A pair-instability supernova occurs when pair production, the production of free electrons and positrons in the collision between atomic nuclei and energetic gamma rays, reduces thermal pressure inside a supermassive star's core. This pressure drop leads to a partial collapse, then greatly accelerated burning in a runaway thermonuclear explosion which blows the star completely apart without leaving a black hole remnant behind. Pair-instability supernovae can only happen in stars with a mass range from around 130 to 250 solar masses and low to moderate metallicity (low abundance of elements other than hydrogen and helium, a situation common in Population III stars). The recently observed objects SN 2006gy, SN 2007bi, SN 2213-1745 and SN 1000+0216 are hypothesized to have been pair-instability supernovae.
Light in thermal equilibrium has a black body spectrum with an energy density proportional to the fourth power of the temperature (hence the Stefan-Boltzmann law). The wavelength of maximum emission from a blackbody is inversely proportional to its temperature. That is, the frequency, and the energy, of the greatest population of photons of black body radiation is directly proportional to the temperature, and reaches the gamma ray energy range at temperatures above 3×108 K.
In very large hot stars, pressure from gamma rays in the stellar core keeps the upper layers of the star supported against gravitational pull from the core. If the energy density of gamma rays is suddenly reduced, then the outer layers of the star will collapse inwards. The sudden heating and compression of the core generates gamma rays energetic enough to be converted into an avalanche of electron-positron pairs, further reducing the pressure. When the collapse stops, the positrons find electrons and the pressure from gamma rays is driven up, again. The population of positrons provides a brief reservoir of new gamma rays as the expanding supernova's core pressure drops.
Pair creation and annihilation
Sufficiently energetic gamma rays can interact with nuclei, electrons, or one another to produce electron-positron pairs, and electron-positron pairs can annihilate, producing gamma rays. From Einstein's equation , gamma rays must have more energy than the mass of the electron–positron pairs to produce these pairs.
At the high densities of a stellar core, pair production and annihilation occur rapidly, thereby keeping gamma rays, electrons, and positrons in thermal equilibrium. The higher the temperature, the higher the gamma ray energies, and the larger the amount of energy transferred.
As temperatures and gamma ray energies increase, more and more gamma ray energy is absorbed in creating electron-positron pairs. This reduction in gamma ray energy density reduces the radiation pressure that supports the outer layers of the star. The star contracts, compressing and heating the core, thereby increasing the proportion of energy absorbed by pair creation. Pressure nonetheless increases, but in a pair-instability collapse, the increase in pressure is not enough to resist the increase in gravitational forces as the star becomes denser.
A star that is rotating fast enough, or that has enough metallicity, will probably not collapse in a pair-instability supernova due to other effects. Pair-instability happens in low metallicity stars, with low to moderate rotation rates. Stars formed by collision mergers having a metallicity Z between 0.02 and 0.001 may end their lives as pair-instability supernovae if their mass is in the appropriate range.
Very large high metallicity stars are probably unstable due to the Eddington limit, and would tend to shed mass during the formation process.
Below 100 solar masses
For lower-mass stars (up to about 100 solar masses) the gamma rays are not energetic enough to produce electron–positron pairs. If a supernova destroys such a star, pair production will not be involved.
100 to 130 solar masses
For stars between 100 and around 130 solar masses, pressure and temperature effects allow larger partial collapses and pressure pulses to occur, initiated by pair production instability in the core, which are too small to fully disrupt the star. These pulses are damped out; they create temporary increased rates of thermonuclear burning, but the star gradually returns to a stable equilibrium. These pulses are expected to lead to ejections of parts of the outer layers of the star, similarly to what happened to the star Eta Carinae in 1843, though that may have had a different underlying mechanism. The pulsing mechanism is thought to cause stars in this mass range to shed mass until their remaining core is small enough to collapse in a normal supernova.
130 to 250 solar masses
For very high mass stars, with mass at least 130 and up to perhaps roughly 250 solar masses, a true pair-instability supernova can occur. In these stars, the first time that conditions support pair creation instability, the situation runs out of control. The collapse proceeds to efficiently compress the star's core; the overpressure is sufficient to allow runaway nuclear fusion to burn it in a few seconds, creating a thermonuclear explosion. With more thermal energy released than the stars' gravitational binding energy, it is completely disrupted; no black hole or other remnant is left behind.
In addition to the immediate energy release, a large fraction of the star's core is transformed to nickel-56, a radioactive isotope which decays with a half-life of 6.1 days into cobalt-56. Cobalt-56 has a half-life of 77 days and then further decays to the stable isotope iron-56 (see Supernova nucleosynthesis). For the hypernova SN 2006gy, studies indicate that perhaps 40 solar masses of the original star were released as Ni-56, almost the entire mass of the star's core regions. Collision between the exploding star core and gas it ejected earlier, and radioactive decay, release most of the visible light.
250 solar masses or more
A different reaction mechanism, photodisintegration, results after collapse starts in stars of at least 250 solar masses. This endothermic (energy-absorbing) reaction causes the star to continue collapse into a black hole rather than exploding due to thermonuclear reactions.
Pair instability supernovae are popularly thought to be highly luminous. This is actually only the case for the most massive progenitors, which can have peak luminosities of over 1037 joules/sec, brighter than type Ia supernovae. However at lower masses, peak luminosities are less than 1035 joules/sec, comparable to or less than typical type II supernovae.
The spectra of Pair instability supernovae depend on the nature of the progenitor star. Thus they can appear as type II or type Ib/c supernova spectra.
In contrast to the spectra, the light curves are quite different from the common types of supernova. The light curves are highly extended, with peak luminosity occurring months after onset. This is due to the extreme amounts of 56Ni expelled, and the optically dense ejecta, as the star is entirely disrupted.
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