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In this work we include black hole (BH) seeding, growth and feedback into oursemi-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 setof mass- and $z$-independent free parameters associated with star formation andBH growth (and feedback) and include suppressed BH growth in low-mass galaxiesto explore a number of physical scenarios including: (i) two types of BH seeds(stellar and those from Direct Collapse BH; DCBH); (ii) the impact ofreionization feedback; and (iii) the impact of instantaneous versus delayedgalaxy mergers on the baryonic growth. While both reionization feedback anddelayed galaxy mergers have no sensible impact on the evolving ultra-violetluminosity function, the latter limits the maximum BH masses achieved at thesehigh-$z$. 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 forall scenarios and our model predicts an expected upper limit of about 20mergers in the case of instantaneous merging and no reionization feedback overthe 4-year mission duration. Including the impact of delayed mergers andreionization feedback reduces this to about 12 events over the sameobservational time-scale.

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