Three-Dimensional Simulations of Rayleigh-Taylor Mixing in Core-Collapse Supernovae

We present multidimensional simulations of the post-explosion hydrodynamics in three different 15 M ☉ supernova models with zero, 10 −4 Z ☉ , and Z ☉ metallicities. We follow the growth of the Rayleigh–Taylor (RT) instability that mixes together the stellar layers in the wake of the explosion. Models are initialized with spherically symmetric explosions and perturbations are seeded by the grid. Calculations are performed in two-dimensional (2D) axisymmetric and three-dimensional (3D) Cartesian coordinates using the new Eulerian hydrodynamics code, CASTRO . We find as in previous work that RT perturbations initially grow faster in 3D than in 2D. As the RT fingers interact with one another, mixing proceeds to a greater degree in 3D than in 2D, reducing the local Atwood number and slowing the growth rate of the instability in 3D relative to 2D. By the time mixing has stopped, the width of the mixed region is similar in the 2D and 3D simulations provided the RT fingers show significant interaction. Our results imply that 2D simulations of light curves and nucleosynthesis in supernovae that die as red giants may capture the features of an initially spherically symmetric explosion in far less computational time than required by a full 3D simulation. However, capturing large departures from spherical symmetry requires a significantly perturbed explosion. Large-scale asymmetries cannot develop through an inverse cascade of merging RT structures; they must arise from asymmetries in the initial explosion.