OCS / Tools / Observing Campaign Planner
Forecast the direct astrometric acceleration test on ω Cen's fast stars: the GM/r² signal versus the least-squares curvature sensitivity of Paper C §5.3, per facility and baseline. The honest answer today is 0.21σ; this page quantifies when (and whether) that changes.
The ω Cen IMBH question has two irreconcilable published bounds: ≥ 8,200 M☉ (stellar kinematics, Häberle 2024) and ≤ 6,000 M☉ (pulsar timing, Bañares 2025). Closing the 2,200 M☉ gap requires an independent astrometric measurement with precision well below that mass window.
The key technical challenge is the inner 0.08 pc — only about 3.0 arcsec at 5.49 kpc. Crowded-field astrometry in this region demands either space-based imaging (Roman) or extreme-AO ground-based (ELT-MICADO).
Distance adopted: 5.49 kpc · Core radius: 0.08 pc · Velocity dispersion: ~18.2 km/s · All figures cite measurements.js.
| Parameter | Value | Notes |
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This is a direct port of the astrometric estimator of Paper C §5.3 (Campaign paper), which supersedes this page's original mass-resolution model. The signal is the quadrupole-beam acceleration a = GM/r² of a central mass at the target star's projected radius, expressed in mas/yr² at the cluster distance (mean projection factors of order unity absorbed). The sensitivity is one least-squares chain: for existing catalogues the catalogue's own proper-motion precision fixes the curvature term through σ_a = 7.75 σ_μ/T (Paper C eq. 3, third form), with archive extension scaled as T^-2.5; for facilities without a catalogue the uniform-cadence chain σ_a = 26.83 σ_pos/(√N T²) at 2 epochs/yr applies. Both give S/N ∝ T^2.5, which is how the goal-baseline extrapolation works.
The per-star coherent acceleration problem is not reduced by averaging many stars: the old √N_stars ensemble claim is gone, as is the epoch-count "feasible in 3 epochs" verdict. Paper C's calibrated conclusion stands: the nominal 2×10⁴ M☉ signal measures 0.21σ on the oMEGACat catalogue (σ_μ = 6.6 μas/yr at T = 20 yr) and crosses 1σ only at T ≈ 38 yr, around 2040, which is why the campaign's decision-grade astrometry routes through photocentric-wander and reference-frame measurements instead.
oMEGACat: existing catalogue, σ_μ = 6.6 μas/yr inside r < 1.5′ on a 20-yr baseline (Haberle et al. 2024, oMEGACat II); chain form, no assumed cadence.
Roman: 15 μas/epoch forward forecast. ELT-MICADO: 80 μas/epoch. Gaia DR4: 40 μas/epoch. Custom: state either a catalogue proper-motion precision (chain form) or a per-epoch precision (forward form).