Dust Growth and Settling in Protoplanetary Disks and Disk Spectral Energy Distributions. I. Laminar Disks

Dust growth and settling considerably affect the spectral energy distributions (SEDs) of protoplanetary disks. We investigated dust growth and settling in protoplanetary disks through numerical simulations to examine time evolution of the disk optical thickness and SEDs. In this paper we considered laminar disks as the first step in a series of papers. As a result of dust growth and settling, a dust layer forms around the midplane of a gaseous disk. After the formation of the dust layer, small dust grains remain floating above the layer. Although the surface density of the floating small grains is much less than that of the dust layer, they govern the disk optical thickness and the emission. Size distributions of the floating grains obtained from numerical simulations are well described by a universal power-law distribution, which is independent of the disk temperature, the disk surface density, the radial position in the disk, etc. The floating small grains settle onto the dust layer in a long timescale compared with the formation of the dust layer. Typically, it takes 10⁶ yr for micron-sized grains. Rapid grain growth in the inner part of disks makes the radial distribution of the disk optical thickness less steep than that of the disk surface density, Σ. For disks with Σ~R^-3/2, the radial distribution of the optical thickness is almost flat for all wavelengths at t<~10⁶ yr. At t>10⁶ yr, the optical thickness of the inner disk (<~a few AU) almost vanishes, which may correspond to disk inner holes observed by Spitzer Space Telescope. Furthermore, we examined time evolution of disk SEDs, using our numerical results and the two-layer model. The grain growth and settling decrease the magnitude of the SEDs, especially at λ>=100 μm. Our results indicate that grain growth and settling can explain the decrease in observed energy fluxes at millimeter/submillimeter wavelengths with timescales of 10⁶-10⁷ yr without depletion of the disks.