A spectroscopic and photometric study of stellar populations in a sample of clusters in the Magellanic Clouds

This Ph.D. Thesis has been carried out in the framework of a long-term and large project devoted to describe the main photometric, chemical, evolutionary and integrated properties of a representative sample of Large and Small Magellanic Cloud (LMC and SMC respectively) clusters. The globular clusters system of these two Irregular galaxies provides a rich resource for investigating stellar and chemical evolution and to obtain a detailed view of the star formation history and chemical enrichment of the Clouds. The results discussed here are based on the analysis of high-resolution photometric and spectroscopic datasets obtained by using the last generation of imagers and spectrographs. The principal aims of this project are summarized as follows: • The study of the AGB and RGB sequences in a sample of MC clusters, through the analysis of a wide near-infrared photometric database, including 33 Magellanic globulars obtained in three observing runs with the near-infrared camera SOFI@NTT (ESO, La Silla). • The study of the chemical properties of a sample of MCs clusters, by using optical and near-infrared high-resolution spectra. 3 observing runs have been secured to our group to observe 9 LMC clusters (with ages between 100 Myr and 13 Gyr) with the optical high-resolution spectrograph FLAMES@VLT (ESO, Paranal) and 4 very young (<30 Myr) clusters (3 in the LMC and 1 in the SMC) with the near-infrared high-resolution spectrograph CRIRES@VLT. • The study of the photometric properties of the main evolutive sequences in optical Color- Magnitude Diagrams (CMD) obtained by using HST archive data, with the final aim of dating several clusters via the comparison between the observed CMDs and theoretical isochrones. The determination of the age of a stellar population requires an accurate measure of the Main Sequence (MS) Turn-Off (TO) luminosity and the knowledge of the distance modulus, reddening and overall metallicity. For this purpose, we limited the study of the age just to the clusters already observed with high-resolution spectroscopy, in order to date only clusters with accurate estimates of the overall metallicity.

Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

Multiwavelenght study of cluster mergers and consequences for the radio emission properties of galaxy clusters

In the present thesis a thourough multiwavelength analysis of a number of galaxy clusters known to be experiencing a merger event is presented. The bulk of the thesis consists in the analysis of deep radio observations of six merging clusters, which host extended radio emission on the cluster scale. A composite optical and X–ray analysis is performed in order to obtain a detailed and comprehensive picture of the cluster dynamics and possibly derive hints about the properties of the ongoing merger, such as the involved mass ratio, geometry and time scale. The combination of the high quality radio, optical and X–ray data allows us to investigate the implications of the ongoing merger for the cluster radio properties, focusing on the phenomenon of cluster scale diffuse radio sources, known as radio halos and relics. A total number of six merging clusters was selected for the present study: A3562, A697, A209, A521, RXCJ 1314.4–2515 and RXCJ 2003.5–2323. All of them were known, or suspected, to possess extended radio emission on the cluster scale, in the form of a radio halo and/or a relic. High sensitivity radio observations were carried out for all clusters using the Giant Metrewave Radio Telescope (GMRT) at low frequency (i.e. ≤ 610 MHz), in order to test the presence of a diffuse radio source and/or analyse in detail the properties of the hosted extended radio emission. For three clusters, the GMRT information was combined with higher frequency data from Very Large Array (VLA) observations. A re–analysis of the optical and X–ray data available in the public archives was carried out for all sources. Propriety deep XMM–Newton and Chandra observations were used to investigate the merger dynamics in A3562. Thanks to our multiwavelength analysis, we were able to confirm the existence of a radio halo and/or a relic in all clusters, and to connect their properties and origin to the reconstructed merging scenario for most of the investigated cases. • The existence of a small size and low power radio halo in A3562 was successfully explained in the theoretical framework of the particle re–acceleration model for the origin of radio halos, which invokes the re–acceleration of pre–existing relativistic electrons in the intracluster medium by merger–driven turbulence. • A giant radio halo was found in the massive galaxy cluster A209, which has likely undergone a past major merger and is currently experiencing a new merging process in a direction roughly orthogonal to the old merger axis. A giant radio halo was also detected in A697, whose optical and X–ray properties may be suggestive of a strong merger event along the line of sight. Given the cluster mass and the kind of merger, the existence of a giant radio halo in both clusters is expected in the framework of the re–acceleration scenario. • A radio relic was detected at the outskirts of A521, a highly dynamically disturbed cluster which is accreting a number of small mass concentrations. A possible explanation for its origin requires the presence of a merger–driven shock front at the location of the source. The spectral properties of the relic may support such interpretation and require a Mach number M < ∼ 3 for the shock. • The galaxy cluster RXCJ 1314.4–2515 is exceptional and unique in hosting two peripheral relic sources, extending on the Mpc scale, and a central small size radio halo. The existence of these sources requires the presence of an ongoing energetic merger. Our combined optical and X–ray investigation suggests that a strong merging process between two or more massive subclumps may be ongoing in this cluster. Thanks to forthcoming optical and X–ray observations, we will reconstruct in detail the merger dynamics and derive its energetics, to be related to the energy necessary for the particle re–acceleration in this cluster. • Finally, RXCJ 2003.5–2323 was found to possess a giant radio halo. This source is among the largest, most powerful and most distant (z=0.317) halos imaged so far. Unlike other radio halos, it shows a very peculiar morphology with bright clumps and filaments of emission, whose origin might be related to the relatively high redshift of the hosting cluster. Although very little optical and X–ray information is available about the cluster dynamical stage, the results of our optical analysis suggest the presence of two massive substructures which may be interacting with the cluster. Forthcoming observations in the optical and X–ray bands will allow us to confirm the expected high merging activity in this cluster. Throughout the present thesis a cosmology with H0 = 70 km s−1 Mpc−1, m=0.3 and =0.7 is assumed.

Chemical and kinematical properties of Blue Straggler stars in Galactic globular clusters

Blue straggler stars (BSSs) are brighter and bluer (hotter) than the main-sequence (MS) turnoff and they are known to be more massive than MS stars.Two main scenarios for their formation have been proposed:collision-induced stellar mergers (COL-BSSs),or mass-transfer in binary systems (MT-BSSs).Depleted surface abundances of C and O are expected for MT-BSSs,whereas no chemical anomalies are predicted for COL-BSSs.Both MT- and COL-BSSs should rotate fast, but braking mechanisms may intervene with efficiencies and time-scales not well known yet,thus preventing a clear prediction of the expected rotational velocities.Within this context,an extensive survey is ongoing by using the multi-object spectrograph FLAMES@VLT,with the aim to obtain abundance patterns and rotational velocities for representative samples of BSSs in several Galactic GCs.A sub-population of CO-depleted BSSs has been identified in 47 Tuc,with only one fast rotating star detected.For this PhD Thesis work I analyzed FLAMES spectra of more than 130 BSSs in four GCs:M4,NGC 6397,M30 and ω Centauri.This is the largest sample of BSSs spectroscopically investigated so far.Hints of CO depletion have been observed in only 4-5 cases (in M30 and ω Centauri),suggesting either that the majority of BSSs have a collisional origin,or that the CO-depletion is a transient phenomenon.Unfortunately,no conclusions in terms of formation mechanism could be drawn in a large number of cases,because of the effects of radiative levitation. Remarkably,however,this is the first time that evidence of radiative levitation is found in BSSs hotter than 8200 K.Finally, we also discovered the largest fractions of fast rotating BSSs ever observed in any GCs:40% in M4 and 30% in ω Centauri.While not solving the problem of BSS formation,these results provide invaluable information about the BSS physical properties,which is crucial to build realistic models of their evolution.