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Time-Series Photometry of Stars in and around the Lagoon Nebula. I. Rotation Periods of 290 Low-Mass Pre-Main-Sequence Stars in NGC 6530

We have conducted a long-term, wide-field, high-cadence photometric monitoring survey of ~50,000 stars in the Lagoon Nebula \ion{H}{2} region. This first paper presents rotation periods for 290 low-mass stars in NGC 6530, the young cluster illuminating the nebula, and for which we assemble a catalog of infrared and spectroscopic disk indicators, estimated masses and ages, and X-ray luminosities. The distribution of rotation periods we measure is broadly uniform for 0.5 < P < 10 d; the short-period cutoff corresponds to breakup. We observe no obvious bimodality in the period distribution, but we do find that stars with disk signatures rotate more slowly on average. The stars' X-ray luminosities are roughly flat with rotation period, at the saturation level ($\log L_X / L_{\rm bol} \approx -3.3$). However, we find a significant positive correlation between $L_X / L_{\rm bol}$ and co-rotation radius, suggesting that the observed X-ray luminosities are regulated by centrifugal stripping of the stellar coronae. The period-mass relationship in NGC 6530 is broadly similar to that of the Orion Nebula Cluster (ONC), but the slope of the relationship among the slowest rotators differs from that in the ONC and other young clusters. We show that the slope of the period-mass relationship for the slowest rotators can be used as a proxy for the age of a young cluster, and we argue that NGC 6530 may be slightly younger than the ONC, making it a particularly important touchstone for models of angular momentum evolution in young, low-mass stars.