2021A&A...650A..40D

Context. The Kepler-30 system consists of a G dwarf star with a rotation period of ∼16 days and three planets orbiting almost coplanar with periods ranging from 29 to 143 days. Kepler-30 is a unique target with which to study stellar activity and rotation in a young solar-like star accompanied by a compact planetary system.
Aims. We use about 4yr of high-precision photometry collected by the Kepler mission to investigate the fluctuations caused by photospheric convection, stellar rotation, and starspot evolution as a function of timescale. Our main goal is to apply methods for the analysis of time-series to find the timescales of the phenomena that affect the light variations. We correlate those timescales with periodicities in the star and the planetary system.
Methods. We model the flux rotational modulation induced by active regions using spot modelling and apply the Multifractal Detrending Moving Average algorithm in standard and multiscale versions to analyse the behaviour of variability and light fluctuations that can be associated with stellar convection and the evolution of magnetic fields on timescales ranging from less than 1 day up to about 35 days. The light fluctuations produced by stellar activity can be described by the multifractal Hurst index that provides a measure of their persistence.
Results. The spot modelling indicates a lower limit to the relative surface differential rotation of ΔΩ/Ω∼0.02±0.01 and suggests a short-term cyclic variation in the starspot area with a period of ∼34 days, which is close to the synodic period of 35.2 days of the planet Kepler-30b. By subtracting the two time-series of the simple aperture photometry and pre-search data conditioning Kepler pipelines, we reduce the rotational modulation and find a 23.1-day period close to the synodic period of Kepler-30c. This period also appears in the multifractal analysis as a crossover of the fluctuation functions associated with the characteristic evolutionary timescales of the active regions in Kepler-30 as confirmed by spot modelling. These procedures and methods may be greatly useful for analysing current TESS and future PLATO data.