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

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

Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

<i>Herschel</i> observations of the debris disc around HIP 92043

Context. Typical debris discs are composed of particles ranging from several micron sized dust grains to km sized asteroidal bodies, and their infrared emission peaks at wavelengths 60-100 μm. Recent Herschel DUNES observations have identified several debris discs around nearby Sun-like stars (F, G and K spectral type) with significant excess emission only at 160 μm. Aims. We observed HIP 92043 (110 Her, HD 173667) at far-infrared and sub-millimetre wavelengths with Herschel PACS and SPIRE. Identification of the presence of excess emission from HIP 92043 and the origin and physical properties of any excess was undertaken through analysis of its spectral energy distribution (SED) and the PACS images. Methods. The PACS and SPIRE images were produced using the HIPE photProject map maker routine. Fluxes were measured using aperture photometry. A stellar photosphere model was scaled to optical and near infrared photometry and subtracted from the far-infared and sub-mm fluxes to determine the presence of excess emission. Source radial profiles were fitted using a 2D Gaussian and compared to a PSF model based on Herschel observations of α Boo to check for extended emission. Results. Clear excess emission from HIP 92043 was observed at 70 and 100 μm. Marginal excess was observed at 160 and 250 μm. Analysis of the images reveals that the source is extended at 160 μm. A fit to the source SED is inconsistent with a photosphere and single temperature black body. Conclusions. The excess emission from HIP 92043 is consistent with the presence of an unresolved circumstellar debris disc at 70 and 100 μm, with low probability of background contamination. The extended 160 μm emission may be interpreted as an additional cold component to the debris disc or as the result of background contamination along the line of sight. The nature of the 160 μm excess cannot be determined absolutely from the available data, but we favour a debris disc interpretation, drawing parallels with previously identified cold disc sources in the DUNES sample

Forming the first planetary systems: debris around Galactic thick disc stars

The thick disc contains stars formed within the first Gyr of Galactic history, and little is known about their planetary systems. The Spitzer MIPS instrument was used to search 11 of the closest of these old low-metal stars for circumstellar debris, as a signpost that bodies at least as large as planetesimals were formed. A total of 22 thick disc stars has now been observed, after including archival data, but dust is not found in any of the systems. The data rule out a high incidence of debris among star systems from early in the Galaxy's formation. However, some stars of this very old population do host giant planets, at possibly more than the general incidence among low-metal Sun-like stars. As the Solar System contains gas giants but little cometary dust, the thick disc could host analogue systems that formed many Gyr before the Sun.Comment: accepted by MNRAS Letters; 5 pages, 4 figure

Lagrange Duality in Set Optimization

Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum are obtained. In particular, a strong duality theorem, which includes the existence of the dual solution, is given under very weak assumptions: The ordering cone may have an empty interior or may not be pointed. "Saddle sets" replace the usual notion of saddle points for the Lagrangian, and this concept is proven to be sufficient to show the equivalence between the existence of primal/dual solutions and strong duality on the one hand and the existence of a saddle set for the Lagrangian on the other hand

A peculiar class of debris disks from Herschel/DUNES - A steep fall off in the far infrared

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 fit analytical models to the available spectral energy distribution (SED) data. Results. The SEDs of the three disks potentially exhibit an unusually steep decrease at wavelengths > 70 um. We investigate the significance of the peculiar shape of these SEDs and the impact on models of the disks provided it is real. Our modeling reveals that such a steep decrease of the SEDs in the long wavelength regime is inconsistent with a power-law exponent of the grain size distribution -3.5 expected from a standard equilibrium collisional cascade. In contrast, a very distinct range of grain sizes is implied to dominate the thermal emission of such disks. However, we demonstrate that the understanding of the data of faint sources obtained with Herschel is still incomplete and that the significance of our results depends on the version of the data reduction pipeline used. Conclusions. A new mechanism to produce the dust in the presented debris disks, deviations from the conditions required for a standard equilibrium collisional cascade (grain size exponent of -3.5), and/or significantly different dust properties would be necessary to explain the potentially steep SED shape of the three debris disks presented. (abridged)Comment: 14 pages, 4 figures, accepted by A&

Debris discs in binaries: a numerical study

Debris disc analysis and modelling provide crucial information about the structure and the processes at play in extrasolar planetary systems. In binary systems, this issue is more complex because the disc should in addition respond to the companion star's perturbations. We explore the dynamical evolution of a collisionally active debris disc for different initial parent body populations, diverse binary configurations and optical depths. We focus on the radial extent and size distribution of the disc at a stationary state. We numerically follow the evolution of $10^{5}$ massless small grains, initially produced from a circumprimary disc of parent bodies following a size distribution in $dN \propto s^{-3.5}$ds . Grains are submitted to both stars' gravity as well as radiation pressure. In addition, particles are assigned an empirically derived collisional lifetime. For all the binary configurations the disc extends far beyond the critical semimajor axis $a_crit$ for orbital stability. This is due to the steady production of small grains, placed on eccentric orbits reaching beyond $a_crit$ by radiation pressure. The amount of matter beyond acrit depends on the balance between collisional production and dynamical removal rates: it increases for more massive discs as well as for eccentric binaries. Another important effect is that, in the dynamically stable region, the disc is depleted from its smallest grains. Both results could lead to observable signatures. We have shown that a companion star can never fully truncate a collisionally active disc. For eccentric companions, grains in the unstable regions can significantly contribute to the thermal emission in the mid-IR. Discs with sharp outer edges, especially bright ones such as HR4796A, are probably shaped by other mechanisms.Comment: accepted for publication in A&

Debris discs around nearby Solar analogues

An unbiased search for debris discs around nearby Sun-like stars is reported. Thirteen G-dwarfs at 12-15 parsecs distance were searched at 850 \umum wavelength, and a disc is confirmed around HD 30495. The estimated dust mass is 0.008 M$_{\oplus}$ with a net limit \la 0.0025 M$_{\oplus}$ for the average disc of the other stars. The results suggest there is not a large missed population of substantial cold discs around Sun-like stars -- HD 30495 is a bright rather than unusually cool disc, and may belong to a few hundred Myr-old population of greater dust luminosity. The far-infared and millimetre survey data for Sun-like stars are well fitted by either steady state or stirred models, provided that typical comet belts are comparable in size to that in the Solar System.Comment: published in MNRA