Four-stage cascade: cluster orbit → tidal stripping → IMBH feeding rate → BZ power budget over OC's remaining lifetime. How many billion years does the civilisation have?
Omega Centauri orbits the Milky Way on a retrograde, mildly eccentric orbit with a period of ~300 Myr. Each pericentre passage strips mass from the cluster. Gaia DR3 proper motions (Vasiliev & Baumgardt 2021) constrain the current pericentre distance to ~1.2 kpc.
At each pericentre, the Milky Way's tidal field strips the outermost stars. The fractional mass loss scales with (r_peri/r_tidal)³ where r_tidal ~ 100 pc is OC's current tidal radius. Baumgardt & Hilker (2018) place the current cluster mass at ~3.5–4.5 × 10⁶ M☉.
As the cluster loses mass, the tidal capture rate (proportional to stellar density squared × cluster mass) decreases. The IMBH grows until the cluster runs out of stars. Total mass accreted by dissolution determines whether spin-up to a★ = 0.95 is achievable before the fuel runs out.
How much BZ energy is available over the cluster's remaining engineerable lifetime? The power increases as spin-up proceeds, then decreases as the cluster loses fuel. This stage assumes spin-up is completed and computes an upper-bound on total extractable energy over T_diss years at the final spin. BZ power scales steeply: P ∝ B² M² a²/(1+√(1−a²))².
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