# New Suns in the Cosmos V: Stellar rotation and multifractality in active \textit{Kepler} stars

## TL;DR

This study applies multifractal analysis to Kepler star photometry, revealing that the Hurst exponent correlates with stellar rotation and activity, and can distinguish stars with differential rotation.

## Contribution

It introduces the use of multifractal analysis and the Hurst exponent to characterize stellar rotation and magnetic activity in Kepler stars, providing new insights into stellar variability.

## Key findings

- Hurst exponent correlates with stellar rotation period
- Hurst index distinguishes stars with and without differential rotation
- Hurst exponent serves as a proxy for magnetic activity

## Abstract

In the present study, high-precision time series photometry for the active \emph{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 $\sim$40 000 active stars. Among these stars, 6486 have surface differential rotation measurement, whereas 1846 have no signature of differential rotation. As a result, the Hurst exponent ($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.