We present CARMA observations of the thermal dust emission from the circumstellar disks around the young stars RY?Tau and DG?Tau at wavelengths of 1.3 mm and 2.8 mm. The angular resolution of the maps is as high as 015, or 20 AU at the distance of the Taurus cloud, which is a factor of 2 higher than has been achieved to date at these wavelengths. The unprecedented detail of the resulting disk images enables us to address three important questions related to the formation of planets. (1) What is the radial distribution of the circumstellar dust? (2) Does the dust emission show any indication of gaps that might signify the presence of (proto-)planets? (3) Do the dust properties depend on the orbital radius? We find that modeling the disk surface density in terms of either a classical power law or the similarity solution for viscous disk evolution reproduces the observations well. Both models constrain the surface density between 15 and 50 AU to within 30% for a given dust opacity. Outside this range, the densities inferred from the two models differ by almost an order of magnitude. The 1.3 mm image from RY?Tau shows two peaks separated by 02 with a decline in the dust emission toward the stellar position, which is significant at about 2σ-4σ. For both RY?Tau and DG?Tau, the dust emission at radii larger than 15 AU displays no significant deviation from an unperturbed viscous disk model. In particular, no radial gaps in the dust distribution are detected. Under reasonable assumptions, we exclude the presence of planets more massive than 5 MJ orbiting either star at distances between about 10 and 60 AU, unless such a planet is so young that there has been insufficient time to open a gap in the disk surface density. The radial variation of the dust opacity slope, β, was investigated by comparing the 1.3 mm and 2.8 mm observations. We find mean values of β of 0.5 and 0.7 for DG?Tau and RY?Tau, respectively. Variations in β are smaller than Δβ = 0.7 between 20 and 70 AU. These results confirm that the circumstellar dust throughout these disks differs significantly from dust in the interstellar medium.
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