The formation of $30M_{\odot }$ merging black holes at solar metallicity

The maximum mass of black holes formed in isolated binaries is determined by stellar winds and the interactions between the binary components. We consider for the first time fully self-consistent detailed stellar structure and binary evolution calculations in population-synthesis models and a new, qualitatively different picture emerges for the formation of black-hole binaries, compared to studies employing rapid population synthesis models. We find merging binary black holes can form with a non-negligible rate ($\sim 4\times {10}^{-7}{M}_{\odot }^{-1}$) at solar metallicity. Their progenitor stars with initial masses $\gtrsim 50M_{\odot }$ do not expand to supergiant radii, mostly avoiding significant dust-driven or luminous blue variable winds. Overall, the progenitor stars lose less mass in stellar winds, resulting in black holes as massive as $\sim 30M_{\odot }$, and, approximately half of them avoid a mass-transfer episode before forming the first-born black hole. Finally, binaries with initial periods of a few days, some of which may undergo episodes of Roche-lobe overflow mass transfer, result in mildly spinning first-born black holes, ${\chi }_{\mathrm{B}\mathrm{H}1}\lesssim 0.2$, assuming efficient angular-momentum transport.