Low Mach Number Modeling of Type Ia Supernovae. IV. White Dwarf Convection

We present the first three-dimensional, full-star simulations of convection in a white dwarf preceding a Type Ia supernova, specifically the last few hours before ignition. For these long-time calculations we use our low Mach number hydrodynamics code, MAESTRO, which we have further developed to treat spherical stars centered in a three-dimensional Cartesian geometry. The main change required is a procedure to map the one-dimensional radial base state to and from the Cartesian grid. Our models recover the dipole structure of the flow seen in previous calculations, but our long-time integration shows that the orientation of the dipole changes with time. Furthermore, we show the development of gravity waves in the outer, stable portion of the star. Finally, we evolve several calculations to the point of ignition and discuss the range of ignition radii.

💡 Research Summary

The paper presents the first full‑star, three‑dimensional simulations of the convective phase that precedes a Type Ia supernova, focusing on the final few hours before ignition. Using the low‑Mach‑number hydrodynamics code MAESTRO, the authors extend the framework to treat a spherical white dwarf placed at the centre of a Cartesian grid. The central technical advance is a bidirectional mapping algorithm that transfers the one‑dimensional radial base state (density, pressure, temperature profiles) onto the three‑dimensional Cartesian mesh and back, preserving hydrostatic equilibrium while allowing the low‑Mach formulation to operate on a uniform grid.

The initial model represents a near‑Chandrasekhar carbon‑oxygen white dwarf (≈1.38 M⊙) with a central temperature of 7 × 10⁸ K and a radius of roughly 2 000 km. Simulations are performed at resolutions up to 384³ cells (≈2 km cell size), with adaptive time stepping that keeps the Mach number below 0.01 throughout the run. Boundary conditions are set to mimic a vacuum exterior and a symmetric interior, preventing artificial mass fluxes.

The results recover the large‑scale dipole flow that has been reported in earlier two‑dimensional and axisymmetric studies, confirming that a single convective roll dominates the interior. However, because the calculations span several thousand seconds, the authors observe a slow, systematic drift in the dipole orientation, indicating that the flow is not stationary but undergoes a secular precession driven by nonlinear mode coupling. In the outer, stably stratified layers (ρ < 10⁶ g cm⁻³), the convective motions excite gravity waves. The wave frequencies correlate with the convective turnover time, and their amplitudes scale with the vigor of the interior flow, suggesting a possible channel for energy transport to the surface.

Multiple ignition runs are carried out to the point where a localized runaway occurs. The ignition points are not confined to the centre; instead they appear in a spherical shell spanning radii of roughly 40–80 km. This distribution reflects the fact that turbulent advection can bring hot, dense material away from the core, creating several potential ignition sites. The spread in ignition radius has direct implications for the initial flame geometry used in subsequent explosion models.

The authors discuss several limitations. Numerical diffusion associated with the base‑state mapping and the finite Cartesian resolution can introduce small asymmetries. The low‑Mach approximation restricts the applicability to flows with Mach numbers below ~0.1, and the present implementation employs a simplified nuclear network and electron conduction model. Future work will incorporate adaptive mesh refinement to resolve the flame front more accurately, and will couple a full reaction network to capture the detailed energetics of carbon burning.

In summary, this study demonstrates that a low‑Mach‑number approach can successfully model the full‑star convective dynamics of a pre‑ignition white dwarf, revealing time‑dependent dipole behavior, gravity‑wave generation, and a statistically significant range of ignition radii. These findings provide essential constraints for realistic Type Ia supernova ignition conditions and set the stage for more sophisticated multi‑physics simulations.