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ABSTRACT Age is a stellar parameter that is both fundamental and difficult to determine. Among middle-aged M dwarfs, the most prolific hosts of close-in and detectable exoplanets, gyrochronology is the most promising method to assign ages, but requires calibration by rotation-temperature sequences (gyrochrones) in clusters of known ages. We curated a catalogue of 249 late K- and M-type (Teff = 3200–4200 K) exoplanet host stars with established rotation periods, and applied empirical, temperature-dependent rotation–age relations based on relevant published gyrochrones, including one derived from observations of the 4-Gyr-old open cluster M67. We estimated ages for 227 of these stars, and upper limits for eight others, excluding 14 which are too rapidly rotating or are otherwise outside the valid parameter range of our gyrochronology. We estimated uncertainties based on observed scatter in rotation periods in young clusters, error in the gyrochrones, and uncertainties in temperature and non-solar metallicity. For those stars with measured metallicities, we provide but do not incorporate a correction for the effects of deviation from solar-metallicity. The age distribution of our sample declines to near zero at 10 Gyr, the age of the Galactic disc, with the handful of outliers explainable by large uncertainties. Continued addition or extension of cluster rotation sequences to more thoroughly calibrate the gyrochronology in time and temperature space, more precise and robust measurement of rotation periods, and more accurate stellar parameter measurements will enable continued improvements in the age estimates of these important exoplanet host stars. 

ABSTRACT Studies of T Tauri discs inform planet formation theory; observations of variability due to occultation by circumstellar dust are a useful probe of unresolved, planet-forming inner discs, especially around faint M dwarf stars. We report observations of 2M0632, an M dwarf member of the Carina young moving group that was observed by Transiting Exoplanet Survey Satellite over two 1-yr intervals. The combined light curve contains >300 dimming events, each lasting a few hours, and as deep as 40 per cent (0.55 magnitudes). These stochastic events are correlated with a distinct, stable 1.86-d periodic signal that could be stellar rotation. Concurrent ground-based, multiband photometry show reddening consistent with interstellar medium-like dust. The star’s excess emission in the infrared and emission lines in optical and infrared spectra reveal a T Tauri-like accretion disc around the star. We confirm membership of 2M0632 in the Carina group by a Bayesian analysis of its Galactic space motion and position. We combine stellar evolution models with Gaia photometry and constraints on Teff, luminosity, and the absence of detectable lithium in the photosphere to constrain the age of the group and 2M0632 to 40–60 Myr, consistent with earlier estimates. 2M0632 joins a handful of long-lived discs which challenge the canon that disc lifetimes are ≲10 Myr. All known examples surround M dwarfs, suggesting that lower X-ray/ultraviolet irradiation and slower photoevaporation by these stars can dramatically affect disc evolution. The multiplanet systems spawned by long-lived discs probably experienced significant orbital damping and migration into close-in, resonant orbits, and perhaps represented by the TRAPPIST-1 system.