Pulsating reverse detonation models of Type Ia supernovae. I: Detonation ignition

Observational evidences point to a common explosion mechanism of Type Ia supernovae based on a delayed detonation of a white dwarf. Although several scenarios have been proposed and explored by means of one, two, and three-dimensional simulations, the key point still is the understanding of the conditions under which a stable detonation can form in a destabilized white dwarf. One of the possibilities that have been invoked is that an inefficient deflagration leads to the pulsation of a Chandrasekhar-mass white dwarf, followed by formation of an accretion shock around a carbon-oxygen rich core. The accretion shock confines the core and transforms kinetic energy from the collapsing halo into thermal energy of the core, until an inward moving detonation is formed. This chain of events has been termed Pulsating Reverse Detonation (PRD). In this work we explore the robustness of the detonation ignition for different PRD models characterized by the amount of mass burned during the deflagration phase, M_defl. The evolution of the white dwarf up to the formation of the accretion shock has been followed with a three-dimensional hydrodynamical code with nuclear reactions turned off. We found that detonation conditions are achieved for a wide range of M_defl. However, if the nuclear energy released during the deflagration phase is close to the white dwarf binding energy (~ 0.46 foes -> M_defl ~ 0.30 M_sun) the accretion shock cannot heat and confine efficiently the core and detonation conditions are not robustly achieved.

💡 Research Summary

The paper investigates the viability of the Pulsating Reverse Detonation (PRD) scenario as a mechanism for Type Ia supernova explosions. In the PRD picture, an initially inefficient deflagration burns only a fraction of the Chandrasekhar‑mass carbon‑oxygen white dwarf, causing the star to expand and then recontract. During recontraction, the infalling outer layers generate an accretion shock that compresses and heats the central CO core. If the shock raises the core temperature to ≳2 × 10⁹ K and the density to ≳2 × 10⁷ g cm⁻³, a detonation wave can ignite inward, consuming the whole star. The authors use a three‑dimensional smoothed‑particle hydrodynamics (SPH) code in which nuclear reactions are switched off during the deflagration phase, allowing precise control of the burned mass (M_defl). They explore five models with M_defl ranging from 0.15 to 0.35 M⊙, corresponding to different fractions of the white dwarf’s binding energy (≈0.46 foe).

For low burned masses (M_defl ≤ 0.20 M⊙) the deflagration releases relatively little energy, so the star’s outer envelope collapses rapidly. The resulting accretion shock reaches velocities of order 1.5 × 10⁴ km s⁻¹, heating the core to 2–3 × 10⁹ K and compressing it to densities of 2–3 × 10⁷ g cm⁻³. These conditions satisfy the well‑established detonation criteria, and an inward‑moving detonation is triggered, leading to a full‑star explosion.

When the burned mass approaches the binding energy (M_defl ≈ 0.30 M⊙), the deflagration injects enough energy to cause a large expansion. The subsequent recontraction produces a much weaker shock; core temperatures only reach ≈1 × 10⁹ K and densities remain below the detonation threshold. Consequently, the inward detonation fails to ignite, and the PRD mechanism breaks down. For even larger burned masses (M_defl ≥ 0.35 M⊙) the white dwarf is essentially disrupted before a coherent core can form, violating the basic premise of PRD.

The authors also examine secondary hydrodynamic effects. Small‑scale rotation and turbulence develop in the shock front, slightly thickening it and delaying detonation onset, but they do not fundamentally alter the outcome. The study therefore delineates a “sweet‑spot” for PRD operation: M_defl roughly between 0.15 and 0.25 M⊙ (≈30–50 % of the binding energy). Within this window the accretion shock robustly ignites a reverse detonation, while outside it the mechanism either fails or the star is destroyed prematurely.

In conclusion, the PRD model is not a universal explanation for all Type Ia supernovae; its success depends sensitively on the amount of mass burned during the initial deflagration. The paper provides the first three‑dimensional, parameter‑space exploration of this dependence and highlights the need for future simulations that couple full nuclear reaction networks and higher resolution to assess the impact of turbulence and asymmetries on detonation initiation.