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Embedded, Class 0/I protostellar disks represent the initial condition forplanet formation. This calls for better understandings of their bulk propertiesand the dust grains within them. We model multi-wavelength dust continuumobservations of the disk surrounding the Class I protostar TMC1A to provideinsight on these properties. The observations can be well fit by agravitationally self-regulated (i.e., marginally gravitationally unstable andinternally heated) disk model, with surface density $\Sigma \sim 1720(R/10au)^{-1.96} g/cm^2$ and midplane temperature $T_{mid} \sim 185(R/10au)^{-1.27} K$. The observed disk contains a $m=1$ spiral substructure; weuse our model to predict the spiral's pitch angle and the prediction isconsistent with the observations. This agreement serves as both a test of ourmodel and strong evidence of the gravitational nature of the spiral. Our modelestimates a maximum grain size $a_{max}\sim 196(R/10au)^{-2.45} \mu m$, whichis consistent with grain growth being capped by a fragmentation barrier withthreshold velocity $\sim 1 m/s$. We further demonstrate that observationalproperties of TMC1A are typical among the observed population of Class 0/Idisks, which hints that traditional methods of disk data analyses based onGaussian fitting and the assumption of the optically thin dust emission couldhave systematically underestimated disk size and mass and overestimated grainsize.

Gravitational instability, spiral substructure, and modest grain growth  in a typical protostellar disk: Modeling multi-wavelength dust continuum  observation of TMC1A