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Periodic Variability of Low-Mass Stars in SDSS Stripe 82

We present a catalog of periodic stellar variability in the "Stripe 82" region of the Sloan Digital Sky Survey (SDSS). After aggregating and recalibrating catalog-level data from the survey, we ran a period-finding algorithm (Supersmoother) on all point-source lightcurves. We used color selection to identify systems that are likely to contain low-mass stars, in particular M dwarfs and white dwarfs. In total, we found 207 candidates, the vast majority of which appear to be in eclipsing binary systems. The catalog described in this paper includes 42 candidate M dwarf / white dwarf pairs, 4 white-dwarf pairs, 59 systems whose colors indicate they are composed of 2 M dwarfs and whose lightcurve shapes suggest they are in detached eclipsing binaries, and 28 M dwarf systems whose lightcurve shapes suggest they are in contact binaries. We find no detached systems with periods longer than 3 days, thus the majority of our sources are likely to have experienced orbital spin-up and enhanced magnetic activity. Indeed, twenty-six of twenty-seven M dwarf systems that we have spectra for show signs of chromospheric magnetic activity, far higher than the 24% seen in field stars of the same spectral type. We also find binaries composed of stars that bracket the expected boundary between partially and fully convective interiors, which will allow the measurement of the stellar mass-radius relationship across this transition. The majority of our contact systems have short orbital periods, with small variance (0.02 days) in the sample near the observed cutoff of 0.22 days. The accumulation of these stars at short orbital period suggests that the process of angular momentum loss, leading to period evolution, becomes less efficient at short periods. (Abridged)