<i>Gaia</i> BH1 and BH2 – evolutionary models with overshooting of the black hole progenitors within the present-day binary separation

ABSTRACT Three black holes (BHs) in wide binaries – Gaia BH1, BH2, and BH3 – were recently discovered. The likely progenitors of the BHs were massive stars that experienced a supergiant phase, reaching radii of $\sim\!\! 1000 \ \mathrm{ R}_{\odot }$, before collapsing to form the BH. Such radii are difficult to accommodate with the present-day orbits of BH1 and BH2 – with semimajor axes of 1.4 and 3.7 au, respectively. In this letter, we show that the maximal radii of the supergiants are not necessarily so large, and realistic stellar evolution models, with some assumed overshooting above the convective core into the radiative stellar envelope, produce substantially smaller maximal radii. The limited expansion of supergiants is consistent with the empirical Humphreys–Davidson limit – the absence of red supergiants above an upper luminosity limit, notably lower than the highest luminosity of main-sequence stars. We propose that the evolution that led to the formation of Gaia BH1 and BH2 simply did not involve an expansion to the cool supergiant phase.