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Filling The Pockets: The Spherical Nature of 3D Deflagration in Thermonuclear Supernovae

S. Shiber, P. Hoeflich, T. Mera, E. Fereidouni, Z. Levy, D. Maci, C. Ashall, E. Baron, M. Shahbandeh, K. Medler, W. B. Hoogendam, C. M. Pfeffer

TL;DR

The paper tackles why 3D deflagration in near-$M_{\rm Ch}$ Type Ia supernovae underproduces pre-expansion, by introducing preexisting smoldering-phase turbulence and magnetic fields into 3D MHD simulations. Using the FLASH code with centrally ignited deflagration in a magnetized, turbulent white dwarf, the authors demonstrate that small-scale turbulent eddies and strong magnetic fields dramatically increase mixing between burned and unburned material, filling the pockets that would otherwise persist. This coupling allows the laminar flame to burn nearby fuel more efficiently, yielding substantial nuclear energy deposition and pre-expansion, with filling factors in the inner regions exceeding ~0.75 for favorable conditions. The results suggest that turbulence and magnetic fields, rather than microphysical flame properties, are key to reconciling 3D models with observed SN Ia characteristics and point to future work on off-center ignition, full deflagration evolution, and EC-element production.

Abstract

We investigate thermonuclear explosions within the delayed detonation framework. While spherical delayed detonation models generally reproduce key observational features, a fundamental inconsistency emerges in three dimensions: 3D hydrodynamic simulations exhibit insufficient white dwarf expansion during the deflagration phase. We identify the early deflagration stage, when the burning is dominated by the laminar speed, as a critical phase and explore potential solutions using three dimensional magnetohydrodynamic simulations performed with the FLASH code. In hydrodynamical simulations, the early deflagration phase produces large pockets of unburned C/O, leading to inefficient burning. Much of the released energy is deposited into buoyantly rising plumes rather than into the global pre-expansion of the white dwarf, which is required to produce the partially burned layers characteristic of SNe Ia. In contrast, when preexisting turbulent velocity fields and strong magnetic fields, on scales expected from the smoldering phase, are included, the effective burning approaches that in spherical models. Both turbulence and magnetic fields promote the entrainment of burned material into unburned pockets, addressing a long-standing problem in multi-dimensional deflagration models. The resulting streaks of burned material enable the conductive ignition of the surrounding unburned fuel. The dominant effect is not a change in the small-scale flame physics (~10^{-3} cm), but rather enhanced mixing between burned and unburned material. As expected, this mechanism is most efficient when the turbulent length scales are smaller than those of the unburned plumes.

Filling The Pockets: The Spherical Nature of 3D Deflagration in Thermonuclear Supernovae

TL;DR

The paper tackles why 3D deflagration in near- Type Ia supernovae underproduces pre-expansion, by introducing preexisting smoldering-phase turbulence and magnetic fields into 3D MHD simulations. Using the FLASH code with centrally ignited deflagration in a magnetized, turbulent white dwarf, the authors demonstrate that small-scale turbulent eddies and strong magnetic fields dramatically increase mixing between burned and unburned material, filling the pockets that would otherwise persist. This coupling allows the laminar flame to burn nearby fuel more efficiently, yielding substantial nuclear energy deposition and pre-expansion, with filling factors in the inner regions exceeding ~0.75 for favorable conditions. The results suggest that turbulence and magnetic fields, rather than microphysical flame properties, are key to reconciling 3D models with observed SN Ia characteristics and point to future work on off-center ignition, full deflagration evolution, and EC-element production.

Abstract

We investigate thermonuclear explosions within the delayed detonation framework. While spherical delayed detonation models generally reproduce key observational features, a fundamental inconsistency emerges in three dimensions: 3D hydrodynamic simulations exhibit insufficient white dwarf expansion during the deflagration phase. We identify the early deflagration stage, when the burning is dominated by the laminar speed, as a critical phase and explore potential solutions using three dimensional magnetohydrodynamic simulations performed with the FLASH code. In hydrodynamical simulations, the early deflagration phase produces large pockets of unburned C/O, leading to inefficient burning. Much of the released energy is deposited into buoyantly rising plumes rather than into the global pre-expansion of the white dwarf, which is required to produce the partially burned layers characteristic of SNe Ia. In contrast, when preexisting turbulent velocity fields and strong magnetic fields, on scales expected from the smoldering phase, are included, the effective burning approaches that in spherical models. Both turbulence and magnetic fields promote the entrainment of burned material into unburned pockets, addressing a long-standing problem in multi-dimensional deflagration models. The resulting streaks of burned material enable the conductive ignition of the surrounding unburned fuel. The dominant effect is not a change in the small-scale flame physics (~10^{-3} cm), but rather enhanced mixing between burned and unburned material. As expected, this mechanism is most efficient when the turbulent length scales are smaller than those of the unburned plumes.
Paper Structure (5 sections, 4 figures, 1 table)

This paper contains 5 sections, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Magnetic properties
  3. Numerical Setup of the Simulations
  4. Results
  5. Conclusions

Figures (4)

  • Figure 1: The initial turbulent velocity (left) and magnetic (right) fields in the highest resolution smallest-scale turbulence simulation D40V170B12, corresponding to smallest eddies size of roughly $40~{\rm km}$ (Kolmagorov's diffusion scale), a rms velocity of $170~{\rm km~s^{-1}}$ and a rms magnetic field of $7\times10^{11}~{\rm G}$. The upper row presents the full grid while the lower row presents a zoom-in view of the central most refined region.
  • Figure 2: Fraction of burnt material at three times, $t=0.15,~0.35,~0.45~{\rm s}$ (top, middle, bottom panels, respectively), at the equatorial plane comparing our simulations. The axes are in units of $100~{\rm km}$. From left to right, the simulations shown are: D300V30B0, D80V170B12, D40V170B12, D40V50B9 as denoted at the top of each column. Velocity vectors are plotted as black arrows.
  • Figure 3: Temperature slices at $t=0.45~{\rm s}$ of the equatorial (top row) and meridional (bottom row) planes, comparing 3 selected simulations with different magnetic field strengths and turbulent conditions. From left to right, the simulations shown are: larger-scale, strong turbulence simulation D80V170B12, smaller-scale, strong turbulence simulation D40V170B12, and smaller-scale, weak turbulence simulation D40V50B9 (denoted at the top of each column).
  • Figure 4: Panels (a),(b), (c), and (d): filling factors as a function of time of our simulations. Shown is the enclosed burnt volume fraction of eight spheres around the center with radii from 100 km to 800 km in jumps of 100 km (orange to gold). Overplotted is the deflagration front distance from the center (in blue). Panel (e): filling factor as a function of radius of our simulations at $t=0.45~{\rm s}$. The vertical lines denote the distance of the deflagration front from the center. Panel (f): kinetic energy as a function of time.