Vertical structure of debris discs

Context. The vertical thickness of debris discs is often used as a measure of these systems' dynamical excitation, and as clues to the presence of hidden massive perturbers such as planetary embryos. However, this argument might be flawed because the observed dust should be naturally placed on inclined orbits by the combined effect of radiation pressure and mutual collisions. Aims. We critically reinvestigate this issue and numerically estimate the natural vertical thickness of a collisionally evolving disc, in the absence of any additional perturbing body. Methods. We use a deterministic collisional code, to follow the dynamical evolution of a population of indestructible test grains suffering mutual inelastic impacts. Grain differential sizes as well as the effect of radiation pressure are taken into account. Results. We find that, under the coupled effect of radiation pressure and collisions, grains naturally acquire inclinations of a few degrees. The disc is stratified with respect to grain sizes, the smallest grains having the largest vertical dispersion and the largest being clustered closer to the midplane. Conclusions. Debris discs should have a minimum natural observed aspect ratio h(min) similar to 0.04 +/- 0.02 from visible to mid-IR wavelengths, where the flux is dominated by the smallest bound grains. These values are comparable to the estimated thicknesses of several vertically resolved debris discs, as illustrated by the specific example of AU Mic. For all systems with h similar to h(min), the presence (or absence) of embedded perturbing bodies cannot be inferred from the vertical dispersion of the disc.