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

Abstract Determining stellar ages is challenging, particularly for cooler main-sequence (MS) 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 High Accuracy Radial Velocity Planet Searcher spectra, calibrated to the Mount Wilson system and converted to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">HK</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">eff</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> index with a temperature-based photospheric correction. Our findings show that the AC relation for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">HK</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">eff</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> is strongly influenced by metallicity. We propose a new age–activity–metallicity relation for solar-type MS stars ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mspace width="0.25em"/> <mml:mi>g</mml:mi> <mml:mo>≳</mml:mo> <mml:mn>4.2</mml:mn> </mml:math> ) with temperatures 5370 ≲ T eff ≲ 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’ rms relative to isochronal ages from 2.6 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.