Nuclear and globular star clusters: the missing link between supermassive black holes and their host galaxies?

Nuclear star clusters (NSC) are ubiquitously observed at the centre of sufficiently resolved galaxies. In dwarfs, they tend to replace the supermassive black hole (SMBH) detected in most massive galaxies. However, in galaxies like our own Milky Way (see picture), they happily co-exist with SMBHs of a similar mass. NSCs are the densest star clusters in the Universe with dynamic masses ranging from 106 to 108 solar masses enclosed in a radius no larger than 5pc. This places them firmly at the bright end of the globular cluster luminosity function (see e.g. the recent review by Neumayer et al, 2020, ARA&A, arXiv: 2001.03626). There exists clear evidence that their physical properties correlate with those of their host galaxies, which makes them key ingredients for our understanding galaxy formation and evolution.
Although they were first detected in the early 1970s, the formation mechanism of NSCs is still debated. Crudely speaking, the formation channels put forward can be divided into two main categories: the ones which invoke an inward migration of star clusters through dynamical friction, and those that argue in favour of in-situ star formation triggered by high gas densities present in the galaxy nucleus.
However, regardless of their mode of formation, if NSCs truly are ubiquitous, those that form in early dwarf galaxies, before the re-ionization epoch, could still be present in the halo of the present-day galaxy which results from the merger of these dwarfs. This provides a hypothesis for the formation of globular clusters (GC) as the remains of NSCs which have been stripped of their gas content, preventing them from being rejuvenated by new star formation.

Moreover, given the extreme environment in which NSCs are located, and the well documented co-existence of NSCs and SMBHs in the nucleus of quite a large fraction of galaxies, it is quite natural to speculate that the formation and evolution of these two components are tightly linked. For instance, early collisions of stars within a dense NSC could easily provide seed black holes which could further grow from tearing apart other stars of the NCS.

Arguably the main reason why little progress has been made on these issues is that the direct modelling of NSCs and GCs (not to mention SMBHs) is difficult because their behaviour is collisional (as opposed to the collisionless approach used to numerically simulate dark matter and ordinarily distributed stars in cosmological simulations of galaxy formation and evolution). This means that direct N-body codes must be used to properly track the dynamical evolution of these star clusters (example N-Body6 (Aarseth 2003)). However, such calculations are currently out of reach of even the most powerful super-computers, especially for massive NSCs (see e.g. DiCintio et al (2021) for a recent review of alternative techniques).