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 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 treatm…
Debris disk images show clumps, rings, warps, and other structures, many of which have been interpreted as perturbations from hidden planets. But so far, no models of these structures have properly accounted for collisions between dust grains. We have developed new steady-state 3D models of debris disks that self-consistently incorporate grain-grain collisions. We summarize our algorithm and use it to illustrate how collisions interact with resonant trapping in the presence of a planet.
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 t…
We analyze two new sets of coagulation calculations for solid particles orbiting within the terrestrial zone of a solar-type star. In models of collisional cascades, numerical simulations demonstrate that the total mass, the mass in 1 mm and smaller particles, and the dust luminosity decline with time more rapidly than predicted by analytic models, $\propto t^{-n}$ with $n \approx$ 1.1-1.2 instead of 1. Size distributions derived from the numerical calculations follow analytic predictions at radii less than 0.1 km but are shallower than predicted at larger sizes. In simulations of planet forma…
Several hundred stars older than 10 million years have been observed to have infrared excesses. These observations are explained by dust grains formed by the collisional fragmentation of hidden planetesimals. Such dusty planetesimal discs are known as debris discs. In a dynamically cold planetesimal disc, collisional coagulation of planetesimals produces planetary embryos which then stir the surrounding leftover planetesimals. Thus, the collisional fragmentation of planetesimals that results from planet formation forms a debris disc. We aim to determine the properties of the underlying planete…
We derive a new analytical model for the evolution of a collisional cascade in a thin annulus around a single central star. In this model, $r_{max}~$ the size of the largest object declines with time (t); $r_{max} \propto t^{-γ}$, with $γ$ = 0.1-0.2. Compared to standard models where $r_{max}~$ is constant in time, this evolution results in a more rapid decline of $M_d$, the total mass of solids in the annulus and $L_d$, the luminosity of small particles in the annulus: $M_d \propto t^{-(γ+ 1)}~$ and $L_d \propto t^{-(γ/2 + 1)}~~$. We demonstrate that the analytical model provides an excellent…
It has been argued that the photometric data and images of the archetypical debris disk around Vega may be in contradiction with the standard, steady-state collisional scenario of the disk evolution. Here we perform physical modeling of the Vega disk "from the sources". We assume that dust is maintained by a "Kuiper belt" of parent planetesimals at ~ 100 AU and employ our collisional and radiative transfer codes to consistently model the size and radial distribution of the disk material and then thermal emission of dust. In doing so, we vary a broad set of parameters, including the stellar pro…
Debris disks are scaled-up analogs of the Kuiper Belt in which dust is generated by collisions between planetesimals. In the "collisional cascade" model of debris disks, dust lost to radiation pressure and winds is constantly replenished by grinding collisions between planetesimals. The model assumes that collisions are destructive and involve large velocities; this assumption has not been tested beyond our Solar System. We present 0"25 ($\approx$2.4 au) resolution observations of the $λ$ = 450 $μ$m dust continuum emission from the debris disk around the nearby M dwarf AU Microscopii with the …
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…
WD 0145+234 is a white dwarf that is accreting metals from a circumstellar disc of planetary material. It has exhibited a substantial and sustained increase in 3-5 micron flux since 2018. Follow-up Spitzer photometry reveals that emission from the disc had begun to decrease by late 2019. Stochastic brightening events superimposed on the decline in brightness suggest the liberation of dust during collisional evolution of the circumstellar solids. A simple model is used to show that the observations are indeed consistent with ongoing collisions. Rare emission lines from circumstellar gas have be…
Millimetre continuum observations of debris discs can provide insights into the physical and dynamical properties of the unseen planetesimals that these discs host. The material properties and collisional models of planetesimals leave their signature on the grain size distribution, which can be traced through the millimetre spectral index. We present 8.8 mm observations of the debris discs HD 48370, CPD 72 2713, HD 131488, and HD 32297 using the Australian Telescope Compact Array (ATCA) as part of the PLanetesimals Around TYpicalPre-main seqUence Stars (PLATYPUS) survey. We detect all four tar…
Aims. We present photometric data of debris disks around HIP 103389 (HD 199260), HIP 107350 (HN Peg, HD206860), and HIP 114948 (HD 219482), obtained in the context of our Herschel Open Time Key Program DUNES (DUst around NEarby Stars). Methods. We used Herschel/PACS to detect the thermal emission of the three debris disks with a 3 sigma sensitivity of a few mJy at 100 um and 160 um. In addition, we obtained Herschel/PACS photometric data at 70 um for HIP 103389. Two different approaches are applied to reduce the Herschel data to investigate the impact of data reduction on the photometry. We fi…
We present a new "collisional grooming" algorithm that enables us to model images of debris disks where the collision time is less than the Poynting Robertson time for the dominant grain size. Our algorithm uses the output of a collisionless disk simulation to iteratively solve the mass flux equation for the density distribution of a collisional disk containing planets in 3 dimensions. The algorithm can be run on a single processor in ~1 hour. Our preliminary models of disks with resonant ring structures caused by terrestrial mass planets show that the collision rate for background particles i…
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…
Multi-epoch infrared photometry from Spitzer is used to monitor circumstellar discs at white dwarfs, which are consistent with disrupted minor planets whose debris is accreted and chemically reflected by their host stars. Widespread infrared variability is found across the population of 37 stars with two or more epochs. Larger flux changes occur on longer time-scales, reaching several tens of per cent over baselines of a few years. The canonical model of a geometrically thin, optically thick disc is thus insufficient, as it cannot give rise to the observed behaviour. Optically thin dust best a…
Observations of circumstellar disks provide a powerful tool for our understanding of planetary systems dynamics. Analogs to the Solar System asteroid belts, debris disks result from the collision of the remaining solid material of the planet formation process. Even if the presence of disk is now reported for hundreds of stars, its detection around stars similar to the Sun is still very sparse. We report the results of a search for debris disks around Kepler stars with surface physical parameters close to solar values, including rotation period, using observations by the Wide-field infrared Sur…
In many ways, the HR 8799 planetary system strongly resembles our own. It features four giant planets and two debris belts, analogues to the Asteroid and Edgeworth-Kuiper belts. Here, we present the results of dynamical simulations of HR 8799's inner debris belt, to study its structure and collisional environment. Our results suggest that HR 8799's inner belt is highly structured, with gaps between regions of dynamical stability. The belt is likely constrained between sharp inner and outer edges, located at ~6 and ~8 au, respectively. Its inner edge coincides with a broad gap cleared by the 4:…
The presence of dusty debris around main sequence stars denotes the existence of planetary systems. Such debris disks are often identified by the presence of excess continuum emission at infrared and (sub-)millimetre wavelengths, with measurements at longer wavelengths tracing larger and cooler dust grains. The exponent of the slope of the disk emission at sub-millimetre wavelengths, `q', defines the size distribution of dust grains in the disk. This size distribution is a function of the rigid strength of the dust producing parent planetesimals. As part of the survey `PLAnetesimals around TYp…
Motivated by the New Horizons mission, we consider how Pluto's small satellites -- currently Styx, Nix, Kerberos, and Hydra -- grow in debris from the giant impact that forms the Pluto-Charon binary. After the impact, Pluto and Charon accrete some of the debris and eject the rest from the binary orbit. During the ejection, high velocity collisions among debris particles produce a collisional cascade, leading to the ejection of some debris from the system and enabling the remaining debris particles to find stable orbits around the binary. Our numerical simulations of coagulation and migration s…
Debris belts on the periphery of planetary systems, encompassing the region occupied by planetary orbits, are massive analogues of the Solar system's Kuiper belt. They are detected by thermal emission of dust released in collisions amongst directly unobservable larger bodies that carry most of the debris disc mass. We estimate the total mass of the discs by extrapolating up the mass of emitting dust with the help of collisional cascade models. The resulting mass of bright debris discs appears to be unrealistically large, exceeding the mass of solids available in the systems at the preceding pr…
In recent years, gas has been observed in an increasing number of debris discs, though its nature remains to be determined. Here, we analyse CO molecular excitation in optically thin debris discs, and search ALMA Cycle-0 data for CO J=3-2 emission in the Fomalhaut ring. No significant line emission is observed; we set a 3-$σ$ upper limit on the integrated line flux of 0.16 Jy km s$^{-1}$. We show a significant dependency of the CO excitation on the density of collisional partners $n$, on the gas kinetic temperature $T_k$ and on the ambient radiation field $J$, suggesting that assumptions widel…
(Abridged) The radii of debris disks and the sizes of their dust grains are tracers of the formation mechanisms and physical processes operating in these systems. We use a sample of 34 debris disks spatially resolved in various Herschel programs to constrain them. While we modeled disks with both warm and cold components, we focus our analysis only on the cold outer disks, i.e. Kuiper-belt analogs. The disk radii derived from the resolved images reveal a large dispersion, but no significant trend with the stellar luminosity, which argues against ice lines as a dominant player in setting the de…
We describe comprehensive calculations of the formation of icy planets and debris disks at 30-150 AU around 1-3 solar mass stars. Disks composed of large, strong planetesimals produce more massive planets than disks composed of small, weak planetesimals. The maximum radius of icy planets ranges from roughly 1500 km to 11,500 km. The formation rate of 1000 km objects - `Plutos' - is a useful proxy for the efficiency of icy planet formation. Plutos form more efficiently in massive disks, in disks with small planetesimals, and in disks with a range of planetesimal sizes. Although Plutos form thro…
Millimeter emission from debris disks around stars of different ages provides constraints on the collisional evolution of planetesimals. We present ALMA 1.3 millimeter observations of a sample of 76 Solar-type stars in the ~115 Myr old Pleiades star cluster. These ALMA observations complement previous infrared observations of this sample by providing sensitivity to emission from circumstellar dust at lower temperatures, corresponding to debris at radii comparable to the Kuiper Belt and beyond. The observations obtain a beam size of 1.5 arcsec (200 au) and a median rms noise of 54 mircoJy/beam,…
Observations of debris disks, the products of the collisional evolution of rocky planetesimals, can be used to trace planetary activity across a wide range of stellar types. The most common end points of stellar evolution are no exception as debris disks have been observed around several dozen white dwarf stars. But instead of planetary formation, post-main-sequence debris disks are a signpost of planetary destruction, resulting in compact debris disks from the tidal disruption of remnant planetesimals. In this work, we present the discovery of five new debris disks around white dwarf stars wi…
Many debris discs reveal a two-component structure, with a cold outer and a warm inner component. While the former are likely massive analogues of the Kuiper belt, the origin of the latter is still a matter of debate. In this work we investigate whether the warm dust may be a signature of asteroid belt analogues. In the scenario tested here the current two-belt architecture stems from an originally extended protoplanetary disc, in which planets have opened a gap separating it into the outer and inner discs which, after the gas dispersal, experience a steady-state collisional decay. This idea i…
We present ATCA continuum observations at a wavelength of 6.8 mm of five debris disks: $β$ Pictoris, q$^1$ Eridani, HD 107146, HD 181327, and HD 95086. These observations provide the detection at the longest wavelengths obtained to date for all these debris disks. By combining our 6.8 mm data with previous detections at shorter sub-millimeter/millimeter wavelengths we measure the long wavelength spectral index of these sources. We then use previous estimates for the temperature of the emitting dust to derive the spectral index of the dust emissivity. Under the assumption that all the detected …
Context. HD 172555 is a young A7 star belonging to the Beta Pictoris Moving Group that harbours a debris disc. The Spitzer IRS spectrum of the source showed mid-IR features such as silicates and glassy silica species, indicating the presence of a warm dust component with small grains, which places HD 172555 among the small group of debris discs with such properties. The IRS spectrum also shows a possible emission of SiO gas. Aims. We aim to study the dust distribution in the circumstellar disc of HD 172555 and to asses the presence of gas in the debris disc. Methods. As part of the GASPS Open …
We present results from two Herschel observing programs using the Photodetector Array Camera and Spectrometer. During three separate campaigns, we obtained Herschel data for 24 stars at 70, 100, and 160 microns. We chose stars that were already known or suspected to have circumstellar dust based on excess infrared emission previously measured with IRAS or Spitzer, and used Herschel to examine long-wavelength properties of the dust. Fifteen stars were found to be uncontaminated by background sources, and possess infrared emission most likely due to a circumstellar debris disk. We analyzed the p…
We present 5 to 15 micron Spitzer Infrared Spectrograph (IRS) low resolution spectral data of a candidate debris disk around an M4.5 star identified as a likely member of the ~40 Myr old cluster NGC2547. The IRS spectrum shows a silicate emission feature, indicating the presence of warm, small, (sub)micron-sized dust grains in the disk. Of the fifteen previously known candidate debris disks around M-type stars, the one we discuss in this paper is the first to have an observed mid-infrared spectrum and is also the first to have measured silicate emission. We combined the IRS data with ancillary…
We consider the ability of three models - impacts, captures, and collisional cascades - to account for a bright cloud of dust in Fomalhaut b. Our analysis is based on a novel approach to the power-law size distribution of solid particles central to each model. When impacts produce debris with (i) little material in the largest remnant and (ii) a steep size distribution, the debris has enough cross-sectional area to match observations of Fomalhaut b. However, published numerical experiments of impacts between 100 km objects suggest this outcome is unlikely. If collisional processes maintain a s…
Debris disk morphology is wavelength dependent due to the wide range of particle sizes and size-dependent dynamics influenced by various forces. Resolved images of nearby debris disks reveal complex disk structures that are difficult to distinguish from their spectral energy distributions. Therefore, multi-wavelength resolved images of nearby debris systems provide an essential foundation to understand the intricate interplay between collisional, gravitational, and radiative forces that govern debris disk structures. We present the SOFIA 35 um resolved disk image of epsilon Eri, the closest de…
We present far-infrared and sub-millimeter images of the eta Crv debris disk system obtained with Herschel and SCUBA-2, as well as Hubble Space Telescope visible and near-infrared coronagraphic images. In the 70 micron Herschel image, we clearly separate the thermal emission from the warm and cold belts in the system, find no evidence for a putative dust population located between them, and precisely determine the geometry of the outer belt. We also find marginal evidence for azimuthal asymmetries and a global offset of the outer debris ring relative to the central star. Finally, we place stri…
White dwarf (WD) pollution is thought to arise from the tidal disruption of planetary bodies. The initial fragment stream is extremely eccentric, while observational evidence suggest that discs are circular or nearly so. Here we propose a novel mechanism to bridge this gap and show that the fragments can rapidly circularise through dust or gas drag when they interact with a pre-existing compact disc. We assume that the tidal stream mainly consists of small cohesive fragments in the size range 10-1000 m, capable of resisting the WD tidal forces, whereas the compact discs span a wide mass range.…
We have used the Submillimeter Array (SMA) to make 1.3 millimeter observations of the debris disk surrounding HD 15115, an F-type star with a putative membership in the beta Pictoris moving group. This nearly edge-on debris disk shows an extreme asymmetry in optical scattered light, with an extent almost two times larger to the west of the star than to the east (originally dubbed the "Blue Needle"). The SMA observations reveal resolved emission that we model as a circumstellar belt of thermal dust emission. This belt extends to a radius of ~110 AU, coincident with the break in the scattered li…
The discovery of numerous debris disks around white dwarfs (WDs), gave rise to extensive study of such disks and their role in polluting WDs, but the formation and evolution of these disks is not yet well understood. Here we study the role of aeolian (wind) erosion in the evolution of solids in WD debris disks. Aeolian erosion is a destructive process that plays a key role in shaping the properties and size-distribution of planetesimals, boulders and pebbles in gaseous protoplanetary disks. Our analysis of aeolian erosion in WD debris disks shows it can also play an important role in these env…
We present 1.3 millimeter observations of the debris disk surrounding the HR 8799 multi-planet system from the Submillimeter Array to complement archival ALMA observations that spatially filtered away the bulk of the emission. The image morphology at $3.8$ arcsecond (150 AU) resolution indicates an optically thin circumstellar belt, which we associate with a population of dust-producing planetesimals within the debris disk. The interferometric visibilities are fit well by an axisymmetric radial power-law model characterized by a broad width, $ΔR/R\gtrsim 1$. The belt inclination and orientatio…
Context: Debris disks are important observational clues for understanding planetary-system formation process. In particular, faint warm debris disks may be related to late planet formation near 1 AU. A systematic search of faint warm debris disks is necessary to reveal terrestrial planet formation. Aims: Faint warm debris disks show excess emission that peaks at mid-IR wavelengths. Thus we explore debris disks using the AKARI mid-IR all-sky point source catalog (PSC), a product of the second generation unbiased IR all-sky survey. Methods : We investigate IR excess emission for 678 isolated mai…
We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple unstable gas giants. We previously showed that the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and debris disks. Here we present new simulations that show that this connection is qualitatively robust to changes in: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk. We discuss how variations in these …
This paper presents a study of circumstellar debris around Sun-like stars using data from the Herschel DEBRIS Key Programme. DEBRIS is an unbiased survey comprising the nearest ~90 stars of each spectral type A-M. Analysis of the 275 F-K stars shows that excess emission from a debris disc was detected around 47 stars, giving a detection rate of 17.1+2.6-2.3 per cent, with lower rates for later spectral types. For each target a blackbody spectrum was fitted to the dust emission to determine its fractional luminosity and temperature. The derived under- lying distribution of fractional luminosity…
We present resolved Herschel images of a circumbinary debris disk in the 99 Herculis system. The primary is a late F-type star. The binary orbit is well characterised and we conclude that the disk is misaligned with the binary plane. Two different models can explain the observed structure. The first model is a ring of polar orbits that move in a plane perpendicular to the binary pericenter direction. We favour this interpretation because it includes the effect of secular perturbations and the disk can survive for Gyr timescales. The second model is a misaligned ring. Because there is an ambigu…
The vertical distribution of dust in debris disks is sensitive to the number and size of large planetesimals dynamically stirring the disk, and is therefore well-suited for constraining the prevalence of otherwise unobservable Uranus and Neptune analogs. Information regarding stirring bodies has previously been inferred from infrared and optical observations of debris disk vertical structure, but theoretical works predict that the small particles traced by short-wavelength observations will be `puffed up' by radiation pressure, yielding only upper limits. The large grains that dominate the dis…
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 $\sim5$ $μ$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 wavel…
Debris disks offer valuable insights into the latest stages of circumstellar disk evolution, and can possibly help us to trace the outcomes of planetary formation processes. In the age range 10 to 100\,Myr, most of the gas is expected to have been removed from the system, giant planets (if any) must have already been formed, and the formation of terrestrial planets may be on-going. Pluto-sized planetesimals, and their debris released in a collisional cascade, are under their mutual gravitational influence, which may result into non-axisymmetric structures in the debris disk. High angular resol…
The multi-wavelength vertical structure of the archetypal $β$ Pictoris debris disk
California Institute of Technology（加州理工学院）；University of Cambridge（剑桥大学）；University of Belgrade（贝尔格莱德大学）；University of Oxford（牛津大学）；ALMA JAO（阿塔卡马大型毫米波/亚毫米波阵列联合运营办公室）；Wesleyan University（卫斯理安大学）；Trinity College Dublin, the University of Dublin（都柏林三一学院，都柏林大学）
Circumstantial evidence suggests that most known extra-solar planetary systems are survivors of violent dynamical instabilities. Here we explore how giant planet instabilities affect the formation and survival of terrestrial planets. We simulate planetary system evolution around Sun-like stars from initial conditions that comprise: an inner disk of planetesimals and planetary embryos, three giant planets at Jupiter-Saturn distances, and a massive outer planetesimal disk. We then calculate dust production rates and debris disk SEDs assuming that each planetesimal particle represents an ensemble…
We measured 304 absorption features in the ultraviolet and visible spectra of the star 51 Oph, which is known to have a debris disk with a high inclination. We analyzed the relative populations of atoms in excited fine-structure and metastable levels that are maintained by optical pumping and collisional excitation by electrons, and we found that most of the gas is situated at about 6AU from the star, has an electron volume density $10^5 < n(e) < 3\times 10^6{\rm cm}^{-3}$, and a temperature T=8000K. Our interpretations reveal that the gas is partly ionized, has a column density of neutral hyd…
Asteroids and comets (planetesimals) are created in gas- and dust-rich protoplanetary discs. The presence of these planetesimals around main-sequence stars is usually inferred from the detection of excess continuum emission at infrared wavelengths from dust grains produced by destructive processes within these discs. Modelling of the disc structure and dust grain properties for those discs is often hindered by the absence of any meaningful constraint on the location and spatial extent of the disc. Multi-wavelength, spatially resolved imaging is thus invaluable in refining the interpretation of…
We present ALMA 1.3 mm (230 GHz) observations of the HD 32297 and HD 61005 debris disks, two of the most iconic debris disks due to their dramatic swept-back wings seen in scattered light images. These observations achieve sensitivities of 14 and 13 $μ$Jy beam$^{-1}$ for HD 32297 and HD 61005, respectively, and provide the highest resolution images of these two systems at millimeter wavelengths to date. By adopting a MCMC modeling approach, we determine that both disks are best described by a two-component model consisting of a broad ($ΔR/R> 0.4$) planetesimal belt with a rising surface densit…
