Limits on the orbits of possible exomoons around Kepler giant planets in the habitable zone

Abstract

Regions of Hill stability were determined using the full three-body theory for the planetary candidates that were found by the Kepler mission to lie in the Habitable Zone of the host star with radii larger than 3 Earth radii. The values obtained give a more accurate assessment of the sphere of influence of a planet than does the Hill radius using the restricted three-body expression. The values given by the two estimates for circular orbits are compared. The variation in the full three-body Hill regions were examined for a variety of possible moon masses and orbital eccentricities and inclinations. It was found that the critical moon planet separation decreased with increased moon orbital eccentricity and inclination but to a far greater extent when the planetary orbital eccentricity increased suggesting they would lie inside the Roche limit and are unlikely to have formed or exist now. The angular separation of the moon and planet and the radial velocity amplitudes of the planets likely to be observed are also affected. This is important for future observations and missions. It was also found that the giant planets in the habitable zone lie in a narrow band that can be fitted by a linear regression relation between log10(Planet luminosity) and log10 (Planet temperature) with a slope of 3.34.