Type Ia Supernovae: Explosion Models versus Observational Constraints

To have confidence in using Type~Ia supernovae (SNe~Ia) to determine the expansion history of the universe, and thereby probe the nature of the dark energy, we must advance our understanding of SN~Ia physics. In the standard model a carbon--oxygen white dwarf accretes matter from a companion star, approaches the Chandrasekhar mass, ignites carbon fusion, encounters a thermonuclear instability, and explodes completely. The final kinetic energy of the ejected matter is the energy released by fusion minus the white--dwarf binding energy. The kinetic energy inferred from observations indicates that practically the whole white dwarf undergoes fusion. The peak luminosity depends on the mass of freshly synthesized $^{56}$Ni, which provides a delayed release of energy while decaying through $^{56}$Co to stable $^{56}$Fe. The observed SN~Ia luminosity requires that nearly half of the mass is synthesized to $^{56}$Ni. Spectroscopic observations indicate that the composition structure of the ejected matter is radially stratified, with a core of iron--group elements surrounded by lighter elements such as calcium, silicon, and oxygen. Spherically symmetric (1D) nuclear-hydrodynamical explosion models that meet these requirements have been calculated, by parameterizing the velocity of the burning front. In recent years more self--consistent 3D models have been calculated. Deflagration models, in which the burning front remains subsonic, undergo insufficient fusion and lack the stratified composition structure. Delayed--detonation models, which invoke a transition to supersonic front propagation, fare better, although it is not known whether the transition really can occur. I will discuss the status of explosion models versus observational constraints (mostly spectroscopic), and the challenging task of relating the various observational manifestations of SN~Ia diversity to their physical causes.