Resolving Black Hole Family Issues Among the Massive Ancestors of Very High-Spin Gravitational-Wave Events Like GW231123

Abstract: The latest detection of GW231123, a binary black hole (BH) merger with exceptionally large masses and high spins for the incoming components, has been suggested as a smoking gun for hierarchical formation. In this scenario, a first generation of BHs resulting from collapsing stars form in a dense environment. Here they can assemble dynamically and undergo subsequent mergers. We discuss three challenges for the formation of a GW231123-like event inside a star cluster: 1) The high masses of the incoming BHs appear to be in the predicted pair-instability mass gap and thus suggest that second-generation or higher-order generation BHs are involved. 2) Very high spins ($\chi_f \gtrsim 0.8$) are very unlikely for dynamically assembled BHs because of the isotropic distribution of spin vectors. 3) Hierarchically formed BHs are susceptible to receive large recoils, which could kick them out of their cluster. We simulate this scenario and show that only a few percent of mergers recover remnants within GW231123's primary spin estimate $\chi_1=0.9^{+0.10}_{-0.19}$ and are retained inside typical star clusters. A large fraction of very rapidly spinning second-generation BHs (including $\chi_f>0.9$) can only form if the first-generation BHs merges with aligned spins. This is a natural outcome of massive binary star evolution scenarios, such as a chemically homogeneous evolution. This scenario also predicts equal masses for the components, implying that the resulting BHs tend to receive very low recoil kicks and would therefore likely be retained inside a cluster. We conclude that GW231123-like events, if formed in a star cluster, could require first-generation BHs with large aligned spins that evolved through stellar binary interaction, followed by the dynamical assembly for a subsequent merger. We discuss the implications for the uncertain lower edge of the putative mass gap 60-130 $\rm M_\odot$.