Constraining AGN accretion physics with black hole mass-luminosity scaling relations

We test how supermassive black holes are fed by combining new black hole mass-luminosity relations with physically motivated feeding models. We build a uniform sample of 1729 unobscured blue quasars at z>2 by cross-matching SDSS DRE16 with eROSITA, and augment it with hyperluminous quasars (WISSH, HYPERION) plus 49 JWST broad-line AGN at z>3.5. We find for the SDSS-eROSITA sample of blue quasars a near-linear scaling of bolometric luminosity with mass (slope 0.91+/-0.01) and a shallower hard-X-ray trend (slope 0.73+/-0.01). Classical hot-mode (Bondi) accretion underpredicts the observed luminosities by about 2 dex at the high-mass end and is inconsistent with the measured slopes. In contrast, Chaotic Cold Accretion (CCA) - in which multiphase gas condenses, collides, and rains onto the nucleus - consistently reproduces both the normalization and the near-linear slope expected from halo thermodynamics. The shallower X-ray relation points to a decreasing coronal power fraction with black hole mass. JWST broad-line AGN frequently appear X-ray weak or Halpha enhanced. The latter case can be due to contributions from collisional ionization and photoionization from star-formation to the broad Halpha emission, leading to overestimate AGN luminosities and black hole masses. In the former case, the X-ray weakness is consistent with coronal shielding or anisotropy at high accretion rates. Overall, the data favor CCA-driven, self-regulated feeding over local spherical capture across the BH mass range 1E7-1E10 solar masses, and motivate extending these tests to lower masses and higher redshifts.