Same data as Fig. 5, but plotted against the original term $a_{\text{p}}^{1/2}/{\beta }_{\text{PR}}$ from Stark & Kuchner (2008) (left) and the modified term $a_{\text{p}}^{1/2}{\left[{\beta }_{\text{PR}}(1+\psi )\right]}^{-1}{M}_{\ast }^{-1/2}$ (right). Since β_PR is inversely proportional to grain size (Eq. 2) and a_p is fixed, higher x-values indicate larger grains. K4 (yellow) and M4 (red) appear to have one fewer point because their 0.3 μm and 1 μm data replace the 0.1 μm points, respectively, causing overlap (see Sect. 2.2.2). See the caption in Fig. 5 for more details on the colors and symbols. A single solid fitted line is shown per spectral type, as only M_p = 1 M_⊕ and a_p = HZ_mid was considered in the main study setup.