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Register a new userModeling Collisional Cascades In Debris Disks: The Numerical Method
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We develop a new numerical algorithm to model 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.
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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.
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 ~ 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 (~ t^-0.8). These later level off to a decay rate of M_tot(t) ~ t^-0.08 and M_dust(t) or L_ir(t) ~ t^-0.6. This is slower than the ~ 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 100 micron observations. Assuming a log-normal distribution of initial disk masses, we generate model population decay curves for the fraction of debris disk harboring stars observed at 24 micron and also model the distribution of measured excesses at the far-IR wavelengths (70-100 micron) at certain age regimes. We show general agreement at 24 micron 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.
Main sequence stars, like the Sun, are often found to be orbited by circumstellar material that can be categorized into two groups, planets and debris. The latter is made up of asteroids and comets, as well as the dust and gas derived from them, which makes debris disks observable in thermal emission or scattered light. These disks may persist over Gyrs through steady-state evolution and/or may also experience sporadic stirring and major collisional breakups, rendering them atypically bright for brief periods of time. Most interestingly, they provide direct evidence that the physical processes (whatever they may be) that act to build large oligarchs from micron-sized dust grains in protoplanetary disks have been successful in a given system, at least to the extent of building up a significant planetesimal population comparable to that seen in the Solar Systems asteroid and Kuiper belts. Such systems are prime candidates to host even larger planetary bodies as well. The recent growth in interest in debris disks has been driven by observational work that has provided statistics, resolved images, detection of gas in debris disks, and discoveries of new classes of objects. The interpretation of this vast and expanding dataset has necessitated significant advances in debris disk theory, notably in the physics of dust produced in collisional cascades and in the interaction of debris with planets. Application of this theory has led to the realization that such observations provide a powerful diagnostic that can be used not only to refine our understanding of debris disk physics, but also to challenge our understanding of how planetary systems form and evolve.
Observations of debris disks offer a window into the physical and dynamical properties of planetesimals in extrasolar systems through the size distribution of dust grains. In particular, the millimeter spectral index of thermal dust emission encodes information on the grain size distribution. We have made new VLA observations of a sample of seven nearby debris disks at 9 mm, with 3 resolution and $sim5$ $mu$Jy/beam rms. We combine these with archival ATCA observations of eight additional debris disks observed at 7 mm, together with up-to-date observations of all disks at (sub)millimeter wavelengths from the literature to place tight constraints on the millimeter spectral indices and thus grain size distributions. The analysis gives a weighted mean for the slope of the power law grain size distribution, $n(a)propto a^{-q}$, of $langle q rangle = 3.36pm0.02$, with a possible trend of decreasing $q$ for later spectral type stars. We compare our results to a range of theoretical models of collisional cascades, from the standard self-similar, steady-state size distribution ($q=3.5$) to solutions that incorporate more realistic physics such as alternative velocity distributions and material strengths, the possibility of a cutoff at small dust sizes from radiation pressure, as well as results from detailed dynamical calculations of specific disks. Such effects can lead to size distributions consistent with the data, and plausibly the observed scatter in spectral indices. For the AU Mic system, the VLA observations show clear evidence of a highly variable stellar emission component; this stellar activity obviates the need to invoke the presence of an asteroid belt to explain the previously reported compact millimeter source in this system.
A significant fraction of nearby young moving group members harbor circumstellar debris dust disks. Due to their proximity and youth, these disks are attractive targets for studying the early evolution of debris dust and planetesimal belts. Here we present 70 and 160$mu$m observations of 31 systems in the $beta$ Pic moving group, and in the Tucana-Horologium, Columba, Carina and Argus associations, using the Herschel Space Observatory. None of these stars were observed at far-infrared wavelengths before. Our Herschel measurements were complemented by photometry from the WISE satellite for the whole sample, and by submillimeter/millimeter continuum data for one source, HD 48370. We identified six stars with infrared excess, four of them are new discoveries. By combining our new findings with results from the literature, we examined the incidence and general characteristics of debris disks around Sun-like members of the selected groups. With their dust temperatures of <45 K the newly identified disks around HD 38397, HD 48370, HD 160305, and BD-20 951 represent the coldest population within this sample. For HD 38397 and HD 48370, the emission is resolved in the 70$mu$m PACS images, the estimated radius of these disks is ~90 au. Together with the well-known disk around HD 61005, these three systems represent the highest mass end of the known debris disk population around young G-type members of the selected groups. In terms of dust content, they resemble the hypothesized debris disk of the ancient Solar System.
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