A Temporary Epoch of Stalled Spin-Down for Low-Mass Stars: Insights from NGC 6811 with Gaia and Kepler

Stellar rotation was proposed as a potential age diagnostic that is precise, simple, and applicable to a broad range of low-mass stars ($\leq$1 $M_\odot$). Unfortunately, rotation period $(P_{\rm rot})$ measurements of low-mass members of open clusters have undermined the idea that stars spin down with a common age dependence (i.e., $P_{\rm rot} \propto \sqrt{\rm age}$): K dwarfs appear to spin down more slowly than F and G dwarfs. Ag\"ueros et al. (2018) interpreted data for the $\approx$1.4-Gyr-old cluster NGC 752 differently, proposing that after having converged onto a slow-rotating sequence in their first 600-700 Myr (by the age of Praesepe), K dwarf $P_{\rm rot}$ stall on that sequence for an extended period of time. We use data from Gaia DR2 to identify likely single-star members of the $\approx$1-Gyr-old cluster NGC 6811 with Kepler light curves. We measure $P_{\rm rot}$ for 171 members, more than doubling the sample relative to the existing catalog and extending the mass limit from $\approx$0.8 to $\approx$0.6 $M_\odot$. We then apply a gyrochronology formula calibrated with Praesepe and the Sun to 27 single G dwarfs in NGC 6811 to derive a precise gyrochronological age for the cluster of 1.04$\pm$0.07 Gyr. However, when our new low-mass rotators are included, NGC 6811's color-$P_{\rm rot}$ sequence deviates away from the naive 1 Gyr projection down to $T_{\rm eff} \approx 4295$ K (K5V, 0.7 $M_\odot$), where it clearly overlaps with Praesepe's. Combining these data with $P_{\rm rot}$ for other clusters, we conclude that the assumption that mass and age are separable dependencies is invalid. Furthermore, the cluster data show definitively that stars experience a temporary epoch of reduced braking efficiency where $P_{\rm rot}$ stall, and that the duration of this epoch lasts longer for lower-mass stars.