Local Ignition in Carbon‐Oxygen White Dwarfs. I. One‐Zone Ignition and Spherical Shock Ignition of Detonations

The details of ignition of Type Ia supernovae remain fuzzy, despite theimportance of this input for any large-scale model of the final explosion.Here, we begin a process of understanding the ignition of these hotspots byexamining the burning of one zone of material, and then investigate theignition of a detonation due to rapid heating at single point. We numerically measure the ignition delay time for onset of burning inmixtures of degenerate material and provide fitting formula for conditions ofrelevance in the Type Ia problem. Using the neon abundance as a proxy for thewhite dwarf metallicity, we then find that ignition times can decrease by ~20%with addition of even 5% of neon by mass. When temperature fluctuations thatsuccessfully kindle a region are very rare, such a reduction in ignition timecan increase the probability of ignition by orders of magnitude. If the neoncomes largely at the expense of carbon, a similar increase in the ignition timecan occur. We then consider the ignition of a detonation by an explosive energy input inone localized zone, eg a Sedov blast wave leading to a shock-igniteddetonation. Building on previous work on curved detonations, we find thatsurprisingly large inputs of energy are required to successfully launch adetonation, leading to required matchheads of ~4500 detonation thicknesses -tens of centimeters to hundreds of meters - which is orders of magnitude largerthan naive considerations might suggest. This is a very difficult constraint tomeet for some pictures of a deflagration-to-detonation transition, such as aZel'dovich gradient mechanism ignition in the distributed burning regime.