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Low-mass (≲1.2M_⊙) main-sequence stars lose angular momentum over time, leading to a decrease in their magnetic activity. The details of this rotation–activity relation remain poorly understood, however. Using observations of members of the ≈700 Myr old Praesepe and Hyades open clusters, we aim to characterize the rotation–activity relation for different tracers of activity at this age. To complement published data, we obtained new optical spectra for 250 Praesepe stars, new X-ray detections for 10, and new rotation periods for 28. These numbers for Hyads are 131, 23, and 137, respectively. The latter increases the number of Hyads with periods by 50%. We used these data to measure the fractional Hαand X-ray luminosities,L_Hα/L_bolandL_X/L_bol, and to calculate Rossby numbersR_o. We found that at ≈700 Myr almost all M dwarfs exhibit Hαemission, with binaries having the same overall color–Hαequivalent width distribution as single stars. In theR_o–L_Hα/L_bolplane, unsaturated single stars follow a power law with indexβ= −5.9 ± 0.8 forR_o> 0.3. In theR_o–L_X/L_bolplane, we see evidence for supersaturation for single stars withR_o≲ 0.01, following a power law with index${\beta }_{\sup }={0.5}_{-0.1}^{+0.2}$, supporting the hypothesis that the coronae of these stars are being centrifugally stripped. We found that the criticalR_ovalue at which activity saturates is smaller forL_X/L_bolthan forL_Hα/L_bol. Finally, we observed an almost 1:1 relation betweenL_Hα/L_bolandL_X/L_bol, suggesting that both the corona and the chromosphere experience similar magnetic heating.

As an open cluster orbits the Milky Way, gravitational fields distort it, stripping stars from the core and forming tidal tails. Recent work has identified tidal tails of the Praesepe cluster; we explore rotation periods as a way to confirm these candidate members. In open clusters, the rotation period distribution evolves over time due to magnetic braking. Since tidally stripped stars originally formed within the cluster, they should follow the same period distribution as in the cluster core. We analyze 96 candidate members observed by NASA’s Transiting Exoplanet Survey Satellite mission. We measure reliable rotation periods for 32 stars, while 64 light curves are noise-dominated. The 32 newly identified rotators are consistent with the period distribution in the core, and with past membership in Praesepe. We therefore suggest that for nearby open clusters, stellar rotation offers a quick and inexpensive method for confirming past members dispersed into tidal tails.

X-ray observations of low-mass stars in open clusters are critical to understanding the dependence of magnetic activity on stellar properties and their evolution. Praesepe and the Hyades, two of the nearest, most-studied open clusters, are among the best available laboratories for examining the dependence of magnetic activity on rotation for stars with masses ≲1M_⊙. We present an updated study of the rotation–X-ray activity relation in the two clusters. We updated membership catalogs that combine pre-Gaia catalogs with new catalogs based on Gaia Data Release 2. The resulting catalogs are the most inclusive ones for both clusters: 1739 Praesepe and 1315 Hyades stars. We collected X-ray detections for cluster members, for which we analyzed, re-analyzed, or collated data from ROSAT, the Chandra X-ray Observatory, the Neil Gehrels Swift Observatory, and XMM-Newton. We have detections for 326 Praesepe and 462 Hyades members, of which 273 and 164, respectively, have rotation periods—an increase of 6× relative to what was previously available. We find that at ≈700 Myr, only M dwarfs remain saturated in X-rays, with only tentative evidence for supersaturation. We also find a tight relation between the Rossby number and fractional X-ray luminosityL_X/L_bolin unsaturated single members, suggesting a power-law index between −3.2 and −3.9. Lastly, we find no difference in the coronal parameters between binary and single members. These results provide essential insight into the relative efficiency of magnetic heating of the stars’ atmospheres, thereby informing the development of robust age-rotation-activity relations.

Two magnetic braking models are implemented inMESAfor use in theMISTstellar model grids. Stars less than about 1.3 solar masses are observed to spin down over time through interaction with their magnetized stellar winds (i.e., magnetic braking). This is the basis for gyrochronology and is fundamental to the evolution of lower-mass stars. The detailed physics behind magnetic braking are uncertain, as are 1D stellar evolution models. Thus, we calibrate our models and compare to data from open clusters. Each braking model tested here is capable of reproducing aspects of the data, with important distinctions; neither fully accounts for the observations. The Matt et al. prescription matches the slowly rotating stars observed in open clusters but tends to overestimate the presence of rapidly rotating stars. The Garraffo et al. prescription often produces too much angular momentum loss to accurately match the observed slow sequence for lower-mass stars but reproduces the bimodal nature of slowly and rapidly rotating stars observed in open clusters fairly well. Our models additionally do not reproduce the observed solar lithium depletion, corroborating previous findings that effects other than rotation may be important. We find additional evidence that some level of mass dependency may be missing in these braking models to match the rotation periods observed in clusters older than 1 Gyr better.