Masses, Mass Ratios, and Pair-Instability Structure

Binary-black-hole masses show population structure, but “mass gap” is not a direct detector label. The waveform measures uncertain detector-frame mass combinations; cosmology maps them to source-frame masses; selection and a population model infer the underlying distribution; stellar theory then predicts where pair instability might suppress first-generation remnants. As of 2026-08-18, broad mass structure is well supported, while a sharp, empty pair-instability gap and a unique origin for high-mass mergers are not.

Helpful background. What a Binary Black-Hole Signal Measures separates detector- and source-frame parameters. Mass and Mass-Ratio Distributions develops the hierarchical models and selection checks used here.

From phase to a population spectrum

Inspiral phase constrains the redshifted chirp mass and, less sharply, the symmetric mass ratio

$$\eta=\frac{m_1m_2}{(m_1+m_2)^2}, \qquad 0\lt\eta\le\frac14.$$

At larger total mass, fewer inspiral cycles lie in band and merger–ringdown modeling contributes more strongly. Mass ratio then competes with aligned spin, precession, higher modes, inclination, and noise transients. Event posteriors are neither delta functions nor direct samples from the source population.

The source-frame transformation

$$m_a^{\rm src}=\frac{m_a^{\rm det}}{1+z}$$

adds distance and cosmological uncertainty. Population inference combines the full event likelihoods and divides by the mass-dependent selection factor. Since more massive systems are often visible farther away, a detected high-mass excess can be much smaller intrinsically; at still higher masses, loss of in-band duration changes the trend.

What “pair-instability structure” predicts

In sufficiently massive, hot stellar cores, electron–positron pair production softens the equation of state. Pulsational pair instability can eject mass before collapse; full pair-instability supernovae can disrupt the star and leave no remnant. The predicted black-hole remnant spectrum can therefore have a pile-up, taper, or depleted interval.

Its location and sharpness depend on helium-core mass, metallicity-dependent winds, nuclear reaction rates, convection, rotation, binarity, and the mapping from progenitor to remnant. Farmer and collaborators quantify large shifts from uncertain nuclear physics Farmer et al. 2020, §§2–4. A single hard boundary inserted into a gravitational-wave prior is thus one theoretical model, not the definition of pair instability.

Even if first-generation stellar collapse leaves a gap, observed mergers can repopulate it through previous black-hole mergers, stellar collisions, accretion, or channels outside the assumed stellar model. Lensing can also bias source-frame masses if ignored, though it must satisfy its own rate and repeated-image constraints. A component inside a proposed interval therefore motivates channel comparison; it does not identify one.

Results at the catalog cutoff

The official GWTC-5.0 population analysis compares parametric peaks, broken or tapered laws, joint two-dimensional mass models, and weakly parameterized reconstructions. The following hierarchy summarizes its detector-level implications LVK 2026, §§3–8.

Evidence line	Supported conclusion	Interpretation ceiling
Broad agreement on a low-mass-scale peak and higher-mass slope change	The merging population is structured, not one unbroken power law	Each feature need not be one channel
Joint mass models find mass-dependent pairing	Primary and secondary masses should not always be factorized	Pairing alone does not identify binary evolution
Flexible models differ on whether higher-mass structure is a peak, turnover, or edge	Fine morphology is model sensitive	No model-independent sharp boundary
Events occupy masses associated with some theoretical gap predictions	At least one assumption behind a strictly empty first-generation gap is incomplete	Pair instability itself is not ruled out

The same catalog reports that a completely empty, sharply delimited primary-mass gap is not clearly required by current reconstructions. It also finds high-mass/spin correlations under particular models, consistent with but not unique to repeated mergers. These are dated, model-conditional observations rather than settled formation history.

Pairing and mass ratio

A feature in $p(m_1)$ can change meaning when the full $p(m_1,m_2)$ is inspected. Equal-mass pairing near one scale, a low-$q$ tail at another, or a feature in the secondary rather than primary distribution can distinguish models. Yet waveform sensitivity to $q$ and selection both change across mass.

A defensible conclusion therefore compares:

• event likelihoods from waveform families with relevant higher modes and precession;
• source-frame conversion under declared cosmologies;
• separable and joint mass-pairing population models;
• catalog-specific injections with adequate support at low $q$ and high mass;
• parametric, flexible, and leave-one-out reconstructions;
• stellar and dynamical forward models predicting rates, spins, redshifts, and pairing together.

Adversarial tests

Waveform test. Recompute influential event likelihoods with credible waveform alternatives. A feature moving by more than its quoted population uncertainty fails robustness.

Smooth-population mock. Generate a smooth two-dimensional mass distribution, select it with the actual injections, and fit the gap model. This calibrates false edges caused by thresholds and finite catalogs.

Gap-recovery mock. Generate a known partial depletion with a taper rather than hard zeros. Determine whether the model can distinguish width, depth, and edge.

Outlier test. Remove each influential high-mass event in turn and compare posterior predictive distributions, not only hyperparameter medians.

Formation forecast. Demand an out-of-sample joint prediction—such as mass-dependent spin or redshift behavior—that separates repeated mergers from alternative stellar pathways.

The evidence should be reviewed after a superseding catalog, corrected event or injection products, a waveform-systematics result, or a stellar-physics calculation that materially changes the predicted remnant interval.

Exercises

1. Redshifted gap. A theory predicts a source-frame feature at mass $m_*$. Where does it appear in detector-frame mass for a source at redshift $z$?

Solution

It appears at $m_*^{\rm det}=(1+z)m_*$. A catalog-wide detector-frame histogram smears a fixed source-frame feature over redshift. Source-frame reconstruction must jointly model distance, cosmology, rate evolution, and selection.

2. An event above a proposed boundary. Does one high-probability source-frame mass above a stellar-collapse boundary falsify pair-instability supernova physics?

Solution

No. It falsifies only the conjunction that the boundary is correct for that progenitor physics, the object is a first-generation remnant from that channel, the event and redshift likelihood are accurate, and no repopulating mechanism contributes. Pair instability can operate while mergers of previous remnants or other stellar pathways populate the interval.

References

• Farmer, R., M. Renzo, S. E. de Mink, M. Fishbach, and S. Justham. “Constraints from Gravitational Wave Detections of Binary Black Hole Mergers on the $^{12}\mathrm C(\alpha,\gamma)^{16}\mathrm O$ Rate.” Astrophysical Journal Letters 902 (2020): L36. DOI. Open PDF.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “GWTC-5.0: Population Properties of Merging Compact Binaries.” arXiv:2605.27226 (2026). Open PDF.

Further reading

• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run and Updates to the Gravitational-Wave Transient Catalog.” arXiv:2605.27225 (2026). Open PDF.
• Stevenson, Simon, Alejandro Vigna-Gómez, Ilya Mandel, Jim W. Barrett, Coenraad J. Neijssel, David Perkins, and Selma E. de Mink. “Formation of the First Three Gravitational-Wave Observations through Isolated Binary Evolution.” Nature Communications 8 (2017): 14906. DOI. Open PDF.