Radiatively Inefficient Flows in Low-Luminosity Nuclei: Densities in M87 and Sagittarius A* Against a Ceiling

This study asks what densities radiatively inefficient accretion flows reach in the nearest low-luminosity nuclei and how they compare with a ceiling. Using published ranges for the relevant source properties and standard relations stated in full, the computation converts the observed quantities into flow density in kilograms per cubic metre and compares each value with a spin-torsion density ceiling and the shear rate derived from it. The headline values are: max_rho_ratio = 1.509e-71, max_rho_kg_m3 = 1.466e-13, max_source = SgrA*, rhoA_kg_m3 = 9.718e+57, shear_max_per_s = 4.037e+24, max_shear_ratio = 3.376e-27. The comparison is a computation from stated assumptions and published inputs, not a measurement, and it is reported at face value: where the converted values fall far from the ceiling, that separation is the result, and where a standard relation is itself placed under strain by the data, that strain is identified separately from any question about the ceiling.