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The Structure and Appearance of Protostellar Accretion Disks: Limits on Disk Flaring

Vertical structure models are used to investigate the structure of protostellar, α-law, accretion disks. Conditions investigated cover a range of mass fluxes (10-9 to 10-5 M☉ yr-1), viscous efficiencies (α = 10-2 and 10-4), and stellar masses (0.5-3 M☉). Analytic formulae for midplane temperatures, optical depths, and volume and surface densities are derived and are shown to agree well with numerical results. The temperature dependence of the opacity is shown to be the crucial factor in determining radial trends. We also consider the effect on disk structure of illumination from a uniform field of radiation such as might be expected of a system immersed in a molecular cloud core or other star-forming environment: Tamb = 10, 20, and 100 K. Model results are compared to Hubble Space Telescope observations of HH30 and the Orion proplyds. Disk shape is derived in both the Rosseland mean approximation and as viewed at particular wavelengths (λλ = 0.66, 2.2, 60, 100, 350, and 1000 μm). In regions where the opacity is an increasing function of temperature (as in the molecular regions where κ ∝ T2), the disk does not flare, but decreases in relative thickness with radius under both Rosseland mean and single wavelength approximations. The radius at which the disk becomes shadowed from central object illumination depends on radial mass flow and varies from a few tenths to about 5 au over the range of mass fluxes tested. This suggests that most planet formation occurred in environments unheated by stellar radiation. Viewing the system at any single wavelength increases the apparent flaring of the disk but leaves the shadow radius essentially unchanged. External heating further enhances flaring at large radii, but, except under extreme illumination (100 K), the inner disk will shield the planet-forming regions of all but the lowest mass flux disks from radiation originating near the origin such as from the star or from an FU Orionis outburst.