Distributions of Gamma-Ray Bursts and Blazars in the lp - ep Plane and Possible

We compare the distributions of gamma-ray bursts (GRBs) and blazars (FSRQs, LBLs, IBLs, and HBLs) observed with the Fermi mission by plotting the synchrotron peak luminosity (L_s) and the corresponding photon energy E_s of blazars in the L_p-E_p plane of gamma-ray bursts, where E_p is the corresponding photon energy of the peak luminosity (L_p) in the time-integrated nu f_nu GRB spectrum. We show that GRBs are in the high-L_p, high-E_p corner of the plane and a tight L_p-E_p relation is found i.e., L_p~ E_p({-1.52±) 0.20}. Both FSRQs and LBLs are clustered in the low-E_p, low-L_p corner and a weak trend that sources with higher L_s tend to have a lower E_s. IBLs and HBLs range in E_s=2× 10(-3) ∼ 10(2) keV and L_s=10(44) ∼ 10(46) erg s(-1) , but no any dependence of L_s on E_s is found. In the framework of the synchrotron radiation mechanism, we show that the tight L_p-E_p relation of GRBs may be due to the synchrotron radiation of the electrons in the fast cooling regime from a highly magnetized ejecta, and the weak anti-correlation of L_s-E_s for FSRQs and LBLs may be attributed to the synchrotron radiation of the electrons in the slow cooling regime from a moderately magnetized ejecta. On the other hand, the distribution of IBLs and HBLs may be explained with the synchrotron radiation of the electrons in the fast cooling regime from a matter dominated ejecta.