🔬 DRAFT RESEARCH PROPOSAL · ADAPTIVE OPTICS ASTROMETRY · ELT/MICADO

ELT/MICADO High-Resolution Proper-Motion Astrometry of Omega Centauri's Fast-Moving Stars

Direct orbital acceleration measurements of the seven Häberle et al. fast-moving stars using ELT's MICADO AO imager — providing independent IMBH mass and orbit constraints at ~5–10 mas angular resolution · Working draft · April 2026

1. Scientific Rationale

1.1 The Limitation of Current Proper-Motion Data

The Häberle et al. (2024) discovery was based on HST proper-motion snapshots: seven stars with velocities exceeding the local escape speed. This establishes a firm lower bound on the central mass (≥8,200 M☉ velocity-only; ≥21,100 M☉ with acceleration constraints at 99% CL), but the existing data cannot yet:

• Detect full orbital curvature (accelerations require multi-epoch measurements spanning years)
• Constrain individual stellar orbits (semi-major axes, eccentricities, inclinations)
• Measure the IMBH mass independently of dynamical modelling assumptions
• Distinguish a single point mass from a concentrated dark cluster via orbital geometry

ELT/MICADO with adaptive optics will provide ~5–10 milliarcsecond resolution — 5–10× better than HST — enabling direct detection of orbital accelerations and, with a sufficient baseline, orbital closure for the tightest-orbiting stars.

1.2 Science Goals

1. Orbital acceleration detection: At r ~ 0.08 pc from a 20,000–50,000 M☉ mass, stars accelerate at ~0.014–0.034 km/s/yr (GM/r²; see §2.1 correction note). With MICADO's ~0.05 mas astrometric precision per epoch, detection requires either stars at smaller radii, a much larger enclosed mass, or a longer baseline than 3–5 years.
2. Mass constraint independent of stellar kinematics modelling: Orbital closure of even one star provides a direct Keplerian mass measurement with <20% uncertainty.
3. IMBH vs dark cluster discrimination: A single point mass produces a smooth 1/r² acceleration field and consistent orbital period distribution. A dark cluster produces stochastic accelerations and a broader distribution of orbital parameters.

1.3 Why ELT Rather Than HST or JWST

The seven fast stars are crowded within a 3 arcsecond core at 5.49 kpc. HST's diffraction limit (~0.05″ at F814W) is barely sufficient to resolve them individually; JWST's angular resolution is comparable to HST in the NIR. ELT at 39m primary mirror provides ~5 mas diffraction limit in the K-band (2.2 µm) with MICADO's single conjugate AO — a factor of ~10 improvement over existing facilities. This directly enables sub-orbit astrometry.

2. Observation Strategy

2.1 Acceleration Detection Threshold

3. Falsification Framework

4. Work Plan

5. Budget

6. References