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

¹ Universidade Federal do Rio de Janeiro, Observatório do Valongo, Ladeira do Pedro Antonio 43, CEP: 20080-090, Rio de Janeiro, RJ, Brazil
e-mail: diego@astro.ufrj.br; gustavo@astro.ufrj.br
² Astrophysics Research Institute, Liverpool John Moores University, Liverpool, L3 5RF, UK
e-mail: R.P.Schiavon@ljmu.ac.uk

Received: 3 July 2016
Accepted: 21 September 2016

Abstract

Context. The Mount Wilson Ca ii index log$\mathrm{\left(}{\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}\mathrm{\right)}$ is the accepted standard metric of calibration for the chromospheric activity versus age relation for FGK stars. Recent results claim its inability to discern activity levels, and thus ages, for stars older than ~2 Gyr, which would severely hamper its application to date disk stars older than the Sun.

Aims. We present a new activity-age calibration of the Mt. Wilson index that explicitly takes mass and [Fe/H] biases into account; these biases are implicit in samples of stars selected to have precise ages, which have so far not been appreciated.

Methods. 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, M 67 clusters, and the Ursa Major moving group.

Results. We further test the calibration with extensive new Gemini/GMOS log ()R'_HK) data of the old, solar [Fe/H] clusters, M 67 and NGC 188. The observed NGC 188 activity level is clearly lower than M 67. 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 ~6 Gyr, where average errors are ~0.14 dex provided that we explicitly account for the mass and [Fe/H] dimensions. We test our calibration against asteroseismological ages, finding excellent correlation (ρ = + 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.