The Solar Twin Planet Search: The age - chromospheric activity relation

It is well known that the magnetic activity of solar type stars decreases with age, but it is widely debated in the literature whether there is a smooth decline or if there is an early sharp drop until 1-2 Gyr followed by a relatively inactive constant phase. We revisited the activity-age relation using time-series observations of a large sample of solar twins whose precise isochronal ages and other important physical parameters have been determined. We measured the Ca II H and K activity indices using 9000 HARPS spectra of 82 solar twins. We measured an average solar activity of $S_{\rm MW}$ = 0.1712 $\pm$ 0.0017 during solar magnetic cycles 23$-$24 covered by HARPS observations and we also inferred an average of $S_{\rm MW}$ = 0.1694 $\pm$ 0.0025 for cycles 10$-$24, anchored on a S index vs. sunspot number correlation. Also, a simple relation between the average and dispersion of the activity levels of solar twins was found. This enabled us to predict the stellar variability effects on the age-activity diagram and, consequently, estimate the chromospheric age uncertainties due to the same phenomena. The age-activity relation is still statistically significant up to ages around 6$-$7 Gyr, in agreement with previous works using open clusters and field stars with precise ages. Our research confirms that Ca II H \& K lines remain a useful chromospheric evolution tracer until stars reach ages of at least 6$-$7 Gyr. We found an evidence that, for the most homogeneous set of old stars, the chromospheric activity indices seem to continue decreasing after the solar age towards the end of the main-sequence. Our results indicate that a significant part of the scatter observed in the age-activity relation of solar twins can be attributed to stellar cycle modulations effects. The Sun seems to have a normal activity level and variability for its age.