Activity and differential rotation of the early M dwarf Kepler-45 from transit mapping

Abstract

Little is known of the activity and differential rotation of low luminosity, early M dwarfs from direct observation. We present the first stellar activity analysis of star-spots and faculae for the hot Jupiter hosting M1V dwarf Kepler-45 from $\it Kepler$ transit light curves. We find star-spot and facula temperatures contrasting a few hundred degrees with the quiet photosphere, hence similar to other early M dwarfs having a convective envelope surrounding a radiative core. Star-spots are prominent close to the centre of the stellar disc, with faculae prominent towards the limbs, similar to what is observed for the Sun. Star-spot and facula mean sizes are about 40 and 45 × 103 km, respectively, and thus faculae occupy a 10 per cent larger surface area than the star-spots. A short-term activity cycle of about 295 d is observed that is reminiscent of those seen for other cool dwarfs. Adopting a solar-type differential rotation profile (faster equatorial rotation than polar rotation), our star-spot and facula temporal mapping indicates a rotation period of 15.520 ± 0.025 d at the transit latitude of −33.2°. From the mean stellar rotation of 15.762 d, we estimate a rotational shear of 0.031 ± 0.004 rad d−1, or a relative differential rotation of 7.8 ± 0.9 per cent. Kepler-45’s surface rotational shear is thus consistent with observations and theoretical modelling of other early M dwarfs that indicate a shear of less than 0.045 rad d−1 and no less than 0.03 rad d−1 for stars with similar stellar rotation periods.

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

“…Using the mean stellar rotation period calculated from LC data and assuming a solar-like differential rotation profile, the differential rotation of KOI-883 may be estimated and assessed relative to differential rotation values for FGKM dwarfs. This methodology has been previously employed to measure stellar rotation for several Kepler solar -type stars: Kepler -17 (Valio et al 2017 ), Kepler-63 (Netto & Valio 2020 ), Kepler-71 (Zaleski et al 2019 ), Kepler-45 (Zaleski et al 2020 ), andKepler-411 (Ara újo &Valio 2021 ).…”

“…For stellar observations taken on shorter time-scales than decades, such as the almost 4 yr of the Kepler mission, short-term stellar activity may be estimated from the star-spots occulted during transit via calculation of a Fourier-like power spectrum of flux deficit (Estrela & Valio 2016 ;Zaleski et al 2020 ). Star-spot physical characteristics can be converted into flux deficits that vary per transit with stellar magnetic activity.…”

“…The shear of cool, early M dwarfs increases from 0.028 to 0.047 rad d −1 as rotation period increases from 1 to 10 d and decreases for longer rotation periods in response to rotational quenching of the α dynamo effect (K üker et al 2019 ). For example, Kepler-45 ( T eff = 3820 K, P rot = 15.76 d) is an M1 dwarf and has a differential rotation of 0.031 ± 0.004 rad d −1 (Zaleski et al 2020 ). In comparison, the M1 dwarf OT Ser is a rapid rotator ( P rot = 3.40 d) with a differential rotation of 0.12 ± 0.02 rad d −1 (Donati et al 2008 ).…”

“…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.…”

Superflares and Starspots: when size does not matter

“…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.…”