Deep Newtonian Afterglows: Theoretical Light Curves for Quasi-spherical Outflows

We investigate late-time gamma-ray burst (GRB) afterglows produced by quasi-spherical outflows propagating into a stratified circumburst medium during the deep Newtonian phase. Sub-relativistic ejecta generated in compact binary mergers or core-collapse explosions naturally develop velocity structures, while additional energy injection from a long-lived central engine, through spin-down luminosity and/or fallback accretion, can substantially modify the afterglow evolution. We develop an analytical framework for synchrotron emission from decelerated ejecta components undergoing energy injection in a stratified environment. The model provides multiwavelength light curves and corresponding closure relations for the deep Newtonian regime. We apply this framework to the late-time multiwavelength observations of GRB 171205A. In addition, we constrain the physical properties of quasi-spherical outflows using observations of short GRBs associated with kilonova candidates, together with long-term radio upper limits obtained years after the burst in a broader GRB sample. Our results show that late-time observations can place meaningful constraints on the dynamics, energetics, and energy-injection history of sub-relativistic quasi-spherical outflows from GRB progenitors.