The X-ray luminosity function of M37 and the evolution of coronal activity in low-mass stars

We use a 440.5 ks Chandra observation of the $\approx$500-Myr-old open cluster M37 to derive the X-ray luminosity functions of its $\leq1.2$ $M_{\odot}$ stars. Combining detections of 162 M37 members with upper limits for 160 non-detections, we find that its G, K, and M stars have a similar median (0.5$-$7 keV) X-ray luminosity L$_X =10^{29.0}$ erg/s, whereas the L$_X$-to-bolometric-luminosity ratio (L$_X$/L$_{bol}$) indicates that M stars are more active than G and K stars by $\approx$1 order of magnitude at 500 Myr. To characterize the evolution of magnetic activity in low-mass stars over their first $\approx$600 Myr, we consolidate X-ray and optical data from the literature for stars in six other open clusters: from youngest to oldest, the Orion Nebula Cluster (ONC), NGC 2547, NGC 2516, the Pleiades, NGC 6475, and the Hyades. For these, we homogenize the conversion of instrumental count rates to L$_X$ by applying the same one-temperature emission model as for M37, and obtain masses using the same empirical mass-absolute magnitude relation (except for the ONC). We find that for G and K stars X-ray activity decreases $\approx$2 orders of magnitude over their first 600 Myr, and for M stars, $\approx$1.5. The decay rate of the median L$_X$ follows the relation L$_X \propto~t^b$, where $b=-0.61\pm0.12$ for G, $-0.82\pm0.16$ for K, and $-0.40\pm0.17$ for M stars. In L$_X$/L$_{bol}$ space, the slopes are $-0.68\pm0.12$, $-0.81\pm0.19$, and $-0.61\pm0.12$, respectively. These results suggest that for low-mass stars the age-activity relation steepens after $\approx$625 Myr, consistent with the faster decay in activity observed in solar analogs at $t>1$ Gyr.