Formation of supermassive black holes in galactic nuclei II: retention
  and growth of seed intermediate-mass black holes
  In many galactic nuclei, a nuclear stellar cluster (NSC) co-exists with a
supermassive black hole (SMBH). In this work, we explore the idea that the NSC
forms before the SMBH through the merger of several stellar clusters that may
contain intermediate-mass black holes (IMBHs). These IMBHs can subsequently
grow by mergers and accretion to form an SMBH. To check the observable
consequences of this proposed SMBH seeding mechanism, we created an
observationally motivated mock population of galaxies, in which NSCs are
constructed by aggregating stellar clusters that may or may not contain IMBHs.
We model the growth of IMBHs in the NSCs through gravitational wave (GW)
mergers with other IMBHs and gas accretion. In the case of GW mergers, the
merged BH can either be retained or ejected depending on the GW recoil kick it
receives. The likelihood of retaining the merged BH increases if we consider
growth of IMBHs in the NSC through gas accretion. We find that nucleated
lower-mass galaxies ($\rm M_{\star} \lesssim 10^{9} \ M_{\odot}$; e.g. M33)
have an SMBH seed occupation fraction of about 0.3 to 0.5. This occupation
fraction increases with galaxy stellar mass and for more massive galaxies ($\rm
10^{9} \ M_{\odot} \lesssim \rm M_{\star} \lesssim 10^{11} \ M_{\odot}$), it is
between 0.5 and 0.8, depending on how BH growth is modelled. These occupation
fractions are consistent with observational constraints. Furthermore, allowing
for BH growth also allows us to reproduce the observed diversity in the mass
range of SMBHs in the $\rm M_{\rm NSC} - M_{\rm BH}$ plane.
