Collisional damping in debris discs: Only significant if collision velocities are low

Context. Dusty debris discs around main sequence stars are observed to vary widely in terms of their vertical thickness. Their vertical structure may be affected by damping in inelastic collisions. Although kinetic models have often been used to study the collisional evolution of debris discs, these models have not yet been used to study the evolution of their vertical structure.Aims. We extend an existing implementation of a kinetic model of collisional evolution to include the evolution of orbital inclinations and we use this model to study the effects of collisional damping in pre-stirred discs.Methods. We evolved the number of particles of different masses, eccentricities, and inclinations using the kinetic model and used Monte Carlo simulations to calculate collision rates between particles in the disc. We considered all relevant collisional outcomes including fragmentation, cratering, and growth.Results. Collisional damping is inefficient if particles can be destroyed by projectiles that are of much lower mass. If that is the case, catastrophic disruptions shape the distributions of eccentricities and inclinations, and their average values evolve slowly and at the same rate for all particle sizes.Conclusions. The critical projectile-to-target mass ratio (Y_{c) and the collisional timescale jointly determine the level of collisional damping in debris discs. If Yc is much smaller than unity, a debris disc retains the inclination distribution that it is born with for much longer than the collisional timescale of the largest bodies in the disc. Such a disc should exhibit a vertical thickness that is independent of wavelength even in the absence of other physical processes. Collisional damping is efficient if Yc is of order unity or larger. For millimetre-sized dust grains and common material strength assumptions, this requires collision velocities of lower than ~40 m s^{−1. We discuss the implications of our findings for exo-Kuiper belts, discs around white dwarfs, and planetary rings.}}