In most debris discs, dust grain dynamics is strongly affected by stellar radiation pressure. As this mechanism is size-dependent, we expect dust grains to be spatially segregated according to their sizes. However, because of the complex interplay between radiation pressure, collisions and dynamical perturbations, this spatial segregation of the particle size distribution (PSD) has proven difficult to investigate with numerical models. We propose to explore this issue using a new-generation code that can handle some of the coupling between dynamical and collisional effects. We investigate how PSDs behave in both unperturbed discs at rest and in discs pertubed by planetary objects. We use the DyCoSS code of Thebault(2012) to investigate the coupled effect of collisions, radiation pressure and dynamical perturbations in systems having reached a steady state. We consider 2 setups: a narrow ring perturbed by an exterior planet, and an extended disc into which a planet is embedded. For both setups we consider an additional unperturbed case with no planet. We also investigate how possible spatial size segregation affect disc images at different wavelengths. We find that PSDs are always strongly spatially segregated. The only case for which they follow a standard dn/dr = C.r**(-3.5) law is for an unperturbed narrow ring, but only within the parent body ring itself. For all other configurations, the PSD can strongly depart from such power laws and have strong spatial gradients. As an example, the geometrical cross section of the disc is rarely dominated by the smallest grains on bound orbits, as it is expected to be in standard PSDs in s**q with q<-3. Although the exact profiles and spatial variations of PSDs are a complex function of the considered set-up, we are however able to derive some robust results that should be useful for image-or-SED-fitting models of observed discs.
Recent observations from NASAs Kepler mission detected the first planets in circumbinary orbits. The question we try to answer is where these planets formed in the circumbinary disk and how far inside they migrated to reach their present location. We investigate the first and more delicate phase of planet formation when planetesimals accumulate to form planetary embryos. We use the hydrodynamical code FARGO to study the evolution of the disk and of a test population of planetesimals embedded in it. With this hybrid hydrodynamical--N--body code we can properly account for the gas drag force on the planetesimals and for the gravitational force of the disk on them. The numerical simulations show that the gravity of the eccentric disk on the planetesimal swarm excites their eccentricities to values much larger than those induced by the binary perturbations only within 10 AU from the stars. Moreover, the disk gravity prevents a full alignment of the planetesimal pericenters. Both these effects lead to large impact velocities, beyond the critical value for erosion. Planetesimals accumulation in circumbinary disks appears to be prevented close to the stellar pair by the gravitational perturbations of the circumbinary disk. The observed planets possibly formed in the outer regions of the disk and then migrated inside by tidal interaction with the disk.
We study planetesimal evolution in circumbinary disks, focusing on the three systems Kepler 16, 34 and 35 where planets have been discovered recently. We show that for circumbinary planetesimals, in addition to secular forcing, eccentricities evolve on a dynamical timescale, which leads to orbital crossings even in the presence of gas drag. This makes the current locations of the circumbinary Kepler planets hostile to planetesimal accretion. We then present results from simulations including planetesimal formation and dust accretion, and show that even in the most favourable case of 100% efficient dust accretion, in situ growth starting from planetesimals smaller than ~10 km is difficult for Kepler 16b, Kepler 34b and Kepler 35b. These planets were likely assembled further out in the disk, and migrated inward to their current location.
