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Paper: Obliquity Tides in Hot Jupiters
Volume: 398, Extreme Solar Systems
Page: 281
Authors: Peale, S.J.
Abstract: Tidal dissipation in HD209458b while it has a very high obliquity has been proposed as a means of inflating the planet to its observed oversize (Winn and Holman, 2005). The high obliquity is maintained by the planet’s being trapped into Cassini state 2 at an obliquity near 90◦ while the planet maintains a rotation rate synchronous with its orbital mean motion. In a Cassini state the spin axis and orbit normal remain coplanar with the normal to the Laplace plane as they precess around the latter, where the orbit has a significant inclination to the Laplace plane. The orbit of HD209458b is inclined to equatorial plane of the star by about 4°. If the stellar equator plane is coincident with the plane of the initially massive nebula, that plane is the Laplace plane on which the orbit is precessing. A planet can evolve to Cassini state 2 by tidal dissipation on a time scale comparable with that of the retardation of the spin rate. The latter time scale can become relatively short as the planet migrates toward the star. While the nebula is there, the orbital precession rate is rapid, Cassini state 2 has a small obliquity, and tidal friction will drive the planet to that state. That evolution may not occur for cases where the obliquity of state 2 is relatively large. As the nebula is dispersed, the orbital precession slows with the result that the Cassini state obliquity increases. The spin follows the Cassini state to high obliquity because the solid angle traced by the spin as it precesses about the Cassini state position is an adiabatic invariant. With no nebula, only the quadrupole moment of the star is left to cause the orbit to precess. At the slow precession rate thus induced, the obliquity of the Cassini state is nearly 90◦, which if maintained while the spin remains synchronous with the orbital motion, causes the dissipation inferred by Winn and Holman.

Implicit in this scenario is the assumption that the synchronous rotation is somehow maintained. Authors of two papers have pointed out that this is not so (Levrard et al. 2007; Fabrycky et al. 2007). The rotation continues to decrease below the synchronous value with increasing obliquity. As is perhaps expected, state 2 becomes unstable as the planet slows. The planet then rapidly evolves to Cassini state 1 with a negligibly small obliquity, and all isolated hot Jupiters will evolve to nearly circular orbits with their spin axes nearly normal to their orbit planes. Obliquity tides cannot be invoked as a means of additional heating of hot gaseous planets.

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