Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters

Abstract

In arXiv:2507.07171, we demonstrate that the high-redshift supermassive black holes in the so-called "little red dots" discovered by James Webb Space Telescope (JWST) can be explained by the primordial black hole (PBH) clustering on small scales. In this paper, we present a comprehensive simulation of the successive PBH mergers within a cluster by solving the Smoluchowski coagulation equation. We derive the coagulation kernel considering both cases with and without the effects of mass segregation. Then we employ the Monte Carlo method to solve the equation, implementing the full-conditioning scheme using the discrete inverse transformation method. Our simulations determine the runaway timescales of clusters and the mass population evolution of PBHs across a wide range of cosmic redshifts, depending on the number of PBHs within the cluster and the associated density.

38 pages, 10 figures; minor corrections on Fig.3-5, version accepted for publication in JCAP

References in corpus (79)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Detailed Decomposition of Galaxy Images. II. Beyond Axisymmetric Models
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Did LIGO detect dark matter?
• Primordial Black Holes as Dark Matter
• Primordial Black Hole Scenario for the Gravitational-Wave Event GW150914
• Taiji Program: Gravitational-Wave Sources
• The merger rate of primordial-black-hole binaries
• The TianQin project: current progress on science and technology
• JADES. The diverse population of infant Black Holes at 4<z<11: merging, tiny, poor, but mighty
• Formation and Evolution of Primordial Black Hole Binaries in the Early Universe
• Gravitational Waves from Primordial Black Hole Mergers
• Primordial Black Holes as Generators of Cosmic Structures
• Detecting a gravitational-wave background with next-generation space interferometers
• JWST CEERS & JADES Active Galaxies at z = 4-7 Violate the Local $M_{\bullet }-M_{\star }$ Relation at $>3\sigma$: Implications for Low-Mass Black Holes and Seeding Models
• Surface Brightness Profile of the Milky Way's Nuclear Star Cluster
• Clusters of primordial black holes
• Primordial Black Holes from Inflation and non-Gaussianity
• Primordial Structure of Massive Black Hole Clusters
• Primordial black holes in non-Gaussian regimes
• Primordial black holes as a tool for constraining non-Gaussianity
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• Early Structure Formation in $\Lambda$PBH Cosmologies
• Bayesian analysis of LIGO-Virgo mergers: Primordial vs. astrophysical black hole populations
• Primordial seeds of supermassive black holes
• Dynamics and Interactions of Binaries and Neutron Stars in Globular Clusters
• Runaway Merging of Black Holes: Analytical Constraint on the Timescale
• Limits on primordial black holes from $\mu$ distortions in cosmic microwave background
• Accelerating early massive galaxy formation with primordial black holes
• Merger Rates of Dark-Matter Haloes
• The Clustering Evolution of Primordial Black Holes
• The Spatial Clustering of Primordial Black Holes
• The Black Hole Mass Function from Gravitational Wave Measurements
• Primordial black holes as biased tracers
• Signatures of non-gaussianity in the isocurvature modes of primordial black hole dark matter
• Correlation function of high-threshold regions and application to the initial small-scale clustering of primordial black holes
• The Science of the Einstein Telescope
• Primordial Black Holes as Dark Matter: Converting Constraints from Monochromatic to Extended Mass Distributions
• Deciphering the JWST spectrum of a 'little red dot' at $z\sim 4.53$: An obscured AGN and its star-forming host
• Primordial black holes from long-range scalar forces and scalar radiative cooling
• Supermassive black holes from primordial black hole seeds
• Primordial black hole merger rates: distributions for multiple LIGO observables
• RUBIES: JWST/NIRSpec Confirmation of an Infrared-luminous, Broad-line Little Red Dot with an Ionized Outflow
• Probing Primordial-Black-Hole Dark Matter with Gravitational Waves
• Self-Consistent Theory of Halo Mergers
• Seeding Supermassive Black Holes with Self-Interacting Dark Matter: A Unified Scenario with Baryons
• Stochastic Coagulation and the Timescale for Runaway Growth
• Initial clustering and the primordial black hole merger rate
• Transmuted Gravity Wave Signals from Primordial Black Holes
• Little red dots as young supermassive black holes in dense ionized cocoons
• Constraints on primordial black holes from LIGO-Virgo-KAGRA O3 events
• Clustering of primordial black holes with non-Gaussian initial fluctuations
• The long-short wavelength mode coupling tightens primordial black hole constraints
• Ruling out Initially Clustered Primordial Black Holes as Dark Matter
• Primordial black hole mergers from three-body interactions
• LIGO/Virgo black holes and dark matter: The effect of spatial clustering
• Early formation of galaxies initiated by clusters of primordial black holes
• Exploring the AGN Fraction of a Sample of JWST's Little Red Dots at $5<z<8$: Overmassive Black Holes Are Strongly Favored
• Clustering of primordial black holes from quantum diffusion during inflation
• Detectability of Gravitational Waves from the Coalescence of Massive Primordial Black Holes with Initial Clustering
• Supermassive Black Hole Merger Rates: Uncertainties from Halo Merger Theory
• Heavy primordial black holes from strongly clustered light black holes
• A black hole in a near-pristine galaxy 700 million years after the Big Bang
• How open is the asteroid-mass primordial black hole window?
• Inhomogeneous non-Gaussianity
• Redshift evolution of primordial black hole merger rate
• Formation of the Little Red Dots from the Core-collapse of Self-interacting Dark Matter Halos
• Primordial black holes: constraints, potential evidence and prospects
• Not-so-little Red Dots: Two massive and dusty starbursts at z~5-7 pushing the limits of star formation discovered by JWST in the COSMOS-Web survey
• Searching for small primordial black holes in planets, asteroids and here on Earth
• Evolution of a black hole cluster in full general relativity
• The properties of primordially-seeded black holes and their hosts in the first billion years: implications for JWST
• Primordial Black Holes as Seeds for Extremely Overmassive AGN Observed by JWST
• Self-Consistent Theory of Halo Mergers - II: CDM Power Spectra
• BlackTHUNDER: Shedding light on a dormant and extreme little red dot at z=8.50
• Primordial Black-Hole-Based Pathways to Little Red Dots
• Gravitational Waves from Primordial Black Hole Dark Matter Spikes
• Direct Collapse Black Hole Candidates from Decaying Dark Matter
• Merger History of Clustered Primordial Black Holes