Statistics of cross sections of Voronoi tessellations

In this paper we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in order to obtain analytical results, Voronoi cells are approximated to spheres. First, the probability density function for the lengths of the radii of the sections is derived and it is shown that it is related to the Meijer $G$-function; its properties are discussed and comparisons are made with the numerical results. Next the probability density function for the areas of cross sections is computed and compared with the results of numerical simulations.Comment: 10 pages and 6 figure

Asteroids dimensions and the Truncated Pareto distribution

In this chapter first the statistics of the standard and truncated Pareto distributions are derived and used to fit empirical values of asteroids diameters from different families, namely, Koronis, Eos and Themis, and from the Astorb database. A theoretical analysis is then carried out and two possible physical mechanisms are suggested that account for Pareto tails in distributions of asteroids diameter.Comment: 11 Pages and 6 figures. arXiv admin note: substantial text overlap with arXiv:0804.030

Female vs Males inmates: Authors' reply and sample size calculation

Bruno and colleagues highlighted the relatively low absolute-percentage of psychiatric morbidity that we found in our sample, as compared to their male sample. They invited to the use of diagnostic tools, specific for personality disorders and suicidal risk factors, to better investigate these critical issues. In summary, our results showed high percentages of psychiatric morbidity (44%), especially anxiety and depression. Female inmates declared to be most stressed by the distance from family and loved ones, and they did not present any antisocial personality diagnosis. They also showed a resilient reaction to their situation, because more than a half of women requested a supportive psychological therapy during their detention (14/25= 56%), and 10 of them were those with a psychiatric disorder (10/11= 90.9%), thus a higher proportion than those reported in male detainees at the Messina jail (56%), by Zoccali and colleagues (Zoccali et al., 2008). As we have acknowledged, we could further explore other personality disorders and not merely the antisocial personality pathological traits, as we did in our study. In conclusion, we agree with them about the need to repeat the screening for mental health and a deeper ascertainment of specific suicidal risk factors, with an adequate sample. Nonetheless, we believe that our data were not biased, and likely represented the psychological asset of the ladies’ detainee with a final sentence at the Pagliarelli jail of Palermo

Blue Stragglers in Low-Luminosity Star Clusters

We examine the blue straggler populations of 13 low-luminosity (M_V_t >~ -6) globular clusters and 2 old open clusters. These clusters test blue straggler formation in environments intermediate between higher luminosity (and usually higher density) clusters and the Galactic field. The anti-correlation between the relative frequency of blue stragglers (F_BSS = N_BSS / N_HB) and cluster luminosity continues to the lowest luminosity clusters, which have frequencies meeting or exceeding that of field stars. In addition we find that the anti-correlation between straggler frequency and central density disappears for clusters with density less than about 300 L_V,sun pc^-3, although this appears to be an artifact of the correlation between cluster luminosity and central density. We argue on observational (wide, eccentric binaries containing blue stragglers in M67, and the existence of very bright stragglers in most of the clusters in our sample) and theoretical grounds that stellar collisions still produce a significant fraction of the blue stragglers in low luminosity star clusters due to the long-term survival of wide binaries.Comment: 13 pages, 3 figures, accepted to ApJ Letter

Towards the absolute planes: a new calibration of the Bolometric Corrections and Temperature scales for Population II Giants

We present new determinations of bolometric corrections and effective temperature scales as a function of infrared and optical colors, using a large database of photometric observations of about 6500 Population II giants in Galactic Globular Clusters (GGCs), covering a wide range in metallicity (-2.0<[Fe/H]<0.0). New relations for BC_K vs (V-K), (J-K) and BC_V vs (B-V), (V-I), (V-J), and new calibrations for T_eff, using both an empirical relation and model atmospheres, are provided. Moreover, an empirical relation to derive the R parameter of the Infrared Flux Method as a function of the stellar temperature is also presented.Comment: 10 pages, 12 .ps figures, MN Latex, accepted by MNRA

FLAMES and XSHOOTER spectroscopy along the two BSS sequences of M30

We present spectroscopic observations acquired with FLAMES and XSHOOTER at the Very Large Telescope for a sample of 15 Blue Straggler Stars (BSSs) in the globular cluster (GC) M30. The targets have been selected to sample the two BSS sequences discovered, with 7 BSSs along the blue sequence and 8 along the red one. No difference in the kinematical properties of the two groups of BSSs has been found. In particular, almost all the observed BSSs have projected rotational velocity lower than ~30 km/s, with only one (blue) fast rotating BSS (>90 km/s), identified as a W UMa binary. This rotational velocity distribution is similar to those obtained in 47 Tucanae and NGC 6397, while M4 remains the only GC studied so far harboring a large fraction of fast rotating BSSs. All stars hotter than ~7800 K (regardless of the parent BSS sequence) show iron abundances larger than those measured from normal cluster stars, with a clearcut trend with the effective temperature. This behaviour suggests that particle trasport mechanisms driven by radiative levitation occur in the photosphere of these stars, as already observed for the BSSs in NGC 6397. Finally, 4 BSSs belonging to the red sequence (not affected by radiative levitation) show a strong depletion of [O/Fe], with respect to the abundance measured in Red Giant Branch and Horizontal Branch stars. This O-depletion is compatible with the chemical signature expected in BSSs formed by mass transfer processes in binary systems, in agreement with the mechanism proposed for the formation of BSSs in the red sequence.Comment: Accepted for publication in Ap

Near-Infrared photometry of four metal-rich Bulge globular clusters: NGC6304, NGC6569, NGC6637, NGC6638

We present high-quality near-Infrared photometry of four Bulge metal-rich globular clusters, namely: NGC 6304, NGC 6569, NGC 6637 and NGC 6638. By using the observed Colour-Magnitude Diagrams we derived a photometric estimates of the cluster reddening and distance. We performed a detailed analysis of the Red Giant Branch, presenting a complete description of morphologic parameters and evolutionary features (Bump and Tip). Photometric estimates of the cluster metallicity have been obtained by using the updated set of relations (published by our group) linking the metal abundance to a variety of near-Infrared indices measured along the Red Giant Branch. The detection of the Red Giant Branch Bump and the Tip is also presented and briefly discussed.Comment: 12 pages, 15 figures, accepted for publication in MNRA

Horizontal-Branch Models and the Second-Parameter Effect. IV. The Case of M3 and Palomar 3

We present a detailed analysis of the "second-parameter pair" of globular clusters M3 (NGC 5272) and Palomar 3. Our main results can be summarized as follows: i) The horizontal-branch (HB) morphology of M3 is significantly bluer in its inner regions (observed with the Hubble Space Telescope) than in the cluster outskirts (observed from the ground), i.e., M3 has an internal second parameter. Most plausibly the mass loss on the red giant branch (RGB) has been more efficient in the inner than in the outer regions of the cluster. ii) The dispersion in mass of the Pal 3 HB is found to be very small -- consistent with zero -- and we argue that this is unlikely to be due to a statistical fluctuation. It is this small mass dispersion that leads to the most apparent difference in the HB morphologies of M3 and Pal 3. iii) The relative HB types of M3 and Pal 3, as measured by mean colors or parameters involving the number of blue, variable, and red HB stars, can easily be accounted for by a fairly small difference in age between these clusters, of order 0.5-1 Gyr -- which is in good agreement with the relative age measurement, based on the clusters' turnoffs, by VandenBerg (2000).Comment: 20 pages, 12 figures, emulateapj5 style. The Astrophysical Journal, in press. Figs. 1, 6, 9, 10 are in png format. The preprint (postscript format) with full resolution (embedded) figures is available from http://www.astro.virginia.edu/~mc6v