IMBH Brownian Wander Predictor

Given IMBH mass and stellar cusp, compute expected proper-motion wander and compare against Gaia DR4 and Roman Space Telescope astrometric floors.

🔬 Merritt 2001 equipartition 🔭 Gaia DR4 / Roman forecasts
The IMBH mass tension — Häberle et al. 2024 (Nature): ≥ 8,200 M☉ lower bound vs. Bañares-Hernández et al. 2025 (A&A 693 A104): ≤ 6,000 M☉ upper bound — predicts very different astrometric wander signatures. Use this tool to see how each scenario maps onto Gaia DR4 and Roman sensitivity.
OC's IMBH candidate, if it exists, is not stationary — it undergoes Brownian motion driven by gravitational kicks from surrounding stars. Merritt 2001 showed that energy equipartition gives a clean prediction for the IMBH's wandering speed: v_BH = σ × √(⟨m_★⟩ / M_BH). For a 8,200 M☉ black hole in OC's σ = 20 km/s core with ⟨m_★⟩ ≈ 0.5 M☉, this yields ~0.156 km/s (1D) — a proper motion of ~6.07 µas/yr at OC's distance. Gaia DR4 (expected 2026) may just reach this level of precision.
Inputs
8,200 M☉
20.0 km/s
0.50 M☉
5.43 kpc
10.0 yr
Outputs — Slider scenario
v_BH 1D (equipartition) —km/s
v_BH 3D —km/s
Proper motion μ_BH —µas/yr
Wander Δθ over baseline —µas
Gaia DR4 verdict —
Roman Space Telescope —
ngEHT / VLBI (~10 µas) —
Mass Tension: Häberle vs. Bañares — Live Comparison

Using current σ_★ and D from sliders. Mass fixed at each scenario value.

Häberle 2024 (8,200 M☉)
v_BH 1D—
μ (µas/yr)—
Δθ over T—
Gaia: —
Roman: —
Bañares 2025 (6,000 M☉)
v_BH 1D—
μ (µas/yr)—
Δθ over T—
Gaia: —
Roman: —

Equipartition derivation

Merritt (2001) showed that an IMBH embedded in a stellar cusp will reach equipartition with the surrounding stars. By kinetic energy equipartition: M_BH × ⟨v_BH²⟩ = ⟨m_★⟩ × σ_★² (one-dimensional, each component). This gives:

v_BH_rms = σ_★ × √(⟨m_★⟩ / M_BH)

The transverse (sky-plane) velocity component is v_t = v_BH_rms (one dimension). Proper motion in µas/yr uses the conversion: μ[µas/yr] = v_t[km/s] / (4.74 × D[kpc]) × 1000.

Instrument thresholds used

Gaia DR4: single-epoch proper motion floor ~15 µas/yr for bright stars; systematic photocenter ~30 µas over 5-year baseline. Detectable if μ > 15 µas/yr, marginal 5–15, undetectable <5.

Roman Space Telescope: projected narrow-field astrometry ~1 µas/yr. Detectable if μ > 1 µas/yr, marginal 0.3–1.

ngEHT/VLBI: ~10 µas absolute astrometry floor for the brightest compact sources.

Citations

Merritt 2001 (AJ 121:2385) — Brownian motion of massive black holes in stellar cusps. Häberle et al. 2024 (Nature 631:285) — IMBH mass ≥ 8,200 M☉ from fast-star kinematics. Bañares-Hernández et al. 2025 (A&A 693:A104) — IMBH mass upper bound ≤ 6,000 M☉ from proper motions. Gaia Collaboration 2022 (A&A 616:A1) — Gaia astrometry performance.