Cosmic large scale structure: insights from radio astronomical experiments

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Scuola Normale Superiore di Pisa

Tesi di perfezionamento in Fisica

COSMIC LARGE SCALE STRUCTURES:

INSIGHTS FROM RADIO

ASTRONOMICAL EXPERIMENTS

Candidate:

Serena Manti

Supervisor :

Prof. Andrea Ferrara

Co-supervisor :

Dr. Simona Gallerani

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Abstract

Understanding the formation of galaxies over cosmic time, their co-evolution with the black holes they contain, as well as their interplay with the large-scale structures (LSS) in which they are immersed, represents an open question at the forefront of current observational and theoretical Cosmology. In particular, observations of z ∼ 6 quasars (QSOs) have shown that these objects are powered by supermassive black holes (SMBHs) that have rapidly grown up to a mass M & 109_M

sun in t < 1 Gyr, namely the age of the Universe

at these epochs. In order to understand these observations in the context of current galaxy and black hole formation models, detections of SMBH progenitors (i.e. MBHs with M ∼ 106− 108_M

sun) are required. Optical/near-infrared (NIR) surveys are limited by

the fact that high-z quasars are likely to be heavily obscured during their growth phase. Instead, the transparency of gas and dust to radio photons makes radio observations a promising tool for detecting obscured quasars and, in particular, SMBH progenitors at very early epochs. This kind of observations would be also fundamental to clarify the role of AGNs in the cosmic reionization (EoR) process.

In this Thesis work we focus on the fundamental role that the Square Kilometre Array (SKA) will play in the search for Radio Recombination Lines (RRLs) from quasars and in radio-continuum observations of large scale structures, as, e.g. galaxy clusters. Moreover, we investigate the relationship between quasars and their host galaxies through studies of the cosmic LSS.

First of all, in order to explore the possibility to detect z > 7 AGNs through their hydrogen RRL emission, we estimate the expected Hnα flux densities from quasars as a function of their absolute AB magnitude and redshift. We include secondary ionizations from X-ray photons and stimulated emission due to nonthermal radiation, which turn out to be fundamental processes to be taken into account for RRL experiments. We find that with 5σ significance, the SKA-MID telescope could detect sources with MAB. −27

(MAB. −26) at z . 8 (z . 3) in tobs< 100 hrs.

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better constrain the role of quasars as reionization sources.

In a subsequent project, we present WSRT multi-wavelenght radio observations of the ABELL 399–401 galaxy cluster pair, which represents the first example of a double radio halo system. We perform a full spectral index analysis of the diffuse emission, which provides significant information on the origin of the radio halos in relation to the cluster merger histories.

Finally, with the aim of understanding the dependence of galaxy formation and evo-lution on the environment, we provide a mathematical classification of the Cosmic Web through the so-called Augmented Lagrangian Perturbation Theory (ALPT) approach, which turns out to be much faster and efficient than many other proposed linearisation methods of the cosmic density field.

In the near future, the Square Kilometre Array (SKA) telescope, with its extraordinary capabilities in terms of frequency coverage, angular resolution and sensitivity, will allow us to improve the kind of experiments discussed in this Thesis and, consequently, to make large progresses in the context of galaxy formation and LSS.

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CONTENTS v

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List of Figures

1.1 Press-Schechter mass function . . . 13

1.2 Scheme of AGN unified model . . . 28

2.1 Scheme of a basic interferometer . . . 33

2.2 Interferometer response and visibility . . . 34

2.3 Comparison of existing and planned deep 1.4 GHz radio surveys 40 2.4 Hydrogen RRL observed frequencies versus redshift . . . 42

3.1 Schematic plot of the quasar SED . . . 47

3.2 Ionization rate versus αEUVand contour plot of the boost due to secondary ionizations versus αX,soft and αEUV . . . 49

3.3 Observed and predicted RRL flux densities versus M1500 AB . . . 53

3.4 Ratio of stimulated to spontaneous emission versus tempera-ture and density of the HII region for RRLs detectable with SKA-MID at z = 0, 6 (LTE) . . . 56

3.5 Ratio of stimulated to spontaneous emission for RRLs de-tectable with SKA-MID at z = 0, 6 (non-LTE) . . . 57

3.6 Evolution of 5σ sensitivity with z for different quasar M1500 AB . 59 4.1 Quasar UV luminosity function versus M1450 AB at 0.5 < z < 6 . 65 4.2 Evolution of the QSO LF parameters versus z at 0 < z < 7 . . 68

4.3 Predicted QSO UV luminosity function versus M_AB1450 at z ∼ 8 69 4.4 AGN comoving ionizing emissivity and HIphotoionization rate versus z for a double power-law and Schechter LF . . . 71

4.5 Predicted sky surface density of quasars in the NIR at z > 6 and H-band depth of NIR surveys . . . 74

4.6 Predicted QSO number counts versus RRL flux for a single observation with SKA-MID at 0 < z < 8 . . . 77

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5.1 25 cm WSRT contours overlayed on the 1.4 GHz VLA image of A399. Contours are drawn at -5σ (dashed, where σ is the noise rms reported in Table 5.1), 5σ and spaced by 2. The colour image units are Jy beam−1. . . 84 5.2 92 cm WSRT contours overlayed to the 1.4 GHz VLA image

of A399–A401 . . . 85 5.3 Zoom into the central area of Fig. 5.2 . . . 86 5.4 Total intensity radio contours of A399 at 1.4 GHz from Murgia

et al. (2010) . . . 86 5.5 XMM X-ray image overlaid to the spectral index map of A399

between 21 cm and 92 cm . . . 88 5.6 Azimuthally averaged brightness profiles of A399 at 346 MHz

and 1.4 GHz and corresponding spectral index radial profile . 89 6.1 PDFs of δk with LPT linearisation at z = 0 . . . 96

6.2 Cell-to-cell correlation between initial overdensity field and corresponding divergence of the displacement field . . . 98 6.3 Initial density field and its logarithm at z = 0 . . . 100 6.4 Cosmic web classification pre-linearisation . . . 102 6.5 Cosmic web classification with 2LPT and ALPT: voids and

sheets . . . 103 6.6 Cosmic web classification with 2LPT and ALPT: filaments

and knots . . . 104 B.1 Schematic plot of the synchrotron spectrum . . . 117 B.2 Thermal bremsstrahlung spectrum . . . 120

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List of Tables

2.1 SKA technical specifications: SKA precursors and SKA 1 . . . 43 2.2 SKA technical specifications: SKA 2 . . . 44 3.1 Observed RRL parameters of local extragalactic sources . . . . 51 3.2 Quantum numbers of RRLs detectable with SKA-MID at z =

0, 6 . . . 55 4.1 Best-fit values and corresponding errors of the QSO LF

pa-rameters at 0.5 < z < 6 . . . 66 5.1 Observational details of the A399–A401 pair with WSRT . . . 82 5.2 Achieved brightness sensitivity . . . 83 6.1 VFF . . . 101 6.2 MFF . . . 102

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List of Acronyms

Acronym Extended name

AGN Active Galactic Nucleus

ALMA Atacama Large Millimeter Array

ALPT Augmented Lagrangian Perturbation Theory

ASKAP Australian Square Kilometre Array Pathfinder

BAO Baryon Acoustic Oscillations

BB Black Body

BH Black Hole

BLR Broad Line Region

CDM Cold Dark Matter

CMB Cosmic Microwave Background

DM Dark Matter

DPL Double Power-Law

EoR Epoch of Reionization

EUV Extreme Ultraviolet

FIR Far Infrared

FR Fanaroff-Riley

FWHM Full Width at Half Maximum

GR General Relativity

HST Hubble Space Telescope

IC Inverse Compton

ICM Intracluster Medium

IGM Intergalactic Medium

IM Intensity Mapping

IR Infrared

ISM Interstellar Medium

ΛCDM Λ Cold Dark Matter

LF Luminosity Function

LOFAR Low-Frequency Array for Radio astronomy

LPT Lagrangian Perturbation Theory

Continued on next page

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Continued from previous page

Acronym Extended name

LSS Large Scale Structure

LTE Local Thermodynamic Equilibrium

MFF Mass Filling Fraction

MWA Murchison Widefield Array

NG Non-Gaussianity

NIR Near Infrared

NLR Narrow Line Region

NRAO National Radio Astronomy Observatory

NVSS NRAO VLA Sky Survey

PDF Probability Distribution Function

PLE Pure Luminosity Evolution

PopIII Population III

PS Power Spectrum

QSO Quasi-Stellar Object

RF Radio-Frequency

RFI Radio Frequency Interference

RLQ Radio-Loud Quasar

RM Rotation Measure

RQQ Radio-Quiet Quasar

RRL Radio Recombination Line

RT Radiative Transfer

SC Spherical Collapse

SED Spectral Energy Distribution

SFR Star Formation Rate

SKA Square Kilometre Array

SMBH Supermassive Black Hole

SN Supernova

Sy Seyfert galaxy

SZ Sunyaev-Zel’dovich

UKIRT United Kingdom Infra-Red Telescope

UV Ultraviolet

VISTA Visible and Infrared Survey Telescope for Astronomy

VLA Very Large Array

VFF Volume Filling Fraction

WFIRST Wide Field Infrared Survey Telescope

WSRT Westerbork Synthesis Radio Telescope

2LPT 2nd-order Lagrangian Perturbation Theory

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Chapter 1 The evolution and large scale

structure of the Universe

The variegated structures that we observe today in the Universe were born from incredibly simple initial conditions. This evidence has posed intriguing questions on which are the mechanisms that could have produced the big complexity of such structures.

The model on which we base our understanding is the Hot Big Bang model, according to which the Universe started from a singularity of infi-nite temperature and density, named Big Bang, about 13.7 billion years ago, and evolved undergoing, in the primordial phase, a period of exponentially accelerated expansion called inflation (Starobinskij 1979, 1980; Guth 1981; Linde 1982), during which its size increased by about 60 orders of magnitude. The basic idea of such theory is that quantum fluctuations on microscopic scales during inflation have generated a primordial spectrum of density per-turbations which, due to the enormous expansion of the Universe, fed the formation of cosmic structures. At the end of inflation the Universe was highly homogeneous on large scales but locally perturbed by quantistic fluc-tuations.

About three minutes after the Big Bang, the temperature of the Universe, which was decreasing with redshift as T ∝ (1 + z), dropped to ∼ 109 _{K, and}

light nuclei formed as the result of strong interactions between neutrons and protons. The Universe was radiation-dominated until z ∼ 3200, moment in which its temperature went down to ∼ 104 _{K and the transition to a matter}

domination occurred. The Universe consisted of an opaque ionized plasma of matter and radiation (in thermal equilibrium and coupled by Compton scattering) until the decoupling time, at z ∼ 1100, when radiation decou-pled from matter at the so-called last scattering surface. At that moment, the Universe became transparent and the Cosmic Microwave Background

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(CMB) originated.

The CMB is a remnant of the Big Bang with a temperature of T = 2.72548 ± 0.00057 K (Fixsen 2009) and a black-body spectrum1_{, unpolarized}

and with very small anisotropies, of the order of 10−5 (Planck Collaboration XV 2014). The Universe was in fact extremely homogeneous at the last scat-tering surface. At that time, the temperature was ∼ 3000 K and protons ed electrons were able to recombine forming hydrogen atoms.

After recombination, the Universe was composed of fully neutral hydrogen and helium, and gravitational instability allowed the density perturbations to grow, leading to the formation of a web-like, filament-dominated struc-ture, called cosmic web: the first stars, and later galaxies, originated mainly in correspondence of the intersections of these filaments.

The period between z ∼ 1100 and z ∼ 20 − 30 is called Dark Ages, due to the lack of any sources of light. The end of this era is determined by the formation of the first stars and galaxies (the Cosmic Dawn): the HIphotons escaping from them started to ionize the hydrogen present in the Intergalac-tic Medium (IGM)2_{, and thus a period of cosmic enlightenment began. Such}

phase is called Cosmic reionization (EoR).

The standard cosmological model, or ΛCDM model, is a parametrization of the Big Bang model in which the Universe is spatially flat and contains the so-called cosmological constant, or vacuum energy (denoted by Λ), and cold dark matter (CDM)3 _{in addition to the ordinary baryonic matter. This}

constitutes the simplest model that provides a reasonably good match to the following observations:

• the existence and structure of the CMB;

• the large-scale structure (LSS) in the distribution of galaxies;

• the abundances of hydrogen (including deuterium), helium and lithium; • the acceleration in the expansion of the Universe, discovered in the nineties (Riess et al. 1998; Perlmutter et al. 1999) through the study

1_{The black-body (BB) radiation is a kind of electromagnetic radiation within or}

sur-rounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (opaque and non-reflective) held at constant, uniform temperature. The BB radiation has a specific spectrum and an intensity which depends only on the temperature of the body.

2_{The IGM refers to a sparse, warm-to-hot plasma which exists in the spaces between}

galaxies: a fluctuating lower density background matter where the sources are immersed.

3_{Dark matter (DM) consists of particles, weakly interacting with the ordinary matter.}

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5 of the relation between luminosity and redshift of type-Ia supernovae (SNIae)4_.

This concordance cosmological model is completely defined once the following parameters are specified: (a) the density of matter, Ωm = Ωdm+ Ωb, where

Ωdm and Ωb represent the density parameters for dark matter and baryons

respectively; (b) the density of the vacuum energy, ΩΛ; (c) the present value

of the Hubble constant, H0 = 100h km s−1 Mpc−1; (d) the baryonic density

parameter, Ωb; (e) the root mean square mass fluctuations in a sphere of size

8 h−1 Mpc at z = 0, σ8, and (f) the spectral index of the primordial

fluctu-ations, ns. Their values from the latest observations5 (Planck Collaboration

XIII 2015) are: Ωm= 0.308 ± 0.012, ΩΛ = 0.692 ± 0.012, h = 0.678 ± 0.009,

σ8 = 0.815 ± 0.009, ns= 0.968 ± 0.006, Ωbh2 = 0.02226 ± 0.00023.

Throughout this Thesis we assume a flat cosmological model with H0 = 67.3

km s−1 Mpc−1, Ωm = 0.315 and ΩΛ = 0.685.

By approximation on scales much larger than the intergalactic distances, the Universe can be modeled as a fluid whose particles are represented by the galaxies, smoothly distributed inside it. Such model is based on the following assumptions:

1. Cosmological Principle (Liddle 2003):

on sufficiently large scales6_{, namely scales much greater than those}

characterizing the largest structures observed in the sky (R 100 Mpc), the Universe can be considered homogeneous and isotropic, i.e. its observational properties result to be more or less the same in each region and each direction. The Cosmological Principle is supported by many observational evidences, e.g. the homogeneity and isotropy ob-served in the distribution of galaxies on scales out to ∼ 100 Mpc (from experiments on galaxy number counts), and, even more important, the isotropy of the CMB (Barrett & Clarkson 2000).

Such observation proves that the Universe, during the epoch of hydro-gen recombination (t ≈ 300000 yrs after the Big Bang), was

homoge-4_{With the term SNIae we refer to a particular kind of supernovae which follow from the}

explosion of a white dwarf, as a result of the accretion process. Due to the uniform mass of the white dwarf, such explosions produce a luminosity peak, which in addition to the fact that the apparent magnitude of the supernovae depends primarily on their distance, allows us to use the SNIae as standard candles for measuring the distance of their host galaxy.

5_{For the definition of the Hubble constant and the density parameters, see Eq. (A.1)}

and (A.5) in Appendix A.

6_{The term “large scale” indicates a length over which the average properties of the}

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neous and isotropic with a precision of hδT T 2 i1/2 ≡ T (θ, φ) − hT i hT i ≈ 10 −5 . (1.1)

2. Weyl postulate (Weyl 1923):

gravity is the only force acting on galaxies and there are no interactions between them; hence, galaxies can be considered as test particles, free-falling in the cosmological fluid.

3. Validity of Einstein’s general theory of relativity (GR) (Einstein 1916): general relativity is a gravitational theory which describes the gravita-tional interaction as an effect of a physical law relating the geometry (or curvature) of space-time to the distribution of mass and energy inside it. In particular, the space-time geometry discriminates among differ-ent reference frames: GR deals with non-inertial systems, which are related to a curved geometry, and it ultimately determines the causal structure of the space-time. Experimental evidences supporting GR are, among others, the precession of Mercury’s perihelion, the light deflection and the gravitational redshift.

In this Chapter, we start with an introduction to the theory of structure formation (Sec. 1.1). Then, we introduce the cosmic web and various ap-proaches to classify it (Sec. 1.2), and we describe the properties of clusters of galaxies, located at the nodes of the filamentary large-scale structure (Sec. 1.3). In Sec. 1.4 we introduce the Active Galactic Nuclei, representing the central compact regions of luminous galaxies, and we end, in Sec. 1.5, by analysing morphology and classification of the extragalactic radio sources.

1.1 Structure formation

In the standard ΛCDM model, the Universe started from a tightly homoge-neous matter distribution with small density fluctuations in the power spec-trum, and evolved through the action of gravity in an expanding background to the present cosmic web structure. Such structure originated when gravita-tional instability allowed DM to collapse around the primordial fluctuations. Then, the falling of gas into the potential wells of the forming DM halos and the subsequent fragmentation led to the birth of the first stars and galaxies. The standard theory for cosmic structure formation is the gravitational instability scenario, based on the following assumptions:

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1.1. STRUCTURE FORMATION 7 1. The Universe is dominated by cold dark matter, collisionless and

non-baryonic.

2. The ordinary, or baryonic, matter (protons, neutrons, electrons,...) is present in the Universe in the amount predicted by the Big Bang nu-cleosynthesis (and observationally verified): 0.01 ≤ Ωbh2 ≤ 0.029.

3. The inflationary Universe model predicts a value of the total density parameter very close to unity: Ω0 ' 1.

4. During the epoch of hydrogen recombination (z ≈ 103_{), the Universe}

was well described by the Robertson-Walker metric7, thus being almost homogeneous and isotropic.

5. The cosmic structures originated from gravitational instability.

6. The galaxies originated afterwards, when the baryonic matter (gas) falls into the potential wells of dark matter halos, attracted by their gravity.

Planets, stars and galaxies have evolved from initial tiny perturbations around the homogeneous and isotropic model (also called the “unperturbed” Uni-verse) under the influence of gravity. Density fluctuations,

δ(x) ≡ ρ(x)

ρ − 1 =

δρ(x)

ρ , (1.2)

where ρ is the matter density and ρ its average, can be considered linear if their value is much less than unity (δ 1), and observations of the CMB ensure that this condition is fully satisfied at z ≈ 1100. Thus, in such limit, their evolution can be studied using the linear (first-order) perturbation theory. When the gravitational growth leads to δ → 1, the regime becomes non-linear, and so the linear theory is no longer applicable. Several analytical models and numerical simulations show that in this limit and under certain conditions, the system undergoes a gravitational collapse and forms a very dense structure (with δ ≈ 102_{), which reaches a virial and stable equilibrium}

between potential and kinetic energy. Such a structure is the so-called dark matter halo.

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1.1.1 The power spectrum

Simple models of inflation predict, and observations show, that in the linear regime cosmological perturbations are Gaussian, or nearly Gaussian. Their Gaussianity is then destroyed on small scales by non-linear structure forma-tion. A generic Gaussian perturbation could be written as follows:

g(x) =X

k

gkeik·x, (1.3)

where g could be the Newtonian potential, the overdensity field or some other linear theory quantity, and the set of Fourier coefficients {gk} is the result of

a Gaussian random process (here we have suppressed the time dependence). To know the random process means to know the probability distribution8 Prob(gk). A Gaussian perturbation is such that the probability distribution

of an individual Fourier component is Gaussian and the probabilities of dif-ferent Fourier modes are independent (i.e. not correlated)9. In addition, the distribution is assumed to be statistically homogeneous and isotropic in space. Like Gaussianity, this is a prediction of typical models of inflation, and seems to be in agreement with data.

All statistical information about a Gaussian perturbation is encoded in a single function of one variable, which gives the spatial dependence of the initial conditions for the perturbations, and is usually treated in terms of the power spectrum (PS). The power spectrum is defined as

Pg(k) ≡ L 2π 3 4πk3h|gk|2i = L3 2π2k 3_h|g k|2i, (1.6)

where k is called comoving momentum or comoving wavenumber10 _{and L}

is such that, considering some cubic region (“box”) of the Universe, in the

8_{The expectation value of a quantity which depends on the complex variable g} k = αk+ iβk is hf (gk)i ≡ Z ∞ −∞ dαk Z ∞ −∞ dβkProb(gk)f (gk), (1.4)

where the integral is computed over the complex plane. Cosmological perturbations are real, hence g−k= g∗k.

9_{The Fourier transformation of some quantity g(x) is defined as follows:}

g(k) = 1 (2π)3/2

Z

g(x)e−ik·xd3x. (1.5)

10_{The comoving momentum has not to be confused with the physical momentum, which}

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1.1. STRUCTURE FORMATION 9 comoving coordinates (and assuming periodic boundary conditions), its co-moving volume is L3_{. The variance of g(x) is}

hg(x)2i = X k h|gk|2i = 2π L 3 X k 1 4πk3Pg(k) → 1 4π Z d3k k3 Pg(k) = Z ∞ 0 dk k Pg(k) = Z ∞ −∞ Pg(k)d ln k. (1.7)

The function g(x)2 of course varies from place to place, but its expectation value is the same everywhere due to statistical homogeneity; hence, the re-sult of Eq. (1.7) does not depend on x. The power spectrum of g gives the contribution of a logarithmic scale interval to the variance of g(x). For Gaussian perturbations, it provides a complete description of all the statis-tical quantities.

In practice, the integration in Eq. (1.7) is not extended all the way from k = 0 to k = ∞, since there are usually some smallest and largest relevant scales, introducing natural cutoffs at both end of the integral. The largest relevant scale can be interpreted as the size of the observable Universe: the perturbation g(x) represents a deviation from the background quantity, and the best estimate for the background may be the average taken over the ob-servable Universe. Therefore, perturbations at larger scales contribute to our estimate of the background value instead of contributing to the perturbation away from it. The smallest relevant scale is assumed to be the end of the linear regime. However, by including non-linear corrections, it is possible to discuss the power spectrum also in the non-linear regime, even if on very small scales the original information has been erased by non-linear processes.

An alternative definition for the power spectrum is

Pg(k) ≡ L3h|gk|2i, (1.8)

which is equivalent to Eq. (1.6) if Pg(k) =

2π2

k3 Pg(k). (1.9)

1.1.2 Jeans instability

In order to understand the process of gravitational instability, we can imagine a uniform distribution of fluid (e.g. dark matter), inside which small density fluctuations are present on each scale. If we consider a region where the dark matter is overdense with respect to the average density, two (antagonists) processes will occur: one the one hand, gravity between particles tends to

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make the region denser and smaller; on the other hand, gas pressure tends to spread and cancel the overdensity. From the balance between these two effects, we can define the Jeans length (Jeans 1928):

λJ = πc2 s Gρ 1/2 , (1.10)

where G is the gravitational constant, cs is the sound speed and ρ is the

density of the gravitationally dominant component, responsible for driving the collapse. The Jeans scale discriminates whether a perturbation can grow over time or not.

For λ λJ (potential energy much greater than kinetic energy), the

time-scale needed for the pressure force to act is much larger than the gravitational one: gravity wins and the perturbation collapses. For λ < λJ (potential

energy smaller than kinetic energy), the pressure force is able to counteract gravity and so the density fluctuation oscillates as a sound wave.

The mass within a sphere of radius λJ/2 is called Jeans mass:

MJ = 4πρ 3 λJ 2 3 . (1.11)

For M > MJ, gravity is much stronger than the pressure force and so the

structure collapses. This sets a limit on the scales that are able to collapse at each epoch.

1.1.3 Linear regime

The Universe can be thought of as a fluid consisting of collisionless dark matter and collisional baryons, with an average mass density ρ. Thus, at any space and time coordinates (x and t respectively), its mass density can be written as

ρ(x, t) = ρ(t)[1 + δ(x, t)], (1.12)

where δ is the overdensity field (also known as density contrast ). The time evolution equation for δ, in the linear regime, is (Peebles 1993)

¨ δ(x, t) + 2H(t) ˙δ(x, t) = 4πGρ(t)δ(x, t) + c 2 s a(t)2∇ 2 δ(x, t), (1.13)

where H(t) = H0[Ωm(1 + z)3+ ΩΛ]1/2 is the Hubble parameter at the time t

and a ≡ (1 + z)−1 is the scale factor of the Universe.

In Fourier space, we can write the overdensity field in the following way: δ(x, t) =

Z _d3_k

(2π)3e ik·x_δ

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1.1. STRUCTURE FORMATION 11 where k is the comoving wavenumber. Eq. (1.14) describes δ at any spatial location as a superposition of modes with different wavelengths. Hence, Eq. (1.13) can be rewritten as follows:

¨ δk+ 2H(t) ˙δk = 4πGρδk− c2 s a2k 2_δ k. (1.15)

Given the initial power spectrum of the perturbations, P (k) ≡ h|δ2

k|i, the

evolution of each mode can be followed using Eq. (1.15); this equation can then be integrated to recover the global spectrum at any time. Inflationary models predict P (k) ∝ kn_{, with n = 1, i.e. a scale invariant PS. Although the}

initial power spectrum is independent on scale, the growth of perturbations leads to a modified final value. While on large scales the power spectrum follows a simple linear evolution, its shape on small scales changes due to gravitational growth (and collapse), resulting in a spectrum P (k) ∝ kn−4_.

In the CDM model of structure formation, most of the power is on small scales, which are therefore the first to become non-linear.

1.1.4 Non-linear regime

Being cold dark matter made of collisionless particles weakly interacting with radiation and the rest of the matter, density perturbations in this compo-nent start growing at early epochs. When the density contrast approaches unity, δ ≈ 1, the linear perturbation theory fails. Since most of the struc-tures observed in the Universe, such as galaxies, galaxy clusters and so on, present a density contrast much larger than unity (δ 1), their evolution and structure can be studied and understood only through a fully non-linear theory.

In 1970 Zel’dovich developed a simple approximation to describe the non-linear stages of gravitational evolution (Zel’dovich 1970), according to which sheet-like structures called “pancakes” are the first non-linear structures to form, from collapse along one principal axis, while the observed filaments and knots originate from the simultaneous collapse along two and three axes re-spectively. Since the probability of collapse along only one axis is the largest, pancakes are the dominant structures in such model. While the results of this approximation agree very well with simulations at the beginning of the non-linear collapse, they are widely inaccurate at the later stages.

This problem can be somehow overcome by analytically following the dynam-ical collapse of a dark matter halo, under the hypothesis that it is spherdynam-ically simmetric and possesses a constant density.

The spherical collapse approximation is important to derive individual halo properties, but does not give any information about the inner structure or the

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abundance of halos. Many results are available on the inner density profile of DM halos (Navarro et al. 1996, 1997; Kravtsov et al. 1998; Avila-Reese et al. 1999; Moore et al. 1999; Del Popolo et al. 2000; Ghigna et al. 2000; Jing 2000; Jing & Suto 2000; Subramanian et al. 2000; Power et al. 2003; Ricotti 2003; Fukushige et al. 2004) but, up to now, there is no consensus on the existence of a universal shape of the DM halo density profile.

There is instead much more information on the abundance of halos. In 1974 Press and Schechter developed an analytic model in which the number density of halos, as a function of mass, can be computed at any redshift z starting from a linear density field through the application of the spherical collapse model, to associate peaks in the field with virialized objects in a full non-linear treatment (Press & Schechter 1974). However, such a model cannot predict the halo spatial distribution, which can be inferred through the excursion set formalism, proposed in 2002 by Sheth and Tormen and applicable for both spherical and ellipsoidal collapse (Sheth & Tormen 2002).

1.1.5 The Sheth-Tormen mass function

The Sheth-Tormen halo mass function (Sheth & Tormen 1999) gives the number density of DM halos (i.e. the fraction of virialized objects) with mass greater than a certain value M at redshift z:

d2_N dV dM = − ρ M ∂ ln σ ∂M r 2 πA 1 + 1 ˆ ν2p ˆ νe−ˆν2/2, (1.16) where ˆ ν ≡√a δc σ(M ). (1.17)

Here δc represents the critical overdensity for spherical collapse11 and σ(M )

is such that the variance of the mass M enclosed in a radius R is σ2(M ) = σ2(R) = 1

2π2

Z ∞

0

dkk2P (k)W2(kR). (1.18)

The parameters A, p and a will be defined and discussed below. In Eq. (1.18), W (kR) and P (k) are respectively the window function

W (kR) = 3[sin(kR) − kR cos(kR)], (1.19)

namely the Fourier transform of a spherical top hat filter of radius R, and the power spectrum of the density fluctuations, extrapolated at z = 0 using

11_{If the overdensity is greater than δ}

c ' 1.686, then the structure collapses (e.g.

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1.1. STRUCTURE FORMATION 13 the linear theory, P (k) = ApknT2(k). Ap is the amplitude of the density

fluctuations calculated by normalizing σ(M ) to σ8, and T (k) is the transfer

function, representing differential growth from early times (Bardeen et al. 1986):

T (k) = 0.43p

−1_{ln(1 + 2.34p)}

[1 + 3.89p + (16.1p)2_{+ (5.46p)}3_{+ (6.71p)}4_]1/4. (1.20)

Figure 1.1: Press-Schechter differential halo mass function at different redshifts: z = 6 (yellow curve), z = 9 (red curve), z = 12 (green curve), z = 15 (blue curve).

The parameters A, p and a in Eqs. (1.16) and (1.17) are modifications to the original Press-Schechter mass function (Press & Schechter 1974; see Fig. 1.1), that allow to obtain a better match with results from very large volume cosmological simulations: A ≈ 0.322, p = 0.3 and a = 0.707 (Sheth et al. 2001).

The Sheth-Tormen halo mass function is retrieved through physical means if shear and ellipticity are included in the collapse model, changing the scale-free δc= δc(z), obtained from spherically symmetric collapse, into a function

of filter scale: δc(M ) = √ aδc 1 + b σ 2 aδ2 c c , (1.21)

where b = 0.5 and c = 0.6. By considering a larger range in redshift and mass, Jenkins (2001) obtained the following parameter values: A = 0.353, p = 0.17, a = 0.73, b = 0.34, and c = 0.81.

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1.2 The Cosmic Web

Observing the Universe with the largest telescopes, we discover that, on cosmological scales, the matter is irregularly distributed. The large-scale distribution of galaxies and the distribution of dark matter, as inferred from its gravitational lensing and reconstructions from large galaxy surveys, give the appearance of mass and light arranged in a web-like structure dominated by linear filaments and concentrated compact knots, with two-dimensional structures called sheets, and vast extended, extremely low density, regions occupied by no or only a few galaxies, the voids (Bond et al. 1996; Kitaura et al. 2009; Jasche et al. 2010; Mu˜noz-Cuartas et al. 2011; Wang et al. 2012).

Thus, there are three features that can be generally observed: underdense regions, which occupy most of the volume, filaments, and dense clumps, located at the intersection of these filaments. Therefore, the cosmic web can be classified into at least three categories: voids (underdense regions), knots (dense clumps), and filaments.

The cosmic web constitutes the astrophysical context in which galaxies form and evolve. Indeed, impressive progress in observations, theory and numerical simulations have provided new insights into its relation to the properties of galaxies. High resolution spectroscopy revealed that over 90% of the baryonic mass resides in the intergalactic medium, which is mostly ionized and follows the LSS pattern.

The cosmic web is one of the most intriguing patterns found in nature, and this makes its analysis and characterization very far from trivial. The absence of an objective procedure for identifying and isolating clusters, filaments and voids in the cosmic matter distribution has been a major obstacle in investigating the structure and dynamics of the cosmic web. Furthermore, the big complexity of the individual structures and their connectivity, the enormous range of densities and the intrinsic multiscale nature prevent the use of simple tools that may be sufficient in less challenging problems.

Over the years, a variety of heuristic measures have been forwarded in order to analyze specific aspects of the spatial patterns in the large-scale Universe. Recently, more solid and well-defined machineries have been de-veloped to this purpose. These address the entire range of weblike features simultaneously, instead of focusing just on voids or filaments in their own right.

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1.2. THE COSMIC WEB 15

1.2.1 The classification of the Cosmic Web

Direct mapping of the mass distribution by weak lensing shows a time-evolving loose network of filaments, connecting rich clusters of galaxies (Massey et al. 2007). The very low resolution of the weak lensing maps cannot reveal the full intricacy of the cosmic web, and in particular the difference between filaments and sheets, even if they show a web structure which is like a gravi-tational scaffold into which gas can accumulate and stars can be built. This poses the intriguing challenge to classify and quantify the cosmic web in a mathematical way.

These efforts are motivated by two reasons. First, the cosmic web is there and so we want to describe it mathematically; second, the web classification might provide some extra parameters quantifying the environment within which DM halos and galaxies form.

There are clear evidences that some observed properties of galaxies de-pend on their environments (Dressler 1980; Avila-Reese et al. 2005; Blanton et al. 2005; Gao et al. 2005; Forero-Romero et al. 2011; Hoffman et al. 2012; Libeskind et al. 2012). For example, the morphology-density relation stipulates that elliptical galaxies are found preferentially in crowded environ-ments and spiral galaxies are present at very low densities (Dressler 1980). The same kind of correlation can be found in terms of the colours of galaxies (Blanton et al. 2005), star formation history and ages. Moreover, the dy-namics of subhalos and satellite galaxies suggests a possible dependence on the environment within which their parent halos reside (Knebe et al. 2004; Libeskind et al. 2005, 2011). Hence, a web classification might extend our theoretical tools to understand such dependence.

According to the current paradigm of structure formation, galaxies form and evolve in dark matter halos (White & Rees 1978). Thus, the analysis of such environmental dependence should start with the attempt to understand the formation of DM halos in the context of the cosmic web (Avila-Reese et al. 2005; Gao et al. 2005; Maulbetsch et al. 2007). This motivates the search for a solid and significant method for classifying the various environments in numerical simulations, and such classification should give the framework to study the environmental dependence of galaxy formation.

A good algorithm for an environment finder should be based on a well-defined numerical scheme and should give a quantitative classification according to the visual impression, a task not trivial to be performed. There is however a very closely related, but less demanding task, which consists in the identi-fication of voids out of the cosmic web (for a comprehensive review on web classifiers, see Colberg et al. 2008). Two are the methods according to which the void finders can be classified: one is based on a geometric approach,

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which deals with the point distribution of galaxies or DM halos, and the other is based on a dynamic approach, which involves smoothed density or potential fields.

The first approach is based on the use of objects (galaxies or DM halos) located in high density environments (Novikov et al. 2006; Arag´on-Calvo et al. 2007; Sousbie et al. 2008). The latter originates from the Zel’dovich approximation (Zel’dovich 1970), which represents the first analytical tool that permits to track the formation of aspherical objects, thus accounting for the formation of filaments, voids, sheets and knots.

A dynamic approach for the cosmic web classification was suggested by Hahn et al. (2007), who assigned at each point in space a property dependent on the LSS dynamics, i.e. on the density and/or velocity fields. In such way, they have been able to classify each point as a void, sheet, filament or knot (corresponding respectively to 0, 1, 2 or 3 positive eigenvalues of the tidal tensor of the underlying mass distribution).

Given that in the linear regime of structure formation the gravitational and velocity fields are basically identical (up to some scaling depending on the cosmological parameters), the dynamical approaches for the cosmic web clas-sification can be reformulated in terms of the velocity shear tensor, namely by looking at the number of its eigenvalues above a certain threshold (Hoff-man et al. 2001, 2012). Hence, the T-web (tidal tensor based cosmic web) and V-web (velocity tensor based web) turn out to be essentially the same in the linear regime, while differing in the non-linear regime (see Sec. 1.2.2). Indeed, the V-web algorithm has been shown to improve the dynamical reso-lution much largely with respect to the T-web, thus enabling the classification of structures on scales of few tens of kpc.

Finally, we point out the presence of a web-like structure on very small scales as well: the cosmic web is observed down to the virial radius of galactic scale halos (Libeskind et al. 2011).

1.2.2 Web classification: algorithm

A DM-only N -body simulation can be described in terms of the density field ρ(r) and velocity field v(r) evaluated on a finite grid. The T-web is defined by the eigenvalues of the Hessian of the gravitational potential, which satisfies the following rescaled Poisson equation:

∇2_{φ = ∆,} _(1.22)

where φ is the gravitational potential rescaled by 4πGρ, and ∆ = ρ/ρ. The deformation tensor, or tidal tensor, is given by the Hessian of the

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gravita-1.2. THE COSMIC WEB 17 tional potential, Tαβ = ∂2φ ∂rα∂rβ , (1.23)

where α and β represent the coordinates x, y, z. Eq. (1.23) assumes that the matter density field is known and smoothed with a finite kernel, which controls the high-frequency behaviour of the derivatives. The three eigenval-ues of the deformation tensor are denoted by λT

1, λT2 and λT3, and satisfy the

following relation:

∆(r) = λT₁(r) + λT₂(r) + λT₃(r). (1.24) The sign of a given eigenvalue at a given grid node determines the behaviour of the gravitational force at the direction of the corresponding eigenvector: if the sign is positive, the force is contracting; if the sign is negative, the force is expanding.

The V-web is defined in terms of the shear tensor, rescaled and defined as Σαβ = − 1 2 ∂vα ∂rβ +∂vβ ∂rα H0, (1.25)

where H0 is the Hubble parameter at the present time. The three eigenvalues

of the shear tensor are denoted by λV

1, λV2 and λV3.

Note that the velocity shear field is identical to the tidal field defined in Eq. (1.23), when smoothed on large enough (i.e. > few Mpc) scales.

The eigenvector corresponding to the greatest eigenvalue of the shear tensor denotes the direction along which material is collapsing fastest (or expanding slowest), and analogously for the intermediate and smallest eigenvalues. In such way, a web classification can be carried out by simply counting the number of axes that are collapsing: 0, 1, 2 or 3 for voids, sheets, filaments or knots, respectively. An axis is said to be “collapsing” if its eigenvalue is greater than some threshold. For example, filaments are defined by two collapsing axes and an expanding one; thus, the expanding axis has the lowest eigenvalue and corresponds to the orientation of the filament, being identical to the third eigenvector of the V-field.

1.2.3 Voids

Voids are large empty regions of space which contain very few, or no, galaxies, and represent the majority of the cosmic volume (van de Weygaert & Platen 2011). Surrounded by elongated filaments, sheet-like walls and dense com-pact clusters, they weave the salient weblike pattern of galaxies and matter pervading the observable Universe. Usually roundish and with dimensions of 10 − 50 h−1 Mpc, they account for about 70-85% of the total volume of

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the galaxy distribution, and their typical size in this distribution depends on the galaxy population used to define them (Hoyle & Vogeley 2002; Plionis & Basilakos 2002).

The sensitivity of voids to global cosmological parameters is due to their unique dynamical status: on the one hand, they tend to evolve into ex-panding, extended, uniform, and underdense regions with a distinct “bucket-shaped” profile12 (Icke 1984; Sheth & van de Weygaert 2004). On the other hand, they are nonlinear objects which mark the transition scale between lin-ear and nonlinlin-ear evolution (Sahni et al. 1994). As such, their morphology and structure reflect and magnify cosmological differences present in the pri-mordial Universe, and their evolution retains the dominant influence of the inhomogeneous cosmological surroundings (Platen et al. 2008). All these factors make voids important cosmological sources of information.

For example, the evolution of the void shape could be a sensitive probe of the nature of dark energy, which is still one of the greatest puzzles in cosmol-ogy (Frieman et al. 2008; Kowalski et al. 2008; Percival et al. 2010; Komatsu et al. 2011). The so-called Alcock-Paczynski test (Alcock & Paczynski 1979), based on the idea that the ratio of observed angular size to radial/redshift size varies with cosmology, can be applied to structures for which we know the physical size or the ratio of its extent along the line of sight and its angu-lar size. If, in particuangu-lar, we had a population of standard spheres scattered throughout cosmic history, we could measure the cosmological expansion di-rectly. If such kind of population is absent, the next best thing is a population of objects whose average shape is spherical, as voids are. Thus, cosmic voids could be very powerful candidates for probing the expansion geometry of the Universe: their structure, morphology and dynamics reflect the nature of dark energy, and their evolving ellipticity is extremely sensitive to the DE equation of state (Lavaux & Wandelt 2010).

Voids can also provide information about the amount and nature of dark matter (Martel & Wasserman 1990; Ryden & Melott 1996) and, given their extreme environments, form a natural resort for exploring the imprints of possible modifications of the general theory of relativity, such as f (R) gravity (Li 2011) and MOND/TeVeS (Llinares 2011).

1.3 Clusters of galaxies

Clusters of galaxies are located at the nodes of the filamentary large-scale structure and, together with the filaments that connect them, represent the

12_{The density in the central parts of the voids has a characteristic value of δ}

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1.3. CLUSTERS OF GALAXIES 19 most massive known gravitationally bound structures (i.e. in which the grav-itational force due to the matter overdensity overcomes the cosmic expan-sion) in the present Universe (Borgani et al. 2008). They can contain up to thousands of galaxies and their total mass is typically of the order of 1015_M

. About 70 − 80% of this mass is in the form of dark matter, while

the rest is in the form of galaxies (few %) and hot (T ∼ 108 K), low-density (n ∼ 10−2 − 10−4

cm−3) gas (15 − 20%), which constitutes the intraclus-ter medium (ICM). This diffuse ICM gas emits X–ray radiation via thermal Bremsstrahlung.

Cosmological simulations (Navarro et al. 1995) have shown that galaxy clusters are the result of subsequent merger events of smaller units and inflow of matter along the filaments (e.g. Evrard & Gioia 2002). Analyses of the morphology and temperature distribution of the plasma through deep X-ray observations may provide relevant information about the dynamical state of the cluster in relation to the evolution of the merger. Merger processes are of primary importance to study such kind of structures, because through the shock waves produced in the cluster environment, they are able to re-accelerate the radio-emitting relativistic particles and release a considerable amount of energy into the ICM (e.g. Brunetti et al. 2009).

In a fraction of galaxy clusters, the morphology and extent of the ICM shows a remarkable connection with diffuse, nonthermal radio emission in the form of radio halos and relics.

The origin of diffuse radio emission in galaxy clusters has been a matter of debate for more than a decade now (Jaffe 1977; Dennison 1980). One of the main difficulties which arises when trying to explain its nature is related to the combination of the halo Mpc size and the short radiative lifetime of the relativistic electrons (t ∼ 108 _{yrs, Sarazin 1999). Indeed,}

the radiative lifetime is much smaller than the diffusion time required for these electrons to cover distances of the order of ∼ 1 Mpc. Thus, several theoretical models have been developed in order to investigate the origin of the relativistic particles and the processes through which energy is transferred to them. Among them, we mention those based on re-acceleration of the electrons through shock waves or magnetohydrodynamical turbulence due to cluster mergers (primary models of radio-halo formation, e.g. Schlickeiser et al. 1987; Petrosian 2001; Brunetti & Lazarian 2007, 2011); continuous injection of relativistic electrons over the entire cluster volume by hadronic collisions between cosmic ray protons and ICM thermal protons (secondary models of radio-halo formation, e.g. Dennison 1980; Pfrommer et al. 2008; Ensslin et al. 2011); acceleration of electrons out of the thermal pool; particle injection from radio galaxies, and combination of these processes (Blasi 2003; Brunetti 2003; Petrosian 2003). Accurate analyses of halo spectral indices

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can help to discriminate among different scenarios.

To date, the most accredited model for explaining the radio emission is that based on cluster turbulence (Norman & Bryan 1999), a phenomenon which is considered as the major process responsible for the supply of en-ergy, and thus for the acceleration, of the radiating electrons (Brunetti et al. 2001; Fujita et al. 2003). Such kind of model has been recently supported by analyses of statistical samples of galaxy clusters (Basu 2012; Cassano et al. 2013; Bernardi et al. 2015; Cuciti et al. 2015; Kale et al. 2015).

The model of electron re-acceleration via turbulence diffuse in the cluster volume relates the radio emission with the cluster merging history (Cassano & Brunetti 2005). Hence, diffuse emission is expected to be present mainly in dynamically active clusters, i.e. those influenced by ongoing merger pro-cesses. The study of such kind of clusters allows us to directly investigate the connection between their dynamical state and the presence in them of diffuse radio sources.

Extended diffuse radio emission associated with the ICM has been de-tected to date in about 30 galaxy clusters (e.g. Giovannini et al. 2009; Feretti et al. 2012), the majority of which showing evidence of an ongoing merger. These radio sources are located at the cluster center and typically present a regular shape, a large linear size of ∼ 1 Mpc, a low radio-surface brightness of ∼ 1 µJy/arcsec2 _{(at 1.4 GHz) and a steep spectrum (α . 1)} (Feretti & Giovannini 1996). Their presence demonstrates that the thermal ICM plasma is mixed with nonthermal components, which are large scale magnetic fields (typically in the range 0.1 − 1 µG) and relativistic parti-cles (with Lorentz factor13 _{γ 1000). The study of radio halos is of great}

relevance to provide information on the cluster history and evolution and to improve our knowledge of the cluster-wide magnetic fields and the population of relativistic electrons in the IGM.

Due to the unique sensitiveness of the radio emission to the shock struc-tures and turbulent processes of large scale environments, radio observations are fundamental to investigate galaxy clusters and cosmic LSS. Future ob-servations with the new radio telescopes, such as LOFAR (Low-Frequency Array for Radio astronomy) and SKA (Square Kilometre Array, see Chapter 2), appropriately complemented by X-ray and γ-ray data, will help in mak-ing some steps forward in this direction, particularly focusmak-ing on the study of nonthermal emission in clusters of galaxies.

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1.4. ACTIVE GALACTIC NUCLEI 21

1.4 Active Galactic Nuclei

Active Galactic Nuclei (AGNs) represent the central compact regions of galaxies which possess a luminosity much higher than ordinary, and emit a significant fraction of their energy over almost all the electromagnetic spec-trum (from the radio to the γ-ray band). The host galaxy of an AGN is called Active Galaxy.

The energy emitted by an AGN cannot be attributed to ordinary nuclear stellar processes, but instead derives from accretion of mass onto the super-massive black hole (SMBH) (with mass of 106−10_M

) located at the center

of the host galaxy (Lynden-Bell 1969; Kazanas et al. 2012). In the standard model of AGNs, the infall material, with its own angular momentum, forms a rotating accretion disc of pc-size. The internal frictions convert the potential and kinetic energy into thermal energy, causing the accretion disc to heat up, thus producing a plasma. This rapidly rotating charged material produces a strong magnetic field, inside which the motion of charged particles gen-erates primarily synchrotron radiation, and thermal bremsstrahlung (in the form of X-rays) to a lesser extent. The temperature decreases from the inner to the outer regions. The observed spectrum of an accretion disc peaks in the optical-ultraviolet band. In addition, the disc heats up the surrounding dust which, while sublimating in the nearby regions, produces a dusty torus opaque to radiation at greater distances (out to ∼ 100 pc and beyond).

Not all the material coming from the accretion disc falls onto the rotating black hole; in fact, the excess part is ejected in the form of polar jets of highly collimated and fast outflows emerging in opposite directions from close to the disc. The orientation of the jets is determined either by the angular momentum axis of the disc or the spin axis of the SMBH, and corresponds to the direction along which the material can escape more easily from the strong magnetic field of the black hole. These relativistic jets radiate in all bands, from the radio to the γ-ray range, via the synchrotron emission and the inverse-Compton scattering process14_.

Furthermore, clouds of ionized gas surrounding the galaxy are thought to be present along the direction of the axis of the torus; due to their proper motion, these clouds can shift the frequency of the emitted radiation through the Doppler effect. They can occupy two regions:

• the Broad Line Region (BLR), constituted by compact and very dense clouds (n & 109 cm−3), which being close to the accretion disc (i.e. inside the torus), present a very high rotation velocity. The BLR

orig-14_{For details about the synchrotron emission, thermal bremsstrahlung and}

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inates the broad emission lines (δv & 1000 km s−1) typical of Seyfert 1 galaxies (see below).

• The Narrow Line Region (NLR), composed by extended clouds with low density (n ∼ 102−6_cm−3_{), which being more far away from the disc}

(i.e. outside the torus), have a smaller rotation velocity with respect to the BLRs. The NLR produces the narrow emission lines (δv . 1000 km s−1) typical of Seyfert 2 galaxies.

The conversion of matter into energy is quantified by the following rela-tion:

E = ηmc2, (1.26)

where η ≈ 0.1 is the efficiency. The observed luminosity of accreting black holes is usually explained invoking the Eddington limit (Rybicki & Lightman 1979), which represents the maximum luminosity that can be achieved by a source in hydrostatic equilibrium, i.e. when the outward radiation pressure balances the inward gravitational force:

LEdd= 4πGM•mpc σT ' 3.2 × 104 M• M L. (1.27)

Here M• is the black hole mass, mp is the proton mass, σT is the Thomson

scattering cross-section for the electron, while M and L are the solar mass

and solar luminosity, respectively. A massive black hole has a high Edding-ton luminosity, and as a result, it can provide the observed high persistent luminosity of AGNs. Once the black hole has incorporated all the surround-ing dust and material, the radiatsurround-ing source turns off and the galaxy becomes a “normal” galaxy.

AGNs are usually divided into two classes, wich are conventionally called radio-quiet (RQ) and radio-loud (RL). The emission from RL AGNs is dom-inated by jets and lobes15, while the jet contribution can be neglected in RQ AGNs. The classification is the following:

1. Radio-quiet AGNs

• Seyfert galaxies. These galaxies, mostly spiral, account for about 10% of all galaxies (Maiolino & Rieke 1995) and present very bright quasar-like nuclear regions, but unlike quasars, their host galaxies are clearly detectable (Petrov 2004). They are thought to be powered by a SMBH accreting the surrounding material, i.e. by

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1.4. ACTIVE GALACTIC NUCLEI 23 the same mechanism responsible for the quasar emission, although they are closer and less luminous than quasars. According to the presence or not of broad hydrogen emission lines in their spectra, these galaxies are classified into Seyfert 1 (Sy1) and Seyfert 2 (Sy2), respectively.

• LINERs (Low-Ionization Nuclear Emission-line Regions). These objects represent the lowest-luminosity class of RQ AGNs, and are characterized by weak nuclear emission-line regions.

• Radio-quiet quasars. These sources are described in detail in the following Section.

2. Radio-loud AGNs

• Radio galaxies. These are active galaxies very powerful in the ra-dio band, with luminosities at 1.4 GHz of the order of ∼ 1023−28

W Hz−1. Their nuclear emission is nonthermal and interests the radio, optical and X-ray bands, with the radio emission being due to the synchrotron process. They are typically large elliptical galaxies, in which the radio emitting region, determined by the interaction between the jets and the external medium and modi-fied by the effects of relativistic beaming, is more extended with respect to the optical counterpart by several orders of magnitude. • Blazars. These are very bright objects characterized by sharp

variations in their luminosity.

• OVVs (Optically Violent Variable objects). These sources consti-tute the radio-quiet counterpart of the blazars. They present a rapidly variable component and broad emission lines.

• Radio-loud quasars. These objects are described in detail in the following Section.

1.4.1 Quasars

Quasars (QUASi-stellAR radio sources) represent the most powerful AGNs. They show strong optical continuum emission, broad and narrow emission lines, and strong X-ray emission, together with nuclear and often extended ra-dio emission; in addition, many quasars present a strong UV excess. Quasars were originally ‘quasi-stellar’ in optical images, as they showed a point-like optical counterpart and optical luminosities that were greater than those of their host galaxies; hence, they are often referred to as QSOs (Quasi-Stellar Objects).

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Their emission is dominated by the point-like and very bright core (with size 1 kpc), and their observed luminosity L ∼ 2 × 1013_L

is about 100 times

greater with respect to the optical luminosity of a giant elliptical galaxy. The quasar host galaxies can be spirals, irregulars or ellipticals. There is a correlation between the quasar luminosity and the mass of its host galaxy, according to which the most luminous quasars inhabit the most massive galaxies (ellipticals).

Based on the strength of their radio emission, QSOs are conventionally divided into quiet (RQQs) and loud objects (RLQs). In radio-loud quasars the emission from jets and lobes dominates the AGN luminosity, at least at radio wavelengths but possibly at some or all others. Radio-quiet objects are simpler since jet and jet-related emission can be neglected. It is sometimes necessary to try to distinguish carefully between RLQs and RQQs. A useful criterion (Cirasuolo et al. 2003, 2006) appears to be the radio-to-optical ratio of specific fluxes at 1.4 GHz and 4400 ˚A:

R∗_1.4 ≡ Lν,1.4 GHz

L_ν,4400˚_A . (1.28) For radio-quiet quasars R∗_1.4 _{is generally . 30, while radio-loud objects} typi-cally have R∗_1.4 _{& 30. While this still leaves some ambiguous cases near the} demarcation line, such criterion for “radio-loudness” appears to be appropri-ate.

1.4.2 Quasars in the early Universe

In the last decade tens of quasars at z ∼ 6 have been discovered through var-ious different surveys, starting from the seminal work by Fan et al. (2001a, 2001b, 2001c, 2003, 2006a, 2006b), and then continued by Willott and col-laborators (2005a, 2005b, 2009, 2010a, 2010b; see also Venemans et al. 2007; Jiang et al. 2008, 2009). Nowadays, new surveys as VIKING and PanSTARRS are discovering even more distant quasars (Morganson et al. 2012; Venemans et al. 2013; Ba˜nados et al. 2014). Follow-up observa-tions of emission lines such as the MgII line have shown that these high-redshift quasars (with bolometric luminosities well in excess of 1047 _erg

s−1) are powered by supermassive black holes rapidly grown up to a mass M• ∼ (0.02 − 1.1) × 1010M (Barth et al. 2003; Priddey et al. 2003; Willott

et al. 2003, 2005a; Jiang et al. 2007a; Wang et al. 2010; Mortlock 2011; Wu et al. 2015) in less than a billion years, depending on a still uncertain initial black hole seed (Haiman 2004; Shapiro 2005; Volonteri & Rees 2006; Tanaka & Haiman 2009; Treister et al. 2013; Lupi et al. 2014; Tanaka 2014).

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1.4. ACTIVE GALACTIC NUCLEI 25 This evidence raises several problems about the formation process and growth of these compact objects (Rees 1978; Volonteri 2010; Latif et al. 2013). Several mechanisms are thought to produce SMBH ancestors, such as the collapse of the first generation of stars (PopIII stars) (Tegmark et al. 1997; Madau & Rees 2001; Palla et al. 2002; Shapiro 2005), gas dynamical instabilities (Haehnelt & Rees 1993; Loeb & Rasio 1994; Eisenstein & Loeb 1995; Bromm & Loeb 2003; Koushiappas et al. 2004; Begelman et al. 2006; Lodato & Natarajan 2006), stellar dynamical processes (Begelman & Rees 1978; Ebisuzaki et al. 2001; Miller & Hamilton 2002; Portegies Zwart & McMillan 2002; Portegies Zwart et al. 2004; G¨urkan et al. 2004, 2006; Freitag et al. 2006a, 2006b) and even direct collapse from the gas phase (Haehnelt & Rees 1993; Begelman et al. 2006; Petri et al. 2012; Yue et al. 2013; Ferrara et al. 2014; Yue et al. 2014; Pallottini et al. 2015).

However, the processes responsible for the growth of initial black holes are still unclear, also because the ancestors of supermassive black holes, namely sources with black hole masses of 106−8Mat z > 7, have never been detected

so far in spite of the enormous progresses produced by deep X-ray and IR surveys.

One of the most important observational probes of the growth of SMBHs over cosmic time is represented by the quasar Luminosity Function (QSO LF; e.g. Yu & Tremaine 2002; Li et al. 2007; Tanaka & Haiman 2009). Given that the details of these growth processes are largely uncertain, the LF can provide vital additional inputs to theoretical models. Furthermore, the study of the QSO LF is of great relevance due to several other reasons.

For instance, the evidence of a strong redshift evolution in the quasar/AGN population (Schmidt 1968, 1972; Braccesi et al. 1980; Schmidt & Green 1983; Boyle et al. 1988, 2000; Goldschmidt & Miller 1998; Hewett et al. 1993; Croom et al. 2004; Richards et al. 2006), showing a number density increase of these sources with time up to z ∼ 2.5 followed by a decline16_{(Osmer 1982;}

Warren et al. 1994; Schmidt et al. 1995; Fan et al. 2001b), has challenged our physical understanding so far.

In addition, observations with X-ray surveys (e.g. Hasinger et al. 2001; Giacconi et al. 2002; Alexander et al. 2003; Worsley et al. 2004) have shown that the space density of brighter sources peaks at higher redshifts than those of less luminous objects, a phenomenon known as “cosmic downsizing” of the quasar activity (Cowie et al. 2003; Ueda et al. 2003; Heckman et al. 2004; Merloni 2004; Barger et al. 2005; Hasinger et al. 2005; Croom et al. 2009). Solidly assessing the redshift evolution of the LF shape is then crucially

16_{Due to the peak in AGN activity, z ∼ 2 − 3 has been often designated as the “quasar}

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important to clarify the physical mechanisms of black hole accretion/growth and AGN activity. For example, the bright end of the QSO LF provides information on quasar properties during Eddington-limited accretion phases (Hopkins et al. 2005; Willott et al. 2010b; Jun et al. 2015); the faint end is instead related to the duration of low accretion rate phases (Hopkins et al. 2007).

In addition to QSO internal processes, an accurate determination of high-z QSO LFs might enable us to set more stringent limits on the ionihigh-zing photon production by these sources during the epoch of reionization. This would be a major result as today the relative contribution by stars in galaxies and accreting sources as quasars/AGNs is far cry from being known.

The usual argument against QSOs being important is based on their sharply decreasing number density at z > 3, which prevents AGNs to produce enough ionizing emissivity at z > 4 (Masters et al. 2012). Therefore, the high-z population of star-forming galaxies is thought to be the most natural candidate for the cosmic reionization (e.g. Madau 1991; Haardt & Madau 1996, 2012; Giallongo et al. 1997; Willott et al. 2010a; Bouwens et al. 2012), provided that at least > 20% of the ionizing photons escape into the IGM, a non-trivial requirement.

However, such persuasion has been shaken by the recent results from Giallongo et al. (2015), who found evidence for a new population of faint quasars (−22.5 . MAB1450 . −18.5) at 4 < z < 6.5. Based on these

observa-tions, Madau & Haardt (2015) obtained an upward revision of the comoving AGN emissivity (Q = 2.5 × 1024 erg s−1 Mpc−3 Hz−1), of ∼ 10 times with

respect to Hopkins et al. (2007) (see also Haardt & Madau 2012), and po-tentially sufficient to keep the IGM ionized at z = 6. If these claims will be confirmed, the contribution of quasars to cosmic reionization could be more relevant than previously estimated (e.g. Glikman et al. 2011). However, it is worth noting that the results from Giallongo et al. (2015) are somewhat controversial (e.g. Georgakakis et al. 2015; Kim et al 2015).

It must be noticed that up to now, given the lack of deep AGN surveys at various wavelengths (Shankar & Mathur 2007), only a very small number of low-luminosity quasars (M1450

AB > −24) at z & 6 has been spectroscopically

identified (Willott et al. 2009; Kashikawa et al. 2015; Kim et al. 2015). This implies that both the faint end of the z ∼ 6 LF and the AGN role in reionization remain very uncertain.

Optical/NIR surveys are limited by the fact that high-z quasars are likely to be heavily obscured during their growth phase. In this case one can exploit obscuration-insensitive experiments, as e.g. radio recombination line emission (see Sec. 2.2.3 and Manti et al. 2016). This technique will become possible thanks to the extraordinary capabilities of the SKA telescope in

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1.4. ACTIVE GALACTIC NUCLEI 27 terms of frequency coverage, angular resolution and sensitivity (Morganti et al. 2015), and will allow the detection of even Compton-thick sources.

1.4.3 The Unified Model of AGNs

Universally accepted in 1995, the Unified Model is based on the idea that the way in which we interpret the properties of the different classes of AGNs is strictly related to projection effects, i.e. radio sources are intrinsically similar, but their detected features are significantly influenced by the angle of observation and relativistic phenomena, such as the Doppler boosting17_.

According to the model proposed by Antonucci & Miller (1985), the incli-nation of the obscuring torus around the central SMBH with respect to the line of sight determines the observed type of radio source. If the axis of the torus is perpendicular to the line of sight, then the central regions, including the black hole, the accretion disc and the BLRs, are obscured. What we directly see are the torus, mostly emitting in the IR band, and the narrow emission lines (from the NLR), while the nuclear emission can be reflected by the hot gas in proximity of the torus, which acts like a “mirror”. The source shows weak jets and luminous lobes. On the contrary, if the axis of the torus points toward the observer, what we detect is a very bright point-like core and a strongly amplified emission from the jets; in this case, the broad emission lines from the BLR are visible.

Nowadays, the AGN population as revealed by radio surveys is usually classified into two main categories (originally introduced by Laing et al. 1994): LEG (Low Excitation Galaxies; e.g. Hine & Longair 1979) and HEG (High Excitation Galaxies).

The former AGN class is normally constituted by radio-loud sources, typi-cally associated with FRI radio galaxies. It is characterized by the production of collimated energetic jets, but with little detected emitted radiation (the characteristic luminosity is typically below ∼ 1% of the Eddington limit). The LEGs are associated with very massive black holes and show no evi-dence for substantial recent star-formation. Furthermore, they present weak (or absent) narrow, low ionisation (LINER-like) emission lines. The latter class instead, is usually composed by radio-quiet AGNs (when RL, they are typically associated with FRII radio galaxies). It is associated with popula-tions of lower-mass black holes and composed by old stars with some ongoing star formation. The HEGs are characterized by strong narrow, high ionisa-tion (QSO/Seyfert-like) emission lines.

17_{The Doppler boosting, or relativistic beaming, effect is the process responsible for the}

modification of the apparent luminosity of the jets due to their relativistic motion (the velocities of the jets are close to the speed of light).