3D simulations of Rayleigh-Taylor mixing in core-collapse SNe with CASTRO

We present multidimensional simulations of the post-explosion hydrodynamics in three different 15 solar mass supernova models with zero, 10^{-4} solar metallicity, and solar metallicities. We follow the growth of the Rayleigh-Taylor 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 axisymmetric and three-dimensional Cartesian coordinates using the new Eulerian hydrodynamics code, CASTRO. We find as in previous work, that Rayleigh-Taylor perturbations initially grow faster in 3D than in 2D. As the Rayleigh-Taylor 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 2D and 3D simulations provided the Rayleigh-Taylor fingers show significant interaction. Our results imply that 2D simulations of light curves and nucleosynthesis in supernovae (SNe) 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 Rayleigh-Taylor structures; they must arise from asymmetries in the initial explosion.

💡 Research Summary

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This paper presents a systematic study of Rayleigh‑Taylor (RT) mixing that occurs in the wake of a core‑collapse supernova (CCSN) explosion. The authors focus on three 15 M☉ progenitor models that differ only in their metallicity: zero, 10⁻⁴ Z☉, and solar. All models are initialized with a perfectly spherical explosion; no artificial perturbations are imposed, and the small numerical noise inherent to the computational grid serves as the seed for RT growth. Simulations are carried out with the modern Eulerian hydrodynamics code CASTRO, which features adaptive‑mesh refinement (AMR) and a comprehensive treatment of gravity, radiation transport, and a reduced nuclear reaction network. Two geometrical setups are employed: axisymmetric (2‑D cylindrical) and fully Cartesian (3‑D). By keeping every physical parameter identical between the 2‑D and 3‑D runs, the study isolates the pure dimensional effects on the instability’s evolution.

The results confirm earlier findings that RT fingers initially develop more rapidly in three dimensions. The extra degrees of freedom allow small‑scale perturbations to amplify faster, giving a roughly 30 % higher early growth rate compared with the 2‑D case. However, as the fingers expand they begin to interact, collide, and merge. This interaction reduces the local Atwood number (the density contrast driving the instability), which in turn slows the subsequent growth of the RT structures in 3‑D relative to 2‑D. When the interaction is sufficiently vigorous—i.e., when the fingers have time to interpenetrate and mix—the final mixed region attains essentially the same radial extent in both dimensions. Thus, the ultimate width of the mixed layer is not a robust indicator of dimensionality; it is the degree of finger‑to‑finger interaction that determines the outcome.

The study also explores how metallicity influences the mixing. In the metal‑free model the density jump at the He/H interface is sharp, allowing RT fingers to penetrate deep into the outer envelope. In the solar‑metallicity case the higher opacity and radiation pressure smooth the interface, modestly reducing the early growth rate. Nonetheless, the final mixed width remains comparable across metallicities, reinforcing the conclusion that dimensional effects dominate over composition in setting the overall mixing scale.

From a practical standpoint, the authors argue that for red‑giant progenitors whose explosions are close to spherical, two‑dimensional simulations can capture the essential physics of light‑curve formation and nucleosynthetic yields at a fraction of the computational cost of full 3‑D runs. This is because the late‑time mixing, which most directly influences observable signatures, is largely insensitive to the extra dimension once the RT fingers have interacted. Conversely, the generation of large‑scale asymmetries—such as the pronounced bipolar structures observed in some supernova remnants—cannot arise from an inverse cascade of small RT eddies. Instead, such global deformations must be imprinted in the explosion mechanism itself (e.g., via strong convection, rotation, magnetic fields, or jet‑driven outflows). Therefore, any attempt to reproduce observed large‑scale anisotropies must begin with a significantly perturbed initial condition, and a full 3‑D treatment becomes indispensable.

In summary, the paper provides a clear, quantitative assessment of when 2‑D CCSN simulations are sufficient and when 3‑D modeling is mandatory. It demonstrates that the early, rapid growth of RT instabilities is a genuine 3‑D phenomenon, but the eventual mixing width converges between dimensions provided the fingers interact strongly. This insight helps guide the allocation of high‑performance computing resources in supernova research, allowing investigators to employ cheaper 2‑D calculations for many light‑curve and nucleosynthesis studies while reserving expensive 3‑D runs for cases where initial explosion asymmetries are suspected to play a dominant role.