Analytical estimate of f_water at 1 au as a function of r_d,0 and Ṁ_g,0. Panels a: The dependence on the disk diffusion timescale t_diff. Panels b: dependence on the photoevaporation rate (Ṁ_pe). The other parameters are St = 0.1 and M_pl,0 = 1M_⊕. In the panels a, we used Ṁ_pe = 10⁻⁹M_⊙ yr⁻¹, and t_diff = 3 × 10⁶ yr in the panels b. The middle panels of panels a and the right panel of panels b are identical. In the right panel of panel b, the region with Ṁ_g,0 < Ṁ_pe is empty because the disks do not exist under that condition. The color scales are log₁₀ f_water.