Monte Carlo techniques for time-dependent radiative transfer in 3-D supernovae

Monte Carlo techniques based on indivisible energy packets are described for computing light curves and spectra for 3-D supernovae. The radiative transfer is time-dependent and includes all effects of $O(v/c)$. Monte Carlo quantization is achieved by discretizing the initial distribution of $\rm ^{56}Ni$ into ${\cal N}$ radioactive pellets. Each pellet decays with the emission of a single energy packet comprising γ-ray photons representing one line from either the $\rm ^{56}Ni$ or the $\rm ^{56}Co$ decay spectrum. Subsequently, these energy packets propagate through the homologously-expanding ejecta with appropriate changes in the nature of their contained energy as they undergo Compton scatterings and pure absorptions. The 3-D code is tested by applying it to a spherically-symmetric SN in which the transfer of optical radiation is treated with a grey absorption coefficient. This 1-D problem is separately solved using Castor's co-moving frame moment equations. Satisfactory agreement is obtained. The Monte Carlo code is a platform onto which more advanced treatments of the interactions of matter and radiation can be added. Some of these have already been developed and tested in previous papers and are summarized here