2018ApJ...863..166V

The M dwarf stars are exciting targets for exoplanet investigations; however, their fundamental stellar properties are difficult to measure. Perhaps the most challenging property is stellar age. Once on the main sequence, M dwarfs change imperceptibly in their temperature and luminosity, necessitating novel statistical techniques for estimating their ages. In this paper, we infer ages for known eccentric-planet-hosting M dwarfs using a combination of kinematics and α-element enrichment, both shown to correlate with age for Sun-like FGK stars. We calibrate our method on FGK stars in a Bayesian context. To measure α-enrichment, we use publicly available spectra from the CARMENES exoplanet survey and a recently developed [Ti/Fe] calibration utilizing individual Ti I and Fe I absorption lines in the Y band. Tidal effects are expected to circularize the orbits of short-period planets on short timescales; however, we find a number of mildly eccentric, close-in planets orbiting old (∼8 Gyr) stars. For these systems, we use our ages to constrain the tidal dissipation parameter of the planets, Q_p. For two mini-Neptune planets, GJ 176 b and GJ 536 b, we find that they have Q_p values more similar to the ice giants than to the terrestrial planets in our solar system. For GJ 436 b, we estimate an age of 8.9_–2.1^+2.3Gyr and constrain the Q_p to be >10⁵, in good agreement with constraints from its inferred tidal heating. We find that GJ 876 d has likely undergone significant orbital evolution over its 8.4_–2.0^+2.2Gyr lifetime, potentially influenced by its three outer companions that orbit in a Laplace resonance.