Vertical structure of debris discs

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 could be flawed because the observed dust should be naturally placed on inclined orbits by the combined effect of radiation pressure and mutual collisions. We critically reinvestigate this issue and numerically estimate what the "natural" vertical thickness of a collisionally evolving disc is, in the absence of any additional perturbing body. We use a deterministic collisional code, following 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. 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, with the smallest grains having the largest vertical dispersion and the bigger ones clustered closer to the midplane. Debris discs should have a minimum "natural" observed aspect ratio $h_{min}\sim 0.04\pm0.02$ at visible to mid-IR wavelengths where the flux is dominated by the smallest bound grains. These values are comparable to the estimated thicknesses of many vertically resolved debris discs, as is illustrated with the specific example of AU Mic. For all systems with $h \sim h_{min}$, the presence (or absence) of embedded perturbing bodies cannot be inferred from the vertical dispersion of the disc