Same data as Fig. 4, but plotted against the modified term $a_{\text{p}}^{1/2}{\left[{\beta }_{\text{PR}}(1+\psi )\right]}^{-1}{M}_{\ast }^{-1/2}$ for Model I (left) and Model II (right). The tangential effective beta term β_t = β_PR (1 + ψ) (see Eq. 7) is used for convenience. See the caption in Fig. 4 for details on colors and symbols. The solid lines show new fits (see Eq. 14 for functional form), truncated to remain within the range relevant to each spectral type for clarity, as the contrast depends on both M_* and M_p unlike the original fits from Stark & Kuchner (2008). Multiple lines of the same color correspond to different M_p, increasing from bottom to top. The x-axis scale in the right panel is reduced compared to Fig. 4, reflecting variations in ψ.