Abstract High energy photon radiations of gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) are dominated by their jet radiations.We examine whether the synchrotron radiations of jets in BL Lacs, flat spectrum radio quasars (FSRQs), and Narrow Line Seyfert 1 galaxies (NLS1s) follow the relation between the prompt gamma-ray emission and the initial Lorentz factor (\(\Gamma_0\)) of GRBs. It is shown that the AGN sample does not agree with the \(L_{\rm p}-E_{\rm p,z}-\Gamma_0\) relation of GRBs. In addition, we obtain a tight relation of \(L_{\rm syn}\propto E_{\rm syn,p}^{0.45\pm0.15}\delta^{3.50\pm0.25}\) for FSRQs and NLS1 galaxies, where \(L_{\rm syn}\) is the luminosity at peak photon energy \(E_{\rm syn,p}\) of the synchrotron radiations. This relation is different from the \(L_{\rm p}-E_{\rm p,z}-\Gamma_0\) relation of GRBs. The dependence of \(L_{\rm syn}\) to \(\delta\) is consistent with the expectation of the Doppler boosting effect for the FSRQs and NLS1 galaxies, but it is not for GRBs. We argue that \(\Gamma_0\) may be a representative of the kinetic power of the radiating region and the tight \(L_{\rm p}-E_{\rm p,z}-\Gamma_0\) relation is shaped by the radiation physics and the jet power together.

Keywords gamma-ray burst: general — quasars: general — BL Lacertae objects: general — galaxies: Seyfert— stars: jets— radiation mechanisms: non-thermal

https://doi.org/10.1088/1674–4527/20/9/141