On the accuracy of the S/N estimates obtained with the exposure time calculator of the Wide Field Planetary Camera 2 on board the Hubble Space Telescope

We have studied the accuracy and reliability of the exposure time calculator (ETC) of the Wide Field Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope (HST) with the objective of determining how well it represents actual observations and, therefore, how much confidence can be invested in it and in similar software tools. We have found, for example, that the ETC gives, in certain circumstances, very optimistic values for the signal-to-noise ratio (SNR) of point sources. These values overestimate by up to a factor of 2 the HST performance when simulations are needed to plan deep imaging observations, thus bearing serious implications on observing time allocation. For this particular case, we calculate the corrective factors to compute the appropriate SNR and detection limits and we show how these corrections vary with field crowding and sky background. We also compare the ETC of the WFPC2 with a more general ETC tool, which takes into account the real effects of pixel size and charge diffusion. Our analysis indicates that similar problems may afflict other ETCs in general showing the limits to which they are bound and the caution with which their results must be taken.Comment: 14 pages, 13 figures, to be published in PASP on July 200

Why is the mass function of NGC 6218 flat?

We have used the FORS-1 camera on the VLT to study the main sequence (MS) of the globular cluster NGC 6218 in the V and R bands. The observations cover an area of 3.4 x 3.4 around the cluster centre and probe the stellar population out to the cluster's half-mass radius (r_h ~ 2.2). The colour-magnitude diagram (CMD) that we derive in this way reveals a narrow and well defined MS extending down to the 5 sigma detection limit at V~25, or about 6 magnitudes below the turn-off, corresponding to stars of ~ 0.25 Msolar. The luminosity function (LF) obtained with these data shows a marked radial gradient, in that the ratio of lower- and higher-mass stars increases monotonically with radius. The mass function (MF) measured at the half-mass radius, and as such representative of the clusters global properties, is surprisingly flat. Over the range 0.4 - 0.8 Msolar, the number of stars per unit mass follows a power-law distribution of the type dN/dm \propto m^{0}, where, for comparison, Salpeter's IMF would be dN/dm \propto m^{-2.35}. We expect that such a flat MF does not represent the cluster's IMF but is the result of severe tidal stripping of the stars from the cluster due to its interaction with the Galaxy's gravitational field. Our results cannot be reconciled with the predictions of recent theoretical models that imply a relatively insignificant loss of stars from NGC 6218 as measured by its expected very long time to disruption. They are more consistent with the orbital parameters based on the Hipparcos reference system that imply a much higher degree of interaction of this cluster with the Galaxy than assumed by those models. Our results indicate that, if the orbit of a cluster is known, the slope of its MF could be useful in discriminating between the various models of the Galactic potential.Comment: 11 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

On the Globular Cluster IMF below 1 Solar Mass

(Abridged) Accurate luminosity functions (LF) for a dozen globular clusters have now been measured at or just beyond their half-light radius using HST. They span almost the entire cluster main sequence below ~ 0.75 Msolar. All these clusters exhibit LF that rise continuously from an absolute I magnitude M_I ~ 6 to a peak at M_I ~ 8.5-9 and then drop with increasing M_I. Transformation of the LF into mass functions (MF) by means of the most recent mass luminosity relations that are consistent with all presently available data on the physical properties of low mass, low metallicity stars shows that all the LF observed so far can be obtained from MF having the shape of a log-normal distribution with characteristic mass m_c=0.33 +/- 0.03 Msolar and standard deviation sigma = 1.81 +/- 0.19. After correction for the effects of mass segregation, the variation of the ratio of the number of higher to lower mass stars with cluster mass or any simple orbital parameter or the expected time to disruption recently computed for these clusters shows no statistically significant trend over a range of this last parameter of more than a factor of 100. We conclude that the global MF of these clusters have not been measurably modified by evaporation and tidal interactions with the Galaxy and, thus, should reflect the initial distribution of stellar masses. Since the log-normal function that we find is also very similar to the one obtained independently for much younger clusters and to the form expected theoretically, the implication seems to be unavoidable that it represents the true stellar IMF for this type of stars in this mass range.Comment: Accepted for publication in The Astrophysical Journal. Contains 28 pages with 6 figure

Self-Organised Schools

Self-Organised Schools: Educational Leadership and Innovative Learning Environments describes the results of the research we carried out at fourteen Italian schools that highlight how there is a positive correlation between the capabilities of school self-organization and the innovativeness of learning environments: in other words, the more self-organized schools are, the more innovative learning environments are. The results of this work are part of the strand of research of bottom-up emergency and self-organization, an extremely fruitful trend as shown by Sugata Mitra, the founder of the Self-Organized Learning Environments, according to whom, "education is a self-organized system where learning is an emerging phenomenon". This book gives new insights on self-organization studies, and most of all, to the idea that change - organizational and educational innovation - sparks from the bottom. This book is aimed specifically at school principals of all levels, scholastic reformers, educational scholars, organisation and management consultants who want to innovate learning and management of learning. These actors will benefit drawing useful examples from more than thirty different learning environments worldwide, fourteen examples of schools that self-organize, two frameworks - and two ready-to-use questionnaires - measuring the innovativeness of a learning environment, and the capability of a school to self-organize. Self-organization is the most fascinating future of innovative principal

Jumping with variably scaled discontinuous kernels (VSDKs)

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Correction to: Jumping with variably scaled discontinuous kernels (VSDKs)

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Very Large Telescope Observations of the peculiar globular cluster NGC6712. Discovery of a UV, H-alpha excess star in the core

We present results from multi-band observations in the central region of the cluster NGC6712 with the ESO-Very Large Telescope. Using high resolution images we have identified three UV-excess stars. In particular two of them are within the cluster core, a few arcsec apart: the first object is star "S" which previous studies identified as the best candidate to the optical counterpart to the luminous X-ray source detected in this cluster. The other UV object shows clearcut H-alpha emission and, for this reason, is an additional promising interacting binary candidate (a quiescent LMXB or a CV). The presence of two unrelated interacting binary systems a few arcsec apart in the core of this low-density cluster is somewhat surprising and supports the hypothesis that the (internal) dynamical history of the cluster and/or the (external) interaction with the Galaxy might play a fundamental role in the formation of these peculiar objects.Comment: 15 pages, 3 figures. ApJL in pres

Engineering model transformations with transML

The final publication is available at Springer via http://dx.doi.org/10.1007%2Fs10270-011-0211-2Model transformation is one of the pillars of model-driven engineering (MDE). The increasing complexity of systems and modelling languages has dramatically raised the complexity and size of model transformations as well. Even though many transformation languages and tools have been proposed in the last few years, most of them are directed to the implementation phase of transformation development. In this way, even though transformations should be built using sound engineering principles—just like any other kind of software—there is currently a lack of cohesive support for the other phases of the transformation development, like requirements, analysis, design and testing. In this paper, we propose a unified family of languages to cover the life cycle of transformation development enabling the engineering of transformations. Moreover, following an MDE approach, we provide tools to partially automate the progressive refinement of models between the different phases and the generation of code for several transformation implementation languages.This work has been sponsored by the Spanish Ministry of Science and Innovation with project METEORIC (TIN2008-02081), and by the R&D program of the Community of Madrid with projects “e-Madrid" (S2009/TIC-1650). Parts of this work were done during the research stays of Esther and Juan at the University of York, with financial support from the Spanish Ministry of Science and Innovation (grant refs. JC2009-00015, PR2009-0019 and PR2008-0185)

HST observations of the metal rich globular clusters NGC6496 and NGC6352

Deep exposures of the metal-rich globular clusters NGC6496 and NGC6352 were obtained with the WFPC2 camera on board the HST through the F606W and F814W filters. The resulting colour-magnitude diagrams reach down to absolute magnitude M_814~10-10.5, approximately 5 magnitudes below the main sequence (MS) turn-off. The MS of the two clusters are sharp and well defined and their fiducial lines overlap almost exactly throughout this range. Their colour is, however, more than 0.1 mag redder than the MS fiducial line of the prototype metal-rich globular cluster 47 Tuc, after proper correction for the relative distances and reddening. This provides solid empirical evidence of a higher metal content, which is not surprising if these objects belong indeed to the bulge as their present location suggests. A good fit to the upper part of the MS of both clusters is obtained with a 10 Gyr-old theoretical isochrone from Baraffe et al. (1998) for a metallicity of [M/H]=-0.5, but at lower luminosity all models depart considerably from the observations, probably because of a deficiency in the treatment of the TiO opacity. The luminosity functions obtained from the observed CMD are rather similar to one another and show a peak at M_814~9. The present day mass functions (PDMF) are derived down to m~0.2 Msolar and are consistent with power-law indices alpha=0.7 for NGC6496 and alpha=0.6 for NGC6352. The PDMF of 47 Tuc is twice as steep in the same mass range (alpha=1.4). We investigate the origin of this discrepancy and show that it can be understood if the two clusters contain a considerably higher fraction of primordial binaries amongst their MS population, similar to that expected in the bulge. We briefly discuss the implications of this finding on the process of star and binary formation and on the universality of the IMF.Comment: Accepted for publication in Astronomy and Astrophysics. Prepared with aatex, 12 pages, 7 figure