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

A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications

We study continuous dependence estimates for viscous Hamilton-Jacobi equations defined on a network Gamma. Given two Hamilton-Jacobi equations, we prove an estimate of the C-2-norm of the difference between the corresponding solutions in terms of the distance among the Hamiltonians. We also provide two applications of the previous estimate: the first one is an existence and uniqueness result for a quasi-stationary Mean Field Games defined on the network Gamma; the second one is an estimate of the rate of convergence for homogenization of Hamilton-Jacobi equations defined on a periodic network, when the size of the cells vanishes and the limit problem is defined in the whole Euclidean space

Romanesque and territory. The construction materials of Sardinian medieval churches: new approaches to the valorization, conservation and restoration

This paper is intended to illustrate a multidisciplinary research project devoted to the study of the constructive materials of the Romanesque churches in Sardinia during the “Giudicati” period (11th -13th centuries). The project focuses on the relationship between a selection of monuments and their territory, both from a historical-architectural perspective and from a more modern perspective addressing future restoration works. The methodologies of the traditional art-historical research (study of bibliographic, epigraphic and archival sources, formal reading of artifacts) are flanked by new technologies: digital surveys executed with a 3D laser-scanner, analyses of the materials (stones, mortars, bricks) with different instrumental methods: X-ray fluorescence (XRF) and inductively coupled mass spectrometry (ICP-MS) for chemical composition, X-ray diffractometer (XRD) to determine the alteration phases (e.g., soluble salts), optical microscopy and electronic (SEM) to study textures, mineral assemblages and microstructures, termogravimetric/differential scanning, calorimetric analysis (TG/DTA) for the composition of the binder mortars. This multidisciplinary approach allows the achieving of important results in an archaeometric context: 1) from a historical point of view, with the possible identification of ancient traffics, trade routes, sources of raw materials, construction phases, wall textures; 2) from a conservative point of view, by studying chemical and physical weathering processes of stone materials compatible for replacement in case of future restoration works. Sardinian Romanesque architectural heritage is particularly remarkable: about 200 churches of different types and sizes, with the almost exclusive use of cut stones. Bi- or poly-chromy, deriving from the use of different building materials, characterizes many of these monuments, becoming also a vehicle for political and cultural meanings. The paper will present some case studies aimed to illustrate the progress of the project and the results achieved

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

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

Wildlife friendly agriculture: which factors do really matter? A genetic study on field vole

The distribution of genetic differentiation and the directions of gene flow were determined mainly by landscape factors: thus the expectation that organic fields act as genetic reservoir was not met. The fact that agricultural area presented more sub-populations than the undisturbed one, together with the importance of connectivity and habitat size in shaping gene flow and genetic differentiation, shows that switching to organic farming might not be enough to ensure the conservation of species in the agricultural environment. These results emphasise the need to include landscape structure in management policies