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Description
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 440.5ks, 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 P_rot_, 278 with X-ray detections, and 76 with both. We calculate Rossby numbers, R_0_=P_rot_/{tau}, where {tau} 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 500Myr. We find that fast rotators, for which R_0_<0.09+/-0.01, show saturated levels of activity, with log(L_X_/L_bol_)=-3.06+/-0.04. For R_0_>=0.09+/-0.01, activity is unsaturated and follows a power law of the form R_0_^{beta}^, where {beta}=-2.03^+0.17^_-1.14_. 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 0.4-1.3M_{sun}_, P_rot_ in the range 0.4-12.8 days, and L_X_ in the range 10^28.4-30.5^erg/s. Our results make M37 a new benchmark open cluster for calibrating the ARAR at ages of ~500Myr.
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