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Bimodal spectral energy distributions (SEDs) of gamma-ray burst (GRB)afterglow of GRBs 190114C, 130427A and 180720B confirm that they are originatedfrom the synchrotron emission (Syn) and synchrotron self-Compton Scatteringprocess (SSC) of electrons accelerated in the jets. The radiation mechanism andthe physics of the observed spectrum-luminosity/energy relations of GRBs remainas open questions. By extracting the Syn component through fitting their earlyafterglow SEDs with the Syn+SSC model, we find that their luminosity ($L_{\rmsyn}$), peak energy ($E_{\rm p,syn,z}$), and the Lorentz factor of theafterglow fireball ($\Gamma_t$) follow the $L_{\rm p, iso}-E_{\rmp,z}-\Gamma_{0}$ relation of prompt gamma-rays, where $L_{\rm p, iso}$ is theisotropic luminosity, $E_{\rm p, z}$ is the peak energy of the $\nu f_\nu$spectrum in the burst frame, and $\Gamma_0$ is the initial Lorentz factor ofthe fireball. To examine whether late afterglows is consistent with thisrelation, we calculate the synchrotron component at late afterglows. It isfound that they also follow the same $L_{\rm p, iso}-E_{\rm p,z}-\Gamma_{0}$relation, albeit they are not consistent with the $L_{\rm p, iso}-E_{\rm p,z}$relation. Our results may imply that the $L_{\rm p, iso}-E_{\rmp,z}-\Gamma_{0}$ would be an universal feature of synchrotron radiations ofelectrons accelerated in GRB jets throughout the prompt and afterglow phasesamong GRBs. Its origin is not fully understood and possible explanations arebriefly discussed.

the astrophysical journal. letters

Afterglow Synchrotron Radiations follow the $L_{\rm p, iso}-E_{\rm  p,z}-\Gamma_0$ relation of Gamma-Ray Bursts? Cases of GRBs 190114C, 130427A,  and 180720B