Dynamics and merger rate of primordial black holes in a cluster

Abstract

The PBHs clusters can be source 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 significantly 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 at 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 characteristic of the cluster, and then decreases according to the dependence $\mathcal{R}\propto t^{-1.48}$. 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.

References in corpus (15)

• Primordial Black Holes as Dark Matter: Recent Developments
• The merger rate of primordial-black-hole binaries
• Pōniuā'ena: A Luminous $z=7.5$ Quasar Hosting a 1.5 Billion Solar Mass Black Hole
• Primordial black hole formation from an axion-like curvaton model
• Testing scenarios of primordial black holes being the seeds of supermassive black holes by ultracompact minihalos and CMB $\mu$-distortions
• Solving puzzles of GW150914 by primordial black holes
• Primordial Black Hole Dark Matter and the LIGO/Virgo observations
• Star Clusters with Primordial Binaries: I. Dynamical Evolution of Isolated Models
• A new Fokker-Planck approach for relaxation-driven evolution of galactic nuclei
• The stochastic gravitational wave background from close hyperbolic encounters of primordial black holes in dense clusters
• Reconstruction of Primordial Power Spectrum of curvature perturbation from the merger rate of Primordial Black Hole Binaries
• Establishing the Non-Primordial Origin of Black Hole-Neutron Star Mergers
• Strong clustering of primordial black holes from Affleck-Dine mechanism
• Mergers of primordial black holes in extreme clusters and the $H_0$ tension
• The Merger Rate of Black Holes in a Primordial Black Hole Cluster

Cited by in corpus (1)

• Influence of early dark matter halos on the primordial black holes merger rate