A Newtonian sandbox for test-particle orbits around an IMBH, plus a Häberle-mode fit against the seven fast stars from the 2024 proper-motion paper. Watch what mass is required to bind those stars to compact central radii.
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The orbit simulation needs the wider viewport and pointer interaction.
Read the description instead →This is a Newtonian gravity sandbox using the Velocity Verlet method. Each test particle obeys a = −GM r̂ / r² with the BH treated as a fixed point mass. Verlet is second-order accurate and conserves energy well over long integrations, which matters for orbital simulations where Euler integration would let orbits drift outward systematically. The tool uses dimensionless units internally (length in r_g, time in r_g/c) and converts back to physical units for display.
Stable orbits (teal) trace closed ellipses. Particles drifting inside the marginally stable orbit (3 r_s = 6 r_g for Schwarzschild) plunge in monotonically and are marked red. Particles with too much energy escape the simulation box and are marked amber. Watching the distribution evolve makes the inner boundary of stable orbits visible.
The integrator does not include GR corrections. Near the ISCO, real Schwarzschild orbits precess and become unstable in a way the Newtonian sandbox can't reproduce. The 6 r_g "ISCO" boundary drawn on the canvas is the GR value flagged onto a Newtonian simulation — useful for orientation, not for prediction.
The Häberle et al. 2024 result is built on seven fast-moving stars in the central 3″ of Omega Centauri, whose proper-motion magnitudes require a compact enclosed mass of at least 8,200 M☉. This tool's Häberle mode places stars at representative positions and assigns each a speed; for the current M_BH slider, it computes the Keplerian circular-orbit speed at each star's radius and shows residuals between observed and model speeds. Low M_BH leaves large residuals (stars moving too fast for the predicted gravity); the right M_BH minimises them.
Important: the seven stars' positions and speeds here are illustrative — chosen to reproduce the qualitative Häberle result, not exact published values. The real fit uses six-parameter astrometry (positions in two epochs plus errors) and includes anisotropic velocity dispersion priors. The point of this tool is to let the visitor feel the mass-fitting argument, not to reproduce the publication.
An IMBH inside a host cluster of mass M_cluster has a Hills (tidal) sphere of radius r_Hills ≈ r·(M_BH/(3 M_cluster))^(1/3), where r is the IMBH's distance from cluster centre. For OC's hypothetical central IMBH (8,200 M☉) inside a 4×10⁶ M☉ cluster, r_Hills/r ≈ 0.09 — i.e., the IMBH's gravitational dominance extends out to ~9% of its offset from cluster centre. The sandbox doesn't include cluster potential; it treats the BH as the sole gravitating body. Real OC dynamics include both.
Real GC simulations use Hermite-style integrators with regularisation for close encounters. Aarseth's NBODY7/NBODY7++ is the gold standard for ~10⁵-body GC simulations including dynamics, stellar evolution, and binary formation. PETAR (Wang et al. 2020) handles ~10⁶ bodies on GPU clusters. Frontier-scale full-N simulations of OC-mass clusters (4×10⁶ stars) became tractable in 2023–2024 and are the technical basis for Baumgardt-style IMBH consistency tests. This tool's Velocity Verlet sandbox is many orders of magnitude simpler — it lacks softening, binary handling, and stellar evolution — and is intended for visual intuition only.
Häberle et al. 2024 identified 7 stars in OC's central 3″ × 3″ with measured proper-motion speeds of ~70–110 km/s. At 5.4 kpc this corresponds to ~3–4 mas/yr transverse motion — at the edge of HST's astrometric capability with ~20 years of multi-epoch imaging. The stars are tagged S1 through S7 in the paper. Their high speeds require a compact enclosed mass within ~0.04 pc, yielding the >8,200 M☉ lower bound. The Bañares 2025 counter-analysis argues some of these stars may be foreground or have systematic position errors, which would shift the inferred mass downward.
The sandbox uses pure Newtonian gravity, which is accurate to ~1% at r > 100 r_g and fails badly only inside the ISCO. For OC's candidate IMBH (8,200 M☉), r_g ≈ 1.2×10⁷ m and the ISCO is ~7×10⁷ m ≈ 7×10⁻¹⁰ pc. The fast stars sit at ~0.04 pc ≈ 6×10⁷ r_g — vastly outside the GR-sensitive zone. Schwarzschild-precession corrections are ~10⁻¹⁵ per orbit. Real OC orbit-fitting uses Newtonian gravity exclusively, with cluster-potential terms (König-Plummer or Wilson profile) layered in.