Revisiting Correlations Between Broad-Line and Radio Variations for AGNs: 3C 120 and 3C 273

We restudy the issue of cross-correlations between broad-line and jet emission variations, and aim to locate the position of radio (and gamma-ray) emitting region in jet of active galactic nuclei (AGNs). Considering the radial profiles of the radius and number density of clouds in a spherical broad-line region (BLR), we derive new formulae connecting jet emitting position $R_{\rm{jet}}$ to time lag $\tau_{\rm{ob}}$ between broad-line and jet emission variations, and BLR radius. Also, formulae are derived for a disk-like BLR and a spherical shell BLR. The model-independent FR/RSS method is used to estimate $\tau_{\rm{ob}}$. For 3C 120, positive lags of about 0.3 yr are found between the 15 GHz emission and the H$\beta$, H$\gamma$ and He II $\lambda 4686$ lines, including broad-line data in a newly published paper, indicating the line variations lead the 15 GHz ones. Each of the broad-line light curves corresponds to a radio outburst. $R_{\rm{jet}}=$1.1--1.5 parsec (pc) are obtained for 3C 120. For 3C 273, a common feature of negative time lags is found in the cross-correlation functions between light curves of radio emission and the Balmer lines, and as well Ly$\alpha \/\ \lambda 1216$ and C~{\sc iv} $\lambda 1549$ lines. $R_{\rm{jet}}=$ 1.0--2.6 pc are obtained for 3C 273. The estimated $R_{\rm{jet}}$ are comparable for 3C 120 and 3C 273, and the gamma-ray emitting positions will be within $\sim$ 1--3 pc from the central engines. Comparisons show that the cloud number density and radius radial distributions and the BLR structures only have negligible effects on $R_{\rm{jet}}$.