Evidence of the pair-instability gap from black-hole masses | Nature

## Summary
Subjects Compact astrophysical objects Stellar evolution Abstract Stellar theory predicts a forbidden range of black-hole masses between approximately 50 M ⊙ and 130 M ⊙ owing to pair-instability supernovae 1 , 2 , 3 , 4 , 5 , 6 , 7 , but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Mind the gap: the location of the lower edge of the pair-instability supernova black hole mass gap. Article ADS CAS Google Scholar Schulze, S. et al. 1100 days in the life of the supernova 2018ibb. M. et al. “Super-kilonovae” from massive collapsars as signatures of black hole birth in the pair-instability mass gap.

## Article Content
Subjects
Compact astrophysical objects
Stellar evolution
Abstract
Stellar theory predicts a forbidden range of black-hole masses between approximately 50
M
⊙
and 130
M
⊙
owing to pair-instability supernovae
1
,
2
,
3
,
4
,
5
,
6
,
7
, but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Early hints of a cut-off in black-hole masses at about 45
M
⊙
disappeared with the subsequent discovery of more massive binary black holes
8
,
9
. Here we report evidence of the pair-instability gap in LIGO–Virgo–KAGRA’s fourth Gravitational-Wave Transient Catalog (GWTC-4), with a lower boundary of
\(4{4}_{-4}^{+5}\,{M}_{\odot }\)
(90% credibility). Although the gap is not present in the distribution of primary masses
m
1
(the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of secondary masses
m
2
, in which
m
2
≤
m
1
. The location of the gap lines up well with a previously identified transition in the binary black-hole spin distribution; binaries with primary components in the gap tend to spin more rapidly than those below the gap. We interpret these findings as evidence for a subpopulation of hierarchical mergers: binaries in which the primary component is the product of a previous black-hole merger and thus populates the gap. Our measurement of the location of the pair-instability gap constrains the
S
-factor for
12
C(
α
,
γ
)
16
O at 300 keV to
\(26{0}_{-108}^{+190}\,{\rm{keV}}\,{\rm{barns}}\)
.
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Fig. 1: Reconstructed distribution of binary black-hole masses.
Fig. 2: Posterior for the lower edge of the mass gap as determined by different properties.
Fig. 3: Primary masses
m
1
and secondary masses
m
2
coloured according to the absolute magnitude of
χ
eff
for GWTC-4 events.
Fig. 4: Constraints on the
12
C(
α
,
γ
)
16
O rate.
Data availability
The results of the analyses in this work can be found on Zenodo at
https://doi.org/10.5281/zenodo.18222409
(ref.
87
). The posterior samples of GWTC-4 events used in the hierarchical Bayesian inference of this work are available on Zenodo as part of LIGO–Virgo–KAGRA’s GWTC-4 data release (
https://doi.org/10.5281/zenodo.16053484
)
88
. For events in GWTC-2.1 and GWTC-3, we used samples from Zenodo found at
https://doi.org/10.5281/zenodo.6513631
(ref.
89
) and
https://doi.org/10.5281/zenodo.5546663
(ref.
90
). We used the cumulative search sensitivity file on Zenodo found at
https://doi.org/10.5281/zenodo.16740128
(ref.
91
).
Code availability
The code for this study is publicly available at
https://github.com/HuiTong5/PISN_mass_gap_GWTC-4
as an implementation of the population models developed in this study using GWPopulation
50
.
References
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Schulze, S. et al. 1100 days in the life of the superno

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## Expert Analysis

### Merits
N/A

### Areas for Consideration
- Subjects Compact astrophysical objects Stellar evolution Abstract Stellar theory predicts a forbidden range of black-hole masses between approximately 50 M ⊙ and 130 M ⊙ owing to pair-instability supernovae 1 , 2 , 3 , 4 , 5 , 6 , 7 , but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive.
- Here we report evidence of the pair-instability gap in LIGO–Virgo–KAGRA’s fourth Gravitational-Wave Transient Catalog (GWTC-4), with a lower boundary of \(4{4}_{-4}^{+5}\,{M}_{\odot }\) (90% credibility).
- Although the gap is not present in the distribution of primary masses m 1 (the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of secondary masses m 2 , in which m 2 ≤ m 1 .

### Implications
- Go to natureasia.com Buy this article Purchase on SpringerLink Instant access to the full article PDF. 39,95 € Prices may be subject to local taxes which are calculated during checkout Fig. 1: Reconstructed distribution of binary black-hole masses.
- The impact of pair-instability mass loss on the binary black hole mass distribution.
- The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system.
- New determination of the 12 C( α , γ ) 16 O reaction rate and its impact on the black-hole mass gap.

### Expert Commentary
This article covers article, google, scholar topics. Areas of concern are also raised. Readability: Flesch-Kincaid grade 0.0. Word count: 2355.