Selberg integrals in 1D random Euclidean optimization problems

We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points $x$ and $y$ is the Euclidean distance between them to an arbitrary power $p\ge1$, and the points are chosen at random with flat measure. We derive the exact average cost for the random assignment problem, for any number of points, by using Selberg's integrals. Some variants of these integrals allows to derive also the exact average cost for the bipartite travelling salesman problem.Comment: 9 pages, 2 figure

Calibration of evolutionary diagnostics in high-mass star formation

The evolutionary classification of massive clumps that are candidate progenitors of high-mass young stars and clusters relies on a variety of independent diagnostics based on observables from the near-infrared to the radio. A promising evolutionary indicator for massive and dense cluster-progenitor clumps is the L/M ratio between the bolometric luminosity and the mass of the clumps. With the aim of providing a quantitative calibration for this indicator we used SEPIA/APEX to obtain CH3C2H(12-11) observations, that is an excellent thermometer molecule probing densities > 10^5 cm^-3 , toward 51 dense clumps with M>1000 solar masses, and uniformly spanning -2 < Log(L/M) < 2.3. We identify three distinct ranges of L/M that can be associated to three distinct phases of star formation in massive clumps. For L/M <1 no clump is detected in CH3C2H , suggesting an inner envelope temperature below 30K. For 1< L/M < 10 we detect 58% of the clumps, with a temperature between 30 and 35 K independently from the exact value of L/M; such clumps are building up luminosity due to the formation of stars, but no star is yet able to significantly heat the inner clump regions. For L/M> 10 we detect all the clumps, with a gas temperature rising with Log(L/M), marking the appearance of a qualitatively different heating source within the clumps; such values are found towards clumps with UCHII counterparts, suggesting that the quantitative difference in T - L/M behaviour above L/M >10 is due to the first appearance of ZAMS stars in the clumps.Comment: Astrophysical Journal Letters, Accepte

C3C^{3} : A Command-line Catalogue Cross-matching tool for modern astrophysical survey data

In the current data-driven science era, it is needed that data analysis techniques has to quickly evolve to face with data whose dimensions has increased up to the Petabyte scale. In particular, being modern astrophysics based on multi-wavelength data organized into large catalogues, it is crucial that the astronomical catalog cross-matching methods, strongly dependant from the catalogues size, must ensure efficiency, reliability and scalability. Furthermore, multi-band data are archived and reduced in different ways, so that the resulting catalogues may differ each other in formats, resolution, data structure, etc, thus requiring the highest generality of cross-matching features. We present $C^{3}$ (Command-line Catalogue Cross-match), a multi-platform application designed to efficiently cross-match massive catalogues from modern surveys. Conceived as a stand-alone command-line process or a module within generic data reduction/analysis pipeline, it provides the maximum flexibility, in terms of portability, configuration, coordinates and cross-matching types, ensuring high performance capabilities by using a multi-core parallel processing paradigm and a sky partitioning algorithm.Comment: 6 pages, 4 figures, proceedings of the IAU-325 symposium on Astroinformatics, Cambridge University pres

Search for massive protostar candidates in the southern hemisphere: II. Dust continuum emission

In an ongoing effort to identify and study high-mass protostellar candidates we have observed in various tracers a sample of 235 sources selected from the IRAS Point Source Catalog, mostly with dec < -30 deg, with the SEST antenna at millimeter wavelengths. The sample contains 142 Low sources and 93 High, which are believed to be in different evolutionary stages. Both sub-samples have been studied in detail by comparing their physical properties and morphologies. Massive dust clumps have been detected in all but 8 regions, with usually more than one clump per region. The dust emission shows a variety of complex morphologies, sometimes with multiple clumps forming filaments or clusters. The mean clump has a linear size of ~0.5 pc, a mass of ~320 Msolar for a dust temperature Td=30 K, an H_2 density of 9.5E5 cm-3, and a surface density of 0.4 g cm-2. The median values are 0.4 pc, 102 Msolar, 4E4 cm-3, and 0.14 g cm-2, respectively. The mean value of the luminosity-to-mass ratio, L/M ~99 Lsolar/Msolar, suggests that the sources are in a young, pre-ultracompact HII phase. We have compared the millimeter continuum maps with images of the mid-IR MSX emission, and have discovered 95 massive millimeter clumps non-MSX emitters, either diffuse or point-like, that are potential prestellar or precluster cores. The physical properties of these clumps are similar to those of the others, apart from the mass that is ~3 times lower than for clumps with MSX counterpart. Such a difference could be due to the potential prestellar clumps having a lower dust temperature. The mass spectrum of the clumps with masses above M ~100 Msolar is best fitted with a power-law dN/dM proportional to M-alpha with alpha=2.1, consistent with the Salpeter (1955) stellar IMF, with alpha=2.35.Comment: 83 pages, 10 figures, 3 tables. Accepted for publication by A&A. The full paper, including Fig.2 with the maps of all the individual regions, complete Tables 1 and 2 can be found at http://www.arcetri.astro.it/~starform/publ2005.ht