We present a theoretical framework for formal study of systematic effects in Supernovae Type Ia (SN Ia) that utilizes two-dimensional simulations to implement a form of the deflagration-detonation transition (DDT) explosion scenario. The framework is developed from a randomized initial condition that leads to a sample of simulated SN Ia whose 56 Ni masses have a similar average and range to those observed, and have many other modestly realistic features such the velocity extent of intermediate mass elements. The intended purpose is to enable statistically well-defined studies of both physical and theoretical parameters of the SN Ia explosion simulation. We present here a thorough description of the outcome of the SN Ia explosions produced by our current simulations.A first application of this framework is utilized to study the dependence of the SN Ia on the 22 Ne content, which is known to be directly influenced by the progenitor stellar population's metallicity. Our study is very specifically tailored to measure how the 22 Ne content influences the competition between the rise of plumes of burned material and the expansion of the star before these plumes reach DDT conditions. This influence arises from the dependence of the energy release, progenitor structure and laminar flame speed on 22 Ne content. For this study, we explore these three effects for a fixed carbon content and DDT density. By setting the density at which nucleosynthesis takes place during the detonation phase of the explosion, the competition between plume rise and stellar expansion controls the amount of material in nuclear statistical equilibrium (NSE) and therefore 56 Ni produced. Of particular interest is how this influence of 22 Ne content compares to the direct modification of the 56 Ni mass via the inherent neutron excess as discussed by Timmes, Brown & Truran (2003). Although the outcome following from any particular ignition condition can change dramatically with 22 Ne content, with a sample of 20 ignition conditions we find that the systematic change in the expansion of the star prior to detonation is not large enough to compete with the dependence discussed by Timmes, . In fact, our results show no statistically significant dependence of the pre-detonation expansion on 22 Ne content, pointing to the morphology of the ignition condition as being the dominant dynamical driver of the 56 Ni yield of the explosion. However, variations in the DDT density, which were specifically excluded here, are also expected to be important and to depend systematically on 22 Ne content.

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