Do Afterglow Synchrotron Radiations Follow the L p,iso – E p,z –Γ 0 Relation of Gamma-Ray Bursts? The Cases of GRBs 190114C, 130427A, and 180720B

Bimodal spectral energy distributions (SEDs) of gamma-ray burst (GRB) afterglow of GRBs 190114C, 130427A, and 180720B confirm that they are originated from the synchrotron emission (Syn) and synchrotron self-Compton scattering (SSC) process of electrons accelerated in the jets. The radiation mechanism and the physics of the observed spectrum-luminosity/energy relations of GRBs remain as open questions. By extracting the Syn component through fitting their early afterglow SEDs with the Syn+SSC model, we find that their luminosity (Lsyn), peak energy (Ep,syn,z), and the Lorentz factor of the afterglow fireball (Γt) follow the Lp,iso–Ep,z–Γ0 relation of prompt gamma rays, where Lp,iso is the isotropic luminosity, Ep,z is the peak energy of the $\nu {f}_{\nu }$ spectrum in the burst frame, and Γ0 is the initial Lorentz factor of the fireball. To examine whether late afterglows are consistent with this relation, we calculate the synchrotron component at late afterglows. It is found that they also follow the same Lp,iso–Ep,z–Γ0 relation, albeit they are not consistent with the Lp,iso–Ep,z relation. Our results may imply that the Lp,iso–Ep,z–Γ0 relation would be a universal feature of synchrotron radiations of electrons accelerated in GRB jets throughout the prompt and afterglow phases among GRBs. Its origin is not fully understood, and possible explanations are briefly discussed.