Locating positions of {γ}-ray--emitting regions in blazars

We propose a new method to locate the gamma-ray--emitting positions R_g from the measured time lags T_ob of gamma-ray emission relative to broad emission lines. The method is also applicable to lower frequencies. R_g depends on parameters T_ob, R_BLR, v_d and theta, where R_BLR is the size of broad-line region, v_d is the travelling speed of disturbances down the jet and theta is the viewing angle of the jet axis to the line of sight. As T_ob=0, T_ob<0 or T_ob>0, the broad lines zero-lag, lag or lead the gamma-rays, respectively. It is applied to 3C 273, in which the lines and the radio emission have enough data, but the gamma-rays have not. We find T_ob<0 and T_ob>0 for the 5, 8, 15, 22 and 37 GHz emission relative to the broad lines Ha, Hb and Hg. The lag may be positive or negative, however current data do not allow to discriminate between the two cases. The measured lags are on the order of years. For a given line, T_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 T_ob=-2.86 years for the 37 GHz emission, which represents that the lines lag the radio emission. The positive lags have T_ob=3.20 years, which represents that the lines lead 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_g </~ R_radio (e.g. Dermer & Schlickeiser 1994; Jorstad et al. 2001), we have R_g </~ 0.40--2.62 pc for the negative lags. For the positive lags, 4.67--30.81<R_g </~ 9.43--62.31 pc. These estimated R_g are consistent with those of other researches. These agreements confirm the reliability of the method and assumptions. The method may be also applicable to BL Lacertae objects, in which broad lines were detected.