Distribution of quasars from 0.7 < z < 1.9 with 3.35 < log(λ _RF) < 3.45 in the τ _perturb, σ _ϵ parameter space. Both τ _perturb, σ _ϵ are corrected to a rest-frame wavelength of 2500 Å. Top row: from left to right, quasars are color-coded by their L _bol, M _BH, and L/L _edd, respectively. The median error bar is displayed in the lower left corner of the left panel. A trend of decreasing L _bol with larger τ _perturb and σ _ϵ is shown in the left panel. Similar trends for M _BH or L/L _edd are not seen in the middle and right panels. Bottom row: same as the top row, but with the y-axis presented in the unit of gravitational radius (R _g ) with r _perturb = (τ _perturb∗ c)/R _g ∝ τ _perturb/M _BH. The median error bar is displayed in the upper right corner of the right panel. The dashed lines are best-fit regression in the form of log(r _perturb) = A∗log(σ _ϵ ) + B∗log(M _BH) + C for M _BH of 10⁸, 10⁹, and 10¹⁰ M _⊙. Weighting τ _perturb by M _BH reduces the scatter seen in the top row and reveals a new trend of increasing r _perturb with increasing L/L _edd (see the bottom right panel).