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In the local Universe, black holes of |$10^{5-6}\, {\rm M_\odot }$| are hosted in galaxies displaying a variety of stellar profiles and morphologies. These black holes are the anticipated targets of LISA, the Laser Interferometer Space Antenna that will detect the low-frequency gravitational-wave signal emitted by binary black holes in this mass interval. In this paper, we infer upper limits on the lifetime of binary black holes of |$10^{5-6}\, {\rm M_\odot }$| and up to |$10^8\, {\rm M_\odot }$|⁠ , forming in galaxy mergers, exploring two underlying stellar density profiles, by Dehnen and by Prugniel & Simien, and by exploiting local scaling relations between the mass of the black holes and several quantities of their hosts. We focus on the phase of the dynamical evolution when the binary is transitioning from the hardening phase ruled by the interaction with single stars to the phase driven by the emission of gravitational waves. We find that different stellar profiles predict very distinct trends with binary mass, with lifetimes ranging between fractions of a Gyr to more than 10 Gyr, and with a spread of about one order of magnitude, given by the uncertainties in the observed correlations, which are larger in the low-mass tail of the observed black hole population. [ABSTRACT FROM AUTHOR]

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 ≳ 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. [ABSTRACT FROM AUTHOR]