The effect of dust settling on the appearance of protoplanetary disks

We analyze how the process of dust settling affects the spectral energy distribution and optical appearance of protoplanetary disks. Using simple analytic estimates on the one hand, and detailed 1+1-D models on the other hand, we show that, while the time scale for settling down to the equator may exceed the life time of the disk, it takes much less time for even small grains of 0.1 micron to settle down to a few pressure scale heights. This is often well below the original location of the disk's photosphere, and the disk therefore becomes effectively 'flatter'. If turbulent stirring is included, a steady state solution can be found, which is typically reached after a few times 1E5 years. Dependent on the strength of the turbulence, the shape of the disk in such a steady state can be either fully flaring, or flaring only up to a certain radius and self-shadowed beyond that radius. We show that these partly self-shadowed disks have a much weaker mid- to far-infrared flux than the fully flaring ones. We also show that these self-shadowed regions of the disk are very weak in resolved images of scattered light, in contrast to the fully flaring disks. From the calculations with compact grains it follows that, after about 1E6 years, most disks should be self-shadowed. The fact that some older disks are still observed with the characteristics of flaring disks therefore seems somewhat inconsistent with the time scales predicted by the settling model based on compact grains. This suggests that perhaps even the small grains (lesssim 0.1 micron) have a porous or fractal structure, or that the different geometries of observed disks is merely a reflection of the turbulent state of these disks.