How hard is dust in debris disks?

Abstract

Observational appearance of debris disks is largely controlled by collisional grinding of their dust grains. However, the mechanical strength of dust at sizes in the micrometer to millimeter range is poorly known. Recent studies suggested that dust particles in the Solar system might have a higher critical fragmentation energy $Q_{D}^*$ value than previously anticipated. Another recent study considered the Fomalhaut debris disk and found lower $Q_{D}^*$ values to provide better fits to the data. In order to constrain the mechanical strength of dust, we investigate collisional evolution of debris disks with $Q_{D}^*$ prescriptions differing by $\sim 3$ orders of magnitude. We find that, above a certain threshold $Q_{D}^*$ value, the disk's collisional evolution is dominated by rebounding -- rather than disruptive or cratering -- collisions. Rebounding (a.k.a. bouncing) collisions are those in which both impactors survive, being only slightly eroded and producing fragments that only carry a minor fraction of their mass. We show that disks dominated by rebounding collisions would have brightness profiles increasing outward outside the parent belt. Since such profiles are not observed, this places an upper limit on how hard the debris dust is allowed to be in order not to violate the observations. We derive an approximate analytic expression for this limit: $Q_{D}^* \approx (1/8) v_{K}^2(r)$ for grains close to the radiation pressure blowout size, where $v_{K}$ in the Keplerian circular speed at a distance $r$ from the star. This implies $Q_{D}^* \lesssim 10^{9...10} \,\hbox{erg}\,\hbox{g}^{-1}$ for micrometer-sized grains in typical debris disks. Even though rebounding collisions are not expected to affect debris disk evolution significantly, we emphasize that these collisions are actually much more frequent than disruptive and cratering ones in all debris disks.