CROSS-CORRELATION METHODOLOGY IN VARIABILITY STUDIES OF ACTIVE GALACTIC NUCLEI - COMMENT

We discuss two separate cross-correlation methodologies, the interpolation method of Gaskell and Sparke and the discrete correlation function of Edelson and Krolik, that are commonly used to quantify the lags between continuum and emission-line flux variations in active galactic nuclei (AGNs). We show that if similar assumptions are made to normalize the cross-correlation functions, the two methods are in good agreement for well-sampled AGN light curves. We also investigate the performance of cross-correlation methodology for less well-sampled data sets through Monte Carlo simulations that employ realistic models of the continuum behavior (based on well-observed Seyfert galaxies) and typical emission-line response times. We find that the interpolation method fairly accurately recovers the emission-line lags as the sampling is degraded (i.e., as the number of observed points is reduced). We find that for the cases investigated, the emission-line lags can be determined with reasonable accuracy even with mean sampling intervals as large as around two weeks.