Identify why a 1.1 M_sun C/O white dwarf with 10^{-3} M_sun added helium fails to detonate despite l_sonic < H_P

Ascertain the mechanism that prevents a helium shell detonation from propagating in the simulated 1.1 solar-mass carbon–oxygen white dwarf after the addition of 10^{-3} solar masses of helium-rich material and relaxation—even though the local condition l_sonic < H_P at the transition layer is satisfied—and determine what additional factors (e.g., compositional structure, thermal profile, geometry, or numerical treatment) necessitate ≥2×10^{-3} solar masses of added helium for successful shell and core detonations.

Background

Using the criterion that a successful shell detonation requires the detonation sonic lengthscale to be shorter than the local pressure scale height (l_sonic ≲ H_P), the authors find that adding small helium masses to massive white dwarfs can enable shell detonations. For the 1.1 M_sun model, the configuration with 10^{-3} M_sun added helium satisfies l_sonic < H_P but does not exhibit a propagating shell detonation in the simulations.

They report that a larger added helium mass (≥2×10^{-3} M_sun) is necessary for successful shell and core detonations in the 1.1 M_sun case, and explicitly note that the reason for the failure at 10^{-3} M_sun is not understood, calling for further investigation.