Inferring (Sub)millimeter Dust Opacities and Temperature Structure in Edge-on Protostellar Disks From Resolved Multi-Wavelength Continuum Observations: The Case of the HH212 Disk

(Sub)millimeter dust opacities are required for converting the observable dust continuum emission to the mass, but their values have long been uncertain, especially in disks around young stellar objects. We propose a method to constrain the opacity 𝜅_𝜈 in edge-on disks from a characteristic optical depth 𝜏_0,𝜈, the density 𝜌_0 and radius 𝑅_0 at the disk outer edge through 𝜅_𝜈 = 𝜏_0,𝜈/(𝜌_0𝑅_0) where 𝜏_0,𝜈 is inferred from the shape of the observed flux along the major axis, 𝜌_0 from gravitational stability considerations, and 𝑅_0 from direct imaging. We applied the 1D semi-analytical model to the embedded, Class 0, HH 212 disk, which has high-resolution data in ALMA Band 9, 7, 6, and 3 and VLA Ka band (𝜆=0.43, 0.85, 1.3, 2.9, and 9.1 mm). The modeling of the HH 212 disk is extended to 2D through RADMC-3D radiative transfer calculations. We find a dust opacity of 𝜅_𝜈 ≈ 1.9×10^-2, 1.3×10^-2, and 4.9×10^-3 cm^2 per gram 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 × 10^-2 (1.3mm/𝜆) cm^2 g^-1 advocated by Beckwith et al. (1990). We inferred a temperature of ∼45 K at the disk outer edge which increases radially inward. It is well above the sublimation temperatures of ices such as CO and N_2, which supports the notion that the disk chemistry cannot be completely inherited from the protostellar envelope.