A method for coupling dynamical and collisional evolution of dust in circumstellar disks: the effect of a dead zone

Dust is a major component of protoplanetary and debris disks as it is the main observable signature of planetary formation. However, since dust dynamics is size-dependent (because of gas-drag or radiation pressure) any attempt to understand the full dynamical evolution of circumstellar dusty-disks that neglect the coupling of collisional evolution with dynamical evolution is thwarted because of the feedback between these two processes. Here, a new hybrid lagrangian/eulerian code is presented that overcomes some of these difficulties. The particles representing "dust-clouds" are tracked individually in a lagrangian way. This system is then mapped on an eulerian spatial grid, inside the cells of which the local collisional evolutions are computed. Finally, the system is remapped back in a collection of discrete lagrangian particles keeping constant their number. An application example on dust growth in a turbulent protoplanetary disk at 1 AU is presented. First the growth of dust is considered in the absence of a dead-zone and the vertical distribution of dust is self-consistently computed. It is found that the mass is rapidly dominated by particles about a fraction of millimeter in size. Then the same case with an embedded dead-zone is investigated and It is found that coagulation is much more efficient and produces, in a short time scale, 1cm-10cm dust pebbles that dominate the mass. These pebbles may then be accumulated into embryos sized objects inside large-scale turbulent structures as shown recently (see e.g. Johansen et al., 2007).