New Suns in the Cosmos. IV. The Multifractal Nature of Stellar Magnetic Activity in Kepler Cool Stars

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, which enables the detection of multifractality in no...

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Bibliographic Details
Published in:The Astrophysical journal 2017-07, Vol.843 (2), p.103
Main Authors: de Freitas, D. B., Nepomuceno, M. M. F., Gomes de Souza, M., Leão, I. C., Das Chagas, M. L., Costa, A. D., Canto Martins, B. L., De Medeiros, J. R.
Format: Article
Language:English
Subjects:
Algorithms
ANGULAR MOMENTUM
Astrophysics
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
COMPARATIVE EVALUATIONS
Cool stars
Correlation
CORRELATIONS
DATA ANALYSIS
DETECTION
DWARF STARS
Hirsch index
MAGNETIC PROPERTIES
methods: data analysis
ROTATION
SPECTRA
stars: activity
stars: solar-type
Stellar evolution
Stellar rotation
SUN
Sun: rotation
Time series
UNIVERSE
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Summary: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, 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, , C, H)-quartet, where A, , 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 Sph 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 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.
ISSN:0004-637X
1538-4357
DOI:10.3847/1538-4357/aa78aa