The differential rotation of the Sun is a crucial ingredient of the dynamo theory responsible for the generation of its magnetic field. Currently, the rotation profile of a star that hosts one or more transiting planet can be estimated. By detecting the same spot in a later transit, it is possible to infer the stellar rotation period at that latitude. In this work, we apply for the first time transit spot mapping to determine the differential rotation of Kepler-411, a K2V-type star with an average rotation period of 10.52 days, a radius of 0.79 R ⊙, and a mass of 0.83 M ⊙. Kepler-411 hosts at least four planets, the inner planet is a super-Earth with a radius of 1.88 R ⊕ and an orbital period of 3.0051 days, whereas the two larger transiting planets are mini Neptunes with radii of 3.27 and 3.31 R ⊕, and periods of 7.834435 and 58.0204 days, respectively. Their orbits are such that they transit the star at latitudes of −11°, −21°, and −49°. Analysis of the transit light curves of the three planets resulted in the detection of a total of 198 spots. For each transit latitude, the rotation period of the star was estimated and the differential rotation pattern estimated independently. Then a solar-like differential rotation profile was fit to the three rotation periods at the distinct latitudes, and the result agreed extremely well with the previous ones, resulting in a differential shear of 0.0500 ± 0.0006 rd day−1 or a relative differential rotation of 8.4% ± 0.1%.

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.

How do the characteristics of starspots influence the triggering of stellar flares? Here we investigate the activity of two K-type stars, similar in every way from mass to rotation periods and planetary systems. Both stars exhibit about a hundred spots, however Kepler-411 produced 65 superflares, while Kepler-210 presented none. The spots of both stars were characterised using the planetary transit mapping technique, which yields the intensity, temperature, and radius of starspots. The average radius was (17 ± 7) × 103 km and (58 ± 23) × 103 km, while the intensity ratio with respect to the photosphere was (0.35 ± 0.24) Ic and (0.64 ± 0.15) Ic, and the temperature was (3800 ± 700) K and (4180 ± 240) K for spots of Kepler-411 and Kepler-210, respectively. Therefore, spots on the star with no superflares, Kepler-210, are mostly larger, less dark, and warmer than those on the flaring star, Kepler-411. This may be an indication of magnetic fields with smaller magnitude and complexity of the spots on Kepler-210 when compared to those on Kepler-411. Thus, starspot area appears not to be the main culprit of superflares triggering. Perhaps the magnetic complexity of active regions is more important.

No abstract

Stellar magnetic activity, just like that of the Sun, manifests itself in the form of flares and spots on the surface of the star. In the solar case, the largest flares originate from large active regions. In this work, we present a study of the activity of the star Kepler-411, including spot modeling from planetary transits. Our goal was to search for a connection between the area of starspots with the energy of superflares produced by this star. Kepler-411 is a K2V-type star with an average rotation period of 10.52 days, radius of 0.79 R ⊙, and a mass of 0.83 M ⊙, which was observed by the Kepler satellite for about 600 days. Transit mapping allowed for the characterization of 198 starspots with estimates of their radius and temperature. Kepler-411 starspots had an average radius of (17 ± 7) × 103 km and a mean temperature of 3800 ± 700 K. Visual inspection of the light curves of Kepler-411 yields the identification of 65 superflares. The detected superflares lasted from 8 to 260 minutes and their energy varied from 1033–1035 ergs. The power-law index of the flare frequency distribution as a function of energy is (−2.04 ± 0.13) for the flare on Kepler-411. A positive correlation between the area of starspots and the energy of superflares was found when considering the averages taken every 16–35 days, with the highest correlation occurring for averages every 21 days. This timing is probably related to the lifetime of the Kepler-411 spots.