Contrast values from the pilot study, plotted against the $a_{\text{p}}^{1/2}/{\beta }_{\text{PR}}$ term for Model I (left) and Model II (right). The data corresponding to F4, G4, K4, and M4 are shown in different colors: blue, green, yellow, and red, respectively. Planetary masses of 0.5, 1.0, and 2.0 M_⊕ are represented by different shapes, with the solid lines indicating the fits from Stark & Kuchner (2008) for each M_p, increasing from bottom to top. For each color and symbol, the three points from left to right correspond to the planets located at the inner, middle, and outer edges of the HZ. We note that these results are shown for s = 50 μm; the trends do not apply to grains smaller than ∼10 μm around F4, ∼3 μm around G4, and ∼1 μm around K4 and M4-type stars, which are blown out or fail to form resonant rings (see Sect. 3.2.1).