Kepler-411 Differential Rotation from Three Transiting Planets

Abstract

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%.

Superflares and Starspots: when size does not matter

“…Spot modelling of Kepler-411 has already been performed by [1] using the transits of the 3 exoplanets. The main parameters of the planets and their orbits are listed on Table 3.…”

“…The main parameters of the planets and their orbits are listed on Table 3. A total of 198 starspots were detected, and these are shown in maps of spot's longitude in time in Figure 3 of [1] obtained from each planetary transit. The spot's average size, intensity with respect to disk centre, and temperature are listed in the Table 1.…”

“…Two stars with similar physical parameters (mass, radius, T ef f , rotation) were compared to understand possible mechanisms of stellar magnetic activity manifested as spots and superflares. In the work of [1] positive correlations were obtained for the distribution of starspots and the energy of superflares in Kepler-411. We investigated whether the same phenomena occurred in another K-type star similar to Kepler-411.…”

“…Basically the height of this small flux variation is a measure of the spot's intensity whereas the duration of this bump reflects the spot's size. This method has been successfully applied to a few solar-type stars [1,20,32,36,44,45]. This technique of spot transit mapping yields the physical parameters of the spots such as: size, intensity, temperature, and location (longitude and latitude) on the surface of the star.…”

Dynamo activity of the K dwarf KOI-883 from transit photometry mapping

“…Applicability of photometric techniques based on the modulation of stellar light curves by star-spots is not limited by stellar rotation rate and magnitude. These techniques include analysis of Lomb-Scargle periodograms (Reinhold, Reiners & Basri 2013 ;Aigrain et al 2015 ) and Lomb-Scargle periodograms combined with autocorrelation of baseline flux (Pan et al 2020 ), phase tracking (Davenport, Hebb & Ha wle y 2015 ), and autocorrelation of flux deficit due to star-spots (Silva-Valio & Lanza 2011 ;Valio et al 2017 ;Zaleski et al 2019Zaleski et al , 2020Ara újo & Valio 2021 ). Calculation of flux deficit requires the physical attributes of individual star-spots (radius, intensity, and longitude) occulted during exoplanetary transits whose parameter estimates are obtained via modelling.…”