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 capture rate is computed here using the gravitational-focusing collision 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 from r_T. Note: this is the geometric encounter rate, not the loss-cone filling rate — the relaxation-driven loss-cone rate is computed separately in the TDE Rate Calculator tool and will give different values. Compact object capture rates are modified by the fact that WDs/NSs must approach more closely (smaller r_T), with gravitational-wave emission enabling EMRI formation on the final orbit. NS/WD EMRIs (Extreme Mass Ratio Inspirals) are GW-driven and have rates that scale steeply with M_BH.

The Hills mass M_Hills ≈ 10^8 (R_*/R_☉)^(3/2) (M_*/M_☉)^(-1) 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 signatures: a main-sequence TDE produces a flare with L_peak ~ L_Edd for weeks to months. WD tidal captures produce quasi-periodic eruptions (QPEs) as the partial debris stream impacts the accretion disk. NS inspirals are quiet until the final coalescence, which could produce a short gamma-ray burst and detectable gravitational waves in future space GW detectors (LISA, TianQin).