Infrared surveys indicate that the dust content in debris disks gradually declines with stellar age. We simulated the long-term collisional depletion of debris disks around solar-type (G2 V) stars with our collisional code. The numerical results were supplemented by, and interpreted through, a new analytic model. General scaling rules for the disk evolution are suggested. The timescale of the collisional evolution is inversely proportional to the initial disk mass and scales with radial distance as r 4.3 and with eccentricities of planetesimals as e −2.3 . Further, we show that at actual ages of debris disks between 10 Myr and 10 Gyr, the decay laws of the dust mass and the total disk mass are different. The reason is that the collisional lifetime of planetesimals is size-dependent. At any moment, there exists a transitional size, which separates larger objects that still retain the "primordial" size distribution set in the growth phase from smaller objects whose size distribution is already set by disruptive collisions. The dust mass and its decay rate evolve as that transition affects objects of everlarger sizes. Under standard assumptions, the dust mass, fractional luminosity, and thermal fluxes all decrease as t ξ with ξ = −0.3...−0.4. Specific decay laws of the total disk mass and the dust mass, including the value of ξ, largely depend on a few model parameters, such as the critical fragmentation energy as a function of size, the primordial size distribution of largest planetesimals, as well as the characteristic eccentricity and inclination of their orbits. With standard material prescriptions and a distribution of disk masses and extents, a synthetic population of disks generated with our analytic model agrees quite well with the observed Spitzer/MIPS statistics of 24 and 70 µm fluxes and colors versus age.

We model a typical debris disk, treated as an idealized ensemble of dust particles, exposed to stellar gravity and direct radiation pressure and experiencing fragmenting collisions. Applying the kinetic method of statistical physics, written in orbital elements, we calculate size and spatial distibutions expected in a steady-state disk, investigate timescales needed to reach the steady state, and calculate mass loss rates. Particular numerical examples are given for the debris disk around Vega. The disk should comprise a population of larger grains in bound orbits and a population of smaller particles in hyperbolic orbits. The cross section area is dominated by the smallest grains that still can stay in bound orbits, for Vega about 10 µm in radius. The size distribution is wavy, implying secondary peaks in the size distribution at larger sizes. The radial profile of the pole-on surface density or the optical depth in the steady-state disk has a power-law index between about −1 and −2. It cannot be much steeper even if dust production is confined to a narrow planetesimal belt, because collisional grinding produces smaller and smaller grains, and radiation pressure pumps up their orbital eccentricities and spreads them outward, which flattens the radial profile. The timescales to reach a steady state depend on grain sizes and distance from the star. For Vega, they are about 1 Myr for grains up to some hundred µm at 100 AU. The total mass of the Vega disk needed to produce the observed amount of micron and submillimeter-sized dust does not exceed several earth masses for an upper size limit of parent bodies of about 1 km. The collisional depletion of the disk occurs on Gyr timescales.

Context. Debris discs are a consequence of the planet formation process and constitute the fingerprints of planetesimal systems. Their solar system counterparts are the asteroid and Edgeworth-Kuiper belts. Aims. The DUNES survey aims at detecting extra-solar analogues to the Edgeworth-Kuiper belt around solar-type stars, putting in this way the solar system into context. The survey allows us to address some questions related to the prevalence and properties of planetesimal systems. Methods. We used Herschel/PACS to observe a sample of nearby FGK stars. Data at 100 and 160 μm were obtained, complemented in some cases with observations at 70 μm, and at 250, 350 and 500 μm using SPIRE. The observing strategy was to integrate as deep as possible at 100 μm to detect the stellar photosphere. Results. Debris discs have been detected at a fractional luminosity level down to several times that of the Edgeworth-Kuiper belt. The incidence rate of discs around the DUNES stars is increased from a rate of ∼12.1% ± 5% before Herschel to ∼20.2% ± 2%. A significant fraction (∼52%) of the discs are resolved, which represents an enormous step ahead from the previously known resolved discs. Some stars are associated with faint far-IR excesses attributed to a new class of cold discs. Although it cannot be excluded that these excesses are produced by coincidental alignment of background galaxies, statistical arguments suggest that at least some of them are true debris discs. Some discs display peculiar SEDs with spectral indexes in the 70-160 μm range steeper than the Rayleigh-Jeans one. An analysis of the debris disc parameters suggests that a decrease might exist of the mean black body radius from the F-type to the K-type stars. In addition, a weak trend is suggested for a correlation of disc sizes and an anticorrelation of disc temperatures with the stellar age.

HR 8799 is a nearby A-type star with a debris disk and three planetary candidates, which have been imaged directly. We undertake a coherent analysis of various observational data for all known components of the system, including the central star, imaged companions, and dust. Our goal is to elucidate the architecture and evolutionary status of the system. We try to further constrain the age and orientation of the system, the orbits and masses of the companions, and the location of dust. On the basis of the high luminosity of debris dust and dynamical constraints, we argue for a rather young system's age of < ∼ 50 Myr. The system must be seen nearly, but not exactly, pole-on. Our analysis of the stellar rotational velocity yields an inclination of 13-30• , whereas i > ∼ 20• is needed for the system to be dynamically stable, which suggests a probable inclination range of 20-30• . The spectral energy distribution, including the Spitzer/IRS spectrum in the mid-infrared as well as IRAS, ISO, JCMT, and IRAM observations, is naturally reproduced by two dust rings associated with two planetesimal belts. The inner "asteroid belt" is located at ∼10 AU inside the orbit of the innermost companion and a "Kuiper belt" at > ∼ 100 AU is just exterior to the orbit of the outermost companion. The dust masses in the inner and outer ring are estimated to be ≈1 × 10 −5 and 4 × 10 −2 Earth masses, respectively. We show that all three planetary candidates may be stable in the mass range suggested in the discovery paper by Marois et al. (2008) (between 5 and 13 Jupiter masses), but only for some of all possible orientations.• is required and the line of nodes of the system's symmetry plane on the sky must lie within between 0• an 50• from north eastward. For higher masses (M b , M c , M d ) from (7, 10, 10) to (11, 13, 13), the constraints on both angles are even more stringent. Stable orbits imply a double (4:2:1) mean-motion resonance between all three companions. We finally show that in the cases where the companions themselves are orbitally stable, the dust-producing planetesimal belts are also stable against planetary perturbations.

Debris disks, which are inferred from the observed infrared excess to be ensembles of dust, rocks, and probably planetesimals, are common features of stellar systems. As the mechanisms of their formation and evolution are linked to those of planetary bodies, they provide valuable information. The few well-resolved debris disks are even more valuable because they can serve as modelling benchmarks and help resolve degeneracies in modelling aspects such as typical grain sizes and distances. Here, we present an analysis of the HD 207129 debris disk, based on its well-covered spectral energy distribution and Herschel/PACS images obtained in the framework of the DUNES (DUst around NEarby Stars) programme. We use an empirical power-law approach to the distribution of dust and we then model the production and removal of dust by means of collisions, direct radiation pressure, and drag forces. The resulting best-fit model contains a total of nearly 10 −2 Earth masses in dust, with typical grain sizes in the planetesimal belt ranging from 4 to 7 µm. We constrain the dynamical excitation to be low, which results in very long collisional lifetimes and a drag that notably fills the inner gap, especially at 70 µm. The radial distribution stretches from well within 100 AU in an unusual, outward-rising slope towards a rather sharp outer edge at about 170-190 AU. The inner edge is therefore smoother than that reported for Fomalhaut, but the contribution from the extended halo of barely bound grains is similarly small. Both slowly self-stirring and planetary perturbations could potentially have formed and shaped this disk.