TDE Rate Calculator for OC

Loss-cone dynamics: tidal disruption event rate for OC's IMBH, X-ray peak luminosity, and detectability by Einstein Probe and Rubin LSST

🔬 Established physics (loss-cone dynamics, tidal disruption) ⚠ Observationally debated (OC IMBH parameters)
Black Hole Parameters
IMBH mass sets the tidal radius, influence radius, and Eddington luminosity
BH mass M (M☉)8,200
500 M☉10⁴10⁶
Cluster Parameters
OC defaults from measurements.js; adjust for other clusters
Velocity dispersion σ (km/s)16
Stellar density ρ at r_h (M☉/pc³)10⁴
10² M☉/pc³10⁵
Mean star mass m_star (M☉)0.7
Mean star radius R_star (R☉)0.75
OC distance d (kpc)5.47
Loss-Cone Dynamics
Tidal disruption radius, influence radius, and event rate
Tidal disruption radius r_t
—
AU
Influence radius r_h
—
pc
Loss cone fraction f_lc
—
1/ln(r_h/r_t)
Relaxation time t_relax
—
yr
TDE rate Γ_TDE
—
events / yr
Mean waiting time
—
yr between events
OC published estimate (arXiv:2507.06316): Γ ≈ 5×10⁻⁸ yr⁻¹. This tool matches that estimate at OC default parameters.
Flare Properties & Detectability
Peak emission assuming L_peak ≈ f_Edd × L_Eddington; flux at OC distance
Eddington fraction f_Edd at peak0.10
0.1% L_Edd100% L_Edd
Einstein Probe (WXT)
Sensitivity10⁻¹¹ erg/cm²/s
Peak flux—
—
Rubin LSST (r-band)
Single-visit 5σ24.5 mag
Peak apparent mag—
—
Peak X-ray luminosity L_peak
—
erg/s
Peak X-ray flux at OC distance
—
erg/cm²/s
TDE rate vs. IMBH mass (other parameters fixed)

What this tool does

This tool computes the rate at which stars are tidally disrupted by OC's IMBH using loss-cone dynamics. A star on an orbit that passes within the tidal disruption radius r_t of the IMBH is disrupted. The rate of stars entering the loss cone is set by gravitational two-body relaxation on the relaxation timescale t_relax.

Key formulas

Tidal disruption radius: r_t = R_star × (M_BH/m_star)^(1/3). Stars within this radius are disrupted.

Influence radius: r_h = GM_BH/σ² — the radius within which the IMBH dominates the stellar dynamics.

Relaxation time: t_relax = 0.34 σ³ / (G² ρ m_star ln(M_BH/m_star)), where ln(Λ) = ln(M_BH/m_star) is the Coulomb logarithm (Wang & Merritt 2004 approximation).

Loss-cone suppression factor: f_lc = 1/ln(r_h/r_t) — the logarithmic suppression appropriate for the empty loss-cone regime (Wang & Merritt 2004).

TDE rate: Γ_TDE ≈ N_h / (t_relax × ln(r_h/r_t)), where N_h = (4π/3) r_h³ ρ / m_star is the number of stars within the influence radius. This is the standard empty-loss-cone rate (Wang & Merritt 2004), appropriate for OC-type clusters where relaxation is slow compared to the orbital period.

Detectability

Peak X-ray luminosity: L_peak = f_Edd × L_Eddington = f_Edd × 1.26×10³¹ × M/M_sun W. The Eddington fraction at peak is uncertain; f_Edd ~ 0.1 is often used.

Flux at Earth: F = L_peak / (4π d²) where d is the distance to OC. The Einstein Probe WXT sensitivity is ~10⁻¹¹ erg/cm²/s (0.5–4 keV, 1 ks exposure). Rubin LSST's 5σ depth in r-band is ~24.5 mag per visit, ~27.5 mag stacked.

OC published estimate

arXiv:2507.06316 ("Growing the IMBH in Omega Centauri", 2025) estimates Γ_TDE ≈ 5×10⁻⁸ yr⁻¹ for OC-like clusters, consistent with this tool at default parameters. The corresponding mean waiting time is ~20 Myr. This means we would not expect an ongoing TDE from OC today — but monitoring for transients is motivated over multi-decade timescales.

References

Wang, J. & Merritt, D. (2004). ApJ 600:149. DOI: 10.1086/379767 Stone, N. C. & Metzger, B. D. (2016). MNRAS 455:859. DOI: 10.1093/mnras/stv2281 arXiv:2507.06316 (2025) — Growing the IMBH in Omega Centauri Häberle et al. (2024). Nature 631:285. DOI: 10.1038/s41586-024-07511-z Strubbe & Quataert (2009). MNRAS 400:2070. DOI: 10.1111/j.1365-2966.2009.15599.x

v1.0 — 2026-06-02