Convert a target mass resolution into a concrete observing budget: required astrometric precision, number of epochs, telescope-hours, and cadence. Feeds directly into the proposal templates.
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 3.3 arcsec at 5.2 kpc. Crowded-field astrometry in this region demands either space-based imaging (Roman) or extreme-AO ground-based (ELT-MICADO).
Distance adopted: 5.2 kpc · Core radius: 0.08 pc · Velocity dispersion: ~20 km/s · All figures cite measurements.js.
| Parameter | Value | Notes |
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Required precision is derived from the target mass resolution via the virial mass estimator: σ² ∝ M/r, so ΔM/M ≈ 2Δσ/σ. Converting to astrometric precision: Δσ (km/s) → Δμ (μas/yr) via proper-motion dispersion at the cluster distance. The number of epochs needed is set by requiring that the cumulative proper-motion baseline √(N_epochs × T_epoch²) reaches the required precision per star, then divided by √(N_stars) for ensemble averaging.
Exposure time per field is instrument-dependent. Roman: ~15 min per field to reach S/N > 100 on G ≈ 18 stars. ELT-MICADO: ~30 min per AO-corrected field. Gaia: fixed by mission cadence.
Roman: single-epoch precision 15 μas (inner-field crowded-field estimate), 15 min/epoch, 10,000 usable stars in core mosaic.
ELT-MICADO: single-epoch precision 80 μas (crowded-field AO astrometry), 30 min/epoch, 2,000 resolvable stars in inner core.
Gaia DR4: single-epoch precision 40 μas (bright stars, G~15, degraded for crowding), fixed cadence, 5-year baseline included.