We investigate the evolution of five multifractal indicators of the Kepler Mission light curves of the moderately young Sun-like Kepler-30 star accompanied by a three-planet system. We focus not only on the fact that the rotational modulation has multifractality properties but also on some studies on these properties based on scale. Then, we systematically investigate the dynamic behaviors of the small and large fluctuations in two types of light curves (PDC and SAP). Those fluctuations indicate that the properties of stellar noise and rotation modulation are highlighted when we apply the Multifractal Detrended Moving Average (MFDMA) algorithm. Our results also demonstrated that the multifractality of the light curve is due to both long-range correlation and broad probability density function, but the main source of multifractality is the long-range correlation. This new approach can be used to develop theoretical and computational models for various stellar magnetic activity-related phenomena and their interactions with the planets, and it can greatly simplify spot modeling from current TESS and future PLATO data.

In this study, we report on the analysis of 701 stars in a solar vicinity defined in three categories namely subsolar, solar, and supersolar with rotation periods between 1 and 70 days, based on rotational modulation signatures inferred from time series from the Kepler mission’s Public Archives. In our analysis, we performed an initial selection based on the rotation period and position in the period–H diagram, where H denotes the Hurst exponent extracted from fractal analysis. To refine our analysis, we applied a fractal approach known as the R/S method, taking into account the fluctuations of the features associated with photometric modulation at different time intervals and the fractality traces that are present in the time series of our sample. In this sense, we computed the so-called Hurst exponent for the referred stars and found that it can provide a strong discriminant of rotational modulation and background noise behavior, going beyond what can be achieved with solely the rotation period itself. Furthermore, our results emphasize that the rotation period of stars is scaled by the exponent H which increases following the increase in the rotation period. Finally, our approach suggests that the referred exponent may be a powerful rotational modulation and noise classifier.