An Improved Age-Activity Relationship for Cool Stars older than a Gigayear

Stars with convective envelopes display magnetic activity, which decreases over time due to the magnetic braking of the star. This age-dependence of magnetic activity is well-studied for younger stars, but the nature of this dependence for older stars is not well understood. This is mainly because absolute stellar ages for older stars are hard to measure. However, relatively accurate stellar ages have recently come into reach through asteroseismology. In this work we present X-ray luminosities, which are a measure for magnetic activity displayed by the stellar coronae, for 24 stars with well-determined ages older than a gigayear. We find 14 stars with detectable X-ray luminosities and use these to calibrate the age-activity relationship. We find a relationship between stellar X-ray luminosity, normalized by stellar surface area, and age that is steeper than the relationships found for younger stars, with an exponent of $-2.80 \pm 0.72$. Previous studies have found values for the exponent of the age-activity relationship ranging between -1.09 to -1.40, dependent on spectral type, for younger stars. Given that there are recent reports of a flattening relationship between age and rotational period for old cool stars, one possible explanation is that we witness a strong steepening of the relationship between activity and rotation.