Game Theoretical Treatment of Material Accountability Problems: Part II

In a previous paper, the optimal strategy for an inspection authority which has to safeguard material on the basis of material accountability principles has been determined with game theoretical methods: Sets of reasonable inspection and diversion strategies have been defined, and a saddlepoint of the overall probability of detection for n inventory periods during the reference time under consideration has been determined. In this paper the problem of the appropriate choice of the number of inventory periods per reference time has been analyzed: it has been shown that the overall probability of detection in the case of one inventory period per reference time is always larger than that in the case of n inventory periods for n>1, and further it has been shown in which way this result is reflected in the expected detection time

Scattered light mapping of protoplanetary disks

High-contrast scattered light observations have revealed the surface morphology of several dozens of protoplanetary disks at optical and near-infrared wavelengths. Inclined disks offer the opportunity to measure part of the phase function of the dust grains that reside in the disk surface which is essential for our understanding of protoplanetary dust properties and the early stages of planet formation. We aim to construct a method which takes into account how the flaring shape of the scattering surface of an (optically thick) protoplanetary disk projects onto the image plane of the observer. This allows us to map physical quantities (scattering radius and scattering angle) onto scattered light images and retrieve stellar irradiation corrected (r^2-scaled) images and dust phase functions. We apply the method on archival polarized intensity images of the protoplanetary disk around HD 100546 that were obtained with VLT/SPHERE in R'-band and VLT/NACO in H- and Ks-band. The brightest side of the r^2-scaled R'-band polarized intensity image of HD 100546 changes from the far to the near side of the disk when a flaring instead of a geometrically flat disk surface is used for the r^2-scaling. The decrease in polarized surface brightness in the scattering angle range of ~40-70 deg is likely a result of the dust phase function and degree of polarization which peak in different scattering angle regimes. The derived phase functions show part of a forward scattering peak which indicates that large, aggregate dust grains dominate the scattering opacity in the disk surface. Projection effects of a protoplanetary disk surface need to be taken into account to correctly interpret scattered light images. Applying the correct scaling for the correction of stellar irradiation is crucial for the interpretation of the images and the derivation of the dust properties in the disk surface layer.Comment: Accepted for publication in A&A, 6 pages, 3 figure

HD 169142 in the eyes of ZIMPOL/SPHERE

We present new data of the protoplanetary disc surrounding the Herbig Ae/Be star HD 169142 obtained in the very broad-band (VBB) with the Zurich imaging polarimeter (ZIMPOL), a sub-system of the Spectro-Polarimetric High-contrast Exoplanet REsearch instrument (SPHERE) at the Very Large Telescope (VLT). Our Polarimetric Differential Imaging (PDI) observations probe the disc as close as 0.03" (3.5au) to the star and are able to trace the disc out to ~1.08" (~126au). We find an inner hole, a bright ring bearing substructures around 0.18" (21au), and an elliptically shaped gap stretching from 0.25" to 0.47" (29-55au). Outside of 0.47", the surface brightness drops off, discontinued only by a narrow annular brightness minimum at ~0.63"-0.74" (74-87au). These observations confirm features found in less-well resolved data as well as reveal yet undetected indications for planet-disc interactions, such as small-scale structures, star-disk offsets, and potentially moving shadows.Comment: Accepted for publication in MNRA

Detection of scattered light from the hot dust in HD 172555

Debris disks or belts are important signposts for the presence of colliding planetesimals and, therefore, for ongoing planet formation and evolution processes in young planetary systems. Imaging of debris material at small separations from the star is very challenging but provides valuable insights into the spatial distribution of so-called hot dust produced by solid bodies located in or near the habitable zone. We report the first detection of scattered light from the hot dust around the nearby (d = 28.33 pc) A star HD 172555. We want to constrain the geometric structure of the detected debris disk using polarimetric differential Imaging (PDI) with a spatial resolution of 25 mas and an inner working angle of about 0.1$''$. We measured the polarized light of HD 172555, with SPHERE-ZIMPOL, in the very broad band (VBB; $\lambda=735$ nm) filter for the projected separations between 0.08$''$ (2.3 au) and 0.77$''$ (22 au). We constrained the disk parameters by fitting models for scattering of an optically thin dust disk taking the limited spatial resolution and coronagraphic attenuation of our data into account. The geometric structure of the disk in polarized light shows roughly the same orientation and outer extent as obtained from thermal emission at 18 $\mu$m. Our image indicates the presence of a strongly inclined ($i\sim 103.5^\circ$), roughly axisymmetric dust belt with an outer radius in the range between 0.3$''$ (8.5 au) and 0.4$''$ (11.3 au). We derive a lower limit for the polarized flux contrast ratio for the disk of $(F_{\rm pol})_{\rm disk}/F_{\rm \ast}> (6.2 \pm 0.6)\cdot 10^{-5}$ in the VBB filter. This ratio is small, only 9 %, when compared to the fractional infrared flux excess ($\approx 7.2\cdot 10^{-4}$). The model simulations show that more polarized light could be produced by the dust located inside 2 au, which cannot be detected with the instrument configuration used.Comment: 16 pages, 10 figure