Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

Mid-infrared interferometry of the massive young stellar object NGC3603 - IRS 9A

We present observations and models for one of these MYSO candidates, NGC3603 IRS 9A. Our goal is to investigate with infrared interferometry the structure of IRS 9A on scales as small as 200AU, exploiting the fact that a cluster of O and B stars has blown away much of the obscuring foreground dust and gas. Observations in the N-band were carried out with the MIDI beam combiner attached to the VLTI. Additional interferometric observations which probe the structure of IRS 9A on larger scales were performed with an aperture mask installed in the T-ReCS instrument of Gemini South. The spectral energy distribution (SED) is constrained by the MIDI N-band spectrum and by data from the Spitzer Space Telescope. Our efforts to model the structure and SED of IRS 9A range from simple geometrical models of the brightness distribution to one- and two-dimensional radiative transfer computations. The target is resolved by T-ReCS, with an equivalent (elliptical) Gaussian width of 330mas by 280mas (2300 AU by 2000 AU). Despite this fact, a warm compact unresolved component was detected by MIDI which is possibly associated with the inner regions of a flattened dust distribution. Based on our interferometric data, no sign of multiplicity was found on scales between about 200AU and 700AU projected separation. A geometric model consisting of a warm (1000 K) ring (400 AU diameter) and a cool (140 K) large envelope provides a good fit to the data. No single model fitting all visibility and photometric data could be found, with disk models performing better than spherical models. While the data are clearly inconsistent with a spherical dust distribution they are insufficient to prove the existence of a disk but rather hint at a more complex dust distribution.Comment: 8 pages, 11 figures. Accepted for publication in A&

Properties of active galactic star-forming regions probed by imaging spectroscopy with the Fourier transform spectrometer (FTS) onboard AKARI

We investigate the structure of the interstellar medium (ISM) and identify the location of possible embedded excitation sources from far-infrared (FIR) line and mid-infrared continuum emission maps. We carried out imaging spectroscopic observations of four giant Galactic star-forming regions with the Fourier Transform Spectrometer (FTS) onboard AKARI. We obtained [OIII] 88 micron and [CII] 158 micron line intensity maps of all the regions: G3.270-0.101, G333.6-0.2, NGC3603, and M17. For G3.270-0.101, we obtained high-spatial-resolution [OIII] 88 micron line-emission maps and a FIR continuum map for the first time, which imply that [OIII] 88 micron emission identifies the excitation sources more clearly than the radio continuum emission. In G333.6-0.2, we found a local [OIII] 88 micron emission peak, which is indicative of an excitation source. This is supported by the 18 micron continuum emission, which is considered to trace the hot dust distribution. For all regions, the [CII] 158 micron emission is distributed widely as suggested by previous observations of star-forming regions. We conclude that [OIII] 88 micron emission traces the excitation sources more accurately than the radio continuum emission, especially where there is a high density and/or column density gradient. The FIR spectroscopy provides a promising means of understanding the nature of star-forming regions.Comment: 14 pages with 15 figures, accepted for publication in Astronomy and Astrophysic

Overlap of QRPA states based on ground states of different nuclei --mathematical properties and test calculations--

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated in order to simulate the overlap of the intermediate nuclear states of the double-beta decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume delta-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.Comment: 17 pages, 15 figures, full paper following arXiv:1205.5354 and Phys. Rev. C 86 (2012) 021301(R

Synthetic CO emission and the XCOX_{\rm CO} factor of young molecular clouds: a convergence study

The properties of synthetic CO emission from 3D simulations of forming molecular clouds are studied within the SILCC-Zoom project. Since the time scales of cloud evolution and molecule formation are comparable, the simulations include a live chemical network. Two sets of simulations with an increasing spatial resolution (d$x=3.9$ pc to d$x=0.06$ pc) are used to investigate the convergence of the synthetic CO emission, which is computed by post-processing the simulation data with the RADMC-3D radiative transfer code. To determine the excitation conditions, it is necessary to include atomic hydrogen and helium alongside H$_2$, which increases the resulting CO emission by ~7-26 per cent. Combining the brightness temperature of $^{12}$CO and $^{13}$CO, we compare different methods to estimate the excitation temperature, the optical depth of the CO line and hence, the CO column density. An intensity-weighted average excitation temperature results in the most accurate estimate of the total CO mass. When the pixel-based excitation temperature is used to calculate the CO mass, it is over-/underestimated at low/high CO column densities where the assumption that $^{12}$CO is optically thick while $^{13}$CO is optically thin is not valid. Further, in order to obtain a converged total CO luminosity and hence factor, the 3D simulation must have d$x\lesssim0.1$ pc. The evolves over time and differs for the two clouds; yet pronounced differences with numerical resolution are found. Since high column density regions with a visual extinction larger than 3~mag are not resolved for d$x\gtrsim 1$~pc, in this case the H$_2$ mass and CO luminosity both differ significantly from the higher resolution results and the local $X_{\rm CO}$ is subject to strong noise. Our calculations suggest that synthetic CO emission maps are only converged for simulations with d$x\lesssim 0.1$ pc.Comment: 23 pages, 22 figures, accepted for publication in MNRA

Probing the centre of the large circumstellar disc in M17

We investigated the nature of the hitherto unresolved elliptical infrared emission in the centre of the ~20000 AU disc silhouette in M 17. We combined high-resolution JHKsL'M' band imaging carried out with NAOS/CONICA at the VLT with [Fe II] narrow band imaging using SOFI at the NTT. The analysis is supported by Spitzer/GLIMPSE archival data and by already published SINFONI/VLT Integral Field Spectroscopy data. For the first time, we resolve the elongated central infrared emission into a point-source and a jet-like feature that extends to the northeast in the opposite direction of the recently discovered collimated H2 jet. They are both orientated almost perpendicular to the disc plane. In addition, our images reveal a curved southwestern emission nebula whose morphology resembles that of the previously detected northeastern one. Both nebulae are located at a distance of 1500 AU from the disc centre. We describe the infrared point-source in terms of a protostar that is embedded in circumstellar material producing a visual extinction of 60 <= Av <= 82. The observed Ks band magnitude is equivalent to a stellar mass range of 2.8 Msun <= Mstar <= 8 Msun adopting conversions for a main-sequence star. Altogether, we suggest that the large M 17 accretion disc is forming an intermediate to high-mass protostar. Part of the accreted material is expelled through a symmetric bipolar jet/outflow.Comment: 6 pages, 3 figures, accepted by MNRAS (16 May 2008

Giant crystals inside mitochondria of equine chondrocytes

The present study reports for the first time the presence of giant crystals in mitochondria of equine chondrocytes. These structures show dark contrast in TEM images as well as a granular substructure of regularly aligned 12 nm small units. Different zone axes of the crystalline structure were analysed by means of Fourier transformation of lattice-resolution TEM images proving the crystalline nature of the structure. Elemental analysis reveals a high content of nitrogen referring to protein. The outer shape of the crystals is geometrical with an up to hexagonal profile in cross sections. It is elongated, spanning a length of several micrometres through the whole cell. In some chondrocytes, several crystals were found, sometimes combined in a single mitochondrion. Crystals were preferentially aligned along the long axis of the cells, thus appearing in the same orientation as the chondrocytes in the tissue. Although no similar structures have been found in the cartilage of any other species investigated, they have been found in cartilage repair tissue formed within a mechanically stimulated equine chondrocyte construct. Crystals were mainly located in superficial regions of cartilage, especially in joint regions of well-developed superficial layers, more often in yearlings than in adult horses. These results indicate that intramitochondrial crystals are related to the high mechanical stress in the horse joint and potentially also to the increased metabolic activity of immature individuals.(VLID)353386

The cool atmospheres of the binary brown dwarf eps Indi B

We have imaged $\epsilon$ Indi B, the closest brown dwarf binary known, with VISIR at the VLT in three narrow-band mid-infrared bandpasses located around 8.6$\mu$m, 10.5$\mu$m and 11.3$\mu$m. We are able to spatially resolve both components, and determine accurate mid-infrared photometry for both components independently. In particular, our VISIR observations probe the NH$_3$ feature in the atmospheres of the cooler and warmer brown dwarfs. For the first time, we can disentangle the contributions of the two components, and find that % our photometry of $\epsilon$ IndiBb is in good agreement with recent ``cloud-free'' atmosphere models having an effective temperature of $T_\mathrm{eff}=800$ K. With an assumed age of 1 Gyr for the $\epsilon$ Indi system, component Ba agrees more with $T_\mathrm{eff} \approx 1100$ K rather than with $T_\mathrm{eff}=1200$ K, as suggested by SPITZER spectroscopic observations of the combined $\epsilon$ Indi B system (Roellig et al., 2004). Even higher effective temperatures appear inconsistent with our absolute photometry, as they would imply an unphysical small size of the brown dwarf $\epsilon$ IndiBa.Comment: 4 pages, 2 figure