GRB Afterglow of the Sub-relativistic Materials with Energy Injection

Sub-relativistic materials launched during the merger of binary compact objects and the core collapse of massive stars acquire velocity structures when expanding in a stratified environment. The remnant (either a spinning magnetized neutron star (NS) or a central black hole) from the compact object or core collapse could additionally inject energy into the afterglow via spin-down luminosity or/and by accreting fallback material, producing a refreshed shock, modifying the dynamics, and leading to rich radiation signatures at distinct timescales and energy bands with contrasting intensities. We derive the synchrotron light curves evolving in a stratified environment when a power-law velocity distribution parameterizes the energy of the shock, and the remnant continuously injects energy into the blast wave. As the most relevant case, we describe the latest multiwavelength afterglow observations ( 3900 days) of the GW170817/GRB 170817A event via a synchrotron afterglow model with energy injection of a sub-relativistic material. The features of the remnant and the synchrotron emission of the sub-relativistic material are consistent with a spinning magnetized NS and the faster blue kilonova afterglow, respectively. Using the multiband observations of some short bursts with evidence of kilonovae, we provide constraints on the expected afterglow emission.