A Sample Bias in Quasar Variability Studies
  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.
