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 ($\le$1 $M_{\odot }$). Unfortunately, rotation period $(P_{\mathrm{rot}})$ measurements of low-mass members of open clusters have undermined the idea that stars spin down with a common age dependence (i.e., $P_{\mathrm{rot}}\propto \sqrt{\mathrm{age}}$): K dwarfs appear to spin down more slowly than F and G dwarfs. Agüeros 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 $P_{\mathrm{rot}}$ 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 $P_{\mathrm{rot}}$ 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_{\mathrm{rot}}$ sequence deviates away from the naive 1 Gyr projection down to $T_{\mathrm{eff}}\approx 4295$ K (K5V, 0.7 $M_{\odot }$), where it clearly overlaps with Praesepe's. Combining these data with $P_{\mathrm{rot}}$ 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 $P_{\mathrm{rot}}$ stall, and that the duration of this epoch lasts longer for lower-mass stars.

18 pages, 8 figures, 1 table

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