A Sample Bias in Quasar Variability Studies

Abstract: When a flux-limited quasar sample is observed at later times, there will be more dimmed quasars than brightened ones, due to a selection bias induced at the time of sample selection. Quasars are continuously varying and there are more fainter quasars than brighter ones. At the time of selection, even symmetrical variability will result in more quasars with their instantaneous fluxes scattered above the flux limit than those scattered below, leading to an asymmetry in flux changes over time. The same bias would lead to an asymmetry in the ensemble structure function (SF) of the sample such that the SF based on pairs with increasing fluxes will be slightly smaller than that based on pairs with decreasing fluxes. We use simulated time-symmetric quasar light curves based on the damped random walk prescription to illustrate the effects of this bias. The level of this bias depends on the sample, the threshold of magnitude changes, and the coverage of light curves, but the general behaviors are consistent. In particular, the simulations matched to recent observational studies with decade-long light curves produce an asymmetry in the SF measurements at the few percent level, similar to the observed values. These results provide a cautionary note on the reported time asymmetry in some recent quasar variability studies.