Dynamics of the halo gas in disc galaxies

This Thesis studies the dynamics of hot and cold gas outside the plane in galaxies like the Milky-Way (extra-planar gas) and focuses on the interaction between disc and halo material. Stationary models for the cold phase of the extra-planar gas are presented. They show that the kinematics of this phase must be influenced by the interaction with an ambient medium that we identify as the hot cosmological corona that surrounds disc galaxies. To study this interaction a novel hydrodynamical code has been implemented and a series of hydrodynamical simulations has been run to investigate the mass and momentum exchange between the cold extra-planar gas clouds and the hot corona. These simulations show that the coronal gas can condense efficiently in the turbulent wakes that form behind the cold clouds and it can be accreted by the disc to sustain star formation. They also predict that the corona cannot be a static structure but it must rotate and lag by approximately 80-120 km/s with respect to the disc. Implications of the results of this Thesis for the evolution of star-forming galaxies and for the large-scale dynamics of galactic coronae are also briefly discussed.

The gaseous halo of the Milky Way

In the last decade, sensitive observations have revealed that disc galaxies are surrounded by multiphase gaseous halos produced by the circulation of gas from the discs to the environment and vice-versa. This Thesis is a study of the gaseous halo of the Milky Way carried out via the modelling of the HI emission and the available absorption-line data. We fitted simple kinematical models to the HI LAB Survey and found that the Galaxy has a massive (~3x10^8 Mo) HI halo extending a few kiloparsecs above the plane. This layer rotates more slowly than the disc and shows a global inflow motion, a kinematics similar to that observed in the HI halos of nearby galaxies. We built a dynamical model of the galactic fountain to reproduce the properties of this layer. In this model, fountain clouds are ejected from the disc by SN feedback and - as suggested by hydrodynamical simulations - triggers the cooling of coronal gas, which is entrained by the cloud wakes and accretes onto the disc when the clouds fall back. For a proper choice of the parameters, the model reproduces well the HI data and predicts an accretion of coronal gas onto the disc at a rate of 2 Mo/yr. We extended this model to the warm-hot component of the halo, showing that most of the ion absorption features observed towards background sources are consistent with being produced in the turbulent wakes that lag behind the fountain clouds. Specifically, the column densities, positions, and velocities of the absorbers are well reproduced by our model. Finally, we studied the gas content of galaxies extracted from a cosmological N-body+SPH simulation, and found that an HI halo with the forementioned properties is not observed, probably due ti the relatively low resolution of the simulations.

The new Beam Halo Monitor for the CMS experiment at the LHC

In the context of increasing beam energy and luminosity of the LHC accelerator at CERN, it will be important to accurately measure the Machine Induced Background. A new monitoring system will be installed in the CMS cavern for measuring the beam background at high radius. This detector, called the Beam Halo Monitor, will provide an online, bunch-by-bunch measurement of background induced by beam halo interactions, separately for each beam. The detector is composed of synthetic quartz Cherenkov radiators, coupled to fast UV sensitive photomultiplier tubes. The directional and fast response of the system allows the discrimination of the background particles from the dominant flux in the cavern induced by pp collision debris, produced within the 25 ns bunch spacing. The readout electronics of this detector will make use of many components developed for the upgrade of the CMS Hadron Calorimeter electronics, with a dedicated firmware and readout adapted to the beam monitoring requirements. The PMT signal will be digitized by a charge integrating ASIC, providing both the signal rise time and the charge integrated over one bunch crossing. The backend electronics will record bunch-by-bunch histograms, which will be published to CMS and the LHC using the newly designed CMS beam instrumentation specific DAQ. A calibration and monitoring system has been designed to generate triggered pulses of UV light to monitor the efficiency of the system. The experimental results validating the design of the detector, the calibration system and the electronics will be presented.

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.

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.

Modeling the cosmological co-evolution of supermassive black holes and galaxies

In this Thesis, we investigate the cosmological co-evolution of supermassive black holes (BHs), Active Galactic Nuclei (AGN) and their hosting dark matter (DM) halos and galaxies, within the standard CDM scenario. We analyze both analytic, semi-analytic and hybrid techniques and use the most recent observational data available to constrain the assumptions underlying our models. First, we focus on very simple analytic models where the assembly of BHs is directly related to the merger history of DM haloes. For this purpose, we implement the two original analytic models of Wyithe & Loeb 2002 and Wyithe & Loeb 2003, compare their predictions to the AGN luminosity function and clustering data, and discuss possible modifications to the models that improve the match to the observation. Then we study more sophisticated semi-analytic models in which however the baryonic physics is neglected as well. Finally we improve the hybrid simulation of De Lucia & Blaizot 2007, adding new semi-analytical prescriptions to describe the BH mass accretion rate during each merger event and its conversion into radiation, and compare the derived BH scaling relations, fundamental plane and mass function, and the AGN luminosity function with observations. All our results support the following scenario: • The cosmological co-evolution of BHs, AGN and galaxies can be well described within the CDM model. • At redshifts z & 1, the evolution history of DM halo fully determines the overall properties of the BH and AGN populations. The AGN emission is triggered mainly by DM halo major mergers and, on average, AGN shine at their Eddington luminosity. • At redshifts z . 1, BH growth decouples from halo growth. Galaxy major mergers cannot constitute the only trigger to accretion episodes in this phase. • When a static hot halo has formed around a galaxy, a fraction of the hot gas continuously accretes onto the central BH, causing a low-energy “radio” activity at the galactic centre, which prevents significant gas cooling and thus limiting the mass of the central galaxies and quenching the star formation at late time. • The cold gas fraction accreted by BHs at high redshifts seems to be larger than at low redshifts.

Stellar Relics of the hierarchical assembly of the Galaxy

This PhD Thesis is part of a long-term wide research project, carried out by the "Osservatorio Astronomico di Bologna (INAF-OABO)", that has as primary goal the comprehension and reconstruction of formation mechanism of galaxies and their evolution history. There is now substantial evidence, both from theoretical and observational point of view, in favor of the hypothesis that the halo of our Galaxy has been at least partially, built up by the progressive accretion of small fragments, similar in nature to the present day dwarf galaxies of the Local Group. In this context, the photometric and spectroscopic study of systems which populate the halo of our Galaxy (i.e. dwarf spheroidal galaxy, tidal streams, massive globular cluster, etc) permits to discover, not only the origin and behaviour of these systems, but also the structure of our Galactic halo, combined with its formation history. In fact, the study of the population of these objects and also of their chemical compositions, age, metallicities and velocity dispersion, permit us not only an improvement in the understanding of the mechanisms that govern the Galactic formation, but also a valid indirect test for cosmological model itself. Specifically, in this Thesis we provided a complete characterization of the tidal Stream of the Sagittarius dwarf spheroidal galaxy, that is the most striking example of the process of tidal disruption and accretion of a dwarf satellite in to our Galaxy. Using Red Clump stars, extracted from the catalogue of the Sloan Digital Sky Survey (SDSS) we obtained an estimate of the distance, the depth along the line of sight and of the number density for each detected portion of the Stream (and more in general for each detected structure along our line of sight). Moreover comparing the relative number (i.e. the ratio) of Blue Horizontal Branch stars and Red Clump stars (the two features are tracers of different age/different metallicity populations) in the main body of the galaxy and in the Stream, in order to verify the presence of an age-metallicity gradient along the Stream. We also report the detection of a population of Red Clump stars probably associated with the recently discovered Bootes III stellar system. Finally, we also present the results of a survey of radial velocities over a wide region, extending from r ~ 10' out to r ~ 80' within the massive star cluster Omega Centauri. The survey was performed with FLAMES@VLT, to study the velocity dispersion profile in the outer regions of this stellar system. All the results presented in this Thesis, have already been published in refeered journals.

Hydrodynamical simulations of early-type galaxies: effects of galaxy shape and stellar dynamics on hot coronae

Early-Type galaxies (ETGs) are embedded in hot (10^6-10^7 K), X-ray emitting gaseous haloes, produced mainly by stellar winds and heated by Type Ia supernovae explosions, by the thermalization of stellar motions and occasionally by the central super-massive black hole (SMBH). In particular, the thermalization of the stellar motions is due to the interaction between the stellar and the SNIa ejecta and the hot interstellar medium (ISM) already residing in the ETG. A number of different astrophysical phenomena determine the X-ray properties of the hot ISM, such as stellar population formation and evolution, galaxy structure and internal kinematics, Active Galactic Nuclei (AGN) presence, and environmental effects. With the aid of high-resolution hydrodynamical simulations performed on state-of-the-art galaxy models, in this Thesis we focus on the effects of galaxy shape, stellar kinematics and star formation on the evolution of the X-ray coronae of ETGs. Numerical simulations show that the relative importance of flattening and rotation are functions of the galaxy mass: at low galaxy masses, adding flattening and rotation induces a galactic wind, thus lowering the X-ray luminosity; at high galaxy masses the angular momentum conservation keeps the central regions of rotating galaxies at low density, whereas in non-rotating models a denser and brighter atmosphere is formed. The same dependence from the galaxy mass is present in the effects of star formation (SF): in light galaxies SF contributes to increase the spread in Lx, while at high galaxy masses the halo X-ray properties are marginally sensitive to SF effects. In every case, the star formation rate at the present epoch quite agrees with observations, and the massive, cold gaseous discs are partially or completely consumed by SF on a time-scale of few Gyr, excluding the presence of young stellar discs at the present epoch.

Constraints on neutrino mass fraction using Redshift Space Distortions

Redshift Space Distortions (RSD) are an apparent anisotropy in the distribution of galaxies due to their peculiar motion. These features are imprinted in the correlation function of galaxies, which describes how these structures distribute around each other. RSD can be represented by a distortions parameter $\beta$, which is strictly related to the growth of cosmic structures. For this reason, measurements of RSD can be exploited to give constraints on the cosmological parameters, such us for example the neutrino mass. Neutrinos are neutral subatomic particles that come with three flavours, the electron, the muon and the tau neutrino. Their mass differences can be measured in the oscillation experiments. Information on the absolute scale of neutrino mass can come from cosmology, since neutrinos leave a characteristic imprint on the large scale structure of the universe. The aim of this thesis is to provide constraints on the accuracy with which neutrino mass can be estimated when expoiting measurements of RSD. In particular we want to describe how the error on the neutrino mass estimate depends on three fundamental parameters of a galaxy redshift survey: the density of the catalogue, the bias of the sample considered and the volume observed. In doing this we make use of the BASICC Simulation from which we extract a series of dark matter halo catalogues, characterized by different value of bias, density and volume. This mock data are analysed via a Markov Chain Monte Carlo procedure, in order to estimate the neutrino mass fraction, using the software package CosmoMC, which has been conveniently modified. In this way we are able to extract a fitting formula describing our measurements, which can be used to forecast the precision reachable in future surveys like Euclid, using this kind of observations.

Improving the cosmic distance ladder. Distance and structure of the Large Magellanic Cloud

The Large Magellanic Cloud (LMC) is widely considered as the first step of the cosmological distance ladder, since it contains many different distance indicators. An accurate determination of the distance to the LMC allows one to calibrate these distance indicators that are then used to measure the distance to far objects. The main goal of this thesis is to study the distance and structure of the LMC, as traced by different distance indicators. For these purposes three types of distance indicators were chosen: Classical Cepheids,``hot'' eclipsing binaries and RR Lyrae stars. These objects belong to different stellar populations tracing, in turn, different sub-structures of the LMC. The RR Lyrae stars (age >10 Gyr) are distributed smoothly and likely trace the halo of the LMC. Classical Cepheids are young objects (age 50-200 Myr), mainly located in the bar and spiral arm of the galaxy, while ``hot'' eclipsing binaries mainly trace the star forming regions of the LMC. Furthermore, we have chosen these distance indicators for our study, since the calibration of their zero-points is based on fundamental geometric methods. The ESA cornerstone mission Gaia, launched on 19 December 2013, will measure trigonometric parallaxes for one billion stars with an accuracy of 20 micro-arcsec at V=15 mag, and 200 micro-arcsec at V=20 mag, thus will allow us to calibrate the zero-points of Classical Cepheids, eclipsing binaries and RR Lyrae stars with an unprecedented precision.

On the Luminous and Dark Matter Distribution in Early-Type Galaxies

The way mass is distributed in galaxies plays a major role in shaping their evolution across cosmic time. The galaxy's total mass is usually determined by tracing the motion of stars in its potential, which can be probed observationally by measuring stellar spectra at different distances from the galactic centre, whose kinematics is used to constrain dynamical models. A class of such models, commonly used to accurately determine the distribution of luminous and dark matter in galaxies, is that of equilibrium models. In this Thesis, a novel approach to the design of equilibrium dynamical models, in which the distribution function is an analytic function of the action integrals, is presented. Axisymmetric and rotating models are used to explain observations of a sample of nearby early-type galaxies in the Calar Alto Legacy Integral Field Area survey. Photometric and spectroscopic data for round and flattened galaxies are well fitted by the models, which are then used to get the galaxies' total mass distribution and orbital anisotropy. The time evolution of massive early-type galaxies is also investigated with numerical models. Their structural properties (mass, size, velocity dispersion) are observed to evolve, on average, with redshift. In particular, they appear to be significantly more compact at higher redshift, at fixed stellar mass, so it is interesting to investigate what drives such evolution. This Thesis focuses on the role played by dark-matter haloes: their mass-size and mass-velocity dispersion correlations evolve similarly to the analogous correlations of ellipticals; at fixed halo mass, the haloes are more compact at higher redshift, similarly to massive galaxies; a simple model, in which all the galaxy's size and velocity-dispersion evolution is due to the cosmological evolution of the underlying halo population, reproduces the observed size and velocity-dispersion of massive compact early-type galaxies up to redshift of about 2.