Tidal dissipation in satellites prevents Hill sphere escape

Abstract

ABSTRACT The transit method is a promising means of detecting exomoons, but few candidates have been identified. For planets close to their stars, the dynamical interaction between a satellite’s orbit and the star must be important in their evolution. Satellites beyond synchronous orbit spiral out due to the tide raised on their planet, and it has been assumed that they would likely escape the Hill sphere. Here we follow the evolution with a three-body code that accounts for tidal dissipation within both the planet and the satellite. We show that tidal dissipation in satellites often keeps them bound to their planet, making exomoons more observable than previously thought. The probability of escape depends on the ratio of tidal quality factors of the planet and satellite; when this ratio exceeds 0.5, escape is usually avoided. Instead, the satellite moves to an equilibrium in which the spin angular momentum of the planet is not transferred into the orbit of the satellite, but is transferred into the orbit of the planet itself. While the planet continues spinning faster than the satellite orbits, the satellite maintains a semi-major axis of approximately 0.41 Hill radii. These states are accompanied with modest satellite eccentricity near 0.1 and are found to be stable over long time-scales.