Validating Inverse Fundamental-Plane IMBH Mass Estimates in the SKA/ngVLA Era

RESUMO

The radio/X-ray/black-hole-mass Fundamental Plane (FP) is widely used to estimate masses of accreting intermediate-mass black hole (IMBH) candidates. Its inverse use is justified only when radio luminosity traces a compact jet core and X-rays arise from the same sub-Eddington hard-state accretion flow. We formulate an accretion-state validity criterion for inverse-FP masses using verified BH X-ray binary radio/X-ray tracks as the empirical reference. Using 424 detections from 21 BHXBs and candidates, we find that both standard and curved tracks are present and the luminosity at which radio/X-ray behavior changes is source dependent. A low X-ray Eddington ratio is therefore not, by itself, sufficient to establish inverse-FP validity. Within a scale-invariant jet/hot-flow framework, track steepening reduces the effective mass leverage of the inversion, while at much lower accretion rates uncertainties in the dominant emission mechanism and compact-core production can invalidate the underlying FP assumptions altogether. We apply the criterion to representative IMBH-relevant systems without fitting a new plane. NGC 4395 is low-Eddington but compact-radio deficient: its VLA-scale and VLBI jet-base luminosities imply formal inverse-FP mass underestimates of about 1.0 and more than 2.8 dex if the deficit is misread as a mass signal. Globular-cluster X-ray populations in NGC 1399 and NGC 4472 are source-identity limited: 71% and 67% lie below $L_{\rm Edd}(10\,M_\odot)$, and the high-luminosity tail alone does not identify an IMBH accretor. The radio non-detection of the $\omega$ Centauri IMBH candidate constrains gas supply, accretion efficiency, and compact-core production rather than excluding the black hole. The resulting test defines which SKA/ngVLA-era radio cores can be converted into FP masses, and which instead constrain gas supply, source identity, or compact-core production.