Thermonuclear Flames in Type Ia Supernova Explosions - A Microscopic View

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Scientists at the Max-Planck Institute for Astrophysics are investigating the structure of thermonuclear flames that cause Type Ia Supernova explosions. In this context the Flame evolution on scales of a few meters is simulates - "microscopic" as compared to the dimension of a star.

The standard picture of Type Ia Supernovae describes these impressive astrophysical events as a thermonuclear explosions of white dwarf stars which consist of carbon and oxygen. These white dwarfs accrete matter from binary companions until reaching a critical mass (the so-called Chandrasekhar mass) where their configuration becomes unstable. At this point thermonuclear burning ignites in the interior of the star and propagates outward as a flame. The corresponding energy release leads to a complete disruption of the star.

As explained in a previous report, the importance of Type Ia supernovae for cosmology motivates astrophysicists to simulate these explosions. This is, however, a very demanding task since one has to resolve a wide range of length scales starting from the flame width of less than a millimeter up to the scale of the star of about 1000 km. A fully resolved simulation of these events is not feasible in the foreseeable future. Therefore approaches to simulate Type Ia supernova explosions on the scale of the star have to make assumptions on the flame structure on small scales. Such simulations have been successfully performed by members of the hydrodynamics group at the MPA. The models for the small scale flame structure employed here are of course limited to a certain range of parameters. Current efforts aim on a thorough examination of the flame structure especially at low densities as are reached at later stages of the supernova explosion.

As is known from combustion theory, a flame is subject to various instabilities. These effects generate turbulence and increase the burning speed of the flame as needed to explain the powerful supernova explosions. While some of the instabilities are accounted for in the large simulations, the so-called hydrodynamic instability ("Landau-Darrieus-instability", named after its discoverers) has been ignored so far. This instability causes small perturbations of the flame shape to grow due to the density contrast between fuel ahead of the flame front and ashes behind it. The reason why it has been regarded as unimportant in the context of supernovae is that there exists a mechanism which counteracts the instability and stabilizes the flame in a cellular shape. This is illustrated in Fig. 1: Following the flame propagation by means of Huygens' principle one observes the formation of a cusp at point A. At this point the burning velocity of the flame exceeds the one at other points on the flame (as can be seen by a simple vector addition).

Figure 1: Flame stabilization in a cellular shape.
(source: Zel'dovich et al., 1985)

It is however yet unknown weather the arising cellular pattern is stable under all conditions. A break-up of the cellular shape could have important consequences for simulations on large scales.

Movie 1 presents a simulation of the flame evolution at a relatively low fuel density. In the beginning the perturbation of the flame shape grows. Then a cusp forms and the flame adopts a cellular shape. In the later stages of the evolution one observes a break-up of the cellular stabilization. The specific circumstances of this phenomenon is currently under investigation.

Movie 1: Simulation of the evolution of a thermonuclear flame in a supernova explosion at a fuel density of 107 g/cm3.
Click on the image above to download the MPEG-movie.
Caution: The file size is more than 12 MB.

Friedrich Röpke, Jens Niemeyer, Wolfgang Hillebrandt

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Last modified: Wed Jul 31 14:23:51 2002
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