The hierarchical assembly of galaxies and black holes in the first billion years: predictions for the era of gravitational wave astronomy

In this work, we include black hole (BH) seeding, growth, and feedback into our semi-analytic galaxy formation model, Delphi. Our model now fully tracks the accretion-and merger-driven hierarchical assembly of the dark matter halo, gas, stellar, and BH masses of high-redshift (z greater than or similar to 5) galaxies. We explore a number of physical scenarios that include (i) two types of BH seeds (stellar and those from direct collapse BH); (ii) the impact of reionization; and (iii) the impact of instantaneous versus delayed galaxy mergers on the baryonic growth. Using a minimal set of mass-and z-independent free parameters associated with star formation and BH growth, and their associated feedback, and including the suppressed BH growth in lower mass galaxies, we show that our model successfully reproduces all available data sets for early galaxies and quasars. While both reionization and delayed galaxy mergers have no sensible impact on the evolving ultraviolet luminosity function, the impact of the former dominates in determining the stellar mass density for observed galaxies as well as the BH mass function. We then use this model to predict the LISA detectability of merger events at high-z. As expected, mergers of stellar BHs dominate the merger rates for all scenarios and our model predicts an expected upper limit of about 20 mergers using instantaneous merging and no reionization feedback over the 4-yr mission duration. Including the impact of delayed mergers and reionization feedback provides about 12 events over the same observational time-scale.