2021MNRAS.501.1316L

(Sub)millimetre dust opacities are required for converting the observable dust continuum emission to the mass, but their values have long been uncertain, especially in discs around young stellar objects. We propose a method to constrain the opacity κ_ν in edge-on discs from a characteristic optical depth τ_0,ν, the density ρ₀, and radius R₀ at the disc outer edge through κ_ν = τ_0,ν/(ρ₀R₀), where τ_0,ν is inferred from the shape of the observed flux along the major axis, ρ₀ from gravitational stability considerations, and R₀ from direct imaging. We applied the 1D semi-analytical model to the embedded, Class 0, HH 212 disc, which has high-resolution data in Atacama Large Millimetre/submillimetre Array (ALMA) bands 9, 7, 6, and 3 and Very Large Array Ka band (λ = 0.43, 0.85, 1.3, 2.9, and 9.1 mm). The modelling is extended to 2D through RADMC-3D radiative transfer calculations. We find a dust opacity of κ_ν ≃ 1.9 x 10^–2, 1.3 x 10^–2, and 4.9 x 10^–3 cm² g^–1 of gas and dust for ALMA bands 7, 6, and 3, respectively, with uncertainties dependent on the adopted stellar mass. The inferred opacities lend support to the widely used prescription κ_λ = 2.3 x 10^–2(1.3mm/λ) cm² g^–1 . We inferred a temperature of ∼45 K at the disc outer edge that increases radially inwards. It is well above the sublimation temperatures of ices such as CO and N₂, which supports the notion that the disc chemistry cannot be completely inherited from the protostellar envelope.