FAUST

Measuring the properties of disks around Class 0/I protostars is crucial for understanding protostellar assembly and early planet formation. We present high-resolution (~7.5 au) ALMA continuum observations at 1.3 and 3 mm of 16 disks around Class 0/I protostars across multiple star-forming regions (Taurus, Ophiuchus, and Corona Australis) and a variety of multiplicities. Our observations show a wide range of deconvolved disk sizes (~2–100 au) and the presence of circumbinary disks (CBDs) in all binaries with separations <100 au. The measured properties show similarities to Class II disks, including (a) low spectral index values ( α disks = 2.1 −0.3 +0.5 ) that increase with disk radius, (b) 3 mm disk sizes only marginally smaller than at 1.3 mm (<10%), and (c) radial intensity morphologies well described by modified self-similar profiles. However, there are some key differences: (i) the α 1.3-3 mm values increase monotonically with radius but exceed two only at the disk edge; (ii) higher brightness temperatures, T b , comparable to or higher than the predicted midplane temperatures due to irradiation; and (iii) an approximately ten times higher luminosity at a given size compared to the Class II disks. Together, the results confirm significant optical depth in the observed Class 0/I disks, most with T bol < 200 K, at both 1.3 and 3 mm. Assuming fully optically thick disks at these wavelengths can explain the higher luminosities compared with Class II disks, but the most compact (≲40 au) disks also require higher temperatures, suggesting additional heating from viscous accretion. Taking into account the high optical depths, most disk dust masses are estimated in the range 30–900 M ⊕ (or 0.01–0.3 M ⊙ in gas), with some disks potentially reaching marginal gravitational instability. Based on the elevated T b 1.3 mm , the median location of the water iceline is ~3 au, but this location can extend to more than 10–20 au for the hottest disks in the sample. The CBDs exhibit lower optical depths at both wavelengths and hence higher spectral index values ( τ 3 mm ≲ 1, α CBD = 3.0 −0.3 +0.2 ), dust masses of ~10 2 M ⊕ , and dust emissivity indices of β CBD ~ 1.5 (two Class 0 CBDs) and ~1 (one Class I CBD), suggesting substantial grain growth only in the more evolved CBD. The high optical depths inferred from our analysis provide a compelling explanation for the apparent scarcity of dust substructures in the younger Class 0/I disks at ~1 mm despite the mounting evidence of early planet formation.