Distributions of Gamma-Ray Bursts and Blazars in the $L_{\rm p}-E_{\rm p}$ Plane and Possible Implications for their Radiation Physics

TL;DR

This study compares the distributions of gamma-ray bursts and blazars in the $L_{p}-E_{p}$ plane, revealing a tight relation for GRBs and suggesting different synchrotron radiation mechanisms for various jet types, offering a unified view of their radiation physics.

Contribution

It provides a comparative analysis of GRB and blazar spectral distributions, proposing a unified leptonic synchrotron radiation framework for their jet emissions.

Findings

GRBs occupy high-$L_{p}$, high-$E_{p}$ region with a tight $L_{p}-E_{p}$ relation.

Blazars cluster in low-$E_{p}$, low-$L_{p}$ corner, with no clear $L_{s}$-$E_{s}$ dependence.

Different electron cooling regimes explain the spectral distributions across sources.

Abstract

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.