Two-dimensional versus Three-dimensional Supernova Hydrodynamic Instability Growth

Numerical simulations using the SN hydrodynamics code PROMETHEUS are carried out to study the difference between growth of two-dimensional versus three-dimensional single-mode perturbations at the He-H and O-He interfaces of SN 1987A. We find that in the rest frame of an unperturbed one-dimensional interface, a three-dimensional single-mode perturbation grows ≈30%-35% faster than a two-dimensional single-mode perturbation, when the wavelengths are chosen to give the same linear stage growth in the planar limit. In simulations where we impose single-mode density perturbations in the O layer of the initial model and random velocity perturbations in the postshock fluid near the He-H interface, we find that both axisymmetric O spikes and three-dimensional O spikes penetrate significantly further than two-dimensional O spikes. The difference between two dimensions and three dimensions predicted by our calculations is not enough to account for the difference between observed ⁵⁶Co velocities in SN 1987A and the results of previous two-dimensional simulations of SN 1987A, but our results suggest that the real three-dimensional hydrodynamics are noticeably different than the two-dimensional simulations predict.