Abstract
Context. The Kepler-30 system consists of a G dwarf star with a rotation
period of similar to 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 4 yr 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 Delta Omega/Omega similar to 0 :02 +/-
0 :01 and suggests a short-term cyclic variation in the starspot area
with a period of similar to 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.
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