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Some explosion models for Type Ia supernovae (SN Ia), such as thegravitationally confined detonation (GCD) or the double detonationsub-Chandrasekhar (DDSC) models, rely on the spontaneous initiation of adetonation in the degenerate C/O material of a white dwarf. The length scalespertinent to the initiation of the detonation are notoriously unresolved inmulti-dimensional stellar simulations, prompting the use of results of 1Dsimulations at higher resolution, such as the ones performed for this work, asguidelines for deciding whether or not conditions reached in the higherdimensional full star simulations successfully would lead to the onset of adetonation. Spontaneous initiation relies on the existence of a suitablegradient in self-ignition (induction) times of the fuel, which we set up with aspatially localized non-uniformity of temperature -- a hot spot. We determinethe critical (smallest) sizes of such hot spots that still marginally result ina detonation in white dwarf matter by integrating the reactive Euler equationswith the hydrodynamics code FLASH. We quantify the dependences of the criticalsizes of such hot spots on composition, background temperature, peaktemperature, geometry, and functional form of the temperature disturbance, manyof which were hitherto largely unexplored in the literature. We discuss theimplications of our results in the context of modeling of SNe Ia.

Spontaneous Initiation of Detonations in White Dwarf Environments: Determination of Critical Sizes