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Register a new userModeling Collisional Cascades In Debris Disks: Steep Dust-Size Distributions
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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.
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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.
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.
The cross section of material in debris discs is thought to be dominated by the smallest grains that can still stay in bound orbits despite the repelling action of stellar radiation pressure. Thus the minimum (and typical) grain size $s_text{min}$ is expected to be close to the radiation pressure blowout size $s_text{blow}$. Yet a recent analysis of a sample of Herschel-resolved debris discs showed the ratio $s_text{min}/s_text{blow}$ to systematically decrease with the stellar luminosity from about ten for solar-type stars to nearly unity in the discs around the most luminous A-type stars. Here we explore this trend in more detail, checking how significant it is and seeking to find possible explanations. We show that the trend is robust to variation of the composition and porosity of dust particles. For any assumed grain properties and stellar parameters, we suggest a recipe of how to estimate the true radius of a spatially unresolved debris disc, based solely on its spectral energy distribution. The results of our collisional simulations are qualitatively consistent with the trend, although additional effects may also be at work. In particular, the lack of grains with small $s_text{min}/s_text{blow}$ for lower luminosity stars might be caused by the grain surface energy constraint that should limit the size of the smallest collisional fragments. Also, a better agreement between the data and the collisional simulations is achieved when assuming debris discs of more luminous stars to have higher dynamical excitation than those of less luminous primaries. This would imply that protoplanetary discs of more massive young stars are more efficient in forming big planetesimals or planets that act as stirrers in the debris discs at the subsequent evolutionary stage.
(Abridged) Debris disks trace remnant reservoirs of leftover planetesimals in planetary systems. A handful of warm debris disks have been discovered in the last years, where emission in excess starts in the mid-infrared. An interesting subset within these warm debris disks are those where emission features are detected in mid-IR spectra, which points towards the presence of warm micron-sized dust grains. Given the ages of the host stars, the presence of these grains is puzzling, and questions their origin and survival in time. This study focuses on determining the mineralogy of the dust around 7 debris disks with evidence for warm dust, based on Spitzer/IRS spectroscopic data, in order to provide new insights into the origin of the dust grains. We present a new radiative transfer code dedicated to SED modeling of optically thin disks. We make use of this code on the SEDs of seven warm debris disks, in combination with recent laboratory experiments on dust optical properties. We find that most, if not all, debris disks in our sample are experiencing a transient phase, suggesting a production of small dust grains on relatively short timescales. From a mineralogical point of view, we find that enstatite grains have small abundances compared to crystalline olivine grains. The main result of our study is that we find evidences for Fe-rich crystalline olivine grains (Fe / [Mg + Fe] ~ 0.2) for several debris disks. This finding contrasts with studies of gas-rich protoplanetary disks. The presence of Fe-rich olivine grains, and the overall differences between the mineralogy of dust in Class II disks compared to debris disks suggest that the transient crystalline dust is of a new generation. We discuss possible crystallization routes to explain our results, and comment on the mechanisms that may be responsible for the production of small dust grains.
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