---
title: Pair-Instability Gap in Stellar Black Holes
url: https://www.emergentmind.com/topics/pair-instability-gap
type: topic
---

# Pair-Instability Gap in Stellar Black Holes

The pair-instability gap is the predicted dearth of stellar-origin black holes produced when very massive stellar cores enter the electron–positron pair-production regime, soften their equation of state, and undergo either pulsational pair-instability mass ejection or complete pair-instability supernova disruption. In the gravitational-wave literature, this “upper black-hole mass gap” is often quoted near \(45\)–\(130\,M_\odot\), but the adopted boundaries vary across studies, and several recent works emphasize that the lower edge depends sensitively on core structure, angular-momentum transport, envelope retention, and the \(^{12}\mathrm{C}(\alpha,\gamma)^{16}\mathrm{O}\) rate [1910.12874] [2007.06220] [2103.07933].

## 1. Physical origin of the gap

The physical mechanism is pair creation in radiation-pressure-supported cores. After core-helium burning, sufficiently massive stars develop large carbon–oxygen cores; at high temperature, photons create \(e^\pm\) pairs, removing pressure-supporting radiation and softening the equation of state. One study summarizes the relevant thermodynamic regime as densities between \(\approx 10^2\) and \(10^6\ {\rm g\ cm^{-3}}\) and temperatures above \(6\times 10^8\) K [2204.03493]. In the same picture, the effective adiabatic index is driven toward or below \(4/3\), the core contracts, and explosive carbon or oxygen burning follows [1910.12874].

Two regimes are distinguished. In pulsational pair instability, the star survives one or more thermonuclear pulses but ejects substantial mass before final collapse; in full pair-instability supernovae, the explosion unbinds the whole star and leaves no compact remnant [1910.12874]. This is why the gap is fundamentally a consequence of pre-collapse thermonuclear evolution rather than of black-hole formation physics at core collapse. The most massive black holes below the gap are produced by stars that enter the pulsational regime but are not fully disrupted, whereas stars above the pulsational regime are completely destroyed until collapse resumes on the far side of the gap [1910.12874] [2401.13038].

## 2. Boundaries, definitions, and theoretical uncertainty

The literature does not use a single pair-instability interval. Several population and detector studies adopt a gap around \(45\)–\(130\,M_\odot\) [2004.05187] [2007.06220] [2401.13038], while collision and young-cluster studies often work with \(\sim 60\)–\(120\,M_\odot\) [2204.03493] [2204.03492] [1907.12562]. Other analyses phrase the lower boundary more broadly as \(\sim 40\)–\(65\,M_\odot\) and the upper boundary as \(\sim 120\,M_\odot\) [2106.00605]. This dispersion reflects different progenitor assumptions: stripped helium stars, H-rich stars retaining envelopes, rotating stars, or post-merger products.

For bare helium-star progenitors, one influential MESA study found the lower edge of the mass gap—equivalently the maximum first-generation black-hole mass below the gap—to be approximately \(45\,M_\odot\), with only small shifts from metallicity, mixing, winds, neutrino physics, and resolution, but a much larger shift from the uncertain \(^{12}C(\alpha,\gamma)^{16}O\) rate. In that calculation, the edge moves from roughly \(40\,M_\odot\) to \(56\)–\(58\,M_\odot\) across the quoted \(1\sigma\) nuclear uncertainty [1910.12874]. Woosley and Heger similarly argued that a value \(M_{\rm lo}=45\)–\(65\,M_\odot\) is reasonable for the lower boundary and that current uncertainties can raise the upper boundary \(M_{\rm hi}\) as large as \(161\,M_\odot\) [2103.07933].

Rotation modifies the lower edge further. For stripped helium stars at \(Z_\odot/50\), the inferred lower edge is \(45.5\,M_\odot\) for non-rotating models, \(47.4\,M_\odot\) for rapidly rotating models with efficient Spruit–Tayler angular-momentum transport, and \(52.4\,M_\odot\) without Spruit–Tayler transport [2007.06220]. This places the uncertainty not only in initial rotation but also in angular-momentum coupling.

A different branch of work emphasizes hydrogen-envelope retention. Detailed low-\(Z\) MESA grids that make no prior assumption about envelope stripping find that, if the H envelope falls into the black hole, the maximum black-hole mass below pair instability can reach \(M_{\rm BH}\simeq 93.3\,M_\odot\) [2401.17327]. Related PARSEC models with H-rich stars at \(Z=0.0003\) find a lower edge of about \(68\,M_\odot\) for the standard \(^{12}C(\alpha,\gamma)^{16}O\) rate if the residual H-rich envelope collapses, a gap of \(\sim 80\)–\(150\,M_\odot\) for the \(-1\sigma\) rate, a gap of \(92\)–\(110\,M_\odot\) for the \(-2\sigma\) rate, and complete removal of the gap in the \(-3\sigma\) case when dredge-up operates; the authors stress that this dredge-up is particularly sensitive to convection and mixing assumptions [2010.02242].

## 3. Channels that populate or circumvent the gap

The pair-instability gap does not imply that black holes in the interval cannot exist; it implies that standard first-generation stellar collapse is suppressed there. Several channels can repopulate the interval.

One channel is stellar collision or stellar merger in dense clusters. Hydrodynamical simulations of a head-on collision between a \(57.6\,M_\odot\) core-helium-burning primary and a \(41.9\,M_\odot\) main-sequence secondary show that the collision ejects about \(11.7\%\) of the initial mass, leaving a bound remnant of \(\approx 87.9\,M_\odot\), with the main-sequence star depositing most of its mass around the primary core and producing a helium-enriched envelope with \(Y_{\rm surf}\approx 0.4\) [2204.03493]. Follow-up stellar-evolution calculations based on that hydrodynamical remnant find that the merger product avoids pair instability and collapses as a blue supergiant to a black hole of \(\approx 87\,M_\odot\) [2204.03492].

A related dynamical young-cluster study found that up to \(\sim 6\%\) of all simulated black holes can lie in the pair-instability gap, depending on metallicity; \(\sim 21\%\), \(10\%\), and \(0.5\%\) of all BBHs have at least one component in the gap at \(Z=0.0002\), \(0.002\), and \(0.02\), respectively; and \(\sim 5\%\) of detectable BBH mergers at Advanced LIGO/Virgo design sensitivity have at least one component in the gap if all stars form in young star clusters [1911.01434]. Population III cluster simulations likewise produce pair-instability-gap black holes through stellar collisions and BBH mergers, with BBH mergers accounting for about \(90\%\) of the contributions in that study [2504.20392].

By contrast, classical isolated binary evolution appears much less effective. Even under deliberately extreme super-Eddington prescriptions, one population-synthesis study finds that at most \(2.35\pm0.06\%\) of merging BBHs contain a black hole with \(M_{\rm BH}>45\,M_\odot\), only \(0.45\pm0.03\%\) have \(M_{\rm tot}>90\,M_\odot\), and no merging systems exceed \(100\,M_\odot\) in total mass [2004.05187]. Another recent analysis argues that efficient first Roche-lobe overflow followed by highly non-conservative second mass transfer can mimic a cutoff in the lighter black-hole component near \(45\,M_\odot\), even when the true pair-instability limit for the heavier component is much higher; in that model, the fraction of systems in which the less massive black hole exceeds \(45\,M_\odot\) is negligible [2604.18676]. This suggests that not every observational cutoff near \(45\,M_\odot\) uniquely diagnoses pair instability.

## 4. Observational status in gravitational-wave catalogs

The modern observational discussion was catalyzed by GW190521, whose primary mass was reported as \(85^{+21}_{-14}\,M_\odot\), inside the traditionally disfavored interval [2204.03493]. A detection-space outlier analysis of the LIGO–Virgo BBH sample concluded that, if the pair-instability gap begins at or below \(65\,M_\odot\), GW190521 is firmly an outlier to the stellar-mass BBH population, with \(p<10^{-4}\); for a lower boundary of \(40\)–\(50\,M_\odot\), the remaining population also becomes difficult to reconcile with a purely stellar-mass model [2106.00605].

More recent GWTC-4-era analyses are not fully uniform in interpretation. One flexible hierarchical-Bayesian study of 153 BBHs finds no evidence for a sharp drop-off in component masses near \(40\)–\(50\,M_\odot\), favoring instead a smooth decline and placing the lower bound on a possible hidden cutoff at \(57^{+17}_{-10}\,M_\odot\) [2510.18867]. In contrast, two other GWTC-4 analyses report evidence for the gap in the **secondary**-mass distribution rather than the primary distribution. One infers a lower boundary of \(45_{-4}^{+5}\,M_\odot\) at \(90\%\) credibility and interprets the absence of a corresponding feature in primary masses as evidence that hierarchical mergers partially fill the gap in \(m_1\) while leaving a cleaner imprint in \(m_2\) [2509.04151]. Another finds a lower edge at \(45.3^{+6.5}_{-4.8}\,M_\odot\) and a transition from a low-spin population below that scale to a high-spin, isotropic population above it, again consistent with hierarchical mergers occupying the gap [2509.04637]. A phase-space reconstruction analysis similarly reports a sharp truncation of the first-generation population at approximately \(45.5\,M_\odot\) [2509.09123].

Taken together, these observational studies suggest that the empirical signature of the pair-instability gap depends on the assumed population model, on whether the primary or secondary mass distribution is examined, and on how strongly hierarchical mergers are allowed to contaminate the high-mass regime.

## 5. Far side of the gap and future measurements

The upper boundary of the gap is conceptually distinct from the lower one. Theory often places the far-side onset near \(\sim 130\,M_\odot\), corresponding to the minimum black-hole mass above the gap once stars become massive enough to collapse again rather than being fully disrupted [2401.13038]. Very low-metallicity environments, especially Population III channels, are frequently invoked as the most plausible first-generation route to these far-side black holes [1907.12562] [2401.13038].

Assuming such far-side black holes exist, future detectors should measure the upper edge as a population feature. One forecasting study finds that next-generation ground-based detectors can constrain the minimum mass beyond the gap, \(m_{\min}\sim130\,M_\odot\), with relative precision \(\Delta m_{\min}/m_{\min}\simeq 4\%(N_{\rm det}/100)^{-1/2}\) at \(90\%\) confidence, where \(N_{\rm det}\) is the number of detected mergers with both components beyond the gap [2401.13038]. Earlier rate forecasts for above-gap binaries similarly predict \(0.4\)–\(7\ {\rm yr}^{-1}\) detections at LIGO/Virgo design sensitivity and \(10\)–\(460\ {\rm yr}^{-1}\) for third-generation detectors, under assumptions that extremely metal-poor stars can form black holes above the gap [1907.12562]. These projections treat the far side of the gap as an observationally accessible probe rather than a purely theoretical boundary.

## 6. Implications for stellar physics and remaining controversies

The pair-instability gap has become a diagnostic of both stellar evolution and compact-object assembly. On the stellar-physics side, the lower edge is especially sensitive to the \(^{12}\mathrm{C}(\alpha,\gamma)^{16}\mathrm{O}\) rate. Farmer and collaborators argue that the lower edge near \(45\,M_\odot\) is otherwise unusually robust for bare helium stars, with the nuclear rate as the dominant exception [1910.12874]. Several GW population studies already translate inferred gap locations into constraints on the astrophysical \(S\)-factor at 300 keV, but the resulting values differ substantially—for example \(256_{-104}^{+197}\ \mathrm{keV\,barns}\) in one analysis and \(242.5^{+310.4}_{-101.5}\ \mathrm{keV\,b}\) in another—showing that the inference remains model-dependent [2509.04151] [2509.04637].

On the compact-object side, the main controversy is whether current catalogs reveal a genuine pair-instability feature or an observationally similar structure generated by binary evolution and channel mixing. Current work supports all of the following statements: the first-generation stripped-star lower edge can sit near \(45\,M_\odot\); rotation can move it into the low \(50\,M_\odot\) range; H-envelope retention can raise the heaviest black holes below the onset of pair instability to \(\sim 90\,M_\odot\); stellar collisions can form \(\sim 87\,M_\odot\) black holes while still avoiding pair instability; and binary mass transfer can mimic a sharp cutoff in the lighter component distribution near \(45\,M_\odot\) [2007.06220] [2401.17327] [2204.03492] [2604.18676].

A plausible implication is that “the pair-instability gap” is best treated not as a single immutable interval but as a model-dependent structure in the black-hole birth function, modified observationally by envelope retention, stellar mergers, hierarchical mergers, and population-selection effects. The central empirical task is therefore no longer only to locate a single lower edge, but to disentangle which parts of the high-mass black-hole population are first-generation stellar-collapse remnants and which are products of subsequent dynamical or binary processing.

Source: https://www.emergentmind.com/topics/pair-instability-gap