The distance scale and Eddington efficiency of luminous quasars

The relation between the central mass and quasar luminosity (M_BH \propto L^{\alpha}FHWM^2) links a given Eddington ratio with a value of H_0, within a cosmology with fixed (\Omega_m,\Omega_{\Lambda}). We point out that because the relation is calibrated at low z using distance independent reverberation mapping to get the BLR size, the derived M_BH interestingly does not depend on H_0, while L/L_Edd is sensitive to H_0, but rather robust to changes of \Omega_{\Lambda} in the standard flat model. This means, e.g., that enough of extragalactic objects radiating at the Eddington limit could be used to study the global Hubble constant in a new way, bypassing the local distance ladder. The method could become practical when systematic errors in derived M_BH are understood and objects with L /leq L_Edd can be independently identified. As an illustration, if we take a sample of tranquil very luminous quasars in the redshift range 0.5 < z < 1.6, and assume that they are radiating with L_bol \leq L_Edd, then the usual numeric factors used for calculating M_BH and L_bol would lead to the result that the Hubble constant must be larger than 45 km/s/Mpc.