Decelerated sub-relativistic material with energy Injection

We investigate the evolution of the afterglow produced by the deceleration of the non-relativistic material due to its surroundings. The ejecta mass is launched into the circumstellar medium with equivalent kinetic energy expressed as a power-law velocity distribution $E\propto (\Gamma\beta)^{-\alpha}$. The density profile of this medium follows a power law $n(r)\propto r^{-k}$ with $k$ the stratification parameter, which accounts for the usual cases of a constant medium ($k=0$) and a wind-like medium ($k=2$). A long-lasting central engine, which injects energy into the ejected material as ($E\propto t^{1-q}$) was also assumed. With our model, we show the predicted light curves associated with this emission for different sets of initial conditions and notice the effect of the variation of these parameters on the frequencies, timescales and intensities. The results are discussed in the Kilonova scenario.