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

Abstract

Stellar rotation was proposed as a potential age diagnostic that is precise, simple, and applicable to a broad range of low-mass stars (≤slant 1 {M}_⊙ ). Unfortunately, rotation period ({P}_{{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}_{{rot}} \propto \sqrt{age}}): K dwarfs appear to spin down more slowly than F and G dwarfs. Agüeros et al. interpreted data for the ≈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}_{{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 ≈1 Gyr-old cluster NGC 6811 with Kepler light curves. We measure {P}_{{rot}} for 171 members, more than doubling the sample relative to the existing catalog and extending the mass limit from ≈ 0.8 to ≈0.6 {M}_⊙ . 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 ± 0.07 Gyr. However, when our new low-mass rotators are included, NGC 6811's color-{P}_{{rot}} sequence deviates away from the naive 1 Gyr projection down to {T}_{{eff}}≈ 4295 K (K5V, 0.7 {M}_⊙ ), where it clearly overlaps with Praesepe’s. Combining these data with {P}_{{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}_{{rot}} stall, and that the duration of this epoch lasts longer for lower-mass stars.