1 ACTIVE GALACTIC NUCLEI 7

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Introduction

Gamma-ray astrophysics is the branch of astrophysics concerning the highest energy win- dow of the whole electromagnetic spectrum, that is above approximately E = m

_e

c

²

w 0.5 M eV , where m

e

is the mass of the electron and c is the velocity of light in the vacuum.

A great part of the radiation produced from Supernova explosions, Active Galactic Nuclei and Galaxy clusters, among the most spectacular and mysterious phenomena of the known Universe, manifests in this domain. GeV to TeV γ − rays in particular are associated with

”non-thermal” processes, since, if thermal, they should be produced from bodies having a temperature comparable to that present during the Big Bang. Such ”non-thermal” Uni- verse, with all its peculiar physical processes, can be fruitfully probed through γ − photons which, being uncharged particles, are not deflected by intergalactic magnetic fields and hence preserve the directional information about the source that produces them. Gamma rays can then provide new cosmological knowledges and together help to better investigate fundamental physics beyond the reach of terrestrial accelerators.

Active Galactic Nuclei are extragalactic objects producing huge amounts of energy (some- times exhibiting apparent luminosities 10

⁴

times bigger than luminosities of typical galax- ies), spanning over a huge range of frequencies (from radio to γ − rays), in very small volumes ( 1pc

³

, where 1 pc w 3.086 × 10

¹⁶

m). Blazars are a specific family of AGNs, defined as radio-loud because they are characterized by a ratio between flux at 5 Ghz and flux in optical B band (∼ 400 − 500 nm) bigger than 10. They generally exhibit ex- treme flux variability at all frequencies, both in amplitude and timescales, and present a compact core constituted by a supermassive black hole which accretes material. Blazars feature narrow jets of relativistic particles perpendicular to their accretion disks planes and oriented at small angle to the observer. It is exactly on the physical bases of these emission jets that my work of thesis focus.

The Spectral Energy Distribution (SED) of blazars is the best tool to analyze them and it

typically shows two main peaks characterizing its overall shape: the peak at lower energies

is positioned between radio and X-ray wavelengths whereas the peak at higher energies is

comprised in the energy range between UV/X-rays and TeV. Blazars are subdivided into

two main classes, basically distinguished according to their optical spectra: Flat Spectrum

Radio Quasars (FSRQs) exhibit strong emission lines whereas BL Lacertae (BL Lacs) are

characterized by weakness of even absence of emission lines in their optical spectra. BL

Lacertae can be then further subdivided in three sub-families depending on the location

of the low energy peaks of their SEDs: Low Frequency Peaked (LBLs, peak in IR band

or at lower frequencies), Intermediate Frequency Peaked (IBLs, peak in the IR/UV band)

and High Frequency Peaked (HBLs, first peak in the UV/X band). IBLs and HBLs in

particular have a spectral emission that has been demonstrated to be the most appropri-

ate to be described through the so-called single-zone Synchrotron Self-Compton (1Z-SSC)

emission model. This model is based on the idea that, due to the extreme compactness

of blazars, there’s a big probability that photons produced by synchrotron processes of

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electrons immersed in the source’s magnetic field are used in subsequent Inverse Compton reactions by the same electrons that generate them. My thesis is devoted to the scrutiny of the capability of 1Z-SSC model to fit different states during the emission history of IBLs and HBLs. To accomplish this task, I have moved on the following path: first, I have gathered, with a big work of systematization, all the presently known models and observed parameters for IBLs and HBLs that have been detected at TeV energies (both 1Z-SSC and models that are alternative to it), studying their distributions and investigating interest- ing correlations among some of the parameters; secondly, I have analyzed VHE (E >100 GeV) data of the HBL Markarian 421, taken through the Major Atmospheric Gamma-ray Imaging Cherenkov telescopes (MAGIC), between March and April 2013, when the source undewent a strong outburst. I have studied this emission in exact coincidence with X-ray data taken through the Swift satellite on the same source so to test with extreme sensibil- ity the fitting power of 1Z-SSC model for this source: simultaneity is indeed an essential ingredient to properly apply the 1Z-SSC model. Because of experimental problems and limits, real multiwavelength and strictly simultaneous observational campaigns are till now as much necessary as rare.

In the first chapter of this thesis, I explain the general physical characteristics of AGNs and their classification. I then focus on spectral energy distributions and their importance for blazars study and on the main properties of the family of blazars detected at TeV energies, that are my principal aim. I also introduce the concept of blazars sequence, a benchmark since its first introduction in 1998 but also an argument on which much experimental work has still to be done because it is still under debate.

In the second chapter, I introduce the physical bases of the synchrotron and Inverse Comp- ton processes from the fundamental time equation for a test particle immersed in a mag- netic field to the whole treatment for a population of interacting particles. These mecha- nisms are the two cornerstones on which the whole one-zone homogeneous synchrotron-self Compton model is based.

In the third chapter, I show in details the principal equations involved in 1Z-SSC model and describe briefly the main alternative emission processes. Then, I introduce the extra- galactic background light (EBL), radiation which has accumulated in the Universe because of stellar formation processes extending on typical wavelengths between UV/optic and in- frared (IR). γ − photons are absorbed by this background giving rise to e

⁺

e

⁻

pairs so that one has to consider that the observed VHE source’s flux is attenuated, if compared to the intrinsic one.

In the fourth chapter, I describe Cherenkov emission and extensive air showers address- ing the main differences between electromagnetic and hadronic showers, the principles of Cherenkov imaging technique and the properties and operation of the MAGIC Florian Goebel telescopes.

In the fifth chapter, I present the statistical analysis of the sample of data I have extracted

from the literature about all the presently known TeV emitting IBLs and HBLs. I show

distributions and outliers concerning the seven fitting parameters of 1Z-SSC model (radius,

magnetic field and Doppler factor of the emitting zone, and break Lorentz factor, spectral

index before and after the break and normalization constant of the injecting electrons dis-

tribution), the seven connected observables usually adopted in the SSC modelization and

from it respected as constraints (frequency and luminosity of both the synchrotron and

inverse Compton peak, minimum observed variability of the source and the two spectral

indices of the SED’s synchrotron peak), and VHE spectral indices. I then study the cor-

relation between magnetic field of the blazar’s emitting region and break Lorentz factor

of the injecting electron distribution, the correlation between the magnetic field and the

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Doppler factor of the emitting region, having repercussion on the identification of typical situations in which Klein-Nishina correction for the emission process are necessary, and the properties of equipartition parameter as benchmark in blazars’ spectral energy distri- butions fits.

In the sixth chapter, I explain all the passages I have fullfilled to analyze MAGIC data about Markarian 421 taken on March 12, 18 and April 11, 12, 13, 14, 15, 2013, from the extraction of raw data from the telescopes database to the creation of narrow-binned lightcurves in strict simultaneity with X-ray Swift’s data and of fitted VHE night-by-night spectra. The data I have so reduced have finally become the input of a 1Z-SSC algorithm from which I have extracted fitting parameters that I have physically interpreted in view also of the correlation between X-rays and VHE data for the Markarian 421’s nights I have analyzed.

In the seventh chapter, I present a summary of the main results I have obtained from

my work, both from the strictly simultaneous analysis of Swift and MAGIC March-April

2013 Markarian 421 data and from the distributions of populations of fitting parameters

I have drawn from the literature about all the presently known TeV IBLs and HBLs. I

in particular focus on a group of sources that, on the base of my investigation, result to

be critical for a standard one-zone synchrotron-self Compton modelization. Hints to the

potential greatly improved capabilities of the forthcoming next generation Imaging Atmo-

spheric Cherenkov Telescopes called CTA (Cherenkov Telescopes Array) are also presented.

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Chapter 1

ACTIVE GALACTIC NUCLEI

The studies of AGNs started when E.A. Fath, in the Lick observatory in 1908, performed his study of the optical spectra of what in these times were called “spiral nebulae”. The concept of galaxies was at the time not yet established. He found that most of these objects showed absorption lines in their spectra, that he understood as coming from the integrated light of a large number of stars present on these “nebulae”. Fath found, however, that the spectrum of the nucleus of one of these galaxies, NGC 1068, showed six emission lines (including the H

_β

line) characteristic of gaseous nebulae. The study of these nuclei was further developed by V.M. Slipher in 1917 and E. Hubble, who discovered two more objects (NGC 4051 and NGC 4151) that showed characteristics similar to the previously mentioned objects. In 1943, C.K. Seyfert published a paper where he demonstrated that a very small fraction among the total galaxies showed spectra with many high-ionization emission lines. He also noted that these nuclei were specially luminous and that the emission lines were broader than the absorption lines present in the spectra of normal galaxies. In his honour, the AGNs that show broad emission lines (that cover a wide range of ionization levels), coming out from a bright, small, and with quasi-stellar appearance nucleus, are nowadays known as Seyfert galaxies. These Seyfert galaxies constitute the most common type of AGN. After Second World War there was a fast development of the radio-astronomy, that allowed to identify optically strong radio sources. One of the detected radio sources, Cygnus A was identified with a faint galaxy with a redshift z = 0.057, proving its extragalactic origin. After this discovery, other similar sources were quickly found, and were subsequently called radiogalaxies. A fraction of the previously detected radio sources were found to show remarkably different characteristics compared to those shown by radiogalaxies. It was not possible to find any sign of nebula or galaxy associated with these radio sources in their optical images. On the other hand their spectra were continuous, with no absorption lines, but with broad emission lines that were not possible to recognize. They were first understood to be a kind of star, perhaps white dwarfs with an unusually high abundance of heavy elements. Their extragalactic origin was understood in 1963, when Maarten Schmidt identified several well known nebular emission lines from the object 3C 273, which had this stellar appearance. It was found that the redshift of this source was very large (for those times standards): z = 0.158.

After this discovery, it soon followed the one of 3C 48, with even a larger redshift: z

= 0.367. The redshift of this last source meant that it was farther than any galaxy

discovered at that time. It was therefore understood that these sources were not stars,

but quasi-stellar, abbreviated as quasar, very luminous and distant radio sources. In

this thesis I will focus on a subclass of quasars, the BL Lac objects. BL Lac objects

were discovered in the 1970s, they are a special class of radio-loud AGNs with extreme

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luminosities and variability characteristics. They were named after their prototype: the

“variable star” BL Lacertae. Before radio-astronomy was well developed, a population of stars that showed very irregular changes in their luminosity was established. In 1968, one of these variable stars, “BL Lacertae”, was identified as a bright, variable radio source.

This source was showing many of the characteristics of quasars, but its optical spectrum showed just continuum emission, without the emission lines present in quasars ([69]). A faint trace of a host galaxy was also found in 1974 by Oke and Gunn who measured the redshift of BL Lacertae as z = 0.07, corresponding to a recession velocity of 21000 km s

⁻¹

with respect to the Milky Way, which reclassified it as an extragalactic object. Since then the study of BL Lac objects flourished and, depending on their observational properties, were subdivided in few groups, lately put together in the more general category of blazars, whose name was originally coined in 1978.

1.1 AGNs: general physical properties

Among all the galaxies that inhabit our Universe, a small family, representing ∼1% of the total, has a central black hole which is in an active state and strongly conditions the life of the whole galaxy. Active galactic nuclei (AGNs) are extragalactic objects characterized with extremely luminous electromagnetic radiation, often outshining their own host galaxy (in some cases apparently as much as 10

⁴

times the luminosity of a typical galaxy, reaching

∼ 10

⁴²

− 10

⁴⁸

erg s

⁻¹

) produced in very compact volumes ( 1 pc

³

) ([129]). The power for AGNs comes from accretion onto massive black holes and if this is true their basic prop- erties depend on a branch of physics which is the strong field relativistic gravity. Direct signatures of the supposed engines of active galactic nuclei, are much harder to see than a variety of more indirect signals and for that reason, at the present level of understanding, one can define AGNs in only an operational way.

AGNs must be very massive, a conclusion supported by two independent arguments. Be- cause of their astonishingly large bolometric luminosities, masses in excess of ∼ 10

⁶

M

are needed for an AGN not to become unbound by its own outpouring of energy. Further- more, according to our best estimates, AGNs remain active for upward of 10

⁷

years: during this period, an enormous amount of material, well over a million solar masses, must be consumed to sustain their luminosity, even assuming a very high efficiency of energy pro- duction. Taken together, these considerations lead to the inescapable conclusion that the source of the nuclear activity is accretion onto a central, supermassive black hole (SMBH, M

BH

∼ 10

⁶

− 10

⁹

M ), whose mass is correlated with the brightness and the dispersion velocity of the galaxy [171]. Black hole’s gravitational potential energy is the ultimate source of the AGN luminosity: matter pulled toward the black hole loses angular momen- tum through viscous or turbulent processes in an accretion disk and since the infalling gas reaches temperature of the order of T=10

⁵

K, most of the power is emitted as UV-X-ray radiation. Hard X-ray emission is also produced very near the black hole. If the black hole is spinning, energy may be extracted electromagnetically from the black hole itself.

At present the approximate structure of AGNs is known but much of the detailed physics is literally hidden from view because of their strongly anisotropic radiation patterns.

AGNs show radiation covering the entire electromagnetic spectral range, from radio to γ

wavelengths and they are therefore detectable with virtually every sort of astronomical

instrument. Their spectral energy distribution is decisively non-stellar: roughly speaking,

AGNs’ power per unit logarithmic frequency interval is constant over seven decades in

frequency, while stars emit nearly all of their power in a frequency range typically a factor

three wide. AGN emission lines are often very prominent (equivalent widths ∼100 ˚ A)

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and this put AGN spectra in great constrast to the spectra of most stars and galaxies, where lines are generally relatively weak and predominantly in absorption. In the optical and UV, they often display emission, and occasionally absorption, lines whose total flux is several percent to tens of percent of the continuum flux. These lines’widths suggest velocities ranging up to ∼ 10

⁴

km s

⁻¹

. Since the many knowledges about atomic physics, spectral lines can give a great deal of information on the nature of AGNs.

AGNs show very small angular sizes, which goes hand in hand with their compactness and great distances. The above-mentioned compactness is derived by an extreme flux vari- ability. AGNs are confined to within the distance light can travel in a typical variability timescale. Variability in all or in a great part of wavelenghts bands is a hallmark of AGN but unlike stars, whose variability is often dominated by periodic components (consider eclipsing binaries or Cepheid variables), AGNs for the most part vary with no special timescales. In other words, their Fourier spectra are broad-band, just as their photons spectra are. In many cases, X-ray variability and, as we will see, γ − ray variability, is observed on time scales of less than a day, and flares on time scales of minutes.

Radio frequencies are the first historically important domain for AGNs study indeed these objects are all characterized by a relatively strong radio emission. At these low frequencies, obtaining resolved images of some AGNs is possible and one often sees variable structure with apparent speeds in the sky plane up to 10-20 c, where c is the speed of light.

The last fundamental operational property to underline is the polarization of AGNs. Most AGNs are weakly polarized but just enough more strongly than other galaxies and stars for their polarization distribution to be statistically distinguishable from the others. AGNs are typically linearly polarized, with fractional polarization ' 0.5-2%. A minority is even more strongly polarized, often ∼ 10% in linear polarization.

Another interesting aspect in the AGN field concerns cosmology since the most luminous active galaxies were a thousand times more numerous at redshift ∼2 than they are to- day. This strong relationship between the luminosity of AGNs and their redshift suggest that there could be some special properties of young galaxies that favour the creation of active nuclei. AGNs are moreover essential instruments for studying gas clouds, galaxies and clusters of galaxies intervening between them and terrestrial observers. The study of AGNs’signal, since coming from huge cosmic distance, is in particular very useful to gather information about the diffuse extragalactic background light (EBL) and the intergalactic magnetic field (IGMF) with which it interacts. EBL is constituted by radiation which has accumulated in the Universe because of stellar formation processes and by a more general extragalactic emission of non identified sources, extending on typical wavelengths between UV/optic and infrared (IR). IGMF is the diffuse magnetic field permeating the Universe at cosmological distances (> 1 Mpc). It can include the traces of magnetic fields produced in the initial phases of the Universe and in general all the magnetic field ejected by galaxies and quasars [93]. Just grounding on this quick overview of properties, it’s evident because AGNs have been becoming the focus of a significant fraction of the world astronomical community’s attention during the last decades.

1.2 AGNs: classification

The acronym AGN contains a great variety of different objects: the principal classes are

Seyfert galaxies, quasars, radio galaxies and blazars. Changes in the angle at which the

AGN is observed, in the spin and/or mass of the black hole, in the accretion rate, and in

the modalities with which the surrounding interstellar medium interacts with the emerging

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AGN flux, account for the varied types found in the AGN zoo. To better understand the main topics that concern my thesis work, it’s useful to taxonomically order this variety.

The optical and radio observations of AGN originate its classification. The AGNs with low optical luminosity are called Seyfert galaxies and Radio Galaxies, whereas the powerful ones in the optical band are quasars or BL Lacs.

Better specifying the classification, AGNs can first of all be divided in two big groups, radio loud and radio quiet AGN. Roughly 15-20% of AGNs are radio-loud and this means they have ratios of the radio (5 GHz) and optical (B band which is comprised between ∼ 3500 and 5500 ˚ A) fluxes R = F

_{5 GHz}

/F

_B

> 10 [95]. Radio quiet AGNs have instead normally 0.1 < R < 1 (like in any schematic classification, there will be then some ambiguous cases:

here, close to the R ∼ 10 demarcation line). The radio-loud AGNs are the ones that also emit VHE (energy > 100 GeV) γ − rays and this is the main energy range investigated in my thesis. Radio-loud AGN are located in elliptical galaxies, while radio-quiet AGN are mostly in gas-rich spirals, and very seldom in ellipticals. With few exceptions, the optical and ultraviolet emission-line spectra and the infrared to soft X-ray continuum of most radio-loud and radio-quiet AGN are very similar and so must be produced in more or less the same way. The characteristic of radio-loudness itself may be related in some way to host galaxy type or to black hole spin [117], which might enable the formation of powerful relativistic jets. Inside of these groups, further sub-classifications exist. The figure below shows a schematic AGN classification, based on the morphology of the host galaxy, the luminosity and the inclination angle with respect to the observer.

Figure 1.1: AGN classification scheme. Figure from [70], based on [203]

The radio-loud AGNs that show developed jets can be further divided according to

their luminosity, that is correlated to differences in the morphology of the jets ([71]). The

usual criterion to distinguish “high” and “low” luminosity sources is the radio luminosity

at 178 MHz. Objects with L

178

> 2.5 × 10

²⁶

W/Hz are highly luminous AGN and show

strong jets that extend far outside the host galaxy. The jet luminosity is increased at

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the outer region, showing extended radio lobes and hot spots. These objects are further divided into FSRQ, Steep Spectrum Radio Quasars (SSRQ), and Fanaroff-Riley type II (FR-II) radio galaxy types. Objects with L

₁₇₈

< 2.5×10

²⁶

W/Hz have jets that are fainter than in the previous, more luminous AGN. Also, the jet luminosity decreases at larger dis- tances from the central engine and the jet does not show hot spots. These objects are then further divided in the BL Lac objects and in Fanaroff-Riley type I (FR-I) radio galaxy types. To go deeper in this classification is now essential to introduce the so-called AGN unification scheme, which is the prevailing picture of the physical structure of AGNs ([112]) The so-called unification models (for example [32] and [203]) explain the main differences of the AGN according to a few characteristics. The primary continuous radiation is repro- cessed by a clumpy shell of photoionized gas close to the accretion disk which constitutes the so-called broad line region (BLR). This name is due to the fact that lines are Doppler- broadened due to the fast (1000-5000 km/s) motion caused by the proximity of this gas to the black hole (∼ 0.1 − 1 pc where a parsec is ∼ 3.086 × 10

¹⁶

m). Farther from the central engine, at ∼100 pc, other clouds with slower motion (500 km/s) constitute a region were both narrow emission and absorption lines (narrow line region, NLR) are observed. The geometric shape of the NLR is not clear: it could be clumpy or cone-shaped. Finally, a dusty torus is present at ∼1-10 pc from the center in the equatorial plane and, depending on the viewing angle, it can obscure all the central region.

Outflows of energetic particles occur along the poles of the disk or torus, escaping and forming collimated radio-emitting jets and sometimes giant radio sources, when the host galaxy is an elliptical, but forming only very weak radio sources when the host is a gas-rich spiral. This inherently axisymmetric model of AGNs implies a radically different AGN appearance at different aspect angles. In practice, AGNs of different orientations will therefore be assigned to different classes.

Figure 1.2: Schematic view of an AGN according to the unified model: arrows indicate the classification depending on the viewing angle with respect to the observer’s line of sight (credits: Pierre Auger Observatory)

If the observation angle of the jet is large, the torus obscures the inner part of the AGN,

and therefore the broad line region, as well as the thermal continuum radiation from the

disk are shielded. In this case, the AGN is classified as a radio galaxy. For intermediate

inclination angles, where the jet is not aligned, but the inner core is not shielded by the

torus, the spectrum contains the broad emission lines and the blue bump from the accretion

disk. These objects are the so-called Steep Spectrum Radio Quasars (SSRQs), in contrast

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to Flat Spectrum Radio Quasars (FSRQs) (explained up ahead), show a steep spectrum with a dominance of the lobes and have always been observed as high luminosity AGNs.

For very small inclination angles (< 12

^◦

), the jet points towards the observer. Since the bulk motion of the jet is relativistic, with the effect of greatly increasing the luminosity from the jet radiation, the radiation from the AGN is dominated by the radiation from the jet. These AGNs show a flat radio spectrum, with a highly variable flux, and polarized radiation, characteristics of a strong beamed emission. The AGN that fit well in the pre- vious description are both the FSRQ and the BL Lac objects, that are commonly grouped in the term blazars. In both cases, the host galaxies are giant ellipticals. The FSRQ are high luminous objects that show a FR-II type jet and strong emission lines, while the BL Lac objects are less luminous objects that show a FR-I type jet and lack strong emission or absorption features (typical equivalent width limits are set at W

_λ

< 5 ˚ A). The main characteristic that distinguishes blazars from the other AGN types is their non-thermal beamed continuum emission, that is attributed to plasma moving at relativistic speeds, along directions close to the line of sight of observation. There are relativistic effects known as relativistic beaming that give rise to distinctive observational features in blazars, such as high observed luminosity (brightness temperature often in excess of the Compton limit T ∼ 10

¹²

K) strongly anisotropic radiation, high polarization (when compared with non- blazar quasars), rapid variability and the apparent superluminal motions [203] . Blazars are bright in all wavelengths and strong radio emitters. The radio emission from their cores dominates the total radio emission. Their optical emission also dominates the one of the host galaxy. Blazars also exhibit strong flux variabilities (from minutes to years time scales) in any observed energy band. The optical emission is strongly polarized (P > 3%) and this is true also for the radio emission (P > 1-2%). Many blazars are strong γ − ray emitters, also very effective in the VHE band. The dramatically enhanced fluxes, due to Doppler-boosted radiation, coupled with the fortitutious orientation of the jet towards the observer, make these objects ideal laboratories to study the underlying physics of AGN jets through multi-wavelength observations of temporal and spectral characteristics of ra- diation from radio to very high energy γ-rays. Although in these type of objects, one sees only a featureless nonthermal optical continuum most of the time, during the minimum brightness stages, weak, emission broad lines can be detected.

Based only on the characteristics of their optical and ultraviolet spectra, AGN can in- stead be separated into the three broad types shown in the table below (adapted from [130]):

Figure 1.3: AGN optical-UV spectral classification (from http://ned.ipac.caltech.edu)

The different broad types are connected with the presence of broad emission lines (Type

1), only narrow lines (Type 2), or weak or unusual line emission (Type 0). Within each

of the groupings different types of AGNs are listed by increasing luminosity and they are

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also organized according to the already explained radio-loudness.

Type 1 AGN are those with bright continua and broad emission lines from hot, high- velocity gas, presumably located deep in the gravitational well of the central black hole.

In the radio-quiet group, these include the Seyfert 1 galaxies and the higher-luminosity radio-quiet quasars (QSO). Seyfert 1 galaxies have relatively low-luminosities and there- fore are seen only nearby, where the host galaxy can be resolved. QSOs are typically seen at greater distances because of their relative rarity locally and thus rarely show an obvious galaxy surrounding the bright central source. In the radio-loud group of the Type 1 family, there are Broad Line Radio Galaxies (BLRGs) at low luminosities and radio-loud quasars at high luminosities, either Steep Spectrum Radio Quasars (SSRQ) or Flat Spectrum Ra- dio Quasars (FSRQ) depending on radio continuum shape. Other than luminosity, little distinguishes Seyfert 1s from radio-quiet quasars, or BLRG from radio quasars.

Type 2 AGNs have weak continua and only narrow emission lines, meaning either that they have no high velocity gas or, as is more probable, the line of sight to such gas is obscured by a thick wall of absorbing material. In the radio-quiet group, Type 2 AGNs include Seyfert 2 galaxies at low luminosities, as well as the narrow-emission-line X-ray galaxies (NELG). The high-luminosity counterparts are not clearly identified but likely candidates are the infrared-luminous IRAS AGN [178], which may show a predominance of Type 2 optical spectra. In the radio-loud Type 2 AGNs, often called Narrow-Line Radio Galaxies (NLRG), there are two distinct morphological types: the low-luminosity Fanaroff-Riley type I radio galaxies, which have often-symmetric radio jets whose intensity falls away from the nucleus,

and the high-luminosity Fanaroff-Riley type II radio galaxies, which have more highly col- limated jets leading to well-defined lobes with prominent hot spots.

The Seyfert I galaxies show both narrow and broad lines, while the Seyfert II galaxies only show narrow lines, and therefore it is understood that the observation inclination makes that the broad line region is obscured by the torus. The Seyfert galaxies do not show beamed emission.

A small number of AGNs have very unusual spectral characteristics and they are usually indicated with the name of Type 0 AGN. These include the BL Lacertae (BL Lac) objects, which are all radio-loud (there are no known radio-quiet BL Lacs) and in some way also FSRQs. Even though the FSRQs have strong broad emission lines like Type 1 objects, they are noted in the Type 0 column in table above because they have the same blazar-like continuum emission as BL Lac objects.

Whether AGN are classified Type 1 or Type 2 depends on obscuration of the luminous nucleus, and whether a radio-loud AGN is a blazar or a radio galaxy depends on the alignment of the relativistic jet with the line of sight [32].

1.3 The Spectral Energy Distribution

The emission from blazars is often shown in Spectral Energy Distribution (SED) plots. A

SED is represented by a graph of the energy emitted by an object as a function of different

wavelengths or frequencies. For blazars it is generally plotted as νF

_ν

against ν, that is a

measure of the power observed at each frequency ν. The spectra of blazars are in general

composed of two parts: the thermal and the non thermal part. The thermal part is also

called blue bump, it has its maximum at optical-UV wavelengths, and is interpreted as

radiation coming from the inner accretion disk. The thermal spectrum can show super-

imposed emission lines. These lines are classified as narrow or broad lines, depending on

their equivalent widths and consequently on their formation processes and source regions.

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The non-thermal continuous emission extends from the radio band to X and γ-rays and dominates the spectral energy distribution of blazars. This emission exhibits a typical two-component structure, with a low-energy component peaking between infrared (IR) and X-ray energies, and a high-energy peak between X and γ- rays. The low energy com- ponent is dominated by synchrotron emission from relativistic electrons in the jet [193]

(see chapter 2 of this thesis). The peak frequency of the synchrotron component of the SED (ν

syn

) is used to sub-classify BL Lacs into low (LBLs, ν

syn

< 10

¹⁴

Hz), intermediate (IBL, ν

_syn

∼ 10

¹⁴

− 10

¹⁵

Hz) and high- frequency-peaked BL Lacs (HBL, ν

_syn

> 10

¹⁵

Hz). The high-energy component of the blazar SED has been historically less studied, due to the later development of hard X-ray and γ-ray detectors compared to those of longer frequency bands. However, during the past 15-20 years with Cherenkov telescopes like HEGRA, Whipple, CANGAROO, GT-48 and TACTIC and then VERITAS, HESS and MAGIC in the VHE regime, satellites like EGRET and now Fermi, designed for high en- ergy study (typically 30 MeV-30 GeV) and Chandra and Swift for X-rays, the study of the high frequency part of AGNs’spectral energy distributions has experienced a great impulse (see chapter 4 of this thesis). About the origin of the high-energy spectral component of the SEDs there is no agreement. The commonly invoked mechanisms are inverse Compton processes, with either the same photons that produce synchrotron emission (synchrotron self Compton models, SSC) or seed photons from external sources (external Compton models, EC) such as an accretion disk, broad line regions (BLR) and/or dusty tori. A possible alterative is the synchrotron radiation of pair cascades powered by hadronic pro- cesses, and synchrotron emission of ultra-high-energy protons and muons (hadronic and lepto-hadronic models) (see section ”Alternative blazars emission models” in this thesis).

Blazars’SEDs are extremely precious information tanks and, modeling them with appro- priate fitting models (see the chapter ”Blazars emission models” in this thesis), one can obtain information on the emitting regions’extension, magnetic field, relativistic properties or also on spectra and specific characteristics of particles that injects the typical blazar emissions. SEDs are the principal instrument in blazar study and then in my work too.

Two typical examples of different possible SEDs are shown below: one for the FSRQ 3C 279 and one for the HBL Markarian 501.

Figure 1.4: SED of the quasar 3C279 during MAGIC detection on February 23, 2006, with

different superposed fits (from [47])

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Figure 1.5: SED of the HBL Mrk 501 as obtained during the 2008 MWL campaign in comparison to low and high states in 2005 (from [126])

1.4 The blazars sequence

From the accurate study of many different blazar SEDs, scientists have many times tried to sort the great variety of blazar population extracting some common denominators and general conclusions. Among these unification attempts, a popular scheme is the so-called blazar sequence, proposed by Fossati et al. (1998) ([75]). In this study, combining X-ray selected BL Lacs (the Slew survey sample), radio-selected BL Lacs (the 1-Jy sample) and FSRQs (Wall and Peacock sample) known at that time, the authors analyzed the SED of 126 blazars and identified in their sample a remarkable continuity. Despite the differences in the continuum shapes of different sub-classes of blazars, blazar continua can be described by a family of analytic curves with the source luminosity as the fundamental parameter.

The ”scheme” (admittedly empirical) determines both the frequency and luminosity of the peaks in the synchrotron and inverse Compton power distributions starting from the radio luminosity only (L

_{5 GHz}

). Authors suggest the presence of a trend: if the luminosity increases, both the synchrotron and the inverse Compton peak move to lower frequencies and meanwhile the inverse Compton peak becomes energetically more dominant. On the base of this trend, sources emitting strongly in the TeV band are forecast to have relatively low intrinsic luminosity and this is what effectively happens. In the proposed scenario, the intrinsic jet power then regulates, in a continuous sequence, the observational properties from the weaker HBL, through IBL and LBL, to the most powerful FSRQs. Fossati et al.

also inspected the possible influence of redshift bias on their concluison and verified that the correlation between ν

peak;sync

and L

5GHz

still held after subtraction of the very strong dependence on redshift.

In this overall simple view, the whole radio-loud AGN population could be unified in a two-parameter space, where one is the intrinsic jet power and the other the viewing angle of the object. The demarcation line between LBL and HBL has been set to some specific values initially for purely practical reasons, while in light of the blazars sequence it as- sumes a more ’physical’meaning. LBLs are more luminous and have their first peak in the infrared–optical band and the second one at keV-MeV energies. In LBLs the high energy component dominates over the low energy one. On the other hand, in HBLs the first peak is found at UV-X-ray frequencies and dominates over the high-energy component, which peaks at GeV-TeV energies. LBL sources have Compton-dominated soft X-ray emission, while in HBL this is pure synchrotron emission.

In the figure below, another interesting conclusion of Fossati et al. emerges: ν

peak;sync

is

here plotted against the γ-ray dominance parameter,which is the ratio between the SED’s

high and low energy peak luminosities.

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Figure 1.6: γ − ray dominance VS synchrotron peak frequency (from [75])

A strong correlation is present over four orders of magnitude in ν

_peak;sync

: a decrease in the γ-ray dominance with an increase of the synchrotron peak frequency is clear. In the same figure authors also plotted the ratio between the γ-ray and optical luminosities. The aim of this plot was to see if the optical luminosity could eventually be a good indicator of the γ-ray dominance, with the advantage of being an observed quantity. In fact there is little difference, at most a factor of 3, for a quantity spanning more than three decades.

Fossati et al. finally observed that the X-ray spectra of their sources became harder while the γ-ray spectra softened with increasing luminosity. They established that this behaviour indicates that the second peak of the SEDs also moves to lower frequencies from

∼ 10

²⁴

− 10

²⁵

Hz for less luminous sources to ∼ 10

²¹

− 10

²²

Hz for the most luminous ones.

Fossati et al. deduced therefore that the frequencies of the two peaks are correlated: the smaller the ν

_peak,sync

, the smaller the peak frequency of the high energy component.

Figure 1.7: Average SEDs for a sample of 126 blazars binned according to radio luminosity

irrespective of the original classification ([75]). The transition from FSRQs to LBLs, IBLs

and HBLs is shown. The lines show a simple leptonic model proposed by Ghisellini (1998)

([84]) (figure from [196]).

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A comparison with the analytic curves, as shown in the figure above, obtained through a simple leptonic model proposed by Ghisellini (1998) ([84]), tells the data are even consis- tent with a constant ratio between the two peak frequencies. The investigation of Fossati et al. have been evidently very deep, they have debated and solved many weak spots of their data sample but their whole work has been during the next years, and is still now, subject to criticisms. Their data sample has, like any sample and especially 15 years ago when the knowledges field was more reduced than now, some limits. First of all, the sam- ple incompleteness. In view of building average SEDs minimizing the bias introduced by incompleteness, authors decided to focus on a few well-covered frequencies, at which fluxes are available for most objects. This led to the choice of seven well-sampled frequencies, sufficient to give the basic information on the SED shape from the radio to the X-ray band:

radio at 5 GHz, millimeter at 230 GHz, far-infrared at 60 and 25 µm, near-infrared (K band) at 2.2 µm, optical (V band) at 5500 ˚ A, and soft X-rays at 1 keV. There is evident deficiency of γ-ray data: only 33 γ-ray detections out of 126 total blazars. Fossati and coauthors then asked whether the small fraction of γ-ray detected sources are represen- tative of each sub-sample as a whole or have peculiar properties that distinguish them from the rest of the objects in the same sub-sample. Moreover, they tried to understand if the γ-ray detected sources in general differ from those belonging to the complete samples.

Except for the case of the Slew survey, authors concluded that the γ-ray detected sources are representative of the samples as a whole, being indistinguishable from the others in terms of radio-to-X-ray broadband properties and power. They also checked that the γ-ray detected sources included in their sample were homogeneous with respect to all of the γ-ray blazars detected until then and concluded that there is no significant differences.

Nevertheless, Fossati et al. were aware that the limited sensitivity of the γ-ray instruments available at the time entailed that at a given radio flux, only the γ-ray loudest sources were detected. Considering that variability is a distinctive property of blazars and has also been observed in γ-rays, often with extremely large amplitude, even greater than a factor 10 (e.g. 3C 279), authors concluded that the average γ − ray luminosities computed in their work were necessarily overestimated. However, they preferred not to correct for this effect given the uncertainties. In particular the ’bias factor’for different classes of blazars could be different if their γ − ray variability properties (amplitude and duty cycle) are different ([201]). This is certainly a critical point of Fossati et al. (1998) theoryzation.

Padovani (2007) ([160]) and Padovani and Giommi (2012) ([159]) has investigated the

validity of the blazars sequence and tested its predictions against more recent observa-

tional data. They concluded that the proposed anti-correlation between radio power and

synchrotron peak frequency in blazars is a consequence of selection effects. Furthermore,

they reported that outliers to the originally proposed sequence had been found, both in

the low-power-low-ν

_peak

and high-power-high-ν

_peak

regions. Morover, there’s a class of

FSRQs with synchrotron peak frequency in the UV/X-ray band, that is as high as those

of LBLs, whose existence is not expected within the blazars sequence, but that had been

found. Padovani also underlined that all observational data at the time were consistent

with the idea that the HBL subclass makes up a small (≈10%) minority among BL Lacs

and this is in contrast to what could be expected if the blazars sequence would hold as

proposed by Fossati et al. (1998). Padovani then concluded that the blazars sequence in

its simplest form cannot be valid but this in any case doesn’t deny the correlation between

low and high-energy peak frequencies. A consequent implication is that HBLs have the

highest high-energy bump peak frequencies, making them more likely to be TeV emitters,

and this is indeed mirrored in the numbers of TeV blazars detection history. The fact

that the maximum synchrotron peak frequency of FSRQs appears to be ∼10-100 times

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smaller than that reached by BL Lacs, already deduced by Fossati et al., remains still valid. It’s still not clear if this is the clue of different jet physics between the two families or if it’s instead a selection effect due to the fact that for really high-power-high-ν

_peak

blazars it might be hard to get a redshift estimate. Padovani and Giommi (2012) more- over claim that sources so far classified as BL Lacs on the basis of their observed weak, or undetectable, emission lines are ascribable to two physically different classes: intrinsically weak-lined objects, more common in X-ray selected samples, and heavily diluted broad- lined sources, more frequent in radio selected samples. This subdivision can help to solve some confusion. Contemporaneously to Padovani’s works, Ghisellini (2009) ([85]) stud- ied the physical properties of all the bright Fermi blazars detected during the first three months of LAT operation. Observationally, that sources seemed to confirm the so-called blazar sequence, relating the bolometric observed non-thermal luminosity to the overall shape of the spectal energy distribution. As result of this study Ghisellini suggests that the division of blazars into the two subclasses of FSRQs and BL Lacs is a consequence of a rather drastic change of the accretion mode: it becomes radiatively inefficient below a critical value of the accretion rate, corresponding to a disk luminosity of ∼1 per cent of the Eddington luminosity. Below this limit, ionizing photons reduce and this causes that the broad line clouds, even if present, cannot produce significant broad lines, with the consequence that the object becomes a BL Lac. This work seems then to confim the physical legitimacy of the blazars sequence.

Definitively, the blazars sequence is still an important benchmark in blazar study and its validity, also if redimensioned if compared with its original significance, is still debated and investigated.

1.5 TeV emitting blazars

The large majority of the established TeV-emitting AGNs belongs to the blazar class and the majority (49) of the TeV blazars belong to the further sub-category of BL Lac objects, with a net preponderance of HBL subclass. Mkn 421 was the first blazar and extragalactic object to be discovered as a VHE γ -ray emitter, detected with the Whipple telescope in 1992, at a redshift of z = 0.031 ([169]) (and it’s also the main target of my study in chapter 6). Since then, different candidate selection methods have been applied to radio, optical, X-ray or HE data with the aim of finding new ”TeV” blazars ([54]; [60]; [33]). To date, 52 blazars have been detected in the VHE regime, consisting of 41 HBLs, 7 IBLs,1 LBLs and 3 FSRQs (http://tevcat.uchicago.edu/).

The distribution in the type of observed AGNs is at least partially biased by the ob-

serving criteria of the Cherenkov telescopes and by an historical tendence to search sources

on the base of their position in the blazars sequence, which clearly favor HBLs as possible

TeV emitters (Costamante and Ghisellini 2002 catalogue). Now other types of selection

criteria are also adopted to choose new VHE observation candidates. Among these, the

principal criterion is the presence of the source in the so-called Fermi LAT 2-Year Source

Catalog (2FGL) which is a catalog of high-energy γ-ray sources detected by the Large

Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope mission during the first

24 months of the science phase of operations. Fermi began its operations on 2008 August 4

and continuously scan the whole sky every three hours searching for γ-ray signals covering

the energy range from about 20 MeV to more than 300 GeV. TeV blazars have rising spec-

tra in the Fermi band, with typical spectral index < 2, and this is considered a big incentive

to stimulate VHE observations of source with this behavior. Another common triggering

situation for TeV observations is the detection of particularly high optical emission from

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the source. This often has given rise to fruitful multiwavelength campaigns like the ones derived from the collaboration between the 1.03 m telescope at the Tuorla Observatory in Finland, the 35 cm KVA telescope on La Palma and the stereoscopic Cherenkov system MAGIC on the same site.

Since BL Lacs do not have significant emission or absorption features in their optical spec- tra, it’s difficult to measure their redshift directly. The redshift is however a fundamental parameter to deeply understand blazars physical processes and the physical processes on which they have repercussions, like the ones involving interaction with the medium com- prised between the source and the observer. The farthest TeV emitting object detected up to now is the IBL 1ES 1424+240, with z>0.6 ([78]), and, among the HBLs, PG 1553+113 whose z > 0.4 ([57]), so the γ-ray window extends now to relatively high redshifts. These great distances imply the need to deal with the so-called extragalactic background light EBL (see section ”The Extragalactic Background light” in this thesis), diffuse radiation caused by stellar formation processes and by a more general extragalactic emission which fills the Universe. EBL extends on wavelenghts typical of the interval between UV/optic and IR ([92]).

Observed TeV sources spectral indices are in general rather steep (∼ 2.5-3.5 from power law fits), with few exceptions in case of strong flares of the sources when the high energy peak of the spectrum is supposed to move toward higher energies, leading to a flattening of the spectral slope (∼2 and even less e.g. during 2004, April flare of Markarian 421).

If EBL deabsorbtion is taken into account, the intrinsic VHE spectral indices become harder. Generally the spectral indices tend to increase with the source distance so that those of the more distant sources are considerably softer, up to ≈4 (e.g [157]). The peak in the measured γ-ray spectrum (in νF

_ν

representation) of these objects lies below the energy range of the TeV instruments. This could partially be due to the mentioned EBL absorption, but perhaps also because a distant AGN must be intrinsically brighter to be detectable ([110]).

Many, but not all, TeV blazars have shown evidence for VHE variability, undergoing episodic flaring activity with short doubling timescales, a phenomenon that could have deep implications on blazars emission models. PKS 2155-304 is the HBL that historically has shown the fastest VHE variability: observations on 2006, July 28-29 revealed a big flare reaching up to 11 times the Crab Nebula flux above 400 GeV with a 172.9σ significance signal detected by the HESS Cherenkov telescope and a variability time scale of the order of ≈5 minutes ([153]) (see appendix B). By studying blazars variability, it is possible to place strong constraints on properties such as the size of the emission region, the strength of the magnetic field at the acceleration site, and the Doppler factor in the jet. Emission from relativistically moving sources is required to overcome γ-ray transparency problems implied by the measured large luminosities and short time variabilities ([61]).

IBLs and HBLs are the best types of sources to observe VHE emission because they show

peak emissions in the TeV range and are indeed the most numerous objects in the official

TeVCat catalogue. Moreover, for IBLs and HBLs, emission models usually do not need

an external radiation field to give rise to Compton emission (often necessary instead for

FSRQs and in part also for LBLs), a fact that goes hand in hand with the total absence, or

in any case reduced presence, of emission lines in these sources. This two aspects together

justify the methodologic choice of my thesis of concentrate on these specific BL Lacs fam-

ilies to underline, with a particular focus on TeV energy range, caveats of the SSC model,

the most popular emission model to appropriate fit IBLs and HBLs broadband emission

(see chapter 3 of this thesis).

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Chapter 2

PHYSICAL BASES OF SYNCHROTRON AND INVERSE COMPTON EMISSION

2.1 Synchrotron emission

The continuum radiation from AGN stretches, like explained in the first chapter of this thesis, over the entire range of the electromagnetic spectrum, from the radio to the high energy γ-ray region. The radiation is produced in elementary processes, the most im- portant of which is synchrotron emission, and is modified, like any type of radiation, by scattering, absorption and reemission.

Synchrotron radiation is emitted when a relativistic particle is accelerated by a magnetic field and for this reason it’s also called magnetic brehmstrahlung. The motion of a charged particle in a magnetic field ~ B is described in electrodynamics by the Lorentz force equation

d

dt (γm~ v) = q

c (~ v × ~ B), (2.1)

where q and m are the charge and rest mass of the particle, ~ v is its velocity and γ = (1 −

^v_c2²

)

^−1/2

is the Lorentz factor, with v the magnitude of the velocity, and c is the speed of light in vacuum. The acceleration dv/dt is normal to the velocity and therefore v and the Lorentz factor γ are constant. Decomposing the equation (2.1) in a direction parallel and another perpendicular to ~ B = B

₀

~ z (magnetic field with constant modulus and direction), one discovers that, for the parallel component, the right member of the equation becomes equal to 0 since there is no force acting on the charged particle. Then the component of the velocity along the magnetic field remains constant:

dv

||

dt = 0. (2.2)

For the perpendicular component v

⊥

one finds instead that dv

⊥

dt = ( q v

⊥

γmc × ~ B). (2.3)

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Multiplying this equation with ~ v

⊥

, one discovers that the modulus of v

⊥

is constant. This equation simply describe a pure rotational motion with frequency

ω

_g

= qB

0

γmc , (2.4)

where ν

_g

= ω

_g

/2π, a quantity known as gyration frequency. The net effect of v

_||

and v

⊥

acting together is that the particle moves in a helix with its axis parallel to ~ B ([204]).

Classical physics teaches that the acceleration of a charged particle produce electromag- netic radiation emission. In small velocities regime, the Larmor equation claims that the total irradiated power, P , in this situation (expressed in cgs units) is:

P = 2 q

²

3 c

³

a

²

, (2.5)

where ~a is the acceleration of the particle. To generalize this equation to relativistic particles, it’s useful to note that P is the ratio between the temporal components of two quadrivectors, the energy and the time. The Larmor power is then a relativistic invariant and can be written in an invariant form in this way:

P = − 2 q

²

3 c

³

a

^µ

a

_µ

, (2.6)

where a

^µ

is the quadriacceleration. From special relativity, one knows that in the rest frame of a particle its acceleration, ~ a

RF

, is related to the acceleration in the motion frame,

~a, through:

a

_RF,||

= γ

³

a

_||

(2.7)

a

_RF,⊥

= γ

²

a

⊥

, (2.8)

where γ is the Lorentz factor of the motion. For the motion of a particle in a magnetic field, it follows from equation (2.1) and a

_||

= 0, that a

⊥

= 2πν

_g

vsinθ, where θ is the angle between the velocity and the magnetic field, called the pitch angle. The acceleration will then be only perpendicular to particle’s velocity and hence only the component a

⊥

= ω

g

v

⊥

will contribute to the emitted power. The emitted synchrotron power is then given by:

P = 2q

²

3c

³

γ

⁴

ω

²_g

v

_⊥²

= 2q

⁴

γ

²

B

²₀

3m

²

c

⁵

v

²

sin

²

θ. (2.9) If the ensemble of particles with which one works has an isotropic velocity distribution, sinθ

²

has to be replaced with its mean value on the distribution:

1 4π

Z

sin

²

θdcosθdφ = 2

3 (2.10)

with θ ranging over [0, π]. This leads to P

S

= 4

3 σ

t

cβ

²

γ

²

U

B

, (2.11)

where U

B

= B

²

/(8π) is the energy density of the magnetic field and σ

t

= 8π(q

²

/mc

²

)

²

/3

is the Thomson scattering cross-section for the particle. In highly relativistic regime it is

usual to set β=1 in P expression. If the particles were not relativistic, i.e. γ ' 1, it would

emit cyclotron radiation at the frequency ν

g

= qB/2πγmc. As the speed increases, the

higher harmonics of ν

_g

begin to contribute to the spectrum with a strength that depends on

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powers of v/c. As the velocity becomes relativistic, γ increases and the gyration frequency decreases because ν

_g

∝ γ

⁻¹

. In the newtonian limit (vc, γ − 1 1), the lost energy in each unit of time is proportinal to v

²

and then to the particle energy (=1/2mv

²

), whereas in the relativistic limit (c-vc, γ 1) the lost energy in each unit of time is proportional to γ

²

and then to the squared particle energy (=γmc

²

). Because of the fact that the lost energy is moreover proportional to the energy density of the magnetic field and the Thomson cross-section, the emitted power goes like m

⁻²

. Then, within an astrophysical plasma containing at the same time ions and electrons, the synchrotron radiation will overwhelmingly comes from this last type of particles, being the lightest. Synchrotron radiation coming from ions will be instead almost always negligible.

For a single electron, it’s possible to define a cooling time t

_cool

≡ E

P = γm

_e

c

²

P ∝ 1

γ . (2.12)

A radiating relativistic electron loses energy at the rate dE/dt = −P ∝ E

²

B

_⊥²

. Given a constant magnetic field, it is straightfroward to integrate this expression to obtain E as a function of t and to find that the time taken by the electron to lose half its energy is

t

_1/2

= ( 3m

⁴

c

⁷

2e

⁴

sin

²

θ ) 1

B

²

E = 8.5 × 10

⁹

( B

⊥

1µG )

⁻²

( E

1GeV )

⁻¹

yr. (2.13) An important effect of the relativistic motion is that even if the particle has, in its reference frame, a totally isotropic emission, the observer who looks at it moving with a Lorentz factor γ 1 sees an emission confined in a narrow cone, with axis in the direction of the instantaneous velocity vector and half-angle θ ∝ 1/γ. As the electron goes round the magnetic field, an observer whose line of sight intersects this cone sees a sequence of pulses with a period equal to the Doppler shifted gyration frequency

ν

_g⁰

= ν

_g

1 − (v/c)cos

²

θ ' ν

_g

sin

²

θ . (2.14)

The width of the pulse ∆t is given by the time taken by the cone to sweep across the observer’s line of sight and, in the highly relativistic case, typical for AGNs

∆t = 1

2πγ

³

ν

g

sinθ . (2.15)

The frequency spectrum of this radiation consists of a series of spikes at ν

_g⁰

and its harmon- ics, with a cut-off at ∼ 1/(2π∆t). Separation among the different lines, being equal to the fundamental frequency, becomes smaller while the particle energy increases: ν

g

→ 0 when γ → ∞. Since in typical astrophysical situations one usually meets big Lorentz factors, one expects the lines are closely spaced with each particle emitting a quasi-continuum. In addition, the frequency of each harmonic is broadened when radiation from an ensemble of particles is considered, because of the distribution of γ and pitch angles. The spec- trum thus appears to be continuous, and can be shown to have a maximum at the critical frequency

ν

crit

= 3qBsinθ 4πmc ( E

mc

²

)

²

= 16.1 × ( B

⊥

1µG )( E

1GeV )

²

M Hz. (2.16) In terms of this critical frequency, the t

_1/2

introduced before becomes

t

_1/2

= 3.7 × 10

⁸

( B

⊥

1µG )

^−3/2

( ν

crit

1GHz )

^−1/2

yr. (2.17)

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In AGN jets, typical magnetic field are smaller than 1 Gauss and electrons energies are ∼ 1 TeV, hence cooling times are expected to be ∼ 1 year and synchrotron peaks are located in the wavelength region corresponding to UV/X (∼ 10

¹⁶

Hz) (see chapter 5 in this thesis).

The emitted power, which is the energy emitted per unit time per unit frequency interval, can be obtained from the Fourier transform of the electric field of the synchrotron pulses and, expressing it as a function of frequency, it is:

P (E, ν) =

√

3e

³

Bsinθ mc

²

F ( ν

ν

C

) (2.18)

with the function F defined by

F (x) = x Z

∞

x

K

_5/3

(ξ)d(ξ) (2.19)

where K

_5/3

(ξ) is the modified Bessel function of order 5/3 and x is the variable ν/ν

_c

. The total power emitted at all frequencies is obtained by integrating P (ν, E) over ν and coincides with formula (2.9), previously obtained in other way. The function F(x) has a maximum in x≈0.29 (F(0.29)≈0.92) and its asymptotic forms are:

F (x) ≈ 4π

√

3Γ(1/3) ( x

2 )

^1/3

(2.20)

if x 1 and

F (x) ≈ ( π

2 )

^1/2

e

^−x

x

^1/2

(2.21)

if x 1. This tells us that the single particle spectrum slowly grows till ν

_crit

, like ν

^1/3

, there it reaches the maximum and then exponentially decreases.

It’s important to underline that the maximum for this spectrum coincides with the critical frequency ν

_crit

(2.16) rather than with the gyration frequency ν

_g

(2.4) and these differ in a factor γ

³

. This is caused by the fact that the particle has a Lorentz factor γ 1.

Considering a particle rotating around a magnetic field line, one can deduce that, for most of the time, it will not be visible with the exception of when its small emission cone points toward the observer. The particle orbit’s visible fraction is only 2/γ so that, knowing the rotational period through the gyration frequency, one can see the particle only during the short time interval T = 2π/γµ

_g

= 2πmc/qB. In any case, the emission that a terrestrial observer can perceive from such a particle lasts even shorter because of the relativistic nature of the source. Indicating with t

0

the time at which the emission cone focuses the observer for the first time, and with t

₀

+ T when it focuses the observer last time, one can cosider these times also the exact moments in which the particle emits, respectively, the first and the last photon reaching the observer itself. A fundamental point is that, between the first and the second emission, the emitting particle is also moving meanwhile and, because of this, the second photon doesn’t leave exactly where the first leaves, but at a distance vT up ahead. During the time T, the first photon goes through a distance cT then, at the moment in which the accelerated particle emits its second photon, the first one has a spatial advantage of (c-v)T. Since the second photon, like every photon in an empty space, moves at c, the two examined photons arrive to the observer with a temporal detachment ∆t = (1 − v/c)T . Being γ 1 in relativistic regime, v/c ≈ 1 − 1/2γ

²

and then the time interval between the two photons is:

∆t = T

2γ

²

= πmc

eBγ

²

. (2.22)

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This determines that, for every particle rotation, during the long overall time scale γmc/eB, the terrestrial observer can see the particle only for the small time ∆t. In this situation, the signal Fourier transform contains frequencies till 1/∆t, at the same order of magni- tude of ν

crit

. This is the reason why relativistic particles have high frequencies in their synchrotron spectra.

2.1.1 Synchrotron emission from many electrons

Looking at blazars, one obviouslly never meets a particle living alone and emitting only on its own. One must instead consider great groups of particles which, working together, will give rise to something more complicated than a single emitting particle spectrum. Con- sidering an ensemble of electrons (ions contribution being negligible for reasons explained above), with energy in the range (E

_min

, E

_max

), if n(E)dE indicates the number density of particles with energy between E and E+dE, the emitted power, as a function of the frequency of the emitted radiation, is:

P (ν) =

Z

Emax

Emin

P (E, ν)n(E)dE. (2.23)

In the synchrotron as well as the Compton case (treated in next paragraph), power law spectra are naturally produced if the emitting particles have a power law distribution of energy. In case of power law distribution, the number density of electrons as a function of energy is given by:

dN = n(E)d(E) = CE

^−p

dE E

_min

≤ E ≤ E

_max

(2.24) where C and p are constants, whereas E is the individual kinetic energy of each particle composing the distribution. Such power law particles can be produced in a variety of ways, such as acceleration reproduced naturally by the Fermi acceleration process through shocks (e.g. [37]). The existence of a class of particles with a typical power law distribution (making them clearly different from thermal spectra) is one of the main peculiarities of high energy astrophysics. They are defined non-thermal particles because their energy distribution doesn’t obey a Maxwell-Boltzmann law. The radiation spectrum produced by electrons having energy E peaks at the same critical frequency obtained in (2.16) and one obtains:

P (ν) =

√ 3e

³

2mc

²

( 3e

4πm

³

c

⁵

)

^(p−1)/2

× C(Bsinα)

^(p+1)/2

ν

^−(p−1)/2

G( ν ν

1

, ν ν

2

, p), (2.25) where ν

₁

and ν

₂

are the critical frequencies corrisponding to the energies E

_min

and E

_max

respectively and

G(x

1

, x

2

, p) = Z

x2

x1

x

^(p−3)/2

F (x)dx, (2.26)

with the function F defined as in equation (2.19). In the spectral regime where ν < ν

₁

, every particles follow F (x) ∝ ν

^1/3

then the spectrum will be P

_ν

∝ ν

^1/3

. In the region where ν > ν

2

, F (x) ≈ e

^−x

, so the emission is negligible: P

ν

≈ 0. The most interesting region is the intermediate one. When ν

₁

ν ν

₂

, that is a very common astrophysical situation, the function G reduces to:

g(p) = G(0, ∞, p) = 2

^(p−3)/2

1 ACTIVE GALACTIC NUCLEI 7

Contents

Introduction 2