K. Robbins Bell NASA / Ames Research Center

To model observations, disks in the planet-forming region (R < approx 10 AU) have traditionally been assumed to be either inifitesimally flat or uniformly flaring. With the advent of detailed vertical structure models, it is now possible to calculate the disk's shape directly. The distance from midplane to the point where the optical depth in the Rosseland mean opacity equals 2/3 (the photosphere) is inevitably controlled by the local opacity. We show that optically thick disks around T Tauri stars have a common shape INDEPENDENT OF ENERGY GENERATION MECHANISM which is determined by the temperature dependence of the opacity and assumes only that the disk's midplane temperature decreases with radius. The disk's surface tilts toward the central star in the inner disk where the midplane is too hot for dust to be condensed. Where dust exists at the midplane, the disk's surface tilts away. For disks with mass fluxes between 10^{-8} and 10^{-7} M_sol/yr, with viscous efficiency alpha between 10^{-2} and 10^{-4}, and with stellar mass between one and three M_sol the shadow radius falls between 0.25 and 2.0 AU. Most of the planet-forming region of the disk is therefore shielded from direct illumination by the central object.

We use the derived shape and calculate disk temperature profiles including the effect of the reprocessing by the disk of photons originating in the disk itself as well as of stellar photons. This "disk-to-disk reprocessing" has never been calculated before and was motivated by the study of the luminous FU Orionis disks. In low mass flux (T Tauri) systems, the inclusion of this effect results in power law temperature profiles flatter than the T proportional to r^{-3/4} predicted by conventional theory. Resulting spectral energy distributions of both FU Ori and T Tauri systems are in better agreement with observations than either flat or uniformly flaring disk models. This agreement supports the hypothesis that the thickness of an optically thick disk is controlled by the midplane opacity.

This work is from a paper recently accepted by the Astrophysical Journal.