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Degenerate Dwarf Supernoavae

A degenerate dwarf is composed of elements that can fuse to heavier elements. If a degenerate dwarf were able to collapse to a smaller size, thermonuclear reactions among these elements would release a significant portion of the star's rest mass energy. The amount of nuclear energy available for release in degenerate dwarf stars composed of carbon and oxygen is about 0.1% of the star's rest mass, which is 5 times the star's gravitational binding energy. If all of this nuclear energy were released rapidly enough, the star would be blown apart, and the remains of the star would travel outward with an average velocity approaching 104 km s-1 and a peak velocity somewhat larger than this value. Much of the star's remnant would be composed of iron and other elements of similar mass, as well as lighter elements such as silicon, calcium, magnesium, and sulfur. In particular, the explosion would produce large amounts of nickel-56, which is highly radioactive. As the nickel-56 decays, it releases energy that heats the ejected material to a high temperature. The brilliant light emitted by this hot material would enable us to see the explosion from across the visible universe.

But degenerate dwarfs are held at a fixed size by the degeneracy pressure of the electrons. Once the electrons become degenerate, the pressure they exert is effectively independent of their temperature. This means that the size and density of the degenerate dwarf is fixed. For a carbon and oxygen degenerate dwarf, this degeneracy pressure keeps the density and temperature of the star below the point that detonates thermonuclear fusion within the star. The nuclear energy will remain lock inside the degenerate dwarf unless some external event can change the characteristics of the degenerate dwarf.

So how might nature release this nuclear energy? We see many degenerate dwarfs in binary star systems. Usually the companion star is a small main-sequence star. Many of these systems are very compact, so that the distance between the stars is about the diameter of the main-sequence star. In such a system, the degenerate dwarf can gradually strip the atmosphere of its companion, pulling the gas onto itself. This leads to two different theories of how a degenerate dwarf composed of carbon and oxygen might explode.

The first theory is that the degenerate dwarf becomes gradually more massive as it accumulates gas from its companion, eventually reaching the Chandrasekhar mass limit. When this mass is reached, the star starts collapsing, with its density and temperature increasing. Eventually the temperature is high enough to trigger a thermonuclear runaway that fully envelopes the star.

The second theory is that, while far below the Chandrasekhar limit, the degenerate dwarf accumulates a layer of helium at its surface that is unstable to thermonuclear fusion. When the helium spontaneously detonates, a shock wave is driven into the star that triggers thermonuclear fusion of carbon and oxygen deep inside the star.

A third theory is inspired by observations of compact binary star systems composed of two degenerate dwarf stars. Over several billion years, such a binary system would lose orbital energy and angular momentum as it radiates gravitational radiation, decreasing the distance between the two stars. Eventually the two degenerate dwarf stars would merge. If the total mass of the two stars is above the Chadrasekhar limit, the star created in the merger would collapse, which may detonate a thermonuclear explosion.

These are the three dominant theories of how to detonate a degenerate dwarf star, and all three require the degenerate star to be in a binary star system. These theories are more than idle speculation. They are motivated by the variety of supernovae observed in other galaxies?supernovae in our own galaxy are once in a lifetime events. One type of supernova in particular, the type 1a supernova, has properties that are consistent with what one expects from the detonation of a degenerate dwarf.

Supernovae were first subdivided by their spectra. Supernovae that have hydrogen absorption lines are labeled type 2, while those without hydrogen absorption lines are labeled type 1 (the spectra of type 1 supernovae were observed for several years before the first type 2 supernova spectrum was observed). The ?a? part of the label refers to the presence of silicon lines in the spectrum during the early and peak emission of the supernova. Other elements that are seen by their spectra are calcium, magnesium, sulfur, oxygen, and iron. The absence of hydrogen lines is consistent with the degenerate dwarf composition, and the presence of silicon and other intermediate-mass elements that are the fusion products of carbon and oxygen, are consistent with the detonation of a degenerate dwarf. The picture is that the supernova is composed of an outer shell of intermediate-mass elements wrapping an inner shell of iron and nickel.

The shape of the silicon lines in a type 1a supernova suggests that the silicon is moving outward in a shell. When a shell of material expands at a single velocity, one sees absorption and emission lines that are Doppler shifted both to the blue and to the red, corresponding to the observation of the shell moving towards the observer and away from the observer. The velocities can be several times 104 km s-1, in line with the velocities possible in a degenerate dwarf explosion.

The type 1a supernova reaches a peak brightness about 20 days after detonation. The absolute magnitude of this supernova is about -19 which makes it a billion times as bright as the Sun. A month after reach its peak, the supernova has fallen by three magnitudes in absolute brightness, and its brightness continues to fall exponentially at this rate. This behavior is consistent with the theory that the decay of nickel-56 generates the energy radiated by the supernova.

The variation of this peak absolute magnitude among supernovae is about a third of a magnitude. This variation correlates with other properties, such as the peak absolute magnitude and the rate at which the supernova brightness changes, in a way that suggests only one free parameter determines all of the variation seen among these supernovae. It is this property that makes type 1a supernovae such good standard candles in cosmological studies, because one can correct for the variation in the absolute magnitude by measuring the rate at which the brightness changes. This property also strongly constrains the possible theories for these events, because it implies all type 1a supernova progenitors are very similar in structure.

All of these properties fit in nicely with the view that the type 1a supernova is the explosion of a degenerate dwarf star. Computer simulations show that the detonation of a white dwarf fits the rise and fall of the supernova's luminosity very nicely, and the elements generated in the detonation of a white dwarf matches the elements portrayed by the supernova's spectrum. For these reasons the astrophysicists working on this problem accept the theory that a degenerate dwarf created the supernova. The only real disagreement is over the detonator for the explosion.

The three theories for type 1a supernovae all have problems. The theory that the degenerate dwarf is pushed over the Chandrasekhar limit produces an explosion that fits the observations very well, but it is not clear that a degenerate star can ever accumulate sufficient mass from its companion to reach the Chandrasekhar limit. The theory that helium accumulated at the surface of a degenerate dwarf acts as a detonator produces the correct evolution of the supernova, but places an outermost layer of helium and nickel around the supernova remnant that would be observed, but is not. The theory that two degenerate dwarfs merge and explode has the greatest difficulty, because the simulations find that the merged star collapses into a neutron star. The merger does not immediate create a giant white dwarf above the Chandrasekhar limit. Instead, one star is disrupted, forming a disk around the other star. As material flows onto the remaining star, thermonuclear fusion converts the star into oxygen, neon, and magnesium. Eventually this star collapses to a neutron star.

While each theory may appear fatally wounded, the shortcomings may have more to do with the difficulty of simulating these theories on current computers than with the physics behind the theory. Think of any picture of a fireball you have seen; the boiling convection seen in those explosions are present in the cores of a burning degenerate dwarf. Making matters more difficult, the thermonuclear fusion within a degenerate dwarf is not uniformly spread throughout the star, as is the case during hydrogen fusion within a main-sequence star, but is instead confined to a complex surface that separates burned material from unburned material. Long fingers of burned material poke into the unburned material. The inability to accurately simulate with computers this and other complex structures within the degenerate dwarf and the binary system may be the reason that none of these theories produce entirely satisfactory results. For this reason, all three theories persist. Of them, the degenerate dwarf at the Chandrasekhar limit is the favorite theory of the theoretical community.

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