Direct Numerical Simulations of Oxygen-Flame-Driven Deflagration-to-Detonation Transition in Type Ia Supernovae

TL;DR

Direct numerical simulations demonstrate that oxygen flames can trigger deflagration-to-detonation transitions in Type Ia supernova progenitors via the Zel'dovich gradient mechanism when a carbon–oxygen separation of about $10\ \mathrm{km}$ is present. Using the Castro hydrodynamics code with the 13-isotope aprox13 network, the authors map a 1D density window of $\rho_0 \in (3.1$--$3.6)\times10^{7}\ \mathrm{g\,cm^{-3}}$ and a minimum carbon-flame thickness of $\gtrsim 20\ \mathrm{m}$ for successful DDT, and show that 2D multidimensional detonation structures can enable carbon detonation at somewhat lower densities. The work provides direct numerical evidence that oxygen-flame–driven DDT is physically plausible in turbulent white-dwarf interiors and highlights the importance of multidimensional effects for SN Ia explosion modeling. These findings have implications for nucleosynthesis and energy release in SNe Ia, emphasizing that local flame separation and shock focusing can govern the transition from deflagration to detonation.

Abstract

We present direct numerical simulations demonstrating deflagration-to-detonation transition (DDT) driven by oxygen flames in Type Ia supernova progenitors. Using the Castro hydrodynamics code coupled with the ``aprox13'' 13-isotope nuclear network, we simulate combustion in isolated fuel regions where oxygen flames trail carbon flames. In a fiducial one-dimensional run at $ρ_{0}=3.5\times10^{7}\ \mathrm{g\ cm^{-3}}$ we observe spontaneous DDT of the oxygen flame via the Zel'dovich gradient mechanism when the carbon-oxygen separation reaches $\sim 10\ \mathrm{km}$. The oxygen detonation then captures the carbon flame and triggers a stable carbon detonation. Systematic one-dimensional parameter scans show that successful carbon DDT requires upstream densities in the range $(3.1$--$3.6)\times10^{7}\ \mathrm{g\ cm^{-3}}$ and a minimum carbon-flame thickness of $\gtrsim 20\ \mathrm{m}$. Two-dimensional simulations confirm DDT and demonstrate that the multidimensional cellular structure of the oxygen detonation can promote carbon detonation at somewhat lower densities than in one dimension. These results provide direct numerical evidence that oxygen-flame-driven DDT is physically plausible in turbulent white-dwarf environments and underscore the importance of multidimensional effects for Type Ia supernova explosion modeling.

Figures (12)

• Figure 1: Schematic illustration of the physical scenario. (a) Schematic of an unburned island: the region enclosed by the arc and located above the main flame consists of unburned carbon and oxygen, while the region below contains the ashes produced by combustion. The dashed and solid curves represent the carbon and oxygen flames, respectively. The radial distribution of the isotopic composition in the blue box is shown in (b): the left side corresponds to unburned fuel, the right side consists of fully burned ash, and the middle region contains material where carbon has been consumed but oxygen remains unburned.
• Figure 2: The reaction network used in the simulation, includes the isotopes marked with blue circles; isotopes shown in gray circles are not explicitly included in the network.
• Figure 3: 1D simulation at $\rho_{0}=3.5\times 10^{7}\ \rm{g\ cm^{-3}}$ showing successful DDT: the evolution of (a) temperature, (b) Mach number, (c) $^{12}\rm{C}$ mass fraction, and (d) $^{16}\rm{O}$ mass fraction, respectively.
• Figure 4: Comparison of the carbon and oxygen flame velocities with the maximum sound speed. Throughout the detonation, the flame velocities consistently exceeds the highest sound speed in the domain.
• Figure 5: 1D simulation at $\rho_{0}=3\times 10^{7}\ \rm{g\ cm^{-3}}$. The upper left, upper right, lower left, and lower right panels show the evolution of temperature, Mach number, $^{12}\rm{C}$ mass fraction, and $^{16}\rm{O}$ mass fraction, respectively.