Exploring the variable sky with the Sloan Digital Sky Survey

We quantify the variability of faint unresolved optical sources using a catalog based on multiple SDSS imaging observations. The catalog covers SDSS stripe 82, which lies along the celestial equator in the southern Galactic hemisphere (22(h)24(m) < alpha(J2000.0) < 04(h)08(m), -1.27 degrees < delta(J2000.0) < +1.27 degrees, similar to 290 deg(2)), and contains 34 million photometric observations in the SDSS ugriz system for 748,084 unresolved sources at high Galactic latitudes (b < -20 degrees) that were observed at least four times in each of the ugri bands (with a median of 10 observations obtained over similar to 6 yr). In each photometric bandpass we compute various low-order light-curve statistics, such as rms scatter, chi(2) per degree of freedom, skewness, and minimum and maximum magnitude, and use them to select and study variable sources. We find that 2% of unresolved optical sources brighter than g 20.5 appear variable at the 0.05 mag level (rms) simultaneously in the g and r bands (at high Galactic latitudes). The majority (2 out of 3) of these variable sources are low-redshift (< 2) quasars, although they represent only 2% of all sources in the adopted flux-limited sample. We find that at least 90% of quasars are variable at the 0.03 mag level (rms) and confirm that variability is as good a method for finding low-redshift quasars as the UV excess color selection (at high Galactic latitudes). We analyze the distribution of light-curve skewness for quasars and find that it is centered on zero. We find that about one-fourth of the variable stars are RR Lyrae stars, and that only 0.5% of stars from the main stellar locus are variable at the 0.05 mag level. The distribution of light-curve skewness in the g - r versus u - g color-color diagram on the main stellar locus is found to be bimodal (with one mode consistent with Algol-like behavior). Using over 600 RR Lyrae stars, we demonstrate rich halo substructure out to distances of 100 kpc. We extrapolate these results to the expected performance by the Large Synoptic Survey Telescope and estimate that it will obtain well-sampled, 2% accurate, multicolor light curves for similar to 2million low-redshift quasars and discover at least 50 million variable stars.