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.

Magnetic fields around radio galaxies from Faraday rotation measure analysis

The purpose of this thesis is to investigate the strength and structure of the magnetized medium surrounding radio galaxies via observations of the Faraday effect. This study is based on an analysis of the polarization properties of radio galaxies selected to have a range of morphologies (elongated tails, or lobes with small axial ratios) and to be located in a variety of environments (from rich cluster core to small group). The targets include famous objects like M84 and M87. A key aspect of this work is the combination of accurate radio imaging with high-quality X-ray data for the gas surrounding the sources. Although the focus of this thesis is primarily observational, I developed analytical models and performed two- and three-dimensional numerical simulations of magnetic fields. The steps of the thesis are: (a) to analyze new and archival observations of Faraday rotation measure (RM) across radio galaxies and (b) to interpret these and existing RM images using sophisticated two and three-dimensional Monte Carlo simulations. The approach has been to select a few bright, very extended and highly polarized radio galaxies. This is essential to have high signal-to-noise in polarization over large enough areas to allow computation of spatial statistics such as the structure function (and hence the power spectrum) of rotation measure, which requires a large number of independent measurements. New and archival Very Large Array observations of the target sources have been analyzed in combination with high-quality X-ray data from the Chandra, XMM-Newton and ROSAT satellites. The work has been carried out by making use of: 1) Analytical predictions of the RM structure functions to quantify the RM statistics and to constrain the power spectra of the RM and magnetic field. 2) Two-dimensional Monte Carlo simulations to address the effect of an incomplete sampling of RM distribution and so to determine errors for the power spectra. 3) Methods to combine measurements of RM and depolarization in order to constrain the magnetic-field power spectrum on small scales. 4) Three-dimensional models of the group/cluster environments, including different magnetic field power spectra and gas density distributions. This thesis has shown that the magnetized medium surrounding radio galaxies appears more complicated than was apparent from earlier work. Three distinct types of magnetic-field structure are identified: an isotropic component with large-scale fluctuations, plausibly associated with the intergalactic medium not affected by the presence of a radio source; a well-ordered field draped around the front ends of the radio lobes and a field with small-scale fluctuations in rims of compressed gas surrounding the inner lobes, perhaps associated with a mixing layer.

The gaseous environment of radio galaxies: a new perspective from high-resolution x-ray spectroscopy

It is known that massive black holes have a profound effect on the evolution of galaxies, and possibly on their formation by regulating the amount of gas available for the star formation. However, how black hole and galaxies communicate is still an open problem, depending on how much of the energy released interacts with the circumnuclear matter. In the last years, most studies of feedback have primarily focused on AGN jet/cavity systems in the most massive galaxy clusters. This thesis intends to investigate the feedback phenomena in radio--loud AGNs from a different perspective studying isolated radio galaxies, through high-resolution spectroscopy. In particular one NLRG and three BLRG are studied, searching for warm gas, both in emission and absorption, in the soft X-ray band. I show that the soft spectrum of 3C33 originates from gas photoionized by the central engine. I found for the first time WA in 3C382 and 3C390.3. I show that the observed warm emitter/absorbers is not uniform and probably located in the NLR. The detected WA is slow implying a mass outflow rate and kinetic luminosity always well below 1% the L(acc) as well as the P(jet). Finally the radio--loud properties are compared with those of type 1 RQ AGNs. A positive correlation is found between the mass outflow rate/kinetic luminosity, and the radio loudness. This seems to suggest that the presence of a radio source (the jet?) affects the distribution of the absorbing gas. Alternatively, if the gas distribution is similar in Seyferts and radio galaxies, the M(out) vs rl relation could simply indicate a major ejection of matter in the form of wind in powerful radio AGNs.

The factorization method for real elliptic problems

The Factorization Method localizes inclusions inside a body from measurements on its surface. Without a priori knowing the physical parameters inside the inclusions, the points belonging to them can be characterized using the range of an auxiliary operator. The method relies on a range characterization that relates the range of the auxiliary operator to the measurements and is only known for very particular applications. In this work we develop a general framework for the method by considering symmetric and coercive operators between abstract Hilbert spaces. We show that the important range characterization holds if the difference between the inclusions and the background medium satisfies a coerciveness condition which can immediately be translated into a condition on the coefficients of a given real elliptic problem. We demonstrate how several known applications of the Factorization Method are covered by our general results and deduce the range characterization for a new example in linear elasticity.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

The Universe 10 Billion years ago: Morphologies, Star-formation rates and Galactic-scale winds in z ∼ 2 Galaxies

This thesis is devoted to the study of the properties of high-redsfhit galaxies in the epoch 1 < z < 3, when a substantial fraction of galaxy mass was assembled, and when the evolution of the star-formation rate density peaked. Following a multi-perspective approach and using the most recent and high-quality data available (spectra, photometry and imaging), the morphologies and the star-formation properties of high-redsfhit galaxies were investigated. Through an accurate morphological analyses, the built up of the Hubble sequence was placed around z ~ 2.5. High-redshift galaxies appear, in general, much more irregular and asymmetric than local ones. Moreover, the occurrence of morphological k-­correction is less pronounced than in the local Universe. Different star-formation rate indicators were also studied. The comparison of ultra-violet and optical based estimates, with the values derived from infra-red luminosity showed that the traditional way of addressing the dust obscuration is problematic, at high-redshifts, and new models of dust geometry and composition are required. Finally, by means of stacking techniques applied to rest-frame ultra-violet spectra of star-forming galaxies at z~2, the warm phase of galactic-scale outflows was studied. Evidence was found of escaping gas at velocities of ~ 100 km/s. Studying the correlation of inter-­stellar absorption lines equivalent widths with galaxy physical properties, the intensity of the outflow-related spectral features was proven to depend strongly on a combination of the velocity dispersion of the gas and its geometry.

Sensitivity analysis of a parabolic-elliptic problem

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L-infinity-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.

Detecting interfaces in a parabolic-elliptic problem from surface measurements

Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new proof of the unique solvability based on Lions’s projection lemma. For the case that the heat conductivity is higher inside the inclusions, we develop an adaptation of the factorization method to this time-dependent problem. In particular this shows that the locations of the interfaces are uniquely determined by boundary measurements. The method also yields to a numerical algorithm to recover the inclusions and thus the interfaces. We demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method, and finally we present some numerical results for the inverse problem.

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.

Dynamical properties and mass-luminosity relation of elliptical galaxies

In questo elaborato abbiamo analizzato un campione di 22 galssie early-type. Utilizzando una tecnica di cross-correlazione, abbiamo ottenuto profili radiali di rotazione e di dis- persione di velocitá. Questi dati ci hanno permesso di investigare molte delle proprietá dinamiche delle nostre galassie. Abbiamo ottenuto indizi sull’anisotropia orbitale e stimato le masse e il rapporto M/L del campione. Le masse misurate variano da 1010 a 1012 M , mentre i valori degli M/L, per cui abbiamo trovato una dipendenza del tipo Log M/L ∝ 0.28 Log L , sono dell’ordine dell’unitá. Abbiamo anche riprodotto le famose relazioni di scala e abbi- amo utlizzato un set di dati sugli indici di Lick/IDS per ricercare relazioni tra le proprietá chimiche e quelle dinamiche. In particolare, abbiamo riscontrato una correlazione tra molti degli indici dipendenti dalla metallicitá e la profonditá della buca di potenziale. Tali indici sembrano correlare anche con il M/L. La rotazione e la forma del profilo di dispersione di velocitá sembrano essere ininfluenti sulle proprietá chimiche. In ultima analisi, abbiamo considerato le implicazioni delle nostre misure riguardo la natura della popolazione stellare e dell’emissione X delle nostre galassie. L’indice di colore e il M/L sembrano indicare che la popolazione stellare delle nostre galassie é dominata da stelle appartenenti alle classi spettrali late-G e early-K. Sembra inoltre esserci una correlazione tra l’emissione X degli elementi del nostro campione e la profonditá della loro buca di potenziale.

Origin of cold gas and dust in massive elliptical galaxies

The recent availability of multi-wavelength data revealed the presence of large reservoirs of warm and cold gas and dust in the innermost regions of the majority of massive elliptical galaxies. To prove an internal origin of cold and warm gas, the investigation of the spatially distributed cooling process which occurs because of non-linear density perturbations and subsequent thermal instabilities is of crucial importance. The first goal of this work of thesis is to investigate the internal origin of warm and cold phases. Numerical simulations are the powerful tool of analysis. The way in which a spatially distributed cooling process originates has been examined and the off-centre amount of gas mass which cools when different and differently characterized AGN feedback mechanisms operate has been quantified. This thesis demonstrates that the aforementioned non-linear density perturbations originate and develop from AGN feedback mechanisms in a natural fashion. An internal origin of the warm phase from the once hot gas is shown to be possible. Computed velocity dispersions of ionized and hot gas are similar. The cold gas as well can originate from the cooling process: indeed, it has been estimated that the surrounding stellar radiation, which is one of the most feasible sources of ionization of the warm gas, does not manage to keep ionized all the gas at 10^4 K. Therefore, cooled gas does undergo a further cooling which can lead the warm phase to lower temperatures. However, the gas which has cooled from the hot phase is expected to be dustless; nonetheless, a large fraction of early type galaxies has detectable dust in their cores, both concentrated in filamentary and disky structures and spread over larger regions. Therefore a regularly rotating disk of cold and dusty gas has been included in the simulations. A new quantitative investigation of the spatially distributed cooling process has therefore been essential: the contribution of the included amount of dust which is embedded in the cold gas does have a role in promoting and enhancing the cooling. The fate of dust which was at first embedded in cold gas has been investigated. The role of AGN feedback mechanisms in dragging (if able) cold and dusty gas from the core of massive ellipticals up to large radii has been studied.

X-ray properties and evolution of high-redshift AGN, and the gas content of host galaxies

In this thesis, I have investigated the evolution of the high-redshift (z > 3) AGN population by collecting data from some of the major Chandra and XMM-Newton surveys. The final sample (141 sources) is one of the largest selected at z> 3 in the X- rays and it is characterised by a very high redshift completeness (98%). I derived the spectral slopes and obscurations through a spectral anaysis and I assessed the high-z evolution by deriving the luminosity function and the number counts of the sample. The best representation of the AGN evolution is a pure density evolution (PDE) model: the AGN space density is found to decrease by a factor of 10 from z=3 to z=5. I also found that about 50% of AGN are obscured by large column densities (logNH > 23). By comparing these data with those in the Local Universe, I found a positive evolution of the obscured AGN fraction with redshift, especially for luminous (logLx > 44) AGN. I also studied the gas content of z < 1 AGN-hosting galaxies and compared it with that of inactive galaxies. For the first time, I applied to AGN a method to derive the gas mass previously used for inactive galaxies only. AGN are found to live preferentially in gas-rich galaxies. This result on the one hand can help us in understanding the AGN triggering mechanisms, on the other hand explains why AGN are preferentially hosted by star-forming galaxies.

The dynamics of early-type galaxies as a tool to understand their hot coronae and their IMF

Dynamical models of galaxies are a powerful tool to study and understand several astrophysical problems related to galaxy formation and evolution. This thesis is focussed on a particular type of dynamical models, that are widely used in literature, and are based on the solution of the Jeans equations. By means of a numerical Jeans solver code, developed on purpose and able to build state-of-the-art advanced axisymmetric galaxy models, two of the main currently investigated issues in the field of research of early-type galaxies (ETGs) are addressed. The first topic concerns the hot and X-ray emitting gaseous coronae that surround ETGs. The main goal is to explain why flat and rotating galaxies generally exhibit haloes with lower gas temperatures and luminosities with respect to rounder and velocity dispersion supported systems. The second astrophysical problem addressed concerns instead the stellar initial mass function (IMF) of ETGs. Nowadays, this is a very controversial issue due to a growing number of works on ETGs, based on different and independent techniques, that show evidences of a systematic variation of the IMF normalization as a function of galaxy velocity dispersion or mass. These studies are changing the previous opinion that the IMF of ETGs was the same as that of spiral galaxies, and hence universal throughout the whole large family of galaxies.