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.

References

For reasons that are unclear, an additional $ \geq 2#1{-3} $ is required for a shell and core detonation for the $1.1 $ model, even though $l_{\rm sonic} < H_P$ is achieved for the $1.1 + 10{-3} $ case. Further investigation is required to understand why a detonation does not propagate in this case.

— Almost All Carbon/Oxygen White Dwarfs Can Host Double Detonations  (2405.19417 - Shen et al., 2024) in Section 4 (Two-dimensional detonations in realistic C/O WDs), subsection High-mass models with added mass

Reactions are not coupled to hydrodynamics and the composition is not evolved, so we cannot say if the burning would spread beyond the candidate material.

— Evolution and mergers of eccentric white dwarf binaries encountering intermediate-mass black holes  (2609.20338 - Pandey et al., 17 Sep 2026) in Appendix, Section “Thermodynamic State and Possible Dynamical Burning”