The afterglow of gamma-ray burst - supernova connections

Abstract

The X-ray afterglow of several long gamma-ray bursts (LGRBs) associated with broad line type Ib/c supernovae (SNe) exhibits a standard non-thermal afterglow, commonly attributed to synchrotron emission from a relativistic jet, and an evolving thermal component whose physical origin is still debated. We investigate whether these thermal and non-thermal components can be described within a common analytical framework and whether their temporal evolution can provide insight into the physical connection between relativistic jets and SN ejecta. We combine a phenomenological description of the synchrotron emission of the non-thermal energy associated with the relativistic jet with a diffusion model describing the thermal evolution of the jet-affected portion of the SN ejecta. The resulting coupled system is solved analytically, leading to closed-form expressions for both non-thermal and thermal luminosities. We apply the model to the following systems: GRB 060218A/SN 2006aj and GRB 171205A/SN 2017iuk. The proposed formalism reproduces the main features of both thermal and non-thermal light curves. In both systems, the thermal luminosity follows a temporal evolution similar to that of the non-thermal component up to the plateau phase. The inferred thermal energy stored in the jet-affected ejecta is found to be a fraction of the energy coupled to the observed non-thermal emission. The characteristic timescales obtained from the fits suggest a direct link between the evolution of the jet and the thermal response of the expanding ejecta. Although simplified, the proposed framework provides a unified analytical description of LGRB afterglows and their thermal counterparts and offers a useful tool for investigating the physical connection between relativistic jets and SNe Ib/c.