Small-Scale Thermonuclear Flames in Type Ia Supernovae

Currently, the accepted model for Type Ia supernovae is the explosion of a carbon-oxygen white dwarf. Observational evidence is inconsistent with the nuclear burning occurring in a prompt detonation mode. Detailed computations show that a detonation predicts excess amounts of iron and fails to account for significant amounts of intermediate mass elements observed in the spectra of supernovae events. For this reason, it is believed that at least the initial phases are governed by the propagation of constant-pressure deflagrations. However, to obtain the energy generation rate needed to explode the star the deflagration must be dramatically accelerated relative to the laminar flame speed of the burning front.

Our method introduces a low Mach number formulation of nuclear flames that alleviates the acoustic time step constraint. This approach, based on low Mach number asymptotics, uses a projection formulation coupled with higher-order Godunov advective differencing that allows time-steps based on advection speeds rather than acoustic speeds. For problems in combustion, governed by an ideal gas equation of state, the low Mach number approach has seen substantial development and has been successfully applied to simulation of laminar and turbulent flames in two and three dimensions. The methodology presented here generalizes the approach of Day and Bell to the nuclear deflagration regime. In particular, we discuss the extension of the low Mach number methodology to degenerate equations of state typical of stellar environments.

Research Highlights

Turbulence-Flame Interactions

Distributed Flames

Buoyant Burning Bubbles

Two-Dimensional Instabilities


Turbulence-Flame Interactions in Type Ia Supernovae

The complex small-scale dynamics of turbulent thermonuclear flames are essential to understanding Type Ia supernovae (SN Ia) explosions.

In this paper we consider a carbon-burning thermonuclear flame at a variety of Karlovitz numbers, spanning a range of burning regimes from the flamelet regime to the distributed burning regime.

For moderate Karlovitz numbers, the thermodiffusively stable nature of the flame leads to local extinction and enhancement, which is correlated with local curvature.

For the highest Karlovitz number simulated here (Ka=230), a fundamentally different burning behavior is observed. Turbulent mixing dominates thermal diffusion and a distributed flame is observed. The local burning rate is greatly reduced, but is outweighed by the volume of fuel burning, and so the resulting turbulent flame speed is around 5 or 6 times faster than the laminar flame speed.

More information can be found here......

Distributed Flames in Type Ia Supernovae

Damkohler (1940) predicted scaling laws for the turbulent flame speed and width of a flame in the small-scale turbulence regime. The high Karlovitz number case from the study above, is in this regime, and provides the base case for the present study.

In this study, we compare three-dimensional simulations of turbulent carbon-burning flames with the theory of Damkohler. By fixing the Karlovitz number and moving to larger and larger domains, turbulent flame speeds can be derived as a function of Damkohler number.

The measured turbulent flame speeds (left) show excellent agreement with Damkohler scaling (shown by the solid black line), and the scaling appears to break down at a Damkohler number of approximately one (shown by the dashed lines), as predicted by the theory.

More information can be found here......

Buoyant Burning Bubbles in Type Ia Supernovae

Flame ignition in type Ia supernovae (SNe Ia) leads to isolated bubbles of burning buoyant fluid. As a bubble rises due to gravity, it becomes deformed by shear instabilities and transitions to turbulent evolution.

Morton, Taylor and Turner (1956) introduced the entrainment assumption for inert thermals.

In this study, we use the entrainment assumption, suitably modified to account for burning, to predict the late-time asymptotic behavior of thermals in SNe Ia, and compare with three-dimensional simulations.

The image on the left is a three-dimensional rendering of a snapshot of the burning case. The burning rate is shown in orange, and the vorticity is shown in blue.


More information can be found here...

Two-Dimensional Instabilities

Within the star there are numerous mechanisms that have the potential to accelerate a deflagration wave. Landau-Darrieus(LD) instabilities can lead to wrinkling of the flame. Because the lighter ash lies below the heavier carbon-oxygen fuel, the flame interface is also subject to Rayleigh-Taylor(RT) and Kelvin-Helmholtz instabilities. Finally, the flame can be accelerated by interaction with turbulence arising from convective instabilities within the flame as well as turbulence generated by the deflagration itself.

The images on the left show the carbon mass fraction and temperature in a study of the Rayleigh-Taylor instability in a carbon-burning thermonuclear flame.

More information can be found here......


A. J. Aspden, J. B. Bell, S. Dong, and S. E. Woosley, "Burning Thermals in Type Ia Supernovae", Astrophysical Journal, 738, 94-107, 2011. [ApJ]

A. J. Aspden, J. B. Bell, and S. E. Woosley, "Distributed Flames in Type Ia Supernovae", Astrophysical Journal, 710, 1654-1663, February 2010. [ApJ]

S. E. Woosley, A. R. Kerstein, V. Sankaran, A. J. Aspden and F. Ropke "Type Ia Supernovae: Calculations of Turbulent Flames Using the Linear Eddy Model", Astrophysical Journal, 704, pp.255-273, 2009. [ApJ]

S. E. Woosley, D. Kasen, H. Ma, G. Glatzmaier, A. J. Aspden, J. B. Bell, M. S. Day, A. R. Kerstein, V. Sankaran, F. Ropke, "Type Ia Supernovae", Proceedings of Science, 10th Symposium on Nuclei in the Cosmos, July 27 - August 1 2008, Mackinac Island, Michigan, USA. [pdf]

S. E. Woosley, A. J. Aspden, J. B. Bell, A. R. Kerstein, V. Sankaran, "Numerical simulation of low Mach number reacting flows", SciDAC 2008, J. of Physics: Conference Series, Seattle, Washington, July 2008. [pdf]

A. J. Aspden, J. B. Bell, M. S. Day, S. E. Woosley, M. Zingale, "Turbulence-Flame Interactions in Type Ia Supernovae", Astrophysical Journal, 689, pp.1173-1185, December 20, 2008. [ApJ]

J. Bell, A. J. Aspden, M. Day, M. Lijewski, "Numerical simulation of low Mach number reacting flows", SciDAC 2007, J. of Physics: Conference Series, Boston, Massachusetts, July 2007. LBNL Report No. LBNL-63088.