# Pair-instability supernova

This illustration explains the pair-instability supernova process that astronomers think triggered the explosion in SN 2006gy. When a star is very massive, the gamma-rays produced in its core can become so energetic that some of their energy is drained away into production of particle and anti-particle pairs. The resulting drop in pressure causes the star to partially collapse under its own huge gravity. After this violent collapse, runaway thermonuclear reactions (not shown here) ensue and the star explodes, spewing the remains into space.

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.[1] 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,[2] SN 2213-1745 and SN 1000+0216[3] are hypothesized to have been pair-instability supernovae.

## Physics

### Photon pressure

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 $E = mc^2$, 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.

### 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 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.

## Stellar susceptibility

For a star to undergo pair-instability supernova, the loss in total outward pressure resulting from the increased creation of positron/electron pairs by gamma ray collisions must be sufficiently great to allow the inward gravitational pressure to overwhelm the remaining outward pressure. Among stellar mechanisms not responsive to the reduction in outward pressure effected by pair creation, rotational speed and metallicity are the most important.

Stars exhibiting these characteristics still contract as gravity's inward pressure increases relative to the star's total outward pressure. Unlike their slower or less metal-rich cousins, however, these stars continue to exert outward pressure sufficient to prevent contractions so great that gravity entirely overwhelms its opposition and collapses the star.

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.[4]

Very large high metallicity stars are probably 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.[5][6]

### 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 at the end of their lives, but the causative mechanisms are unrelated to 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.

### 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.[6] With more thermal energy released than the star's 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.[5] 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.

## Appearance

### Luminosity

Pair instability supernovae are popularly thought to be highly luminous. This is 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.[7]

### Spectrum

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.[7]

### Light curves

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.[7] This is due to the extreme amounts of 56Ni expelled, and the optically dense ejecta, as the star is entirely disrupted.

## References

1. ^ Fraley, Gary S. (1968). "Supernovae Explosions Induced by Pair-Production Instability". Astrophysics and Space Science 2 (1): 96–114. Bibcode:1968Ap&SS...2...96F. doi:10.1007/BF00651498.
2. ^ Gal-Yam, A.; Mazzali, P.; Ofek, E. O.; et al. (3 December 2009), "Supernova 2007bi as a pair-instability explosion", Nature 462: 624–627, arXiv:1001.1156, Bibcode:2009Natur.462..624G, doi:10.1038/nature08579
3. ^ Cooke, J.; Sullivan, M.; Gal-Yam, A.; Barton, E. J.; Carlberg, R. G.; Ryan-Weber, E. V.; Horst, C.; Omori, Y.; Díaz, C. G. (2012). "Superluminous supernovae at redshifts of 2.05 and 3.90". Nature 491 (7423): 228–231. doi:10.1038/nature11521. PMID 23123848. edit
4. ^ Belkus, H.; Van Bever, J.; Vanbeveren, D. (2007). "The Evolution of Very Massive Stars". The Astrophysical Journal 659 (2): 1576–1581. arXiv:astro-ph/0701334. Bibcode:2007ApJ...659.1576B. doi:10.1086/512181.
5. ^ a b Smith, Nathan; Li, Weidong; Foley, Ryan J.; Wheeler, J. Craig; Pooley, David; Chornock, Ryan; Filippenko, Alexei V.; Silverman, Jeffrey M.; Quimby, Robert; Bloom, Joshua S.; Hansen, Charles (2007). "SN 2006gy: Discovery of the Most Luminous Supernova Ever Recorded, Powered by the Death of an Extremely Massive Star like η Carinae". The Astrophysical Journal 666 (2): 1116–1128. arXiv:astro-ph/0612617. Bibcode:2007ApJ...666.1116S. doi:10.1086/519949.
6. ^ a b Fryer, C.L.; Woosley, S. E.; Heger, A. (2001). "Pair-Instability Supernovae, Gravity Waves, and Gamma-Ray Transients". The Astrophysical Journal 550 (1). arXiv:astro-ph/0007176. Bibcode:2001ApJ...550..372F. doi:10.1086/319719.
7. ^ a b c Kasen, D.; Woosley, S. E.; Heger, A. (2011). "Pair Instability Supernovae: Light Curves, Spectra, and Shock Breakout" (pdf). The Astrophysical Journal 734 (2): 102. arXiv:1101.3336. Bibcode:2011ApJ...734..102K. doi:10.1088/0004-637X/734/2/102. edit