Modeling Collisional Cascades In Debris Disks: Steep Dust-Size Distributions

We explore the evolution of the mass distribution of dust in collision-dominated debris disks, using the collisional code introduced in our previous paper. We analyze the equilibrium distribution and its dependence on model parameters by evolving over 100 models to 10 Gyr. With our numerical models, we confirm that systems reach collisional equilibrium with a mass distribution that is steeper than the traditional solution by Dohnanyi (1969). Our model yields a quasi steady-state slope of n(m) ~ m^{-1.88} [n(a) ~ a^{-3.65}] as a robust solution for a wide range of possible model parameters. We also show that a simple power-law function can be an appropriate approximation for the mass distribution of particles in certain regimes. The steeper solution has observable effects in the submillimeter and millimeter wavelength regimes of the electromagnetic spectrum. We assemble data for nine debris disks that have been observed at these wavelengths and, using a simplified absorption efficiency model, show that the predicted slope of the particle mass distribution generates SEDs that are in agreement with the observed ones.