Using high-resolution simulations of black hole formation from the direct collapse of massive stars undergoing pulsational pair-instability supernovae (PPISN), we find a new phenomenon which significantly affects the explosion and leads to two peaks in the resulting black hole mass function (BHMF). Lighter stars experiencing the pair-instability can form a narrow shell in which alpha ladder reactions take place, exacerbating the effect of the PPISN. The shell temperature in higher mass stars ($>62M_{\odot }$ at the onset of helium burning for population-III stars with metallicity $Z={10}^{-5}$) is too low for this to occur. As a result, the spectrum of black holes as a function of the initial stellar mass $M_{\mathrm{BH}}(M_i)$ exhibits a shoulder feature whereby a large range of initial masses result in near-identical black hole masses. PPISN therefore predict two peaks in the mass function of astrophysical black holes—one corresponding to the location of the upper black hole mass gap at $57M_{\odot }$ and a second corresponding to the location of the shoulder at $49M_{\odot }$. This shoulder effect may explain the peak at ${35}_{-2.9}^{+1.7}{M}_{\odot }$ in the LIGO/Virgo/KAGRA GWTC-3 catalog of merging binary black holes for variations in the stellar parameters, for example if the ${}^{12}\mathrm{C}(\alpha ,\gamma {)}^{16}\mathrm{O}$ rate is increased by $3\sigma$.

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• Gravitational wave sources
• Gravitational waves
• Astronomical black holes
• Stars