Stellar cycle variability in Mount Wilson stars and dynamo models: Rotation rate and dynamo number dependency

Similar to the solar cycle, the magnetic cycles of other solar-type stars are also variable. How the variability of the stellar cycle changes with the rotation rate or the dynamo number is a valuable information for understanding the stellar dynamo process. We examine the variability in the stellar magnetic cycles by studying 81 stars from the data of the Mount Wilson Observatory, which started observations in 1966. For 28 stars, we have time series data available till 2003, while for others, the data are limited till 1995. We specifically explore how the variability changes with respect to three rotation-related parameters. We find a modest positive correlation between the variability and the stellar rotation period. In addition, we find suggestive negative correlations between the variability and the inverse squared Rossby number ($Ro^{-2}$), and the ratio of the mean cycle duration and rotation period ($\log \, (\langle P_{\rm cyc} \rangle / P_{\rm rot})^2$). Variability computed from the magnetic field of stellar dynamo models also show similar trends. Finally, inspired by previous studies, we examine dynamo number scaling in our model data and find that $Ro^{-0.6}$ (instead of $Ro^{-2}$ as suggested in the linear $\alpha \Omega$ dynamo theory) and $(\langle P_{\rm cyc} \rangle /P_{\rm rot})^{0.6}$ (instead of $\log \, (\langle P_{\rm cyc} \rangle / P_{\rm rot})^2$ as predicted in previous observations) are a good measure of the dynamo number. In conclusion, our results demonstrate that the stellar magnetic cycle variability decreases with the increase of the rotation rate or the dynamo number.