1 Constraints 2 Evidence 3 Microlensing 4 Timeline 5 Campaign 6 Proposals

Workflow · Peer-reviewed chain

Settle the ω Cen IMBH Question

Two published measurements flatly contradict each other. Stellar kinematics demand a central mass of at least 8,200 M☉. Pulsar timing allows no more than 6,000 M☉. The gap is not a rounding error — it is a 2,200 M☉ tension with no agreed resolution. This workflow chains six tools to build the case from first principles: what do we know, how confident are we, what measurement would settle it, and what would that observation actually cost?

≥ 8,200 M☉
Häberle et al. 2024 · Nature 631:285
Stellar kinematic lower bound
≤ 6,000 M☉
Bañares-Hernández et al. 2025 · A&A 693:A104
Pulsar timing upper bound
NGC 5139 · Omega Centauri d = 5.2 kpc IMBH candidate Bayesian three-hypothesis framework Register: peer-reviewed
1
Stage 1 — First tool
Stack the mass constraints
constraint-stacker

Before reasoning about evidence, establish what the mass constraints are. The Constraint Stacker plots the five independent methods — stellar kinematics, pulsar timing, N-body limits, proper-motion dispersion, and accretion limits — on a single axis and marks the overlap region (or the gap, as is the case here).

Key output: the gap between the kinematic lower bound and the pulsar upper bound is not a statistical outlier. It sits at 2,200 M☉ — larger than the individual uncertainties. Something is methodologically inconsistent between the two measurements.

What to look for
Kinematic lower bound: 8,200 M☉ (Häberle 2024)
Pulsar upper bound: 6,000 M☉ (Bañares 2025)
Overlap: none — the bounds exclude each other at >1σ
Best compromise: treat midpoint 7,100 M☉ as planning value; never collapse to one number

After exploring the constraints → proceed to Stage 2 to assign Bayesian weight to each line of evidence.

2
Stage 2 — Bayesian aggregation
Weigh all the evidence
evidence-ledger

The Evidence Ledger applies the three-hypothesis Bayesian framework: HIMBH (single IMBH), HDC (dark stellar cluster), HNULL (no central mass). For each evidence line you set two log₁₀ Bayes factors — how much does the data favour IMBH over DC, and how much does it favour any central mass over nothing?

Six evidence lines are pre-loaded with published defaults: stellar kinematics, pulsar timing, proper-motion dispersion, accretion limits, N-body simulations, and astrometric microlensing. Adjust any slider to explore the sensitivity of the posterior to contested inputs.

Default posterior (prior: IMBH 30%, DC 45%, NULL 25%)
HIMBH: ~45–60% depending on microlensing weight
HDC: ~25–40%
HNULL: <10%
The posterior is sensitive to the pulsar BF — the most contested input.

After setting your posterior → proceed to Stage 3 to understand the astrometric microlensing line of evidence independently.

3
Stage 3 — Independent check
Simulate astrometric microlensing
astrometric-microlensing

Astrometric microlensing is the most direct mass measurement that bypasses both kinematic and timing assumptions. When a background star passes within the Einstein radius of the IMBH, its apparent position deflects by a measurable amount — the deflection amplitude directly encodes the lens mass.

This tool calculates the Einstein radius, peak deflection angle, event duration, and astrometric signal amplitude for a lens at the ω Cen distance. It also flags whether the signal is detectable by Gaia, Roman, or ELT-MICADO.

Detectability sketch for M = 7,100 M☉ at d = 5.2 kpc
Einstein radius θE ≈ 3.2 mas
Peak astrometric deflection ≈ 0.6–1.6 mas (impact-parameter dependent)
Detectable by: Roman (yes), ELT-MICADO (yes), Gaia (marginal)
Event duration: months to years — single-epoch programmes will miss events

After microlensing → proceed to Stage 4 to see which instrument reaches decision confidence first.

4
Stage 4 — Decision timeline
Forecast when we settle this
detection-forecast

The Detection Forecast renders a timeline for four instruments — Gaia DR4, Roman, ELT-MICADO, LISA — and marks when each can reach a target confidence level for a given science goal. It treats the two mass bounds as inputs and computes the required mass resolution gap to close at 3σ or 5σ.

Quickest route to 3σ resolution of the tension: ELT-MICADO first light (2028) with an immediate astrometric programme, or Roman from 2029 with a wider-field proper-motion survey. LISA (2037+) would be decisive but is 11 years away.

Key numbers
Required mass resolution to close tension at 3σ: ~1,100 M☉
Required astrometric precision at 5.2 kpc: ~0.15 μas/yr (ensemble, 500 stars)
Gaia DR4 alone: likely insufficient for the inner 0.08 pc (crowding)
Roman: feasible; ELT-MICADO: feasible; LISA: decisive but distant

After the timeline → proceed to Stage 5 to convert the decisive experiment into a concrete observing budget.

5
Stage 5 — Resource planning
Design the observing campaign
observing-campaign-planner

The Observing Campaign Planner takes your instrument choice and science goal from Stage 4 and converts them into a complete resource budget: required astrometric precision per epoch, number of visits, total telescope-hours, cadence, and a traffic-light feasibility assessment.

It caps the stellar sample at the instrument's field-of-view limit and flags marginal cases where a longer baseline or additional instrument is needed. The output directly drives the observational proposal templates.

Illustrative Roman campaign to resolve tension
Precision needed: ~0.15 μas/yr (ensemble 500 stars)
Roman single-epoch: 15 μas → 15 epochs needed at 6-month cadence
Total time: ~3.75 hours · Campaign: ~7 years
Feasibility: AMBER — requires long baseline; combine with ELT for faster resolution

After designing the campaign → proceed to Stage 6 to explore the existing proposal templates.

6
Stage 6 — Submit
Observational proposals
proposals

Eleven detailed observational proposal templates cover the full instrument portfolio: ELT-MICADO crowded-field astrometry, Roman proper-motion survey, JWST infrared imaging, MeerKAT pulsar timing, LISA gravitational-wave detection, and more. Each proposal includes scientific justification, technical feasibility, requested time, and explicit links to the tension this workflow has quantified.

The Campaign Planner output (Stage 5) populates the resource tables in these proposals directly. If you arrived here from Stage 5, the numbers are consistent.

Workflow complete. Return to any stage to adjust assumptions, or explore the related workflows below.

What would it take to settle this?

The kinematic–pulsar tension is real and methodologically deep. No single adjustment to either measurement collapses it. Settling the ω Cen IMBH question at 3σ confidence requires an independent astrometric mass measurement with precision below ~1,100 M☉ — achievable with Roman or ELT-MICADO but not Gaia alone. An astrometric microlensing detection would be decisive in a single event.

Until that measurement arrives, the Bayesian posterior sits near 50% for HIMBH — the least satisfying scientific position. The observational window is 2027–2032: the instruments exist, the science case is funded, and the cluster is bright enough. The question is whether the community prioritises the campaign.

Workflow version 1.0 · 2026-06-10 · All tools: Code MIT · Prose CC BY 4.0 · The Omega Centauri Society