Total ¹³CO line optical depth τ (panels a and d), ¹³CO column density (panels b and e), and ¹³CO intensity radial profiles for simple power-law disk models (top panels) and self-similar disk models (bottom panels). The total disk mass is set to M_disk = 10⁻⁴M_⊙ and γ = 1. The shaded regions in panels a and d show the range where τ < 1, which holds for radii larger than those shown by the dotted lines. The shaded region in panels b and e shows the region where ¹³CO column densities are larger than 10¹⁵ cm⁻², i.e., for radii smaller than those shown by the dashed lines. The shaded regions in panels c and f show the range of ¹³ CO line intensityfor which the conditions τ < 1 and N¹³CO > 10¹⁵ cm⁻² hold. The fit of γ is performed over the “slope–pivot region” between the dotted and dashed lines, shown by the red arrow in panel c.