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FAUST. XXVIII. High-Resolution ALMA Observations of Class 0/I Disks: Structure, Optical Depths, and Temperatures

We present high-resolution (~7.5 au) ALMA observations at 1.3 and 3 mm of 16 disks around Class 0/I protostars across multiple star-forming regions and a variety of multiplicities, showing a range of disk sizes (~2-100 au) and including circumbinary disks (CBDs) in binaries with separations <100 au. The disk properties show similarities to Class II disks, including (a) low spectral index (SI) values (alpha=2.1) that increase with disk radius, (b) 3 mm disk sizes only marginally smaller than at 1.3 mm (<10%), and (c) radial intensity profiles well described by modified self-similar profiles. We also find key differences: (i) SI values increasing with radius, but exceeding 2 only at the disk edge (ii) higher brightness temperatures Tb, in some cases higher than the predicted temperatures due to irradiation, and (iii) ~10x higher luminosity at a given size compared to the Class II disks. These results confirm significant optical depth in the observed Class 0/I disks, at both 1.3 and 3 mm, helping to explain their higher luminosities, but higher temperatures are also required for the most compact (< 40 au) disks, suggesting additional viscous heating. Considering optical depth, most disk dust masses are estimated in the range 30-900 Mearth (0.01-0.3 Msun in gas), resulting in some disks reaching marginal gravitational instability. The median location of the water iceline is ~3 au, but it can extend beyond 10-20 au for the hottest disks. CBDs exhibit lower optical depths at both wavelengths and hence higher SI values (alpha=3.0), dust masses of 100 Mearth, and beta~1.5 (2 Class 0 CBDs) and beta~1 (1 Class I CBD), suggesting substantial grain growth only in the more evolved CBD. The inferred high optical depths provide a compelling explanation for the apparent scarcity of dust substructures in the younger disks at ~ 1 mm, despite mounting evidence for early planet formation (ABRIDGED).