Using a sample of over 25000 spectroscopically confirmed quasars from the Sloan Digital Sky Survey , we show how quasar variability in the rest frame optical/UV regime depends upon 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 two years .
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-fit by a single power law with an index \gamma = 0.246 \pm 0.008 , on timescales from days to years .
There is an anti-correlation of variability amplitude with rest wavelength – e.g. quasars are about twice as variable at 1000 à as 6000 à – and quasars are systematically bluer when brighter at all redshifts .
There is a strong anti-correlation of variability with quasar luminosity – variability amplitude decreases by a factor of about four 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 RASS 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 weak 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 .