Chemo-kinematic ages of eccentric-planet-hosting M dwarf stars

Abstract

M dwarf stars are exciting targets for exoplanet investigations; however, their fundamental stellar properties are difficult to measure. Perhaps the most challenging property to measure 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 $\alpha$-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 $\alpha$-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 $Y$ 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 ($\sim$8 Gyr) stars. For these systems, we use our ages to constrain the tidal dissipation parameter of the planets, $Q_{\mathrm{p}}$. For two mini-Neptune planets, GJ 176b and GJ 536b, we find they have $Q_{\mathrm{p}}$ values more similar to the ice giants than the terrestrial planets in our Solar System. For GJ 436b, we estimate an age of $8.9_{-2.1}^{+2.3}$ Gyr and constrain the $Q_{\mathrm{p}}$ to be $>10^5$, in good agreement with constraints from its inferred tidal heating. We find that GJ 876d has likely undergone significant orbital evolution over its $8.4_{-2.0}^{+2.2}$ Gyr lifetime, potentially influenced by its three outer companions which orbit in a Laplace resonance.

arXiv commentaccepted for publication in ApJ

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