Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Faint Galaxies in the Megaparsec-Scale Environments of Hyperluminous QSOs at Redshifts 2 < z < 3

This thesis presents detailed observational studies of the extended distributions of gas, galaxies, and dark matter around hyperluminous quasars (HLQSOs) at high redshift. Taken together, these works aim to coherently describe the relationships between these massive, accreting black holes and their environments: the nature of the regions that give rise to such massive black holes, the effect of HLQSO radiation on their surrounding galaxies and gas, and the ability of both galaxies and black holes to shed new light on the formation and evolution of the other.

Chapter 2 focuses on the continuum-color-selected galaxies drawn from the Keck Baryonic Structure Survey (KBSS). The KBSS is a uniquely deep spectroscopic survey of star-forming galaxies in the same volumes of space as 15 HLQSOs at 2.5 < z < 2.9. The three-dimensional distribution of these galaxies among themselves and the nearby HLQSOs is used to infer the extent to which these black holes are associated with overdense peaks in the dark matter and galaxy distribution as quantified by clustering statistics. In conjunction with recent dark-matter simulations, these data provide the first estimates of the host dark-matter halo masses for HLQSOs, providing new insight into the formation and evolution of the most massive black holes at high redshift.

Chapter 3 describes the first results from a new survey (KBSS-Lyα) conducted for this thesis. The KBSS-Lyα survey uses narrowband imaging to identify Lyα-emitters (LAEs) in the ~Mpc regions around eight of the KBSS HLQSOs. Many of these LAEs show the effect of reprocessed HLQSO radiation in their emission through the process known as Lyα fluorescence. In this chapter, these fluorescent LAEs are used to generate a coarse map of the average HLQSO ionizing emission on Mpc scales, thereby setting the first direct constraints of the lifetime and angular distribution of activity for a population of these uniquely luminous black holes.

Chapter 4 contains a more detailed description of the KBSS-Lyα survey itself and the detailed properties of the star-forming and fluorescent objects selected therein. Using imaging and spectroscopic data covering rest-frame UV and optical wavelengths, including spectra from the new near-infrared spectrometer MOSFIRE, we characterize this population of nascent galaxies in terms of their kinematics, enrichment, gas properties, and luminosity distribution while comparing and contrasting them with previously-studied populations of continuum-selected galaxies and LAEs far from the effects of HLQSO emission.

At the conclusion of this thesis, I briefly present future directions for the continuation of this research. In Appendix A, I provide background information on the instrumentation used in this thesis, including my own contributions to MOSFIRE.

Maximum Principle for Elliptic and Parabolic Equations

Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Sub-kiloparsec alma imaging of compact star-forming galaxies at z ~ 2.5: revealing the formation of dense galactic cores in the progenitors of compact quiescent galaxies

We present spatially resolved Atacama Large Millimeter/submillimeter Array (ALMA) 870 μm dust continuum maps of six massive, compact, dusty star-forming galaxies at z ~ 2.5. These galaxies are selected for their small rest-frame optical sizes (r_e,F160W ~ 1.6 kpc) and high stellar mass densities that suggest that they are direct progenitors of compact quiescent galaxies at z ~ 2. The deep observations yield high far-infrared (FIR) luminosities of L_IR = 10^12.3-12.8 L_⨀ and star formation rates (SFRs) of SFR = 200–700 M_⊙ yr^−1, consistent with those of typical star-forming "main sequence" galaxies. The high spatial resolution (FWHM ~ 0 12–0 18) ALMA and Hubble Space Telescope photometry are combined to construct deconvolved, mean radial profiles of their stellar mass and (UV+IR) SFR. We find that the dusty, nuclear IR–SFR overwhelmingly dominates the bolometric SFR up to r ~ 5 kpc, by a factor of over 100× from the unobscured UV–SFR. Furthermore, the effective radius of the mean SFR profile (r_e,SFR ~ 1 kpc) is ~30% smaller than that of the stellar mass profile. The implied structural evolution, if such nuclear starburst last for the estimated gas depletion time of Δt = ±100 Myr, is a 4×increase of the stellar mass density within the central 1 kpc and a 1.6× decrease of the half-mass–radius. This structural evolution fully supports dissipation-driven, formation scenarios in which strong nuclear starbursts transform larger, star-forming progenitors into compact quiescent galaxies.

Space density distribution of galaxies in the absolute magnitude - rotation velocity plane: a volume-complete Tully-Fisher relation from CALIFA stellar kinematics

We measured the distribution in absolute magnitude - circular velocity space for a well-defined sample of 199 rotating galaxies of the Calar Alto Legacy Integral Field Area Survey (CALIFA) using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early-type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled because of the low number of bins, foreground contamination, or significant interaction, we performed Markov chain Monte Carlo modelling of the velocity fields, from which we obtained the rotation curve and kinematic parameters and their realistic uncertainties. We performed an extinction correction and calculated the circular velocity v_circ accounting for the pressure support of a given galaxy. The resulting galaxy distribution on the M-r - v(circ) plane was then modelled as a mixture of two distinct populations, allowing robust and reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that we were able to correct for the incompleteness of the sample. The 199 galaxies were weighted by volume and large-scale structure factors, which enabled us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r - v_circ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20 > M_r > -22 mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.

The SHIVir Survey: A Dynamical Catalogue of Virgo Cluster Galaxies and their Scaling Relations

By virtue of its proximity and richness, the Virgo galaxy cluster is a perfect testing ground to expand our understanding of structure formation in the Universe. Here, we present a comprehensive dynamical catalogue based on 190 Virgo cluster galaxies (VCGs) in the "Spectroscopy and H-band Imaging of the Virgo cluster" (SHIVir) survey, including kinematics and dynamical masses. Spectroscopy collected over a multi-year campaign on 4-8m telescopes was joined with optical and near-infrared imaging to create a cosmologically-representative overview of parameter distributions and scaling relations describing galaxy evolution in a rich cluster environment. The use of long-slit spectroscopy has allowed the extraction and systematic analysis of resolved kinematic profiles: Halpha rotation curves for late-type galaxies (LTGs), and velocity dispersion profiles for early-type galaxies (ETGs). The latter are shown to span a wide range of profile shapes which correlate with structural, morphological, and photometric parameters. A study of the distributions of surface brightnesses and circular velocities for ETGs and LTGs considered separately show them all to be strongly bimodal, hinting at the existence of dynamically unstable modes where the baryon and dark matter fractions may be comparable within the inner regions of galaxies. Both our Tully-Fisher relation for LTGs and Fundamental Plane analysis for ETGs exhibit the smallest scatter when a velocity metric probing the galaxy at larger radii (where the baryonic fraction becomes sub-dominant) is used: rotational velocity measured in the outer disc at the 23.5 i-mag arcsec^{-2} level, and velocity dispersion measured within an aperture of 2 effective radii, respectively. Dynamical estimates for gas-poor and gas-rich VCGs are merged into a joint analysis of the stellar-to-total mass relation (STMR), stellar TFR, and Mass-Size relation. These relations are all found to contain strong bimodalities or dichotomies between the ETG and LTG samples, alluding to a "mixed scenario'' evolutionary sequence between morphological/dynamical classes that involves both quenching and dry mergers. The unmistakable differentiation between these two galaxy classes appears robust against different classification schemes, and supports the notion that they are driven by different evolutionary histories. Future observations using integral field spectroscopy and including lower-mass galaxies should solidify this hypothesis.

An efficient Jeans modelling of axisymmetric galaxies with multiple stellar components

Dynamical models of stellar systems represent a powerful tool to study their internal structure and dynamics, to interpret the observed morphological and kinematical fields, and also to support numerical simulations of their evolution. We present a method especially designed to build axisymmetric Jeans models of galaxies, assumed as stationary and collisionless stellar systems. The aim is the development of a rigorous and flexible modelling procedure of multicomponent galaxies, composed of different stellar and dark matter distributions, and a central supermassive black hole. The stellar components, in particular, are intended to represent different galaxy structures, such as discs, bulges, halos, and can then have different structural (density profile, flattening, mass, scale-length), dynamical (rotation, velocity dispersion anisotropy), and population (age, metallicity, initial mass function, mass-to-light ratio) properties. The theoretical framework supporting the modelling procedure is presented, with the introduction of a suitable nomenclature, and its numerical implementation is discussed, with particular reference to the numerical code JASMINE2, developed for this purpose. We propose an approach for efficiently scaling the contributions in mass, luminosity, and rotational support, of the different matter components, allowing for fast and flexible explorations of the model parameter space. We also offer different methods of the computation of the gravitational potentials associated of the density components, especially convenient for their easier numerical tractability. A few galaxy models are studied, showing internal, and projected, structural and dynamical properties of multicomponent galaxies, with a focus on axisymmetric early-type galaxies with complex kinematical morphologies. The application of galaxy models to the study of initial conditions for hydro-dynamical and $N$-body simulations of galaxy evolution is also addressed, allowing in particular to investigate the large number of interesting combinations of the parameters which determine the structure and dynamics of complex multicomponent stellar systems.

On the role of AGN feedback in shaping galaxies across cosmic time

Understanding how Active Galactic Nuclei (AGN) shape galaxy evolution is a key challenge of modern astronomy. In the framework where black hole (BH) and galaxy growth are linked, AGN feedback must be tackled both at its “causes” (e.g. AGN-driven winds) and its “effects” (alteration of the gas reservoir in AGN hosts). The most informative cosmic time is z~1-3, at the peak of AGN activity and galaxy buildup, the so-called cosmic noon. The aim of this thesis is to provide new insights regarding some key questions that still remain open in this research field: i) What are the properties of AGN-driven sub-pc scale winds at z>1? ii) Are AGN-driven winds effective in influencing the life of galaxies? iii) Do AGN impact directly on star formation (SF) and gas content of their hosts? I first address AGN feedback as “caught in the act” by studying ultra-fast outflows (UFOs), X-ray AGN-driven winds, in gravitationally lensed quasars. I build the first statistically robust sample of high-z AGN, not preselected based on AGN-driven winds. I derive a first estimate of the high-z UFO detection fraction and measure the UFO duty cycle of a single high-z quasar for the first time. I also address the “effects” of AGN feedback on the life of host galaxies. If AGN influence galaxy growth, then they will reasonably impact the molecular gas reservoir first, and SF as a consequence. Through a comparative study of the molecular gas content in cosmic-noon AGN hosts and matched non-active galaxies (i.e., galaxies not hosting an AGN), we find that the host galaxies of more regular AGN (not selected to be the most luminous) are generally similar to non-active galaxies. However, we report on the possibility of a luminosity effect regulating the efficiency by which AGN might impact on galaxy growth.

Cross-population radio galaxies as a test of the jet-accretion relationship

Radio galaxies (RGs) are extremely relevant in addressing important unknowns concerning the interaction among black hole accretion, radio jets, and the environment. In the classical scheme, their accretion rate and ejection of relativistic jets are directly linked: efficient accretion (HERG) is associated with powerful edge-brightened jets (FRIIs); inefficient accretion (LERG) is associated with weak edge-darkened jets (FRIs). The observation of RGs with an inefficient engine associated with edge-brightened radio emission (FRII-LERGs) broke this scheme. FRII-LERGs constitute a suitable population to explore how accretion and ejection are linked and evaluate the environment's role in shaping jets. To this aim, we performed a multiwavelength study of different RGs catalogs spanning from Jy to mJy flux densities. At first, we investigated the X-ray properties of a sample of 51 FRIIs belonging to the 3CR catalog at z<0.3. Two hypotheses were invoked to explain FRII-LERGs behavior: evolution from classical FRIIs; the role of the environment. Next, we explored the mJy sky by studying the optical-radio properties of hundreds of RGs at z<0.15 (Best & Heckman 2012 sample). FRII-LERGs appear more similar to the old FRI-LERGs than to the young FRII-HERGs. These results point towards an evolutive scenario, however, nuclear time scale changes, star population aging, and kpc-Mpc radio structure modification do not agree. The role of the Mpc environment was then investigated. The Wen et al. 2015 galaxy clusters sample, built exploiting the SDSS survey, allowed us to explore the habitat of 7219 RGs at z<0.3. Most RGs are found to live in outside clusters. For these sources, differences among RG classes are still present. Thus, the environment is not the key parameter, and the possibility of intrinsic differences was reconsidered: we speculated that different black hole properties (spin and magnetic field at its horizon) could determine the observed spread in jet luminosity.

Mock HI observations of Milky Way-like simulated galaxies

L'obiettivo di questo lavoro di tesi consiste nel descrivere sia il processo necessario per la creazione di osservazioni sintetiche di galassie simulate simili alla Via Lattea nella riga di emissione a 21 cm dell'idrogeno neutro (HI), sia il lavoro di analisi fondamentale che serve a confrontare in modo efficace l'output generato con delle osservazioni di galassie reali. Come prima cosa è descritta la teoria quantistica che sta alla base dell'emissione a 21 cm di HI, illustrando l'importanza di tale riga di emissione nell'ambito dell'astronomia e come si possano ottenere informazioni fondamentali sulle sorgenti di questa radiazione a partire dai dati osservativi. Il lavoro poi si focalizza sull'utilizzo del software MARTINI per la creazione di osservazioni sintetiche della linea a 21 cm per una galassia simulata con proprietà simili alla Via Lattea generata utilizzando il modello numerico SMUGGLE. Infine, si passa ad una breve descrizione dell'analisi dei dati sintetici creati, e al loro confronto con dei dati provenienti da osservazioni reali di galassie con proprietà simili, per ottenere una valutazione qualitativa della bontà del modello SMUGGLE impiegato nella simulazione numerica.

Dynamics of galaxies in the cluster environment: a resonant origin for the ISP?

The internal dynamics of elliptical galaxies in clusters depends on many factors, including the environment in which the galaxy is located. In addition to the strong encounters with the other galaxies, we can also consider the gravitational interaction with the ubiquitous Cluster Tidal Field (CTF). As recognized in many studies, one possible way in which CTF affects the dynamics of galaxies inside the cluster is related to the fact that they may start oscillating as “rigid bodies” around their equilibrium positions in the field, with the periods of these oscillations curiously similar to those of stellar orbits in the outer parts of galaxies. Resonances between the two motions are hence expected and this phenomenon could significantly contribute to the formation of the Intracluster Stellar Population (ISP), whose presence is abundantly confirmed by observations. In this thesis work, we propose to study the motion of an elliptical galaxy, modelled as a rigid body, in the CTF, especially when its center of mass traces a quasi-circular orbit in the cluster gravitational potential. This case extends and generalizes the previous models and findings, proceeding towards a much more realistic description of galaxy motion. In addition to this, the presence of a further oscillation, namely that of the entire galaxy along its orbit, will possibly increase the probability of having resonances and, consequently, the rate of ISP production nearly to observed values. Thus, after reviewing the dynamics of a rigid body in a generic force field, we will assess some physically relevant studies and report their main results, discussing their implications with respect to our problem. We will conclude our discussion focusing on the more realistic scenario of an elliptical galaxy whose center of mass moves on a quasi-circular orbit in a spherically symmetric potential. The derivation of the fundamental equations of motion will serve as the basis for future modelling and discussions.

The molecular gas content of star-forming galaxies in the ALPINE fields.

In this thesis, I aim to study the evolution with redshift of the gas mass fraction of a sample of 53 sources (from z ∼ 0.5 to z > 5) serendipitously detected in ALMA band 7 as part of the ALMA Large Program to INvestigate C II at Early Times (ALPINE). First, I used SED-fitting software CIGALE, which is able to implement energy balancing between the optical and the far infrared part, to produce a best-fit template of my sources and to have an estimate of some physical properties, such as the star formation rate (SFR), the total infrared luminosity and the total stellar mass. Then, using the tight correlation found by Scoville et al. (2014) between the ISM molecular gas mass and the rest-frame 850 μm luminosity, I used the latter, extrapolating it from the best-fit template using a code that I wrote in Python, as a tracer for the molecular gas. For my sample, I then derived the most important physical properties, such as molecular gas mass, gas mass fractions, specific star formation rate and depletion timescales, which allowed me to better categorize them and find them a place within the evolutionary history of the Universe. I also fitted our sources, via another code I wrote again in Python, with a general modified blackbody (MBB) model taken from the literature (Gilli et al. (2014), D’Amato et al. (2020)) to have a direct method of comparison with similar galaxies. What is evident at the end of the paper is that the methods used to derive the physical quantities of the sources are consistent with each other, and these in turn are in good agreement with what is found in the literature.