A pair-instability supernova is a type of supernova predicted to occur when pair production — the production of free electrons and positrons in the collision between atomic nuclei and energetic gamma rays — temporarily reduces the internal radiation pressure supporting a supermassive star's core against gravitational collapse. This pressure drop leads to a partial collapse, which in turn causes greatly accelerated burning in a runaway thermonuclear explosion, resulting in the star being blown completely apart without leaving a stellar 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).
Physics
Photon emission Photons given off by a body in thermal equilibrium have a black-body spectrum with an energy density proportional to the fourth power of the temperature, as described by the Stefan–Boltzmann law. Wien's law states that the wavelength of maximum emission from a black body is inversely proportional to its temperature. Equivalently, the frequency, and the energy, of the peak emission is directly proportional to the temperature.
Photon pressure in stars In very massive, hot stars with interior temperatures above about 300000000 K (3×108 K), photons produced in the stellar core are primarily in the form of very high-energy gamma rays. The pressure from these gamma rays fleeing outward from the core helps to hold up the upper layers of the star against the inward pull of gravity. If the emission of gamma rays (the energy density) is reduced, then the outer layers of the star will begin to collapse inwards. Gamma rays with sufficiently high energy can interact with nuclei, electrons, or one another. One possible interaction is to form pairs of particles, such as electron-positron pairs; these pairs can then meet and annihilate each other to create additional gamma rays, in accordance with Albert Einstein's mass-energy equivalence equation E = m c² . At the very high density of a large stellar core, pair production and annihilation occur rapidly. Gamma rays, electrons, and positrons are overall held in thermal equilibrium, ensuring the star's core remains stable. By random fluctuation, the sudden heating and compression of the core can generate gamma rays energetic enough to be converted into an avalanche of electron-positron pairs. This reduces 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-instability 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 resists gravitational collapse and supports the outer layers of the star. The star contracts, compressing and heating the core, thereby increasing the rate of energy production. This increases the energy of the gamma rays that are produced, making them more likely to interact, and so increases the rate at which energy is absorbed in further pair production. As a result, the stellar core loses its support in a runaway process, in which gamma rays are created at an increasing rate; but more and more of the gamma rays are absorbed to produce electron–positron pairs, and the annihilation of the electron–positron pairs is insufficient to halt further contraction of the core. Finally, the thermal runaway ignites detonation fusion of oxygen and heavier elements. When the temperature reaches the level when electrons and positrons carry the same energy fraction as gamma-rays, pair production cannot increase any further; it is balanced by annihilation. Contraction no longer accelerates, but the core now produces much more energy than prior to collapse, and this results in a supernova: the outer layers of the star are blown away by sudden large increase of power production in the core. Calculations suggest that so much of the outer layers are lost that the very hot core itself is no longer under sufficient pressure to keep it intact, and it is completely disrupted too.
Stellar susceptibility For a star to undergo pair-instability supernova, the increased creation of positron/electron pairs by gamma ray collisions must reduce outward pressure enough for inward gravitational pressure to overwhelm it. High rotational speed and/or metallicity can prevent this. Stars with these characteristics still contract as their outward pressure drops, but unlike their slower or less metal-rich cousins, these stars continue to exert enough outward pressure to prevent gravitational collapse. 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 likely unstable due to the Eddington limit, and would tend to shed mass during the formation process.
Stellar behavior
Several sources describe the stellar behavior for large stars in pair-instability conditions.
Below 100 solar masses Gamma rays produced by stars of fewer than 100 or so solar masses are not energetic enough to produce electron-positron pairs. Some of these stars will undergo supernovae of a different type at the end of their lives, but the causative mechanisms do not involve pair-instability.
100 to 130 solar masses These stars are large enough to produce gamma rays with enough energy to create electron-positron pairs, but the resulting net reduction in counter-gravitational pressure is insufficient to cause the core-overpressure required for supernova. Instead, the contraction caused by pair-creation provokes increased thermonuclear activity within the star that repulses the inward pressure and returns the star to equilibrium. It is thought that stars of this size undergo a series of these pulses until they shed sufficient mass to drop below 100 solar masses, at which point they are no longer hot enough to support pair-creation. Pulsing of this nature may have been responsible for the variations in brightness experienced by Eta Carinae in 1843, though this explanation is not universally accepted.
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