3D Synthetic Convective Velocity Fields to Initialise Core-Collapse Supernova Simulations from 1D Progenitors

TL;DR

The paper addresses the need for realistic 3D pre-collapse velocity fields to seed core-collapse supernova (CCSN) simulations while avoiding the computational cost of full 3D stellar convection. It introduces a vector spherical harmonics (VSH)–based framework under the anelastic approximation to synthesize 3D velocity fields from 1D progenitor models, enforcing non-radial vorticity and zero net angular momentum, and achieving isotropy by multi-mode superposition with random phases. The method uses a radial basis function h(r) and chooses the dominant angular wavenumber ell from shell geometry, with four radial-basis options and density-weighting variants, interfaced via open-source Python code compatible with MESA profiles. Validation is qualitative, showing agreement with large-scale convective patterns observed in 3D simulations, and the work enables efficient exploration of how pre-SN asymmetries impact CCSN outcomes, with future extensions to turbulence spectra, rotation, and magnetic fields.

Abstract

Core-collapse supernovae (CCSNe) are among the most energetic and complex astrophysical phenomena, requiring threedimensional (3D) simulations to capture their intricate explosion mechanisms. One of the key ingredients for such simulations is the 3D pre-collapse structure, which can impact the development and geometry of the subsequent explosion. While stellar convection simulations can provide such 3D initial conditions, these remain too expensive and demanding for widespread use. In this work, we present a method to generate synthetic 3D velocity fields for convective zones from 1D initial conditions, creating initial conditions for CCSN simulations using a vector spherical harmonics expansion without the need for expensive hydrodynamic progenitor simulations. The synthetic velocity field is designed to capture the typical scales and velocities of the convective flow as the most relevant parameters for the subsequent explosions. In addition, it respects relevant physical constraints such as the near-anelasticity of flow, vanishing radial vorticity, and zero net angular momentum in the convective zones. A Python implementation of this method is publicly available, offering the CCSN community a practical tool for generating synthetic velocity fields for multi-dimensional simulations to study the impact of 3D progenitor asymmetries on the CCSN mechanism.

Figures (8)

• Figure 1: Contour plot of radial velocity (in arbitrary units) for a random superposition of modes with $\ell=6$ on a sphere of radius $1.5$ in the middle of a convective shell between $R_\mathrm{i}=1$ and $R_\mathrm{o}=2$.
• Figure 2: Plot visualising the different options for radial basis functions currently implemented.
• Figure 3: 3D vector plot (left) and 2D vector slice for a dimensionless dipole velocity field configuration ($\ell$ = 1). The vector arrows include all three velocity components, but the colourbar indicates just the radial velocity.
• Figure 4: 2D polar slices of the synthetically generated radial velocity field with dimensionless units for a range of dominant angular wavenumbers ($\ell$ = 1, 2, 4, 6, 8, 14).
• Figure 5: 2D polar slices showing all three velocity components of a dimensionless velocity field for $\ell$ = 1 and 4 (left: $v_r$, middle: $v_\theta$, right: $v_\phi$).