Tidal Capture Rate

The tidal disruption radius for a star of mass M_* and radius R_* is r_T = R_* (M_BH/M_*)^(1/3). A tidal disruption event (TDE) occurs when a star's orbit brings it within r_T. For compact objects (white dwarfs, neutron stars), r_T is much smaller — a WD can survive inside a main-sequence TDE radius and instead be tidally captured into a tight, circularizing orbit.

The rate computed on this page is the gravitational-focusing encounter rate: Γ ≈ n × π r_T² × (1 + v_esc²/σ²) × σ, where n is the stellar number density and v_esc is the escape speed at r_T. It is an encounter rate only — the relaxation-driven loss-cone flux, the disruption/capture decision, gravitational-wave capture and the inspiral stage all have their own physics and efficiencies that this page does not model (a previous version mislabelled it and per-stage "rates" derived from it by bare factors; removed 2026-09-24, audit P0-13). The tidal-radius grid above carries the real geometric decisions: r_T compared with r_S (swallow) and the Hills mass per object type.

The Hills mass M_Hills ≈ 10^8 (R_*/R_☉)^(3/2) (M_*/M_☉)^(-1/2) M_☉ is the IMBH mass above which main-sequence stars are swallowed whole (tidal radius inside the Schwarzschild radius). For ωCen's IMBH at 6,000–8,200 M_☉, we are well below the Hills mass for main-sequence stars, but a solar-type star's tidal radius is only ~10–20 Schwarzschild radii — partial disruptions are likely. For white dwarfs, the tidal radius is comparable to the Schwarzschild radius for M_BH ≳ 10^5 M_☉, so WDs are viable targets for ωCen's IMBH.

X-ray / GW signatures of the distinct downstream stages (MS TDE flares with L_peak ~ L_Edd and t^-5/3 decay, WD capture QPEs, NS EMRI chirps and possible short GRBs) are real astrophysics but are not predicted by this page's encounter rate — see the TDE Rate Calculator for a loss-cone treatment.