Stellar Obliquity from Spot Transit Mapping of Kepler-210

Abstract

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.