2018ApJ...859..168Y

The production site of gamma-rays in a blazar jet is an unresolved problem. We present a method to locate a gamma-ray emission region in the framework of a one-zone emission model. From measurements of the core-shift effect, the relation between the magnetic field strengths (B') in the radio cores of the jet and the distances (R) of these radio cores from the central supermassive black hole (SMBH) can be inferred. Therefore, once the magnetic field strength in the gamma-ray emission region (B_diss^′^) is obtained, one can use the relation of B'-R to derive the distance (R_diss) of the gamma-ray emission region from the SMBH. Here, we evaluate the lower limit of B_diss^′^ by using the criteria that the optical variability timescale t_var should be longer than or equal to the synchrotron radiation cooling timescale of the electrons that emit optical photons. We test the method with the observations of PSK 1510-089 and BL Lacertae, and derive R_diss< 0.15δ_D^1/3(1+A)^2/3 pc for PSK 1510-089 with t_var ∼ a few hours and R_diss< 0.003δ_D^1/3(1+A)^2/3 pc for BL Lacertae with t_var ∼ a few minutes. Here, δ_D is the Doppler factor and A is the Compton dominance (i.e., the ratio of the Compton to the synchrotron peak luminosities).