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, baryonic and BH masses of high-redshift ($z>5$) galaxies. We use a minimal set of mass- and $z$-independent free parameters associated with star formation and BH growth (and feedback) and include suppressed BH growth in low-mass galaxies to explore a number of physical scenarios including: (i) two types of BH seeds (stellar and those from Direct Collapse BH; DCBH); (ii) the impact of reionization feedback; and (iii) the impact of instantaneous versus delayed galaxy mergers on the baryonic growth. While both reionization feedback and delayed galaxy mergers have no sensible impact on the evolving ultra-violet luminosity function, the latter limits the maximum BH masses achieved at these high-$z$. We then use this model, baselined against all available high-$z$ galaxy and BH data-sets, to predict the LISA detectability of merger events at $z > 5$. As expected, the merger rate is dominated by stellar BH mergers for all scenarios and our model predicts an expected upper limit of about 20 mergers in the case of instantaneous merging and no reionization feedback over the 4-year mission duration. Including the impact of delayed mergers and reionization feedback reduces this to about 12 events over the same observational time-scale.