Suspicious Siblings: The Distribution of Mass and Spin Across Component Black Holes in Isolated Binary Evolution

The LIGO and Virgo gravitational-wave detectors have uncovered binary black hole systems with definitively nonzero spins, as well as systems with significant spin residing in the more massive black hole of the pair. We investigate the ability of isolated binary evolution in forming such highly spinning, asymmetric-mass systems through both accretion onto the first-born black hole and tidal spin-up of the second-born black hole using a rapid population synthesis approach with detailed considerations of spin-up through tidal interactions. Even with the most optimistic assumptions regarding the efficiency at which an accreting star receives material from a donor, we find that it is difficult to form systems with significant mass asymmetry and moderate or high spins in the primary black hole component. Assuming efficient angular momentum transport within massive stars and Eddington-limited accretion onto black holes, we find that $< 1.5\%$ of systems in the underlying binary black hole population have a primary black hole spin greater than 0.2 and a mass asymmetry of greater than 2:1 in our most optimistic models, with most models finding that this criteria is only met in $\sim 0.01\%$ of systems. The production of systems with significant mass asymmetries and spin in the primary black hole component is thus an unlikely byproduct of isolated evolution unless highly super-Eddington accretion is invoked or angular momentum transport in massive stars is less efficient than typically assumed.