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Pair-instability (PI) is expected to open a gap in the mass spectrum of blackholes (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 ofGW190521, 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 envelopecollapse. With the standard $^{12}$C($\alpha$, $\gamma$)$^{16}$O rate, thelower edge of the mass gap can be 70 M$_\odot$ if we allow for the collapse ofthe residual H-rich envelope at metallicity $Z\leq{}0.0003$. Adopting theuncertainties given by the STARLIB database, for models computed with the$^{12}$C($\alpha$, $\gamma$)$^{16}$O rate $-1\, \sigma$, we find that the PImass 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 episodeduring the core helium-burning phase, that extracts matter from the coreenriching the envelope. As a consequence of the He-core mass reduction, a starwith $M_{\rm ZAMS} =160$ M$_\odot$ may avoid the PI and produce a BH of 150M$_\odot$. In the $-2\,{}\sigma{}$ case, the PI mass gap ranges from 92M$_\odot$ to 110 M$_\odot$. Finally, in models computed with $^{12}$C($\alpha$,$\gamma$)$^{16}$O $-3\,{}\sigma{}$, the mass gap is completely removed by thedredge-up effect. The onset of this dredge-up is particularly sensitive to theassumed model for convection and mixing. The combined effect of H-rich envelopecollapse and low $^{12}$C($\alpha$, $\gamma$)$^{16}$O rate can lead to theformation of BHs with masses consistent with the primary component of GW190521.

monthly notices of the royal astronomical society

Formation of GW190521 from stellar evolution: the impact of the  hydrogen-rich envelope, dredge-up and $^{12}$C($\alpha$, $\gamma$)$^{16}$O  rate on the pair-instability black hole mass gap