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.

Solving the cooling flow problem through mechanical AGN feedback

A fundamental gap in the current understanding of collapsed structures in the universe concerns the thermodynamical evolution of the ordinary, baryonic component. Unopposed radiative cooling of plasma would lead to the cooling catastrophe, a massive inflow of condensing gas toward the centre of galaxies, groups and clusters. The last generation of multiwavelength observations has radically changed our view on baryons, suggesting that the heating linked to the active galactic nucleus (AGN) may be the balancing counterpart of cooling. In this Thesis, I investigate the engine of the heating regulated by the central black hole. I argue that the mechanical feedback, based on massive subrelativistic outflows, is the key to solving the cooling flow problem, i.e. dramatically quenching the cooling rates for several billion years without destroying the cool-core structure. Using an upgraded version of the parallel 3D hydrodynamic code FLASH, I show that anisotropic AGN outflows can further reproduce fundamental observed features, such as buoyant bubbles, cocoon shocks, sonic ripples, metals dredge-up, and subsonic turbulence. The latter is an essential ingredient to drive nonlinear thermal instabilities, which cause cold gas condensation, a residual of the quenched cooling flow and, later, fuel for the AGN feedback engine. The self-regulated outflows are systematically tested on the scales of massive clusters, groups and isolated elliptical galaxies: in lighter less bound objects the feedback needs to be gentler and less efficient, in order to avoid drastic overheating. In this Thesis, I describe in depth the complex hydrodynamics, involving the coupling of the feedback energy to that of the surrounding hot medium. Finally, I present the merits and flaws of all the proposed models, with a critical eye toward observational concordance.

A new global wheat marketmodel (GLOWMM) for the analysis of wheat export prices

Food commodity prices fluctuations have important impacts on poverty and food insecurity across the world. Conventional models have not provided a complete picture of recent price spikes in agricultural commodity markets, while there is an urgent need for appropriate policy responses. Perhaps new approaches are needed in order to better understand international spill-overs, the feedback between the real and the financial sectors and also the link between food and energy prices. In this paper, we present results from a new worldwide dynamic model that provides short and long-run impulse responses of wheat international prices to various real shocks.

Econometrics of default risk

This thesis is the result of a project aimed at the study of a crucial topic in finance: default risk, whose measurement and modelling have achieved increasing relevance in recent years. We investigate the main issues related to the default phenomenon, under both a methodological and empirical perspective. The topics of default predictability and correlation are treated with a constant attention to the modelling solutions and reviewing critically the literature. From the methodological point of view, our analysis results in the proposal of a new class of models, called Poisson Autoregression with Exogenous Covariates (PARX). The PARX models, including both autoregressive end exogenous components, are able to capture the dynamics of default count time series, characterized by persistence of shocks and slowly decaying autocorrelation. Application of different PARX models to the monthly default counts of US industrial firms in the period 1982-2011 allows an empirical insight of the defaults dynamics and supports the identification of the main default predictors at an aggregate level.

Micro and Macro essays in Applied Fiscal Policy

This thesis analysis micro and macro aspect of applied fiscal policy issues. The first chapter investigates the extent to which local budget spending composition reacts to fiscal rules variations. I consider the budget of Italian municipalities and exploit specific changes in the Domestic Stability Pact’s rules, to perform a difference-in-discontinuities analysis. The results show that imposing a cap on the total amount of consumption and investment is not as binding as two caps, one for consumption and a different one for investment. More specifically, consumption is triggered by changes in wages and services spending, while investment relies on infrastructure movements. In addition, there is evidence that when an increase in investment is achieved, there is also a higher budget deficit level. The second chapter intends to analyze the extent to which fiscal policy shocks are able to affect macrovariables during business cycle fluctuations, differentiating among three intervention channels: public taxation, consumption and investment. The econometric methodology implemented is a Panel Vector Autoregressive model with a structural characterization. The results show that fiscal shocks have different multipliers in relation to expansion or contraction periods: output does not react during good times while there are significant effects in bad ones. The third chapter evaluates the effects of fiscal policy announcements by the Italian government on the long-term sovereign bond spread of Italy relative to Germany. After collecting data on relevant fiscal policy announcements, we perform an econometric comparative analysis between the three cabinets that followed one another during the period 2009-2013. The results suggest that only fiscal policy announcements made by members of Monti’s cabinet have been effective in influencing significantly the Italian spread in the expected direction, revealing a remarkable credibility gap between Berlusconi’s and Letta’s governments with respect to Monti’s administration.