A Method for Locating a High-energy Dissipation Region in a Blazar

Abstract

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 ( ) 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 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 pc for PSK 1510-089 with t var  ∼ a few hours and 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).