Dust coagulation in protoplanetary disks: A rapid depletion of small grains

Max Planck Institut für Astrophysik, PO Box 1317, 85741 Garching, Germany e-mail: dullemon@mpia.de Sterrenkundig Instituut “Anton Pannekoek”, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands e-mail: dominik@science.uva.nl

Received: 28 September 2004
Accepted: 29 November 2004

Abstract

We model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance. Our model involves the detailed solution of the coagulation equation at every location in the disk. At regular time intervals we feed the resulting 3D dust distribution functions into a continuum radiative transfer code to obtain spectral energy distributions. We find that, even if only the very basic – and well understood – coagulation mechanisms are included, the process of grain growth is much too quick to be consistent with infrared observations of T Tauri disks. Small grains are removed so efficiently that, long before the disk reaches an age of 10⁶ years typical of T Tauri stars, the SED shows only very weak infrared excess. This is inconsistent with observed SEDs of most classical T Tauri stars. Small grains must be replenished, for instance by aggregate fragmentation through high-speed collisions. A very simplified calculation shows that when aggregate fragmentation is included, a quasi-stationary grain size distribution is obtained in which growth and fragmentation are in equilibrium. This quasi-stationary state may last 10⁶ years or even longer, depending on the circumstances in the disk, and may bring the time scales into the right regime. If this is indeed the case, or if other processes are responsible for the replenishment of small grains, then the typical grain sizes inferred from infrared spectral features of T Tauri disks do not necessarily reflect the age of the system (small grains young, larger grains older), as is often proposed. Indeed, there is evidence reported in the literature that the typical inferred grain sizes do not correlate with the age of the star. Instead, it is more likely that the typical grain sizes found in T Tauri star (and Herbig Ae/Be star and Brown Dwarf) disks reflect the state of the disk in some more complicated way, e.g. the strength of the turbulence, the amount of dust mass transformed into planetesimals, the amount of gas lost via evaporation etc. A simple evolutionary scenario in which grains slowly grow from pristine m grains to larger grains over a period of a few Myr is most likely incorrect.