Starspot rotation rates vs. activity cycle phase

We phase-fold these measurements with the cycle period. To reduce random errors we perform averages over stars with comparable mean rotation rates and effective temperature at fixed activity-cycle phases. We detect a clear correlation between the variation of activity level and the variation of the starspot rotation rate.

The sign and amplitude of this correlation depends on the mean stellar rotation and -- to a lesser extent -- on the effective temperature. For slowly rotating stars (rotation periods between 15-28 days) the starspot rotation rates are clearly anti-correlated with the level of activity during the activity cycles. A transition is observed around rotation periods of 10-15 days, where stars with effective temperature above 4200K instead show positive correlation.

Our measurements can be interpreted in terms of a stellar "butterfly diagram", but these appear different from the Sun's since the starspot rotation rates are either in phase or anti-phase with the activity level. Alternatively, the activity cycle periods observed by Kepler are short (around 2.5 years) and may therefore be secondary cycles, perhaps analogous to the solar quasi-biennial oscillations.