We present a spectral analysis for a sample of redshift known GRBs observed with { \em Fermi}/GBM. Together with the results derived from our systematical spectral energy distribution modeling with the leptonic models for a { \em Fermi}/LAT blazar sample, we compare the distributions of the GRBs and the blazars by plotting the synchrotron peak luminosity ($L_{ \rm s}$) and the corresponding peak photon energy $E_{ \rm s}$ of blazars in the $L_{ \rm p}-E_{ \rm p}$ plane of GRBs, where $L_{ \rm p}$ and $E_{ \rm p}$ are the peak luminosity and peak photon energy of the GRB time-integrated $\nu f_\nu$ spectrum, respectively. The GRBs are in the high-$L_{ \rm p}$, high-$E_{ \rm p}$ corner of the plane and a tight $L_{ \rm p}-E_{ \rm p}$ relation is found, i.e., $L_{ \rm p}\propto E_{ \rm p}^{ 2.13^{ +0.54}_{ -0.46}}$. Both FSRQs and LBLs are clustered in the low-$E_{ \rm p}$, low-$L_{ \rm p}$ corner. IBLs and HBLs have $E_{ \rm s}\sim 2\times 10^{ -3} - 10^{ 2}$ keV and $L_{ \rm s} \sim 10^{ 44} - 10^{ 47}$ erg s$^{ -1}$, but no dependence of $L_{ \rm s}$ on $E_{ \rm s}$ is found. We show that the tight $L_p-E_p$ relation of GRBs is potentially explained with the synchrotron radiation of fast-cooling electrons in a highly magnetized ejecta, and the weak anti-correlation of $L_{ \rm s}-E_{ \rm s}$ for FSRQs and LBLs may be attributed to synchrotron radiation of slow-cooling electrons in a moderately magnetized ejecta. The distributions of IBLs and HBLs in the $L_{ \rm p}-E_{ \rm p}$ plane may be interpreted with synchrotron radiation of fast-cooling electrons in a matter-dominated ejecta. These results may present a unified picture for the radiation physics of relativistic jets in GRBs and blazars within the framework of the leptonic synchrotron radiation models.
Categories: astro-ph.HE