  Astrophysical data, in the domains of time, involve a wide range of stellar
variability phenomena, among them the magnetic activity of the order of a few
hours until the signature of an extra-solar planet which can cover a scale of
time of a few days until tens of years. Numerous instruments are being
developed to detect Earth-sized exoplanets. Exoplanets with this dimension
challenge scientific instrumentation and the field of research in the data
processing. In this context, our study offers a powerful framework to explain
dynamical properties as a function of timescale in light curves with the
planetary signal. For that, we selected the stellar target Kepler-30 to test
our methods and procedures. In this sense, we investigate the multifractal
behavior of the Kepler-30 system composed of a sun-like star with a rotation
period of ~16 days and three planets with masses between 2 Earth and 2.5
Jupiter masses. Furthermore, this system has an orbital period varying from 29
to 143 days and orbits almost coplanar. This system is highly interesting
because starspots dynamics are strongly affected by the passing of a planet in
front of the star. We used about 1600 days of high-precision photometry
collected by the Kepler mission to investigate the quasi-periodic variation
caused by the rotation of the star and the effect of spot evolution as a
function of timescale. We applied indexes extract from multifractal analysis to
model the flux rotational modulation induced by active regions. Our results
that stellar flux variations in Kepler-30 star caused by rotational modulation
can be replicated in detail with just four recent-known multifractal indexes.
These indexes will greatly simplify spot modelling of current TESS and future
PLATO data.
