Recent measurements of rotation periods ( ) in the benchmark open clusters Praesepe (670 Myr), NGC 6811 (1 Gyr), and NGC 752 (1.4 Gyr) demonstrate that, after converging onto a tight sequence of slowly rotating stars in mass–period space, stars temporarily stop spinning down. These data also show that the duration of this epoch of stalled spin-down increases toward lower masses. To determine when stalled stars resume spinning down, we use data from the K2 mission and the Palomar Transient Factory to measure for 58 dwarf members of the 2.7 Gyr old cluster Ruprecht 147, 39 of which satisfy our criteria designed to remove short-period or near-equal-mass binaries. Combined with the Kepler data for the approximately coeval cluster NGC 6819 (30 stars with M ⋆ > 0.85 ), our new measurements more than double the number of ≈2.5 Gyr benchmark rotators and extend this sample down to ≈0.55  . The slowly rotating sequence for this joint sample appears relatively flat (22 ± 2 days) compared to sequences for younger clusters. This sequence also intersects the Kepler intermediate-period gap, demonstrating that this gap was not created by a lull in star formation. We calculate the time at which stars resume spinning down and find that 0.55  stars remain stalled for at least 1.3 Gyr. To accurately age-date low-mass stars in the field, gyrochronology formulae must be modified to account for this stalling timescale. Empirically tuning a core–envelope coupling model with open cluster data can account for most of the apparent stalling effect. However, alternative explanations, e.g., a temporary reduction in the magnetic braking torque, cannot yet be ruled out.

Open clusters are collections of stars with a single, well-determined age, and can be used to investigate the connections between angular-momentum evolution and magnetic activity over a star's lifetime. We present the results of a comparative study of the relationship between stellar rotation and activity in two benchmark open clusters: Praesepe and the Hyades. As they have the same age and roughly solar metallicity, these clusters serve as an ideal laboratory for testing the agreement between theoretical and empirical rotation-activity relations at ≈600 Myr. We have compiled a sample of 720 spectra -more than half of which are new observations -for 516 high-confidence members of Praesepe; we have also obtained 139 new spectra for 130 high-confidence Hyads. We have also collected rotation periods (P rot ) for 135 Praesepe members and 87 Hyads. To compare Hα emission, an indicator of chromospheric activity, as a function of color, mass, and Rossby number R o , we first calculate an expanded set of χ values, with which we can obtain the Hα to bolometric luminosity ratio, L Hα /L bol , even when spectra are not flux-calibrated and/or stars lack reliable distances. Our χ values cover a broader range of stellar masses and colors (roughly equivalent to spectral types from K0 to M9), and exhibit better agreement between independent calculations, than existing values. Unlike previous authors, we find no difference between the two clusters in their Hα equivalent width or L Hα /L bol distributions, and therefore take the merged Hα and P rot data to be representative of 600-Myr-old stars. Our analysis shows that Hα activity in these stars is saturated for R o ≤ 0.11 +0.02 −0.03 . Above that value activity declines as a power-law with slope β = −0.73 +0.16 −0.12 , before dropping off rapidly at R o ≈ 0.4. These data provide a useful anchor for calibrating the age-activity-rotation relation beyond 600 Myr.

We analyze K2 light curves for 132 low-mass (1 > ∼ M * > ∼ 0.1 M ⊙ ) members of the 600-800 Myrold Hyades cluster and measure rotation periods (P rot ) for 116 of these stars. These include 93 stars with no prior P rot measurement; the total number of Hyads with known P rot is now 232. We then combine literature binary data with Gaia DR2 photometry and astrometry to select single star sequences in the Hyades and its roughly coeval Praesepe open cluster, and derive a new reddening value of A V = 0.035±0.011 for Praesepe. Comparing the effective temperature-P rot distributions for the Hyades and Praesepe, we find that solar-type Hyads rotate, on average, 0.4 d slower than their Praesepe counterparts. This P rot difference indicates that the Hyades is slightly older than Praesepe: we apply a new gyrochronology model tuned with Praesepe and the Sun, and find an age difference between the two clusters of 57 Myr. However, this P rot difference decreases and eventually disappears for lower-mass stars. This provides further evidence for stalling in the rotational evolution of these stars, and highlights the need for more detailed analysis of angular-momentum evolution for stars of different masses and ages.

We analyze K2 light curves for 794 low-mass (1 > ∼ M * > ∼ 0.1 M ⊙ ) members of the ≈650-Myr-old open cluster Praesepe, and measure rotation periods (P rot ) for 677 of these stars. We find that half of the rapidly rotating > ∼ 0.3 M ⊙ stars are confirmed or candidate binary systems. The remaining > ∼ 0.3 M ⊙ fast rotators have not been searched for companions, and are therefore not confirmed single stars. We found previously that nearly all rapidly rotating > ∼ 0.3 M ⊙ stars in the Hyades are binaries, but we require deeper binary searches in Praesepe to confirm whether binaries in these two co-eval clusters have different P rot distributions. We also compare the observed P rot distribution in Praesepe to that predicted by models of angular-momentum evolution. We do not observe the clear bimodal P rot distribution predicted by Brown (2014) for >0.5 M ⊙ stars at the age of Praesepe, but 0.25−0.5 M ⊙ stars do show stronger bimodality. In addition, we find that >60% of early M dwarfs in Praesepe rotate more slowly than predicted at 650 Myr by Matt et al. (2015), which suggests an increase in braking efficiency for these stars relative to solar-type stars and fully convective stars. The incompleteness of surveys for binaries in open clusters likely impacts our comparison with these models, since the models only attempt to describe the evolution of isolated single stars.

Stellar rotation was proposed as a potential age diagnostic that is precise, simple, and applicable to a broad range of low-mass stars (≤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 ∝ √ age): K dwarfs appear to spin down more slowly than F and G dwarfs. Agüeros et al. (2018) 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.