Universita` degli Studi di Napoli \Federico II" Dipartimento di Fisica \Ettore Pancini" Corso di Laurea in Fisica Anno Accademico 2017/2018 Tesi di Laurea Magistrale Morphology and kinematics of z ∼ 1 galaxies as seen through gravitational telescopes Relatore: Prof. Giovanni Covone Candidato: Maria Vittoria Milo Matricola: N94000352 Se parlassi le lingue degli uomini e degli angeli, ma non avessi amore, sarei un rame risonante o uno squillante cembalo. Se avessi il dono di profezia e conoscessi tutti i misteri e tutta la scienza e avessi tutta la fede in modo da spostare i monti, ma non avessi amore, non sarei nulla. Se distribuissi tutti i miei beni per nutrire i poveri, se dessi il mio corpo a essere arso, e non avessi amore, non mi gioverebbe a niente. (1 Corinzi 13:1-3) ii Abstract Observing high−z galaxies is an hard challenge for astrophysicists. As much we go back in time (and therefore far away in space), the Universe in which we live becomes smaller, denser and hotter. On the other hand, at high redshift, astro- nomical objects result as fainter as smaller to make their detection impossible even for the most powerful today's telescopes. Hence, trying to determine the morphol- ogy of these high−z galaxies and even to characterize their physical properties (such as kinematics) would result just a dream of a crazy astrophysicist. Fortu- nately, Nature offers a way out, allowing us to overcome the obstacle. Telescopes able to observe regions of the Universe never before reached by any human or artificial \eye" already exist! These are galaxy clusters, the largest known grav- itationally bound structures in the Universe. Through a phenomenon known as strong gravitational lensing, galaxy clusters can provide enormous magnification and amplification of distant sources that lie behind them, allowing us to study their physical and morphological properties. This is the reason why they are con- sidered \natural telescopes" or \cosmic telescopes". In this work of thesis, I took advantage of this extraordinary role that galaxy clusters have to reconstruct the morphology of z ∼ 1 galaxies and to characterize their kinematics . In Chapter 1, I will deal with the main characteristics of ΛCDM Model of Cosmology and General relativity. The ΛCDM model describes a flat universe in which ∼ 75 percent of the energy density is due to a cosmological constant Λ, ∼ 21 percent is due to cold dark matter (CDM) and the remaining 4 percent is due to the baryonic matter out of which stars and galaxies are made. In such a Universe, the formation of a structure (like a galaxy) could be linked to density perturbations by quantum fluctuations at early times. General relativity is a revolutionary theory of gravity formulated by Einstein in 1915, according to which the structure of space-time is determined by the mass distribution in the Universe through field equation. A direct conse- iii quence of General Relativity is gravitational lensing, an astronomical phenomenon characterized by the bending of the paths of the light rays by gravitational field of massive bodies. This will be the principal argument of Chapter 2. In particular, I will describe the so-called strong gravitational lensing regime, i.e. lensing pro- duced by galaxy clusters in the case in which occurs the production of giant arcs, multiple images and arclets. In Chapter 3 there will be a brief description of what are galaxy clusters and I will also introduce a way in which strong lensing can be used to build models of cluster mass distribution through a Bayesian approach. Finally, in Chapter 4 I will present my data analysis. Through the Cleanlens mode in the gravitational lensing software Lenstool, I have reconstructed the morphology of three different galaxies, at three different redshift, lensed by three different mas- sive galaxy clusters (A370, AS1063 and A2667). Furthermore, taking advantage of the relatively new spectroscopic technique provided by MUSE, I have derived the 2D kinematics of the galaxy lensed by A370 and producing the giant gravitational arc known as the \Dragon". In particular, I have obtained the rotational curve of this galaxy through a study of the [OII] emission line in the spectrum and I have deduced its total mass. The same procedure has been applied to get the rotational curve and the total mass of a galaxy lensed by AS1063. Finally, I have represented my small sample of three galaxies lensed by A370, AS1063 ans A2667 on a graph showing the stellar-mass Tully-Fisher Relation (smTFR) for 64 galaxies, realized by Puech et al. [1]. Contents 1 Introduction 1 1.1 The ΛCDM Model of Cosmology . .1 1.2 General Relativity . .5 1.3 Galaxy formation and evolution . .8 1.3.1 Galaxy formation: state of art . .8 1.3.2 Galaxy formation: open questions . 10 1.3.3 Evolution of the Tully-Fisher . 12 2 Gravitational lensing 15 2.1 What is gravitational lensing? . 15 2.2 The Fermat Principle . 19 2.3 The lens equation . 23 2.3.1 The effective lensing potential . 29 2.4 Lens mapping and magnification . 30 2.5 Strong and weak lensing regimes . 37 2.6 Strong gravitational lensing . 38 3 Galaxy clusters as gravitational lenses 43 3.1 What are galaxy clusters? . 43 3.2 Galaxy clusters as gravitational telescopes . 46 v vi Contents 3.3 Strong lensing modeling . 47 3.3.1 Bayesian approach . 50 3.4 From the source to the lensed image . 51 3.5 Lenstool . 53 4 Data analysis 55 4.1 Frontier Fields . 55 4.2 Our sample of lensed galaxies . 56 4.3 Source plane reconstruction in Abell 370 . 57 4.4 Source plane reconstruction in Abell S1063 . 62 4.5 Source plane reconstruction in Abell 2667 . 66 4.6 Integral Field Units . 69 4.6.1 The integral field spectrograph MUSE . 72 4.7 Kinematics of the two galaxies lensed by A370 and AS1063 . 75 4.8 Results . 82 5 Conclusions 85 References 87 Chapter 1 Introduction In this Chapter, I will explain the main characteristics of the two pillars upon which modern cosmology (and hence this thesis) rest: the ΛCDM Model and General Relativity. The first one is just one of the many possible scenarios proposed to date to describe the Universe in which we live while the second one is a theory of gravity formulated by Einstein in 1915 and published in 1916 [2] according to which the structure of space-time is determined by the mass distribution in the Universe through field equations. Moreover, I will give a brief description of the process according to which it is believed a galaxy forms. 1.1 The ΛCDM Model of Cosmology The ΛCDM Model of Cosmology is also called the Standard Model because, at the moment, is the simplest model that better reproduces the observations, providing reasonably good account of the following properties of the cosmos: • the existence and structure of the cosmic microwave background (CMB); • the large-scale structure in the distribution of galaxies; 1 2 Chapter 1. Introduction • the abundance of elements (Big Bang Nucleosynthesis); • the accelerating expansion of the Universe observed in the light from distant galaxies and supernovae. The expansion of the Universe was confirmed in 1929 when Edwin P. Hubble [3] observed a redshift in the spectra of distant galaxies, which indicated that these galaxies were receding from us at a velocity proportional to their distance from us. The ΛCDM model is based upon the Cosmological Principle, i.e. the hy- pothesis that the Universe, at large scales (I mean at scales larger than 100Mpc, that correspond about at 300 million light years), is spatially homogeneous and isotropic. The adjective \homogeneous" refers to the fact that our point of obser- vation is neither different nor privileged compared to any other point within our Universe. \Isotropic" means that there is no preferential direction in the Universe, that is, in any direction we observe, what we see must be in principle the same. The most general metric satisfying homogeneity and isotropy at large scales is the Friedmann-Lema^ıtre-Robertson-Walker (FRW) metric, written here in terms 2 µ ν of the invariant geodesic distance ds = gµνdx dx : dr2 ds2 = dt2 + a2(t) + r2(dθ2 + sin2 θdφ2) ; (1.1.1) 1 − Kr2 characterized by just two quantities: • a(t) is the scale factor of the Universe at the time t; • K is a constant which characterizes the spatial curvature of the Universe and that can assume only three possible values: K = +1 for a spherical geometry, that is a closed space-time, K = 0 for a flat or Euclidean geometry, that is a flat and open space-time, K = −1 for an hyperbolic geometry, that is open and divergent space-time. 1.1. The ΛCDM Model of Cosmology 3 The Standard Model describes a Universe filled by a classical and perfect fluid which satisfies Bianchi's identity and comes in the form of radiation in the pri- mordial epoch and in the form of dust in the present epoch. The equations that define this model are: a¨ 4πG = − ; (1.1.2) a 3c2 a_ 2 Kc2 8πG + = "; (1.1.3) a a2 3c2 a_ "_ + 3 (" + p); (1.1.4) a p = γ"; (1.1.5) 2 cs 2 where " = ρc is the total energy density of the Universe and γ = ( c ) is an adiabatic index describing how the fluid propagates. The first two equation come from the Einstein field equations (that I will discuss later): 1 8πG R − g R − Λg = T (1.1.6) µν 2 µν µν c4 µν where Rµν is the Ricci tensor, describing the local curvature of space-time, R is the curvature scalar,gµν is the metric, Tµν is the energy-momentum tensor of the matter content of the Universe and Λ is the cosmological constant, which was introduced by Einstein to obtain a static Universe (the \biggest blunder" of his life).