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

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

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

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

Another brick in understanding chemical and kinematical properties of BSSs: NGC 6752

We used high-resolution spectra acquired with the multifiber facility FLAMES at the Very Large Telescope of the European Southern Observatory to investigate the chemical and kinematical properties of a sample of 22 Blue Straggler Stars (BSSs) and 26 red giant branch stars in the nearby globular cluster NGC 6752. We measured radial and rotational velocities and Fe, O and C abundances. According to radial velocities, metallicity and proper motions we identified 18 BSSs as likely cluster members. We found that all the BSSs rotate slowly (less than 40 km/s), similar to the findings in 47 Tucanae, NGC 6397 and M30. The Fe abundance analysis reveals the presence of 3 BSSs affected by radiative levitation (showing [Fe/H] significantly higher than that measured in "normal" cluster stars), confirming that element transport mechanisms occur in the photosphere of BSSs hotter than 8000 K. Finally, BSS C and O abundances are consistent with those measured in dwarf stars. No C and O depletion ascribable to mass transfer processes has been found on the atmospheres of the studied BSSs (at odds with previous results for 47 Tucanae and M30), suggesting the collisional origin for BSSs in NGC 6752 or that the CO-depletion is a transient phenomenon.Comment: ApJ accepte

The Red Giant Branch in Near-Infrared Colour-Magnitude Diagrams. II: The luminosity of the Bump and the Tip

We present new empirical calibrations of the Red Giant Branch (RGB) Bump and Tip based on a homogeneous near-Infrared database of 24 Galactic Globular Clusters. The luminosities of the RGB Bump and Tip in the J, H and K bands and their dependence on the cluster metallicity have been studied, yielding empirical relationships. By using recent transformations between the observational and theoretical planes, we also derived similar calibrations in terms of bolometric luminosity. Direct comparison between updated theoretical models and observations show an excellent agreement. The empirical calibration of the RGB Tip luminosity in the near-Infrared passbands presented here is a fundamental tool to derive distances to far galaxies beyond the Local Group, in view of using the new ground-based adaptive optics facilities and, in the next future, the James Webb Space Telescope.Comment: 7 pages, 7 figures, accepted for publication in MNRA

Mean number of visits to sites in Levy flights

Formulas are derived to compute the mean number of times a site has been visited during symmetric Levy flights. Unrestricted Levy flights are considered first, for lattices of any dimension: conditions for the existence of finite asymptotic maps of the visits over the lattice are analysed and a connection is made with the transience of the flight. In particular it is shown that flights on lattices of dimension greater than one are always transient. For an interval with absorbing boundaries the mean number of visits reaches stationary values, which are computed by means of numerical and analytical methods; comparisons with Monte Carlo simulations are also presented