Locating positions of γ-ray-emitting regions in blazars

Abstract

We propose a new method to locate the γ-ray-emitting positions Rγ from the measured time lags τob of γ-ray emission relative to broad emission lines. The method is also applicable to lower frequencies. Rγ depends on parameters τob, RBLR, vd and θ, where RBLR is the size of the broad-line region, vd 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 τob= 0, τob < 0 or τob > 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 τob < 0 and τob > 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, τob 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 τob=-2.86 yr for the 37 GHz emission, which represents the lines lagging the radio emission. The positive lags have τob= 3.20 yr, which represents the lines leading the radio emission. We obtain the radio-emitting positions Rradio= 0.40-2.62pc and Rradio= 9.43-62.31pc for the negative and positive lags, respectively. From the constraint of Rγ≲Rradio, we have Rγ≲ 0.40-2.62pc for the negative lags. For the positive lags, 4.67-30.81 < Rγ≲ 9.43-62.31pc. These estimated Rγ 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. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.