On the Reliability of Cross‐Correlation Function Lag Determinations in Active Galactic Nuclei

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Abstract
Many active galactic nuclei (AGNs) exhibit a highly variable luminosity. Some AGNs 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 ~1–100 days, depending upon which line is used and the luminosity of the AGN. In the best sampled AGN, NGC 5548, the Hβ lag shows year‐to‐year changes, ranging from ~8.7 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.
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