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

Star Formation in the Starburst Cluster in NGC 3603

We have used new, deep, visible and near infrared observations of the compact starburst cluster in the giant HII region NGC 3603 and its surroundings with the WFC3 on HST and HAWK-I on the VLT to study in detail the physical properties of its intermediate mass (~ 1 - 3 M_sun) stellar population. We show that after correction for differential extinction and actively accreting stars, and the study of field star contamination, strong evidence remains for a continuous spread in the ages of pre-main sequence stars in the range ~ 2 to ~ 30 Myr within the temporal resolution available. Existing differences among presently available theoretical models account for the largest possible variation in shape of the measured age histograms within these limits. We also find that this isochronal age spread in the near infrared and visible Colour-Magnitude Diagrams cannot be reproduced by any other presently known source of astrophysical or instrumental scatter that could mimic the luminosity spread seen in our observations except, possibly, episodic accretion. The measured age spread and the stellar spatial distribution in the cluster are consistent with the hypothesis that star formation started at least 20-30 Myrs ago progressing slowly but continuously up to at least a few million years ago. All the stars in the considered mass range are distributed in a flattened oblate spheroidal pattern with the major axis oriented in an approximate South-East - North-West direction, and with the length of the equatorial axis decreasing with increasing age. This asymmetry is most likely due to the fact that star formation occurred along a filament of gas and dust in the natal molecular cloud oriented locally in this direction.Comment: 21 pages, 19 figures, accepted for publication in Astrophysics & Space Scienc

Molecular Outflows and a Mid-Infrared Census of the Massive Star Formation Region Associated with IRAS 18507+0121

We have observed the central region of the infrared-dark cloud filament associated with IRAS 18507+0121 at millimeter wavelengths in CO(J = 1-0), ^(13)CO(J = 1-0), and C^(18)O(J = 1-0) line emission and with Spitzer at mid-infrared wavelengths. Five massive outflows from two cloud cores were discovered. Three outflows are centered on or near an ultracompact (UC) H II region (G34.4+0.23), while the remaining two outflows originate from the millimeter core G34.4+0.23 MM. Modeling of the spectral energy distributions of the mid-infrared sources identified 31 young stellar objects in the filament with a combined stellar mass of ~127 ± 27 M_☉. An additional 22 sources were identified as probable cluster members based on the presence of strong 24 μm emission. The total star formation efficiency in the G34.4 cloud filament is estimated to be ~7%, while the massive and intermediate-mass star formation efficiency in the entire cloud filament is estimated to be roughly 2%. A comparison of the gravitational binding energy with the outflow kinetic energy suggests that the compact core containing G34.4+0.23 MM is being destroyed by its molecular outflows, whereas the outflows associated with the more massive core surrounding the G34.4 UC H II region are not likely to totally disrupt the cloud. In addition, a qualitative evaluation of the region appears to suggest that stars in this region may have formed in two stages: first lower mass stars formed and then, a few Myr later, the more massive stars began to form

The photometric evolution of dissolving star clusters I: First predictions

We calculated the broad-band photometric evolution of unresolved star clusters, including the preferential loss of low-mass stars due to mass segregation. The stellar mass function of a cluster evolves due to three effects: (a) the evolution of massive stars; (b) early tidal effects reduce the mass function independently of the stellar mass; (c) after mass segregation has completed, tidal effects preferentially remove the lowest-mass stars from the cluster. Results: (1) During the first ~40% of the lifetime of a cluster the cluster simply gets fainter due to the loss of stars by tidal effects. (2) Between ~40 and ~80% of its lifetime the cluster gets bluer due to the loss of low-mass stars. This will result in an underestimate of the age of clusters if standard cluster evolution models are used (0.15 -- 0.5 dex). (3) After ~80% of the total lifetime of a cluster it will rapidly get redder. This is because stars at the low-mass end of the main sequence, which are preferentially lost, are bluer than the AGB stars that dominate the light at long wavelengths, resulting in an age overestimate. (4) Clusters with mass segregation and the preferential loss of low-mass stars evolve along almost the same tracks in colour-colour diagrams as clusters without mass segregation. Therefore it will be difficult to distinguish this effect from that due to the cluster age for unresolved clusters, unless the total lifetime of the clusters can be estimated. (5) The changes in the colour evolution of unresolved clusters due to the preferential loss of low-mass stars will affect the determination of the SFHs. (6) The preferential loss of low-mass stars might explain the presence of old (~13 Gyr) clusters in NGC 4365 which are photometrically disguised as intermediate-age clusters (2 - 5 Gyr). [Abridged]Comment: accepted for publication in A&

Photon Dominated Regions in NGC 3603

Aims: We aim at deriving the excitation conditions of the interstellar gas as well as the local FUV intensities in the molecular cloud surrounding NGC 3603 to get a coherent picture of how the gas is energized by the central stars. Methods: The NANTEN2-4m submillimeter antenna is used to map the [CI] 1-0, 2-1 and CO 4-3, 7-6 lines in a 2' x 2' region around the young OB cluster NGC 3603 YC. These data are combined with C18O 2-1 data, HIRES-processed IRAS 60 and 100 micron maps of the FIR continuum, and Spitzer/IRAC maps. Results: The NANTEN2 observations show the presence of two molecular clumps located south-east and south-west of the cluster and confirm the overall structure already found by previous CS and C18O observations. We find a slight position offset of the peak intensity of CO and [CI], and the atomic carbon appears to be further extended compared to the molecular material. We used the HIRES far-infrared dust data to derive a map of the FUV field heating the dust. We constrain the FUV field to values of \chi = 3 - 6 \times 10^3 in units of the Draine field across the clouds. Approximately 0.2 to 0.3 % of the total FUV energy is re-emitted in the [CII] 158 {\mu}m cooling line observed by ISO. Applying LTE and escape probability calculations, we derive temperatures (TMM1 = 43 K, TMM2 = 47 K), column densities (N(MM1) = 0.9 \times 10^22 cm^-2, N(MM2) = 2.5 \times 10^22 cm^-2) and densities (n(MM1) = 3 \times 10^3 cm^-3, n(MM2) = 10^3 -10^4 cm^-3) for the two observed molecular clumps MM1 and MM2. Conclusions: The cluster is strongly interacting with the ambient molecular cloud, governing its structure and physical conditions. A stability analysis shows the existence of gravitationally collapsing gas clumps which should lead to star formation. Embedded IR sources have already been observed in the outskirts of the molecular cloud and seem to support our conclusions.Comment: 13 pages, 10 figures, accepted for publication by A&

Investigating grain growth in disks around southern T Tauri stars at millimetre wavelengths

CONTEXT - Low-mass stars form with disks in which the coagulation of grains may eventually lead to the formation of planets. It is not known when and where grain growth occurs, as models that explain the observations are often degenerate. A way to break this degeneracy is to resolve the sources under study. AIMS - To find evidence for the existence of grains of millimetre sizes in disks around in T Tauri stars, implying grain growth. METHODS - The Australia Telescope Compact Array (ATCA) was used to observe 15 southern T Tauri stars, five in the constellation Lupus and ten in Chamaeleon, at 3.3 millimetre. The five Lupus sources were also observed with the Submillimeter Array (SMA) at 1.4 millimetre. Our new data are complemented with data from the literature to determine the slopes of the spectral energy distributions in the millimetre regime. RESULTS - Ten sources were detected at better than 3sigma with the ATCA, with sigma ~1-2 mJy, and all sources that were observed with the SMA were detected at better than 15sigma, with sigma ~4 mJy. Six of the sources in our sample are resolved to physical radii of ~100 AU. Assuming that the emission from such large disks is predominantly optically thin, the millimetre slope can be related directly to the opacity index. For the other sources, the opacity indices are lower limits. Four out of six resolved sources have opacity indices <~1, indicating grain growth to millimetre sizes and larger. The masses of the disks range from < 0.01 to 0.08 MSun, which is comparable to the minimum mass solar nebula. A tentative correlation is found between the millimetre slope and the strength and shape of the 10-micron silicate feature, indicating that grain growth occurs on similar (short) timescales in both the inner and outer disk.Comment: 13 pages, 7 figures, 5 tables, accepted for publication in A&

Hydrogen embrittlement risk of high strength galvanized steel in contact with alkaline media

The critical conditions for hydrogenembrittlement (HE) risk of highstrengthgalvanizedsteel (HSGS) wires and tendons exposed to alkaline concrete pore solutions have been evaluated by means of electrochemical and mechanical testing. There is a relationship between the hydrogenembrittlementrisk in HSGS and the length of hydrogen evolution process in alkalinemedia. The galvanizedsteel suffers anodic dissolution simultaneously to the hydrogen evolution which does not stop until the passivation process is completed. HSGS wires exposed to a very highalkalinemedia have showed HE risk with loss in mechanical properties only if long periods with hydrogen evolution process take place with a simultaneous intensive galvanized coating reduction

Massive Star Formation in the W49 Giant Molecular Cloud: Implications for the Formation of Massive Star Clusters

We present results from JHKs imaging of the densest region of the W49 molecular cloud. In a recent paper (Alves & Homeier 2003), we reported the detection of (previously unknown) massive stellar clusters in the well-known giant radio HII region W49A, and here we continue our analysis. We use the extensive line-of-sight extinction to isolate a population of objects associated with W49A. We constrain the slope of the stellar luminosity function by constructing an extinction-limited luminosity function, and use this to obtain a mass function. We find no evidence for a top-heavy MF, and the slope of the derived mass function is -1.6 \pm 0.3. We identify candidate massive stars from our color-magnitude diagram, and we use these to estimate the current total stellar mass of 5-7x10^4 M_sun in the region of the W49 molecular cloud covered by our survey. Candidate ionizing stars for several ultra-compact HII regions are detected, with many having multipe candidate sources. On the global molecular cloud scale in W49, massive star formation apparently did not proceed in a single concentrated burst, but in small groups, or subclusters. This may be an essential physical description for star formation in what will later be termed a 'massive star cluster'.Comment: Accepted for publication in Astronomy & Astrophysic

A VLT/NACO Study of Star Formation in the Massive Embedded Cluster RCW 38

We present adaptive optics (AO) near-infrared (JHKs) observations of the deeply embedded massive cluster RCW 38 using NACO on the VLT. Narrowband AO observations centered at wavelengths of 1.28, 2.12, and 2.17 micron were also obtained. The area covered by these observations is about 0.5 pc square, centered on the O star RCW 38 IRS2. We use the JHKs colors to identify young stars with infrared excess. Through a detailed comparison to a nearby control field, we find that most of the 337 stars detected in all three infrared bands are cluster members (~317), with essentially no contamination due to background or foreground sources. Five sources have colors suggestive of deeply embedded protostars, while 53 sources are detected at Ks only; their spatial distribution with respect to the extinction suggests they are highly reddened cluster members. Detectable Ks-band excess is found toward 29 +/- 3 % of the stars. For comparison to a similar area of Orion observed in the near-infrared, mass and extinction cuts are applied, and the excess fractions redetermined. The resulting excesses are then 25 +/- 5 % for RCW 38, and 42 +/- 8 % for Orion. RCW 38 IRS2 is shown to be a massive star binary with a projected separation of ~500 AU. Two regions of molecular hydrogen emission are revealed through the 2.12 micron imaging. One shows a morphology suggestive of a protostellar jet, and is clearly associated with a star only detected at H and Ks, previously identified as a highly obscured X-ray source. Three spatially extended cometary-like objects, suggestive of photoevaporating disks, are identified, but only one is clearly directly influenced by RCW 38 IRS2. A King profile provides a reasonable fit to the cluster radial density profile and a nearest neighbor distance analysis shows essentially no sub-clustering.Comment: 45 pages (17 figures), and full source table. Full resolution version available at http://www.cfa.harvard.edu/~bourke/rcw38