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 mum 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 X 105 years. In this state, the downward settling motion of the dust is balanced by vertical stirring. 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, These geometries are similar to the geometries that were found for disks around Herbig Ae/Be stars in our previous papers (Dullemond 2002, AA, 395, 853; Dullemond & Dominik 2004, A&A, 417, 159, henceforth DD04). In those papers, however, the reason for a disk to turn self-shadowed was by loss of optical depth through dust grain growth. Here we show that dust settling can achieve a similar effect without loss of vertical optical depth, although the self-shadowing in this case only affects the outer regions of the disk, while in DD04 the entire disk outside of the puffed-up inner rim was shadowed. In reality it is likely that both grain growth and grain settling act Simultaneously. The spectral energy distributions of such self-shadowed - or partly self-shadowed - disks have a relatively weak far-infrared excess (in comparison to flaring disks). We show here that, when dust settling is the cause of self-shadowing, these self-shadowed regions of the disk are also very weak in resolved images of scattered light. A reduction in the brightness was already predicted in DD04, but we find that dust settling is far more efficient than grain growth at dimming the scattered light image of the disk. Settling is also efficient in steepening the spectral energy distribution at mid- to far-infrared wavelengths. From the calculations with compact grains it follows that, after about 10(6) 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 (less than or similar to0.1 mum) have a porous or fractal structure, slowing down the settling. Alternatively, it could mean that the different geometries of observed disks is merely a reflection of the turbulent state of these disks.