We investigate classical planetesimal accretion in a binary star system of separation a b ≤50 AU by numerical simulations, with particular focus on the region at a distance of 1 AU from the primary. The planetesimals orbit the primary, are perturbed by the companion and are in addition subjected to a gas drag force. We concentrate on the problem of relative velocities ∆v among planetesimals of different sizes. For various stellar mass ratios and binary orbital parameters we determine regions where ∆v exceed planetesimal escape velocities v esc (thus preventing runaway accretion) or even the threshold velocity v ero for which erosion dominates accretion. Gaseous friction has two crucial effects on the velocity distribution: it damps secular perturbations by forcing periastron alignment of orbits, but at the same time the size-dependence of this orbital alignment induces a significant ∆v increase between bodies of different sizes. This differential phasing effect proves very efficient and almost always increases ∆v to values preventing runaway accretion, except in a narrow e b ≃ 0 domain. The erosion threshold ∆v > v ero is reached in a wide (a b , e b ) space for small < 10 km planetesimals, but in a much more limited region for bigger ≃ 50 km objects. In the intermediate v esc < ∆v < v ero domain, a possible growth mode would be the type II runaway growth identified by Kortenkamp et al. (2001).

Context. New generations of instruments provide, or are about to provide, pan-chromatic images of debris discs and photometric measurements, that require new generations of models, in particular to account for their collisional activity. Aims. We present a new multi-annulus code for the study of collisionally evolving extended debris discs. We first aim to confirm and extend our preliminary result obtained for a single-annulus system, namely that the size distribution in realistic debris discs always departs from the theoretical collisional "equilibrium" dN ∝ R −3.5 dR power law, especially in the crucial size range of observable particles (R < ∼ 1 cm), where it displays a characteristic wavy pattern. We also study how debris discs density distributions, scattered light luminosity profiles, and Spectral Energy Distributions (SEDs) are affected by the coupled effect of collisions and radial mixing due to radiation pressure affected small grains. Methods. The size distribution evolution is modeled over 10 orders of magnitude, going from µm-sized grains to 50 km-sized bodies. The model takes into account the crucial influence of radiation pressure-affected small grains. We consider the collisional evolution of a fiducial, idealized a = 120 AU radius disc with an initial surface density Σ(a) ∝ a α . Several key parameters are explored: surface density profile, system's dynamical excitation, total dust mass, collision outcome prescriptions. Results. We show that the system's radial extension plays a crucial role and that the waviness of the size distribution is amplified by inter-annuli interactions: in most regions the collisional and size evolution of the dust is imposed by small particles on eccentric or unbound orbits produced further inside the disc. Moreover, the spatial distribution of all grains < ∼ 1 cm departs significantly from the initial profile in Σ(a) ∝ a α , while the bigger objects, containing most of the system's mass, still follow the initial distribution. This has consequences on the scattered-light radial profiles which get significantly flatter. We propose an empirical law to trace back the distribution of large unseen parent bodies from the observed profiles. We also show that the the waviness of the size distribution has a clear observable signature in the far-infrared and at (sub-)millimeter wavelengths. This suggests a test of our collision model, which requires observations with future facilities such as Herschel, SOFIA, SCUBA-2 and ALMA. Finally, we provide empirical formulae for the collisional size distribution and collision timescale which can be used for future debris disc modeling.

Observations of extrasolar planets reveal that planets can be found in close binary systems, where the semi-major axis of the binary orbit is less than 20 AU. The existence of these planets challenges planet formation theory, because the strong gravitational perturbations due to the companion increase encounter velocities between planetesimals and make it difficult for them to grow through accreting collisions. We study planetesimal encounter velocities in binary systems, where the planetesimals are embedded in a circumprimary gas disc that is allowed to evolve under influence of the gravitational perturbations of the companion star. We find that the encounter velocities between planetesimals of different size strongly depend on the gas disc eccentricity. In all cases studied, inclusion of the full gas dynamics increases the encounter velocity compared to the case of a static, circular gas disc. Full numerical parameter exploration is still impossible, but we derive analytical formulae to estimate encounter velocities between bodies of different sizes given the gas disc eccentricity. The gas dynamical evolution of a protoplanetary disc in a binary system tends to make planetesimal accretion even more difficult than in a static, axisymmetric gas disc.Comment: 18 pages, 13 figures, accepted for publication in MNRA