Constraining the Rotation Rate of Transiting Extrasolar Planets by Oblateness Measurements

The solar system gas giant planets are oblate due to their rapid rotation. A measurement of the planet’s projected oblateness would constrain the planet’s rotational period. Planets that are synchronously rotating with their orbital revolution will be rotating too slowly to be significantly oblate; these include planets with orbital semi-major axes ∼< 0.2 AU (for MP ∼ MJ and M∗ ∼ M ). Jupiter-like planets in the range of orbital semi-major axis 0.1 AU to 0.2 AU will tidally evolve to synchronous rotation on a timescale similar to main sequence stars’ lifetimes. In this case an oblateness detection will help constrain the planet’s tidal Q value. The projected oblateness of a transiting extrasolar giant planet is measurable from a very highphotometric-precision transit light curve. For a sun-sized star and a Jupiter-sized planet the normalized flux difference in the transit ingress/egress light curve between a spherical and an oblate planet is a few to 15×10−5 for oblateness similar to Jupiter and Saturn respectively. The transit ingress and egress are asymmetric for an oblate planet with an orbital inclination different from 90◦ and a non-zero projected obliquity. A photometric precision of 10−4 has been reached by HST observations of the known transiting extrasolar planet HD 209458 b. Kepler, a NASA discovery-class mission designed to detect transiting Earth-sized planets requires a photometric precision of 10−5 and expects to find 30 to 40 transiting giant planets with orbital semi-major axes < 1 AU, about 20 of which will be at > 0.2 AU. Furthermore, partper-million photometric precision (reached after averaging over several orbital periods) is expected from three other space telescopes to be launched within the next three years. Thus an oblateness measurement of a transiting giant planet is realistic in the near future. Subject headings: planetary systems — planets and satellites: general