Kepler-39b is a gas-giant planet in orbit around an F-type star. It is 18 times Jupiter’s mass, 1.22 times Jupiter’s radius and it transits its host star every 21.09 days. A study by Wei Zhu et al. (2014) using data from NASA’s Kepler space telescope found that Kepler-39b has an oblateness of 0.22 ± 0.11. In fact, this is the first tentative detection of oblateness for a planet outside the Solar System. When an oblate planet transits its host star, the transit light curve will exhibit small differences from that of a purely spherical planet.
In the Solar System, the gas-giant planets Jupiter and Saturn are oblate in shape due to their rapid rotations. The oblateness of an object is expressed as the ratio of its equatorial-polar radius difference to its equatorial radius. The equatorial radius is larger than the polar radius by 7 percent for Jupiter and by 10 percent for Saturn. As such, Jupiter’s oblateness is 0.07 and Saturn’s oblateness is 0.1. With an oblateness of 0.22 ± 0.11, Kepler-39b is substantially more oblate than any planet in the Solar System.
The large oblateness of Kepler-39b is most likely rotationally induced. With that, its rotation period is estimated to be 1.6 ± 0.4 hours. For comparison, the rotation periods of Jupiter and Saturn are 9.9 and 10.6 hours, respectively. Although the rotation of Kepler-39b is remarkably fast, it is lower than its estimated break-up rotation period of ~0.9 hours. In addition to its large oblateness, Kepler-39b is also inflated in size. Its close proximity to its host star and its estimated equilibrium temperature of around 900 K is insufficient to account for its inflated size.
Wei Zhu et al. (2014), “Constraining the Oblateness of Kepler Planets”, arXiv:1410.0361 [astro-ph.EP]