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Thermonuclear Supernovae

White dwarfs (degenerate dwarfs) are the biggest thermonuclear bombs in the universe; we see their explosions as the type Ia supernovae.  The amount of thermonuclear energy locked within a white dwarf is consistent with the energy released in a type Ia supernova.  More important for the association between white dwarfs and supernovae, most type Ia supernovae consistently release about the same amount of energy, which would be expected if the exploding white dwarfs were all about the same mass.  Specifically, if a white dwarf were pushed above the 1.4 solar mass Chandrasekhar limit, where it is gravitationally unstable, it would collapse and release its thermonuclear energy in a massive explosion.  This is the original theory for type Ia supernovae, but other theories exist for triggering a thermonuclear explosion in a white dwarf.[1]

Principal Observed Characteristics

A type Ia supernova reaches its peak brightness about 20 days after the explosion, with an absolute visual magnitude of about −19.3, or almost 10 billion time the luminosity of the Sun.  After peaking, the supernova declines in brightness by 3 magnitudes over a month and then by 1 magnitude every subsequent month until it fades from sight.

The features that mark a supernova as type Ia are the absence of hydrogen lines and the presence of silicon lines in the spectrum.  The spectrum also shows the lines of intermediate mass elements such as oxygen, calcium, magnesium, and sulfur.  Two weeks after the supernova reaches its peak magnitude, its spectrum shows the lines of iron and other elements of similar mass such as cobalt.  The debris emitting this light moves at a very high velocity away from the explosion site.  The highest velocities are about 10% of the speed of light.

The type Ia supernovae behave as though a single variable determines all of their characteristics; the shape of the spectrum, the change in luminosity with time, and the velocity of the debris are all set by the total amount of energy released in the explosion.  Most supernovae differ from the average peak visual absolute magnitude by less than 0.3 magnitudes.  Low-luminosity supernovae are redder and shorter-lived, with debris moving at a lower velocity, than high-luminosity supernovae.  A consequence of this behavior is that if one knows the spectrum of a type Ia supernova at the peak apparent magnitude, one can infer the peak absolute magnitude.  This property permits astronomers to use the type Ia supernovae as a standard candle for deriving the distances to the farthest galaxies and for studying the expansion of the universe.

Strictly speaking, not all type Ia supernovae behave in the same way.  About 85% of these supernovae behave according to the single-variable pattern just described.  The remaining nonconforming type Ia supernovae can differ in a variety of ways, including being several magnitudes less luminous than the conforming 85%.  They are believed to have a different origin than the conforming 85%.  They may be produced by the thermonuclear explosion of white dwarfs under different conditions than the conforming supernovae, or they may be from massive stars undergoing core collapse.

Basic Bomb Theory

Theorists uniformly believe that the conforming 85% of type Ia supernovae are white-dwarf thermonuclear explosions.  Most of the theoretical effort has been directed at the explosion of carbon-oxygen white dwarfs, although some theorists believe that the detonation of oxygen-neon-magnesium white dwarfs may be responsible for some other supernova subclass.  The basic theory is that a white dwarf composed of carbon and oxygen releases most of its thermonuclear energy in a sudden burst.  Thermonuclear burning in the outer parts of the star convert the carbon and oxygen into intermediate-mass elements, such as sulfur.  The burning in the white-dwarf interior converts the carbon and oxygen into nickel, which is the lowest-energy atomic nucleus that can be rapidly created through fusion.  This sudden release of energy heats the interior to energies far above the white dwarf's gravitational binding energy, so the star expands outward at a very high velocity, leaving nothing behind.  As the stellar debris expands and dissipates, it is heated by the radioactive decay of nickel into cobalt and then iron.  The expanding photosphere drifts to deeper, hotter regions within the debris.  This combination of increasing surface area and increasing temperature of the photosphere causes the debris to emit more power over time, causing the brightening that we see in a supernova.  The lines we see in the spectrum of a type Ia supernova is the progression of thermonuclear products created in the supernova, starting with the intermediate elements created in the outer layers of the expanding debris, and ending with cobalt and iron.  When the debris has expanded enough for light to escape from the center of the explosion, it cools, and the supernova fades from sight.

All of these properties fit in nicely with the view that the type Ia 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, astrophysicists working on this problem accept the theory that a degenerate dwarf creates the supernova.   The only real disagreement is over the detonator for the explosion.

Three Detonator Theories

At the end of a star's evolution, when electron degeneracy pressure halts the gravitational shrinking of a star, it also halts the thermonuclear fusion of carbon and oxygen into heavier elements.  With a fixed density and a cooling core, a white dwarf is unable to sustain thermonuclear fusion.  If the thermonuclear energy in a white dwarf is to be released, something must drive up the temperature and density within the white dwarf.  Theorists have come up with three plausible ways of detonating a white dwarf.  All three rely on the white dwarf being in a compact binary system.

In the first theory, detonation occurs when the white dwarf's mass grows larger than the Chandrasekhar mass limit; the white dwarf grows by pulling gas from its companion onto itself, and when its mass exceeds the Chandrasekhar mass limit, it becomes gravitationally unstable, shrinking in radius until the temperature and density within the white dwarf ignites thermonuclear fusion.  In the second theory, the white dwarf is detonated by the thermonuclear explosion of an outer layer of helium.  The helium layer is created when the white dwarf pulls gas from a companion helium star onto itself.  If the helium layer remains cool enough to prevent the slow thermonuclear conversion of helium to carbon, helium can accumulate to a point that the layer becomes unstable to a thermonuclear runaway.  This runaway is triggered by the high density at the base of the helium layer.  The helium layer then acts like a blasting cap, driving a shock wave into the white dwarf that initiates thermonuclear fusion of the carbon and oxygen.  In the third theory, two white dwarf stars are in a binary system together. Over time, as the binary system emits gravitational radiation, the distance between the white dwarfs shrinks, until the two stars merge into a single star with a mass above the Chandrasekhar mass limit.  As in the first theory, the newly-created white dwarf collapses under its own gravity, igniting a thermonuclear explosion.

Each of these three theories have problems.   The first theory, where a degenerate dwarf is pushed over the Chandrasekhar limit, produces an explosion that fits the observations very well, but theorists have a difficult time getting the degenerate star to accumulate sufficient mass from its companion to reach the Chandrasekhar limit.   The second theory, where a layer of helium acts as a detonator, produces the correct evolution of the supernova, but it places an outermost layer of helium 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 merger does not immediately 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; instead, it is 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 remains the favorite theory of the theoretical community.

[1]Hillebrandt, Wolfgang, and Niemeyer, Jens C.  “Type Ia Supernova Explosion Models.”  Annual Review of Astronomy and Astrophysics 38 (2000): 191–230.

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