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 _ { \mathrm { 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 _ { \mathrm { defl } } .
However , if the nuclear energy released during the deflagration phase is close to the white dwarf binding energy ( \sim 0.46 \times 10 ^ { 51 } ~ { } \mathrm { erg } \Rightarrow M _ { \mathrm { defl } } \sim 0.30 M _ { \odot } ) the accretion shock can not heat and confine efficiently the core and detonation conditions are not robustly achieved .