The first mass peak of merging black holes from core binding energies and jet-driven explosions

We show that the jittering-jets explosion mechanism (JJEM) can qualitatively reproduce the shape of the black hole (BH) mass distribution observed by LIGO-Virgo-KAGRA and quantitatively reproduce the peak around $M_{p1} \simeq 10 M_\odot$. To show this, we construct a toy model that captures the JJEM physics that explodes all massive stars, even when BHs form. According to the JJEM, BHs form when the star's binding energy is large, implying a massive progenitor with initial mass $M_i \gtrsim 25 M_\odot$, and when jets are launched along a fixed axis, implying a rapidly rotating pre-collapse stellar core. In this case, the jets are launched along the core's angular momentum and are inefficient at removing mass near the equatorial plane; when the stellar binding energy is large, a large fraction of the equatorial mass is accreted to form the BH. The toy model includes two parameters: the threshold binding energy in the core for BH formation and the jet opening angle along the poles. Although our finding is encouraging for the JJEM, future hydrodynamical simulations must determine the exact condition for BH formation in the JJEM and the BH mass.