Simulations show a 40-50 solar-mass black-hole cutoff is not guaranteed to be confidently recovered from GWTC-4-like catalogs, spurious detections are unlikely, and O4 data would reduce cutoff-mass uncertainty by at least 20 percent while yielding only a lower bound on the carbon-alpha reaction rate
For- mation of GW190521 from stellar evolution: the impact of the hydrogen-rich envelope, dredge-up, and 12C(α, γ)16O rate on the pair-instability black hole mass gap
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abstract
Pair-instability (PI) is expected to open a gap in the mass spectrum of black holes (BHs) between $\approx{}40-65$ M$_\odot$ and $\approx{}120$ M$_\odot$. The existence of the mass gap is currently being challenged by the detection of GW190521, with a primary component mass of $85^{+21}_{-14}$ M$_{\odot}$. Here, we investigate the main uncertainties on the PI mass gap: the $^{12}$C($\alpha$, $\gamma$)$^{16}$O reaction rate and the H-rich envelope collapse. With the standard $^{12}$C($\alpha$, $\gamma$)$^{16}$O rate, the lower edge of the mass gap can be 70 M$_\odot$ if we allow for the collapse of the residual H-rich envelope at metallicity $Z\leq{}0.0003$. Adopting the uncertainties given by the STARLIB database, for models computed with the $^{12}$C($\alpha$, $\gamma$)$^{16}$O rate $-1\, \sigma$, we find that the PI mass gap ranges between $\approx{}80$ M$_\odot$ and $\approx{}150$ M$_\odot$. Stars with $M_{\rm ZAMS}>110$ M$_\odot$ may experience a deep dredge-up episode during the core helium-burning phase, that extracts matter from the core enriching the envelope. As a consequence of the He-core mass reduction, a star with $M_{\rm ZAMS} =160$ M$_\odot$ may avoid the PI and produce a BH of 150 M$_\odot$. In the $-2\,{}\sigma{}$ case, the PI mass gap ranges from 92 M$_\odot$ to 110 M$_\odot$. Finally, in models computed with $^{12}$C($\alpha$, $\gamma$)$^{16}$O $-3\,{}\sigma{}$, the mass gap is completely removed by the dredge-up effect. The onset of this dredge-up is particularly sensitive to the assumed model for convection and mixing. The combined effect of H-rich envelope collapse and low $^{12}$C($\alpha$, $\gamma$)$^{16}$O rate can lead to the formation of BHs with masses consistent with the primary component of GW190521.
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Using a joint effective-spin and precession-spin model on 155 gravitational-wave events, the authors infer that the hierarchical (second-generation) merger fraction rises sharply above ~46 M_sun and peaks again near 15.7 M_sun.
GWTC-4 data analysis yields a pair-instability mass gap lower edge at 44.3^{+5.9}_{-3.5} M_⊙, an S-factor of 268^{+195}_{-116} keV b for ^{12}C(α,γ)^{16}O, and two populations supporting both direct formation and hierarchical mergers.
An isolated hierarchical triple channel with chemically homogeneous evolution and triple common envelope can produce PISN mass-gap BBH mergers matching GW190706 at ~22% of the observed rate.
GWTC-2.1 adds eight new high-significance compact binary coalescence events to the prior catalog, extending the observed black hole mass range and including candidates inside the pair-instability mass gap.
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