Abstract
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, Delta alpha, C, H)-quartet, where A, Delta alpha,
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
Poincare 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.
Users
Please
log in to take part in the discussion (add own reviews or comments).