Closing the Constraint Window

The Bañares-Hernández et al. 2025 constraint comes from 5 pulsars in OC's core. Adding more pulsars reduces the uncertainty on the gravitational potential. The MeerKAT timing sensitivity on the upper mass limit scales as 1/√N_psr × 1/√baseline. The key threshold: √(N×B) > 3.66 drives the projected upper limit below the 8,200 M☉ lower bound, meaning the two measurement sets become mutually exclusive at stated confidence. At N=5 pulsars a baseline of only ~2.7 years crosses it. Crossing is not a resolution: further investment only deepens the exclusivity, the signature of a genuine systematic conflict.

Chen et al. 2025 placed an upper limit on IMBH accretion luminosity from JWST NIRCam/MIRI observations, which translates to a mass limit only under assumptions about the accretion efficiency ε. The constraint weakens for low ε — at ε = 10⁻³ the limit is ~6,000 M☉, consistent with Bañares, but at ε = 10⁻⁵ (radiatively inefficient flow) the limit weakens to ~60,000 M☉, compatible with any proposed mass. The ambient gas density sets the Bondi rate. Note that the "JWST mass upper limit" above is a hand-scaled anchor pinned to 6,000 M☉ at the nominal ε/n; the Bondi ṁ, luminosity, and Eddington-ratio figures below it are computed independently and evaluated at the Stage-1 lower bound, not solved for their own mass limit. The two are separate estimates on this page, not cross-validated to agree.

If a stellar-mass black hole in OC spirals into the IMBH, LISA will measure the chirp mass via δM/M ≈ 1/(SNR × √N_cycles) from the inspiral gravitational waveform. This translates to an IMBH mass posterior width that depends on the mass ratio q = m_stellar/M_IMBH and the signal-to-noise ratio; at the fiducial defaults (SNR = 100, q = 10⁻³) this computes to ~0.0012% (not the ~0.1% a naive estimate might suggest). A single IMRI detection definitively closes the constraint window. The expected IMRI rate for a ~10,000 M☉ IMBH in a dense globular cluster is ~10⁻⁸ yr⁻¹ per cluster.