Statistical properties of Radio Halos and the re-acceleration model

Galaxy clusters occupy a special position in the cosmic hierarchy as they are the largest bound structures in the Universe. There is now general agreement on a hierarchical picture for the formation of cosmic structures, in which galaxy clusters are supposed to form by accretion of matter and merging between smaller units. During merger events, shocks are driven by the gravity of the dark matter in the diffuse barionic component, which is heated up to the observed temperature. Radio and hard-X ray observations have discovered non-thermal components mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance as it calls for a “revision” of the physics of the ICM. The bulk of present information comes from the radio observations which discovered an increasing number of Mpcsized emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics (at the cluster periphery). These sources are due to synchrotron emission from ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio Halos are the most spectacular evidence of non-thermal components in the ICM and understanding the origin and evolution of these sources represents one of the most challenging goal of the theory of the ICM. Cluster mergers are the most energetic events in the Universe and a fraction of the energy dissipated during these mergers could be channelled into the amplification of the magnetic fields and into the acceleration of high energy particles via shocks and turbulence driven by these mergers. Present observations of Radio Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration scenario in which MHD turbulence injected during these cluster mergers re-accelerates high energy particles in the ICM. The physics involved in this scenario is very complex and model details are difficult to test, however this model clearly predicts some simple properties of Radio Halos (and resulting IC emission in the hard X-ray band) which are almost independent of the details of the adopted physics. In particular in the re-acceleration scenario MHD turbulence is injected and dissipated during cluster mergers and thus Radio Halos (and also the resulting hard X-ray IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr) associated with dynamically disturbed clusters. The physics of the re-acceleration scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated electrons, which is due to the balance between turbulent acceleration and radiative losses. The energy at which this cut-off occurs, and thus the maximum frequency at which synchrotron radiation is produced, depends essentially on the efficiency of the acceleration mechanism so that observations at high frequencies are expected to catch only the most efficient phenomena while, in principle, low frequency radio surveys may found these phenomena much common in the Universe. These basic properties should leave an important imprint in the statistical properties of Radio Halos (and of non-thermal phenomena in general) which, however, have not been addressed yet by present modellings. The main focus of this PhD thesis is to calculate, for the first time, the expected statistics of Radio Halos in the context of the re-acceleration scenario. In particular, we shall address the following main questions: • Is it possible to model “self-consistently” the evolution of these sources together with that of the parent clusters? • How the occurrence of Radio Halos is expected to change with cluster mass and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy clusters changes with the observing radio frequency? • How many Radio Halos are expected to form in the Universe? At which redshift is expected the bulk of these sources? • Is it possible to reproduce in the re-acceleration scenario the observed occurrence and number of Radio Halos in the Universe and the observed correlations between thermal and non-thermal properties of galaxy clusters? • Is it possible to constrain the magnetic field intensity and profile in galaxy clusters and the energetic of turbulence in the ICM from the comparison between model expectations and observations? Several astrophysical ingredients are necessary to model the evolution and statistical properties of Radio Halos in the context of re-acceleration model and to address the points given above. For these reason we deserve some space in this PhD thesis to review the important aspects of the physics of the ICM which are of interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters, and in particular, the clusters formation process; in Chapt. 2 we review the main observational properties of non-thermal components in the ICM; and in Chapt. 3 we focus on the physics of magnetic field and of particle acceleration in galaxy clusters. As a relevant application, the theory of Alfv´enic particle acceleration is applied in Chapt. 4 where we report the most important results from calculations we have done in the framework of the re-acceleration scenario. In this Chapter we show that a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers can be channelled into the injection of Alfv´en waves at small scales and that these waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray emission. The main part of this PhD work, the calculation of the statistical properties of Radio Halos and non-thermal phenomena as expected in the context of the re-acceleration model and their comparison with observations, is presented in Chapts.5, 6, 7 and 8. In Chapt.5 we present a first approach to semi-analytical calculations of statistical properties of giant Radio Halos. The main goal of this Chapter is to model cluster formation, the injection of turbulence in the ICM and the resulting particle acceleration process. We adopt the semi–analytic extended Press & Schechter (PS) theory to follow the formation of a large synthetic population of galaxy clusters and assume that during a merger a fraction of the PdV work done by the infalling subclusters in passing through the most massive one is injected in the form of magnetosonic waves. Then the processes of stochastic acceleration of the relativistic electrons by these waves and the properties of the ensuing synchrotron (Radio Halos) and inverse Compton (IC, hard X-ray) emission of merging clusters are computed under the assumption of a constant rms average magnetic field strength in emitting volume. The main finding of these calculations is that giant Radio Halos are naturally expected only in the more massive clusters, and that the expected fraction of clusters with Radio Halos is consistent with the observed one. In Chapt. 6 we extend the previous calculations by including a scaling of the magnetic field strength with cluster mass. The inclusion of this scaling allows us to derive the expected correlations between the synchrotron radio power of Radio Halos and the X-ray properties (T, LX) and mass of the hosting clusters. For the first time, we show that these correlations, calculated in the context of the re-acceleration model, are consistent with the observed ones for typical µG strengths of the average B intensity in massive clusters. The calculations presented in this Chapter allow us to derive the evolution of the probability to form Radio Halos as a function of the cluster mass and redshift. The most relevant finding presented in this Chapter is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio powers because of the decrease of the electron re-acceleration efficiency in smaller galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio Halos and compare them with available observations: we claim that » 100 Radio Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more than 1000 Radio Halos are expected to be discovered in the next future by LOFAR at 150 MHz. This is the first (and so far unique) model expectation for the number counts of Radio Halos at lower frequency and allows to design future radio surveys. Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on a “revision” of the occurrence of Radio Halos. We combine past results from the NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the possibility to test our model expectations with the number counts of Radio Halos at z » 0.05 − 0.4. The most relevant limitation in the calculations presented in Chapt. 5 and 6 is the assumption of an “averaged” size of Radio Halos independently of their radio luminosity and of the mass of the parent clusters. This assumption cannot be released in the context of the PS formalism used to describe the formation process of clusters, while a more detailed analysis of the physics of cluster mergers and of the injection process of turbulence in the ICM would require an approach based on numerical (possible MHD) simulations of a very large volume of the Universe which is however well beyond the aim of this PhD thesis. On the other hand, in Chapt.8 we report our discovery of novel correlations between the size (RH) of Radio Halos and their radio power and between RH and the cluster mass within the Radio Halo region, MH. In particular this last “geometrical” MH − RH correlation allows us to “observationally” overcome the limitation of the “average” size of Radio Halos. Thus in this Chapter, by making use of this “geometrical” correlation and of a simplified form of the re-acceleration model based on the results of Chapt. 5 and 6 we are able to discuss expected correlations between the synchrotron power and the thermal cluster quantities relative to the radio emitting region. This is a new powerful tool of investigation and we show that all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now become well understood in the context of the re-acceleration model. In addition, we find that observationally the size of Radio Halos scales non-linearly with the virial radius of the parent cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.

Sviluppo, implementazione e valutazione funzionale di un nuovo modello protesico di caviglia

Total ankle arthroplasty (TAA) is still not as satisfactory as total hip and total knee arthroplasty. For the TAA to be considered a valuable alternative to ankle arthrodesis, an effective range of ankle mobility must be recovered. The disappointing clinical results of the current generation of TAA are mostly related to poor understanding of the structures guiding ankle joint mobility. A new design (BOX Ankle) has been developed, uniquely able to restore physiologic ankle mobility and a natural relationship between the implanted components and the retained ligaments. For the first time the shapes of the tibial and talar components in the sagittal plane were designed to be compatible with the demonstrated ligament isometric rotation. This resulted in an unique motion at the replaced ankle where natural sliding as well as rolling motion occurs while at the same time full conformity is maintained between the three components throughout the flexion arc. According to prior research, the design features a spherical convex tibial component, a talar component with radius of curvature in the sagittal plane longer than that of the natural talus, and a fully conforming meniscal component. After computer-based modelling and preliminary observations in several trial implantation in specimens, 126 patients were implanted in the period July 2003 – December 2008. 75 patients with at least 6 months follow-up are here reported. Mean age was 62,6 years (range 22 – 80), mean follow-up 20,2 months. The AOFAS clinical score systems were used to assess patient outcome. Radiographs at maximal dorsiflexion and maximal plantar flexion confirmed the meniscalbearing component moves anteriorly during dorsiflexion and posteriorly during plantarflexion. Frontal and lateral radiographs in the patients, show good alignment of the components, and no signs of radiolucency or loosening. The mean AOFAS score was observed to go from 41 pre-op to 74,6 at 6 month follow-up, with further improvement at the following follow-up. These early results reveal satisfactory clinical scores, with good recovery of range of motion and reduction of pain. Radiographic assessment reveals good osteointegration. All these preliminary results confirm biomechanical studies and the validity of this novel ligamentcompatible prosthesis design. Surely it will be important to re-evaluate these patients later.

Ricerche di campo per lo sviluppo della tecnologia del maschio sterile nella lotta ad Aedes albopictus (Skuse)

Aedes albopictus (Skuse), comunemente detta Zanzara Tigre, ha invaso, negli ultimi anni, molti paesi, soprattutto in modo passivo attraverso il commercio di pneumatici usati. Questa specie è particolarmente adatta all'applicazione della tecnica dell'insetto sterile (SIT), basata su allevamento massale, sterilizzazione e rilascio in campo di un gran numero di maschi della specie vettrice. I maschi sterili rilasciati devono essere in grado di volare, di disperdersi sul territorio, di sopravvivere, di essere sessualmente attivi abbastanza a lungo per coprire il tempo tra una fase di rilascio e la successiva, di individuare le femmine vergini selvatiche e competere con successo per l'accoppiamento con i maschi selvatici. La dispersione e la sopravvivenza dei maschi di Ae. albopictus allevati in laboratorio, sono state studiate mediante tecniche di marcatura, rilascio e ricattura. Le catture sono state eseguite da tecnici specializzati, in un raggio di 350 m dal sito di rilascio. Gli esperimenti condotti hanno dimostrato che i maschi sono in grado di disperdersi, dal sito di rilascio, per circa 200 m ma la loro longevità in campo è fortemente dipendente dalle condizioni climatiche. In studi di semi-campo e di campo è stato valutato uno speciale dispositivo progettato per essere incluso nella stazione di rilascio dei maschi in grado di fornire loro fonti energetiche per migliorarne le prestazioni. I risultati ottenuti sono stati positivi. Studi di competitività sono stati condotti in tunnel costruiti in un ambiente naturale al fine di validare un protocollo per studi sulla competitività dei maschi in questo modello sperimentale. Maschi irraggiati mediante l'applicazione di raggi gamma alla dose di 30 Gy sono stati messi in competizione con maschi fertili per l'accoppiamento con femmine vergini con diversi rapporti. I risultati ottenuti hanno dimostrato le buone prestazioni e l'affidabilità di questo modello sperimentale rimanendo però irrisolto il problema dell’elevata variabilità.