Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 05/05 Archiv

Galaxy clusters, the massive systems host hundreds of galaxies, are invaluable cosmological probes and astrophysical laboratories. Besides these fascinating galaxies, the concentration of dark matter creates a deep gravitational potential well, where even light passing by is bended and the background image is distorted. The baryonic gas falling into the potential well is heated up to more than 10^7 K that free electrons start to emitting in X-ray. Observing those phenomena leads to a throughout understanding of gravity, particle physics and hydrodynamics. In addition, residing on the top of the density perturbations, clusters are sensitive to the initial condition of the Universe, such that they are complimentary tools for cosmology studies. In this thesis we first introduce the basic framework of the Universe and supporting observational evidence. Following that, we sketch the principle to use clusters for cosmology study via their redshift and mass distribution. However cluster mass is not a direct observable, so we need to estimate it by other channels. We briefly exhibit cluster observations in optical, X-ray and microwave bands and discuss the challenges in estimating the underlying cluster mass with them. After this introduction, we present our results on three aspects of the cluster cosmology study. First, we present a study of Planck Sunyaev-Zel’dovich effect (SZE) selected galaxy cluster candidates using Panoramic Survey Telescope & Rapid Response System (Pan-STARRS) imaging data. To fulfil the strength of SZE survey, the redshifts of clusters are required. In this work we examine 237 Planck cluster candidates that have no redshift in the Planck source catalogue. Among them, we confirmed 60 galaxy clusters and measure their redshifts. For the remaining sample, 83 candidates are so heavily contaminated by stars due to their location near the Galactic plane that we do not identify galaxy members and assign reliable redshifts. For the rest 94 candidates we find no optical counterparts. By examining with 150 Planck confirmed clusters with spectroscopy redshifts, our redshift estimations have an accuracy of σ_{z/(1+z)}~0.022. Scaling for the already published Planck sample, we expect the majority of the unconfirmed candidates to be noise fluctuations, except a few at high redshift that the Pan-STARRS1 (PS1) data are not sufficiently deep for confirmation. Thus we use the depth of the optical imaging for each candidate together with a model of the expected galaxy population for a massive cluster to estimate a redshift lower limit, beyond which we would not have expected to detect the optical counterpart. Second, we use 95GHz, 150GHz, and 220GHz observations from South Pole Telescope (SPT) to study the SZE signatures of a sample of 46 X-ray selected groups and clusters drawn from ~6 deg^2 of the XMM-Newton Blanco Cosmology Survey (XMM-BCS). The wide redshift range and low masses make this analysis complementary to previous studies. We develop an analysis tool that using X-ray luminosity as a mass proxy to extract selection-bias corrected constraints on the SZE significance- and Y_{SZ}-mass relations. The SZE significance- mass relation is in good agreement with an extrapolation of the relation obtained from high mass clusters. However, the fit to the Y_{SZ}-mass relation at low masses, while in agreement with the extrapolation from high mass SPT sample, is in tension at 2.8σ with the constraints from the Planck sample. We examine the tension with the Planck relation, discussing sample differences and biases that could contribute. We also analyse the radio galaxy point source population in this ensemble of X-ray selected systems. We find 18 of our systems have 1 GHz Sydney University Molonglo Sky Survey (SUMSS) sources within 2 arcmin of the X-ray centre, and three of these are also detected at significance >4 by SPT. Among these three, two are associated with the brightest cluster galaxies, and the third is a likely unassociated quasar candidate. We examined the impact of these point sources on our SZE scaling relation result and find no evidence of biases. We also examined the impact of dusty galaxies. By stacking the 220 GHz data, we found 2.8σ significant evidence of flux excess, which would correspond to an average underestimate of the SZE signal that is (17±9) % in this sample of low mass systems. Finally we predict a factor of four to five improvements on these SZE mass-observable relation constraints based on future data from SPTpol and XMM-XXL. In the end we present a study using clusters as tools to probe deviations from adiabatic evolution of the Cosmic Microwave Background (CMB) temperature. The expected adiabatic evolution is a key prediction of standard cosmology. We measure the deviation of the form T(z)=T_0(1+z)^{1-α} using measurements of the spectrum of the SZE with SPT. We present a method using the ratio of the SZE signal measured at 95 and 150 GHz in the SPT data to constrain the temperature of the CMB. We validate that this approach provides unbiased results using mock observations of cluster from a new set of hydrodynamical simulations. Applying this method to a sample of 158 SPT-selected clusters, we measure α=0.017^{+0.030}_{−0.028} consistent with the standard model prediction of α=0. Combining with other published results, we find α=0.005±0.012, an improvement of ~ 10% over published constraints. This measurement also provides a strong constraint on the effective equation of state, w_{eff}=−0.994±0.010, which is presented in models of decaying dark energy.

This Ph.D. Thesis has as general subject the study of extrasolar planets using the radial velocity technique from both, instrumental and observative, points of view. Two main parts compose the work: the upgrade of the spectrograph FOCES, a high resolution spectrograph that will be installed next year at the Wendelstein Observatory, and the search of giant planets around stars in the open cluster Messier-67 (M67).

Combining all knowledge we have gathered about the origin, evolution and current state of the universe it appears indisputable that 95% of the mass-energy density in today's universe is comprised of unknown substances called dark matter and dark energy. This thesis explores different aspects of and develops models for the formation of the largest structures we observe in the universe, because these structures -- the cosmic web made of dark matter halos, clusters of galaxies and galaxies -- sensitively depend on properties of dark matter and dark energy, in particular on their abundances, the equation of state of and possible new interactions mediated by dark energy. Current and upcoming surveys map the large scale structure (LSS) with increasingly higher precision and in larger volumes. In order to optimally extract cosmological parameters we need to build accurate models for LSS formation that also describe how LSS is perceived by real observers trough processes affecting light propagation. Only then can we reliably reconstruct the cosmological parameters and identify the models for dark matter and dark energy preferred by the data. Therefore this thesis contributes to the endeavor to ultimately uncover the nature of dark matter and dark energy. Chapter 2 studies a dark energy model which mediates a ``fifth force'' enhancing Newtonian gravity only on large scales due to the chameleon mechanism, but leads to an expansion history indistinguishable from the case where dark energy is a cosmological constant. Hence the only observables that can discriminate them are related to structure formation. We study the abundance of dark matter halos per halo mass with semi-analytical techniques to find a fit function depending on the model parameter responsible for the range and strength of the fifth force. We find good agreement with Monte-Carlo and N-body simulations of the mass function. Our result is a fit function for the halo mass function that can be used to constrain this model and to look for signatures of the chameleon effect in observations of galaxy of clusters. In Chapters 3 and 4 we show why it is justified to use Newtonian gravity instead of General Relativity on all scales to accurately describe LSS formation in a universe governed by a cosmological constant and cold dark matter. In Chapter 5 we show that a complex scalar field solving the Schrödinger-Poisson equation is able describe collisionless selfgravitating dark matter with the same number of degrees of freedom as the popular dust fluid. In contrast to the dust model it does not suffer from singularities and thus allows the analytical and numerical study of fully nonlinear effects like halo formation. In Chapter 6 we study the clustering of halos as observed in redshift space, by developing an improved model for the halo dynamics based on a coarse grained dust model and by extending the so called Gaussian streaming model to general phase space distribution functions. We compare our results to a N-body simulation halo catalog and find that the coarse grained dust model significantly improves the accuracy of theoretical redshift space correlation functions.

Although thermophoresis, i.e. the directed movement of molecules in a temperature gradient, was discovered more than 150 years ago, its molecular origin is not jet fully understood. Nonetheless thermophoresis is used as a principle in biomolecular binding measurements. Both topics are interesting and worth a scientific discussion. In this thesis, systematic experiments over a large parameter space were conducted. From these measurements a combination of different theories about its molecular origin could be verified. Thus, the first result of this thesis is that the phenomenon thermophoresis consists of different additive contributions. Some of them relate to the ionic nature of the molecule and are non-existent when the molecule is electrically neutral. The microscopic mechanism of these ionic contributions to thermophoresis is discussed in the first part. It continues the work on the capacitor model and explains a further contribution, which we call Seebeck effect in analogy to solid state physics. Through the different contributions we bridge the gap between local thermodynamic equilibrium approaches and non-equilibrium theories. Several applications will greatly benefit from understanding the molecular physics of thermophoresis. Pharmacological screens are conducted to determine the binding affinity of a whole molecular library to a target molecule and thus to identify the best candidates for a new drug. These screens will be improved when thermophoresis can be predicted and for example the influence of the buffer can be determined. Binding measurements of biomolecules can already be conducted in cell lysate. The second part of this thesis will show thermophoresis measurements inside living cells for the first time. This paves the way for in vivo binding measurements inside cells. To make thermophoresis measurements compatible to cell culture, the setup was changed in great parts, now using total internal reflection fluorescence (TIRF) microscopy.

When the optical pulses emitted by a laser become so short in time that they encompass only a few cycles of the carrier wave, the phase between carrier and envelope becomes a crucial parameter. The ability to control this carrier-envelope phase (CEP) is elemental to experiments probing the fastest processes in the microcosm, occurring on the time-scale of attoseconds. More than a decade into the attosecond era, the limitations of the established CEP stabilisation technique have begun to curtail experimental progress. First, increasingly complex experiments require many hours of uninterrupted operation at the same waveform. Second, the pulses used in experiments are approaching the single-cycle boundary, calling for ever-decreasing CEP noise. With the conventional stabilisation technique, already these two requirements cannot be fulfilled simultaneously. Ultimately, the low efficiency of the underlying nonlinear processes can only be compensated by driver lasers at a higher repetition rate than available at present. In order to advance attosecond pulse generation, novel approaches to CEP control thus face a threefold challenge that outlines this thesis: To simultaneously provide low CEP noise and long-term operation to present-day few-cycle lasers and amplifiers, and to investigate CEP control capability in high average power sources that are currently under development. This thesis describes the adaptation of cavity-external CEP stabilisation for use with few-cycle pulses. The intrinsic limitations of the conventional feed-back technique are lifted. A laser oscillator is demonstrated to maintain record-low CEP noise for tens of hours of operation free from phase discontinuities. In addition, a modification of the technique is presented that further enhances the applicability to amplified systems. Two routes are investigated to achieve CEP control in system architectures that represent potential megahertz repetition rate driver sources. In combination with temporal pulse compression, a thin-disk laser is shown to yield few-cycle pulses. Experiments are presented that provide the groundwork towards the first CEP-stabilised thin-disk oscillator. The second approach targets the seed oscillator of a fibre chirped-pulse amplifier. The CEP noise properties of different amplification regimes are examined. Intensity enhancement of the output pulses in a passive resonator is shown to benefit greatly even from a coarse lock of the CEP slip rate. For few-cycle pulse energy to reach the millijoule level and above, amplification and temporal compression will remain indispensable in the foreseeable future. Maintaining CEP stability across such stages is crucial, irrespective of the technology employed. Cavity-external CEP control is demonstrated to enable more than 24 hours of constant-CEP operation in chirped-pulse amplifiers. Furthermore, a novel actuator is introduced that, in conjunction with a fast means of measuring the CEP, is able to provide phase correction of the amplified waveform up to several kilohertz bandwidth. The result is a train of millijoule-level pulses with residual CEP noise comparable to that of state-of-the-art nanojoule oscillators. Eventually, an experiment is presented to examine the influence of different types of hollow-core fibre-based temporal compression on the CEP. The findings shed new light on the origin of adverse effects introduced by this technique, and point out ways towards effective compensation.

This thesis contributes to the understanding of impurity models. It is divided into two main parts, with a general introduction given in Part I and the research related to it presented in Part II, with the second part being subdivided into two main projects. In the first project, the influence of two many-body effects, the Kondo effect and the Fermi edge singularity, on the absorption and emission spectra of self-assembled quantum dots (QDs) is examined. Whereas the Kondo effect so far was always examined with transport experiments, we show that it has been observed with optical methods for the first time, by comparing experimental data for the absorption line shapes of QDs to calculations with the numerical renormalization group. We continue by examining a QD with strong optical coupling of the energy levels. The resulting interplay of Rabi-oscillations and Kondo effect leads to a new many-body state, a secondary, outer Kondo effect, with Kondo-like correlations between the spin-Kondo and the trion state. The last work regarding optics at QDs addresses the Fermi edge singularity. We show that for QDs this phenomenon can be described numerically on a quantitative level. The second project concerns transport properties of impurity models. First, we present a comprehensive study of the Kondo effect for an InAs-nanowire QD, a system for which the Kondo effect was observed only a few years ago. The second study regarding transport concerns the Kondo effect in bulk metals with magnetic impurities. Although nowadays the Kondo effect is often studied with QDs, it was discovered for iron impurities in noble metals like gold and silver. However, it was unknown for a long time which exact realization of Kondo model describes these systems. We identify the model by comparing numerical calculations for the magnetoresistivity and the dephasing rate for different models to experimental results. The third work about transport concerns the phenomenon that for a fixed type of Kondo model quantities like the magnetoresistivity or the conductivity, respectively, can be scaled onto a universal curve for different parameters, when energies are rescaled with the the Kondo temperature $T_K$, since it is the only relevant low energy scale of the problem. For finite bandwidth, however, different definitions of $T_K$ (which coincide in the limit of infinite bandwidth) lead to different $T_K$-values. We show that with a very common definition of $T_K$, finite bandwidth, which is always present at numerical calculations, can deteriorate the universality of rescaled curves, and we offer an alternative definition of $T_K$ which ensures proper scaling. In the last study presented in this thesis we calculate the Fermi-liquid coefficients for fully screened multi-channel Kondo models. For temperatures below $T_K$, these models show Fermi-liquid behavior, and the impurity density of states and certain quantities which depend on it, like resistivity, show quadratic dependencies on parameters like temperature or magnetic field, described by the Fermi-liquid coefficients. We calculate these coefficients both analytically and numerically.

Convective phenomena in the atmosphere, such as convective storms, are characterized by very fast, intermittent and seemingly stochastic processes. They are thus difficult to predict with Numerical Weather Prediction (NWP) models, and difficult to estimate with data assimilation methods that combine prediction and observations. In this thesis, nonlinear data assimilation methods are tested on two idealized convective scale cloud models, developed in [58] and [59]. The aim of this work was to apply the particle filter, a method specifically designed for nonlinear models, to the two toy models that resemble some properties of convection. Potential problems and characteristic features of particle filter methodology were analyzed, having in mind possible tests on far more elaborate NWP models. The first model, the stochastic cloud model, is a one-dimensional birth-death model initialized by a Poisson distribution, where clouds randomly appear or die independently from each other on a set of grid-points. This purely stochastic model is physically unreal- istic, but since it is highly nonlinear and non-Gaussian, it contains minimal requirements for representing main features of convection. The derivation of the transition probability density function (PDF) of the stochastic cloud model made it possible to understand better the weighting mechanism involved in the particle filter. This mechanism, which associates a weight to particles (state vectors) according to their likelihood with respect to observa- tions and to their evolution in time, is followed by resampling, where particles with high probability are replicated, and others eliminated. The ratio between magnitudes of the ob- servation probability distribution and the transition probability is shown to determine the selection process of particles at each time step, where data and prediction are combined. Further, a strong sensitivity of the filter to the observation density and to the speed of the cloud variability (given by the cloud life time) is demonstrated. Thus, the particle filter can outperform some simpler methods for certain observation densities, whereas it does not bring any improvement when using others. Similarly, it leads to good results for stationary cloud fields while having difficulties to follow fast varying cloud fields, because any change in the model state variable is potentially penalized. The main difficulty for the filter is the fact that this model is discrete, while the filter was designed for data assimilation of continuous fields. However, by representing an extreme testbed for the particle filter, the stochastic cloud model shows the importance of the observation and model error densities for the selection of particles, and it stresses the influence of the chosen model parameters on the filter’s performance. The second model considered was the modified shallow water model. It is based on the shallow water equations, to which is added a small stochastic noise in order to trigger convection, and an equation for the evolution of rain. It contains spatial correlations and is represented by three dynamical variables - wind speed, water height and rain concentration - which are linked together. A reduction of the observation coverage and of the number of updated variables leads to a relative error reduction of the particle filter compared to an ensemble of particles that are only continuously pulled (nudged) to observations, for a certain range of nudging parameters. But not surprisingly, reducing data coverage in- creases the absolute error of the filter. We found that the standard deviation of the error density exponents is a quantity that is responsible for the relative success of the filter with respect to nudging-only. In the case where only one variable is assimilated, we formulated a criterion that determines whether the particle filter outperforms the nudged ensemble. A theoretical estimate is derived for this criterion. The theoretical values of this estimate, which depends on the parameters involved in the assimilation set up (nudging intensity, model and observation error covariances, grid size, ensemble size,...), are roughly in accor- dance with the numerical results. In addition, comparing two different nudging matrices that regulate the magnitude of relaxation of the state vectors towards the observations, showed that a diagonally based nudging matrix leads to smaller errors, in the case of assimilating three variables, than a nudging matrix based on stochastic errors added in each integration time step. We conclude that the efficient particle filter could bring an improvement with respect to conventional data assimilation methods, when it comes to the convective scale. Its success, however, appears to depend strongly on the parameters of the test setting.

Aerosols are an important part of our atmosphere. As they are very inhomogenously distributed both in time and space the estimation of their influence on the climate is very complex. So it is important to improve the knowledge about the aerosol distribution. In this study the distribution of aerosols above the region around Munich, Germany in the time period 2007 to 2010 is studied with measurements from remote sensing instruments. Thereby the main focus is set on the lidar data from the ground based lidar system MULIS of the Meteorological Institute Munich and the space lidar CALIOP onboard the satellite CALIPSO which both deliver aerosol information height resolved. As an addition and for a better comparison with previous studies, aerosol information from the AERONET Sunphotometer in Munich and the satellite spectroradiometer MODIS are used. With help of these four datasets several aerosol parameters could be studied: on average the aerosol optical depth (AOD) above the Munich region is at 1064 nm about 0.05 to 0.06, at 532 nm about 0.12 to 0.17, and at 355 nm about 0.22 to 0.28. The height of the boundary layer top decreases from 1.68 km in spring to 0.73 km in winter, while the thickness of the elevated layers is more stable (spring: 1.43 km, winter: 1.02 km). The occurrence of ELs is highest in spring (in 75 % of all measurements), and lowest in winter (36 %). Measurements of the particle linear depolarization ratio and the Ångström exponent show that the aerosols in elevated layers clearly differ from the aerosols in the PBL. Especially in spring the average EL depolarization is large (25 %) indicating transportation of strongly depolarizing aerosols like Saharan dust in the free troposphere. The dominant aerosol type in the Munich region is smoke (also called biomass burning), polluted continental can occur in high concentrations especially during summer time. Dust occurs only in rare occasions, mainly mixed with other aerosol types (polluted dust). One important finding from the comparison of the four datasets is that CALIPSO strongly underestimates the AOD. To study the significances of different causes for this, the CALIPSO extinction coefficient profiles are compared with coincidentally performed measurements of MULIS. The underestimation of the AOD above Munich by CALIPSO is mainly found to be due to the failure of the layer detection: its effect on the AOD underestimation is about 36 %. Also the wrong assumption of the lidar ratio contributes to the underestimation, though on a smaller account of about 5 %. The influence of clouds in the surroundings on the AOD is not quantifiable, but the analysis shows that clouds lead to an overestimation of the AOD. To compensate these reasons and to get detailed profiles from CALIPSO, it could be shown that -for case studies- it is very efficient to calculate the extinction coefficients from CALIPSO raw data (L1B) manually.

Wir untersuchen stark gekoppelte Phänomene unter Verwendung der Dualität zwischen Eich- und Gravitationstheorien. Dabei liegt ein besonderer Fokus einerseits auf Vortex Lösungen, die von einem magnetischem Feld verursacht werden, und andererseits auf zeitabhängigen Problemen in holographischen Modellen. Das wichtigste Ergebnis ist die Entdeckung eines unerwarteten Effektes in einem einfachen holografischen Modell: ein starkes nicht abelsches magnetisches Feld verursacht die Entstehung eines Grundzustandes in der Form eines dreieckigen Gitters von Vortices. Die Dualität zwischen Eich- und Gravitationstheorien ist ein mächtiges Werkzeug welches bereits verwendet wurde um stark gekoppelte Systeme vom Quark-Gluonen Plasma in Teilchenbeschleunigern bis hin zu Festkörpertheorien zu beschreiben. Die wichtigste Idee ist dabei die der Dualität: Eine stark gekoppelte Quantenfeldtheorie kann untersucht werden, indem man die Eigenschaften eines aus den Einsteinschen Feldgleichungen folgenden Gravitations-Hintergrundes bestimmt. Eine der Gravitationstheorien, die in dieser Arbeit behandelt werden, ist eine Einstein--Yang--Mills Theorie in einem AdS--Schwarzschild Hintergrund mit SU(2)-Eichsymmetrie. Der Ansatz für das Eichfeld ist so gewählt, dass die zugehörige Quantenfeldtheorie einem externen Magnetfeld ausgesetzt ist. Oberhalb eines kritischen Magnetfeldes wird die Konfiguration instabil und zeigt einen Phasenübergang zu einem Supraleiter. Die Instabilität wird mit zwei Ansätzen untersucht. Zum einen werden Fluktuationen des Hintergrunds betrachtet und die Quasinormalmoden analysiert. Zum anderen zeigt die numerische Analyse der Bewegungsgleichungen, dass das effektive Schrödinger-Potential mit stärker werdendem Magnetfeld sich so lange verändert, bis ein gebundener Zustand möglich wird. Der sich ergebende supraleitende Grundzustand ist durch ein dreieckiges Vortexgitter gegeben, wie eine störungstheoretische Entwicklung über einem kleinen Parameter proportional zur Größe des Kondensats zeigt. Zur Bestimmung des energetisch bevorzugten Zustands wird mithilfe der holographischen Übersetzungsvorschrift die Gesamtenergie verschiedener Lösungen berechnet. Hierfür wird die Lösung der Bewegungsgleichungen zur dritten Ordnung in oben genanntem Parameter berechnet. Zusätzlich wird gezeigt, dass dieses Ergebnis auch für den Fall einer AdS--hard wall Geometrie gilt, also einer Feldtheorie mit Confinement. Als nächstes erweitern wir das einfache Gravitationsmodell um ein chemisches Potential und wiederholen die Untersuchung. Sind das chemische Potential, das magnetische Feld oder beide groß genug, so befindet sich das System in einer supraleitenden Phase. Wir berechnen das Phasendiagramm des Systems numerisch. Der Grundzustand der supraleitenden Phase nahe dem Phasenübergang ist ein dreieckiges Vortexgitter, wobei der Gitterabstand nur von der Stärke des magnetischen Feldes abhängt. Die Relevanz dieser Ergebnisse wird im Zusammenhang mit inhomogenen Grundzuständen in holographischen Supraleitern diskutiert, einem Themengebiet welches in letzter Zeit viel Interesse auf sich gezogen hat. Die erhaltenen Resultate sind nicht nur aufgrund der vorher unbekannten inhomogenen Lösung der Gravitationstheorie mit Schwarzem Loch neuartig. Es ist auch interessant, dass ein großes magnetisches Feld die Vortexstruktur im Grundzustand induziert anstatt sie zu unterdrücken. Des Weiteren untersuchen wir zeitabhängige Phänomene in einer holographischen Erweiterung des Kondomodells. Letzteres beschreibt ein einfaches Modell in der Festkörperphysik, in welchem eine magnetische Verunreinigung stark an ein Elektronenreservoir koppelt. Die holographische Beschreibung erfordert Techniken der numerischen Relativitätstheorie und erlaubt uns die Entwicklung des Systems nach einem plötzlichen Sprung in der Kopplungskonstante zu simulieren. Diese Doktorarbeit basiert auf Ergebnissen, die der Autor während des Studiums am Max-Planck-Institut-für-Physik in München, Deutschland unter der Betreuung von PD Dr. J. K. Erdmenger von August 2011 bis Mai 2014 erreicht hat. Die relevanten Veröffentlichungen sind: [1] M. Ammon, J. Erdmenger, P. Kerner, and M. Strydom, “Black Hole Instability Induced by a Magnetic Field,” Phys.Lett. B706 (2011) 94–99, arXiv:1106.4551 [hep-th], [2] Y.-Y. Bu, J. Erdmenger, J. P. Shock, and M. Strydom, “Magnetic field induced lattice ground states from holography,” JHEP 1303 (2013) 165, arXiv:1210.6669 [hep-th].

Deep radio observations provide a dust unbiased view of both black hole (BH) and star formation (SF) activity and therefore represent a powerful tool to investigate their evolution and their possible mutual influence across cosmic time. Radio astronomy is therefore becoming increasingly important for galaxy evolution studies thanks also to the many new radio facilities under construction or being planned. To maximise the potentiality of these new instruments it is crucial to make predictions on what they will observe and to see how best to complement the radio data with multi-wavelength information. These are the motivations of my Thesis in which I studied a sample of 900 sources detected in one of the deepest radio surveys ever made. The observations have been performed at 1.4 GHz with the Very Large Array on the Extended Chandra Deep Field South. I developed a multi-wavelength method to identify the optical-infrared counterparts of the radio sources and to classify them as radio-loud active galactic nuclei (RL AGNs), radio-quiet (RQ) AGNs, and star forming galaxies (SFGs). I was able for the first time to quantify the relative contribution of these different classes of sources down to a radio flux density limit of ∼30 μJy. I characterized the host galaxy properties (stellar masses, optical colors, and morphology) of the radio sources; RQ AGN hosts and SFGs have similar properties with disk morphology and blue colors while radio-loud AGN hosts are more massive, redder and mostly ellipticals. This suggests that the RQ and RL activity occurs at two different evolutionary stages of the BH-host galaxy co-evolution. The RQ phase occurs at earlier times when the galaxy is still gas rich and actively forming stars while the radio activity of the BH appears when the galaxy has already formed the bulk of its stellar population, the gas supply is lower, and the SF is considerably reduced. I quantified the star formation rate (SFR) of the radio sources using two independent tracers, the radio and far-infrared luminosities. I found evidence that the main contribution to the radio emission of RQ AGNs is the SF activity in their host galaxy. This result demonstrates the remarkable possibility of using the radio band to estimate the SFR even in the hosts of bright RQ AGNs where the optical-to-mid-infrared emission can be dominated by the AGN. I have shown that deep radio surveys can be used to study the cosmic star formation history; I estimated the contribution of the so-called ”starburst” mode to the total SFR density and quantified the AGN occurrence in galaxies with different levels of SF.