Carbon Deflagration in Type Ia Supernova: I. Centrally Ignited Models

A leading model for Type Ia supernovae (SNe Ia) begins with a white dwarf near the Chandrasekhar mass that ignites a degenerate thermonuclear runaway close to its center and explodes. In a series of papers, we shall explore the consequences of ignition at several locations within such dwarfs. Here we assume central ignition, which has been explored before, however, the problem is worth revisiting, if only to validate those previous studies and to further elucidate the relevant physics for future work. A perturbed sphere of hot iron ash with a radius of ~100 km is initialized at the middle of the star. The subsequent explosion is followed in several simulations using a thickened flame model in which the flame speed is either fixed --- within the range expected from turbulent combustion --- or based on the local turbulent intensity. Global results, including the explosion energy and bulk nucleosynthesis (e.g. 56Ni of 0.48--0.56 $\Msun$) turn out to be insensitive to this speed. In all completed runs, the energy released by the nuclear burning is adequate to unbind the star, but not enough to give the energy and brightness of typical SNe Ia. As found previously, the chemical stratification observed in typical events is not reproduced. These models produce a large amount of unburned carbon and oxygen in central low velocity regions, which is inconsistent with spectroscopic observations, and the intermediate mass elements and iron group elements are strongly mixed during the explosion.