L_(syn)-E_(syn,p)-δ relation in active galactic nucleus jets and implication for the physical origin of the L_p-E_(p,z)-Γ_0 relation of gamma-ray bursts

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(Γ_0) of GRBs.It is shown that the AGN sample does not agree with the L_p-E_(p,z)-Γ_0 relation of GRBs.In addition,we obtain a tight relation of ■ for FSRQs and NLS1 galaxies,where L_(syn) is the luminosity at peak photon energy E_(syn,p) of the synchrotron radiations.This relation is different from the L_p-E_(p,z)-Γ_0 relation of GRB s.The dependence of L_(syn) to δ 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 Γ_0 may be a representative of the kinetic power of the radiating region and the tight L_p-E_(p,z)-Γ_0 relation is shaped by the radiation physics and the jet power together.