Cellular Dynamics of Helium-rich Detonation on sub-Chandrasekhar Mass White Dwarf

The gist The cellular structure was observed at all the parameter range we explored; the upstream density in the range of 105 - 106g cm−3 and the envelope composition of XHe =0.0 and 0.6-1.0 (with the rest devided into 12C and 16O with equal mass fractions>

Cellular Dynamics

The study investigates the cellular dynamics of helium detonation in the base of a white-dwarf (WD) envelope, focusing on reproducing thresholds for initiation and quenching using terrestrial cell-based theories The cellular structure is observed at a range of upstream density and envelope composition explored in the present work C/O contamination by the WD core material reduces the cell width rapidly, as accelerated by the α-capture reaction It is also indicated that nickel production could be significantly delayed for the C/O-rich composition The small cell width makes it extremely demanding to resolve the detonation structure in full-star simulations of SNe Ia This issue may be overcome by sub-grid modeling that incorporates the cellular dynamics acquired in resolved simulations

Numerical Setup and Resolution Criteria

The 2D hydrodynamic code was an extension of a 1D version described in Iwata & Maeda (2022), except for the absence of gravity because the present study focuses on the local detonation structure in a uniform medium The discretization schemes are common to our previous studies, and an operator splitting method is used to evolve the flow and reaction separately in time The model setup follows that of Gamezo et al. (1999), using a rectangular area discretized to 2000×1200 uniform square Eulerian meshes A detonation-fixed coordinate is realized by adding inertial force to control the longitudinal position of detonation The choice of the methods to disturb the ZND profiles depends on the computational cases, with a white-noise perturbation applied to the more helium-rich detonation

Spatial Scales and Resolution Requirements

Choosing the resolution for simulating the cellular detonation is one major issue that has been investigated extensively in terrestrial detonation, because it affects the size of the observed cellular structure The spatial scale for exothermicity, or the temperature increase, serves as a fundamental quantity In terrestrial detonation, the scales for the maximum heat release and the half-reaction length are both close to the scale for the temperature increase Therefore, we find that Lq is better as the basic scale to be resolved, which is close to LC for XHe=0.0 cases, and LO for XHe=0.6,0.9,1.0 cases In the following 2D study, twenty meshes are placed within Lq The cell width was found to be 8.0×10 squared cm for the standard mesh size of 2 cm, and varied to 6.0, 9.3, and 6.3 ×10 squared cm for 1, 5, and 7 cm resolution, respectively

Cellular Structure Observations

The cellular structure is observed at all the parameter range we explored; the upstream density in the range of 105 - 106g cm−3 and the envelope composition of XHe =0.0 and 0.6-1.0 (with the rest devided into 12C and 16O with equal mass fractions> The cellular structure is induced by the instability of the exothermic shock front associated with the first increase of the accumulated nuclear energy generation For XHe=0.6, sequential images of the pressure distribution in two selected cases are shown with a constant interval in step number The general behavior of the cellular structure is found to be common in the present parameter space The averaged cell width, as calculated by the number of transverse waves in the lateral direction, in these two simulations are 5.5 cm and 1.2×10 4 cm, respectively

Chemical Abundance Structure

The multi-D inhomogeneity in the chemical abundance is much stronger for the He/C/O mixture with moderate He content (XHe=0.6) than the pure-He medium (XHe=0.0) This demonstrates the stronger sensitivity of the reaction system to the local shock speed Vortical structures, produced at the collision point of the transverse waves and then convected downstream, are clearly seen in the abundance distributions This vortex production originates from the Kelvin-Helmholtz instability caused by the velocity imbalance between the region behind a Mach stem and incident shock front

Conclusion

The scale of cellular detonation is typically far below the pressure scale height of such WDs, except for the pure-He condition This finding supports the idea that the double-detonation model can be a feasible scenario for normal SNe Ia, if the high contamination of the core material in the envelope is possible Significant delay of nickel production suggested for the intermediate helium mass fraction could also be a key to fulfilling the constraint from the early-time observables Sub-grid modeling approach may be one solution to bridge the gap The present work highlights the importance of bridging the research fields of astrophysical detonation and terrestrial detonation

References

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Crane, J., Lipkowicz, J. T., Shi, X., et al. 2023, Proceedings of the Combustion Institute, 39, 2915, doi: https://doi.org/10.1016/j.proci.2022.10.019<ref:2412.

1. No longer relying solely on full-star simulations for SNe Ia; AI systems can now incorporate sub-grid modeling based on cellular dynamics to bridge the gap, enabling more realistic explosion scenarios by bridging the gap between resolved and unresolved scales.

2. Improved initiation and quenching criteria determination; AI can use the terrestrial cell-based theories to reproduce thresholds, as demonstrated by Iwata & Maeda (2024), allowing for more robust prediction of detonation success or failure in simulations.

3. Enhanced chemical abundance structure modeling; AI can predict the complex multi-stage reaction sequences by tracking isotope production and consumption, specifically noting that the difference in the consumption scales of 12C and 16O depends on the condition, which is crucial for understanding early-time observables like nickel production delay.

4. Resolution requirement assessment: AI can dynamically determine the necessary mesh size by analyzing characteristic spatial scales, such as finding that Lq is better as the basic scale to be resolved, thereby optimizing computational resources for high-fidelity simulations.

5. Cellular structure parameterization: AI systems can quantify cell widths by establishing a relationship, such as λ is roughly proportional to Lq with the proportionality coefficient being in the range of 6-17, providing a predictive tool for scaling cellular dynamics across different progenitor compositions.

Most previous efforts for hydrodynamic studies on detonation in the context of Type Ia supernovae did not take into account the scale of the cellular structure for a criterion in initiation, propagation, quenching, and the resolution requirement of detonation, whereas it is quite common to consider cell sizes in the discussion on terrestrial detonation in chemically reactive systems. In our recent study, the terrestrial cell-based theories, which incorporates the cell-size data acquired in 2D simulations of helium detonation in the double-detonation model, were demonstrated to be a powerful diagnostics in reproducing the thresholds in the initiation and quenching provided by previous studies. In the present study, 2D simulation results of the cellular detonation in the base of white-dwarf (WD) envelope are described in detail, in terms of the dynamic wave morphology and chemical abundance structure. The cellular structure is observed at a range of upstream density and envelope composition explored in the present work. C/O contamination by the WD core material reduces the cell width rapidly, as accelerated by the α-capture reaction. It is also indicated that nickel production could be significantly delayed for the C/O-rich composition. The small cell width makes it extremely demanding to resolve the detonation structure in full-star simulations of SNe Ia; this could raise a concern on the robustness of the outcomes of some numerical simulations in terms of the success and failure of detonation. This issue may be overcome by sub-grid modeling that incorporates the cellular dynamics acquired in resolved simulations.