Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters
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arXiv
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2026
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| author | Zhang, Borui Feng, Wei-Xiang An, Haipeng |
| author_facet | Zhang, Borui Feng, Wei-Xiang An, Haipeng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_01684 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters Zhang, Borui Feng, Wei-Xiang An, Haipeng Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Computational Physics 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. |
| title | Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Computational Physics |
| url | https://arxiv.org/abs/2604.01684 |