The Ensemble Photometric Variability of ~25,000 Quasars in the Sloan Digital Sky Survey

Using a sample of over 25,000 spectroscopically confirmed quasars from the Sloan Digital Sky Survey, we show how quasar variability in the rest-frame optical/UV regime depends on rest-frame time lag, luminosity, rest wavelength, redshift, the presence of radio and X-ray emission, and the presence of broad absorption line systems. Imaging photometry is compared with three-band spectrophotometry obtained at later epochs spanning time lags up to about 2 yr. The large sample size and wide range of parameter values allow the dependence of variability to be isolated as a function of many independent parameters. The time dependence of variability (the structure function) is well fitted by a single power law with an index γ = 0.246 ± 0.008, on timescales from days to years. There is an anticorrelation of variability amplitude with rest wavelength—e.g., quasars are about twice as variable at 1000 Å as at 6000 Å—and quasars are systematically bluer when brighter at all redshifts. There is a strong anticorrelation of variability with quasar luminosity—variability amplitude decreases by a factor of about 4 when luminosity increases by a factor of 100. There is also a significant positive correlation of variability amplitude with redshift, indicating evolution of the quasar population or the variability mechanism. We parameterize all of these relationships. Quasars with ROSAT All-Sky Survey X-ray detections are significantly more variable (at optical/UV wavelengths) than those without, and radio-loud quasars are marginally more variable than their radio-quiet counterparts. We find no significant difference in the variability of quasars with and without broad absorption line troughs. Currently, no models of quasar variability address more than a few of these relationships. Models involving multiple discrete events or gravitational microlensing are unlikely by themselves to account for the data. So-called accretion disk instability models are promising, but more quantitative predictions are needed.