For a < 0.2 AU, eccentricities are much smaller (most e < 0.2), a characteristic widely attributed to damping by tides after the planets formed and the protoplanetary gas disk dissipated. Previous estimates of the tidal damping considered the tides raised on the planets, but ignored the tides raised on the stars. They also assumed specific values for the planets' poorly constrained tidal dissipation parameter Qp. Perhaps most important, the strongly coupled evolution between e and a was ignored. We have integrated the coupled tidal evolution equations for e and a over the estimated age of each planet, and confirmed that the distribution of initial e values of close-in planets matches that of the general population for reasonable Q values, with the best fits for stellar and planetary Q being ~105.5 and ~106.5 , respectively. The accompanying evolution of a values shows most close-in planets had significantly larger a at the start of tidal migration. The earlier gas disk migration did not bring all planets to their current orbits. The current small values of a were only reached gradually due to tides over the lifetimes of the planets. These results may have important implications for planet formation models, atmospheric models of "hot Jupiters", and the success of transit surveys.

During the course of this tidal evolution, tidal distortion of the figure of the planet can result in substantial amounts of internal heating at the expense of orbital energy. As a result, the heating rate as a function of time is directly related to the rate of evolution of the orbit. In a typical case, tidal heating might have begun modest, but then increased as tides reduced the semi-major axis a. As the tides became stronger, they circularize the orbit and shut down the tidal heating mechanism. Theoretical models to date have not taken into account the history of tidal heating for close-in planets, and of course those are the planets most likely to have radii measurable by transits. As a first cut at addressing this issue, I also present the tidal heating histories that would accompany the orbital evolution.

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