Nonextensive formalism is a generalization of the Boltzmann-Gibbs statistics. In this formalism the entropic index q is a quantity characterizing the degree of nonextensivity, and is interpreted as a parameter of long-memory or long-range interactions between the components of the system. Since its proposition in 1988, this formalism has been applied to investigate a wide variety of natural phenomena. In stellar astrophysics, theoretical distribution function based on nonextensive formalism (q-distributions) has been successfully applied to reproduce the distribution of stellar radial and rotational velocity data. In this paper, we investigate the time variation of the entropic index q obtained from the distribution of rotation, V sin i, for a sample of 254 rotational data for solar-type stars from 11 open clusters aged between 35.5 Myr and 2.6 Gyr. As a result, we have found an anti-correlation between the entropic index q and the age of clusters, and that the distribution of rotation V sin i for these stars becomes extensive for an age greater than about 170 Myr. Assuming that the parameter q is associated with long-memory effects, we suggest that the memory of the initial angular momentum of solar-type stars can be scaled by the entropic index q. We also propose a physical link between the parameter q and the magnetic braking of stellar rotation.

In present paper, we investigate the multifractality signatures in hourly time series extracted from CoRoT spacecraft database. Our analysis is intended to highlight the possibility that astrophysical time series can be members of a particular class of complex and dynamic processes which require several photometric variability diagnostics to characterize their structural and topological properties. To achieve this goal, we search for contributions due to nonlinear temporal correlation and effects caused by heavier tails than the Gaussian distribution, using a detrending moving average algorithm for one-dimensional multifractal signals (MFDMA). We observe that the correlation structure is the main source of multifractality, while heavy-tailed distribution plays a minor role in generating the multifractal effects. Our work also reveals that rotation period of stars is inherently scaled by degree of multifractality. As a result, analyzing the multifractal degree of referred series, we uncover an evolution of multifractality from shorter to larger periods.

In the present study, we investigate the multifractal nature of a long-cadence time series observed by the Kepler mission for a sample of 34 M dwarf stars and the Sun in its active phase. Using the Multifractal Detrending Moving Average algorithm (MFDMA), which enables the detection of multifractality in nonstationary time series, we define a set of multifractal indices based on the multifractal spectrum profile as a measure of the level of stellar magnetic activity. This set of indices is given by the (A,∆α,C,H)-quartet, where A, ∆α and C are related to geometric features from the multifractal spectrum and the global Hurst exponent H describes the global structure and memorability of time series dynamics. As a test, we measure these indices and compare them with a magnetic index defined as S ph and verify the degree of correlation among them. First, we apply the Poincaré plot method and find a strong correlation between the S ph index and one of the descriptors that emerges from this method. As a result, we find that this index is strongly correlated with long-term features of the signal. From the multifractal perspective, the S ph index is also strongly linked to the geometric properties of the multifractal spectrum except for the H index. Furthermore, our results emphasize that the rotation period of stars is scaled by the H index, which is consistent with Skumanich's relationship. Finally, our approach suggests that the H index may be related to the evolution of stellar angular momentum and a star's magnetic properties.

In the present study, high-precision time series photometry for the active Kepler stars is described in the language of multifractals. We explore the potential of using the rescaled range analysis (R/S) and multifractal detrended moving average analysis (MFDMA) methods to characterize the multiscale structure of the observed time series from a sample of ∼40 000 active stars. Among these stars, 6486 have surface differential rotation measurement, whereas 1846 have no signature of differential rotation. As a result, the Hurst exponent (H) derived from both methods shows a strong correlation with the period derived from rotational modulation. In addition, the variability range R var reveals how this correlation follows a high activity "line". We also verify that the H-index is an able parameter for distinguishing the different signs of stellar rotation that can exist between the stars with and without differential rotation. In summary, the results indicate that the Hurst exponent is a promising index for estimating photometric magnetic activity.