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(Sub)millimeter dust opacities are required for converting the observabledust continuum emission to the mass, but their values have long been uncertain,especially in disks around young stellar objects. We propose a method toconstrain the opacity $\kappa_\nu$ in edge-on disks from a characteristicoptical depth $\tau_{0,\nu}$, the density $\rho_0$ and radius $R_0$ at the diskouter edge through $\kappa_\nu=\tau_{0,\nu}/(\rho_0 R_0)$ where $\tau_{0,\nu}$is inferred from the shape of the observed flux along the major axis, $\rho_0$from gravitational stability considerations, and $R_0$ from direct imaging. Weapplied 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($\lambda$=0.43, 0.85, 1.3, 2.9, and 9.1 mm). The modeling of the HH 212 diskis extended to 2D through RADMC-3D radiative transfer calculations. We find adust opacity of $\kappa_\nu \approx $ $1.9\times 10^{-2}$, $1.3\times 10^{-2}$,and $4.9\times 10^{-3}$ 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$\kappa_\lambda=2.3\times 10^{-2} (1.3 {\rm mm}/\lambda)$ cm$^2$ g$^{-1}$advocated by Beckwith et al. (1990). We inferred a temperature of ~45K at thedisk outer edge which increases radially inward. It is well above thesublimation temperatures of ices such as CO and N$_2$, which supports thenotion that the disk chemistry cannot be completely inherited from theprotostellar envelope.

monthly notices of the royal astronomical society

Inferring (Sub)millimeter Dust Opacities and Temperature Structure in  Edge-on Protostellar Disks From Resolved Multi-Wavelength Continuum  Observations: The Case of the HH 212 Disk