IMBH Seed Formation Calculator

What this tool models

Two channels can seed an IMBH in a dense stellar cluster. Runaway stellar collisions require a short core-collapse timescale (≲3 Myr) and low metallicity so that stellar winds do not ablate the colliding stars. Under those conditions a very massive star (VMS) exceeding 10³–10⁴ M☉ forms within ~1 Myr and collapses directly into an IMBH. Repeated black-hole mergers are slower but universally available: stellar-mass BHs (50–200 M☉) sink to the core through dynamical friction and merge through gravitational-wave radiation, building mass hierarchically over many Gyr.

The growth trajectory uses a power-law model calibrated to the Monte Carlo N-body results of González Prieto et al. (2025), who find that OC-like clusters starting with 500–5,000 M☉ seeds reach ~50,000 M☉ after 12 Gyr primarily through loss-cone stellar tidal disruption events and compact-object accretion.

Physics approximations

The half-mass relaxation time uses the Spitzer (1987) formula: t_rh ≈ 0.138 N / ln(0.4N) × √(r_h³/GM_cl), with mean stellar mass 0.6 M☉. Core collapse is estimated at 1.5% of t_rh (Portegies Zwart & McMillan 2002). Core density assumes the inner 10% of the half-mass radius contains 25% of the cluster mass. The growth model M(t) is a calibrated power law anchored to the González Prieto et al. Monte Carlo results; it is illustrative, not a substitute for full N-body integration.

Key references

González Prieto, Rodriguez & Cabrera (2025), ApJL, arXiv:2507.06316 — Monte Carlo N-body models of OC with loss-cone dynamics; seeds of 500–5,000 M☉ grow to ~50,000 M☉ in 12 Gyr.

Vergara et al. (2025), A&A, arXiv:2505.07491 — Direct N-body simulations showing runaway collisions form VMS >50,000 M☉ within 1 Myr in dense, metal-poor clusters.

Mapelli et al. (2026), A&A, doi:10.1051/0004-6361/202557230 — Parameter-space study of IMBH formation across young clusters, globular clusters, and nuclear star clusters.