The cellular structure is considered to be a key as a criterion in initiation, propagation, and quenching of terrestrial detonation. While a few studies on type Ia supernovae, which are known to involve detonation, have addressed the importance of the cellular structure, further detailed treatment will benefit enhanced understanding of the explosion outcomes. In the present study, we bridge this gap in the astrophysics and engineering fields, focusing on the detonation in a helium-rich white dwarf envelope as the triggering process for the so-called double-detonation model. The cellular structures are quantified via high-resolution two-dimensional simulations. We demonstrate that widely accepted terrestrial-experimental criteria for quenching and initiation of detonation can indeed explain the results of previous hydrodynamic simulations very well. The present study highlights the potential of continuing to apply the insight from terrestrial detonation experiments to astrophysical problems, specifically the long unresolved problem of the explosion mechanism of type Ia supernovae.
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