Four independent spin-constraint methods for OC's IMBH — QPO resonance, BZ radio upper bound, superradiance spin-down, and LISA ringdown — synthesized into a joint (mass, spin) posterior grid. Highlights the BZ-efficient regime where MTH engineering becomes viable.
Grid shading: ● Ruled out by ≥1 active constraint | ● Marginal | ● Allowed by all active constraints | ★ BZ-optimal zone (a★≥0.9)
The 3:2 parametric epicyclic resonance model predicts QPO frequencies ν_U and ν_L from ISCO orbital frequencies: ν_U = ν_K(r_res) and ν_L = ν_K/2, where r_res depends on spin. For a given observed ν_U, the spin is determined by inverting this relation. No QPO has been detected in OC's IMBH yet; the slider sets a hypothetical future detection.
The Blandford–Znajek (1977) jet power P_BZ ∝ B² M² a². The radio luminosity of a jet scales as L_R ∝ P_BZ^α (α ~ 0.7). Given a radio upper limit, this sets an upper bound on a★ (assuming a fiducial magnetic field B at the horizon). At OC's current radio non-detection level (~10⁻⁸ W/Hz), the BZ spin constraint is weak unless B is constrained.
Rotating black holes can transfer angular momentum to ultralight boson fields if the Compton wavelength matches the gravitational radius: m_b c² / ℏ ≈ GM/c³ × 2π. For OC's IMBH (~10⁴ M☉), the resonant boson mass is ~5.6×10⁻¹⁵ eV (10⁻¹⁸ eV corresponds to SMBH-scale BHs of ~10⁶–10⁷ M☉). If such bosons exist (ALP dark matter), superradiance would have spun down the BH on a timescale much shorter than OC's age — implying either a low spin or no such boson at that mass.
A compact object (neutron star or stellar BH) inspiraling into OC's IMBH produces quasi-normal mode (QNM) ringdown that encodes the spin. The dominant (l=m=2) QNM frequency scales as f_QNM ≈ c³/(2πGM) × 0.37 (1 − 0.23 a★) for near-Schwarzschild. LISA sensitivity at ~mHz covers this for an IMBH at OC's distance if mass ratio q > 10⁻³.
Török et al. 2011 (A&A 531:A59) · Blandford & Znajek 1977 (MNRAS 179:433) · Arvanitaki & Dubovsky 2011 (PRD 83:044026) · Amaro-Seoane 2022 (Living Reviews in Relativity)