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Stephanie T. Douglas

Publications and source records attributed to Stephanie T. Douglas.

At least 19 recordsLinked to original sources

Open Clusters as Laboratories for Cool Star Evolution: Highlights from the Cool Stars 23 Splinter Session

Open clusters remain among the most powerful laboratories for calibrating how fundamental stellar properties such as rotation, magnetic activity, surface chemistry, and internal structure evolve over the pre-main-sequence to main-sequence and post-main-sequence stellar lifetime. Because cluster members share a common age, galactic environment, and initial composition, they provide empirical anchors upon which age-dating techniques such as gyrochronology, activity-age relations, and chemical clocks are built. This paper summarizes the Cool Stars 23 splinter session - Open Clusters as Laboratories for Cool Star Evolution, held on 15 June 2026 in Tokyo, Japan. The session comprised one invited review, ten contributed talks, and ten poster pop-up presentations, organized around three themes: the evolution of rotation, magnetic activity, and chemical abundances (Li-depletion, [C/N], [Y/Mg], and neutron-capture elements). We close with a summary of the open questions identified in the panel discussion and the observational and theoretical work that new surveys (e.g. Gaia DR4, 4MOST, WEAVE) and missions (e.g. PLATO, Roman) will enable over the coming years. Together, these efforts will help assess the current state of the field and shape its future directions.

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Spectroscopic Follow-up of Young High-$α$ Dwarf Star Candidates: Still Likely Genuinely Young

The question of whether genuinely young high-$α$ stars exist has been discussed for over a decade since their discovery from asteroseismology of giant stars as it is challenging to break the degeneracy between the binary interaction and the genuinely young scenarios. Young high-$α$ stars are hard to explain with traditional chemical evolution model as the high-$α$ disk is typically associated with the early epoch of star formation in the Milky Way. Combined with recent advances of gyrochronology, and that $^7$Li can serve as an unambiguous indicator for identifying merger products in dwarfs thanks to its low burning temperature, we identified young high-$α$ dwarf candidate stars through their fast rotation in a previous study. In this paper, we performed high-resolution spectroscopic follow-up of these candidates using Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI), and confirm 3 additional stars that are most likely genuinely young. Together with the star from the earlier paper, we find three out of four of them center around [Fe/H]=-0.5 dex, are ~5 Gyr old, and have a similar amount of elevated Li (~0.5 dex) and Al (~0.1 dex) compared to stars with matching $\log g$, $T_{\rm eff}$, Mg, and Fe within observational uncertainties, hinting at their common formation pathway.

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A transiting multi-planet system in the 61 million year old association Theia 116

Observing and characterizing young planetary systems can aid in unveiling the evolutionary mechanisms that sculpt the mature exoplanet population. As an all-sky survey, NASA's Transiting Exoplanet Survey Satellite (TESS) has expanded the known young planet population as it has observed young comoving stellar populations. This work presents the discovery of a multiplanet system orbiting the 61 Myr old G4V star TIC 434398831 (M = 0.99 Msun, R = 0.91 Rsun, Teff = 5638 K, Tmag = 11.31) located in the Theia 116 comoving population. We estimate the population's age based on rotation periods measured from the TESS light curves, isochrone fitting, and measurements of lithium equivalent widths in the spectra of Theia 116 members. The TESS FFI light curves reveal a mini-Neptune (Rb = 3.51 Rearth, Pb = 3.69 days) and super-Neptune (Rc = 5.63 Rearth, Pc = 6.21 days) with an orbital period ratio slightly larger than 5:3. Follow-up observations from CHEOPS and ground-based telescopes confirm the transits of TIC 434398831 b and c, and constrain their transit times. We explore the potential mass-loss histories of the two planets in order to probe possible initial conditions of the planets immediately after formation.

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ChronoFlow: A Data-Driven Model for Gyrochronology

Gyrochronology is a technique for constraining stellar ages using rotation periods, which change over a star's main sequence lifetime due to magnetic braking. This technique shows promise for main sequence FGKM stars, where other methods are imprecise. However, the observed dispersion in rotation rates for similar coeval stars has historically been difficult to characterize. To properly understand this complexity, we have assembled the largest standardized data catalog of rotators in open clusters to date, consisting of $\approx$8,000 stars across 30 open clusters/associations spanning ages of 1.5 Myr to 4 Gyr. We have also developed ChronoFlow: a flexible data-driven model which accurately captures observed rotational dispersion. We show that ChronoFlow can be used to accurately forward model rotational evolution, and to infer both cluster and individual stellar ages. We recover cluster ages with a statistical uncertainty of 0.06 dex ($\approx$15%), and individual stellar ages with a statistical uncertainty of 0.7 dex. Additionally, we conducted robust systematic tests to analyze the impact of extinction models, cluster membership, and calibration ages. These contribute an additional 0.06 dex of uncertainty in cluster age estimates, resulting in a total error budget of 0.08 dex. We apply ChronoFlow to estimate ages for M34, NGC 2516, NGC 6709, and the Theia 456 stellar stream. Our results show that ChronoFlow can precisely estimate the ages of coeval stellar populations, and constrain ages for individual stars. Furthermore, its predictions may be used to inform physical spin down models. ChronoFlow is publicly available at https://github.com/philvanlane/chronoflow.

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Short-Term Balmer Line Emission Variability in M Dwarfs

M Dwarfs make up the majority of stars, offering an avenue for discovering exoplanets due to their smaller sizes. However, their magnetic activity poses challenges for exoplanet detection, characterization, and planetary habitability. Understanding its magnetic activity, including surface starspots and internal dynamos, is crucial for exoplanet research. In this study, we present short-term variability in four Balmer emission lines \ha, \hb, \hg, and \hd\ for a sample of 77 M dwarfs of varying spectral types, and binarity. Stars were observed using the MDM Observatory's Ohio State Multi-Object Spectrograph on the 2.4m Telescope and the Modular Spectrograph on the 1.3 m Telescope. These data are combined with TESS photometry to explore the connection between spectroscopic and photometric variability. We observe sporadic short-term variability in Balmer lines for some stars, on timescale $\gtrsim$ 15-min, but much shorter than the stellar rotation period. We calculate periods for stars lacking those measurements, re-evaluated the relationship between amplitude (\rvar)-activity relation for the \ha \ line from \citet{garcia_soto_contemporaneous_2023}, and extended our analysis to the \hb, \hg \ and \hd \ lines, which indicates that the relation becomes increasingly dispersed for higher-order Balmer lines. This is consistent with increased intrinsic variability from lower to higher order lines. Additionally, we compute the Balmer decrement, using \hb \ as the fiducial, for stars where we could measure \hg \ and/or \hd. The Balmer decrement can show distinct patterns during white-light flares, with significant differences even for the same star. We also find evidence for dark spots on \object{TIC 283866910}.

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The occurrence of small, short-period planets younger than 200 Myr with TESS

Within the first few hundreds of millions of years, many physical processes sculpt the eventual properties of young planets. NASA's TESS mission has surveyed young stellar associations across the entire sky for transiting planets providing glimpses into the various stages of planetary evolution. Using our own detection pipeline, we search a magnitude-limited sample of 7219 young stars ($\leq$200 Myr) observed in the first four years of TESS for small (2-8 R$_\oplus$), short period (1.6-20 days) transiting planets. The completeness of our survey is characterized by a series of injection and recovery simulations. Our analysis of TESS 2-minute cadence and Full Frame Image (FFI) light curves recover all known TOIs, as well as four new planet candidates not previously identified as TOIs. We derive an occurrence rate of $35^{+13}_{-10}$% for mini-Neptunes and $27^{+10}_{-8}$% for super-Neptunes from the 2-minute cadence data, and $22^{+8.6}_{-6.8}$% for mini-Neptunes and $13^{+3.9}_{-4.9}$% for super-Neptunes from FFI data. To independently validate our results, we compare our survey yield with the predicted planet yield assuming Kepler planet statistics. We consistently find a mild increase in the occurrence of super-Neptunes and a significant increase in the occurrence of Neptune-sized planets with orbital periods of 6.2-12 days when compared to their mature counterparts. The young planet distribution from our study is most consistent with evolution models describing the early contraction of hydrogen-dominated atmospheres undergoing atmospheric escape and inconsistent with heavier atmosphere models offering only mild radial contraction early on.

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Contemporaneous Observations of $Hα$ Luminosities and Photometric Amplitudes for M Dwarfs

While many M dwarfs are known to have strong magnetic fields and high levels of magnetic activity, we are still unsure about the properties of their starspots and the origin of their magnetic dynamos. Both starspots and chromospheric heating are generated by the surface magnetic field; they produce photometric variability and Halpha emission, respectively. Connecting brightness variations to magnetic activity therefore provides a means to examine M dwarf magnetism. We survey 30 M dwarfs previously identified as fast rotating stars (Prot < 10 days). We present time-series optical photometry from the Transiting Exoplanet Survey Satellite (TESS) and contemporaneous optical spectra obtained using the Ohio State Multi-Object Spectrograph (OSMOS) on the 2.4m Hiltner telescope at MDM Observatory in Arizona. We measure rotation periods and photometric amplitudes from TESS light curves using Gaussian Processes. From the OSMOS spectra, we calculate the equivalent width of Halpha, and LHalpha/Lbol. We find a weak positive correlation between Halpha luminosity and the semi-amplitude, Rvar p=0.005_{-0.005}^{+0.075}. We also observe short-term variability (between 20-45 minutes) in Halpha equivalent widths and possible enhancement from flares consistent to recent literature.

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Hyades Member K2-136c: The Smallest Planet in an Open Cluster with a Precisely Measured Mass

K2-136 is a late-K dwarf ($0.742\pm0.039$ M$_\odot$) in the Hyades open cluster with three known, transiting planets and an age of $650\pm70$ Myr. Analyzing K2 photometry, we found that planets K2-136b, c, and d have periods of $8.0$, $17.3$, and $25.6$ days and radii of $1.014\pm0.050$ R$_\oplus$, $3.00\pm0.13$ R$_\oplus$, and $1.565\pm0.077$ R$_\oplus$, respectively. We collected 93 radial velocity measurements (RVs) with the HARPS-N spectrograph (TNG) and 22 RVs with the ESPRESSO spectrograph (VLT). Analyzing HARPS-N and ESPRESSO data jointly, we found K2-136c induced a semi-amplitude of $5.49\pm0.53$ m s$^{-1}$, corresponding to a mass of $18.1\pm1.9$ M$_\oplus$. We also placed $95$% upper mass limits on K2-136b and d of $4.3$ and $3.0$ M$_\oplus$, respectively. Further, we analyzed HST and XMM-Newton observations to establish the planetary high-energy environment and investigate possible atmospheric loss. K2-136c is now the smallest planet to have a measured mass in an open cluster and one of the youngest planets ever with a mass measurement. K2-136c has $\sim$75% the radius of Neptune but is similar in mass, yielding a density of $3.69^{+0.67}_{-0.56}$ g cm$^{-3}$ ($\sim$2-3 times denser than Neptune). Mass estimates for K2-136b (and possibly d) may be feasible with more RV observations, and insights into all three planets' atmospheres through transmission spectroscopy would be challenging but potentially fruitful. This research and future mass measurements of young planets are critical for investigating the compositions and characteristics of small exoplanets at very early stages of their lives and providing insights into how exoplanets evolve with time.

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TOI-4562 b: A highly eccentric temperate Jupiter analog orbiting a young field star

We report the discovery of TOI-4562 b (TIC-349576261), a Jovian planet orbiting a young F7V-type star, younger than the Praesepe/Hyades clusters (< $700$ Myr). This planet stands out because of its unusually long orbital period for transiting planets with known masses ($P_{\mathrm{orb}}$ = $225.11781^{+0.00025}_{-0.00022}$ days), and because it has a substantial eccentricity ($e$ = $0.76^{+0.02}_{-0.02}$). The location of TOI-4562 near the southern continuous viewing zone of TESS allowed observations throughout 25 sectors, enabling an unambiguous period measurement from TESS alone. Alongside the four available TESS transits, we performed follow-up photometry using the South African Astronomical Observatory node of the Las Cumbres Observatory, and spectroscopy with the CHIRON spectrograph on the 1.5 m SMARTS telescope. We measure a radius of $1.118_{+0.013}^{-0.014}$ $R_{\mathrm{J}}$ and a mass of $2.30^{+0.48}_{-0.47}$ $M_{\mathrm{J}}$ for TOI-4562 b. The radius of the planet is consistent with contraction models describing the early evolution of the size of giant planets. We detect tentative transit timing variations at the $\sim$ 20 min level from five transit events, favouring the presence of a companion that could explain the dynamical history of this system if confirmed by future follow-up observations. With its current orbital configuration, tidal timescales are too long for TOI-4562 b to become a hot-Jupiter via high eccentricity migration, though it is not excluded that interactions with the possible companion could modify TOI-4562 b eccentricity and trigger circularization. The characterisation of more such young systems is essential to set constraints on models describing giant planet evolution.

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Using stellar rotation to identify tidally stripped members of the Praesepe open cluster

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 (TESS) 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.

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The Factory and the Beehive. IV. A Comprehensive Study of the Rotation X-ray Activity Relation in Praesepe and the Hyades

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 lower than $\approx 1\ M_{\odot}$. 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$\times$ relative to what was previously available. We find that at $\approx$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 luminosity $L_\mathrm{X}/L_\mathrm{bol}$ in 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.

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A Mini-Neptune from TESS and CHEOPS Around the 120 Myr Old AB Dor member HIP 94235

The TESS mission has enabled discoveries of the brightest transiting planet systems around young stars. These systems are the benchmarks for testing theories of planetary evolution. We report the discovery of a mini-Neptune transiting a bright star in the AB Doradus moving group. HIP 94235 (TOI-4399, TIC 464646604) is a Vmag=8.31 G-dwarf hosting a 3.00 -0.28/+0.32 Rearth mini-Neptune in a 7.7 day period orbit. HIP 94235 is part of the AB Doradus moving group, one of the youngest and closest associations. Due to its youth, the host star exhibits significant photometric spot modulation, lithium absorption, and X-ray emission. Three 0.06% transits were observed during Sector-27 of the TESS Extended Mission, though these transit signals are dwarfed by the 2% peak-to-peak photometric variability exhibited by the host star. Follow-up observations with CHEOPS confirmed the transit signal and prevented the erosion of the transit ephemeris. HIP 94235 is part of a 50 AU G-M binary system. We make use of diffraction limited observations spanning 11 years, and astrometric accelerations from Hipparchos and Gaia, to constrain the orbit of HIP 94235 B. HIP 94235 is one of the tightest stellar binaries to host an inner planet. As part of a growing sample of bright, young planet systems, HIP 94235 b is ideal for follow-up transit observations, such as those that investigate the evaporative processes driven by high-energy radiation that may sculpt the valleys and deserts in the Neptune population.

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HAZMAT. VIII. A Spectroscopic Analysis of the Ultraviolet Evolution of K Stars: Additional Evidence for K Dwarf Rotational Stalling in the First Gigayear

Efforts to discover and characterize habitable zone planets have primarily focused on Sun-like stars and M dwarfs. K stars, however, provide an appealing compromise between these two alternatives that has been relatively unexplored. Understanding the ultraviolet (UV) environment around such stars is critical to our understanding of their planets, as the UV can drastically alter the photochemistry of a planet's atmosphere. Here we present near-UV and far-UV \textit{Hubble Space Telescope}'s Cosmic Origins Spectrograph observations of 39 K stars at three distinct ages: 40 Myr, 650 Myr, and $\approx$5 Gyr. We find that the K star (0.6 -- 0.8 M$_{\odot}$) UV flux remains constant beyond 650 Myr before falling off by an order of magnitude by field age. This is distinct from early M stars (0.3 -- 0.6 M$_{\odot}$), which begin to decline after only a few hundred Myr. However, the rotation-UV activity relation for K stars is nearly identical to that of early M stars. These results may be a consequence of the spin-down stalling effect recently reported for K dwarfs, in which the spin-down of K stars halts for over a Gyr when their rotation periods reach $\approx$10 d, rather than the continuous spin down that G stars experience. These results imply that exoplanets orbiting K dwarfs may experience a stronger UV environment than thought, weakening the case for K stars as hosts of potential "super-habitable" planets.

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Three K2 Campaigns Yield Rotation Periods for 1013 Stars in Praesepe

We use three campaigns of K2 observations to complete the census of rotation in low-mass members of the benchmark, $\approx$670-Myr-old open cluster Praesepe. We measure new rotation periods (\prot) for 220 $\lesssim$1.3~\Msun\ Praesepe members and recover periods for $97\%$ (793/812) of the stars with a \prot\ in the literature. Of the 19 stars for which we do not recover a \prot, 17 were not observed by K2. As K2's three Praesepe campaigns took place over the course of three years, we test the stability of our measured \prot\ for stars observed in more than one campaign. We measure \prot\ consistent to within $10\%$ for $>95\%$ of the 331 likely single stars with $\geq$2 high-quality observations; the median difference in \prot\ is $0.3\%$, with a standard deviation of $2\%$. Nearly all of the exceptions are stars with discrepant \prot\ measurements in Campaign 18, K2's last, which was significantly shorter than the earlier two ($\approx$50~d rather than $\approx$75~d). This suggests that, despite the evident morphological evolution we observe in the light curves of $38\%$ of the stars, \prot\ measurements for low-mass stars in Praesepe are stable on timescales of several years. A \prot\ can therefore be taken to be representative even if measured only once.

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Two young planetary systems around field stars with ages between 20-320 Myr from TESS

Planets around young stars trace the early evolution of planetary systems. We report the discovery and validation of two planetary systems with ages $\lesssim 300$ Myr from observations by the Transiting Exoplanet Survey Satellite. TOI-251 is a 40-320 Myr old G star hosting a 2.74 +0.18/-0.18 REarth mini-Neptune with a 4.94 day period. TOI-942 is a 20-160 Myr old K star hosting a system of inflated Neptune-sized planets, with TOI-942b orbiting with a period of 4.32 days, with a radius of 4.81 +0.20/-0.20 REarth, and TOI-942c orbiting in a period of 10.16 days with a radius of 5.79 +0.19/-0.18 REarth. Though we cannot place either host star into a known stellar association or cluster, we can estimate their ages via their photometric and spectroscopic properties. Both stars exhibit significant photometric variability due to spot modulation, with measured rotation periods of $\sim 3.5$ days. These stars also exhibit significant chromospheric activity, with age estimates from the chromospheric calcium emission lines and X-ray fluxes matching that estimated from gyrochronology. Both stars also exhibit significant lithium absorption, similar in equivalent width to well-characterized young cluster members. TESS has the potential to deliver a population of young planet-bearing field stars, contributing significantly to tracing the properties of planets as a function of their age.

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When Do Stalled Stars Resume Spinning Down? Advancing Gyrochronology with Ruprecht 147

Recent measurements of rotation periods ($P_\text{rot}$) 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 $P_\text{rot}$ 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 $Kepler$ $P_\text{rot}$ data for the approximately coeval cluster NGC 6819 (30 stars with $M_\star > 0.85$ M$_\odot$), our new measurements more than double the number of $\approx$2.5 Gyr benchmark rotators and extend this sample down to $\approx$0.55 M$_\odot$. The slowly rotating sequence for this joint sample appears relatively flat (22 $\pm$ 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 M$_\odot$ 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.

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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. 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 $P_{\rm rot}$ 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.

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A search for radius inflation among active M-dwarfs in Praesepe

Rotation periods from Kepler K2 are combined with projected rotation velocities from the WIYN 3.5-m telescope, to determine projected radii for fast-rotating, low-mass ($0.15 \leq M/M_{\odot} \leq 0.6$) members of the Praesepe cluster. A maximum likelihood analysis that accounts for observational uncertainties, binarity and censored data, yields marginal evidence for radius inflation -- the average radius of these stars is $6\pm4$ per cent larger at a given luminosity than predicted by commonly-used evolutionary models. This over-radius is smaller (at 2-sigma confidence) than was found for similar stars in the younger Pleiades using a similar analysis; any decline appears due to changes occurring in higher mass ($>0.25 M_{\odot}$) stars. Models incorporating magnetic inhibition of convection predict an over-radius, but do not reproduce this mass dependence unless super-equipartition surface magnetic fields are present at lower masses. Models incorporating flux-blocking by starspots can explain the mass dependence but there is no evidence that spot coverage diminishes between the Pleiades and Praesepe samples to accompany the decline in over-radius. The fastest rotating stars in both Praesepe and the Pleiades are significantly smaller than the slowest rotators for which a projected radius can be measured. This may be a selection effect caused by more efficient angular momentum loss in larger stars leading to their progressive exclusion from the analysed samples. Our analyses assume random spin-axis orientations; any alignment in Praesepe, as suggested by Kovacs (2018), is strongly disfavoured by the broad distribution of projected radii.

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