Circular polarization emerging from dierent dust grain models

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The supermassive black hole (SMBH)

Quasars and AGN are the most powerful and long-term stable astronomical sources known. Not uncommonly, L 1046 erg.s 1, which is 10 times the luminosity of the brightest galaxies. However, while being stable for long periods, their intrinsic luminosity may vary in a timescale of hours or less, depending on the energy domain considered. Considering the propagation of radiation level change at the speed of light, the overall emission region is necessarily compact and of a phenomenal energy. A stellar-origin fueling of the AGN was soon studied by Lynden-Bell (1969a), who showed that any attempt to power quasars by nuclear reactions alone was largely insu cient. Demonstration:
Let’s consider that most of the 1061 erg energy released by an AGN is stocked inside its radio halo. By measuring the size of the emission region, one can nd that 1061 ergs corresponds to a mass of 107 M . Knowing that nuclear reactions give less than 1 % conversion matter $ energy, of which 0.75 % comes from hydrogen to helium conversion, the initial mass of the AGN inner region must be about 109 M .
If all the mass in concentrated within the radius R of the central, nuclear object, then its binding energy would be greater than 3GM2 / 5R. If R = 1.50 1013 cm (equals to 1 astronomical unit), then Ebind 1064 erg.
It is not unusual that a quasar luminosity varies by one magnitude within 10 hours. From speed of light crossing distance considerations, R would be lower than 1015 cm, implying the gravitational binding energy of the nuclear core to be superior to 1062 erg. So, while trying to fuel our model with nuclear energy, we ended with a model producing enough energy by gravitational contraction. The work of Salpeter (1964) and Zel’dovich & Novikov (1964) braced Lynden-Bell (1969a)’s hypothesis on the gravitational fueling theory while, in the meantime, exotic black hole alternatives such as single supermassive stars (Hoyle & Fowler 1963) and spinars (Ginzburg & Ozernoi 1977) were shown to be dynamically unstable and hence short-lived (Lynden-Bell 1978).

Accretion onto SMBH

The previous section showed that a gravitational-origin fueling of AGN is the most probable mechanism to produce extreme amounts of radiation. To do so, matter around the SMBH must somehow loose its energy; but placing an isolated particle (with angular momentum) around a potential well only results in a circular motion. By removing energy and angular moment from the particle, the trajectory of the particle is altered and starts to spiral inwards the gravitational potential until it ultimately crosses the Schwarzschild radius4 . The amount of energy available through such a process is equal to the binding energy of the innermost stable circular orbit (ISCO, with rISCO < rS). Below the ISCO radius, no stable circular motions are possible. It follows that the more compact the object is, the more energy can be extracted. According to Pringle (1981), of the order of 10 % of the rest mass of the particle can be released from orbits around a neutron star and up to around 40 % for orbits around a rotating Kerr black hole.
In theory, accretion processes are e cient enough to produce high amounts of energies by converting rest mass into radiation. But, in order to ignite accretion, energy and angular momentum must be removed from the particles. According to the theory developed by Pringle & Rees (1972) and Shakura & Sunyaev (1973), black holes are surrounded by large amount of hot gases, rotating around the potential well (see Fig 2.3). A particle colliding with other gas elements transfers its kinetic and potential energy to the medium, while being heated by shocks and then radiatively cooled. Since the orbit of least energy for a given angular momentum is a circular one, the gas settles into moving on circular orbits in the form of a thin, optically thick disk around the black hole. The accretion itself is due to viscosity processes (Shakura & Sunyaev 1973), also know as the alpha viscosity prescription that describes the resistance of a uid to the deformation induced by either shear or tensile stresses. Viscosity is damping out shearing motions while the energy is dissipated in the uid as heat, and thence radiated away with a temperature pro le similar to a quasi-black body5 with T(R) / R 3=4. Thus, viscosity extracts the only energy source present in the gas (that comes from the gravitational potential) and makes the accretion disk particles to fall into the potential well. In theory, such a viscous prescription is the most e cient manner to convert gravitational potential energy into an AGN-required amount of radiation. However, it is interesting to note that several authors proved that ordinary molecular viscosity is too weak in real astrophysical accretion disks and should be replaced by a model of turbulences driven by magneto-rotational instability (MRI, Balbus & Hawley 1991; Hawley & Balbus 1991; Balbus & Hawley 1998; Abramowicz & Fragile 2011).

The hot corona

Within the theories described by Pringle & Rees (1972) and Shakura & Sunyaev (1973), the UV and optical continuum radiation is expected to be produced by accretion onto a supermassive black hole. However, the presence of high X-ray uxes observed in AGN (Walter & Courvoisier 1992) is a serious challenge for the accretion disk theory as it is unable to explain their origin and spectral shape.
If we consider that accretion disks are the only radiation sources in AGN, then one of the easiest way to produce X-ray photons is to consider (multiple) inverse Compton upscattering events in a hot plasma. By Comptonization processes (Sunyaev & Titarchuk 1980), ultraviolet seed photons emerging from the accretion disk are reprocessed in a hypothetical, optically thin plasma situated in both sides of the disk surface (the accretion disk corona, Haardt & Maraschi 1991, 1993). The resulting X-ray spectrum then only depends on two parameters of the corona: its electron temperature and optical depth. The relative strength of the hard X-ray component of the spectrum, in comparison with the UV/soft X-ray tail, de nes the hardness of the spectra and reveals the predominance of energy dissipation in the accretion disk (soft excess, Pringle & Rees 1972; Frank et al. 2002) or of energy dissipation in the corona by thermal comptonization (hard excess, Rees et al. 1982; Narayan & Yi 1994; Abramowicz et al. 1995).
Empirically, a power law of the form NE / E , with a photon index 2 best describes the 1-100 keV X-ray emission coming from the accretion disk corona, below 30 RS, for radio-quiet AGN and quasar with 0.5 < z < 6 (Reeves & Turner 2000; Page et al. 2005). The variation of is considered as an accretion rate indicator in AGN seen from the pole (Boroson & Green 1992), as high accretion rate would increase the accretion disk temperature, hence producing more soft X-ray radiation and, at the same time, increase the Compton cooling of the corona and steepen the hard X-ray power law; low accretion rate hardens the power law via the inverse mechanism (Shemmer et al. 2006). The interaction between the matter driven away from the accretion disk by radiation pressure and the hot corona is rather complicated as it couples the processes producing X-rays and UV pho-tons (Proga 2005). Galeev et al. (1979) and Field & Rogers (1993) explored magnetic connections between energy dissipation from the accretion disk and the heating mechanism of the corona but a detailed investigation of the radiative coupling between an accretion disk and a hot corona presented in Liu et al. (2002, 2003) shows that the energy deposit in the corona is not enough to keep itself hot above the disk against strong Compton cooling in AGN systems. Other heating mechanisms besides the disk-born out ow are required to maintain such a hot temperature in the corona lying above the disk and to produce the observed X-ray luminosity. A promising mechanism arises from coupling MRI in the disk and the upward force exerted by the magnetic eld, resulting in magnetic reconnection events in the corona that can heat the plasma up to 109 Kelvin (Di Matteo 1998; Di Matteo et al. 1999; Miller & Stone 2000). Moreover, magnetic reconnection might explain the time variability observed in AGN and help to create an inhomogeneous medium (Kawaguchi et al. 2000). Unfortunately, due to the proximity between the corona and the SMBH, direct measurements of the plasma morphology, opacity and radiation mechanisms remain impossible (Reynolds & Nowak 2003 and Fig 2.4).

The Broad Line Regions (BLRs)

Since the rst optical spectroscopic observation of AGN by Seyfert (1943), it is unambiguous that all quasars have relatively strong emission lines. Since then, the shapes and intensities of the emission lines are used as tracers of the physical and kinematic properties in the central part of AGN. While the emission mechanism of narrow lines is identi ed with a quite well-characterized AGN component (the Narrow Line Region, see Sect. 2.2.6), much questions remain about the original region responsible for the broad lines. In particular, it is quite puzzling to reconcile the presence of broad emission (in type-1 AGN) and absorption line (in BALQSO) under a uni ed picture.
When looking at spectroscopic observations of AGN, one can deduce from the broad emission lines that the actual amount of emission-line gas required is rather small as line emission is very ef-cient in high-density gases (taking into account that the emissivity per unit volume is proportional to n2e). The broad line region (BLR) must be then dense. From the variation of the emission-line uxes in comparison with the continuum ux, the BLR signal varies with a very short time delay (e.g. Akn 564: tcont=line 3 days at = 1216 A, for a SMBH of 8 106 M , Collier et al. 2001). Hence, using light-travel time arguments, the BLR is necessary quite small and thus close to the central engine (Akn 564: RBLR 1 light day, Collier et al. 2001). As the BLR is located on a relatively small distances from the AGN central energy source, the matter in the BLR is likely to be irradiated by the strong continuum ux originating from the accretion disk and the hot corona. Kwan & Krolik (1981) were the rst to suggest that the UV and optical irradiation of the BLR was leading to photo-ionization of the matter, heating the gas up and being responsible for the observed spectra of AGN. Plus, if the gas is photo-ionized, the BLR must be optically thick to ionizing continuum radiation. This led to the idea that the BLR comprises discrete gas clouds associated with the accreting supermassive black hole at the heart of AGN (Davidson & Netzer 1979; Mathews & Capriotti 1985). Non-radiatively heating processes such as recombination and collisional excitation were also considered by Dumont et al. (1998) and were found to be relevant processes in the physics of the BLR. In particular, at larger ionization parameters recombination cannot be neglected; at low ionization parameters, the collisional excitation also becomes important (Osterbrock 1989; Popovic et al. 2008).

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Out owing polar winds (UFO, NLR, WA)

In more than 50 % of the Seyfert 1 galaxies (Crenshaw et al. 2003; Kriss 2004; Steenbrugge et al. 2005) and quasars (Piconcelli et al. 2005; Misawa et al. 2007), X-ray and UV out ows have been detected in absorption with velocities comprised between 500 and 5000 km s 1. Similarly, out ows have also been observed in [O III] emission lines, using the HST/STIS instrument, showing slowly increasing velocities out to 100 pc and then decreasing in motion at larger distances (Crenshaw & Kraemer 2000; Das et al. 2005, 2007). More recently, evidences have been emerging for much higher velocity (up to 0.4 c) out ows (also known as ultra fast winds, \UFO ») seen in absorbed X-ray lines (Chartas et al. 2002, 2007; Pounds et al. 2003; O’Brien et al. 2005; Tombesi et al. 2010, 2011, 2012a). Depending on the distance from the inner AGN core, the out ow density, ionization stage, velocity and most of the other characteristics are found to be di erent in X-ray energies and UV/optical wave bands. Interpreting the di erent observations in order to draw a \uni ed » model of AGN winds (Gallagher & Everett 2007; Tombesi et al. 2012b) is an actual debate (Kaspi & Behar 2006; Pounds & Page 2006).
The most fundamental question is: where do quasar winds originate? The AGN out ows extend up to hundreds of parsec from the central source in a conic or double conic geometry, as revealed by narrow-band images around some luminous AGN, particularly radio-loud quasars) as well as radio galaxies (Stockton et al. 2006). Similar ionization cones irradiated by the intense radiation from the AGN core often appear in lower luminosity Seyfert galaxies (Unger et al. 1987; Tadhunter & Tsvetanov 1989; Wilson 1996). Such a geometry may be explained if we consider that the out ows, originating close to the SMBH, are collimated by the inner funnel of the circumnuclear torus. When expelled from the inner AGN core, the out ows are blocked by the torus inner walls and escape along the polar directions in a characteristic hourglass shape. It is interesting to note that the problem can be solved starting from the other end: the energetic, polar out ows may blast away a primeval spherical dust layer surrounding the AGN core, leaving only obscuring matter along the equatorial plane (Lawrence 1991).
Independently of the shaping mechanism, measuring the AGN ionized out ow location re-quires the independent determination of a quantity which is not directly observable: the electron density ne of the out owing material. Such a parameter might be derived from the emission lines of helium-like ions in the X-ray out ows (Porquet & Dubau 2000; Porquet et al. 2010) or inferred from the evolution in time of the ionization degree of the gas coupled to time-evolving photo-ionization models (Nicastro et al. 2008). A major step forward was recently taken by Tombesi et al. (2012b) who found signi cant correlations indicating that there is a proportional relation between the dis-tance from the SMBH and the out ows ionization stage, column density and out owing velocity. The out owing medium is thought to be continuous, with UFO detected close to the central engine and warm absorbers (WA) at the end of the cloud distribution. It indicates a possible, similar origin for all the X-ray winds detected so far.
The ionized medium seen in optical and UV wavelengths is already thought to be associated with the WA (Komossa 1999). The distant narrow line region (NLR), responsible for the narrow absorption and emission lines seen in type 1 and 2 AGN, might be the nal extension of the AGN out ow were an optically thin dust medium can survive beyond the sublimation radius. All hints tend to point to a global picture of AGN out ows, summarized in Fig 2.7.

Table of contents :

1 Introduction 
2 A broad overview of Active Galactic Nuclei 
2.1 Historical discovery
2.2 The complex composition of AGN
2.2.1 The supermassive black hole (SMBH)
2.2.2 Accretion onto SMBH
2.2.3 The hot corona
2.2.4 The Broad Line Regions (BLRs)
2.2.5 Circumnuclear obscuration
2.2.6 Outowing polar winds (UFO, NLR, WA)
2.2.7 Jet emission
2.2.8 AGN feedback
2.3 The unied scheme
3 Exploring AGN using polarimetry 
3.1 Theory of polarization
3.1.1 Principles
3.1.2 Stokes formalism
3.1.3 Mueller matrices
3.2 Polarization mechanisms from the optical to the X-ray band
3.2.1 Thomson scattering
3.2.2 Rayleigh scattering
3.2.3 Compton scattering
3.2.4 Inverse Compton scattering
3.2.5 Mie scattering
3.2.6 Dichroic extinction
3.2.7 Resonant scattering
3.2.8 Raman eect
3.2.9 Bremsstrahlung
3.2.10 Atomic recombination
3.2.11 Fluorescent emission
3.3 stokes: Radiative transfer and polarization
3.3.1 Radiative transfer
3.3.2 The Monte Carlo method
3.3.3 Past – Overview of the code’s rst version
3.3.4 Present – Improvements
3.3.5 Future – Pushing forward the code’s limits
4 Polarization signature induced by multiple scattering in complex AGN models
4.1 Polarization signatures of individual reprocessing regions
4.1.1 Obscuring, dusty tori
4.1.2 Ionized out ows
4.1.3 NLRs
4.1.4 Radiation-supported disk
4.2 Exploring the radiative coupling between two reprocessing regions
4.2.1 Equatorial scattering disk and electron-lled outows
4.2.2 Radiation-supported disk and obscuring torus
4.2.3 Electron polar outows and obscuring torus
4.3 Modeling a three-component AGN
4.3.1 Spectral modeling results
4.3.2 Wavelength-integrated polarization images
4.3.3 The impact of geometry and optical depth
4.4 A step further by including dusty polar outows
4.4.1 Spectropolarimetric signatures
4.4.2 Wavelength-integrated polarization maps
4.4.3 Extensive grids of parameters
4.5 Summary and discussion
4.5.1 Comparison with previous modeling work
4.5.2 Polarization at type-1 and type-2 viewing angles
4.5.3 Constraining particular AGN classes
4.5.4 More general geometries for the reprocessing regions
5 The continuum polarization of NGC 1068 
5.1 A model of NGC 1068 from broadband observations
5.1.1 The correlation between the optical depth of dust and hydrogen
5.1.2 Asymmetric model setup
5.2 UV and optical continuum polarization of NGC 1068
5.2.1 Spectropolarimetric and imaging results
5.2.2 Comparison with observations
5.2.3 Investigating the dependence on the azimuthal angle
5.2.4 Importance of the dust grain model
5.3 Summary and discussion
5.3.1 The complex geometry of the outows in NGC 1068
5.3.2 Fragmentation of the winds
5.3.3 Detection of circular polarization in NGC 1068
6 Exploring the circular polarization induced by AGN tori
6.1 Producing circular polarization
6.1.1 Circular polarization from multiple scattering
6.1.2 Spectropolarimetric signatures of the torus
6.1.3 Circular polarization emerging from dierent dust grain models
6.2 Comparison with the circular polarization in NGC 1068
6.3 Summary and discussion
6.3.1 Other mechanisms responsible for optical circular polarization
6.3.2 Fragmented tori
7 Enhancing the complexity with fragmented reprocessing media 
7.1 Hints for clumpy structures in AGN
7.2 Impact of fragmentation on the polarization signature of individual reprocessing regions
7.2.1 Building a fragmented model
7.2.2 Clumpy torus model
7.2.3 Fragmented polar outows
7.2.4 Disrupted accretionow
7.3 AGN modeling with clumpy structures
7.4 Summary and discussion
7.4.1 Further modeling
7.4.2 An alternative solution to fragmentation
8 Investigating disk-born winds 
8.1 Model geometry
8.2 The warm, highly ionized medium
8.2.1 Testing the electron-dominated outows
8.2.2 Exploring dierent bending and opening angles of the wind
8.3 Dust in the wind
8.3.1 A pure absorbing wind model
8.3.2 BAL obscured outows
8.4 A two-phase medium
8.4.1 Modeling two-phase outows
8.4.2 Investigating dierent opening angles
8.4.3 Exploring a range of dust optical depths
8.5 Summary and discussion
8.5.1 Discriminating between dierent wind models
8.5.2 Polarization upper limits from Seyfert-atlases
8.5.3 The test case of the Seyfert galaxy NGC 5548
8.5.4 The morphology of the outow in IC 5063
8.5.5 The tilted outow of NGC 1068
9 X-ray polarimetry: the complementarity of multi-wavelength observations 169
9.1 AGN modeling from the optical to the X-ray domain
9.1.1 Results for the optical/UV band
9.1.2 Results for the X-ray band
9.2 Is X-ray polarimetry powerful enough to discriminate between absorption and reection scenarios in type-1 Seyfert galaxies?
9.2.1 Exploring models for MCG-6-30-15
9.2.2 Exploring models for NGC 1365
9.3 Overview of the X-ray polarimeter possibilities
9.3.1 Technology: how to measure X-ray polarization?
9.3.2 Past X-ray mission proposals (including a polarimeter)
9.3.3 Observational prospects for MCG-6-30-15 and NGC 1365
9.4 Summary and discussion
9.4.1 Rening the absorption and relativistic modeling
9.4.2 Polarization measurement across the iron line
10 Conclusions and perspectives 
10.1 Brief overview of the results
10.2 Towards more sophisticated models
10.3 Scaling down to X-ray binaries
Appendix
A Acronyms 
B Polarization induced by magnetic elds 
B.1 Synchrotron radiation
B.2 Faraday rotation
B.3 Zeeman eect
B.4 Hanle eect
C Personal publication 
D (accepted) Observing Time proposals 
Bibliography 

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