Dust opacity slope, β_mm, as a function of the maximum grain size, a_max. The slopes between two wavelengths given in the legend are derived by calculating the mass absorption coefficients (κ_abs). To calculate κ_abs, we adopted the MIE scattering theory, assuming the DSHARP dust composition (see Sec. 2.3). The grain size distribution follows a power law, N(a) ∝ a^−3.5, with the minimum dust size fixed to a_min = 0.01 μm. The vertical dashed line marks the 0.4 mm boundary that divides the a_max values into two regimes (a small size region and a large size region) according to the β(1.3–3 mm) curve.