Rotation-activity relationship and gyrochronology

We use R'HK and rotation period to investigate the rotation-activity relationship. Instead of the traditional two-interval model, we apply a three-interval model to fit the rotation-activity relationship in the range of the Rossby number Ro<0.7. We also use the X-ray data to verify our new model.

We find that the rotation-activity relationship is best fitted by three intervals in the rang of Ro<0.7. We associate those intervals to the convective, gap and interface phases of gyrochronology. The mean Ro of the C-to-g and g-to-I transition is ~0.022 and ~0.15, respectively.

The g-to-I transition is on the edge of the intermediate-period gap, indicating that the transition of surface brightness from spot-dominated to the facula-dominated can be associated with the transition from gap to I sequence. Furthermore, based on previous studies, we suggest an additional epoch at late times of the I phase (Ro>0.7; weakened magnetic breaking phase) from the perspective of activity. We further use the three-interval models to fit the period-activity relationship in temperature bins and determine the duration of the transition phase as a function of effective temperature.

By comparing the critical temperature and period of the g-to-I transition with the slowly rotating sequence of 10 young open clusters whose ages range from 1Myr to 2.5Gyr, we conclude that our new model finds the pure I sequence without fast rotating outliers, which defines the zero-age I sequence (ZAIS). We propose that there is an ambiguous consensus on when the I sequence starts to work. This ambiguity is from the visually convergent sequence of the color-period diagrams in open clusters.

This visually convergent sequence is younger than the ZAIS and is actually the pre-I sequence that can be associated with the stall of the spin-down. Our results unify the rotation-activity relationship and gyrochronology for the stellar evolution of low-mass stars, for which we coined the "CgIW" scenario.