Left: relation between the Eddington ratio with M_BH computed from the scaling law of VP and with the r_BLR from Bentz et al. (2013) employing an uncorrected FWHM value (black circles). The open circles represent estimates using (Eq. (4)) and r_BLR corrected following Eq. (5). Red squares represent L/L_Edd estimates from the McConnell et al. (2011) scaling law, with the restriction of σ_⋆ ≳ 150 km s⁻¹ . The oblique dot-dashed line is the equality line; the horizontal one marks the conventional limit separating Pop. A and Pop. B. The filled line is the result of an unweighted least squares fitting between the VP and the uncorrected Bentz et al. (2013)M_BH estimates. Right: relation between the Eddington ratio with M_BH computed from the scaling law of VP and the fundamental plane of Du et al. (2016a) (black circles), and after the refit of this paper (red circles).