Collisional processes and size distribution in spatially extended debris discs

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 proportional to R-3.5 dR power law, especially in the crucial size range of observable particles (R less than or similar to 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 mu m-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 Sigma(a) proportional to a(alpha). 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 less than or similar to 1 cm departs significantly from the initial profile in Sigma(a) proportional to a(alpha), 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.