The age-mass-metallicity-activity relation for solar-type stars: comparisons with asteroseismology and the NGC 188 open cluster

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The Mount Wilson Ca II index log$(R'_{\rm HK})$ is the accepted standard metric of calibration for the chromospheric activity versus age relation of FGK stars. Recent results claim its inability to discern activity levels, and thus ages, for stars older than $\sim$2 Gyr, which would severely hamper its application to date disk stars older than the Sun. We present a new activity-age calibration of the Mt. Wilson index explicitly taking into account mass and $[$Fe/H$]$ biases, implicit in samples of stars selected to have precise ages, that have so far gone unappreciated. We show that these selection biases tend to blur the activity-age relation for large age ranges. We calibrate the Mt. Wilson index for a sample of field FGK stars with precise ages, covering a wide range of mass and $[$Fe/H$]$, augmented with data from the Pleiades, Hyades, M67 clusters, and the Ursa Major moving group. We further test the calibration with extensive new Gemini/GMOS log$(R'_{\rm HK})$ data of the old, solar $[$Fe/H$]$ clusters M67 and NGC 188. The observed NGC 188 activity level is clearly lower than M67. We correctly recover the isochronal age of both clusters and establish the viability of deriving usable chromospheric ages for solar-type stars up to at least $\sim$6 Gyr, average errors being $\sim$0.14 dex provided that the mass and $[$Fe/H$]$ dimensions are explicitly accounted for. We test our calibration against asteroseismological ages, finding excellent correlation ($\rho$ = +0.89). We show that our calibration improves the chromospheric age determination for a wide range of ages, masses, and metallicities in comparison to previous age-activity relations.