Accretion models in active galactic nuclei

Thesis

Reference

Accretion models in active galactic nuclei

ISHIBASHI, Wakiko

Abstract

L'accrétion dans les noyaux actifs de galaxies (AGN) est en général discuté dans le cadre des modèles de disque d'accrétion géométriquement mince et optiquement épais. Mais ces modèles rencontrent des difficultés lorsque les prédictions théoriques sont comparées aux résultats observationnels. Nous étudions ici une forme d'accrétion plus complexe et chaotique où les interactions entre les différents éléments de matière donnent lieu à des chocs. Dans notre modèle la succession ou cascade de chocs est à l'origine du rayonnement ultraviolet et X observé dans les AGN. Nous dérivons un temps caractéristique de variabilité X qui reproduit la relation empirique entre le temps caractéristique, la masse du trou noir, et le taux d'accrétion. Les propriétés spectrales X prédites, en accord avec les observations, pourraient aussi expliquer la relation spectre-variabilité. Nous considérons enfin l'accélération de particules dans les chocs et discutons l'origine de l'émission radio dans différentes classes d'AGN.

ISHIBASHI, Wakiko. Accretion models in active galactic nuclei. Thèse de doctorat : Univ.

Genève, 2011, no. Sc. 4313

URN : urn:nbn:ch:unige-166954

DOI : 10.13097/archive-ouverte/unige:16695

Available at:

http://archive-ouverte.unige.ch/unige:16695

Disclaimer: layout of this document may differ from the published version.

Accretion Models in

Active Galactic Nuclei

Th` ese

pr´esent´ee `a la Facult´e des sciences de l’Universit´e de Gen`eve pour obtenir le grade de Docteur `es sciences,

mention Astronomie et Astrophysique

par

Wakiko (Wako) Ishibashi

de

Kyushu (Japon)

Th`ese N^o 4313

Le ph´enom`ene de noyaux actifs de galaxies (Active Galactic Nuclei ou AGN) est attribu´ee `a l’accr´etion de mati`ere dans le potentiel gravitationnel du trou noir su- permassif pr´esent au centre des galaxies. Dans le processus d’accr´etion, une fraction de l’´energie gravitationnelle de la mati`ere en effondrement est convertie en ´energie radiative.

La plupart des mod`eles d’accr´etion, aussi bien dans les syst`emes binaires que dans les noyaux galactiques, sont bas´es sur le paradigme du disque d’accr´etion. Le mod`ele standard pr´esume un disque d’accr´etion g´eometriquement mince et optiquement

´epais (Shakura & Sunyaev 1973). Mais les mod`eles de disque d’accr´etion rencon- trent des difficult´es lorsque ses pr´edictions sont compar´ees aux observations des AGN (Koratkar & Blaes 1999). En effet, certaines propri´et´es observ´ees, comme les corr´elations de variabilit´e entre les courbes de lumi`ere observ´ees `a diff´erentes longueurs d’onde, l’origine de l’´emission `a haute ´energie (rayons X durs), et la na- ture de la viscosit´e, sont difficiles `a expliquer dans le cadre du mod`ele de disque.

Plusieurs modifications ont ´et´e apport´ees au mod`ele standard de disque d’accr´etion, avec l’introduction d’´el´ements additionnels, tels que par exemple des couronnes op- tiquement minces entourant le disque optiquement ´epais. Ces mod`eles sont ainsi devenus toujours plus complexes sans pour autant ˆetre compl`etement satisfaisants.

Vu les difficult´es du mod`ele de disque d’accr´etion, il est int´eressant de consid´erer des solutions alternatives et d’´etudier d’autres formes d’accr´etion dans les AGN. Con- trairement au cas des syst`emes binaires, l’accr´etion dans les AGN suit une forme plus complexe et chaotique, avec la mati`ere accret´ee sous forme d’´el´ements individuels (clumps) et caract´eris´ee par une distribution de moment cin´etique. Les interactions entre les diff´erents ´el´ements donnent lieu `a des collisions physiques ou chocs (Cour- voisier & T¨urler 2005). Nous ´etudions par la suite les propri´et´es radiatives r´esultant de la succession de chocs dans le flot d’accr´etion et comparons les r´esultats de notre mod`ele avec les observations.

La collision entre deux clumps forme tout d’abord un choc optiquement ´epais suivi d’une expansion rapide, semblable `a une explosion de supernova. Suite `a la col- lision, une fraction de l’´energie cin´etique est convertie en ´energie radiative. La temp´erature photosph´erique que nous estimons est de quelques∼10⁴K, correspon- dant `a la temp´erature de l’´emission primaire visible/UV observ´ee dans les AGN.

Au-del`a du rayon photosph´erique, l’enveloppe gazeuse devient optiquement mince,

et les enveloppes provenant de diff´erents ´ev´enements interagissent entre elles dans les r´egions internes. Il se forme alors une deuxi`eme g´en´eration de chocs, cette fois-ci dans des conditions optiquement minces. Le refroidissement des ´electrons par ray- onnement Compton inverse conduit `a l’´emission de rayons X. Dans notre mod`ele, la succession ou cascade de chocs est `a l’origine du rayonnement observ´e dans les AGN:

les chocs optiquement ´epais et optiquement minces donnent lieu aux composantes UV et X, respectivement. Les rapports des luminosit´es X/UV que nous calculons sont en accord avec les rapports observ´es (Ishibashi & Courvoisier 2009a).

La variabilit´e de l’´emission X est une propri´et´e caract´eristique des AGN. Les ob- servations sugg`erent l’existence d’une ´echelle de temps caract´eristique de variabilit´e d´etermin´ee par la masse du trou noir central et le taux d’accr´etion (McHardy et al.

2006). Nous d´erivons un temps caract´eristique de variabilit´e X du mod`ele que nous comparons avec le temps caract´eristique associ´e au ‘break’ mesur´e dans le spectre de puissance (Ishibashi & Courvoisier 2009b). Nous obtenons une d´ependance du temps caract´eristique X sur la masse du trou noir et le taux d’accr´etion, reproduisant exactement la relation empirique de McHardy et al. (2006).

Le spectre des AGN dans le domaine des rayons X durs est en g´en´eral mod´elis´e par une loi de puissance. En nous basant sur les solutions analytiques exactes pour l’indice spectral donn´ees par Titarchuk & Lyubarskij (1995), nous calculons la pente spectrale de la loi de puissance `a partir de la temp´erature des ´electrons et de la pro- fondeur optique d´eriv´ees dans le cadre de notre mod`ele. Les relations pr´edites entre l’indice spectral et le taux d’accr´etion pourraient expliquer les corr´elations observ´ees dans diff´erents ´echantillons d’AGN (Ishibashi & Courvoisier 2010).

Comme le mod`ele d’accr´etion ´etudi´e ici est bas´e sur une s´equence de chocs, il est aussi naturel de consid´erer l’acc´el´eration de particules dans les chocs et le rayon- nement synchrotron associ´e. Nous estimons la luminosit´e radio ´emis par le proces- sus synchrotron, et nous proposons les chocs comme une possibilit´e pour l’origine de l’´emission radio dans certaines classes d’AGN (Ishibashi & Courvoisier 2011).

La Th`ese est structur´ee comme suit. Dans la premi`ere partie, nous rappelons les

´

el´ements de base de l’accr´etion sur les trous noirs et d´ecrivons les propri´et´es car- act´eristiques des noyaux actifs de galaxies. Nous ´etudions ensuite la th´eorie du disque d’accr´etion, et nous analysons en particulier les difficult´es du mod`ele stan- dard. Dans la deuxi`eme partie, nous pr´esentons les principaux r´esultats obtenus dans le cadre de notre mod`ele d’accr´etion que nous comparons avec les observations.

La th`ese se termine sur une courte description du travail fait en relation avec les op´erations scientifiques du satellite INTEGRAL pour lequel l’ISDC est responsable.

1 Introduction 1

2 Accretion onto black holes 5

2.1 Black holes in General Relativity . . . 6

2.1.1 Schwarzschild metric . . . 6

2.1.2 Kerr metric . . . 7

2.2 The accretion luminosity . . . 9

2.3 The Eddington limit . . . 10

2.4 Accretion onto astrophysical black holes . . . 12

2.4.1 Supermassive black holes in active galactic nuclei . . . 13

2.4.2 Stellar-mass black holes in binary systems . . . 19

2.5 On the scale invariance of accreting black holes . . . 25

3 Active Galactic Nuclei 27 3.1 AGN classes and classification . . . 27

3.1.1 Quasars . . . 27

3.1.2 Seyfert galaxies . . . 28

3.1.3 Low-luminosity AGN (LLAGN) . . . 29

3.1.4 Blazars . . . 30

3.1.5 Radio galaxies . . . 31

3.2 Spectral Energy Distribution (SED) and physical components . . . . 33

3.2.1 The blue bump . . . 34

3.2.2 X-rays . . . 38

3.2.3 Infrared emission and the obscuring torus . . . 41

3.2.4 Radio emission and the relativistic jet . . . 43

3.3 The radio-loud/radio-quiet dichotomy . . . 44

3.4 Unified models . . . 47

3.4.1 Unification by obscuration . . . 47

3.4.2 Unification by beaming . . . 50

4 Accretion disc theory 51 4.1 Conservation laws . . . 53

4.2 Steady state discs . . . 54

4.3 Accretion disc spectrum . . . 55

4.4 Accretion disc timescales . . . 58

4.5 The nature of viscosity . . . 59

4.5.1 Magneto-rotational instability (MRI) . . . 60

5 Difficulties of standard accretion disc models 63 5.1 Spectral shape of the blue bump component . . . 64

5.2 Quasi-simultaneity of optical/UV variations . . . 65

5.3 The origin of X-ray emission and the X-ray to blue bump luminosity ratio . . . 66

5.4 Other observational problems . . . 67

5.4.1 Lyman edge . . . 68

5.4.2 Polarisation . . . 68

5.4.3 Double-peaked line profiles . . . 68

5.4.4 Variability correlations . . . 68

5.5 Instabilities . . . 70

5.6 The angular momentum problem . . . 71

6 Other forms of accretion 75 6.1 Clumpy accretion flows: a cascade of shocks? . . . 77

7 UV and X-ray luminosities 79 7.1 Optically thick shocks and optical/UV emission . . . 81

7.2 Optically thin shocks and X-ray emission . . . 82

7.3 Model classes and identification with AGN classes . . . 83

7.4 X-ray and UV luminosity components: the modelLX/LU V ratio . . 84

7.5 Comparison with observations . . . 85

7.6 Paper I (2009a, A&A, 495, 113) . . . 89

8 X-ray variability 97 8.1 Power Spectral Density (PSD) . . . 98

8.2 Measurements of PSD break timescales in AGN . . . 99

8.3 The variability Fundamental Plane . . . 100

8.4 Physical origin of the break timescale . . . 102

8.4.1 Accretion disc timescales . . . 102

8.4.2 Propagating fluctuations . . . 103

8.4.3 Clumpy accretion . . . 105

8.5 Paper II (2009b, A&A, 504, 61) . . . 107

9 X-ray spectra 113 9.1 Compton processes . . . 114

9.1.1 Comptonisation . . . 115

9.2 Analytical estimates of the power law slope . . . 116

9.3 Applications to coronal models . . . 119

9.4 X-ray power law spectra: observational results . . . 120

9.4.1 Measurements of the photon index Γ . . . 120

9.4.2 The Γ−L/LE and Γ−MBH relations . . . 121

9.4.3 Spectral-timing relation . . . 123

9.5 Interpretation within the clumpy accretion scenario . . . 124 9.6 Paper III (2010, A&A, 512, A58) . . . 127

10 Synchrotron radio emission 133

10.1 Synchrotron theory . . . 134 10.2 Synchrotron radiation in clumpy accretion flows . . . 136 10.3 Comparison with observations . . . 138 10.4 Implications on the origin of radio emission in radio-quiet AGN . . . 140 10.5 Paper IV (2011, A&A, 525, A118) . . . 143

11 Conclusions and future perspectives 149

A INTEGRAL-related activities 153

A.1 INTEGRAL . . . 153 A.2 Shifts at ISDC . . . 155

B List of publications 157

C Acknowledgements 159

List of Figures 167

List of Tables 169

Bibliography 177

Introduction

Accretion of matter into the deep gravitational potential well of a black hole is con- sidered as the solution to explain the extraordinary activity observed at the centre of galaxies. The gravitational energy of accreting matter is converted into radiative energy, which is eventually released as electromagnetic radiation. The conversion ef- ficiency is much greater in the case of accretion onto black holes, compared to nuclear reactions occurring in stellar interiors. Moreover, the stability of black holes ensures that the accreting system can be powered over cosmological timescales. Finally, black holes are thought to constitute an inevitable endpoint of any astrophysical system, through the evolution and collapse of dense stellar clusters (Rees 1984).

The efficiency, stability, and inevitability arguments strongly favour the black hole hypothesis (Blandford 1990).

A black hole itself does not radiate, and its presence can be revealed only through its gravitational influence on the surrounding environment. Accretion onto black holes is closely coupled with emission of high-energy photons, and the strongest ob- servational evidence for black holes come from observations of X-ray binary systems.

Indeed the detection of X-rays from stellar binary systems, in which the compact object exceeds the maximum stable mass predicted by general relativity, might be considered as a proof of the existence of black holes (Shakura & Syunyaev 1973).

Today, around twenty such stellar-mass black holes, known as black hole binaries, are observed in our Galaxy (Remillard & McClintock 2006).

Supermassive black holes, with masses of million to billion of solar masses, are be- lieved to exist at the centre of galaxies. In some cases, the accretion process onto these central black holes shows extreme activity, leading to the phenomenon of Ac- tive Galactic Nuclei (henceforth AGN). AGN are characterised by huge luminosities coming from tiny volumes, and radiate over the entire electromagnetic spectrum, from radio waves to γ-rays. The broad-band emission is observed to vary on a range of timescales, from a few hours to several years. Broad emission lines, in- dicating gas velocities of several thousand km/s, are observed in their optical-UV spectra. In some sources, spectacular radio structures, such as collimated radio jets and giant radio lobes, are observed to extend from the central nucleus up to in-

tergalactic scales. All these characteristic features of AGN are uncommon among normal galaxies, formed by an ensemble of stars. Thus AGN have also been defined as energetic phenomena occurring in galactic nuclei, which cannot be directly at- tributed to stellar activity. The great nuclear luminosity of AGN is found to vary on short timescales, of order days. Causality arguments then provide constraints on the size of the source, since flux variations cannot propagate on timescales shorter than the light crossing time. This implies that the size of the continuum-emitting region must be of order light-days. The surprising result is that the luminosity of an entire galaxy is emitted from a region of size comparable to our solar system. This combination of large luminosity and rapid variability is one of the strongest support for accreting black holes.

The variety of phenomena observed in AGN is ultimately attributed to the accretion process. In general, accreting matter has non negligible angular momentum with respect to the central black hole, and needs to loose most of its specific angular mo- mentum in order to be swallowed by the black hole. For a given angular momentum, the orbit of least energy is a circular orbit. At a given distance, where gravitational forces are balanced by centrifugal forces, accreting material starts to rotate follow- ing circular orbits, leading to the formation of an accretion disc. In a differentially rotating disc, particles lose angular momentum through friction between adjacent layers, slowly spiraling toward the central black hole. Viscosity causes dissipation in the disc; the energy dissipated in the fluid is eventually released as radiation.

The accretion disc in fact provides an efficient way to convert gravitational energy into radiation (Pringle 1981) and accretion in AGN is most generally discussed in the framework of the accretion disc model (Lynden-Bell 1969). In a standard, ge- ometrically thin and optically thick accretion disc, the outward transfer of angular momentum is attributed to some form of viscosity, which is parametrised in the famousα-prescription (Shakura & Syunyaev 1973).

However, standard accretion disc models are known to face a number of difficul- ties when compared with observations of AGN (Koratkar & Blaes 1999). Several observational properties are indeed difficult to explain within disc models, such as the quasi-simultaneity of the optical and UV variations, the similarities in the UV spectral features observed in different sources, and the origin of hard X-ray emission.

Different modifications have been proposed, with the introduction of additional el- ements, such as irradiation and coronal structures, leading to more or less complex variants of the simple disc model.

Given the difficulties met by standard accretion disc models in explaining the ob- served AGN properties, one can consider alternative scenarios for the fueling of the central black hole. In view of the interest in widening the study of accretion modes in AGN, here we study a somewhat different form of accretion. We expect accretion in AGN to follow more complex and chaotic flows than in the well-ordered disc ac- cretion case, since accreting matter in AGN arrive from a range of directions with a distribution of angular momentum. We consider clumpy accretion flows, due to the

presence of density contrasts and inhomogeneities within the accreting material. In this picture, interactions or shocks between different accreting elements (clumps) are at the origin of the observed radiation. Accretion proceeds via a sequence of shocks, in which optically thick shocks give rise to optical/UV emission, while optically thin shocks lead to X-ray emission. This cascade of shocks accounts for the different emission components of AGN. We study the resulting luminosity, variability, spec- tral, and particle acceleration properties within this framework, and compare our model results with observations.

The present Thesis is structured as follows. In the first part, we summarise the general properties of AGN, and present the standard accretion disc theory; in the second part, we describe the main results obtained in this Thesis. The detailed derivations are given in the corresponding publications placed at the end of each Chapter (Chapters 7-10). We first recall some basics of black hole physics and introduce the two main families of accreting black holes existing in the Universe, i.e.

active galactic nuclei and black hole binaries (Chapter 2). The different AGN classes, their spectral energy distribution, and possible unification scenarios are discussed in Chapter 3. We review the standard accretion disc theory in Chapter 4 and analyse its difficulties in Chapter 5. The general framework of our accretion model is introduced in Chapter 6. We start by analysing the properties of the UV and X-ray emission components and their relation within the clumpy accretion scenario (Chapter 7).

We then study the X-ray variability properties (Chapter 8) and investigate the X- ray spectral properties (Chapter 9) within this framework. Shocks are known to be an efficient mechanism of particle acceleration, we thus discuss the resulting synchrotron radio emission in Chapter 10. Some general conclusions are mentioned in the final Chapter (Chapter 11), where we also sketch possible directions for future developments.

Accretion onto black holes

The gravitational potential energy released by accretion of a massm onto a central body of massM and radiusR is

∆E_acc= GM m

R . (2.1)

A fraction of the gravitational energy is converted into radiative energy, and will eventually be released as electromagnetic radiation. The efficiency of the accretion process is determined by the compactness parameter, given by the mass-to-radius ratio (M/R) of the accreting object. The M/R ratio is maximised in the case of compact objects, with large masses contained within small radii, such as black holes.

The accretion efficiency associated with accretion onto black holes is of the order of∼0.1. This is to be compared with the efficiency of∼0.007 of ordinary nuclear reactions occurring in stars. The most luminous objects in the Universe, such as quasars, are thus believed to be powered by accretion in the deep gravitational po- tential well of the central black hole. In addition, there are a number of observational features, such as rapid X-ray variability and relativistic radio jets, that are difficult to interpret without invoking the presence of black holes. Therefore the great variety of phenomena observed in active galactic nuclei (AGN) is now interpreted in terms of black hole models (Rees 1984).

Black holes are thus at the basis of all the observed AGN phenomenology. The physics of black holes is discussed in many classical textbooks on general relativity.

Here we recall the main mathematical properties of Schwarzschild and Kerr black holes, following Courvoisier (2011). We then discuss general aspects of the accretion mechanism and introduce the Eddington limit. Accretion processes in different as- trophysical sources are reviewed in Frank et al. (2002). Two forms of astrophysical black holes are observed in nature: stellar-mass black holes in binary systems and supermassive black holes in galactic nuclei. We briefly discuss the main characteris- tics of the two families, and mention the possible scale invariance relating accreting black holes of different scales.

2.1 Black holes in General Relativity

The Einstein equation relates the space-time curvature density to the density of mass-energy:

Gµν =κTµν, (2.2)

whereGµν =Rµν−¹₂Rgµν is the Einstein curvature tensor,κ= ^8πG_c4 is the coupling constant, andT_µν is the stress-energy tensor. Thus the matter content (T_µν) deter- mines the geometry (G_µν) of space-time.

2.1.1 Schwarzschild metric

The Schwarzschild solution is a solution of the Einstein equation in vacuum, which describes a spherically symmetric metric about a point massM. The Schwarzschild metric is given by ¹

ds² =

1−2GM rc²

dt²− 1 c²

"

1

1−^2GM_rc2 dr²+r²dΩ²

#

, (2.3)

wheredΩ²=dθ²+ sin²θ dφ².

From Eq. (2.3) we see that the Schwarzschild metric has two singularities. The singularity at the origin (r = 0) is a real physical singularity, in which curvature is infinite and matter collapses into a singular point. The singularity at r = ^2GM_c2 is an apparent singularity, coming from the choice of the particular coordinate system.

The radial distance r = RS = ^2GM_c2 has a particular significance and is known as the Schwarzschild radius. According to general relativity, no radiation can escape from within the Schwarzschild radius and this defines the event horizon of the black hole. Note that the Schwarzschild black hole has a spherical symmetry and can be characterised by one single parameter, the massM of the black hole.

The equation of motion for a particle in the gravitational field is given by 1

c² dr

dτ 2

+V²(r) =E², (2.4)

where we consider the proper timeτ, and E is the energy per unit mass.

The effective potential V(r) is given by V²(r) =

1− 2GM

rc² 1 + l² r²c²

, (2.5)

1We leave the dimensional constants, the gravitational constantGand the speed of lightc (cf Longair (1994)).

wherelis the angular momentum per unit mass.

Circular orbits (r=r_c= cst) occur forδV /δr= 0:

r_c= l²± q

l⁴−12l^2G2_c^M4 ²

2GM c²

. (2.6)

The innermost stable circular orbit (ISCO) is located at:

r_c= 6GM

c² (= 3R_S), (2.7)

withl= 2√ 3^GM_c2 .

The binding energy of a particle is given by the difference between the rest mass energy of the particle and its energy at infinity:

E_b= 1−E. (2.8)

For a circular orbit, ^dr_dτ = 0, which implies E² = V²(r), and considering the last stable orbit (r =r_c, l= 2√

3^GM_c2 ) one obtains:

E_b= 1− r8

9

∼= 0.057. (2.9)

The maximal accretion efficiency is given by the binding energy at the last stable orbit, which is of the order of∼6% for a non-rotating Schwarzschild black hole.

2.1.2 Kerr metric

According to the no-hair theorem of general relativity, a black hole resulting from gravitational collapse is characterised by only two parameters, mass and spin, and is described by the Kerr metric. The Kerr metric is a solution of the Einstein equation in vacuum and describes the space-time around a rotating black hole. In the Boyer-Lindquist coordinates, the Kerr metric has the form

ds²=

1− 2GM r Σc²

dt²− 1 c²

4GM rasin²θ

Σc dtdφ

−1 c²

Σ

∆dr²+ Σdθ²+

r²+a²+2GM ra²sin²θ Σc²

sin²θdφ²

, (2.10)

where a := _{M c}^J is the angular momentum of the black hole per unit mass, ∆ :=

r²−^{2GM r}_c2 +a², and Σ :=r²+a²cos²θ.

The metric coefficients are independent oft andφ, and thus the Kerr metric is sta- tionary and axisymmetric. Note that the Kerr metric reduces to the Schwarzschild metric in the limit of no-rotation (a= 0).

As in the case of the Schwarzschild black hole, the Kerr metric has two singularity points. The singularity at Σ = 0 is the real physical singularity. The singularity at

∆ = 0 is an apparent singularity and defines the horizon of a rotating black hole:

r₊= GM c² +

"

GM c²

2

− J

M c 2#1/2

. (2.11)

If the angular momentumJ of the system is too large, no black hole will be formed.

The maximum allowed value isJ = ^GM_c². For a maximally rotating Kerr black hole, the event horizon is located at

r₊= GM

c² . (2.12)

The dragging of inertial frames leads to the existence of a critical radius, known as the static limit, within which all particles must corotate with the black hole. The static radius r_stat, is located at

r_stat= GM c² +

"

GM c²

2

− J

M c 2

cos²θ

#1/2

. (2.13)

The region between the static limit and the event horizon, from which particles can still escape, is called the ergosphere.

Figure 2.1: Schematics of a rotating black hole. The ergosphere is located between the outer event horizon and the static limit. Particles in the ergosphere can still escape, and energy may be extracted via the Penrose process. (from hubblesite.org)

Although the Kerr metric has only a cylindrical geometry, circular orbits can be defined in the equatorial plane. For a Kerr black hole, the location of the innermost stable circular orbit (ISCO) depends on the direction of rotation of a particle with respect to that of the black hole. In the case of a maximally rotating Kerr black hole, the last stable orbit is located at r =r+ =GM/c² for co-rotating particles, and atr =r₊ = 9GM/c² for counter-rotating particles.

The maximal accretion efficiency is given by the binding energy at the co-rotation radius

E_b= 1− 1

√3

∼= 0.423, (2.14)

and is of the order of 42%.

We see that the efficiency for maximally rotating Kerr black holes is much higher (∼0.42) than in the case of Schwarzschild black holes (∼0.06).

Figure 2.2: Location of the innermost stable circular orbit (ISCO, in units of the gravita- tional radius) as a function of the spin parameter. The ISCO is at 6Rg for a non-rotating Schwarzschild black hole, while it is at 1Rg for a maximally rotating Kerr blalck hole. From Miller (2007).

2.2 The accretion luminosity

The gravitational potential energy around a central massM with radiusR is given by

U = GM m

R . (2.15)

This is the maximal energy that can be released by accretion of a mass m onto the central mass M. We have seen that the efficiency of the accretion process is determined by the compactness parameter of the accreting object, given by the mass-to-radius ratioM/R. The accretion efficiency is greater for more compact sys- tems, i.e. having larger values of the M/R parameter.

In the case of black holes, the gravitational radius is proportional to the black hole mass:

R_g = GM

c² ∝M, (2.16)

and thus theM/R ratio does not depend on the mass of the black hole. The accre- tion efficiency is thus independent of the mass of the central object and only depends on the location of the last stable orbit, which is set by the black hole spin.

The rate of potential energy release of the accreting matter is dU

dt = GM R

dm

dt = GMM˙

R , (2.17)

and the accretion luminosity is given by L≈·GMM˙

R , (2.18)

where is a dimensionless parameter measuring the efficiency of the conversion of rest mass into radiation.

Expressing the radius of the compact object in units of the gravitational radius, R_g = ^GM_c2 , the luminosity is written as

L=M c˙ ². (2.19)

The radiative efficiency depends on the location of the innermost stable circular orbit, which is determined by the black hole spin. A canonical value of ∼0.1 is usually adopted.

2.3 The Eddington limit

The luminosity released by the accretion process cannot exceed a maximal value, known as the Eddington luminosity. The Eddington limit sets the maximal lumi- nosity over which forces due to the outward radiation pressure exceed those due to the inward gravitational attraction.

Consider a steady, spherically symmetric accretion, and assume that the accreting matter is composed of ionised hydrogen. The outward force of radiation pressure

must be counter-balanced by the inward force of gravity. The radiative energy flux is

S = L

4πr². (2.20)

The momentum carried by a photon, of energyE =hν, is p= E

c. (2.21)

The outward momentum flux, or radiation pressure, is given by Prad = F

c = L

4πr²c. (2.22)

The outward force of radiation acting on each electron is obtained by multiplying the radiation pressure by the Thomson cross section

Frad =Prad·σT = F

c = L

4πr²c ·σT. (2.23)

Due to the attractive electrostatic Coulomb interactions, electrons drag protons in their outward motion.

The total gravitational force acting on an electron-positron pair is F_grav = GM(m_p+m_e)

r²

∼= GM m_p

r² , (2.24)

asmemp.

Equating the outward radiation force and the inward gravity force:

Lσ_T

4πr²c = GM mp

r² , (2.25)

we obtain the Eddington luminosity:

L_E = 4πGcm_p σT

M. (2.26)

This sets the maximum luminosity beyond which the outward pressure of radiation would exceed the inward gravitational attraction. This prevents further accretion of matter, and in a naive picture, the excess material is expelled in the form of a wind or outflow which sweeps away the surrounding material. Thus outflows are a natural consequence of super-Eddington accretion.

We note that the Eddington luminosity is only determined by the central mass:

LE ∝M. (2.27)

The Eddington limit also sets the corresponding Eddington accretion rate, M˙_E, defined as

M˙_E = LE

c². (2.28)

In the literature, the accretion rate is often expressed in terms of the Eddington ratio, _L^L

E, defined as a fraction of the Eddington luminosity.

We have seen that the Eddington luminosity is proportional to the black hole mass, LE ∝ M (Eq. 2.27). Moreover, assuming that the luminosity scales with the accretion rate,L∝M˙ (Eq. 2.19), the Eddington ratio can be written as

L

L_E ∝ M˙

M_BH. (2.29)

2.4 Accretion onto astrophysical black holes

An astrophysical black hole is uniquely defined by two fundamental parameters:

mass and spin (electric charge is not relevant in this case, and it is assumed that black holes are electrically neutral). However, the sole presence of a black hole in vacuum is not a sufficient condition to explain the variety of phenomena observed in galactic nuclei and binary systems; interactions with the surrounding environment, in the form of accretion of matter, need to be considered. Thus, in addition to mass and spin, the accretion rate becomes another fundamental parameter.

There exists two main families of accreting black holes in the Universe: stellar- mass black holes (MBH ∼10M) in binary systems, and supermassive black holes (M_BH ∼10⁶−10⁹M) in galactic nuclei. ² At least eight orders of magnitudes are covered in the mass range, from stellar-mass to supermassive black holes. Introduc- ing the dimensionless spin parameter, defined asa? =J/Jmax =cJ/GM², the spin parameter varies froma_? = 0 for a non-rotating Schwarzschild black hole toa_? = 1 for a maximally rotating Kerr black hole. We have seen that the black hole spin determines the location of the innermost stable circular orbit (ISCO), which in turn determines the accretion efficiency given by the binding energy at the last stable orbit. The corresponding theoretical accretion efficiency varies from ∼ 0.06 for a stationary Schwarzschild black hole to∼0.42 for a maximally rotating Kerr black hole. But in real astrophysical situations, one has to take into account the radiation emitted by the accretion disc and the capture of photons by the black hole. This produces a counter-acting torque that prevents spin-up beyond a limiting state. The corresponding maximum radiative efficiency is of the order of∼30% (Thorne 1974).

2There might be an intermediate population of intermediate-mass black holes, with masses in the rangeMBH∼10²−10⁴M, such as in ultra-luminous X-ray sources (ULXs).

The black hole mass can be measured relatively far from the black hole (by reverber- ation mapping techniques) and the difference in mass between black hole binaries and AGN is quite clear.

Figure 2.3: Predicted line profiles for a non-rotating Schwarzschild black hole (red) and for a maximally rotating Kerr black hole (blue). The difference in the line profiles is clearly seen. The asymmetry in the line profile, and in particular the extent of the red wing, are determined by the black hole spin. The analysis of iron line profiles thus provides a method of black hole spin measurement. From Miller (2007).

But measurements of the spin parameter are more subtle, and need to be performed in the immediate vicinity of the black hole. In this context, the analysis of X-ray emission, originating within a few gravitational radii from the centre, provides useful diagnostics of the innermost accretion flow. The profile of the broad iron line seen in the X-ray spectra of accreting black hole systems, provides important constraints on the spin parameter. The spin of the black hole in binary systems is thought to be set by the original spin of the precursor star. By contrast, the black hole spin in AGN evolves as a result of the accretion history, depending on whether matter has been accreted in prolonged disc-mode accretion with constant angular momentum, or from more chaotic accretion episodes with random angular momenta (Volonteri et al. 2007; King et al. 2008). Therefore there are complex interplays between the three fundamental parameters, with the accretion mode affecting both the mass and spin evolution of the accreting system.

2.4.1 Supermassive black holes in active galactic nuclei

The high luminosities observed in AGN imply large central masses, and supermas- sive black holes, with masses in the range ∼10⁶−10⁹M, are believed to exist at the centre of galactic nuclei. The Eddington luminosity for a typical massive AGN is

L_E ∼= 1.3·10⁴⁷

M 10⁹M

erg/s, with a corresponding Eddington ratio of∼20M/yr.

Below we briefly introduce the main characteristics of AGN, which will be discussed in more detail in Chapter 3. AGN are reviewed in a number of textbooks, including Krolik (1998) and Peterson (1997). Observational and theoretical aspects of AGN physics are discussed in the Saas-Fee Lecture Notes 1990 (Blandford et al. 1990).

Broad-band continuum

The emission of AGN covers the whole electromagnetic spectrum, extending from radio waves to γ-rays. The luminosity per energy band is roughly constant over several orders of magnitude in frequency, and the spectrum is relatively flat from the infrared domain to the X-rays. This is in clear contrast with the spectra of nor- mal galaxies, in which the radiative power is confined within a narrow wavelength range, mainly centered in the optical region. In fact, the fractions of the bolometric luminosity emitted in the radio and X-ray bands are several orders of magnitude larger in AGN than in normal galaxies.

Figure 2.4: Comparison of the Spectral Energy Distribution (SED) of an AGN (Seyfert 1 galaxy NGC 3783, black dots) and a normal galaxy (type Sbc, thin black line). The typical spectrum of a normal galaxy, formed by an ensemble of stars, is confined within a narrow wavelength range with a peak in the optical/UV region. In contrast, the spectrum of the AGN extends from the radio domain to theγ-rays. From Peterson (1997).

The Spectral Energy Distribution (SED) can be plotted as flux density (Fν) versus frequency (ν) in logarithmic scales. The overall SED can be roughly modelled by a power law, of the form Fν ∝ν^−α, with α ∼ 1. This means that the continuum is

broad-band, with no strong domination by one particular energy domain, although local maxima are present. In a logFν versus logνplot, the power law is the primary component, with an excess emission observed in the optical/UV region, referred to as the (big) blue bump. Alternatively, the AGN spectra are often plotted in the so-called ‘νFν representation’, as log (νFν) versus log ν. In this representation the dominant power law component (with slope α ∼1) becomes a flat horizontal line.

A peak in this representation indicates the energy range where most of the radiative power is emitted. Deviations from the primary power law component are emphasized in the luminosity plot, and we can distinguish the different emission components in- dicating distinct physical cooling mechanisms.

Figure 2.5: The overall average SED of the bright quasar 3C 273 in the Fν vs. ν rep- resentation (top panel) and in the νFν representation (bottom panel). To a zeroth order approximation, the spectrum can be described by a power law,Fν∝ν⁻¹. In theνFν plot, the flux is observed to be roughly constant over several orders of magnitude in frequency with two local maxima, one in the far ultraviolet and the other around 1 MeV. The excess continuum with a peak near 10 eV, is known as the (big) blue bump. The contributions of the outer jet (green line) and of the host elliptical galaxy (blue line) are also shown. From ISDC.

High energy radiation is another characteristic feature of AGN, with emission ob- served to extend up to the TeV domain in some objects. The most common feature is the X-ray emission; a significant fraction of the bolometric luminosity is emitted in the X-rays, and new AGN have been discovered in X-ray surveys. A spectral steepening is observed in the X-ray spectra of AGN at very high energies, with pos- sible cut-offs around several hundred keV. In fact, a limit on the X-ray emission is imposed by the diffuse X-ray background (XRB): a cut-off must occur in order to ensure that the flux in the X-ray background is not exceeded. Thus the X-ray background provides an integral constraint on the total flux emitted by active nu- clei. Radio emission is also a distinguishing mark of AGN, especially in a historical perspective. The first quasars were indeed discovered as quasi-stellar objects (QSO) identified with bright radio sources. However, we now know that strong radio emis- sion is rather a particularity associated with relativistic jets in radio-loud objects, and that these objects only form a minority of the total AGN population.

Line emission

Strong emission lines are observed in the optical/UV spectra of AGN. This is to be contrasted with the weak lines and in absorption seen in normal galaxies. It is assumed that lines of the same element, with the same width, arise from the same emission region. Line emission is very efficient in high-density gas, as the emis- sivity per unit volume increases as n²_e. Blend of lines can sometimes produce fake continuum-like features, leading to the so-called cosmic conspirancy.

Emission lines can have broad and narrow components. The broad components have Doppler widths corresponding to velocities typically in the 1000-10’000 km/s range, and arise in gas of high density (n_e >10⁹cm⁻³) known as the Broad Line Region (BLR); whereas the narrow components have Doppler widths usually less than 500 km/s, and arise in relatively low-density (ne≈10³cm⁻³) gas called the Narrow Line Region (NLR). It is interesting to note that the average emission line spectra are observed to be very similar in different objects. This suggests that the physical parameters, such as temperature, particle density, and ionisation states, are similar in different sources.

The emission-line fluxes are observed to vary with the continuum flux, but with a certain time delay. This suggests that the line-emitting gas is photoionised by the central engine, with the photoionisation equilibrium attained when the rate of photoionisation is balanced by the rate of recombination. The characteristic equilib- rium temperature is of the order of∼10⁴K, and corresponds to thermal line widths of ∼10 km/s. It is thus evident that the velocity of the line-emitting gas must be supersonic, suggesting motions in a deep gravitational potential well. The physical dimension of the line emitting region can be estimated from the observed time delays between continuum and line emission variations. The broad emission lines respond to variations of the continuum with a short time delay, indicating that the BLR is compact and located close to the central source. Conversely, the narrow emission

lines do not vary on short timescales, indicating that the NLR is spatially extended and located farther out than the BLR.

Figure 2.6: Composite spectra from the Sloan Digital Sky Survey (SDSS). Note the sim- ilarity of the average line spectra of sources of different luminosities. From vanden Berk et al. (2004).

Variability

Variability is another characteristic feature of AGN, covering a wide range of timescales and amplitudes over the entire electromagnetic spectrum. In general, the observed light curves are characterised by aperiodic fluctuations, without clear periodic be- haviours, suggesting that the underlying variability mechanism has a random nature.

Significant optical variability is seen on timescales of years, and since normal galax- ies are not variable on comparable timescales, variability can even be used to search for new AGN candidates.

As a general trend, one can note that the characteristic timescale for variability scales with the luminosity of the source, and that the amplitude of variability is inversely correlated with the timescale. The shortest timescale variability is ob- served in the X-ray domain, with timescales down to minutes. The observed rapid variability provides an upper limit to the size of the emitting region, suggesting that X-rays are emitted in the innermost regions, within a few gravitational radii from the central black hole. In the optical/UV region, the characteristic variability timescales are longer, of order weeks to several months. The optical/UV emitting region is larger than the X-ray emitting region and located farther out, around hun- dreds of Schwarzschild radii. The lack of short timescale variability in the infrared

indicates that the IR emission comes from dust located at greater distances, on∼pc scales. Extreme variability properties, with large amplitudes and short timescales, are observed in objects whose radiation is dominated by relativistically beamed com- ponents, such as in the blazar class. General variability properties in radio-quiet and radio-loud AGN are reviewed by Ulrich et al. (1997).

Figure 2.7: Multi-wavelength lightcurves of the BL Lac object PKS 2155-304. Data are taken from the 1991 November multi-wavelength campaign: X-ray, UV, and optical data are obtained by ROSAT, IUE, and FES monitor on IUE, respectively. From Edelson et al.

(1995).

The physical origin of the variations is still not clearly established. The observed variability timescales can be compared with predicted timescales from different mod- els, and such comparisons provide important constrains on theoretical models of AGN emission. In particular, the study of correlations between energy bands is thought to provide important information on the physical emission mechanisms and causal links relating the different emission regions. Consequently, much effort has been put in multi-wavelength monitoring campaigns (cf sect. 5.4.4).

Internal structure

The AGN phenomenon covers a huge dynamic range (∼ 10⁹), from the innermost central black hole to the host galaxy scales and beyond. We have mentioned some observational characteristics of AGN, which should be associated with distinct phys- ical components forming the active nucleus. According to the standard paradigm, the AGN is formed by a central supermassive black hole which is surrounded by a geometrically thin, optically thick accretion disc; the disc emits optical/UV radi- ation and is responsible of the main blue bump component. Broad emission lines

are produced in clouds moving at high velocities in the potential well of the central black hole (Broad Line Region), while narrow emission lines are produced by slower moving clouds of gas located farther out from the centre (Narrow Line Region). The central engine is in turn surrounded by a dusty molecular torus, located between the broad and narrow line regions, which absorbs a fraction of the central continuum emission reprocessing it into infrared emission. In some objects, collimated rela- tivistic outflows or radio jets, escape along the poles of the accretion disc or torus leading to extended radio structures, observable on galactic scales.

Figure 2.8: Schematic diagram of a radio-loud AGN according to the standard paradigm.

Broad emission lines are produced by high-velocity clouds located in the inner regions (dark grey blobs); while narrow emission lines are produced by slower moving clouds located farther out (light grey blobs). The dusty torus obscures the central engine from some lines of sight. The two-symmetric radio jets escape along the poles of the torus. From Urry &

Padovani (1995).

2.4.2 Stellar-mass black holes in binary systems

Beyond the maximum stable mass of a neutron star, which is about∼3M, the com- pact object in a binary system is most likely to be a black hole. Dynamical evidence suggests that there are a number of X-ray binary systems in which the compact object exceeds the maximum mass limit. Stellar-mass black holes, with estimated masses of ∼10M, are observed in our Galaxy. These are found in mass-exchange binaries in which the black hole primary accretes matter from the non-degenerate secondary companion star. For a typical stellar-mass black hole in a binary system,

Figure 2.9: Scale drawings of 16 black hole binaries in our Galaxy. The primary black hole accretes material, through an accretion disc, from the non-degenerate secondary star. The colour of the companion star roughly indicates its surface temperature. From Remillard &

McClintock (2006).

the Eddington luminosity is of the order ofL_E ∼= 1.3·10³⁸

M M

erg/s. In a binary system, the mass transfer from the companion star to the black hole, takes place via an accretion disc. A significant fraction of the emission is radiated in the X-rays and spectral states are defined in the X-ray domain. Black hole binaries (hereafter BHB), and in particular their X-ray properties, are reviewed in Remillard & McClintock (2006). Radiative processes in different spectral states are discussed in Zdziarski &

Gierli´nski (2004).

Actually, there are around 20 confirmed black hole binaries in our Galaxy. BHB are very heterogeneous systems, both in size and companion characteristics, as can be seen from the scaled drawings. The first discovered source, Cygnus X-1, is a per- sistently bright X-ray source; while A 0620-00 is an X-ray nova, discovered in 1975 when it suddenly brightened in an outburst, and later decayed back into quiescence.

In fact, the majority of BHB are transient systems, characterised by more or less recurrent outbursts, generally attributed to some form of accretion disc instabilities.

X-ray binaries often show rapid fluctuations in the X-ray domain; these transient and discrete features are known as quasi-periodic oscillations (QPO).

Spectral states

Two main components, thermal and non-thermal, contribute to the X-ray spectra of black hole binaries. The thermal component is associated with blackbody emission from the optically thick accretion disc, peaking around∼1 keV, with a tail extend- ing toward higher energies. The non-thermal component, which dominates at higher energies (around ∼100 keV), is usually modeled by a power law, and is attributed to Compton upscattering of soft seed photons.

Three main X-ray spectral states are defined according to the relative importance of the thermal and non-thermal components: a thermal (high/soft) state, a hard (low/hard) state, and a steep power law (SPL) state. The relative importance of the thermal and non-thermal components can vary, and transitions between spectral states are observed. The hard state is characterised by a hard power law component (Γ.2) with a high-energy cut-off around a few hundred keV (&100-200 keV), and a weak cool blackbody contribution. In the hard state, the power in hard upscattered photons is larger than the power in soft blackbody photons (L_H L_S). Reflection features due to reprocessing by a cold medium, such as the Compton reflection hump and the iron line emission, are also observed. The hard state is usually associated with a steady radio jet. In the hard state, QPO may be either present or absent.

The thermal or soft state (Γ&2), is characterised by a strong blackbody component which dominates over the power law component, at least for energies below 10 keV.

Contrary to the hard state, the power in soft photons is larger than that in the hard Comptonised photons (LS LH). A non-thermal tail extends to higher energies, and no high-energy cut-off has been observed (Zdziarski & Gierli´nski 2004). In the soft state, the radio emission is suppressed with respect to the hard state, and the radio jet seems to be quenched. In the thermal state, QPO are absent or very weak.

Figure 2.10: The figure illustrates the three main spectral states (left panels) and corre- sponding variability power spectral densities (right panels) of the black hole binary GRO J1655-40. The spectra are decomposed into a thermal blackbody component (red, solid line), a power law component (blue, dashed line), and a relativistically broadened Fe Kα line component (black, dotted line). From Remillard & McClintock (2006).

The steep power law (SPL) state or very high state (VHS) is characterized by a strong power law component, with a steep photon index (Γ∼2.5), and with a non negligible blackbody contribution. The VHS state dominates at high luminosities and usually takes place during the transitions from the hard state to the soft state.

In the intermediate state, powers in the hard and soft photons are comparable (L_H ∼ L_S). During the hard to soft state transitions, outbursts of radio emission are observed, with relativistic ejections attributed to internal shocks. The SPL state is often associated with high-frequency QPO.

Figure 2.11: ‘Unified models for radio jets’: schematic representation of the disk-jet cou- pling in black hole binaries. The upper panel is a hardness intensity diagram (HID), i.e. a plot of the X-ray intensity versus the hardness ratio, defined as a ratio of detector counts in two energy bands. The bottom panel shows the variations of the bulk Lorentz factor of the jet (blue curve) and the inner disk radius (red curve) as a function of X-ray hardness. The solid vertical line indicates the ‘jet line’. To the right of the jet line the system is in the hard state, and a steady radio jet is present; while to the left of the jet line, the system is in the thermal state and the radio jet is quenched. Violent matter ejections and internal shocks occur along the jet line, as can be seen from the corresponding spike in the bulk Lorentz factor. From Fender et al. (2004).

There seems to be a link between spectral state and the presence of radio jets, with the radio emission correlating with the X-ray spectral state. Indeed distinct spec- tral states are associated with distinct jet properties. Since X-ray emission can be

considered as a tracer of the accretion flow, while radio emission is a tracer of jet activity, the observed correlation between X-ray spectral state and radio jet emission should provide clues on the underlying disc-jet coupling mechanism.

The truncation paradigm

The soft emission dominating the thermal state is attributed to blackbody radia- tion from the geometrically thin, optically thick accretion disc. Hard photons are produced by Compton upscattering of seed photons by hot electrons in a corona sur- rounding the disc. A possible geometry is that of a ‘truncated disc/hot inner flow’

configuration, where an optically thick accretion disc and an optically thin corona coexist in the inner regions. At high accretion rates, there is a standard accretion disc; as the accretion rate decreases, a hole opens at the centre where the optically thick disc starts to be replaced by a hot optically thin flow. In this picture, modi- fications in the disc-corona configurations give rise to the different spectral states.

Figure 2.12: Schematic representation of the truncation paradigm. Panel (a) shows the geometry in the hard state: the optically thick accretion disc is truncated far away from the centre, and the inner region is filled with a hot optically thin flow. Soft seed photons emitted by the disc are Compton upscattered in the hot inner flow. Panel (b) shows the geometry in the soft state: the optically thick accretion disc extends close to the last stable orbit. Soft photons from the disc are upscattered in the active regions (flares) located above the disc.

In both cases, hard photons are partially reflected by the cold, optically thick medium of the accretion disc. From Zdziarski & Gierli´nski (2004).

In the soft state, the optically thick accretion disc extends close to the last stable orbit, and the bulk of the radiation is provided by the disc. The disc also provides the seed blackbody photons which are Compton-upscattered in the optically thin corona. The Compton cooling of the hot corona is very efficient leading to soft Comptonized spectra.

In the hard state, the accretion disc is truncated far away from the centre, and the inner region is filled with the hot optically thin flow. In this geometry, only a fraction of seed photons from the disc interacts with the hot corona, thus the Comp- ton cooling of the hot electrons is not very efficient, leading to hard Comptonized spectra. The emission is dominated by the inner optically thin flow. A fraction of hard photons emitted by the corona can be reprocessed by the cold medium of the optically thick disc giving rise to the reflection components (Compton reflection and iron line emission).

The truncation of the disc and its replacement by the hot flow are somehow related to the accretion rate, with the transition radius between the two regimes becoming larger with decreasing accretion rate. In general, the truncated disc moves pro- gressively outwards, as the mass accretion rate decreases, and the transition radius seems to increase monotonically with decreasing luminosity. In this picture, the hot inner flow also constitutes the base of the steady radio jet, possibly explaining the observed correlation between radio and X-ray emissions.

2.5 On the scale invariance of accreting black holes

We have seen some general characteristics of the two main classes of accreting black hole systems. Although the physical scales span several orders of magnitude between the two classes (∼8 orders of magnitude in mass), the black holes are governed by the same mathematical properties. The fundamental scale of accreting black hole systems is set by the gravitational radius:

R_G= GMBH

c² , (2.30)

which is directly proportional to the black hole mass.

Similarly, the free-fall velocity can be defined by a single scaling parameter,ξ, when the radial distance from the centre is expressed in units of the Schwarzschild radius, R=ξRS:

v_{f f}(R=ξR_S) =

r2GM_BH

R = c

√ξ. (2.31)

We have seen that the accretion efficiency is given by the binding energy at the in- nermost stable circular orbit (ISCO), which location is determined by the black hole spin. For a Schwarzschild black hole, the ISCO is located atR_ISCO = 6R_G(= 3R_S);

while for a maximally rotating Kerr black hole the ISCO is at R_ISCO = R_G(=

1/2RS). Due to the linear radius-mass dependence (R ∝ MBH), the M/R ratio turns out to be the same to within a factor of six, independently of the black hole mass (Fender 2010).

The resulting mathematical simplicity led to the suggestion that accreting black hole systems are scale-invariant on all mass scales. In addition, there are a number of common features observed in both stellar-mass and supermassive black hole systems.

These include similarities in the X-ray variability properties and radio jet emission.

Such considerations are at the basis of the so-called unification scenario, according to which the underlying accretion process is the same in black hole binaries and active galactic nuclei. The scale-invariance of accreting black hole systems has the appealing property that knowledge gained on one side can be directly applied to the other class, via appropriate scaling factors. Moreover, characteristic timescales are known to scale linearly with the black hole mass. This is particularly interesting, since observations of galactic black holes, which vary on human timescales, may give us clues to understand the evolution of AGN on cosmological timescales.

Active Galactic Nuclei

3.1 AGN classes and classification

A variety of AGN classes has been defined based on both intrinsic physical differ- ences of the source and external observational factors. AGN classes can be organized according to differences in their spectral, variability, and polarisation properties.

However, the assignment of a given source to a particular class also depends on observational parameters, such as the orientation of the observer with respect to the source symmetry axis and the instrumental resolution. Thus the same object might be assigned to a different class, based on different classification criteria. Rather than entering into detailed sub-divisions and introducing new sub-classes, it is perhaps more interesting to study the underlying common aspects relating the different AGN classes. Indeed the classification picture is complex and somewhat confusing, and here we only mention the main classes of AGN.

3.1.1 Quasars

Quasars form the most luminous class of AGN. Their high luminosities, up to

L & 10⁴⁷erg/s, require large central masses. Quasars are usually associated with

very massive black holes, M_BH & 10⁹M, accreting at significant fractions of the Eddington rate. In the early optical observations, quasars appeared as spatially un- resolved sources due to the extreme luminosities of their nucleus compared to that of the underlying host galaxy (leading to the historical naming of quasi-stellar ob- ject or QSO). The spectrum of quasars is characterised by a strong emission in the optical/UV region, called the (big) blue bump, and by broad emission lines whose widths indicate velocities of ∼ 10⁰000km/s. Variability is also a common feature among quasars; the characteristic timescale for significant optical/UV variations is typically of a few months.

Although the first discovered quasars were identified with bright radio sources, it is now established that radio-loud quasars, with strong radio emission, are rare and comprise only a minority (∼10%) of the total population. The majority is formed by radio-quiet quasars, characterised by weak radio emission relative to the optical

component. A small sub-set of radio-quiet quasars, known as Broad Absorption Line (BAL) quasars, show broad and blueshifted absorption lines in their optical spectra.

These features are interpreted in terms of massive outflows with near relativistic velocities (v ∼ 0.01−0.1c) from the central engine. XMM-Newton and Chandra observations have recently confirmed the existence of such X-ray outflows in a num- ber of quasars, accreting at rates close to the Eddington limit (Chartas et al. 2002;

Pounds et al. 2003; Reeves et al. 2003).

3.1.2 Seyfert galaxies

Seyfert galaxies are on average two orders of magnitude less luminous than quasars, and form a lower luminosity class of AGN. Seyfert galaxies are associated with smaller central black holes, MBH ∼ 10⁷−10⁸M, with a range of accretion rates.

A typical value of the Eddington ratio is of the order of L/L_E ∼0.1. The spectra of Seyfert galaxies are very similar to the spectra of radio-quiet quasars, with broad emission lines in the optical region and a fall-off in the radio domain. Observation- ally, a Seyfert galaxy appears as a quasar-like nucleus at the centre of the host galaxy which is clearly visible. In fact the distinction between quasars and Seyfert galaxies depends on whether the host galaxy is detectable against the bright central nucleus.

For a Seyfert galaxy, the optical luminosity of the nucleus is comparable to that of the host galaxy; while for a quasar, the luminosity of the nucleus overwhelms that of the underlying host. Thus the distinction between the two classes is not based on intrinsic physical differences, but rather on instrumental resolution. It is now believed that Seyfert galaxies and quasars form a continuous sequence in luminosity, with overlapping properties at their respective ends.

Figure 3.1: Left: visible image of 3C 273 taken with the KPNO 4-meter Mayall telescope.

(credit: NOAO/AURA/NSF) Right: photograph of the nearest Seyfert galaxy NGC 4395, taken with the Palomar 200-inch telescope, in which the spiral structure of the host galaxy can be seen (credit: Allan Sandage, Carnegie Institution)

Two sub-classes of Seyfert galaxies are defined based on their optical spectra: Seyfert 1 galaxies having both broad and narrow emission lines, and Seyfert 2 galaxies show- ing only narrow emission lines. The broad lines, with line widths corresponding to

velocities up to 10’000 km/s, are emitted by clouds in the Broad Line Region; while narrow lines, with line widths of only up to 1000 km/s, come from the Narrow Line Region. The absence of broad line components in the Seyfert 2 spectra, and the distinction between the two categories of Seyfert galaxies, are now attributed to ob- servational effects (cf unified models). In general, objects showing both sets of lines, broad and narrow, are called Type 1 objects, while objects showing only narrow components are classified as Type 2 sources.

There is another particular sub-class of Seyfert galaxies, with unusual spectral and variability properties. These are called Narrow-Line Seyfert 1 galaxies (NLS1) and are identified by the unusual narrowness of the broad component of their Hβ lines.

They are characterised by very steep X-ray spectra in the hard band and very rapid and large amplitude variability (Leighly 1999). NLS 1 galaxies are usually believed to be powered by small black holes accreting at very high rates, close to the Edding- ton limit.

3.1.3 Low-luminosity AGN (LLAGN)

Low-luminosity AGN (LLAGN), including low-ionisation nuclear emission line (LINER) galaxies form the low-luminosity end of the AGN population. LINERs have gener- ally weaker and narrower emission lines than classical Seyfert galaxies and can be identified by their different locations in diagnostic diagrams defined by two pairs of line ratios, known as the BPT (Baldwin, Phillips, & Terlevich 1981) diagram.

Figure 3.2: Diagnostic diagram plotting the [O III]λ5007/Hβ flux ratio versus the [N II]λ6583/Hαflux ratio. An empirical division can be drawn between the HII regions, ionised by hot stars, and the AGN photoionised by a central engine. LINERs can be distinguished from HII regions by higher values of [N II]λ6583/Hα. From Ho (2008).