Geometry of Banach spaces and biorthogonal systems

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system

The structure of Abell 1351: a bimodal galaxy cluster with peculiar diffuse radio emission

We aim to review the internal structure and dynamics of the Abell 1351 cluster, shown to host a radio halo with a quite irregular shape. Our analysis is based on radial velocity data for 135 galaxies obtained at the Telescopio Nazionale Galileo. We combine galaxy velocities and positions to select 95 cluster galaxy members and analyse the internal dynamics of the whole cluster. We also examine X-ray data retrieved from Chandra and XMM archives. We measure the cluster redshift, =0.325, the line-of-sight (LOS) velocity dispersion, \sigma_v~1500 km/s, and the X-ray temperature, kT~9 keV. From both X-ray and optical data independently, we estimate a large cluster mass, in the 1--4 $10^{15}$ M$_\odot$ range. We attribute the extremely high value of \sigma_v to the bimodality in the velocity distribution. We find evidence of a significant velocity gradient and optical 3D substructure. The X-ray analysis also shows many features in favour of a complex cluster structure, probably supporting an ongoing merger of substructures in Abell 1351. The observational scenario agrees with the presence of two main subclusters in the northern region, each with its brightest galaxy (BCG1 and BCG2), detected as the two most important X-ray substructures with a rest-frame LOS velocity difference of \Delta v~2500 km/s (in the rest frame) and probably being in large part aligned with the LOS. We conclude that Abell 1351 is a massive merging cluster. The details of the cluster structure allow us to interpret the quite asymmetric radio halo as a `normal' halo plus a southern relic, strongly supporting a previous suggestion based only on inspection of radio and preliminary X-ray data.Comment: 13 pages, 13 figures, 1 tabl

Gravitational Lensing in the metric theory proposed by Sobouti

Recently, Y. Sobouti (2007) has provided a metric theory f(R) that can account for certain dynamical anomalies observed in spiral galaxies. Mendoza & Rosas-Guevara (2007) have shown that in this theory there is an extra-bending as compared to standard general relativity. In the present work we have developed in more specific detail this additional lensing effect and we have made evaluations of the alpha parameter used in the model adjusting the theory to observations in X-rays of 13 clusters of galaxies with gravitational lensing (Hoekstra (2007)).Comment: 7 pages, 2 figure

The possibility of determining open-cluster parameters from BVRI photometry

In the last decades we witnessed an increase in studies of open clusters of the Galaxy, especially because of the good determination for a wide range of values of parameters such as age, distance, reddening, and proper motion. The reliable determination of the parameters strongly depends on the photometry available and especially on the U filter, which is used to obtain the color excess E(B-V) through the color-color diagram (U-B) by (B-V) by fitting a zero age main-sequence. Owing to the difficulty of performing photometry in the U band, many authors have tried to obtain E(B-V) without the filter. But because of the near linearity of the color-color diagrams that use the other bands, combined with the fact that most fitting procedures are highly subjective (many done "by eye") the reliability of those results has always been questioned. Our group has recently developed, a tool that performs isochrone fitting in open-cluster photometric data with a global optimization algorithm, which removes the need to visually perform the fits and thus removes most of the related subjectivity. Here we apply our method to a set of synthetic clusters and two observed open clusters (Trumpler 1 and Melotte 105) using only photometry for the BVRI bands. Our results show that, considering the cluster structural variance caused only by photometric and Poisson sampling errors, our method is able to recover the synthetic cluster parameters with errors of less than 10% for a wide range of ages, distances, and reddening, which clearly demonstrates its potential. The results obtained for Trumpler 1 and Melotte 105 also agree well with previous literature values.Comment: 5 pages, 5 figures, accepted for publication in Astronomy&Astrophysic

How Universal are the Young Cluster Sequences? - the Cases of LMC, SMC, M83 and the Antennae

Aims.Recently a new analysis of cluster observations in the Milky Way found evidence that clustered star formation may work under tight constraints with respect to cluster size and density, implying the presence of just two sequences of young massive cluster. These two types of clusters each expand at different rates with cluster age. Methods. Here we investigate whether similar sequences exist in other nearby galaxies. Results:We find that while for the extragalactic young stellar clusters the overall trend in the cluster-density scaling is quite comparable to the relation obtained for Galactic clusters, there are also possible difference. For the LMC and SMC clusters the densities are below the Galactic data points and/or the core radii are smaller than those of data points with comparable density. For M83 and the Antenna clusters the core radii are possibly comparable to the Galactic clusters but it is not clear whether they exhibit similar expansion speeds. These findings should serve as an incentive to perform more systematic observations and analysis to answer the question of a possible similarity between young galactic and extragalactic star clusters sequences.Comment: 6 pages, 4 figures, A&A in pres

Integrated parameters of star clusters: A comparison of theory and observations

(Abridged) This paper presents integrated magnitude and colours for synthetic clusters. The integrated parameters have been obtained for the whole cluster population as well as for the main-sequence (MS) population of star clusters. We have also estimated observed integrated magnitudes and colours of MS population of galactic open clusters, LMC and SMC star clusters. It is found that the colour evolution of MS population of star clusters is not affected by the stochastic fluctuations, however these fluctuations significantly affect the colour evolution of the whole cluster population. The fluctuations are maximum in $(V-I)$ colour in the age range 6.7 $<$ log (age) $<$ 7.5. Evolution of integrated colours of MS population of the clusters in the Milky Way, LMC and SMC, obtained in the present study are well explained by the present synthetic cluster model. The observed integrated $(B-V)$ colours of MS population of LMC star clusters having age $\geq$ 500 Myr seem to be distributed around $Z=$ 0.004 model, whereas $(V-I)$ colours are found to be more bluer than those predicted by the $Z=$ 0.004 model. $(V-I)$ vs $(B-V)$ two-colour diagram for the MS population of the Milky Way star clusters shows a fair agreement between the observations and present model, however the diagrams for LMC and SMC clusters indicate that observed $(V-I)$ colours are relatively bluer. Possible reasons for this anomaly have been discussed.Comment: 35 pages, 20 figs, accepted for publication in MNRA