Large discrepancies in error estimates for reverberation times derived from light curves of active galactic nuclei

Abstract

Light-travel-time delays provide one of the most powerful ways of learning about the structure and kinematics of active galactic nuclei (AGNs). Estimating delays from observations of AGN variability presents statistical challenges because the time series are almost invariably irregularly sampled. Correct assessment of errors in lag estimates is important for evaluating results. The most widely used method of determining phase lags has been the interpolated cross-correlation function method introduced by Gaskell and Sparke (1986, GS). It is shown here that the widely used modified smooth bootstrap method of Peterson et al. (1998) significantly overestimates the error in lags derived using the GS, especially for poorly sampled light curves. The remarkably high accuracy claimed for lags obtained by the JAVELIN method of Zu et al. (2011) (more than an order of magnitude improvement for 25% of cases) is spurious and the accuracy no better than the GS method. A related method proposed by Li et al. (2013) suffers from similar but less serious problems. A slightly modified version of the analytic formula of Gaskell and Peterson (1987) gives an easy and accurate way of estimating lag errors for well-sampled, high-quality data. The width of the continuum autocorrelation function is shown to be proportional to the square root of the luminosity. This is useful in planning observing campaigns. The discrete correlation function method is less powerful than the GS method and for many typical situations gives errors in the lag twice as large as those of the GS method.