For a given object falling toward a black hole, is r_ISCO outside the tidal disruption radius (object swallowed whole, no flare) or inside it (object shredded, bright TDE flare)? The crossover BH mass is the headline number.
The tidal disruption radius is where the differential gravity across the object's diameter exceeds the object's self-gravity. The order-of-magnitude expression is r_td ≈ R_obj · (M_BH / M_obj)^(1/3). The leading numerical coefficient depends on the object's internal structure and what counts as "disruption" — for self-gravitating fluid bodies (stars), Hills (1975) and Rees (1988) give a coefficient of ~1.0 to ~2.4 depending on which criterion you use. This tool uses the coefficient 1 throughout, so quoted values should be read as order-of-magnitude.
The ISCO radius uses the exact Kerr prograde formula (Bardeen, Press & Teukolsky 1972): r_ISCO/r_g = 3 + Z₂ − √((3−Z₁)(3+Z₁+2Z₂)), where Z₁ = 1 + (1−a²)^(1/3) · ((1+a)^(1/3) + (1−a)^(1/3)) and Z₂ = √(3a² + Z₁²). At a = 0 this gives 6 r_g (the Schwarzschild ISCO); at a = 0.998 it gives ~1.24 r_g; at a = 1 it gives r_g.
r_td > r_ISCO: the object is shredded outside the ISCO. Tidal forces overcome self-gravity, the object spreads into a stream of gas, half falls back onto the BH, and accretion produces a bright transient flare — a Tidal Disruption Event (TDE). Hundreds have been observed; ASAS-SN and ZTF discover several per year.
r_ISCO > r_td: the object crosses the ISCO before tidal forces can shred it. It falls in whole — no spreading, no flare, no electromagnetic signature beyond the brief gravitational disturbance. This is the regime for very dense or very compact objects (white dwarfs, neutron stars) falling onto supermassive black holes.
Setting r_td = r_ISCO and solving for M_BH gives the crossover: above this BH mass, the object falls in whole; below it, the object is shredded. The crossover depends on the object's mean density (denser objects can survive closer to the horizon) and the BH's spin (higher spin pulls ISCO inward, increasing the range where the object can survive).
OC's candidate IMBH (~8,200 M☉) would tidally disrupt essentially any stellar-mass object that strayed close enough — Sun-like stars get shredded at any IMBH mass below ~10⁷ M☉, and even white dwarfs are shredded below ~3×10⁴ M☉. The corollary: an active IMBH in OC should produce TDEs occasionally as cluster stars wander in. The absence of detected optical/X-ray TDEs from OC's centre is a (weak) constraint on either (a) the IMBH mass or (b) the rate at which stars are scattered onto plunging orbits.
Material strength. The Hills/Rees formula assumes self-gravitating fluid bodies (stars, gas giants). Solid bodies held together by material strength — rocky planets, asteroids, spacecraft — survive much deeper plunges than the formula predicts, because their tidal disruption is set by yield stress vs. tidal strain, not gravity vs. tidal differential. For the "Small body" preset specifically, the Hills-formula crossover mass shown here is an overestimate; a real 10 m chondritic rock would survive far closer to the horizon than the threshold computed here.
Relativistic corrections to the tidal radius (Servin & Kesden 2017) shift the value by ~10–30% near maximally spinning holes — small compared to the order-of-magnitude nature of the basic formula. Penetration factor (how deep the object plunges relative to r_td) determines flare brightness but not the threshold. Spin-axis orientation matters for Kerr ISCO selection (prograde vs. retrograde); this tool assumes prograde throughout.
The first confirmed stellar TDE was NGC 5905 (Bade, Komossa & Dahlem 1996) via soft X-ray flare. Modern surveys discover several TDEs per year: ASAS-SN has reported ~30 since 2014; ZTF reported ~40 since 2018; the Vera Rubin LSST (first light expected 2026) is forecast to discover ~10⁰⁰⁰ TDEs in its 10-year survey. Bolometric peak luminosities range from 10⁴⁴ to 10⁴⁵ erg/s — comparable to Type Ia supernovae. Notable individual events: AT2019qiz (closest TDE at 65 Mpc), AT2019dsg (multi-messenger candidate with IceCube neutrino), AT2022cmc (jetted TDE with relativistic outflow). The Hills mass at which Sun-like stars are swallowed whole is ~10⁸ M☉ for Schwarzschild and ~7×10⁸ M☉ for maximally spinning Kerr — supermassive holes above this don't produce TDE flares.
The Hills/Rees formula r_td ≈ R · (M_BH/M_obj)^(1/3) applies to fluid self-gravitating bodies — stars, gas giants, white dwarfs. For solid bodies held together by material strength (rocky planets, asteroids, spacecraft), the relevant comparison is tidal stress vs material yield stress, not gravity vs tidal differential. A 10 m chondritic asteroid has tensile strength ~10⁷ Pa and survives disruption at depths the Hills formula says it would shred. For Tool 15's "Small body" preset: the Hills-formula crossover (~5×10⁷ M☉) is overstated for solid bodies by orders of magnitude — they'd survive plunges into IMBHs and likely most stellar-mass BHs.
Typical TDE rates per galaxy are 10⁻⁵ to 10⁻⁴ per year, set by the rate at which stars are scattered onto plunging orbits. For an OC-mass IMBH, the per-cluster rate would be ~10⁻⁸ per year (lower by ~10³ because the cluster mass is smaller). The OC IMBH, if it exists at the Häberle mass, should produce a TDE every ~10⁸ years — far rarer than the ~10⁰ yr observation baseline. So the absence of a detected TDE flare from OC's centre is not a strong constraint; it would take a complete galactic-scale survey over millions of years to be informative.