OC Dissolution Timeline

Given current cluster mass, orbital period, tidal stripping rate, and two-body relaxation time, compute OC's future mass curve and dissolution epoch.

🔬 Established cluster dynamics 🔭 OC orbital constraints
Omega Centauri is currently losing mass to two competing processes: tidal stripping at each Galactic pericentre passage (~300 Myr period, ~1.2 kpc pericentre), and slow two-body evaporation driven by stellar gravitational encounters (relaxation time ~14 Gyr). Baumgardt & Hilker 2018 place the current cluster mass at 3.5–4.5 × 10⁶ M☉; Gieles et al. 2021 estimate the cluster will survive for another ~10–20 Gyr under nominal conditions. When dissolution occurs, OC's IMBH — if it exists — becomes a bare wandering black hole in the Milky Way halo.
Inputs
4.00×10⁶ M☉
300 Myr
3.0%
14.0 Gyr
8,200 M☉
Outputs
Pericentre passages remaining —
Half-mass time T₁/₂ —Gyr
Dissolution time (1% threshold) —Gyr
Mass at T+1 Gyr —
Mass at T+5 Gyr —
Mass at T+10 Gyr —
IMBH Brownian wander velocity —km/s
Computing…

Mass loss model

Two processes deplete the cluster mass simultaneously. Tidal stripping removes a fraction f_strip of the remaining mass at each pericentre passage. After i passages, the tidal contribution gives M_tidal(i) = M_cl × (1 − f_strip)^i. Two-body evaporation is a continuous exponential: M_evap(t) = exp(−t / t_rh), where t_rh is the half-mass relaxation time. Combined:

M(t) = M_cl × (1 − f_strip)^(t/T_orb) × exp(−t / t_rh)

This treats the number of pericentre passages as a continuous variable (t/T_orb), which is an approximation; the discrete version produces a staircase that averages to the same curve.

Dissolution thresholds

T_diss(1%) is the smallest t where M(t)/M_cl < 0.01. T₁/₂ is where M(t)/M_cl < 0.5. These are solved numerically by scanning t from 0 to 50 Gyr in 10 Myr steps.

IMBH Brownian motion

While the cluster exists, the IMBH undergoes energy-equipartition Brownian motion (Merritt 2001): v_BH = σ × √(⟨m_★⟩ / M_BH), where σ ~ 20 km/s and ⟨m_★⟩ ~ 0.5 M☉. After dissolution, the stellar restoring force vanishes and the IMBH wanders freely through the Galactic halo at a velocity comparable to its orbital speed in the Milky Way (~100–200 km/s).

Citations

Baumgardt & Makino 2003 (ApJ 600:204) — N-body dissolution timescales for tidally limited clusters. King 1962 (AJ 67:471) — tidal radius and King profile for globular clusters. Baumgardt & Hilker 2018 (MNRAS 478:1520) — photometric mass for Omega Centauri: 3.55 × 10⁶ M☉. Gieles et al. 2021 (MNRAS 507:4788) — OC survival timescale and tidal stripping. Merritt 2001 (AJ 121:2385) — Brownian motion of IMBH in stellar cusp.