Twinkle, twinkle, quasi-star Biggest puzzle from afar How unlike the other ones Brighter than a billion suns Twinkle, twinkle, quasi-star How I wonder what you are.
- George Gamow
ABSTRACT
This thesis describes the analysis of Very High Energy (VHE) emission from the Active Galactic Nucleus PKS 0537-441. It also aims to put the results in a wider context by imple- menting previous work done on this source. The data chosen for the analysis is provided by the Fermi-LAT satellite and covers the energy range between 300 MeV and 300 GeV. Initially a lightcurve of the received flux from the source was generated, containing data from August 2008 to April 2017, with a mean flux of 4 ∗ 10−8 photons per second per squared centimeter.
The lightcurve contained sections of different flux intensities giving periods of special interest, such as a flaring period at August 2008 to August 2011, an enormous flare at April 2010 and a less active period between April 2013 - January 2016 that could be identified for further investigations. The differences in observed flux over time was tested and PKS 0537-441 was found to be a significantly variable source.
Spectral Energy Distribution (SED) analysis was performed over both the entire period as well as over the selected subperiods and fitted against models using the tools provided by the Fermi Science Support Center (FSSC). The models used in the fitting was PowerLaw2, LogParabola and PLSuperExpCutoff and the best fit for the data was obtained from the PLSuperExpCutoff, except for the less intense period where the LogParabola gave the best fit. The result from the SED analysis was integrated with results from previous work done on the source, ranging over multiple wavelengths in order to get a SED which spanned over the entire electromagnetic spectrum. Finally, modeling of this multi wavelength SED was performed in order to obtain parameters for the physical processes involved in the creation of the radiation received from PKS 0537-441.
Contents
1 The AGN PKS 0537-441 6
1.1 Active galactic nuclei . . . 6
1.1.1 Black holes . . . 6
1.1.2 Accretion disc . . . 7
1.1.3 The Jet . . . 10
1.2 Different types of AGN . . . 11
1.2.1 Classifications . . . 11
1.2.2 Blazars . . . 12
1.3 The physics of jet emission . . . 12
1.3.1 Synchrotron radiation . . . 14
1.3.2 Inverse Compton scattering . . . 16
1.3.3 Relativistic beaming . . . 17
1.3.4 Synchrotron Self Compton model . . . 18
1.3.5 Parameters of the SSC-model . . . 19
1.4 PKS 0537-441 . . . 20
2 The Fermi-LAT satellite 22 2.1 Large Area Telescope . . . 22
2.1.1 Converter tracker . . . 22
2.1.2 Calorimeter . . . 23
2.1.3 Anticoincidence detector . . . 23
2.1.4 Data acquisition system . . . 24
2.1.5 Fermi Support Science Centre . . . 25
3 Analysis method 26 3.1 Computer resources . . . 26
3.2 Analysis tools and statistics . . . 26
3.2.1 Binned data . . . 27
3.2.2 Likelihood . . . 27
3.2.3 Likelihood ratio test . . . 28
3.2.4 Source detection . . . 28
3.2.5 Dataset of the analysis . . . 29
3.2.6 Variability . . . 29
3.2.7 Spectral analysis . . . 30
3.2.8 Models of the spectral analysis . . . 30
3.2.8.1 PowerLaw2 . . . 31
3.2.8.2 LogParabola . . . 31
3.2.8.3 PLSuperExpCutoff . . . 31
3.2.8.4 Determining the best fit . . . 32
3.2.8.5 Accuracy of the analysis . . . 32
3.3 Modeling . . . 32
3.3.1 Modeling the physics behind the SED . . . 32
3.3.2 Models for extracting the Extragalactic Background Light . . . 32
4 Analysis of PKS 0537-441 34 4.1 Results . . . 34
4.1.1 Light Curves . . . 34
4.1.2 Variability . . . 35
4.1.3 SED . . . 39
4.1.3.1 The SED in the range 300 MeV to 300 GeV . . . 39
4.1.3.2 Multiwaveband SED . . . 41
4.1.4 Modeling . . . 43
4.1.5 EBL . . . 44
5 Conclusions and reflections 46 5.1 Conclusions . . . 46
5.2 Reflections . . . 47
Introduction
Far from earth, at a distance well beyond human comprehension, lies the blazar PKS 0537- 441. In order to define a blazar one must first understand what Active Galactic Nuclei (AGN) are. An AGN is a very compact region in the centre of a galaxy which is believed to be powered by a supermassive black hole accreting matter through its enormous gravitational force. The inward flow of this mass forms an accretion disc around the black hole and through processes not yet fully understood, matter is ejected from the disc in jets. One of the current models for describing this powerful event is called the Synchrotron Self Compton (SSC)- model. SSC models describe how the ejected matter initially generates synchrotron radiation from electrons that are being violently accelerated in magnetic fields, then the models describe how the generated radiation then scatters to higher energies by inverse Compton processes in the jet. When the jet of an AGN is aligned, or nearly so, with our line of sight it is called a blazar and this category includes the source which is presented and studied in this thesis:
PKS 0537-441.
In order to investigate astronomical objects such as blazars we rely on photons emitted by the source of interest. Fortunately, PKS 0537-441 radiates generously over all wavelengths and provides much information that we can use as a probe for the understanding of the physics involved. One major tool is to study the distribution of energy among the different wavelengths of the radiation emitted by the source under study. The behavior of this spectral distribution provides important clues concerning the origin of the radiation. The spectral distribution of AGN often displays two separated bumps, which are usually interpreted by the SSC-model as two linked processes behind the emitted radiation.
With a redshift of nearly 0.9, PKS 0537-441 is a very distant source and the photons received from this blazar have travelled through space for a fraction of eternity, which means that studying these photons is equivalent to looking very far back in time. So, as a conse- quence of this, scientists develop the knowledge of tomorrow by looking deep into the past.
A truly staggering fact.
Chapter 1
The AGN PKS 0537-441
1.1 Active galactic nuclei
There are still a lot of unanswered questions regarding the physics of Active Galactic Nuclei (AGN) and the quest to gain more understanding about these violent objects is ongoing.
The development of our models depends on our capacity to gather and analyze the radiation created by these sources, a capability that is constantly being upgraded due to improvements in our technology. We have gained a lot of information about AGN but it is still no simple task to put it all together in a unwavering model. Our present knowledge on these objects and their physical properties involve supermassive black holes, strong tangled magnetic fields, particles with superluminal1 speeds and other processes beyond anything we can create in our laboratories here on earth. Even though there are a lot of unverified operations involved concerning AGN, the following physical properties are the most established.
The information about AGN throughout this section is mainly acquired from the book High Energy Astrophysics by Malcolm S. Longair [1] with references to relevant chapters.
Where other sources are used, they are cited in the text.
1.1.1 Black holes
An active galactic nucleus is a very dense region at the centre of a galaxy and it is believed that it acquires its energy from an adjacent supermassive black hole (106− 109 solar masses).
A black hole represents an object which is so compact that its gravity keeps even light from escaping its surroundings and hence it appears black. It originates from the death of a very massive star, which collapses into such a small point in space that a singularity is created.
Although the existence of black holes is still to be confirmed with absolute certainty, they are currently accepted to scientists as one of the most intriguing objects of the cosmos. This acceptance is based on what can be described as indirect proofs. By studying the motion of stars at the centre of our Galaxy, it has been possible to demonstrate that black holes exist.
Another way to search for the existence of black holes is to investigate the behavior of binary stars. If one of the stars is more massive it burns through its nuclear supplies faster than the other star and when it runs out of fuel it can, if massive enough, collapse into a black
1The particles does not actually exert speeds larger than the speed of light in vacuum. This effect is rather a consequence from relativistic particles emitting light while moving towards an observer. The speed of the particles is close to the speed of the emitted light and this can create an illusion of the particles moving faster than light, i.e. superluminal motion.
hole. After this process, the binary system now consists of a black hole and a star connected by the orbit around their common center of mass. By tidal forces the black hole can draw matter from the remaining star at an astonishing rate. The path and energy released from this stolen matter can be detected and the presence of a black hole can be determined [21].
When describing the physics around very dense objects it is convenient to implement time as a fourth dimension in space. One of these descriptions of space-time was created by Karl Schwarschild when he solved Einstein’s field equations. These equations concern general relativity and they, simply put, describe the curvature of space-time under the influence of gravity. One result from Schwarschilds calculations involves the properties of black holes [ch 13]. In the following, G is the gravitational constant, M the mass of the star and c the speed of light.
The radius of a very massive object where light experiences an infinite, gravitational redshift is defined as the Schwarzschild radius, rg:
rg = 2GM
c2 (1.1)
At infinite redshift light is trapped and no electromagnetic radiation gets away, i.e. we can not see the object. Matter that passes this limit is also irretrievably lost.
In the case of the Schwarzschild black hole, mass is the only parameter used for the derivation of its behavior. Another solution to the field equations was provided by Kerr in 1962. In his general solution he included angular momentum, describing the case of a rotating system. It was later understood that the Kerr metric describes a rotating black hole with finite electric charge [ch 13]. From this solution it was realized that black holes could only possess three properties; mass, angular momentum and charge. But not without limitations.
If the angular momentum is very large it can counteract the force of gravity to such a degree that a black hole cannot form. This upper limit on the angular momentum, J, is represented by the following formula [ch 13]:
J = GM2
c2 (1.2)
This limit is used for describing a maximally rotating black hole and to find the radius for the point of no return. This radius is found to be half of that representing the same critical horizon for a Schwarzschild black hole [ch 13]:
rkerr = GM
c2 (1.3)
1.1.2 Accretion disc
An object, as for example a star, with mass M and radius R can accrete matter from its surroundings via the force of gravity. If matter free-falls onto an object, the total energy E can be expressed as:
E = Ekinetic+ Egravitational = 1
2mv2 − GM m
r (1.4)
Considering that matter is falling in from infinity (vinitial = 0) and taking into account the conservation of energy we have:
Einitial = 0 = Ef inal (1.5)
and
1
2mv2− GM m
r = 0 (1.6)
and therefore:
1
2mv2 = GM m
r (1.7)
As matter moves closer and closer to the accreting object the radius decreases and the energy from gravitational potential approaches negative infinity; r → 0 and Egrav → −∞. Since the sum of the energies is zero, as Egrav decreases, Ekin increases.
When matter reaches the surface of the object, i.e. r = R, incoming particles decelerate rapidly and accrete on the surface of the object. In this case Ekin is radiated away as heat.
Now let us suppose that the rate at which matter is accreted onto an object is ˙m, we have:
0 = 1
2mv˙ f inal2 − GM ˙m
R (1.8)
and the energy that can be radiated away as heat per second is Ekin˙ = 1
2mv˙ f inal2 = GM ˙m
R (1.9)
where this last expression denotes the rate at which Ekin dissipates at r = R.
This emitted radiation equals a Luminosity with the same energy:
L = GM ˙m
R (1.10)
Now, recalling the expression for the critical radius of an object, i.e. the Schwarzschild radius, given in equation 1.1, we can express the gravitational constant G as:
G = rgc2
2M (1.11)
and substituting this last expression in the Luminosity formula, we get:
L = ˙mc2rg 2R
(1.12)
The ratio 2Rrg is a measure of how efficiently the object can convert the rest-mass of the accreted matter into energy in the form of heat.
If the object is a black hole then R represents the distance to the centre of the black hole instead of the physical radius of the object. In this case there is no solid surface on which matter can accrete and therefore matter could pass through the Schwarzschild radius and fall straight into the black hole resulting in no radiated heat. Since there is energy coming from the edge of the black hole, there must be another mechanism present. The explanation is that the incoming matter acquire angular momentum thanks to small fluctuations in the gravitational potential. Since angular momentum must be conserved it prevents the matter from falling directly into the black hole. Even though the angular momentum keeps matter from falling in the perpendicular direction and into the hole, it can still collapse along the rotational axis by centrifugal forces. It is this collapse that creates a disk of matter around the black hole; the accretion disk. In order for matter to leave the accretion disk and fall into the hole it must loose its angular momentum, something that can be achieved through viscous forces present in the disc. These forces give rise to two important effects; the first is that there is transfer of angular momentum outwards and the second is that they act as a frictional force that causes dissipation of heat. As matter looses momentum it drifts inward until it reaches the last stable orbit around the black hole. After this stage it spirals into the singularity with no possibility of turning back [ch 14].
The maximum energy that can be released by the accretion process near a black hole is given by the energy lost by the matter in order for it to reach the last stable orbit, but there are limitations regarding how much energy that can be released. As the luminosity increases so does the radiation pressure. The force of this pressure originates from elastic scattering of photons by free, charged particles in the plasma found in the disc. This scattering is called Thomson scattering and is very similar to Compton scattering except for its lower energy limit. If the radiation pressure gets high enough it prevents matter from accumulating which puts an upper limit to the released energy. The luminosity at which there is balance between the inward force of gravity and the outward pressure of radiation is called the Eddington luminosity, LEdd. It can be derived from the following expressions concerning gravitational force (Fg) and the force from radiation pressure (Fp) [2]:
Fg = GM µmpNe
r2 (1.13)
Fp = NeσT 4πr2c
ˆ∞
0
Lνdν = NeσT
4πr2cL (1.14)
Where Neis the electron density, µis the mean number of nucleons (protons and neutrons) for each electron, mp is the proton mass, ris the distance to the centre of the black hole, σT is
the Thomson cross section and Lis the total luminosity. As long as Fg > Fp the accretion of matter can continue but as Fp increases the accretion process slows down since the force from the radiation pressure starts to reject the incoming matter. When Fg = Fp the Eddington Luminosity is reached:
Fg = Fp → GM µmpNe
r2 = NeσT
4πr2cL (1.15)
LEdd = 4πGM µmpc
σT (1.16)
where the unknown parameter is the mass M of the central source. This mass can be expressed in terms of solar masses, M/M , and the luminosity can be calculated including this ratio:
LEdd' 1.5 ∗ 1031 M M
(J/s) (1.17)
The Eddington Luminosity is often expressed in terms of erg per second, erg. One erg represents 10−7J:
LEdd ' 1.5 ∗ 1031 M M
(J/s)/10−7 ' 1.5 ∗ 1038 M M
erg s−1 (1.18) These expressions are derived from the assumption that the entire plasma involved in the reaction is ionized. In real cases part of the gas may very well be neutral which gives a much larger opacity, resulting in a much lower Eddington Luminosity [2]. In spite of this limitation, accretion is a very efficient mechanism for converting mass into energy. Compared to the mass transformed into energy by nuclear fusion, the accretion process onto black holes can be as much as 60 times more efficient [ch 14].
1.1.3 The Jet
By processes not fully understood matter can be ejected in two streams perpendicular to the rotation axis of the accretion disk, see the galaxy Cygnus A in Fig 1.1. These bipolar jets represent enormous outflows of matter which generates radiation that provides clues regarding the physics involved. A jet can also be described as “a supersonic, highly collimated flow”
[3]. This flow would require a big amount of pressure that could potentially be powered by magnetic fields [3]. The charged particles in the accretion disc generate a magnetic field and the field lines are believed to follow the different rotational speeds in the disk and be winded up into a helix propagating away from the plane of accretion [21]. The field expands as it gets further away from the black hole which corresponds to a decrease in magnetic pressure. This difference in pressure accelerates the flow of mass and the jet is created. Another explanation for this phenomenon involves gas dynamics in dense central regions surrounding the black
hole [ch 21], but as far as this thesis is concerned the model containing tangled magnetic field-lines will be used when trying to model the results.
Jets are often of relativistic nature in AGN, meaning that the particles that constitute the jet reach relativistic speeds and with that very high kinetic energies. The power of jets is most likely correlated to the luminosity of the accretion disk [4, 5]and it generates large amounts of radiation, ranging over all wavelengths.
Figure 1.1: The figure shows the galaxy Cygnus A with its bipolar jets. Credits: Outer Space Central [35]
1.2 Different types of AGN
There are many different types of AGN and to make strict classifications concerning them has proven difficult. There are quite a few studied AGN that don’t fit into just one specified type, but seem to either belong to multiple types or reside in between.
1.2.1 Classifications
The apparent difference between AGN may in many cases be just explained by the different direction of the jet compared to our line of sight. Similar AGN can therefore appear to be very different, and their classification is in many cases based more on observational parameters instead of intrinsic properties. But this does not mean that they are all the same.
When the first discoveries of AGN were made their true nature was not known and many of them were called "quasi stellar sources", or quasars, which is now considered a historical term [30]. Today, the classification of AGN is far more intricate. Depending on their brightness in the radio area they are called radio-loud or radio-quiet AGN and these two classes can contain additional subtypes. Radio-loud galaxies are often elliptical and their power output in the radio waveband is in the range of 1033 − 1038 W, which is in the order of the total output from an average galaxy [30].
Another group is called Seyfert galaxies after Carl Seyfert who 1943 made discoveries of bright, pointlike sources in the form of galactic nuclei. About 1% of all bright spiral galaxies detected belong to the Seyfert classes [32]. They were observed to have broad emission lines and their most prominent radiation was in the UV region of the spectra. The emission lines were thought to be produced in surrounding gas moving at high velocities. There are now several types of Seyfert galaxies defined, where the most prominent are called type I and type
II. Type I includes Seyfert galaxies that display broad emission lines produced in the dense gas near the nucleus and type II represent galaxies with much narrower lines, where the denser gas are thought to be obscured by the disc [32]. Emission lines from forbidden transitions emerge in more diffuse gas further out and are more prominent in type II galaxies. Transitions in this context signify energy changes in atoms or molecules and are defined by changes in the configuration of quantum numbers. These transitions are mediated by the emission or absorption of photons and proofs for their occurrences can be found in emission/absorption lines in the spectra of the observed source. Not all changes regarding the quantum numbers are allowed due to the conservation of angular momentum and the restrictions for this is described in the selection rules that describe which steps the quantum numbers may use when changing their configuration. Transitions that follow these rules are called allowed and those who deviate from the rules are called forbidden [31]. Compared to the allowed transitions, the forbidden ones have a much lower probability for occurring, but they are not impossible.
The direction of the jet is often the most influencing parameter when trying to classify AGN. When seen from the side, AGN often belongs to one of the radio-galaxies, but when the jet is pointing straight at the observer the AGN is called a blazar, which reveals the enormous power of active galactic nuclei.
1.2.2 Blazars
Blazars can be divided into two main types; BL Lacertae (BL Lac) and Flat Spectrum Radio Quasar (FSRQ). Blazar jet emission is always characterized by a Spectral Energy Distribution (SED), i.e. luminosity as a function of frequency (see Fig. 1.2), with two bumps. The first bump at low energy is thought to be generated by synchrotron emission of relativistic electrons moving in the magnetic fields present in the jet, while the second bump at higher energy is created by the same synchrotron photons which are boosted to higher energy through inverse Compton emission, see Fig. 1.3 and 1.4. More details about the two components will be given later in the text.
From the SEDs one can immediately see the observational differences between BL Lacs and FSRQs. For FSRQs, the peaks of the two bumps are shifted to lower energies and the luminosities are higher with respect to blazars. Further types of AGN can be obtained from the FSRQ’s that contain the optically violent variable quasar (OVV) and Highly polarized quasars (HPQ), whose names reveal their characteristics. Blazars make suitable objects for astrophysical studies because of their orientation. When the jet is pointed straight at us their radiation is magnified due to relativistic effects, which is believed to enhance the radiated flux [29]. Transformation between the co-moving frame of the jet and the observers frame is not trivial and a simplified result for this is given in Sec. 1.3.3.
1.3 The physics of jet emission
Active galactic nuclei emit radiation over all wavebands. Most of this radiation is non-thermal and originates in the jet, but a thermal component can also be seen in the SED which can be explained as emission from the accretion disk.
When charged particles, presumably electrons, are accelerated in the jet they produce synchrotron radiation. The synchrotron photons are believed to interact with the electrons
Figure 1.2: The Blazar Sequence. Illustrates the difference between FSRQ’s and BL Lacs based on their spectral energy distribution. The main difference is the relative levels of the two peaks. The peaks represent synchrotron radiation (left) and inverse Compton radiation (right). Credit: Fossati et al 1998; Donato et al 2001
in the jet through inverse Compton scattering and be boosted to higher energies. This model is called Synchrotron Self Compton (SSC-model). In some cases this model requires adjust- ments with an additional component of external photons involved in the inverse Compton scattering.
1.3.1 Synchrotron radiation
When very energetic electrons are accelerated they emit electromagnetic radiation, i.e. syn- chrotron radiation. This occurs for instance in the jet of blazars when the path of electrons turns under the influence of the magnetic field. This influence is mainly mediated by the Lorentz force that drives the electrons to gyrate around the magnetic field lines [29], see figure 1.3. The Lorentz force represents the combined forces of the magnetic and electric fields present and can be described as:
F = qE + qv × B (1.19)
where q is the charge of the particle, E the electric field, v the velocity of the particle and B the magnetic field.
The different parts of the Lorentz force affects the electron in different directions and their combined effect force the electrons in circular motions and with this an acceleration occurs, which results in the production of radiation [31]. This radiation mostly belongs to the IR, optical, UV or soft X-ray waveband, but it can also go as low as radio emission.
Figure 1.3: Schematic view of synchrotron emission. Credit: Cosmic River [46]
A single, charged particle moving through a magnetic field with the relative speed of β = vc experiences a loss of energy due to synchrotron processes. The rate at which this energy is lost can be described in terms of particle Lorentz factor, Γ , and expressed as the following formula [6]:
dΓ dt
sync
= −4
3cσT uB
mec2Z4me m
3
β2Γ2 (1.20)
Γ = 1
p1 − β2 (1.21)
β = v
c (1.22)
Where σT is the Thompson cross section, Z is the particle charge expressed in the unit charge of the electron (e), m is the mass of the particle, meis the electron mass, uBrepresents the energy density of the magnetic field and v is the velocity of the particle.
If the particle is an electron most of the emitted radiation is close to a frequency equal to [6]:
νc = 3Γ2eBsinΨ
4πmec (1.23)
where Ψ is the angle between the direction of motion of the particle and the direction of the local magnetic field B and e is the electron charge.
With these two non-trivial equations an approximation regarding the total power radiated away from a population of electrons can be made by averaging among all possible directions and assuming that all power is emitted at the frequency νc [6]:
Pνsync,δ(Γ) = 32π 9
e2 mec2
2
uBβ2Γ2δ (ν − νc) (1.24) δ (ν − νc) is called Diracs δ-function or distribution which is equal to 1 at the frequency vc, and equal to 0 at all other frequencies. To get a coefficient for the emission of synchrotron radiation, integration of the particle energy distribution including the energy loss rate is needed [6]. The integration is performed over all possible energies as follows:
jνsync= 1 4π
ˆ ∞ 1
dΓn (Γ) Pνsync,δ(Γ) (1.25)
Where n (Γ) describes the particle energy distribution as a function of Γ , in this case a power-law distribution:
n (Γ) = kΓ−p (1.26)
for Γmin ≤ Γ ≤ Γmax
The equations (1.20 - 1.26) predict a power-law emission for the emission coefficient concerning synchrotron radiation [6]:
jνsync ∝ ν(p−1)/2 (1.27) An emission coefficient describes the power output per unit time of an electromagnetic source.
The exact derivation of these formulas is beyond the scope of this thesis; they provide a look at the surface of the theory behind the synchrotron emission. The peak of the syn- chrotron emission varies between different AGN but it is usually located somewhere in the IR/optical/X-ray band, see also Fig 3.5 and 3.6. Depending on where the peak is found AGN are called low (LSP), intermediate (ISP) or high (HSP) synchrotron peaked [7].
The plasma is now a mix of synchrotron radiation with its associated radiation field and highly relativistic particles. These particles still have a total energy that exceeds that of the synchrotron photons. This enables transfer of energy from the particles to the photons by Inverse Compton scattering (IC); boosting the photons to the very high energies represented by gamma radiation.
1.3.2 Inverse Compton scattering
The relatively low-energy photons of the synchrotron radiation interact with the highly en- ergetic electrons in the jet. In less extreme environments, the electron would gain energy from an incident photon and the wavelength of the photon would decrease according to this loss, a process known as Compton Scattering. In the relativistic jet the opposite occurs: the energy of the electron is very high compared to that of the photons present in the medium, therefore in the interactions between the two, it is the electron that looses energy in favor of the photon. When a photon gains energy, its wavelength shortens and so the photons are boosted from optical/UV/soft X-ray up to the more powerful gamma radiation, see Fig. 1.4.
Figure 1.4: The figure illustrates the basics of inverse Compton scattering. The symbols ν and ν´ represent the photon before and after the interaction, where ν´ has the shorter wavelength (and thus higher energy) compared to ν. Credit: [47]
The equations regarding inverse Compton scattering are far from trivial, but an approxi- mate description can be made. This is based on the assumption that all scatterings result in
emission of radiation and that the frequency of this radiation depends only on the original frequency of the photon and the energy of the scattering particle. As for the synchrotron radiation, the derivation of the formula for the emission coefficient will be left outside this thesis. The result of the calculations is the following formula [6]:
jνIC,δ = hcσT2S 8π
ˆ ∞
S
dΓne(Γ ) Γ4
ˆ ∞
S/(2Γ2)
dnγ()
2 (1.28)
Where ne and nγ are the energy distributions of the electrons and photons respectively, Γ is the Lorentz factor of the electrons and the symbols and S signifies the energies of the photon before and after scattering:
= mhν
ec2 and (S) = hνm(S)
ec2
Where h is the Planck constant, me is the mass of the electron and the denominator normalizes the energy to the rest-mass of the electron.
For energetic electrons this process effectively transfers energy to the photons, whose frequency after scattering is roughly proportional to the squared Lorentz bulk factor of the plasma, Γplasma2 . This increase in frequency, combined with the relativistic boosting in the jet, greatly enhances the observed flux Fobs and is connected to the doppler factor, δ [6]:
Fνobsobs = δ3Fνemittedemitted (1.29)
δ = 1
Γplasma(1 − βΓplasmaµobs) (1.30)
Where µobs is the cosine of the angle between the plasmas direction of movement and the observers line of sight. Similar calculations can be made regarding the total luminosity of a blazar.
1.3.3 Relativistic beaming
When making calculations concerning the radiation produced by jet, a “blob” theory is often used. This means the the electrons producing the radiation are not distributed evenly across the entire jet, but they come in dense groups called blobs [34]. Focusing on a single of these blobs, the beaming effect due to relativity can be expressed as [29]:
Lobs = δ4Lemitted (1.31)
There are some assumptions present in the derivation of this result and the exponent for the doppler factor can differ between different models. Fig. 1.5 shows a schematic view of the beaming effect.
Figure 1.5: Schematic view over the enhanced emission seen in the observer’s frame. Credits:
SED tool by Andrea Tramacere [34]
1.3.4 Synchrotron Self Compton model
The Synchrotron Self Compton model (SSC-model) aims to describe and predict the be- havior of the spectral energy distribution of AGN. It is a leptonic model which means that it based on the behavior of leptons, more specifically electrons, in the jet. The shape of the spectral energy distribution is explained with the radiation processes described above.
Synchrotron radiation is generated by gyrating electrons driven by magnetic power and the photons emitted is scattered to higher energies due to inverse Compton effects. For some AGN the SSC-model demands an external component of additional photons to be scattered, i.e. an External Compton (EC). Sources for these photons can be radiation from the accre- tion disk, radiation that has been reprocessed in circumnuclear material such as a dust torus or the broad line region or coming from synchrotron emission in another part of the jet, see [22]. The SSC model, in some cases including an EC component, have been used successful for many AGN. To generalize one can say that for High Frequency Peaked BL Lac (HBL) a pure SSC model gives a good fit, whereas for FSRQ’s an EC component is often necessary, see [22]. In many cases though, the SSC model fails to explain the rapid variability seen in many BL Lacs or the role of hadronic processes concerning other particles present in the jet, see [23]. There are other models, as for instance hadronic models, that include processes concerning the presence and interactions of protons instead of only electrons. It demands that a large fraction of the power present in the jet is used in order to accelerate the heavier protons to relativistic speeds, so that synchrotron processes can occur. It is possible for this model to explain the SED’s, but it gets very complicated in comparison with the SSC-model which therefore is preferred, see [22].
Figure 1.6 illustrates a schematic view of the emission in jets according to the leptonic model, including external photons from the broad line region (BLR) and intergalactic clouds.
When relativistic plasma is moving in strong magnetic fields they produce radiation as described above, but they also generate shock fronts and are exposed to instabilities. Some of these instabilities can be suppressed by a large bulk factor [6]. The bulk factor is represented by Γ, see equation 1.21. Γ and the viewing angle (θ) are, as described above, connected to the doppler factor for the plasma that is in turn connected to the boosting of emissions to
larger intensities.
Figure 1.6: Schematic view over the radiation process in AGN. Credits: SED tool by Andrea Tramacere [34]
1.3.5 Parameters of the SSC-model
The SSC-model contains several free parameters representing the physics behind the produced radiation. First those regarding the jet, see also [34]:
• R: the size of the spherical emitting region in cm
• B: the intensity of the entangled magnetic field (expressed in Gauss) within the emitting region with size R
• z: the redshift of the host galaxy
• Γ: the Bulk Lorentz factor of the emitting region
• θ: the Jet viewing angle
Furthermore, the SSC model contains parameters describing the properties of the electrons;
including the model for energy distribution, electron density and minimal/maximal energies.
There are also additional parameters regarding the presence of external components of pho- tons and models for their use. In short, modeling the SED’s takes a lot of work and its no easy task trying to fit all the parameters to obtained data.
Figure 1.7: Images of PKS 0537-441, which is marked by red circles. Credit: Hamburg Quasar monitoring [44]
1.4 PKS 0537-441
Somewhere in between the characteristics of BL Lacs and of FSRQ:s we find the blazar PKS 0537-441. It was first detected in the gamma ray waveband in 1991 by the EGRET telescope [33]. It possesses a large redshift of 0.894 which suggests that before its photons reached our detectors they travelled through space for over seven billion years, see [9]. It is located in the southern sky, in the vicinity of the constellations Columba (the dove) and Dorado (the swordfish). Images of this distant source is given in Fig 1.7.
PKS 0537-441 is a well-studied object and has been monitored by several different tele- scopes, operating in different wavebands. It has been found to be a highly variable source over a large magnitude of wavelengths. The variability was so significant that it was ini- tially suspected that PKS 0537-441 was under the influence of gravitational lensing which is known to enhance properties like variability. In the case of gravitational lensing, one must refer to the "variability of the observations", while normally "variability" is intended as the
"variability of the source itself", as for instance the jet emission variability. A source can be stable but the flux detected on Earth can be variable due to gravitational lensing.
As the gravitational lensing effect gets more substantial on cosmological distances, PKS 0537-441 is a suitable candidate for this kind of investigation because of its very high redshift.
A galaxy in the foreground can intervene with the radiation from the source of interest and induce violent fluctuations that can create complex variability over the observed spectrum, see [12]. Multiple studies have been done on this subject, none of them being able to confirm any interference by this phenomena concerning PKS 0537-441, see [12, 19].
A variability in the optical and X-ray wavebands was detected by the REM and swift telescopes in January-February 2005, see [10, 11, 15, 18]. The optical band flux was enhanced with a factor 60 while the X-ray flux varied by the more modest factor of two, see [10, 11]
Figure 1.8: Multiwavelength monitoring of PKS 0537-442, from August 2008 to April 2010.
From the top: Fermi (gamma-ray), Swift-XRT (0.3-10 KeV), Swift-UVOT (UV/optical, filters W1, M2, W2), Swift-UVOT (UV/optical, filters V, B, U), REM (optical, I,V bands), REM and ATOM (optical, R bands), REM (optical, J, H ,K bands) and SMA (radio) Credit: F.
D’Ammando et al [18]
A more recent study of this object, August 2008-April 2010, is shown in figure 1.8. This study was performed by F. D’Ammando et al in [18], where it compares the behavior of the radiation at different wavebands under the same period of time. They found that the source possesses strong variability in the gamma-ray part of the spectra and that there were indications of correlations for this variability in the X-ray and optical waveband.
The majority of the work done explaining the SED of the source has started with the SSC-model but in order to get a better fitting an external component has been added in a large portion of the studies, see [10, 11, 13, 18]. This is why this source is not a pure BL Lac but believed to harbor some adjacent clouds giving it some of the properties of FSRQ’s.
With the success of the Fermi mission, massive amount of information from PKS 0537- 441 is available, and further long-term analysis of this source will hopefully enhance our understanding on the source itself, as well as that for other AGN.
Chapter 2
The Fermi-LAT satellite
Gamma-rays cannot be reflected by any material because of their very short wavelengths.
The wavelength of gamma rays is in the same order of magnitude as the size of atoms so gamma rays can easily pass through obstacles of matter. To be able to study this kind of radiation we must instead focus on the effects that gamma-rays induce. One of these effects is the conversion of high energy photons into electron-positron pairs:
γ → e−+ e+ (2.1)
The generated e− and e+are charged particles that can be detected and reveal the nature of the original photons. The Fermi satellite helps us with the detection of gamma-rays in the energy range from 10 MeV to 300 GeV and the satellite is located in orbit around Earth, something which is necessary in order to avoid the obstructive atmosphere of our planet.
The satellite completes one orbit in 90 minutes, changing between the northern and southern hemisphere each orbit and is hence able to survey the entire sky in three hours.
Where no source is cited in the text, the information about the Fermi satellite and its components are retrieved from the Fermi Science Support Centre (FSSC), see [20].
2.1 Large Area Telescope
The main instrument associated with the Fermi satellite is the Large Area Telescope (LAT).
The LAT is constructed by 16 separate modules of detectors arranged in a four-by-four pattern and contains multiple instruments; a converter tracker with a calorimeter surrounded by an anticoincidence detector that filters out the unwanted cosmic radiation, see Fig. 2.1. It also has a data acquisition system that combines the information from the different detectors.
2.1.1 Converter tracker
A photon doesn’t have any mass, but it possesses momentum as well as energy.
The momentum of a photon is:
pγ = h λ = Eγ
c (2.2)
Eγ= pγc (2.3) According to the theory of relativity:
Eγ2 = Erest2 + (paf terc)2 (2.4)
Where Eγ is the total energy of the photon before the pair production, Erest = 2mec2 is the sum of the masses of the electron and positron and paf ter is the total momentum after the reaction.
paf ter = 1 c
q
Eγ2− Erest2 (2.5)
Comparing the initial pγ with paf ter: 1 c
q
Eγ2 − Erest2 < Eγ
c (2.6)
The momentum after the pair production is smaller than before which leads to the con- clusion that the reaction can not take place in vacuum.
A suitable region for the transformation of the photon into an electron/positron pair is the atomic nucleus. The nucleus has the ability to absorb momentum and the rate at which pairs are created associated to a nucleus is connected to a property called radiation length.
This property describes the amount of energy lost by electromagnetic particles, i.e. photons, interacting with a nucleus. Heavier nuclei cause electromagnetic particles to have shorter radiation lengths which means that the probability for pair conversion is higher compared to lighter nuclei. When choosing a material for the detector an element with high Z value is preferable, since it is heavier. The converter in Fermi LAT is made out of tungsten that has an atomic number of 74 and an atomic mass of 183.84 u, which makes it a suitable candidate for easily absorbing the excess momentum. When the electron/positron pair has been created they easily interact with surrounding material and the high Z of the converter material is no longer an advantage, see [42].To avoid scattering of the particles before their paths can be detected the converter material is organized in layers of thin foils combined with layers of trackers. The trackers record the passages of charged particles and these passages can be used to derive the direction of the incident gamma-ray. They are made of silicon strip detectors with a detection efficiency of > 99% and an excellent position resolution.
2.1.2 Calorimeter
The purpose of the calorimeter is to measure the energy deposition of the created particles.
It is made of optically isolated cesium iodide crystals containing photodiodes on opposite sides. These diodes measure the differences in the transmitted scintillation light through the crystal which can be used to derive the energy deposition of the particles.
2.1.3 Anticoincidence detector
Even though the Earth is enclosed by a magnetic field, the space in vicinity of the planet is still exposed to energetic cosmic radiation, see [42]. This radiation is hitting the Fermi- LAT telescope along with the gamma-rays from sources of interest. In order to filter out
the undesired radiation the telescope is coated by an anticoincidence detector (ACD) made of a plastic scintillator. Plastic is a very useful material in this context because of its high efficiency to detect particles at the same time as it possesses very low probability for absorbing gamma-rays. If the anticoincidence detector signals a passage of a particle, events seen LAT are rejected and only gamma-ray event candidates are processed in the analysis..
Figure 2.1: Schematic view of one of the 16 towers of the Fermi-LAT. Credits: [online]
https://www-glast.stanford.edu/instrument.html
2.1.4 Data acquisition system
The data acquisition system (DAQ) collects data from the other systems in order to trans- mit them to the ground control on Earth. The software is optimized to remove the charged particle background in order to maximize the rate of gamma-ray events being detected, see [43]. The DAQ consists of a group of different subsystems arranged in a hierarchical order.
At the lowest level the Tower Electronics Model (TEM) can be found. It provides interface to the calorimeters and trackers in the 16 towers of the Fermi-LAT. Then there is a collec- tion of different systems called GASU, which stands for Global trigger/ACD-module/Signal distribution Unit which contains the following software:
• The Global trigger Electronics Module (GEM) that generates signals concerning read- out based on information from the triggers in TEM and ACD.
• The ACD Electronics Module (AEM) that operates with the ACD
• The Command Response Unit (CRU) that sends and receives commands within DAQ
• The Event Builder Module (EBM) that, based on information provided by the TEM and AEM, builds complete events and sends these to be further processed in the Event Processor Unit (EPU)
Communications are handled by the Tracking and Data Relay Satellite System (TDRSS) that acts as the downlink for data. The data is sent to the Fermi Mission Operations Centre (MOC) which is responsible for separating LAT data from other data concerning transmis- sion. The final stage for data processing takes place at Stanford University in California at the LAT Instrument Science Operations Centre (ISOC), see [41]. After all these steps the
data are now ready to be published at the Fermi Support Science Centre (FSSC) associated with the Goddard Space Flight Center in Maryland (NASA).
2.1.5 Fermi Support Science Centre
At NASA’s Goddard Space Flight Center in Maryland the Fermi Support Science Centre (FSSC) can be found. It is the last stop for the processed data from the Fermi mission before it can be downloaded for analysis. The FSSC also provides software tools and suitable support for the analysis of the data. Documentations concerning the Fermi mission so far can also be found here, see [20]. A compilation of the gamma ray sky provided by the FSSC can be seen in Fig. 2.2.
Figure 2.2: The plot shows the entire sky for energies greater than 1 GeV based on five years of data from the LAT instrument. Brighter colors indicate brighter gamma-ray sources. The AGN of this thesis, PKS 0537-441, is marked with a green circle in the lower right of the figure. The distinct band across the middle of the figure represents the gamma radiation from the Milky Way’s galactic plane. Credits: NASA/DOE/Fermi LAT Collaboration
Chapter 3
Analysis method
3.1 Computer resources
When processing the amount of data available for an analysis of an astrophysical source seen by Fermi, strong computational resources are required. For the analysis done in this thesis, the center for scientific and technical computing at Lund University, Lunarc, has been used. The computers at Lunarc are a facility offered by The Swedish National Infrastructure for Computing, SNIC, which provides connection to a variety of supercomputers including storage resources for data analysis. The computing resource used for this thesis is called Aurora and consists of over 200 compute nodes where 180 of these are used by SNIC. The specifications of the nodes are described at the Lunarc centre webpage, see [36]: “Each node has two Intel Xeon E5-2650 v3 processors (Haswell), offering 20 compute cores per node. The nodes have 64 GB of DDR4 ram installed.”
3.2 Analysis tools and statistics
The software required for running the analysis on Fermi data is called “Fermi Tools” and is freely retrieved from FSSC, as well as the data itself. The tools provided by the FSSC are installed via scripts and the idea is that they can be used by someone who doesn’t have prior knowledge about the files, libraries or system variables. As a complement to the official Fermi tools, the Enrico command line tools can be used as a way to ease the analysis. With simple and straightforward commands, enrico software assists the analysis by its very user-friendly approach, see [28].
The analysis concerns detection, flux determination and spectral modeling of Fermi-LAT sources and this is accomplished by using a maximum likelihood optimization technique.
Likelihood is defined as the probability of obtaining the data from the tested input model.
The models used for the likelihood test describe the distribution of the gamma ray sources in the sky, including intensity and spectra. These models are based on a deep understanding about how the detectors of the Fermi telescope respond to the incident flux.
The specifications regarding the statistics and models of the analysis are retrieved from the FSSC, see [20].
3.2.1 Binned data
For the analyzes performed here, binned data is used which means that data is collected in groups instead of treated as single events; data is quantized. For the flux analyzes, the data is binned after a chosen time interval which are in the order of weeks or a month.
When creating maps of a source, data for positions represented by a pixel can be binned into clusters of pixels, covering a larger area.
Reasons for using binned data can be to reduce the time needed for calculations or to suppress the effects of minor errors that are more prominent for isolated data. The less desired effects is that information on single events is no longer distinguishable in the bin, but the time saved when performing the calculations typically outweighs this disadvantage.
3.2.2 Likelihood
The likelihood L for binned data is the product of the probability of observing the detected count for each bin.
A given model expects mi counts for the i : th bin. Since the models are different, the value for mi can differ as well.
The probability of detecting ni counts in the i : th bin is defined as:
Pi = mniie−mi× 1
ni! = e−mi ×mnii
ni! (3.1)
The total L is then the product of all Pi for i : 1 → Nb, where Nb represents the number of bins. Focusing on the exponential part for all values of i:
e−m1 × e−m2 × e−m3 × ... × e−mi−1× e−mi = e−PNbi=1mi (3.2)
−
Nb
X
i=1
mi = −Nexp (3.3)
Nexp = Total number of expected counts, from all bins
e−PNbi=1mi = e−Nexp (3.4)
Lcan now be written as the product of all Pi:
L = e−Nexp
Nb
Y
i=1
mnii
ni! (3.5)
When using binned data, some of the information connected to single data point is de- stroyed or lost, because the event characteristics are mixed with those of all other events in the bin. This can be avoided by using smaller bins. By letting the size of the bins approach zero the probability of detecting a count, ni , is either one or zero. Since 0! = 1! = 1, the total likelihood can be simplified to:
L = e−Nexp
Nb
Y
i=1
mi (3.6)
The index inow represents the number of counts rather than the current bin. In this formula, miis the precise value for each count, and so this unbinned analysis is more accurate.
For small number of counts this method is preferred but as the number of counts grows the time required for the calculations becomes unpractical and the data is binned in order to speed up the process.
3.2.3 Likelihood ratio test
When comparing two different models the likelihood ratio test can be used, which is simply the ratio between the probabilities of different models. One model, the one with the least degrees of freedom, is called the null hypothesis and it is compared to a model containing more free parameters in order to determine which is the best fit to the data. The logarithm of the likelihood can be used and the test is then referred to as the Log Likelihood ratio test. When comparing the likelihoods of models, the Test Statistics (TS) is obtained by the following formulas:
T S = −2log H0 H1
(3.7)
T S = 2(log(H1) − log(H0)) (3.8)
According to Wilk’s theorem the distribution of T S can be approximated as chi-square, χ2, if the sample is large enough. Based on this, √
T S can be used as an approximation for the significance of the hypothesis in the test. For √
T S > 0, the null hypothesis is rejected in favor of the model represented by H1.
3.2.4 Source detection
The analysis of PKS 0537-441 is based on a list of event counts detected by the LAT. This list is the result from event processing by the DAQ system, the event reconstruction procedures and the final analysis, where, among other things, the distinction between a gamma-ray and a photon initiated signal is made1. When determining the detection of a source, different models over the gamma ray sky are being compared. The basic model, the null hypothesis,
1This procedure is called "signal over background discrimination"
is compared to a model with an additional source at a specific location. The likelihoods of the different models can be labeled as L0, with a maximal likelihood of Lmax,0, for the null hypothesis and L1 and Lmax,1 for the hypothesis containing the source. The likelihood ratio test is used to compare the models and the value of T S is maximized on a grid. This is the same as maximizing the likelihood Lmax,1 on the grid, since a large value for T S means that the null hypothesis is wrong and there is a source present.
T S = −2log Lmax,0 Lmax,1
(3.9) The significance for the probability of detection,√
T Sσ, should be higher than 5σ in order to be sure that systematic effects from the detector are not affecting the measurement.
3.2.5 Dataset of the analysis
Fermi is sensitive to energies between 10 MeV - 300 GeV and the angular resolution (or
“Point Spread Function”) is highly dependent on the event energy. At 100 MeV 68% of the counts is found within a 3.5 degree radius from the assumed source. For counts with higher energies, this radius decreases. This means that when searching for counts, a wider area around the point of interest should be used. This, however, gives rise to contamination from nearby sources, which need to be included in the models. To get the greatest accuracy of the models, the entire gamma-ray sky should be included, but this is obviously not practical so a more restricted region is used, called the Region Of Interest (ROI). The width of the ROI is set based on how energetic the source is. For sources with their strongest emission around 100 MeV the ROI is set to 10 degrees, while it for 1 GeV events can be decreased down to 5 degrees.
3.2.6 Variability
One characteristic feature of AGN’s is their flux variability, which appears to be both unpre- dictable and aperiodic, see [24]. The variability of the emissions is thought to be correlated to the mass of the central engine (the black hole), the redshift, the Eddington ratio as well as optical properties, and is an active field of research, see [25]. The variability of AGN has been extensively studied with X-ray observatories, and the physical interpretation of these observations is deeply connected to the measurements performed in the gamma-ray band at study in this thesis.
A tool used for examination of variability is the Power Spectral Density (PSD). The PSD represents the amount of variability power as a function of temporal frequency in the units of the mean squared amplitude and an inverse timescale. By integrating under the PSD the variance of the source can be obtained, see [24]. This integral can be estimated by the excess variance, σrms2 , which gives a quantitive measure of the variability amplitude of the data, see [25]. The excess variance is defined as:
σrms2 = 1 (Nobs− 1) (x)2
Nobs
X
i=1
(xi− (x)2) − 1 Nobs(x)2
Nobs
X
i=1
σerr,i2 (3.10)
Where Nobs is the number of observations, x is the average flux, xi is the single measure- ment and σerr,i represents the error of xi.
After subtracting the statistical error, σ2rms reveals how much of the total flux per obser- vation is variable. The error of the excess variance is:
err(σ2rms) = v u u u t
r 2 Nobs
σ2err (x)2
!2
+
s
σerr2 Nobs
2Fvar x
2
(3.11)
Where Fvar =pσ2rms is the fractional variability and σerr2 is the mean squared error:
σerr2 = 1 Nobs
N
X
i=1
σerr,i2 (3.12)
This calculation is not the whole truth and other sources of errors exist. These errors can be connected to the number of counts, the frequency considered and how the sampling for the lightcurve is done, but the formula above can be used as an acceptable approximation, see [25].
If the observed source is not variable, i.e. the intrinsic σ2rms is equal to zero, the measured variance can be negative due to statistical fluctuations. If, however, σ2rms− err(σ2rms) > 0 the source is considered to be variable with an upper limit of σ2rms+ err(σ2rms).
The variability of PKS 0537-441 will be tested with this model in this thesis, but no further conclusions on the origins of the eventual variability will be made. Such investigations are beyond the scope of this thesis.
3.2.7 Spectral analysis
When a source is detected and localized, the spectral analysis can be performed. The model with the highest probability of its output resulting in the recorded data will show the highest likelihood value.
The spectral analysis begins with the selection of data within a spatial region around the source. This is because of the spread of the data away from a single point in space; something that is being regulated by overlapping the point spread functions of nearby sources, see [40].
These functions are embedded in the Fermi analysis tools. The next step is to chose which models to use in the spectral analysis. These models include the position of the source itself as well as nearby sources, calculations for diffuse emission, functional form of spectra and values for spectral parameters. The parameters for the models are varied until the likelihood for each model is maximized.
3.2.8 Models of the spectral analysis
When performing the spectral analysis on PKS 0537-441, three models provided by the Fermi tools have been used; PowerLaw2, LogParabola and PLSuperExpCutoff. They possess different degrees of freedom and are somewhat specialized to different AGN’s, but this does not prevent their use on a variety of sources.
3.2.8.1 PowerLaw2
This spectral model contains two degrees of freedom, the spectral index γ and the integrated flux N.
dN
dE = N (γ + 1)Eγ
Emaxγ+1− Eminγ+1 (3.13)
N - Integral γ - Spectral index
Emin - Lower energy limit (fixed) Emax - Upper energy limit (fixed) 3.2.8.2 LogParabola
When modeling spectra from blazars the LogParabola model is widely used. This model adds another degree of freedom compared to the PowerLaw2 model.
dN dE = N0
E Eb
−(α+βlog(E/Eb))
(3.14)
N0 - Normalization α - alpha
β - beta
Eb - Scale parameter, the value is set near the lower energy range of the spectrum and is usually treated as fixed.
3.2.8.3 PLSuperExpCutoff
The PowerLawSuperExponentialCutoff model is especially developed for pulsars, but can be used for very far blazars where the spectrum at high energies often falls off rapidly. A shorter name for this model is Power Law Exponential Cutoff (PLExpCutoff).
dN
dE = N0 E E0
γ1
e−(EcE)γ2 (3.15)
N0 - Prefactor γ1 - Index 1 γ2 - Index 2
E0 - Scale parameter (fixed) Ec - Cutoff energy (fixed)
3.2.8.4 Determining the best fit
In order to determine which of the models fit the data most accurately the likelihood ratio test described in Sec 3.1.3 can be used. When performing the spectral analysis with the Fermi software the value for the likelihood of the model is provided in a neat file and can easily be inserted in the formula for the comparisons. The limitation with this method is that models with equal degrees of freedom can not be compared directly, such as the LogParabola and the PLSuperExpCutoff. They can however be compared in a secondary manner. Both LogParabola and PLSuperExpCutoff are tested with respect to the PowerLaw2 model and the values obtained from this can be compared to one another. If the statistical test shows that one of the two models is more significantly fitting the data than the simpler PowerLaw2 model, then this second model will be used as the preferred model for describing the observations.
3.2.8.5 Accuracy of the analysis
The three above mentioned models are seldom perfectly fitting the data because these are just simple mathematical descriptions of a spectral shape. Plots over the fit accuracy of these models are generated when performing the spectral analysis. The first is called the Counts plot and contains a comparison of the source itself with its interferences and the actual data.
The second plot is called Residuals plot and it shows the ratio of the deviation between model and actual counts; (counts-model)/model, i.e. the deviation of the observed data (counts) from the predictions. These plots help in understanding how well the spectral models used fit the data.
3.3 Modeling
3.3.1 Modeling the physics behind the SED
The shape of the best fit for the multi-wavelength Spectral Energy Distribution (SED) can be fitted to different models such as the SSC model, with or without external components. In order to do this, the energy distribution over all wavelengths is required. The way radiation is detected over the full electromagnetic spectrum varies significantly depending on the photon energy considered. A compilation over the available data for spectral analysis can be found at ASI Science Data Center (ASDC) which also offers tools for trying to fit the data to a physical model [45]. This tool and the SED tool provided online by A. Tramacere [34] was used for modeling the emissions from PKS 0537-441 and the parameters from this analysis is given i Sec. 3.1.4.
3.3.2 Models for extracting the Extragalactic Background Light
The extragalactic space is not empty. It is filled with a low-energy Extragalactic Background Light (EBL) that acts as a fundamental source of opacity for high-energy photons propagating throughout spacetime, see [26]. The energetic photons affected by the EBL absorption are in the range between 0.1 and 100 TeV. Highly energetic gamma-rays interact with the low-energy photons of the EBL and if their combined energy is sufficient, i.e. 2mec2, pair-conversion takes place and electron-positron pairs are created. Photons with energies above 100 TeV are affected by another background radiation, left from the early Universe; the Cosmic Microwave
