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

The Luminosity Function of Omega Centauri

Deep HST-WFPC2 observations of the stellar population in the globular cluster Omega Cen (NGC 5139) have been used to measure the luminosity function of main sequence stars at the low-mass end. Two fields have been investigated, located respectively ~4.6' and ~7' away from the cluster center, or near the half-light radius of this cluster (~4.8'). The color-magnitude diagrams derived from these data show the cluster main sequence extending to the detection limit at I ~ 24. Information on both color and magnitude is used to build the luminosity functions of main sequence stars in these fields and the two independent determinations are found to agree very well with each other within the observational uncertainty. Both functions show a peak in the stellar distribution around M_I ~ 9 followed by a drop at fainter magnitudes well before photometric incompleteness becomes significant, as is typical of other globular clusters observed with the HST. This result is at variance with previous claims that the luminosity function of Omega Cen stays flat at low masses, but is in excellent agreement with recent near-IR NICMOS observations of the same cluster.Comment: To appear in The Astronomical Journal. Contains 7 pages, 4 figures, prepared with the AAS LaTeX macr

Image reconstruction from scattered Radon data by weighted positive definite kernel functions

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented

NGC2298: a globular cluster on its way to disruption

We have studied the stellar main sequence (MS) of the globular cluster NGC2298 using deep HST/ACS observations in the F606W and F814W bands covering an area of 3.4' x 3.4' around the cluster centre or about twice the cluster's half-mass radius. The colour-magnitude diagram that we derive in this way reveals a narrow and well defined MS extending down to the 10 sigma detection limit at m_606~26.5, m_814~25, corresponding to stars of ~0.2 Msolar. The luminosity function (LF) obtained with these data, once corrected for the limited effects of photometric incompleteness, reveals a remarkable deficiency of low-mass stars as well as a radial gradient, in that the LF becomes progressively steeper with radius. Using the mass-luminosity relation appropriate for the metallicity of NGC2298, we derive the cluster's global mass function (GMF) by using a multi-mass Michie-King model. Over the range 0.8 - 0.2 Msolar, the number of stars per unit mass decreases following a power-law distribution of the type dN/dm \propto m^(0.5), where, for comparison, typical halo clusters have dN/dm \propto m^(-1.5). If the IMF of NGC2298 was similar to that of other metal poor halo clusters, like e.g. NGC6397, the present GMF that we obtain implies that this object must have lost of order 85% of its original mass, at a rate much higher than that suggested by current models based on the available cluster orbit. The latter may, therefore, need revision.Comment: 9 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

The global mass function of M15

Data obtained with the NICMOS instrument on board the Hubble Space Telescope (HST) have been used to determine the H-band luminosity function (LF) and mass function (MF) of three stellar fields in the globular cluster M15, located ~7' from the cluster centre. The data confirm that the cluster MF has a characteristic mass of ~0.3 Msolar, as obtained by Paresce & De Marchi (2000) for a stellar field at 4.6' from the centre. By combining the present data with those published by other authors for various radial distances (near the centre, at 20" and at 4.6'), we have studied the radial variation of the LF due to the effects of mass segregation and derived the global mass function (GMF) using the Michie-King approach. The model that simultaneously best fits the LF at various locations, the surface brightness profile and the velocity dispersion profile suggests that the GMF should resemble a segmented power-law with the following indices: x ~ 0.8 for stars more massive than 0.8 Msolar, x ~ 0.9 for 0.3 - 0.8 Msolar and x ~ -2.2 at smaller masses (Salpeter's IMF would have x=1.35). The best fitting model also suggests that the cluster mass is ~5.4 10^5 Msolar and that the mass-to-light ratio is on average M/L_V ~ 2.1, with M/L_V ~ 3.7 in the core. A large amount of mass (~ 44 %) is found in the cluster core in the form of stellar heavy remnants, which may be sufficient to explain the mass segregation in M15 without invoking the presence of an intermediate-mass black hole.Comment: 12 pages, 10 figures, accepted for publication in A&

Partition of unity interpolation using stable kernel-based techniques

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient

Why haven't loose globular clusters collapsed yet?

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or VLT data. All the high-concentration clusters in the sample have a steep GMF, most likely reflecting their initial mass function. Conversely, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, more concentrated clusters should have lost proportionately more stars and have a shallower GMF than low concentration clusters, contrary to what is observed. It is possible that severely depleted GCs have also undergone core collapse and have already recovered a normal radial density profile. It is, however, more likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. In either case, we may have so far seriously underestimated the number of post core-collapse clusters and many may be lurking in the Milky Way.Comment: Four pages, one figure, accepted for publication in ApJ Letter