Gamma-ray transfer and energy deposition in supernovae

Solutions to the energy-independent (gray) radiative transfer equations are compared to results of Monte Carlo simulations of the \Ni and \Co radioactive decay \GR energy deposition in supernovae. The comparison shows that an effective, purely absorptive, gray opacity, \KG $\sim (0.06 \pm 0.01)Y_e$ cm$^2$ g$^{-1}$, where $Y_e$ is the total number of electrons per baryon, accurately describes the interaction of \GRs with the cool supernova gas and the local \GR energy deposition within the gas. The nature of the \GR\ interaction process (dominated by Compton scattering in the relativistic regime) creates a weak dependence of \KG on the optical thickness of the (spherically symmetric) supernova atmosphere: The maximum value of \KG applies during optically thick conditions when individual \GRs undergo multiple scattering encounters and the lower bound is reached at the phase characterized by a total Thomson optical depth to the center of the atmosphere \te \LA 1. Our results quantitatively confirm that the quick and efficient solution to the gray transfer problem provides an accurate representation of \GR energy deposition for a broad range of supernova conditions.