Non-Linear Pricing in Imperfectly Competitive Markets

This thesis is dedicated to the analysis of non-linear pricing in oligopoly. Non-linear pricing is a fairly predominant practice in most real markets, mostly characterized by some amount of competition. The sophistication of pricing practices has increased in the latest decades due to the technological advances that have allowed companies to gather more and more data on consumers preferences. The first essay of the thesis highlights the main characteristics of oligopolistic non-linear pricing. Non-linear pricing is a special case of price discrimination. The theory of price discrimination has to be modified in presence of oligopoly: in particular, a crucial role is played by the competitive externality that implies that product differentiation is closely related to the possibility of discriminating. The essay reviews the theory of competitive non-linear pricing by starting from its foundations, mechanism design under common agency. The different approaches to model non-linear pricing are then reviewed. In particular, the difference between price and quantity competition is highlighted. Finally, the close link between non-linear pricing and the recent developments in the theory of vertical differentiation is explored. The second essay shows how the effects of non-linear pricing are determined by the relationship between the demand and the technological structure of the market. The chapter focuses on a model in which firms supply a homogeneous product in two different sizes. Information about consumers' reservation prices is incomplete and the production technology is characterized by size economies. The model provides insights on the size of the products that one finds in the market. Four equilibrium regions are identified depending on the relative intensity of size economies with respect to consumers' evaluation of the good. Regions for which the product is supplied in a single unit or in several different sizes or in only a very large one. Both the private and social desirability of non-linear pricing varies across different equilibrium regions. The third essay considers the broadband internet market. Non discriminatory issues seem the core of the recent debate on the opportunity or not of regulating the internet. One of the main questions posed is whether the telecom companies, owning the networks constituting the internet, should be allowed to offer quality-contingent contracts to content providers. The aim of this essay is to analyze the issue through a stylized two-sided market model of the web that highlights the effects of such a discrimination over quality, prices and participation to the internet of providers and final users. An overall welfare comparison is proposed, concluding that the final effects of regulation crucially depend on both the technology and preferences of agents.

Collective effects for the LHC injectors: non-ultrarelativistic approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the LHC performances in exploring new physics frontiers. One of the main limitations to the upgrade is represented by the collective instabilities. These are intensity dependent phenomena triggered by electromagnetic fields excited by the interaction of the beam with its surrounding. These fields are represented via wake fields in time domain or impedances in frequency domain. Impedances are usually studied assuming ultrarelativistic bunches while we mainly explored low and medium energy regimes in the LHC injector chain. In a non-ultrarelativistic framework we carried out a complete study of the impedance structure of the PSB which accelerates proton bunches up to 1.4 GeV. We measured the imaginary part of the impedance which creates betatron tune shift. We introduced a parabolic bunch model which together with dedicated measurements allowed us to point to the resistive wall impedance as the source of one of the main PSB instability. These results are particularly useful for the design of efficient transverse instability dampers. We developed a macroparticle code to study the effect of the space charge on intensity dependent instabilities. Carrying out the analysis of the bunch modes we proved that the damping effects caused by the space charge, which has been modelled with semi-analytical method and using symplectic high order schemes, can increase the bunch intensity threshold. Numerical libraries have been also developed in order to study, via numerical simulations of the bunches, the impedance of the whole CERN accelerator complex. On a different note, the experiment CNGS at CERN, requires high-intensity beams. We calculated the interpolating Hamiltonian of the beam for highly non-linear lattices. These calculations provide the ground for theoretical and numerical studies aiming to improve the CNGS beam extraction from the PS to the SPS.

Hydrodynamical simulations of galaxy clusters in dark energy cosmologies

In this work we investigate the influence of dark energy on structure formation, within five different cosmological models, namely a concordance $\Lambda$CDM model, two models with dynamical dark energy, viewed as a quintessence scalar field (using a RP and a SUGRA potential form) and two extended quintessence models (EQp and EQn) where the quintessence scalar field interacts non-minimally with gravity (scalar-tensor theories). We adopted for all models the normalization of the matter power spectrum $\sigma_{8}$ to match the CMB data. For each model, we perform hydrodynamical simulations in a cosmological box of $(300 \ {\rm{Mpc}} \ h^{-1})^{3}$ including baryons and allowing for cooling and star formation. We find that, in models with dynamical dark energy, the evolving cosmological background leads to different star formation rates and different formation histories of galaxy clusters, but the baryon physics is not affected in a relevant way. We investigate several proxies for the cluster mass function based on X-ray observables like temperature, luminosity, $M_{gas}$, and $Y_{X}$. We confirm that the overall baryon fraction is almost independent of the dark energy models within few percentage points. The same is true for the gas fraction. This evidence reinforces the use of galaxy clusters as cosmological probe of the matter and energy content of the Universe. We also study the $c-M$ relation in the different cosmological scenarios, using both dark matter only and hydrodynamical simulations. We find that the normalization of the $c-M$ relation is directly linked to $\sigma_{8}$ and the evolution of the density perturbations for $\Lambda$CDM, RP and SUGRA, while for EQp and EQn it depends also on the evolution of the linear density contrast. These differences in the $c-M$ relation provide another way to use galaxy clusters to constrain the underlying cosmology.

Computer simulations of microstructures related to the olivine spinel transition

Tiefherd-Beben, die im oberen Erdmantel in einer Tiefe von ca. 400 km auftreten, werden gewöhnlich mit dem in gleicher Tiefe auftretenden druckabhängigen, polymorphen Phasenübergang von Olivine (α-Phase) zu Spinel (β-Phase) in Verbindung gebracht. Es ist jedoch nach wie vor unklar, wie der Phasenübergang mit dem mechanischen Versagen des Mantelmaterials zusammenhängt. Zur Zeit werden im Wesentlichen zwei Modelle diskutiert, die entweder Mikrostrukturen, die durch den Phasenübergang entstehen, oder aber die rheologischen Veränderungen des Mantelgesteins durch den Phasenübergang dafür verantwortlich machen. Dabei sind Untersuchungen der Olivin→Spinel Umwandlung durch die Unzugänglichkeit des natürlichen Materials vollständig auf theoretische Überlegungen sowie Hochdruck-Experimente und Numerische Simulationen beschränkt. Das zentrale Thema dieser Dissertation war es, ein funktionierendes Computermodell zur Simulation der Mikrostrukturen zu entwickeln, die durch den Phasenübergang entstehen. Des Weiteren wurde das Computer Modell angewandt um die mikrostrukturelle Entwicklung von Spinelkörnern und die Kontrollparameter zu untersuchen. Die Arbeit ist daher in zwei Teile unterteilt: Der erste Teil (Kap. 2 und 3) behandelt die physikalischen Gesetzmäßigkeiten und die prinzipielle Funktionsweise des Computer Modells, das auf der Kombination von Gleichungen zur Errechnung der kinetischen Reaktionsgeschwindigkeit mit Gesetzen der Nichtgleichgewichtsthermodynamik unter nicht-hydostatischen Bedingungen beruht. Das Computermodell erweitert ein Federnetzwerk der Software latte aus dem Programmpaket elle. Der wichtigste Parameter ist dabei die Normalspannung auf der Kornoberfläche von Spinel. Darüber hinaus berücksichtigt das Programm die Latenzwärme der Reaktion, die Oberflächenenergie und die geringe Viskosität von Mantelmaterial als weitere wesentliche Parameter in der Berechnung der Reaktionskinetic. Das Wachstumsverhalten und die fraktale Dimension von errechneten Spinelkörnern ist dabei in guter Übereinstimmung mit Spinelstrukturen aus Hochdruckexperimenten. Im zweiten Teil der Arbeit wird das Computermodell angewandt, um die Entwicklung der Oberflächenstruktur von Spinelkörnern unter verschiedenen Bedigungen zu eruieren. Die sogenannte ’anticrack theory of faulting’, die den katastrophalen Verlauf der Olivine→Spinel Umwandlung in olivinhaltigem Material unter differentieller Spannung durch Spannungskonzentrationen erklärt, wurde anhand des Computermodells untersucht. Der entsprechende Mechanismus konnte dabei nicht bestätigt werden. Stattdessen können Oberflächenstrukturen, die Ähnlichkeiten zu Anticracks aufweisen, durch Unreinheiten des Materials erklärt werden (Kap. 4). Eine Reihe von Simulationen wurde der Herleitung der wichtigsten Kontrollparameter der Reaktion in monomineralischem Olivin gewidmet (Kap. 5 and Kap. 6). Als wichtigste Einflüsse auf die Kornform von Spinel stellten sich dabei die Hauptnormalspannungen auf dem System sowie Heterogenitäten im Wirtsminerals und die Viskosität heraus. Im weiteren Verlauf wurden die Nukleierung und das Wachstum von Spinel in polymineralischen Mineralparagenesen untersucht (Kap. 7). Die Reaktionsgeschwindigkeit der Olivine→Spinel Umwandlung und die Entwicklung von Spinelnetzwerken und Clustern wird durch die Gegenwart nicht-reaktiver Minerale wie Granat oder Pyroxen erheblich beschleunigt. Die Bildung von Spinelnetzwerken hat das Potential, die mechanischen Eigenschaften von Mantelgestein erheblich zu beeinflussen, sei es durch die Bildung potentieller Scherzonen oder durch Gerüstbildung. Dieser Lokalisierungprozess des Spinelwachstums in Mantelgesteinen kann daher ein neues Erklärungsmuster für Tiefbeben darstellen.

Crystal Engineering of bright luminescent copper iodide clusters with phosphorus and nitrogen-based ligands

Copper(I) halide clusters are recently considered as good candidate for optoelectronic devices such as OLEDs . Although the copper halide clusters, in particular copper iodide, are very well known since the beginning of the 20th century, only in the late ‘70s the interest on these compounds grew dramatically due their particular photophysical behaviour. These complexes are characterized by a dual triplet emission bands, named Cluster Centred (3CC) and Halogen-to-Ligand charge transfer (3XLCT), the intensities of which are strictly related with the temperature. The CC transition, due to the presence of a metallophylic interactions, is prevalent at ambient temperature while the XLCT transition, located preferentially on the ligand part, became more prominent at low temperature. Since these pioneering works, it was easy to understand the photophysical properties of this compounds became more interesting in solid-state respect to solution with an improvement in emission efficiency. In this work we aim to characterize in SS organocopper(I)iodide compounds to valuate the correlation between the molecular crystal structure and the photophysical properties. It is also considered to hike new strategies to synthesize CuI complexes from the wet reactions to the more green solvent free methods. The advantages in using these strategies are evident but, obtain a single crystal suitable for SCXRD analysis from these batches is quite impossible. The structure solution still remains the key point in this research so we tackle this problem solving the structure by X-ray powder diffraction data. When the sample was fully characterized we moved to design and development of the associated OLED-device. Since copper iodide complexes are often insoluble in organic solvents, the high vacuum deposition technique is preferred. A new non-conventional deposition process have also been proposed to avoid the low complex stability in this practice with an in-situ complex formation in a layer-by layer deposition route.

Emissione non termica in ammassi di galassie in relazione con la massa del sistema

L'oggetto di studio di questa tesi e' l'analisi degli ammassi di galassie (galaxy clusters) e delle loro proprieta', attraverso un introduttiva analisi morfologica e dinamica, considerazioni sulle proprieta' termiche (con caratteristiche collegate direttamente dalla temperatura), ed infine l'ispezione dei meccanismi che generano le emissioni non termiche e le loro sorgenti. Cercheremo delle relazioni fra le une e le altre. In particolare studieremo specifiche conformazioni del mezzo intergalattico (ICM, intracluster medium) all'interno degli ammassi, quali Aloni, Relitti e Mini Aloni, attraverso le radiazioni che essi sprigionano nella banda dei raggi X e onde radio. Le prime osservazioni sugli ammassi di galassie sono state effettuate gia' alla fine del '700 da Charles Messier, che, al fine di esaminare il cielo alla ricerca di comete, forni un catalogo di 110 oggetti cosmici che, pur apparendo nebulosi per via della limitatezza di risoluzione dei telescopi di allora, non erano sicuramente comete. Fra questi oggetti vi erano anche ammassi di galassie. I primi studi approfonditi si ebbero soltanto con il rapido incremento tecnologico del XX secolo che permise di capire che quelle formazioni confuse altro non erano che agglomerati di galassie. Telescopi piu' grandi, e poi interferometri, radiotelescopi osservazioni agli X hanno sostanzialmente aperto il mondo dell'astrofisica. In particolare Abell stabili' nel primo dopoguerra il primo catalogo di ammassi su determinazione morfologica. Altri astronomi ampliarono poi i parametri di classificazione basandosi su caratteristiche ottiche e meccaniche. Le analisi piu' recenti infine basano le loro conclusioni sullo studio delle bande non ottiche dello spettro, principalmente i raggi X e onde Radio.

EPR spectroscopy as a tool for the elucidation of non-covalent structuring principles in complex soft matter

This thesis aims at connecting structural and functional changes of complex soft matter systems due to external stimuli with non-covalent molecular interaction profiles. It addresses the problem of elucidating non-covalent forces as structuring principle of mainly polymer-based systems in solution. The structuring principles of a wide variety of complex soft matter types are analyzed. In many cases this is done by exploring conformational changes upon the exertion of external stimuli. The central question throughout this thesis is how a certain non-covalent interaction profile leads to solution condition-dependent structuring of a polymeric system.rnTo answer this question, electron paramagnetic resonance (EPR) spectroscopy is chosen as the main experimental method for the investigation of the structure principles of polymers. With EPR one detects only the local surroundings or environments of molecules that carry an unpaired electron. Non-covalent forces are normally effective on length scales of a few nanometers and below. Thus, EPR is excellently suited for their investigations. It allows for detection of interactions on length scales ranging from approx. 0.1 nm up to 10 nm. However, restriction to only one experimental technique likely leads to only incomplete pictures of complex systems. Therefore, the presented studies are frequently augmented with further experimental and computational methods in order to yield more comprehensive descriptions of the systems chosen for investigation.rnElectrostatic correlation effects in non-covalent interaction profiles as structuring principles in colloid-like ionic clusters and DNA condensation are investigated first. Building on this it is shown how electrostatic structuring principles can be combined with hydrophobic ones, at the example of host-guest interactions in so-called dendronized polymers (denpols).rnSubsequently, the focus is shifted from electrostatics in dendronized polymers to thermoresponsive alkylene oxide-based materials, whose structuring principles are based on hydrogen bonds and counteracting hydrophobic interactions. The collapse mechanism in dependence of hydrophilic-hydrophobic balance and topology of these polymers is elucidated. Complementarily the temperature-dependent phase behavior of elastin-like polypeptides (ELPs) is investigated. ELPs are the first (and so far only) class of compounds that is shown to feature a first-order inverse phase transition on nanoscopic length scales.rnFinally, this thesis addresses complex biological systems, namely intrinsically disordered proteins (IDPs). It is shown that the conformational space of the IDPs Osteopontin (OPN), a cytokine involved in metastasis of several kinds of cancer, and BASP1 (brain acid soluble protein one), a protein associated with neurite outgrowth, is governed by a subtle interplay between electrostatic forces, hydrophobic interaction, system entropy and hydrogen bonds. Such, IDPs can even sample cooperatively folded structures, which have so far only been associated with globular proteins.

Constraining mass and shape of galaxy clusters through large scale structures

The mass estimation of galaxy clusters is a crucial point for modern cosmology, and can be obtained by several different techniques. In this work we discuss a new method to measure the mass of galaxy clusters connecting the gravitational potential of the cluster with the kinematical properties of its surroundings. We explore the dynamics of the structures located in the region outside virialized cluster, We identify groups of galaxies, as sheets or filaments, in the cluster outer region, and model how the cluster gravitational potential perturbs the motion of these structures from the Hubble fow. This identification is done in the redshift space where we look for overdensities with a filamentary shape. Then we use a radial mean velocity profile that has been found as a quite universal trend in simulations, and we fit the radial infall velocity profile of the overdensities found. The method has been tested on several cluster-size haloes from cosmological N-body simulations giving results in very good agreement with the true values of virial masses of the haloes and orientation of the sheets. We then applied the method to the Coma cluster and even in this case we found a good correspondence with previous. It is possible to notice a mass discrepancy between sheets with different alignments respect to the center of the cluster. This difference can be used to reproduce the shape of the cluster, and to demonstrate that the spherical symmetry is not always a valid assumption. In fact, if the cluster is not spherical, sheets oriented along different axes should feel a slightly different gravitational potential, and so give different masses as result of the analysis described before. Even this estimation has been tested on cosmological simulations and then applied to Coma, showing the actual non-sphericity of this cluster.

COSMIC-LAB: Unexpected Results from High-resolution Spectra of AGB Stars in Globular Clusters

We have used high-resolution spectra, acquired with UVES@ESO-VLT, to determine the chemical abundances of different samples of AGB and RGB stars in 4 Galactic globular clusters, namely 47Tuc, NGC3201, M22 and M62. For almost all the analyzed AGB stars we found a clear discrepancy between the iron abundance measured from neutral lines and that obtained from single ionized lines, while this discrepancy is not obtained for the RGB samples observed in the same clusters and analyzed with the same procedure. Such a behavior exactly corresponds to what expected in the case of Non-Local Thermodynamical Equilibrium (NLTE) in the star atmosphere. These results have a huge impact on the proper determination of GC chemistry. In fact, one of the most intriguing consequences is that, at odds with previous claims, no iron spread is found in NGC3201 and M22 if the iron abundance is obtained from ionized lines only.

The gas mass fraction and the dynamical state in x-ray luminous clusters of galaxies at low redshift

Gli ammassi di galassie sono le strutture gravitazionalmente legate con le più profonde buche di potenziale, pertanto è previsto che questi contengano una frazione di barioni non molto diversa da quella cosmologica. Con l’introduzione di modelli sempre più accurati di fisica barionica all’interno di simulazioni idrodinamiche è stato possibile predire la percentuale cosmica di barioni presente negli ammassi di galassie. Unendo questi modelli previsionali con misure della frazione di gas in ammassi e informazioni sulla densità di barioni dell’Universo si può ottenere una stima della densità di materia cosmica Ωm. L'obiettivo di questo lavoro di Tesi è la stima di Ωm a partire dalla frazione di gas osservata in questi sistemi. Questo lavoro era stato già fatto in precedenza, ma tenendo in considerazione solo gli ammassi più massivi e dinamicamente rilassati. Usando parametri che caratterizzano la morfologia della distribuzione di brillanza superficiale nei raggi X, abbiamo classificato i nostri oggetti come rilassati o disturbati, laddove presentassero evidenze di recenti attività di interazione. Abbiamo dunque valutato l’impatto degli oggetti disturbati sulla stima del parametro cosmologico Ωm, computando il Chi2 tra la frazione di massa barionica nell’Universo e quella da noi ricavata. Infine abbiamo investigato una relazione tra il valore della frazione di gas degli ammassi rilassati e quello dei disturbati, in modo da correggere quindi questi ultimi, riportandoli nei dintorni del valore medio per i rilassati e usarli per ampliare il campione e porre un vincolo più stringente su Ωm. Anche con il limitato campione a nostra disposizione, è stato possibile porre un vincolo più stretto su Ωm, utilizzando un maggior numero di oggetti e riducendo così l’errore statistico.

Non-thermal properties of two galaxy filament candidates from JVLA observations

Large-scale structures can be considered an interesting and useful "laboratory" to better investigate the Universe; in particular the filaments connecting clusters and superclusters of galaxies can be a powerful tool for this intent, since they are not virialised systems yet. The large structures in the Universe have been studied in different bands, in particular the present work takes into consideration the emission in the radio band. In the last years both compact and diffuse radio emission have been detected, revealing to be associated to single objects and clusters of galaxies respectively. The detection of these sources is important, because the radiation process is the synchrotron emission, which in turn is linked to the presence of a magnetic field: therefore studying these radio sources can help in investigating the magnetic field which permeates different portions of space. Furthermore, radio emission in optical filaments have been detected recently, opening new chances to further improve the understanding of structure formation. Filaments can be seen as the net which links clusters and superclusters. This work was made with the aim of investigating non-thermal properties in low-density regions, looking for possible filaments associated to the diffuse emission. The analysed sources are 0917+75, which is located at a redshift z = 0.125, and the double cluster system A399-A401, positioned at z = 0.071806 and z = 0.073664 respectively. Data were taken from VLA/JVLA observations, and reduced and calibrated with the package AIPS, following the standard procedure. Isocountour and polarisation maps were yielded, allowing to derive the main physical properties. Unfortunately, because of a low quality data for A399-A401, it was not possible to see any radio halo or bridge.

Connection between x-ray and radio properties of cool-core galaxy clusters hosting radio mini-halos

Gli ammassi di galassie sono gli oggetti gravitazionalmente legati più grandi dell’Universo. Questi emettono principalmente in banda X tramite bremsstrahlung. Una frazione mostra anche emissione radio diffusa da parte di elettroni relativistici che spiraleggiano nel campo magnetico. Si possono classificare tre tipi di emissione: alon, relitti e mini-aloni radio (MH). I MH sono sorgenti radio su scale di ≥ 200 – 500 kpc, osservate al centro di ammassi caratterizzati dalla presenze di cool-core (CC). L’origine dei MH non è ancora chiara. Gli elettroni relativistici che emettono in banda radio hanno tempi di vita radiativi di molto inferiori a quelli necessari per diffondere sulle scale dell’emissione diffusa. Quindi non sono semplicemente iniettati dalle galassie presenti negli ammassi ed è necessario un meccanismo di accelerazione “in-situ” nell’ICM. I MH testimoniano la presenza di meccanismi che canalizzano parte del budget energetico disponibile nei CC nell’ICM.Quindi lo studio è importante per comprendere la fisica dell’ICM e l’interazione fra le componenti non termiche e termiche. I MH si formano attraverso la riaccelerazione delle particelle relativistiche ad opera della turbolenza del gas. L’origine di questa turbolenza tuttavia non è ancora ben compresa. Gli ammassi CC sono caratterizzati da un picco della brillanza X nelle regioni centrali e da un drop della temperatura verso il centro accompagnata da aumento della densità del gas. Si ritiene che questo sia dovuto al raffreddamento del gas che quindi fluisce nelle zone centrali. Recenti osservazioni in X risultan inconsistenti con il modello classico di CF, suggerendo la presenza di una sorgente di riscaldamento del gas su scale del core degli ammassi. Recentemente Zhuravleva (2014) hanno mostrato che il riscaldamento dovuto alla turbolenza prodotta dall'AGN centrale è in grado di bilanciare il processo di raffreddamento. Abbiamo assunto che la turbolenza responsabile del riscaldamento del gas è anche responsabile dell’accelerazione delle particelle nei MH. Nell’ambito di questo scenario ci si aspetta una correlazione tra la potenza del cooling flow, PCF, che è una misura del tasso di energia emessa dal gas che raffredda nei CC, e la luminosità radio, che è una frazione dell’energia della turbolenza che è canalizzata nell’accelerazione delle particelle. In questo lavoro di tesi abbiamo utilizzato il più grande campione disponibile di MH, allo scopo di studiare la connessione fra le proprietà dei MH e quelle del gas termico nei core degli ammassi che li ospitano. Abbiamo analizzato i dati di 21 ammassi e ricavato i parametri fisici all’interno del raggio di cooling e del MH. Abbiamo ricavato la correlazione fra luminosità radio, e PCF. Abbiamo trovato che le due quantità correlano in modo quasi-lineare confermando i risultati precedenti. Tale correlazione suggerisce uno stretto legame fra le proprietà del gas nei CC e l’origine dei MH.

Determinazione della massa e relazione tra massa e proprietà non termiche in ammassi di galassie

Nella presente tesi, di argomento astrofisico, sono esaminati gli ammassi di galassie (galaxy clusters), ovvero gli oggetti virializzati più grandi dell’Universo. Attraverso una introduttiva analisi morfologica vengono descritte le proprietà di luminosità in banda X e radio dovute alle galassie che li compongono ed al caldo gas intergalattico (ICM IntraCluster Medium) tra queste interposto. In particolare è presa in esame l’emissione radio diffusa di natura non termica di sottostrutture del gas, note con il nome di Aloni, relitti e mini-aloni. Nei capitoli II e III l’attenzione si concentra sul non facile problema della determinazione della massa di un ammasso, proprietà che costituisce il principale oggetto di studio del presente lavoro, passando in rassegna e descrivendo i metodi più utilizzati: analisi dinamica delle galassie (equazione di Jeans ed equazione del viriale), osservazioni in banda X dell’ICM, weak lensing (WL), strong lensing (SL) ed infine WL e SL accoppiati. Una analisi critica ed un confronto tra questi metodi è sviluppata nel capitolo IV, prendendo in considerazione l’ammasso RCS2327. Il conclusivo capitolo V racchiude e collega gli argomenti delle sezioni precedenti cercando una possibile correlazione tra le proprietà emissive non termiche (in banda radio) e le masse di un campione di 28 ammassi, determinate mediante tecnica di weak lensing e strong lensing accoppiate.

Radio relics and magnetic fields in galaxy clusters

Radio relics are diffuse synchrotron sources generally located in the peripheries of galaxy clusters in merging state. According to the current leading scenario, relics trace gigantic cosmological shock waves that cross the intra-cluster medium where particle acceleration occurs. The relic/shock connection is supported by several observational facts, including the spatial coincidence between relics and shocks found in the X-rays. Under the assumptions that particles are accelerated at the shock front and are subsequently deposited and then age downstream of the shock, Markevitch et al. (2005) proposed a method to constrain the magnetic field strength in radio relics. Measuring the thickness of radio relics at different frequencies allows to derive combined constraints on the velocity of the downstream flow and on the magnetic field, which in turns determines particle aging. We elaborate this idea to infer first constraints on magnetic fields in cluster outskirts. We consider three models of particle aging and develop a geometric model to take into account the contribution to the relic transverse size due to the projection of the shock-surface on the plane of the sky. We selected three well studied radio relics in the clusters A 521, CIZA J2242.8+5301 and 1RXS J0603.3+4214. These relics have been chosen primarily because they are almost seen edge-on and because the Mach number of the shock that is associated with these relics is measured by X-ray observations, thus allowing to break the degeneracy between magnetic field and downstream velocity in the method. For the first two clusters, our method is consistent with a pure radiative aging model allowing us to derive constraints on the relics magnetic field strength. In the case of 1RXS J0603.3+4214 we find that particle life-times are consistent with a pure radiative aging model under some conditions, however we also collect evidences for downstream particle re-acceleration in the relic W-region and for a magnetic field decaying downstream in its E-region. Our estimates of the magnetic field strength in the relics in A 521 and CIZA J2242.8+5301 provide unique information on the field properties in cluster outskirts. The constraints derived for these relics, together with the lower limits to the magnetic field that we derived from the lack of inverse Compton X-ray emission from the sources, have been combined with the constraints from Faraday rotation studies of the Coma cluster. Overall results suggest that the spatial profile of the magnetic field energy density is broader than that of the thermal gas, implying that the ε_th /ε_B ratio decreases with cluster radius. Alternatively, radio relics could trace dynamically active regions where the magnetic field strength is biased high with respect to the average value in the cluster volume.

Emissione non termica in ammassi di galassie: analisi di radiosorgenti diffuse

Gli ammassi di galassie (galaxy clusters) sono aggregati di galassie legate dalla forza di attrazione gravitazionale. Essi sono le più grandi strutture virializzate dell’Universo e la loro luminosità è dovuta alle galassie che li compongono e al cosiddetto intracluster medium (ICM), gas intergalattico in grado di raggiungere temperature di milioni di gradi. L’ICM è caratterizzato da emissioni sia di tipo termico che non termico, rispettivamente nella banda X e nella banda Radio, dovute soprattutto al meccanismo di bremsstrahlung termica e all’emissione di sincrotrone. Lo studio delle radiazioni emesse da questo gas primordiale ha permesso di studiare alcuni processi caratteristici nella dinamica degli ammassi di galassie, come i fenomeni di merger e cooling flow , e di ottenere quindi una maggiore comprensione della formazione ed evoluzione degli ammassi. Essendo le più grandi strutture dell’Universo che abbiano raggiunto l’equilibrio viriale, il loro studio risulta infatti molto importante, in quanto fornisce un valido strumento per la formulazione di un Modello Cosmologico. Lo scopo di questo lavoro di tesi consiste in particolare nell'analisi di Aloni e Relitti radio, con maggiore approfondimento sui primi, e sulla ricerca di una correlazione della potenza Radio dei clusters sia con la loro luminosità nella banda X, che con la loro dimensione spaziale. La raccolta e l’elaborazione dei dati è stata svolta presso l’osservatorio di radioastronomia (ORA) situato nel CNR di Bologna.