On the reliability of cross-correlation function lag determinations in active galactic nuclei

Many active galactic nuclei (AGNs) exhibit a highly variable luminosity. Some ACNs also show a pronounced time delay between variations seen in their optical continuum and in their emission lines. In effect, the emission lines are light echoes of the continuum. This light-travel time delay provides a characteristic radius of the region producing the emission lines. The cross-correlation function (CCF) is the standard tool used to measure the time lag between the continuum and line variations. For the few well-sampled AGNs, the lag is similar to 1-100 days, depending upon which line is used and the luminosity of the AGN. In the best sampled AGN, NGC 5548, the H beta lag shows year-to-year changes, ranging from similar to 8.7 to similar to 22.9 days over a span of 8 years. In this paper it is demonstrated that, in the context of AGN variability studies, the lag estimate using the CCF is biased too low and subject to a large variance. Thus the year-to-year changes of the measured lag in NGC 5548 do not necessarily imply changes in the AGN structure. The bias and large variance are consequences of finite-duration sampling and the dominance of long timescale trends in the light curves, not of noise or irregular sampling. Lag estimates can be substantially improved by removing low-frequency power from the light curves prior to computing the CCF.