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Formation and growth of intermediate-mass black holes in dense star clusters: Lessons from N-body and MOCCA Monte Carlo Simulations

Abbas Askar, Marcelo C. Vergara, Sohaib Ali

TL;DR

Dense star clusters are viable environments for forming intermediate-mass black holes (IMBHs) via collisional runaway that creates a very massive star (VMS) which collapses to an IMBH within a few million years. The study employs two complementary numerical approaches—direct N-body simulations and MOCCA Monte Carlo methods—to model VMS formation and IMBH growth through mergers with black holes, stars, and remnants. The results show IMBHs of order $10^3$–$10^4$ solar masses can form within ≤5 Myr under extreme densities, with subsequent growth yielding detectable gravitational-wave and tidal-disruption signatures, including light IMRIs within next-generation detector bands. These findings provide testable predictions for gravitational-wave and transient surveys and highlight the value of cross-validating N-body and Monte Carlo approaches to refine IMBH formation scenarios.

Abstract

Dense star clusters are promising nurseries for the formation and growth of intermediate-mass black holes (IMBHs; $\sim 10^2-10^5\,\mathrm{M}_{\odot}$), with increasing observational evidence pointing to their presence in massive star clusters and stripped dwarf-galaxy nuclei. During the early evolution of compact clusters, massive stars can rapidly segregate to the center, where frequent collisions may trigger the runaway growth of a very massive star (VMS). This object can subsequently collapse to form an IMBH or merge with a stellar-mass black hole. We carried out direct $N$-body and Monte Carlo simulations of star clusters with initial core densities between $10^6$ to $4\times 10^8\,\mathrm{M}_{\odot}\,\mathrm{pc}^{-3}$ and total masses of $5.9\times 10^5$ and $1.3\times 10^6\,\mathrm{M}_{\odot}$. These models show that IMBHs of $10^3-10^4\,\mathrm{M}_{\odot}$ can form within $\leq 5$ Myr through the runaway collision channel. At later times, the IMBHs continue to grow through mergers with black holes, stars, and compact remnants, providing predictions testable with future gravitational-wave and transient surveys.

Formation and growth of intermediate-mass black holes in dense star clusters: Lessons from N-body and MOCCA Monte Carlo Simulations

TL;DR

Dense star clusters are viable environments for forming intermediate-mass black holes (IMBHs) via collisional runaway that creates a very massive star (VMS) which collapses to an IMBH within a few million years. The study employs two complementary numerical approaches—direct N-body simulations and MOCCA Monte Carlo methods—to model VMS formation and IMBH growth through mergers with black holes, stars, and remnants. The results show IMBHs of order – solar masses can form within ≤5 Myr under extreme densities, with subsequent growth yielding detectable gravitational-wave and tidal-disruption signatures, including light IMRIs within next-generation detector bands. These findings provide testable predictions for gravitational-wave and transient surveys and highlight the value of cross-validating N-body and Monte Carlo approaches to refine IMBH formation scenarios.

Abstract

Dense star clusters are promising nurseries for the formation and growth of intermediate-mass black holes (IMBHs; ), with increasing observational evidence pointing to their presence in massive star clusters and stripped dwarf-galaxy nuclei. During the early evolution of compact clusters, massive stars can rapidly segregate to the center, where frequent collisions may trigger the runaway growth of a very massive star (VMS). This object can subsequently collapse to form an IMBH or merge with a stellar-mass black hole. We carried out direct -body and Monte Carlo simulations of star clusters with initial core densities between to and total masses of and . These models show that IMBHs of can form within Myr through the runaway collision channel. At later times, the IMBHs continue to grow through mergers with black holes, stars, and compact remnants, providing predictions testable with future gravitational-wave and transient surveys.

Paper Structure

This paper contains 4 sections, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. First study: Million-body compact cluster model
  3. Second study: MOCCA simulations of dense clusters
  4. Conclusions and Outlook

Figures (2)

  • Figure 1: Formation and growth of IMBHs in MOCCA models. Left: rapid seeding via VMS–sBH collisions and early sBH mergers. Right: long-term growth from MS stars, WDs, and BHs.
  • Figure :