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Astrophysical data, in the domains of time, involve a wide range of stellarvariability phenomena, among them the magnetic activity of the order of a fewhours until the signature of an extra-solar planet which can cover a scale oftime of a few days until tens of years. Numerous instruments are beingdeveloped to detect Earth-sized exoplanets. Exoplanets with this dimensionchallenge scientific instrumentation and the field of research in the dataprocessing. In this context, our study offers a powerful framework to explaindynamical properties as a function of timescale in light curves with theplanetary signal. For that, we selected the stellar target Kepler-30 to testour methods and procedures. In this sense, we investigate the multifractalbehavior of the Kepler-30 system composed of a sun-like star with a rotationperiod of ~16 days and three planets with masses between 2 Earth and 2.5Jupiter masses. Furthermore, this system has an orbital period varying from 29to 143 days and orbits almost coplanar. This system is highly interestingbecause starspots dynamics are strongly affected by the passing of a planet infront of the star. We used about 1600 days of high-precision photometrycollected by the Kepler mission to investigate the quasi-periodic variationcaused by the rotation of the star and the effect of spot evolution as afunction of timescale. We applied indexes extract from multifractal analysis tomodel the flux rotational modulation induced by active regions. Our resultsthat stellar flux variations in Kepler-30 star caused by rotational modulationcan be replicated in detail with just four recent-known multifractal indexes.These indexes will greatly simplify spot modelling of current TESS and futurePLATO data.

Multifractal charactarization as a function of timescale in the light curves with planetary signal observed by the kepler mission