Thermonuclear Explosions of White Dwarfs: What have supernova explosions and combustion engines in common?

Because calibrated light curves of thermonuclear (Type Ia) supernovae have become a major tool to determine the local expansion rate of the Universe, and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most Type Ia supernovae are the explosions of white dwarf stars, consisting mainly of carbon and oxygen only, that have approached the Chandrasekhar mass, M_chan ≈ 1.39 M_⊙, and are disrupted by thermonuclear fusion of carbon and oxygen. Recent progress in modeling Type Ia supernovae as well as several of the still open questions are addressed in this talk. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics and numerical modeling of turbulent nuclear combustion in degenerate stars, we also discuss observational implications and constraints, including consequences for cosmology.