The local dust foregrounds in the microwave sky: I. Thermal emission spectra

Analyses of the cosmic microwave background (CMB) radiation maps made by the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed anomalies not predicted by the standard inflationary cosmology. In particular, the power of the quadrupole moment of the CMB fluctuations is remarkably low, and the quadrupole and octopole moments are aligned mutually and with the geometry of the Solar system. It has been suggested in the literature that microwave sky pollution by an unidentified dust cloud in the vicinity of the Solar system may be the cause for these anomalies. In this paper, we simulate the thermal emission by clouds of spherical homogeneous particles of several materials. Spectral constraints from the WMAP multi-wavelength data and earlier infrared observations on the hypothetical dust cloud are used to determine the dust cloud's physical characteristics. In order for its emissivity to demonstrate a flat, CMB-like wavelength dependence over the WMAP wavelengths (3 through 14 mm), and to be invisible in the infrared light, its particles must be macroscopic. Silicate spheres from several millimetres in size and carbonaceous particles an order of magnitude smaller will suffice. According to our estimates of the abundance of such particles in the Zodiacal cloud and trans-neptunian belt, yielding the optical depths of the order of 1E-7 for each cloud, the Solar-system dust can well contribute 10 microKelvin (within an order of magnitude) in the microwaves. This is not only intriguingly close to the magnitude of the anomalies (about 30 microKelvin), but also alarmingly above the presently believed magnitude of systematic biases of the WMAP results (below 5 microKelvin) and, to an even greater degree, of the future missions with higher sensitivities, e.g. PLANCK.Comment: 33 pages, 9 figures, 1 table. The Astrophysical Journal, 2009, accepte

Collisions and drag in debris discs with eccentric parent belts

Context: High-resolution images of circumstellar debris discs reveal off-centred rings that indicate past or ongoing perturbation, possibly caused by secular gravitational interaction with unseen stellar or substellar companions. The purely dynamical aspects of this departure from radial symmetry are well understood. However, the observed dust is subject to additional forces and effects, most notably collisions and drag. Aims: To complement the studies of dynamics, we therefore aim to understand how new asymmetries are created by the addition of collisional evolution and drag forces, and existing ones strengthened or overridden. Methods: We augmented our existing numerical code "Analysis of Collisional Evolution" (ACE) by an azimuthal dimension, the longitude of periapse. A set of fiducial discs with global eccentricities ranging from 0 to 0.4 is evolved over giga-year timescales. Size distribution and spatial variation of dust are analysed and interpreted. The basic impact of belt eccentricity on spectral energy distributions (SEDs) and images is discussed. Results: We find features imposed on characteristic timescales. First, radiation pressure defines size cutoffs that differ between periapse and apoapse, resulting in an asymmetric halo. The differences in size distribution make the observable asymmetry of the halo depend on wavelength. Second, collisional equilibrium prefers smaller grains on the apastron side of the parent belt, reducing the effect of pericentre glow and the overall asymmetry. Third, Poynting-Robertson drag fills the region interior to an eccentric belt such that the apastron side is more tenuous. Interpretation and prediction of the appearance in scattered light is problematic when spatial and size distribution are coupled.Comment: Accepted for publication in A&A, 14 pages, 16 figure

Collisional modelling of the debris disc around HIP 17439

We present an analysis of the debris disc around the nearby K2 V star HIP 17439. In the context of the Herschel DUNES key programme the disc was observed and spatially resolved in the far-IR with the Herschel PACS and SPIRE instruments. In a first model, Ertel et al. (2014) assumed the size and radial distribution of the circumstellar dust to be independent power laws. There, by exploring a very broad range of possible model parameters several scenarios capable of explaining the observations were suggested. In this paper, we perform a follow-up in-depth collisional modelling of these scenarios trying to further distinguish between them. In our models we consider collisions, direct radiation pressure, and drag forces, i.e. the actual physical processes operating in debris discs. We find that all scenarios discussed in Ertel et al. are physically sensible and can reproduce the observed SED along with the PACS surface brightness profiles reasonably well. In one model, the dust is produced beyond 120au in a narrow planetesimal belt and is transported inwards by Poynting-Robertson and stellar wind drag. A good agreement with the observed radial profiles would require stellar winds by about an order of magnitude stronger than the solar value, which is not supported, although not ruled out, by observations. Another model consists of two spatially separated planetesimal belts, a warm inner and a cold outer one. This scenario would probably imply the presence of planets clearing the gap between the two components. Finally, we show qualitatively that the observations can be explained by assuming the dust is produced in a single, but broad planetesimal disc with a surface density of solids rising outwards, as expected for an extended disc that experiences a natural inside-out collisional depletion. Prospects of discriminating between the competing scenarios by future observations are discussed.Comment: Astronomy and Astrophysics (accepted for publication). 11 pages, 8 figure

Collisional modelling of the AU Microscopii debris disc

The spatially resolved AU Mic debris disc is among the most famous and best-studied debris discs. We aim at a comprehensive understanding of the dust production and the dynamics of the disc objects with in depth collisional modelling including stellar radiative and corpuscular forces. Our models are compared to a suite of observational data for thermal and scattered light emission, ranging from the ALMA radial surface brightness profile at 1.3mm to polarisation measurements in the visible. Most of the data can be reproduced with a planetesimal belt having an outer edge at around 40au and subsequent inward transport of dust by stellar winds. A low dynamical excitation of the planetesimals with eccentricities up to 0.03 is preferred. The radial width of the planetesimal belt cannot be constrained tightly. Belts that are 5au and 17au wide, as well as a broad 44au-wide belt are consistent with observations. All models show surface density profiles increasing with distance from the star as inferred from observations. The best model is achieved by assuming a stellar mass loss rate that exceeds the solar one by a factor of 50. While the SED and the shape of the ALMA profile are well reproduced, the models deviate from the scattered light data more strongly. The observations show a bluer disc colour and a lower degree of polarisation for projected distances <40au than predicted by the models. The problem may be mitigated by irregularly-shaped dust grains which have scattering properties different from the Mie spheres used. From tests with a handful of selected dust materials, we derive a preference for mixtures of silicate, carbon, and ice of moderate porosity. We address the origin of the unresolved central excess emission detected by ALMA and show that it cannot stem from an additional inner belt alone. Instead, it should derive, at least partly, from the chromosphere of the central star.Comment: Astronomy and Astrophysics (accepted for publication), 18 pages, 11 figure

Sub-millimeter images of a dusty Kuiper belt around eta Corvi

We present sub-millimeter and mid-infrared images of the circumstellar disk around the nearby F2V star eta Corvi. The disk is resolved at 850um with a size of ~100AU. At 450um the emission is found to be extended at all position angles, with significant elongation along a position angle of 130+-10deg; at the highest resolution (9.3") this emission is resolved into two peaks which are to within the uncertainties offset symmetrically from the star at 100AU projected separation. Modeling the appearance of emission from a narrow ring in the sub-mm images shows the observed structure cannot be caused by an edge-on or face-on axisymmetric ring; the observations are consistent with a ring of radius 150+-20AU seen at 45+-25deg inclination. More face-on orientations are possible if the dust distribution includes two clumps similar to Vega; we show how such a clumpy structure could arise from the migration over 25Myr of a Neptune mass planet from 80-105AU. The inner 100AU of the system appears relatively empty of sub-mm emitting dust, indicating that this region may have been cleared by the formation of planets, but the disk emission spectrum shows that IRAS detected an additional hot component with a characteristic temperature of 370+-60K (implying a distance of 1-2AU). At 11.9um we found the emission to be unresolved with no background sources which could be contaminating the fluxes measured by IRAS. The age of this star is estimated to be ~1Gyr. It is very unusual for such an old main sequence star to exhibit significant mid-IR emission. The proximity of this source makes it a perfect candidate for further study from optical to mm wavelengths to determine the distribution of its dust.Comment: 22 pages, 4 figures. Scheduled for publication in ApJ 10 February 2005 issu

Transience of hot dust around sun-like stars

There is currently debate over whether the dust content of planetary systems is stochastically regenerated or originates in planetesimal belts evolving in steady state. In this paper a simple model for the steady state evolution of debris disks due to collisions is developed and confronted with the properties of the emerging population of 7 sun-like stars that have hot dust <10AU. The model shows there is a maximum possible disk mass at a given age, since more massive primordial disks process their mass faster. The corresponding maximum dust luminosity is f_max=0.00016r^(7/3)/t_age. The majority (4/7) of the hot disks exceed this limit by >1000 and so cannot be the products of massive asteroid belts, rather the following systems must be undergoing transient events characterized by an unusually high dust content near the star: eta Corvi, HD69830, HD72905 and BD+20307. It is also shown that the hot dust cannot originate in a recent collision in an asteroid belt, since there is also a maximum rate at which collisions of sufficient magnitude to reproduce a given dust luminosity can occur. Further it is shown that the planetesimal belt feeding the dust in these systems must be located further from the star than the dust, typically at >2AU. Other notable properties of the 4 hot dust systems are: two also have a planetesimal belt at >10AU (eta Corvi and HD72905); one has 3 Neptune mass planets at <1AU (HD69830); all exhibit strong silicate features in the mid-IR. We consider the most likely origin for the dust in these systems to be a dynamical instability which scattered planetesimals inwards from a more distant planetesimal belt in an event akin to the Late Heavy Bombardment in our own system, the dust being released from such planetesimals in collisions and possibly also sublimation.Comment: 16 pages, accepted by ApJ, removed HD128400 as hot dust candidat

The cold origin of the warm dust around epsilon Eridani

Context: The K2V star eps Eri hosts one known inner planet, an outer Kuiper belt analog, and an inner disk of warm dust. Spitzer/IRS measurements indicate that the warm dust is present at distances as close as a few AU from the star. Its origin is puzzling, since an "asteroid belt" that could produce this dust would be unstable because of the known inner planet. Aims: Here we test the hypothesis that the observed warm dust is generated by collisions in the outer belt and is transported inward by Poynting-Robertson (P-R) drag and strong stellar winds. Methods: We simulated a steady-state distribution of dust particles outside 10AU with a collisional code and in the inner region (r<10AU) with single-particle numerical integrations. By assuming homogeneous spherical dust grains composed of water ice and silicate, we calculated the thermal emission of the dust and compared it with observations. We investigated two different orbital configurations for the inner planet inferred from RV measurements, one with a highly eccentric orbit of e=0.7 and another one with a moderate one of e=0.25. We also produced a simulation without a planet. Results: Our models can reproduce the shape and magnitude of the observed SED from mid-IR to sub-mm wavelengths, as well as the Spitzer/MIPS radial brightness profiles. The best-fit dust composition includes both ice and silicates. The results are similar for the two possible planetary orbits and without a planet. Conclusions: The observed warm dust in the system can indeed stem from the outer belt and be transported inward by P-R and stellar wind drag. The inner planet has little effect on the distribution of dust, so that the planetary orbit could not be constrained. Reasonable agreement between the model and observations can only be achieved by relaxing the assumption of purely silicate dust and assuming a mixture of silicate and ice in comparable amounts.Comment: 9 pages, 9 figures, abstract abridge

How much large dust could be present in hot exozodiacal dust systems?

An infrared excess over the stellar photospheric emission of main-sequence stars has been found in interferometric surveys, commonly attributed to the presence of hot exozodiacal dust (HEZD). While submicrometer-sized grains in close vicinity to their host star have been inferred to be responsible for the found near-infrared excesses, the presence and amount of larger grains as part of the dust distributions are weakly constrained. We quantify how many larger grains (above-micrometer-sized) could be present in addition to submicrometer-sized grains, while being consistent with observational constraints. This is important in order to distinguish between various scenarios for the origin of HEZD and to better estimate its observational appearance when observed with future instruments. We extended a model suitable to reproduce current observations of HEZD to investigate a bimodal size distribution. By deriving the characteristics of dust distributions whose observables are consistent with observational limits from interferometric measurements in the $K$ and $N$ bands we constrained the radii of sub- and above-micrometer-sized grains as well as their mass, number, and flux density ratios. In the most extreme cases of some of the investigated systems, large grains $\gtrsim 10\,\mu$m might dominate the mass budget of HEZD while contributing up to 25$\,$% of the total flux density originating from the dust at a wavelength of 2.13$\,\mu$m and up to 50$\,$% at a wavelength of 4.1$\,\mu$m; at a wavelength of 11.1$\,\mu$m their emission might clearly dominate over the emission of small grains. While it is not possible to detect such hot-dust distributions using ALMA, the ngVLA might allow us to detect HEZD at millimeter wavelengths. Large dust grains might have a more important impact on the observational appearance of HEZD than previously assumed, especially at longer wavelengths.Comment: Accepted for publication in Astronomy & Astrophysics. 18 pages, 7 figure

Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in beta Pic, HR 4796A, and other debris disks. We derive dust masses for small particles, 1 mm and smaller, and large particles, 1 mm and larger, as a function of the initial conditions in the planetesimal disk. The dust luminosities derived from these masses are similar to those observed in Vega, HR 4796A, and other debris disks. The calculations produce bright rings and dark gaps. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of text; 17 figures at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

Collisional Velocities and Rates in Resonant Planetesimal Belts

We consider a belt of small bodies around a star, captured in one of the external or 1:1 mean-motion resonances with a massive perturber. The objects in the belt collide with each other. Combining methods of celestial mechanics and statistical physics, we calculate mean collisional velocities and collisional rates, averaged over the belt. The results are compared to collisional velocities and rates in a similar, but non-resonant belt, as predicted by the particle-in-a-box method. It is found that the effect of the resonant lock on the velocities is rather small, while on the rates more substantial. The collisional rates between objects in an external resonance are by about a factor of two higher than those in a similar belt of objects not locked in a resonance. For Trojans under the same conditions, the collisional rates may be enhanced by up to an order of magnitude. Our results imply, in particular, shorter collisional lifetimes of resonant Kuiper belt objects in the solar system and higher efficiency of dust production by resonant planetesimals in debris disks around other stars.Comment: 31 pages, 11 figures (some of them heavily compressed to fit into arxiv-maximum filesize), accepted for publication at "Celestial Mechanics and Dynamical Astronomy