Linking Stellar Coronal Activity and Rotation at 500 Myr: A Deep Chandra Observation of M37

Empirical calibrations of the stellar age-rotation-activity relation (ARAR) rely on observations of the co-eval populations of stars in open clusters. We used the Chandra X-ray Observatory to study M37, a 500-Myr-old open cluster that has been extensively surveyed for rotation periods (P-rot). M37 was observed almost continuously for five days, for a total of 440.5 ks, to measure stellar X-ray luminosities (L-X), a proxy for coronal activity, across a wide range of masses. The cluster's membership catalog was revisited to calculate updated membership probabilities from photometric data and each star's distance to the cluster center. The result is a comprehensive sample of 1699 M37 members: 426 with Prot, 278 with X-ray detections, and 76 with both. We calculate Rossby numbers, R-o = P-rot/T, where T is the convective turnover time, and ratios of the X-ray-to-bolometric luminosity, L-X/L-bol, to minimize mass dependencies in our characterization of the rotation-coronal activity relation at 500 Myr. We find that fast rotators, for which R-o< 0.09 +/- 0.01, show saturated levels of activity, with log(L-X/L-bol) = -3.06 +/- 0.04. For R-o. 0.09 +/- 0.01, activity is unsaturated and follows a power law of the form Ro b, where beta = -2.03(-0.14)(+0.17). This is the largest sample available for analyzing the dependence of coronal emission on rotation for a single-aged population, covering stellar masses in the range 0.4-1.3 M-circle dot, P-rot in the range 0.4-12.8 days, and L-X in the range 10(28.4-30.5) erg s(-1). Our results make M37 a new benchmark open cluster for calibrating the ARAR at ages of approximate to 500 Myr.