2010ApJ...716..850C

Knowledge of an exoplanet's oblateness and obliquity would give clues about its formation and internal structure. In principle, a light curve of a transiting planet bears information about the planet's shape, but previous work has shown that the oblateness-induced signal will be extremely difficult to detect. Here, we investigate the potentially larger signals due to planetary spin precession. The most readily detectable effects are transit depth variations (TδV's) in a sequence of light curves. For a planet as oblate as Jupiter or Saturn, the transit depth will undergo fractional variations of order 1%. The most promising systems are those with orbital periods of approximately 15-30 days, which are short enough for the precession period to be less than about 40 yr and long enough to avoid spin-down due to tidal friction. The detectability of the TδV signal would be enhanced by moons (which would decrease the precession period) or planetary rings (which would increase the amplitude). The Kepler mission should find several planets for which precession-induced TδV signals will be detectable. Due to modeling degeneracies, Kepler photometry would yield only a lower bound on oblateness. The degeneracy could be lifted by observing the oblateness-induced asymmetry in at least one transit light curve or by making assumptions about the planetary interior.