On the formation of Lyman α emission from resonantly scattered continuum photons of GRB's afterglow

We study the formation and evolution of the spectral imprint of resonantly scattered Lyman $\alpha$ photons in the context of GRB's continuum optical afterglow. Based on an analytic model and a complete treatment of all the scatterings using Monte Carlo simulations, we found that the flux of the Ly$\alpha$ emission is mainly contributed by photons which are scattered only once. The flux is of order $10^{-4}$ to $10^{-9}$ relative to the undecayed maximum flux of the transmitted continuum, making the feature negligible but potentially observable. If not obscured by host galaxy's DLA or intergalactic neutral hydrogen, the feature may appear sometime from one hour to several years when the directly transmitted light has faded away.This scattered emission feature can be distinguished from Ly$\alpha$ photons of other origins by its luminosity evolution, and by its gradual narrowing of profile with time. The typical time scale for spectral variance is that of the light crossing time of a hydrogen clump close to the GRB.