By M. Gaspari

We carry out a comprehensive Bayesian correlation analysis between hot halos and direct masses of supermassive black holes (SMBHs), by retrieving the X-ray plasma properties (temperature, luminosity, density, pressure, masses) over galactic to cluster scales for 85 diverse systems. We find new key scalings, with the tightest relation being the M_•−T_x, followed by M_•−L_x. The tighter scatter (down to 0.2 dex) and stronger correlation coefficient of all the X-ray halo scalings compared with the optical counterparts (as the M_•−σ_e) suggest that plasma halos play a more central role than stars in tracing and growing SMBHs (especially those that are ultramassive). Moreover, M_• correlates better with the gas mass than dark matter mass. We show the important role of the environment, morphology, and relic galaxies/coronae, as well as the main departures from virialization/self-similarity via the optical/X-ray fundamental planes. We test the three major channels for SMBH growth: hot/Bondi-like models have inconsistent anti-correlation with X-ray halos and too low feeding; cosmological simulations find SMBH mergers as sub-dominant over most of the cosmic time and too rare to induce a central-limit-theorem effect; the scalings are consistent with chaotic cold accretion (CCA), the rain of matter condensing out of the turbulent X-ray halos that sustains a long-term self-regulated feedback loop. The new correlations are major observational constraints for models of SMBH feeding/feedback in galaxies, groups, and clusters (e.g., to test cosmological hydrodynamical simulations), and enable the study of SMBHs not only through X-rays, but also via the Sunyaev-Zel'dovich effect (Compton parameter), lensing (total masses), and cosmology (gas fractions).