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We explore the collisional decay of disk mass and infrared emission in debris disks. With models, we show that the rate of the decay varies throughout the evolution of the disks, increasing its rate up to a certain point, which is followed by a leveling off to a slower value. The total disk mass falls off α t -0.35 at its fastest point (where t is time) for our reference model, while the dust mass and its proxy-the infrared excess emission-fades significantly faster (α t -0.8). These later level off to a decay rate of Mtot(t ) α t -0.08 and Mdust(t) or Lir(t ) α t -0.6. This is slower than the α t -1 decay given for all three system parameters by traditional analytic models. We also compile an extensive catalog of Spitzer and Herschel 24, 70, and 100μm observations. Assuming a log-normal distribution of initial disk masses, we generate model population decay curves for the fraction of stars harboring debris disks detected at 24μm. We also model the distribution of measured excesses at the far-IR wavelengths (70-100μm) at certain age regimes. We show general agreement at 24μm between the decay of our numerical collisional population synthesis model and observations up to a Gyr. We associate offsets above a Gyr to stochastic events in a few select systems. We cannot fit the decay in the far-infrared convincingly with grain strength properties appropriate for silicates, but those of water ice give fits more consistent with the observations (other relatively weak grain materials would presumably also be successful). The oldest disks have a higher incidence of large excesses than predicted by the model; again, a plausible explanation is very late phases of high dynamical activity around a small number of stars. Finally, we constrain the variables of our numerical model by comparing the evolutionary trends generated from the exploration of the full parameter space to observations. Amongst other results, we show that erosive collisions are dominant in setting the timescale of the evolution and that planetesimals on the order of 100 km in diameter are necessary in the cascades for our population synthesis models to reproduce the observations. [ABSTRACT FROM AUTHOR]

We develop a new numerical algorithmtomodel collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions. [ABSTRACT FROM AUTHOR]

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. 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 spectral energy distributions that are in agreement with the observed ones. [ABSTRACT FROM AUTHOR]