The unresolved high-mass frontier of the black hole Fundamental Plane

Abstract

Accreting black holes follow a Fundamental Plane (FP) linking radio and X-ray luminosities to black hole mass, but whether this relation changes in the ultramassive regime, above $\sim10^{10}\,\Msun$, remains unresolved. Brightest cluster galaxies (BCGs) provide the most direct access to this regime, although earlier claims of enhanced radio emission relied largely on heterogeneous nuclear measurements and black hole masses inferred from host-galaxy proxies. We recalibrate the forward FP using galaxies with direct dynamical mass measurements and reassess the evidence for a high-mass radio excess using the available BCG data. We find that the archival proxy-mass sample cannot uniquely establish such an excess because the inferred signal remains sensitive to the mass calibration and radio-selection properties of the sample. Using mock observing programs, we further show that the predictive width measured from existing observations makes a high-mass transition difficult to both detect and localize with present samples. The existing data therefore provide no compelling evidence for a distinct high-mass branch of the FP. Resolving this question will require a substantially larger, uniformly selected sample of galaxies with direct black hole masses and matched, preferably quasi-simultaneous, nuclear radio and X-ray measurements. A focused pilot survey of several dozen direct-mass systems would provide a practical first step toward establishing whether the required precision is achievable.