The convective Urca process

One possible fate of an accreting white dwarf is explosion in a type Ia supernova. However, the route to the thermonuclear runaway has always been uncertain owing to the lack of a convective model consistent with the Urca process. We derive a formalism for convective motions involving two radial flows. This formalism provides a framework for convective models that guarantees self-consistency for chemistry and energy budget, allows time-dependence and describes the interaction of convective motions with the global contraction or expansion of the star. In the one-stream limit, we reproduce several already existing convective models and allow them to treat chemistry. We also suggest as a model easy to implement in a stellar evolution code. We apply this formalism to convective Urca cores in Chandrasekhar mass white dwarfs. We stress that in degenerate matter, nuclear reactions that change the number of electrons strongly influence the convective velocities. We point out the sensitivity of the energy budget on the mixing. We illustrate our model by computing stationary convective cores with Urca nuclei. We show that even a very small mass fraction of Urca nuclei (10 −8) strongly influences the convective velocities. Finally, we present preliminary computations of the late evolution of a close to Chan-drasekhar mass C+O white dwarf including the convective Urca process. 1. Prelude to thermonuclear explosions When a CO white dwarf accretes matter, its centre gets denser and hotter. At some point, the CC burning ignites mildly in the centre. When the radiative luminosity can no longer get rid of the heat produced, a convective core forms and grows as the burning releases more and more energy. During the burning process, Urca pairs such as 23 Na− 23 Ne are produced. These release neutrinos through emission and capture of electrons preferentially around Urca shells. The net amount of energy released and the change in the electron fraction at the time of the explosion have always been uncertain due to the lack of a convective model self-consistent with the energy and chemistry budgets [ to describe the interplay between convection and chemistry have all left open the question of energy conservation. A better understanding of the phase immediately preceding the thermal runaway pro