A Monte Carlo code (ARTIS) for modelling time-dependent three-dimensional spectral synthesis in chemically inhomogeneous models of Type Ia supernova ejecta is presented. Following the propagation of gamma-ray photons, emitted by the radioactive decay of the nucleosynthesis products, energy is deposited in the supernova ejecta and the radiative transfer problem is solved self-consistently, enforcing the constraint of energy conservation in the co-moving frame. Assuming a photoionisation dominated plasma, the equations of ionisation equilibrium are solved together with the thermal balance equation adopting an approximate treatment of excitation. Since we implement a fully general treatment of line formation, there are no free parameters to adjust. Thus a direct comparison between synthetic spectra and light curves, calculated from hydrodynamic explosion models, and observations is feasible. The code is applied to the well known W7 explosion model and the results tested against other studies. Finally the effect of asymmetric ejecta on broad band light curves and spectra is illustrated using an elliptical toy model.
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