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.

Evaluation of slope stability under water and seismic load through the Minimum Lithostatic Deviation method

The main objective of this thesis is to obtain a better understanding of the methods to assess the stability of a slope. We have illustrated the principal variants of the Limit Equilibrium (LE) method found in literature, focalizing our attention on the Minimum Lithostatic Deviation (MLD) method, developed by Prof. Tinti and his collaborators (e.g. Tinti and Manucci, 2006, 2008). We had two main goals: the first was to test the MLD method on some real cases. We have selected the case of the Vajont landslide with the objective to reconstruct the conditions that caused the destabilization of Mount Toc, and two sites in the Norwegian margin, where failures has not occurred recently, with the aim to evaluate the present stability state and to assess under which conditions they might be mobilized. The second goal was to study the stability charts by Taylor and by Michalowski, and to use the MLD method to investigate the correctness and adequacy of this engineering tool.

The XENON1T experiment: Monte Carlo background estimation and sensitivity curves study

Despite the scientific achievement of the last decades in the astrophysical and cosmological fields, the majority of the Universe energy content is still unknown. A potential solution to the “missing mass problem” is the existence of dark matter in the form of WIMPs. Due to the very small cross section for WIMP-nuleon interactions, the number of expected events is very limited (about 1 ev/tonne/year), thus requiring detectors with large target mass and low background level. The aim of the XENON1T experiment, the first tonne-scale LXe based detector, is to be sensitive to WIMP-nucleon cross section as low as 10^-47 cm^2. To investigate the possibility of such a detector to reach its goal, Monte Carlo simulations are mandatory to estimate the background. To this aim, the GEANT4 toolkit has been used to implement the detector geometry and to simulate the decays from the various background sources: electromagnetic and nuclear. From the analysis of the simulations, the level of background has been found totally acceptable for the experiment purposes: about 1 background event in a 2 tonne-years exposure. Indeed, using the Maximum Gap method, the XENON1T sensitivity has been evaluated and the minimum for the WIMP-nucleon cross sections has been found at 1.87 x 10^-47 cm^2, at 90% CL, for a WIMP mass of 45 GeV/c^2. The results have been independently cross checked by using the Likelihood Ratio method that confirmed such results with an agreement within less than a factor two. Such a result is completely acceptable considering the intrinsic differences between the two statistical methods. Thus, in the PhD thesis it has been proven that the XENON1T detector will be able to reach the designed sensitivity, thus lowering the limits on the WIMP-nucleon cross section by about 2 orders of magnitude with respect to the current experiments.

Cold cloud climatology over Europe and the Mediterranean during the warm season from Meteosat IR imagery

Thermal infrared (IR, 10.5 – 12.5 m) images from the Meteosat Visible and Infrared Imager (MVIRI) of cold cloud episodes (cloud top brightness temperature < 241 K) are used as a proxy of precipitating clouds to derive a warm season (May-August) climatology of their coherency, duration, span, and speed over Europe and the Mediterranean. The analysis focuses over the 30°-54°N, 15°W-40°E domain in May-August 1996-2005. Harmonic analysis using discrete Fourier transforms is applied together with a statistical analysis and an investigation of the diurnal cycle. This study has the objective to make available a set of results on the propagation dynamics of the cloud systems with the aim of assist numerical modellers in improving summer convection parameterization. The zonal propagation of cold cloud systems is accompanied by a weak meridional component confined to narrow latitude belts. The persistence of cold clouds over the area evidences the role of orography, the Pyrenees, the Alps, the Balkans and Anatolia. A diurnal oscillation is found with a maximum marking the initiation of convection in the lee of the mountains and shifting from about 1400 UTC at 40°E to 1800 UTC at 0°. A moderate eastward propagation of the frequency maximum from all mountain chains across the domain exists and the diurnal maxima are completely suppressed west of 5°W. The mean power spectrum of the cold cloud frequency distribution evidences a period of one day all over Europe disappearing over the ocean (west of 10°W). Other maxima are found in correspondence of 6 to 10 days in the longitudes from 15° W to 0° and indicate the activity of the westerlies with frontal passage over the continent. Longer periods activities (from 15 up to 30 days) were stronger around 10° W and from 5° W to 15° E and are likely related to the Madden Julian Oscillation influence. The maxima of the diurnal signal are in phase with the presence of elevated terrain and with land masses. A median zonal phase speed of 16.1 ms-1 is found for all events ≥ 1000 km and ≥ 20 h and a full set of results divided by years and recurrence categories is also presented.

The stratigraphic record of the quaternary sea level fluctuations and the impact of the post-glacial sea level rise (Termination I) in the Adriatic basin (Mediterranean sea)

The modern stratigraphy of clastic continental margins is the result of the interaction between several geological processes acting on different time scales, among which sea level oscillations, sediment supply fluctuations and local tectonics are the main mechanisms. During the past three years my PhD was focused on understanding the impact of each of these process in the deposition of the central and northern Adriatic sedimentary successions, with the aim of reconstructing and quantifying the Late Quaternary eustatic fluctuations. In the last few decades, several Authors tried to quantify past eustatic fluctuations through the analysis of direct sea level indicators, among which drowned barrier-island deposits or coral reefs, or indirect methods, such as Oxygen isotope ratios (δ18O) or modeling simulations. Sea level curves, obtained from direct sea level indicators, record a composite signal, formed by the contribution of the global eustatic change and regional factors, as tectonic processes or glacial-isostatic rebound effects: the eustatic signal has to be obtained by removing the contribution of these other mechanisms. To obtain the most realistic sea level reconstructions it is important to quantify the tectonic regime of the central Adriatic margin. This result has been achieved integrating a numerical approach with the analysis of high-resolution seismic profiles. In detail, the subsidence trend obtained from the geohistory analysis and the backstripping of the borehole PRAD1.2 (the borehole PRAD1.2 is a 71 m continuous borehole drilled in -185 m of water depth, south of the Mid Adriatic Deep - MAD - during the European Project PROMESS 1, Profile Across Mediterranean Sedimentary Systems, Part 1), has been confirmed by the analysis of lowstand paleoshorelines and by benthic foraminifera associations investigated through the borehole. This work showed an evolution from inner-shelf environment, during Marine Isotopic Stage (MIS) 10, to upper-slope conditions, during MIS 2. Once the tectonic regime of the central Adriatic margin has been constrained, it is possible to investigate the impact of sea level and sediment supply fluctuations on the deposition of the Late Pleistocene-Holocene transgressive deposits. The Adriatic transgressive record (TST - Transgressive Systems Tract) is formed by three correlative sedimentary bodies, deposited in less then 14 kyr since the Last Glacial Maximum (LGM); in particular: along the central Adriatic shelf and in the adjacent slope basin the TST is formed by marine units, while along the northern Adriatic shelf the TST is represented by costal deposits in a backstepping configuration. The central Adriatic margin, characterized by a thick transgressive sedimentary succession, is the ideal site to investigate the impact of late Pleistocene climatic and eustatic fluctuations, among which Meltwater Pulses 1A and 1B and the Younger Dryas cold event. The central Adriatic TST is formed by a tripartite deposit bounded by two regional unconformities. In particular, the middle TST unit includes two prograding wedges, deposited in the interval between the two Meltwater Pulse events, as highlighted by several 14C age estimates, and likely recorded the Younger Dryas cold interval. Modeling simulations, obtained with the two coupled models HydroTrend 3.0 and 2D-Sedflux 1.0C (developed by the Community Surface Dynamics Modeling System - CSDMS), integrated by the analysis of high resolution seismic profiles and core samples, indicate that: 1 - the prograding middle TST unit, deposited during the Younger Dryas, was formed as a consequence of an increase in sediment flux, likely connected to a decline in vegetation cover in the catchment area due to the establishment of sub glacial arid conditions; 2 - the two-stage prograding geometry was the consequence of a sea level still-stand (or possibly a fall) during the Younger Dryas event. The northern Adriatic margin, characterized by a broad and gentle shelf (350 km wide with a low angle plunge of 0.02° to the SE), is the ideal site to quantify the timing of each steps of the post LGM sea level rise. The modern shelf is characterized by sandy deposits of barrier-island systems in a backstepping configuration, showing younger ages at progressively shallower depths, which recorded the step-wise nature of the last sea level rise. The age-depth model, obtained by dated samples of basal peat layers, is in good agreement with previous published sea level curves, and highlights the post-glacial eustatic trend. The interval corresponding to the Younger Dyas cold reversal, instead, is more complex: two coeval coastal deposits characterize the northern Adriatic shelf at very different water depths. Several explanations and different models can be attempted to explain this conundrum, but the problem remains still unsolved.