Approximating Convective Urca Cooling in a Simmering White Dwarf

Type Ia supernovae are bright thermonuclear explosions that play important roles in many areas of astronomy such as cosmology and galaxy evolution. The near Chandrasekhar mass white dwarf is a potential progenitor for these supernovae. This model entails a white dwarf accreting material from a companion and gaining mass to the point of igniting carbon fusion in the core. The onset of carbon fusion, called the simmering phase, drives convection and alters the evolution of the white dwarf as it approaches the thermonuclear explosion. A key factor during this phase is the convective Urca process which links convection with weak nuclear reactions that leak energy from the star. To study the effects of the convective Urca process, it is vital to accurately model the turbulent convection in the core. This necessitates 3D hydrodynamic simulations which are computationally expensive. As a point of comparison and to aid in exploring initial conditions, we use the “quick mixing” approximation, which assumes convective mixing is efficient enough to produce a uniform composition in the convection zone. Utilizing this approximation, we can predict the ratio of the A = 23 Urca pair as well as the resulting neutrino loss rates without running full 3D simulations. We compare the results of a 3D hydrodynamic simulation, run using the low Mach number hydrodynamic code MAESTROeX, to the quick mixing calculation. Additionally, we investigate how varying the size of the convection zone influences the convective Urca process and sets approximate bounds on reasonable initial conditions.