What would Omega Centauri's central stellar proper-motion field look like under a given IMBH mass hypothesis? Renders ~200 test stars in a King-like profile, then assigns each one a velocity from cluster rotation + IMBH Keplerian influence + random dispersion. Toggle to a schematic of the Häberle 2024 observed field for comparison.
This tool is best viewed on a desktop or tablet.
The proper-motion arrow field needs the wider viewport.
Read the description instead →Star positions are sampled from a profile of the form ρ(r) ∝ (1 + (r/r_c)²)^(−3/2) with core radius r_c = 1.5″ — a simplified Plummer-style stand-in for the central few arcsec of a King model. Each star's velocity vector has three additive contributions in the plane of the sky:
1. Cluster rotation. Solid-body in the inner region: v_rot = Ω × r with magnitude scaled so v_rot ≈ 5 km/s at r = 5″. This contributes a gentle global rotational pattern.
2. IMBH Keplerian. For each star, compute distance r' to the IMBH position; then v_kep = √(GM_BH/r') perpendicular to the displacement vector. The sign of the perpendicular is chosen randomly per star (prograde vs retrograde) so the central region shows a swirl rather than a coherent ring. v_kep dominates for stars near the IMBH at high M_BH; vanishes at M_BH = 0.
3. Random dispersion. Isotropic Gaussian with σ = 20 km/s (approximately OC's measured central dispersion). This is the "noise" floor — at low M_BH and away from the IMBH, the field is dominated by this.
It is: a fast, intuitive way to see how the proper-motion signature of a central IMBH scales with mass, and how it compares to the noise floor set by ordinary cluster velocity dispersion. Drag M_BH from 0 to 4×10⁴ and watch the central swirl emerge from the noise.
It isn't: a fit, an inversion of the Häberle measurements, or a generator of synthetic data with realistic per-star measurement errors. It doesn't include anisotropic dispersion, mass segregation, binary contamination, or the multiple-population kinematics that OC actually exhibits. For the real fit against the Häberle seven stars, switch to Orbital Dynamics Lab in Häberle mode.
The "Schematic of Häberle (2024)" view shows a hand-built field that approximates the qualitative shape of the published figure — concentration of stars in the central few arcsec, the seven fast stars highlighted, and an overall rotation pattern. It is not the published dataset; published proper-motion catalogs at this level of detail are released via the oMEGACat collaboration (Sommer et al. 2025) and the original Häberle data products. The toggle is here to let visitors compare the simulation's overall pattern to "what the data sort of looks like" without claiming to reproduce measurements.
The oMEGACat collaboration (Sommer et al. 2025, ApJ; Häberle et al. 2024 Nature 631:285 for the IMBH-focused subset) produced the canonical OC proper-motion dataset by combining ~20 years of HST/ACS and HST/WFC3 imaging. The full release contains 1.4 million stellar proper motions with per-star precision ~50 μas/yr for the brightest sources, dropping to ~200 μas/yr near the faint magnitude limit. The catalog is publicly available through MAST. This tool's ~200-star synthetic field is a vastly simplified stand-in; for the actual published per-star kinematics use the oMEGACat data products directly.
Real OC stellar density follows a King 1962 profile with core radius r_c ≈ 1.4 arcmin (~2.2 pc projected) and tidal radius r_t ≈ 57 arcmin (~90 pc), giving concentration parameter c = log(r_t/r_c) ≈ 1.6. This tool's simplified Plummer-like profile (∝ (1 + (r/r_c)²)^(−3/2)) uses r_c = 1.5″ for the central few-arcsec field of view; the real cluster is much more spatially extended but flatter in density at the centre. King-profile fits are standard practice — Trager, King & Djorgovski 1995 catalogued profiles for ~140 Milky Way GCs.
The seven fast-moving stars in the central 3″ are highlighted in the schematic toggle. Real OC properties: 50% of stars in the inner 1″ have proper-motion magnitudes > 30 km/s (oMEGACat); the central velocity dispersion is ~19–21 km/s (Sommer et al. 2025); the half-light radius is 4.8 pc. The Häberle stars are remarkable not for their absolute speeds but for being concentrated in a small region while moving in different directions — the geometry that requires a central compact mass. The Synthetic Observation tool's simulation gives users a feel for what the proper-motion field would look like; the real data has noise patterns and observational selection effects this simulation deliberately doesn't model.