Abstract
The PBH clusters can be sources of gravitational waves, and the merger rate depends on the spatial distribution of PBHs in the cluster which changes over time. It is well known that gravitational collisional systems experience the core collapse that leads to significant increase of the central density and shrinking of the core. After core collapse, the cluster expands almost self-similarly (i.e., density profile extends in size without changing its shape). These dynamic processes affect the merger rate of PBHs. In this paper, the dynamics of the PBH cluster is considered using the Fokker–Planck equation. We calculate the merger rate of PBHs on cosmic time scales and show that its time dependence has a unique signature. Namely, it grows by about an order of magnitude at the moment of core collapse which depends on the characteristics of the cluster, and then decreases according to the dependence R∝t−1.48. It was obtained for monochromatic and power-law PBH mass distributions with some fixed parameters. Obtained results can be used to test the model of the PBH clusters via observation of gravitational waves at high redshift.
Highlights
The hypothesis of the formation of primordial black holes (PBHs) in the early Universe was proposed in the works [1,2,3]
The PBH clusters can be sources of gravitational waves, and the merger rate depends on the spatial distribution of PBHs in the cluster which changes over time
The merger rate was considered for the PBHs cluster with both the narrow and the wide mass distribution of BHs
Summary
The hypothesis of the formation of primordial black holes (PBHs) in the early Universe was proposed in the works [1,2,3]. This study considers the model of cluster formation due to collapse of domain walls produced as a result of quantum fluctuations of scalar field(s) at the inflation stage [36,37,38] Following this model, a falling power-law mass distribution is assumed here in a wide PBH mass range. The dynamics of a PBHs cluster was considered in the works [22,47,48] with help of the N-body simulation Such calculations are only suitable for clusters with a small number of black holes. The obtained results might be used to test the model of the PBH cluster with the help of a future generation of gravitational waves detectors which will be able to detect black holes mergers at high redshifts. Effects giving constraints on PBHs as DM and constraints themselves in case of PBH clustering should be reconsidered [11]
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