A New Age-Activity Relation For Solar Analogs that Accounts for Metallicity

Abstract: Determining stellar ages is challenging, particularly for cooler main-sequence stars. Magnetic evolution offers an observational alternative for age estimation via the age-chromospheric activity (AC) relation. We evaluate the impact of metallicity on this relation using near one-solar-mass stars across a wide metallicity range. We analyze a sample of 358 solar-type stars with precise spectroscopic parameters determined through a line-by-line differential technique and with ages derived using Yonsei-Yale isochrones. We measured chromospheric activity (S-index) using high-quality HARPS spectra, calibrated to the Mount Wilson system, and converted to the $R^{\prime}_{\mathrm HK}(T_{\mathrm{eff}})$ index with a temperature-based photospheric correction. Our findings show that the AC relation for $R^{\prime}_{\mathrm HK}(T_{\mathrm{eff}})$ is strongly influenced by metallicity. We propose a new age-activity-metallicity relation for solar-type main-sequence (MS) stars ($\log{g} \gtrsim 4.2 $) with temperatures 5370 $\lesssim$ $T_{\mathrm{eff}}$ $\lesssim$ 6530 K and metallicities from -0.7 to +0.3 dex. We show that taking metallicity into account significantly enhances chromospheric ages' reliability, reducing the residuals' root mean square (RMS) relative to isochronal ages from 2.6 Gyr to 0.92 Gyr. This reflects a considerable improvement in the errors of chromospheric ages, from 53\% to 15\%. The precision level achieved in this work is also consistent with previous age-activity calibration from our group using solar twins.