Theoretical Models of Type I Supernovae

One of the most important things to keep in mind when you study the theories of Type I supernovae is that no one, not even the experts, really know what is going on when a Type I occurs. To date, a number of theories and models have been put forward, some of which follow the observed light intensities and spectra, most of which don't match in many ways. The only thing which is held by almost everyone is that Type Ia supernovae involve a white dwarf interacting with a companion star. The other Type I (Ib and Ic) are not even understood to the extent that their progenitor stars can be classified.

Type Ia supernovae in particular have recently come under scrutiny, as they are used to measure the distance to far away galaxies. Because they are used as a distance measurement, many Astrophysicists are working to understand the mechanism by which the supernovae occur. It is generally believed from spectrographic evidence that Type Ia supernovae result from binary evolution involving a carbon/oxygen white dwarf.(Wheeler, 1995) When the star reaches a critical point, a thermonuclear explosion occurs. However, this is about all that can be agreed upon at this time. The various models which have been suggested have acheived mixed results.

There are three main scenarios which describe Type Ia supernovae.

The first scenario requires a carbon/oxygen white dwarf with a mass close to the Chandrasekhar mass. This WD accretes mass though Roche lobe overflow from a companion star. In this scenario, the ignition of the thermonuclear explosion is triggered by compressional heating. The difficulty, and thus disagreement, found in these scenarios is describing how the flame propigates through the WD. Three models have been suggested: detonation, deflagration, and delayed detonation, which requires that the flame starts as a deflagration and then turns into a detonation. (Hoflich and Khokhlov, 1996)

The second scenario begins with two low mass white dwarfs in a close orbit. When this orbit has decayed sufficiently through gravitational radiation, the two WDs will merge. During their merging, there will be an intermediate step in which there is a low density WD with a carbon/oxygen envelope. This envelope will then ignite into the observed thermonuclear blast. (Hoflich and Khokhlov, 1996)

The third scenario starts with a low mass carbon/oxygen white dwarf. This model then predicts a double detonation of the WD, with the blast triggered by a detonation of the helium layer. This model is of particular interest because of the cosmological consequenses that it would have. First, because low-mass white dwarfs are far more common than high mass, supernova statistics would have to be rethought, including their impact on the evolution of elements in galaxies. Second, because calculations indicate that helium detonated Type Ia could be dimmer by as much as 0.4 magnitudes. This would thus cause a decrease in many intergalactic distances, with a corresponding change in H0. (Hoflich and Khokhlov, 1996)

Due to the observations of several different light curves of Type Ia supernovae, it is difficult to eliminate any of the models out of hand. There is no reason the all three of the models could not be the acutal mechanism of some of the supernovae observed. In fact, the third scenario, in which the low mass white dwarf explodes could explain the anomolous Type Ia supernovae which have been redder and whose magnitudes have decreased rapidly with time. The light curves produced by these supernovae are remarkably similar to those produced with low mass models. (Hoflich and Khokhlov, 1996)

However, the most succesful modeling of Type Ia to date have been the models which involve a high mass white dwarf near the Chandrasekhar limit. The most succesful of these to date are the ones which involve a carbon detonation. However, since these models have been primarily one dimensional, and the carbon detonations are inherently unstable, they will most likely (in higher dimensional simulations) result in less complete burning than is required for the observed luminosity. (Wheeler, 1995) Central carbon deflagrations involving a precursor shock and subsonic burning provide more stable results. Without the precursor shock, the deflagration occurs at too high a density, resulting in the reaction nearing completion, and thus not leaving enough intermediate mass elements unburned. The precursor shock, on the other hand, results in a lower density during the thermonuclear burn, and thus a higher proportion of intermediate mass elements.(Wheeler, 1995)

An interesting variation on these models are the pulsating delayed detonation models. In them, the first deflagration stage causes an expansion in the white dwarf, without sufficient energy to eject mass. When the mass surges back, it will compress the atmosphere to densities sufficient reignite the carbon. The major benefit of this model is that it provides a plausible explanation for carbon detonation although the original densities are relatively weak. The major difficulty is that the transition from a deflagration to a detonation is an unsolved problem in both astro and terrestrial physics. One school of thought is that the destruction of the burn surface by turbulence mixes the burned and unburned material, causing the detonation. While this is plausible and expected in the pulsating model, but it has not been demonstrated to occur.(Wheeler, 1995)

These pulsating delayed detonation models have a free parameter: the density at which the deflagration becomes a detonation. Within the probable range of this parameter, the high mass models match the observed dispersion of the light curve properties. (Wheeler, 1995) This is primarily due to the fact that the majority of the energy fueling the supernova comes from burning carbon to silicon, with little energy released in the burning from silicon to iron. This is crucial to the success of the model, and the delayed detonation model succeeds quite well in burning the majority of the carbon to silicon and other intermediate elements, thus providing the kinetic energy and radiation flux observed in Type Ia supernovae. Unfortunately, this causes highly variable nickel end mass, even in models which clearly have ample energy to result in a supernova. This is drawback because, in the past, the observed quantity of nickel has been tied directly to the explosion energy to constrain the distance scale on the Type Ia supernovae.(Wheeler, 1995) In spite of this drawback, the delayed detonation model of supernova provides a superb fit to the light curves of SN1994d in particular. (Hoflich and Khokhlov, 1996)

If you'd like to see a full color, 2D simulation of convection before a supernova or on the surface of a soon to be white dwarf before a nova, check out these MPEGs:

• supernova convection
• nova convection

Keep in mind that they are rather large, if you have a slow connection. They are very good for illustrating the types and sophistication of the models used for these events. For info about them, click here.

This page was written by Jamey Minnis. HTML coding by Jamey Minnis. Please direct any questions about this material to him.

Wheeler, J. Craig. "Binary Evolution of Type Ia Supernovae." The Supernova Research Group at the University of Texas at Austin.