Pair-Instability Supernova

A supernova that leaves nothing behind

Most supernovae leave a corpse. Type Ia destroys a white dwarf but explains why the universe is full of iron. Core-collapse Type II builds neutron stars and black holes. Pair-instability supernovae do neither. They take an entire 200 M☉ star and turn it into a glowing remnant cloud — no compact object, no surviving core, no point source ten thousand years later. The energy budget actually works out: nuclear burning of an oxygen core to nickel releases roughly 10⁵² erg, while the gravitational binding energy of a 200 M☉ star bound by its own gravity is around a few × 10⁵¹ erg. Nuclear beats gravity by a factor of three to ten, and gravity loses.

The trigger that ties it together is one of the strangest in stellar physics. As the oxygen core heats above roughly 6 × 10⁸ K, the high-energy tail of the blackbody photon distribution starts converting into electron-positron pairs. That conversion drains thermal radiation pressure into rest mass, the adiabatic index dips below the 4/3 threshold for hydrostatic stability, and the core begins to contract because pair creation has briefly taken its support away. Contraction raises the temperature, which raises the pair fraction, which lowers the pressure further. The instability is intrinsically self-amplifying — and it ends not with a thermal correction but with explosive oxygen burning catching up before the star can recover.

The energy budget — why nuclear wins

It is easy to see why pair instability disrupts the star outright while normal core collapse leaves a remnant. The number you compare is the energy released by oxygen-burning to silicon and nickel against the gravitational binding energy that has to be undone to unbind the star.

Quantity	Core-collapse SN (15 M☉)	Pair-instability SN (200 M☉)
Binding energy of star	~ 3 × 10⁵¹ erg	~ 3 × 10⁵¹ erg (envelope) + ~ 10⁵² erg (core)
Energy source	Neutron-star formation (grav.)	Explosive O burning (nuclear)
Available energy	~ 3 × 10⁵³ erg (mostly ν)	~ 10⁵²-10⁵³ erg (mostly KE+light)
Energy that reaches ejecta	~ 10⁵¹ erg (~ 1%)	~ 10⁵² erg (~ 50-100%)
Compact remnant	Neutron star or BH	None
⁵⁶Ni produced	~ 0.07 M☉ (Type II-P)	3 - 50 M☉

The 100-fold difference in ⁵⁶Ni is what makes the light curve of a PISN candidate so distinctive. Most of the explosion luminosity in any radioactive-powered supernova comes from the decay ⁵⁶Ni → ⁵⁶Co → ⁵⁶Fe, with characteristic e-folding times of 8.8 and 111 days respectively. A PISN with 10 M☉ of ⁵⁶Ni will glow at ~10⁴⁴ erg/s for months after a slow rise that already takes 70-100 days, simply because that much radioactive material must lose its photons through a massive optically thick ejecta.

The pair instability in slow motion

Consider an isolated 200 M☉ Population III progenitor as it finishes core helium burning. It has a degenerate, hot, oxygen-dominated core of M_O ≈ 80 M☉ at central T ~ 6 × 10⁸ K and ρ ~ 5 × 10⁵ g/cm³. The core is supported almost entirely by radiation pressure, so the adiabatic index is close to Γ₁ = 4/3 by design. Stability is marginal.

Three things now happen in sequence over a few seconds:

1. Pair creation begins. The thermal photon distribution at T = 10⁹ K extends well past m_e c² = 0.511 MeV, so the reaction γγ → e⁺e⁻ proceeds. Each pair created costs roughly 2 m_e c² of photon energy and adds to the rest-mass density but contributes only a small thermal pressure (the pairs are quasi-cold). The ratio of pair pressure to total pressure can reach 5-10% at peak — small in absolute terms, decisive for the index.
2. Γ₁ drops below 4/3. In the region of phase space where the pair-creation rate climbs steeply with temperature, the equation of state softens. Detailed computations (Barkat, Rakavy, Sack 1967; Bond, Arnett, Carr 1984; Heger & Woosley 2002) show Γ₁ dipping to ~1.30 over a window of central temperature ~ 1 × 10⁹ K. Hydrostatic equilibrium requires Γ₁ > 4/3 averaged over the whole star; with the core dropping below, the star starts collapsing.
3. Explosive oxygen burning ignites. The contracting core heats from 10⁹ K to 3-5 × 10⁹ K in a few tenths of a second — much faster than the nuclear timescale for oxygen burning. The reactions ¹⁶O + ¹⁶O → ²⁸Si + α, ³²S + γ release roughly 5 × 10¹⁷ erg/g. Burning ~ 50 M☉ of oxygen yields ~ 5 × 10⁵² erg, several times the binding energy. The runaway terminates the contraction in a burst that disrupts the entire star.

The whole sequence runs on a dynamical timescale of seconds, never gives the neutron-star core a chance to form (the inner regions are still on the O/Si side of the burning chain), and propels the entire star outward at velocities of 5,000-15,000 km/s. The luminosity arrives later, powered by ⁵⁶Ni decay diffusing out of the optically thick ejecta.

Three regimes set by helium core mass

The full pair-instability picture, as worked out by Heger and Woosley (2002) and refined since, comes in three regimes that depend on the He core mass M_He at the end of helium burning:

• M_He ~ 40-65 M☉ — Pulsational pair instability (PPISN). The instability is real but releases less nuclear energy than the envelope binding energy. The star bounces, ejects a few solar masses of shell, recovers a hydrostatic configuration, contracts again, and may pulse several times over years. After the last pulse the core collapses to a black hole. The colliding shells produce delayed circumstellar-interaction-powered light curves; many recent superluminous Type IIn supernovae fit this picture.
• M_He ~ 65-135 M☉ — Full pair-instability supernova (PISN). Nuclear release exceeds the binding energy. The star is completely disrupted. No remnant. The expected ⁵⁶Ni mass scales steeply with M_He, from ~ 0.5 M☉ near the lower edge to ~ 50 M☉ near the upper edge — which is why the brightest PISN events are at the heavy end.
• M_He > 135 M☉ — Direct photodisintegration collapse. The core temperature climbs high enough that gamma photons photodisintegrate Fe and lighter nuclei back into nucleons before pair instability dominates. The endothermic disintegration takes thermal energy out of the gas; the core collapses directly to a black hole with no explosion. The star is buried, not seen.

The PISN window is therefore both upper- and lower-bounded. Outside it, the star either survives in pieces or vanishes silently. The width of the window — about 70 M☉ in helium core mass — is what carves the upper edge of the stellar-mass black-hole mass gap.

What the data should look like

A confirmed PISN should match a tight pattern of observables:

• Slow rise. The diffusion time through massive ejecta (M_ej ~ 100 M☉) at v ~ 10⁴ km/s is t_diff ~ (3 κ M_ej / 4 π v c)^(1/2) ~ 70-100 days. Compare to a Type II-P which peaks in ~ 20 days. A 70-day rise is a strong PISN flag.
• ⁵⁶Co-decay tail. After peak, the bolometric light curve should decline on the ⁵⁶Co half-life of 77.2 days (about 1 mag / 100 d in luminosity). A faster decline rules PISN out.
• Large ⁵⁶Ni mass. Reverse-engineering the peak luminosity through Arnett's rule gives M_Ni in the few-to-tens of M☉ range. SN 2007bi inferred M_Ni ≈ 3-5 M☉; that is the high end of plausible non-PISN nickel masses.
• No early-time interaction signatures. The hydrogen-rich envelope is often shed beforehand by Wolf-Rayet-like winds in metal-poor systems, leaving the explosion to interact with low-density media. Strong narrow H lines argue against a clean PISN.
• Low-metallicity host. Mass loss by line-driven winds scales with metallicity. Only at metallicities below ~ 1/3 Z☉ can a star retain enough mass to enter the PISN regime; finding PISN candidates in dwarf, low-metal hosts is consistent.
• Spectra dominated by intermediate-mass elements at peak, iron at late times. Strong Ca II, O I, Si II early; later, [Fe II] and [Co III] lines as the inner ejecta become transparent.

Candidates and their interpretations

• SN 2007bi. Discovered at z = 0.127. Slow rise (~ 70 days), slow ⁵⁶Co decline, inferred ⁵⁶Ni mass ~ 3-7 M☉, oxygen-rich nebular spectrum, low-metallicity dwarf host. Gal-Yam et al. (2009) advanced it as the clearest PISN candidate. Later models (Dessart et al. 2012) showed a magnetar-powered model could reproduce the light curve at lower ⁵⁶Ni mass, weakening the claim — but the PISN interpretation remains plausible.
• SN 2006gy. Brightest known SN at the time of discovery (peak ~ -22 mag). Originally suggested as PISN. The very narrow H lines and short rise have since pushed the consensus toward circumstellar interaction with a dense, dust-rich shell from a luminous-blue-variable progenitor — a related but different mechanism.
• SLSN-I sample (PS1-11ap, PTF12dam, SN 2015bn, etc.). A growing population of hydrogen-poor superluminous supernovae. Most light curves fit magnetar-powered models more economically than PISN; the magnetar's spin-down power can be tuned to match the observed shape. PISN remains a viable subset, but identifying it definitively in the SLSN-I population is hard.
• Pop III PISN at high redshift. The cleanest PISN sample is theoretical — the first stars, formed at z ~ 15-30 in metal-free gas, are thought to dominate the PISN channel. JWST, the Roman Space Telescope, and the Vera Rubin LSST should detect Pop III PISN candidates as red, slow transients at z ≳ 6.

The connection to LIGO's mass gap

The PISN window leaves a footprint on the remnant black-hole distribution that gravitational-wave detectors can see. Below M_He ≈ 40 M☉, stars collapse to BHs that grow with progenitor mass. Between M_He ≈ 40 and 65 M☉, pulsational pair instability ejects mass and caps the BH mass near 45 M☉. Between M_He ≈ 65 and 135 M☉, the star is destroyed and no BH forms. Above M_He ≈ 135 M☉, direct collapse can produce a BH starting near 135 M☉ (and rising to thousands for the highest masses).

This carves an "upper mass gap" in the stellar BH distribution between roughly 45 and 135 M☉, with the exact boundaries set by uncertain reaction rates (especially the ¹²C(α,γ)¹⁶O rate) and rotation. GW190521 — a binary BH merger with primary mass ~ 85 M☉, squarely in the predicted gap — therefore demanded explanation. Candidate resolutions include hierarchical mergers in dense star clusters, primordial black holes, super-Eddington accretion in AGN disks, and shifts in the PISN boundary from updated nuclear physics. Whichever wins, the BH mass gap is the most direct observational handle on pair instability physics available today.

Back-of-envelope: when does pair instability turn on?

For a thermal photon gas at temperature T, the equilibrium number of e⁺e⁻ pairs per unit volume scales as

n_± ≈ (m_e c / ℏ)³ · (T / T_e)^(3/2) · exp(− T_e / T)

where T_e ≡ m_e c² / k_B ≈ 6 × 10⁹ K. The pair fraction is suppressed by exp(−T_e/T), which is severe at T = 10⁹ K (exp(−6) ≈ 0.0025) but climbs rapidly with temperature. At fixed entropy of a radiation-dominated core, the cost of producing pairs becomes comparable to the available thermal energy when T ~ 6-7 × 10⁸ K, which is exactly where the cores of massive stars sit at the end of carbon and oxygen burning. The Goldilocks region is set by stellar evolution, not by tuned parameters.

Common pitfalls

• Calling every superluminous SN a PISN. SLSN-I are bright because something powers them past the radioactive luminosity ceiling. PISN is one option; magnetar spin-down is another (often a better fit); circumstellar interaction is a third. A confident PISN classification requires the full ⁵⁶Co-decay tail and a Ni mass derived from late-time bolometric flux, not just brightness at peak.
• Confusing PISN with PPISN. Pulsational pair instability is a sibling mechanism that ejects mass without disrupting the star. PPISN ends in a black hole; PISN does not. The light-curve signatures overlap in some interaction-powered cases, so distinguishing the two requires careful modelling of shell collisions and late-time photospheric retreat.
• Assuming "no remnant" means "no ejecta". The lack of a remnant refers only to a compact stellar corpse. A PISN does leave a chemically enriched expanding ejecta cloud — typically rich in oxygen, calcium, and iron-peak elements — that mixes into the surrounding ISM and serves as one of the cleanest channels for distributing freshly synthesized α-elements at early cosmic times.
• Treating the mass gap as a hard wall. The PISN boundaries depend on nuclear reaction rates, especially the ¹²C(α,γ)¹⁶O rate, on rotation, and on convective mixing. A factor-of-two change in the carbon rate can shift the boundary by 5-15 M☉. The mass gap is sharp in models but observationally fuzzy.
• Ignoring the metallicity prerequisite. Modern Population I stars in the Galaxy lose mass too fast through line-driven winds to ever enter the PISN regime — a 200 M☉ ZAMS star in solar-metallicity gas ends its life as a ~ 30 M☉ Wolf-Rayet star and core-collapses. PISN events require metal-poor progenitors, which is why the cleanest hosts are dwarf, low-metallicity galaxies.