Abstract
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 methods to characterize
the multiscale structure of the observed time series from a sample of
similar to 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.
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