Constraining the physical parameters of blazars using the seed factor approach

Abstract

The discovery that blazars dominate the extra-galactic $\gamma$ -ray sky is a triumph in the Fermi era. However, the exact location of $\gamma$ -ray emission region still remains in debate. Low-synchrotron-peaked blazars (LSPs) are estimated to produce high-energy radiation through the external Compton process, thus their emission regions are closely related to the external photon fields. We employed the seed factor approach proposed by Georganopoulos et al. It directly matches the observed seed factor of each LSP with the characteristic seed factors of external photon fields to locate the $\gamma$ -ray emission region. A sample of 1 138 LSPs with peak frequencies and peak luminosities was adopted to plot a histogram distribution of observed seed factors. We also collected some spectral energy distributions (SEDs) of historical flare states to investigate the variation of $\gamma$ -ray emission region. Those SEDs were fitted by both quadratic and cubic functions using the Markov-chain Monte Carlo method. Furthermore, we derived some physical parameters of blazars and compared them with the constraint of internal $\gamma\gamma$ -absorption. We find that dusty torus dominates the soft photon fields of LSPs and most $\gamma$ -ray emission regions of LSPs are located at 1–10 pc. The soft photon fields could also transition from dusty torus to broad line region and cosmic microwave background in different flare states. Our results suggest that the cubic function is better than the quadratic function to fit the SEDs.