Stellar Obliquity from Spot Transit Mapping of Kepler-210

Stellar obliquity, the angle between the stellar spin and the perpendicular to the planetary orbit, also known as the spin-orbit angle, holds clues to the formation and evolution of planetary systems. When a planet transits a star periodically, it may cross in front of a stellar spot, producing a noticeable signal on the transit light curve. Spot transit mapping can be used to measure stellar obliquity. Here we present the analysis of Kepler-210, a K-dwarf star with two mini-Neptune-size planets in orbit. Interestingly, the spot mapping from the outer planet, Kepler-210 c, resulted in a spot distribution with no spots detected at longitudes >38°, whereas the spots occulted by Kepler-210 b displayed all range of longitudes. The best explanation for this was that Kepler-210 c exhibited an inclined orbit, while the orbit of Kepler-210 b was parallel to the stellar equator. Thus, transits of Kepler-210 c occulted different latitude bands of the star. The observed maximum spot topocentric longitude of 38° implied an orbital obliquity of 18°-45° for Kepler-210 c. Further considering a symmetric spot distribution in latitude with respect to the stellar equator, the obliquity was restricted to 34.°8, implying a maximum spot latitude of 40°. The differential rotation profile calculated from the oblique orbit for Kepler-210 c agreed with that obtained from the spots occulted by Kepler-210 b. Combining results from both planets yields a rotational shear of ΔΩ = 0.0353 ± 0.0002 rad day^-1 and a relative rotational shear of 6.9%. The causes of the Kepler-210 c misalignment remain to be explained.