Poisson Clustering and Seed Effect of PBHs: Implications for Microlensing, Gravitational Waves, Little Red Dots and Ultra-Faint Dwarf Galaxies

Abstract

The existence of primordial black holes (PBHs) could have significant effects on the formation of cosmic structures through both the seed effect and the Poisson effect. For an extended PBH mass function, this should lead to dark virialised bound clusters of black holes with modest mass, together with central black holes of larger mass. We consider the combination of three effects: the inevitable gravitational binding of small-scale inhomogeneities due to Poisson and seed fluctuations; the dilution through dynamical heating of all clusters smaller than around $10^{6}\,M_{\odot}$; the survival of clusters in the outer Galactic halo (i.e. towards the Magellanic Clouds) but their destruction in the central halo region through tidal disruption and collisions. We examine the implications of this for the constraints on the fraction of dark matter in PBHs from microlensing surveys and gravitational-wave events. Although the clustering of PBHs with the expected mass and radius is unlikely to relax the microlensing limits, the decline of the Galactic rotation curve might do so, allowing much of the dark matter to be in solar-mass PBHs formed at the quantum chromodynamics transition. We also emphasise that binary merger rates must be revised: binaries formed in PBH clusters can dominate the merger rate, which may be compatible with the LIGO-Virgo-KAGRA gravitational-wave limits if PBHs provide the dark matter. More positively, Ultra-Faint Dwarf Galaxies and Little Red Dots might arise through a combination of the seed and Poisson effects. Our conclusions could be modified for PBHs produced from primordial fluctuations with exponential non-Gaussian tails, since the clustering would then exceed the Poissonian prediction, opening up new possibilities to explain dark matter with solar-mass PBHs.