New Suns in the Cosmos IV: the multifractal nature of stellar magnetic activity in \textit{Kepler} cool stars
arXiv:1706.02935 · doi:10.3847/1538-4357/aa78aa
Abstract
In the present study, we investigate the multifractal nature of a long-cadence time series observed by the \textit{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 (,,,)-quartet, where , and are related to geometric features from the multifractal spectrum and the global Hurst exponent 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 and verify the degree of correlation among them. First, we apply the Poincaré plot method and find a strong correlation between the 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 index is also strongly linked to the geometric properties of the multifractal spectrum except for the index. Furthermore, our results emphasize that the rotation period of stars is scaled by the index, which is consistent with Skumanich's relationship. Finally, our approach suggests that the index may be related to the evolution of stellar angular momentum and a star's magnetic properties.
arXiv comment8 figures and 3 tables (Accepted to ApJ)
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