Evaluation of the cross-correlation method and the size of AGN emission-line regions

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Abstract
We have developed a probablistic way to evaluate the significance of the cross-correlation method, as applied to the measurement of active galactic nuclei (AGN) emission-line region sizes. The distribution function, denoted CCPD (cross-correlation peak distribution) is calculated numerically for any continuum light curve and gas distribution. It enables us to estimate the probability of getting a certain value for the broad line region (BLR) dimensions from cross-correlation. Comparison with other uncertainty estimates, such as the one suggested by Gaskell & Peterson, indicates that the CCPD method is more reliable. We apply the method to the published data for Akn 120 and NGC4151 and investigate the results obtained so far. In contrast to previous studies of this kind, we find that the significance of the results depends strongly on the assumptions concerning the BLR geometry and the continuum variability time-scale. Present BLR size estimates are of low significance. In particular, the inferred size of the BLR of NCG 4151 is consistent with standard photo-ionization theory, and an emission region of 30 light-days for Akn 120 cannot be ruled out at a high confidence level, despite the smaller size obtained from present observations. Sampling frequency and measurement error (even uncorrelated) are major sources of uncertainty.

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