PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS. II. EXTENSION TO FAINTER SOURCES

We present new results from a significant extension of our previous high angular resolution (0 ''.3 approximate to 40 AU) submillimeter array survey of the 340 GHz (880 mu m) thermal continuum emission from dusty circumstellar disks in the similar to 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 alpha (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(circle dot)), but a narrow distribution of surface density gradients (gamma = 0.4-1.1) that is consistent with a uniform value <gamma > = 0.9 +/- 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 approximate to 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 similar to 20-40 AU of their central stars.