A New Look at an Old Cluster: The Membership, Rotation, and Magnetic Activity of Low-Mass Stars in the 1.3-Gyr-Old Open Cluster NGC 752

The nearby open cluster NGC 752 presents a rare opportunity to study stellar properties at ages >1 Gyr. However, constructing a membership catalog for it is challenging; most surveys have been limited to identifying its giants and dwarf members earlier than mid-K. We supplement past membership catalogs with candidates selected with updated photometric and proper-motion criteria, generating a list of 258 members, a >50% increase over previous catalogs. Using a Bayesian framework to fit MESA Isochrones & Stellar Tracks evolutionary models to literature photometry and the Tycho-Gaia Astrometric Solution data available for 59 cluster members, we infer the age of, and distance to, NGC 752: 1.34$\pm$0.06 Gyr and 438$_{-6}^{+8}$ pc. We also report the results of our optical monitoring of the cluster using the Palomar Transient Factory. We obtain rotation periods for 12 K and M cluster members, the first periods measured for such low-mass stars with a well-constrained age >1 Gyr. We compare these new periods to data from the younger clusters Praesepe and NGC 6811, and to a theoretical model for angular-momentum loss, to examine stellar spin down for low-mass stars over their first 1.3 Gyr. While on average NGC 752 stars are rotating more slowly than their younger counterparts, the difference is not significant. Finally, we use our spectroscopic observations to measure Halpha for cluster stars, finding that members earlier than $\approx$M2 are magnetically inactive, as expected at this age. Forthcoming Gaia data should solidify and extend the membership of NGC 752 to lower masses, thereby increasing its importance for studies of low-mass stars.