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

TL;DR

This study analyzes the variability of magnetic activity cycles in solar-type stars using 37 years of Mount Wilson S-index data for 81 stars, linking cycle variability to rotation and dynamo number. It uses cycle fitting with a quasi-Planck profile, converts to $R'_{HK}$, and defines variability as $\text{var}(R)=\Delta R'_{HK}/\langle R'_{HK} \rangle$, exploring correlations with $P_{rot}$, $(Ro)^{-2}$, and $\log (\langle P_{cyc} \rangle / P_{rot})^2$. The authors compare observations with three axisymmetric dynamo models, finding qualitative agreement that variability decreases with increasing rotation rate and dynamo number, and that dynamo number proxies scale as $D\propto Ro^{-0.6}$ and $D\propto (\langle P_{cyc} \rangle / P_{rot})^{0.6}$. These results support a nonlinear quenching picture in highly supercritical dynamos and suggest that the stellar samples studied lie away from chaotic regimes. The work provides a quantified link between observed stellar activity variability and dynamo theory, informing how stellar magnetism evolves with rotation and fundamental dynamo parameters.

Abstract

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 $αΩ$ 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.

Figures (7)

• Figure 1: Time series plots of MWO raw $S$-index data and the respective quasi-Planck fittings for the seven additional GK25 stars considered in this study. Two stars, HD 81809 and HD 166620, that have relatively well defined cycles, and which were studied by Garg19, are also shown for cycle comparison. Properties of the stars are tabulated in Table \ref{['tab:data']}, while the fit parameters are given in Table \ref{['tab:fitParams']}.
• Figure 2: Scatter plot between the parametrized variability (Equation (\ref{['eq:var-rhk']})) and the inverse squared Rossby number for the GK19 set of stars. The Spearman rank correlation $r$ is also provided.
• Figure 3: Same as Figure \ref{['fig:gk19rossby']} but for evaluating the variability and rotation period correlation of GK25$+$ set of stars using the quasi-Planck fit data.
• Figure 4: Scatter plot between the parametrized variability and the rotational period for the B95$+$ set of stars. The variability class data is obtained from Table 5.3 in Egeland:2017:thesis. Stars are classified into different variability classes, either non-cyclic: 'flat', 'long' (may have $P_{\rm cyc}>20$ yrs) and 'var' (highly variable); or cyclic: 'poor', 'fair', 'good' and 'excellent'. Stars with the small dot marker do not have a variability class. Rest of the layout remains same as Figure \ref{['fig:gk19rossby']}.
• Figure 5: Same as Figure \ref{['fig:b95+prot']} but for evaluating the variability and $P_{\rm cyc}/P_{\rm rot}$ correlations. Only the stars that have the mean cycle period available in Table \ref{['tab:data']} are included.