2011MNRAS.414..155L

We propose a new method to locate the γ-ray-emitting positions R_γ from the measured time lags τ_obof γ-ray emission relative to broad emission lines. The method is also applicable to lower frequencies. R_γ depends on parameters τ_ob, R_BLR, v_d and θ, where R_BLRis the size of the broad-line region, v_d is the travelling speed of disturbances down the jet and θ is the viewing angle of the jet axis to the line of sight. As τ_ob= 0, τ_ob< 0 or τ_ob> 0, the broad lines zero-lag, lag or lead the γ-rays, respectively. It is applied to 3C 273, in which the lines and the radio emission have enough data, but the γ-rays do not. We find τ_ob< 0 and τ_ob> 0 for the 5, 8, 15, 22 and 37 GHz emission relative to the broad lines Hα, Hβ and Hγ. The lag may be positive or negative; however, current data do not allow discrimination between the two cases. The measured lags are of the order of years. For a given line, τ_ob generally decreases as radio frequency increases. This trend most likely results from the radiative cooling of relativistic electrons. The negative lags have an average of τ_ob=-2.86 yr for the 37 GHz emission, which represents the lines lagging the radio emission. The positive lags have τ_ob= 3.20 yr, which represents the lines leading the radio emission. We obtain the radio-emitting positions R_radio= 0.40–2.62 pc and R_radio= 9.43–62.31 pc for the negative and positive lags, respectively. From the constraint of R_γ ≲ R_radio, we have R_γ ≲ 0.40–2.62 pc for the negative lags. For the positive lags, 4.67–30.81 < R_γ ≲ 9.43–62.31 pc. These estimated R_γ are consistent with those of other studies. These agreements confirm the reliability of the method and assumptions. The method may also be applicable to BL Lacertae objects, in which broad lines were detected.