We present new results from a significant extension of our previous high angular resolution ( 0 \farcs 3 \approx 40 AU ) Submillimeter Array survey of the 340 GHz ( 880 \mu m ) thermal continuum emission from dusty circumstellar disks in the \sim 1 Myr-old Ophiuchus star-forming region .
An expanded sample is constructed to probe disk structures that emit significantly lower millimeter luminosities ( hence dust masses ) , down to the median value for T Tauri stars .
Using a Monte Carlo radiative transfer code , the millimeter visibilities and broadband spectral energy distribution for each disk are simultaneously reproduced with a two-dimensional parametric model for a viscous accretion disk that has a surface density profile \Sigma \propto ( R / R _ { c } ) ^ { - \gamma } \exp { [ - ( R / R _ { c } ) ^ { 2 - \gamma } ] } .
We find wide ranges of characteristic radii ( R _ { c } = 14 -198 AU ) and disk masses ( M _ { d } = 0.004 -0.143 M _ { \odot } ) , but a narrow distribution of surface density gradients ( \gamma = 0.4 -1.1 ) that is consistent with a uniform value \langle \gamma \rangle = 0.9 \pm 0.2 and independent of mass ( or millimeter luminosity ) .
In this sample , we find a correlation between the disk luminosity/mass and characteristic radius , such that fainter disks are both smaller and less massive .
We suggest that this relationship is an imprint of the initial conditions inherited by the disks at their formation epoch , compare their angular momenta with those of molecular cloud cores , and speculate on how future observations can help constrain the distribution of viscous evolution timescales .
No other correlations between disk and star properties are found .
The inferred disk structures are briefly compared with theoretical models for giant planet formation , although resolution limitations do not permit us to directly comment on material inside R \approx 20 AU .
However , there is some compelling evidence for the evolution of dust in the planet formation region : 4/17 disks in the sample show resolved regions of significantly reduced millimeter optical depths within \sim 20-40 AU of their central stars .