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

Twisted debris: how differential secular perturbations shape debris disks

Resolved images suggest that asymmetric structures are a common feature of cold debris disks. While planets close to these disks are rarely detected, their hidden presence and gravitational perturbations provide plausible explanations for some of these features. To put constraints on the properties of yet undetected planetary companions, we aim to predict what features such a planet imprints in debris disks undergoing continuous collisional evolution. We discuss the basic equations, analytic approximations and timescales governing collisions, radiation pressure and secular perturbations. In addition, we combine our numerical model of the collisional evolution of the size and spatial distributions in debris disks with the gravitational perturbation by a single planet. We find that the distributions of orbital elements in the disks are strongly dependent on grain sizes. Secular precession is differential with respect to involved semi-major axes and grain sizes. This leads to observable differences between the big grains tracing the parent belt and the small grains in the trailing halo. Observations at different wavelengths can be used to constrain the properties of a possible planet.Comment: 12 pages, 7 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

Using debris disk observations to infer substellar companions orbiting within or outside a parent planetesimal belt

Aims. We analyze whether the effects of secular perturbations, originating from a substellar companion, on the dust dynamics in a debris disk can be investigated with spatially resolved observations. Methods. We numerically simulated the collisional evolution of narrow and eccentric cold planetesimal belts around a star of spectral type A3V that are secularly perturbed by a companion that orbits either closer to or farther from the star than the belt. Based on the resulting spatial dust distributions, we simulated spatially resolved maps of their surface brightness in the $K$, $N$, and $Q$ bands and at wavelengths of 70$\mu$m and 1300$\mu$m. Results. Assuming a nearby debris disk seen face-on, we find that the brightness distribution varies significantly with observing wavelength, for example between the $N$ and $Q$ band. This can be explained by the varying relative contribution of the emission of the smallest grains near the blowout limit. The orbits of both the small grains that form the halo and the large grains close to the parent belt precess due to the secular perturbations induced by a companion orbiting inward of the belt. The halo, being composed of older grains, trails the belt. The magnitude of the trailing decreases with increasing perturber mass and hence with increasing strength of the perturbation, a trend we recovered in synthetic maps of surface brightness by fitting ellipses to lines of constant brightness. Systems with an outer perturber do not show a uniform halo precession since the orbits of small grains are strongly altered. We identified features of the brightness distributions suitable for distinguishing between systems with a potentially detectable inner or outer perturber, especially with a combined observation with JWST/MIRI in the $Q$ band tracing small grain emission and with ALMA at mm wavelengths tracing the position of the parent planetesimal belt.Comment: Accepted for publication in Astronomy & Astrophysics. 25 pages, 21 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

Self-gravity of debris discs can strongly change the outcomes of interactions with inclined planets

Drastic changes in protoplanets' orbits could occur in the early stages of planetary systems through interactions with other planets and their surrounding protoplanetary or debris discs. The resulting planetary system could exhibit orbits with moderate to high eccentricities and/or inclinations, causing planets to perturb one another as well as the disc significantly. The present work studies the evolution of systems composed of an initially inclined planet and a debris disc. We perform N-body simulations of a narrow, self-gravitating debris disc and a single interior Neptune-like planet. We simulate systems with various initial planetary inclinations, from coplanar to polar configurations considering different separations between the planet and the disc. We find that except when the planet is initially on a polar orbit, the planet-disc system tends to reach a quasi-coplanar configuration with low vertical dispersion in the disc. When present, the Zeipel--Kozai--Lidov oscillations induced by the disc pump the planet's eccentricity and, in turn, affect the disc structure. We also find that the resulting disc morphology in most of the simulations looks very similar in both radial and vertical directions once the simulations are converged. This contrasts strongly with massless disc simulations, where vertical disc dispersion is set by the initial disc-planet inclination and can be high for initially highly inclined planets. The results suggest caution in interpreting an unseen planet's dynamical history based only on the disc's appearance.Comment: 15 pages, 6 figures. Accepted for publication in MNRA

Debris disc candidates in systems with transiting planets

Debris discs are known to exist around many planet-host stars, but no debris dust has been found so far in systems with transiting planets. Using publicly available catalogues, we searched for infrared excesses in such systems. In the recently published Wide-Field Infrared Survey Explorer (WISE) catalogue, we found 52 stars with transiting planets. Two systems with one transiting "hot Jupiter" each, TrES-2 and XO-5, exhibit small excesses both at 12 and 22 microns at a > 3 sigma level. Provided that one or both of these detections are real, the frequency of warm excesses in systems with transiting planets of 2-4 % is comparable to that around solar-type stars probed at similar wavelengths with Spitzer's MIPS and IRS instruments. Modelling suggests that the observed excesses would stem from dust rings with radii of several AU. The inferred amount of dust is close to the maximum expected theoretically from a collisional cascade in asteroid belt analogues. If confirmed, the presence of debris discs in systems with transiting planets may put important constraints onto formation and migration scenarios of hot Jupiters.Comment: Accepted for publication in MNRAS Letter

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

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