Flat-Spectrum Radio Quasars as Gamma-Ray and Neutrino...

Arbeit zur Erlangung des akademischen GradesMaster of Science

Flat-Spectrum Radio Quasars asGamma-Ray and Neutrino SourcesAnalysis of 3C 279 and Neutrino Flux Calculation

vorgelegt von

Melanie Engelkemeier

geboren in Paderborn

Lehrstuhl für Experimentelle Physik VFakultät Physik

Technische Universität Dortmund

September 2016

Erstgutachter: Prof. Dr. RhodeZweitgutachter: Prof. Dr. KröningerAbgabedatum: 20. September 2016

AbstractFlat-spectrum radio quasars (FSRQ) are a special group of blazars from which it isexpected to emit very high energy gamma-rays. The FSRQ 3C279 is detected as avery high energy gamma-ray emitter, despite a high redshift of 𝑧=0.536. In 2015 and2016 the source is observed again by the MAGIC telescopes. Assuming a hadronicmodel for the explanation of the second bump of the spectral energy distribution(SED) of blazars, these sources and especially flat-spectrum radio quasars also mightbe suitable neutrino sources.The analysis of the source 3C 279 of the data measured by the MAGIC telescopes isaccomplished within the MAGIC analysis chain. The analysis is done by differentprograms of the MARS software package (MAGIC Analysis and ReconstructionSoftware). An estimation for a possible number of emitted neutrinos from differentblazars is given by the decay of the 𝛥+-resonance as a particle of the hadronic SEDmodel via pions in gamma-ray photons and neutrinos.3C 279 is finally detected with a significance of about 6.41𝜎 and the energy spectrumof the source is obtained during the analysis. On average a flux of 3C 279 is obtainedto 𝐹 (E>150GeV) = 1.313⋅10-11 cm-2s-1. Applying the model for an estimatedneutrino number to different blazars, a total number of 25.727 neutrinos is obtained.

KurzfassungFlach-Spektrum Radio Quasare (FSRQ) sind eine spezielle Gruppe der Blazare, vondenen erwartet wird hochenergetische Gamma-Strahlung zu emittieren. Der FSRQ3C279 wurde trotz einer hohen Rotverschiebung von 𝑧=0.536 als hochenergetischeGamma-Strahlen Quelle detektiert. In 2015 und 2016 wurde die Quelle wieder durchdie MAGIC-Teleskope observiert. Unter der Annahme eines hadronischen Modelsfür die Erklärung des zweiten Höckers der spektralen Energiedistribution (SED) vonBlazaren, könnten diese Quellen und speziell Flach-Spektrum Radio Quasaren auchgeeignete Neutrino Quellen sein.Die Analyse der Quelle 3C 279, gemessen mit den MAGIC-Teleskopen, wird inner-halb der MAGIC Analysekette durchgeführt. Die Daten werden mit verschiednenProgrammen des MARS Software-Pakets (MAGIC Analysis and ReconstructionSoftware) analysiert. Eine abgeschätzte Anzahl an möglichen emittierten Neutrinosvon verschiedenen Blazaren ist gegeben durch den Zerfall der 𝛥+-Resonanz, alsTeilchen des hadronischen SED Models, via Pionen in Gamma-Ray Photonen undNeutrinos.3C 279 wurde mit einer Signifikanz von 6.41𝜎 detektiert und das Energiespektrumder Quelle wurde innerhalb der Analyse berechnet. Der mittlere Gamma-StrahlenFluss der Quelle wurde auf 𝐹 (E>150GeV) = 1.313⋅10-11 cm-2s-1 berechnet. Einegesamte Anzahl an 25.727Neutrinos wurde durch anwenden des Models einer abge-schätzen Zahl an Neutrinos auf verschiedene Blazare, berechnet.

Contents

1 Introduction 1

2 Gamma-Ray Astronomy 32.1 Production and Acclerating Processes of Gamma-Rays . . . . . . . . 42.2 Sources of Gamma-Rays . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Experiments in Gamma-Ray Astronomy . . . . . . . . . . . . . . . . 8

3 Gamma-Ray Astronomy with the MAGIC Telescopes 113.1 The MAGIC Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 The MAGIC Analysis Chain . . . . . . . . . . . . . . . . . . . . . . . 13

3.2.1 Calibration, Parametrisation and Stereoscopic Reconstruction 133.2.2 Direction Reconstruction, Hadroness and Energy Estimation 143.2.3 Skymaps and Signal Detection . . . . . . . . . . . . . . . . . 163.2.4 Energy Spectrum and Lightcurve . . . . . . . . . . . . . . . . 18

4 Analysis of the FSRQ 3C 279 data from 2015 and 2016 214.1 Selected Data Samples for Analysis . . . . . . . . . . . . . . . . . . . 224.2 Gamma-Hadron Separation, Energy Estimation and Direction Re-

construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3 Signal Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4 Sky Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 Energy Spectrum and Lightcurve . . . . . . . . . . . . . . . . . . . . 37

5 Flat-Spectrum Radio Quasars as Sources of Neutrinos 485.1 The Connection between Cosmic Rays, Neutrinos and Gamma-Rays 505.2 Method for the Estimation . . . . . . . . . . . . . . . . . . . . . . . 515.3 Application to Different Source Types . . . . . . . . . . . . . . . . . 56

6 Conclusion and Outlook 596.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A Appendix 62A.1 Off Sources and Mola Output . . . . . . . . . . . . . . . . . . . . . . 62

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Contents

A.2 Skyplots Crab Nebula for HE and FR . . . . . . . . . . . . . . . . . 69A.3 Lightcurve and Energy Spectrum of Crab Nebula . . . . . . . . . . . 69A.4 Inputcards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Bibliography 77

Acknowlegement 82

Selbstständigkeitserklärung 85

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1 Introduction

Equipped with his five senses,man explores the universe around him

and calls the adventure Science.- Edwin Hubble, The Nature of Science, 1954

Before Edwin Hubble said this honourable sentence, Viktor Hess discovered theionising radiation from space. He explored the so-called cosmic radiation withhis balloon experiments and discovered, that the ionisation rate increases in theatmosphere with increasing height [Hes12]. This discovery was the beginning of theresearch of cosmic rays and therefore the basis of astroparticle physics. Based onthis discovery, the search for sources of cosmic rays, the processes of the productionof messenger particles and their propagation through the universe were a growingcomponent of the research in astronomy and cosmology.

Over the years, different messengers of cosmic rays have been explored: charged(e.g. protons, electrons) and uncharged particles (e.g. neutrinos, photons). Chargedparticles of cosmic rays are not suitable for the research, since they are deflectedby magnetic fields during the propagation through the universe and thereby theirorigins cannot be reconstructed. Neutrinos and photons are traceable to their originand therefore most suitable as particles for the exploration of the universe. Sincethe cross section of neutrinos is very small, the detection of this particle requires alarge detection volume and still their event rate is rather small.

Gamma-ray astronomy covers the whole electromagnetic spectrum, which makesthis part of the particle astrophysics, such interesting for the studies of phenomenaand sources in the universe. The number of the messenger particles decreases withincreasing the energy, which leads to big detection volumes for the detection ofvery high energy gamma-rays from 100GeV up to 100TeV. In contrast to satelliteexperiments, which are limited in their detection volumes, ground-based experimentsuse the atmosphere as a detector. The messenger particles interact with the particlesin the earth’s atmosphere, which results in an extensive air shower (EAS). Secondaryparticles in the EAS constitute Cherenkov radiation, which is detectable withImaging Air Cherenkov Telescopes (IACT), such as the MAGIC telescopes.

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1 Introduction

The most suitable sources, which are capable for the acceleration of messengerparticles of cosmic rays into very high energies, are active galactic nuclei. Thesesources are observed in all wavebands to perceive the structure, the acceleratingprocesses of messenger particles and the composition of particles inside of them.Blazars, which are a subclass of AGN, are assumed to emit very high energygamma-rays from 100GeV up to 100TeV. Flat-spectrum radio quasars (FSRQs),a special type of blazars, are found to reveal much larger jet energy than otherblazars.

The FSRQ 3C279 is detected in 2006 as a very high energy gamma-ray source,belongs to one of the most distant objects with 𝑧=0.536 ever detected at very highenergies. The brightness and the distance of 3C 279 makes it an ideal candidate forthe study of jet emission models and the absorption by the extragalactic backgroundlight photon field. In 2015 and 2016 this source is observed again by the MAGICtelescopes during a high 𝛾-ray state. The results of this observation performedwith the MAGIC telescopes are obtained within the MAGIC analysis chain in thisthesis. Assuming, that the gamma-ray emission of blazars is mainly due to theinteraction of hadrons, they are most suitable as neutrino sources. Neutrinos canbe messenger particles of interaction by charged cosmic rays, which can be directlyconnected to gamma-ray photons via hadronic interactions in the jets of blazars. Amodel for the calculation of the neutrino rate from different blazars is estimated andthe contribution of blazars to the neutrino rate measured by the IceCube neutrinodetector is discussed.This thesis is structured the following way:

In chapter 2 an introduction to aspects of gamma-ray astronomy is given.Production mechanisms of gamma-ray photons and possible gamma-ray sourcesare described and the different approaches for the detection of gamma-rays, suchas IACT, are outlined.

The MAGIC telescopes are described in chapter 3, as well as the analysis ofthe measured data. The construction of the MAGIC telescopes will be describedbriefly, whereas the basic analysis chain of the data is explained theoretically.

The results of the data analysis of the flat-spectrum radio quasar 3C279 isshown in chapter 4. The steps of processing the data measured by MAGICand scientific results, like the energy spectrum and the lightcurve of 3C 279 arepresented.

In chapter 5 a model for the calculation the neutrino rate of different blazarsis presented. The neutrino rate is estimated by the gamma-ray flux of differentblazars.

A conclusion of the results and an outlook are provided in chapter 6.

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2 Gamma-Ray Astronomy

Figure 2.1: Overview of astroparticle physics: Sources like AGN (active galacticnuclei), SNR (supernova remnant) and GRB (Gamma-Ray bursts) emitting chargedparticles (e.g. proton and electrons) and uncharged particles (e.g. neutrinos andphotons). The particles propagate through magnetic fields, interstellar dust, cloudsand background radiation fields. They are detected by different satellite- orground-based experiments [Dre09].

Gamma-ray astronomy connects topics of particle physics, astronomy and cos-mology for the research and the understanding of high energy sources. Theproduction of high energy cosmic and gamma-rays is associated with the acceler-ation and interaction of particles in different processes [Per09]. Figure 2.1 givesan overview of astroparticle physics ranging from the sources and messengers tothe detection principles.Messenger of these sources can be charged (e.g. protons, electrons) and unchargedparticles (e.g. neutrinos, photons). Gamma-ray astronomy handles especiallythe exploration of high energy gamma-ray photons. Very high energy particles(100GeV to 100TeV range) arise within different processes in sources emittingcosmic and gamma-rays, like active galactic nuclei, supernova remnants andgamma-ray bursts.

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Charged particles are not suitable as messenger particles for studying pointsources of high energy radiation. They are not traceable to their origin, becauseof the deflection of charged particles by intergalactic magnetic fields. The inter-action of these particles with interstellar dust clouds and background radiationmodifies the spectral index of the measured flux [Lip08].Neutral particles like gamma-ray photons and neutrinos are most suitable as mes-senger particles, because they are not deflected by magnetic fields. Interactionswith other particles on their propagation through the universe is negligible forneutrinos, due to their small cross section. This fact requires very big detectionvolumes for the measurement of neutrinos. Neutrinos are detected indirectly bythe observation of neutrino-induced leptons, which interact with the detectormaterial. The measurement is accompanied by a large background of atmosphericmuons from cosmic ray (CR) air showers [FR12; KS11; Lip08].Compared to neutrinos, the detection of gamma-rays is simpler and a higherevents statistic can be achieved. Gamma-ray photons are attenuated by theinteraction with the extragalactic background light (EBL), which consists oflow energy photons from starlight and from interstellar dust clouds. The mea-surable gamma-ray flux is very low compared to the charged cosmic ray flux,but nevertheless, gamma-ray photons are the most suitable messenger particlesfor the research of very high energy sources. They are detected, for example,directly with satellite-based experiments or indirectly with ground-based experi-ments[FR12], where satellite experiments measure in MeV to GeV energy rangeand Cherenkov telescopes in GeV to TeV energy range.

2.1 Production and Acclerating Processes of Gamma-Rays

Very high energy (VHE) gamma-ray photons are produced in non-thermal pro-cesses by high energetic cosmic rays via Bremsstrahlung, synchrotron radiation,inelastic collision and inverse Compton scattering. Further information aboutacclerating processes is provided in [DM09; PRT07].

Inelastic collision of high energy cosmic ray particles produces mainly pions.The charged pions decay into neutrinos and muons:

𝜋− → 𝜇− + 𝜈u� (2.1)𝜋+ → 𝜇+ + 𝜈u�, (2.2)

whereas the neutral pion decay is the relevant process for gamma-ray astronomy:

𝜋0 → 𝛾 + 𝛾. (2.3)

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2.2 Sources of Gamma-Rays

Neutral pions decay in two photons with a probability of approximately 99%,which imply that other processes are negligible [FR12; VA09]. Since the ratioof pions in hadronic interaction is equal, a source producing gamma-rays viahadronic cosmic rays should also be an efficient neutrino emitter.

The annihilation of an electron-positron pair at low energies produces twophotons according to the following process:

𝑒+ + 𝑒− → 𝛾 + 𝛾 (2.4)

Electron-positron annihilation at very high energies produces other particles, likebosons [FR12; PRT07].

Bremsstrahlung is a form of electromagnetic radiation. It occurs whenevercharged particles (e.g. electrons, protons) are accelerated by other chargedparticles or nuclei. The accelerated particle loses, within that process, a part ofits kinetic energy and emits a photon. The energy of this photon corresponds tothe difference of energy of the accelerated particle. For this mechanism a densemedium is necessary [Wee03].

Whenever a charged particle moves through a magnetic field, synchrotronradiation is emitted. Charged particles propagate through magnetic fieldsand similar to processes in Bremsstrahlung, photons are emitted. High energyphotons can only be produced as long as the charged particles themselves havehigh energies. The emission efficiency of synchrotron radiation depends on themagnetic strength and therefore allows conclusions about the strength of themagnetic field of the source [BHK12].

Inverse Compton scattering occurs in sources, such as active galactic nuclei.High energy electrons scatter with low energy photons and transfer a fraction oftheir energy to these photons:

𝑒−before + 𝛾low → 𝑒−after + 𝛾high (2.5)

Via this process, photons are scattered to very high energies up to TeV range byrelativistic electrons [FR12].


Sources of gamma-rays can be divided into galactic and extragalactic, which canbe for example supernova remnants, active galactic nuclei and gamma-ray bursts.[FR12].

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When a massive star achieves the last burning stage, the inner core becomesthermally unstable. Due to the high gravitational pressure compared to thethermal pressure, the star collapses until protons become neutrons. Highlyrelativistic electrons scatter inelastic with protons and therefore neutrons areproduced by the inverse beta decay. The external shell collides with the highlycompressed core of neutrons and is thrown back as a shock-wave. The remainingcore, which is typically a neutron-star, and its surrounding emission nebulais called a supernova remnant. SNRs are a prime candidate for being acontributor to the cosmic ray spectrum. The most famous example of a SNR isthe Crab Nebula [WWW12].

Gamma-ray bursts are spontaneous, fast, highly energetic radiation outbursts,which seem to appear randomly in the sky. At this point of time, there is nomodel available to explain the origin of GRBs, but some scientists assume thatHypernovae (Supernovae, where the core collapses into a black hole) could beone kind of durable GRB sources [VA09].

The term active galactic nuclei (AGN) unites different types of sources, whichare classified independently before this term was introduced. Figure 2.2 gives anoverview of the structure and the main different types of active galactic nuclei.The structure of the AGN can be divided into three components: a massive black

Figure 2.2: Overview of the structure and the different types of active galacticnuclei. In the centre of an AGN is a massive black hole, which is surrounded by anaccretion disc with a dust torus. The jets are accelerated perpendicularly to theaccretion disc. AGN are mainly distinguished by the radio-loudness, the existenceof jets and by the angle between their jets and the observer [BS12].

hole in the centre, an acceleration disc with a dust torus and some AGN have two

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bipolar relativistic jets. If a particle descends into a black hole, it converts itskinetic energy into thermal energy due to scattering by other particles. This highthermal energy causes the very bright gamma-ray radiation of AGN. The matteraccumulates in the accretion disc before it disappears into the event horizon ofthe black hole. Charged particles of the accretion disc move through the twistedmagnetic field lines, which are generated by the spin of the black hole and theangular momentum of the surrounding accretion disc. The jets are defined bythe relativistic ejection of plasma from the accretion disc along the magneticfields [BL09].

AGN are distinguished first order by their radio loudness: Radio-loud objectsemit strong radio waves, whereas radio-quiet sources emit less in the radio band.An example of radio-quiet sources are Seyfert galaxies, which have only weakdefined jets. Seyfert galaxies are spiral galaxies containing bright nuclei withbroad emission lines caused by the motion of very hot gases at the centre [UP95].

Quasars (quasi-stellar radio sources) and Blazars (blazing quasi-stellar object)summarise the most luminous group of radio-loud AGN, which seem to bepoint-like in the optical spectrum similar to stars and not extended like galaxies.They are very compact quasars with a bright nucleus containing a supermassive

Figure 2.3: Spectral energy distribution of FSRQs and two kinds of BL Lacs,low-frequency peaked (LBLs) and high-frequency peaked (HBLs) BL Lacs. Thesynchrotron bump of LBLs and FSRQs is in the infrared to the optical wavebandwhereas HBLs peak at X-ray frequencies. The second peak arises at the highestgamma-ray energies [Urr98].

black hole. Blazars have a small angle between the jets and the line of sight fromthe observer and they are stronger gamma-ray emitter compared to other AGNclasses.

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The spectral energy distribution (SED) of blazars is characterized by a two-bumpstructure (see Figure 2.3). The low energy bump originates by synchrotronemission at X-ray frequencies, but the origin of the high energy bump is not fullyunderstood yet. Currently, there are different models for the possible explanationof the high energy bump in the SED of blazars, such as the leptonic and thehadronic model. The leptonic model uses the inverse Compton scattering forthe explanation, in which photons are scattered to high energies by relativisticelectrons (see Equation 2.5). The hadronic model assumes hadronic particles inthe jets of a blazar and uses the 𝜋0-decay to explain the high energetic gamma-rayemission. Hybrid models of leptonic and hadronic models also provide possibleexplanations for this question. The hadronic model is used in chapter 5 for theneutrino flux calculation of FSRQs and more information is provided in [HH10].

Blazars are divided into two subtypes: BL Lac (BL Lacertae objects) and FSRQs(flat-spectrum radio quasars). The difference between these types is based ontheir spectrum. Whereas BL Lacs show very weak or no optical emission linesin their spectrum, FSRQs have quasar-like broad optical emission lines [UP95;Fos+98; Urr98]. An example of a FSRQ is the very high energy gamma-rayemitter 3C 279, which is analysed in chapter 4.

2.3 Experiments in Gamma-Ray Astronomy

Gamma-rays experiments can be divided into space experiments with satellitesand ground-based experiments, such as atmospheric Cherenkov experiments andatmospheric fluorescence experiments. Satellite experiments are limited in thedetection volumes by the transport in a transfer orbit around the earth. Thegamma-rays are detected, for example, via Compton-scattering or via pair pro-duction. The Fermi Gamma-ray Space Telescope with the Fermi-Large TelescopeArray (Fermi-LAT) use a calorimeter for the pair production detection, whichis able to detect gamma-ray photons with an energy range from 20MeV up to300GeV [MAR10]. Atmospheric fluorescence and atmospheric Cherenkov experi-ments make use of the indirect measurement of the gamma-rays via Cherenkovradiation or fluorescence of particles in extensive air showers.

Extensive Air ShowersParticles, which reach the earth’s atmosphere interact with the atmosphere’smolecules and initiates extensive air shower (EAS), which are shown schematicallyin Figure 2.4 for gamma- and for hadron-induced showers. Cosmic ray inducedair shower consists of three different components: a hadronic, a muonic and anelectromagnetic component. Charged pions from the hadronic component decay

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2.3 Experiments in Gamma-Ray Astronomy

Figure 2.4: Schematic overview of an extensive air shower induced by gamma-rayphotons (left) and by protons (right) as primary particles. The electromagneticcomponents consist of photons (green) and electrons and positrons (blue). Hadroniccomponents are protons, charged and uncharged pions (red) and hadrons in general(black). A munonic component consists of muons (red) and neutrinos (orange).

into muons and neutrinos (see Equation 2.1), whereas neutral pions decay intotwo photons a shown in Equation 2.3. Electrons and positrons are produced bypair production:

𝛾 → 𝑒+ + 𝑒−. (2.6)

Processes in gamma-ray induced air showers are Bremsstrahlung and pair-production and the interaction of the primary gamma-ray photon with an at-mospheric molecule produces an electron-positron pair. Further photons areproduced by Bremsstrahlung. Due to this circumstance, cosmic ray inducedEAS are broader in the transversal spread and more divergent than gamma-rayinduced EAS [RS98].

Whenever high energy particles propagate through the Earth’s atmosphere with ahigher velocity than light in a medium, Cherenkov radiation is emitted. A chargedparticle polarises the molecules along its way through the atmosphere, which emitelectromagnetic radiation while they return to their normal state. If the velocityis smaller than light, the emitted radiation interferes destructively with light. Inthe other case, the emitted radiation interferes constructively with the Cherenkovradiation and results in a spherical wavefront of the electromagnetic radiation ina forward directed cone with an opening angle 𝜃, which depends on the energyand direction of the primary particle. Fluorescence light is emitted isotropic bythe polarisation of the earth’s atmospehere molecules in the ultraviolet waveband[Gri10].

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Different types of experiments are possible to detect Cherenkov radiation andfluorescence of cosmic ray air showers. Pierre-Auger, for example, uses watertanks for the detection of cosmic ray showers via Cherenkov radiation of sec-ondary particles in the EASs and uses telescopes for the fluorescence detectionvia the reflection of the fluorescence in a camera [Aa11]. Another possibility todetect Cherenkov radiation are the Imaging Air Cherenkov Telescopes, whichuse similar methods as the fluorescence telescopes.

Imaging Air Cherenkov TelescopesThe Imaging Air Cherenkov Telescopes (IACT) are a special type of Cherenkovexperiments, which measure gamma-rays indirectly via Cherenkov radiation,whereas hadronic cosmic rays belong to the background of the gamma-ray events,measured by telescopes, since they are not the target of measurement.A schematic overview of the functionality of Imaging Air Cherenkov Telescopesis given in Figure 2.5. Cherenkov light of the shower hits the dish and thusis reflected in the camera. IACT resolve the shower structure and show a realimage of it [Wee03]. The shower image parameters, like the amount of light

Figure 2.5: A schematic layout of an Imaging Air Cherenkov Telescope. Theemission of Cherenkov light by the extensive air shower reaches the mirror ofthe telescope and is reflected into the camera. The shower image is elliptical forgamma-ray induced EASs [Ste12].

and the position of the image in the camera, allow conclusions about the di-rection and type of the primary particle and its energy. These parameters forthe characterisation of EASs are summarised by the Hillas parameters [Hil85].Currently, different IACTs such as MAGIC (see chapter 3) and FACT on LaPalma [Ale+16b; And+13] are operating. The next generation IACTs is alreadyplanned: the CTA (Cherenkov Telescope Array) project [Sad+16].

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3 Gamma-Ray Astronomy with the MAGICTelescopes

3.1 The MAGIC Telescopes

Figure 3.1: The MAGIC telescopes on the Roque de los Muchachos on theCanarian Island of La Palma [Wag09].

The MAGIC telescopes (Major Atmospheric Gamma-ray Imaging Cherenkovtelescopes) are two IACT on the Roche de los Muchachos (28.8∘ N, 17.8∘ W) atabout 2200m height above sea level on the Canarian Island of La Palma in Spain.The first MAGIC telescope started operating in 2004 as a single IACT and in2009 the second telescope start operating at a distance of 85m, thus allowingstereoscopic measurements [Ale+11b].The telescopes are operated by an international collaboration involving insti-tutes from Germany, Spain, Italy, Japan, India, Poland, Croatia, Bulgaria andSwitzerland. German institutions are the TU Dortmund, DESY (DeutschesElektron-Synchrotron) Zeuthen, the University of Würzburg and Max PlanckInstitute for Physics in Munich [MAG16].

The MAGIC Collaboration observate different high-energy objects like supernovaremnants (SNRs), pulsars and pulsar wind nebulae (PWNe), active galactic nuclei

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3 Gamma-Ray Astronomy with the MAGIC Telescopes

(AGNs) and Gamma-Ray Bursts (GRBs). Observation of cosmic rays, DarkMatter searches and Lorentz invariance violations tests fulfil the fundamentalphysics part of this program [Tib12].

DesignThe telescopes are built for the observation of very high energy gamma-raysfrom different source types (see section 2.2). With a 17m diameter dish anda mirror surface area of around 240m2, the MAGIC telescopes are two verylarge IACTs. Air shower of gamma-rays with an energy range between 50GeVand 50TeV can be detected in stereoscopic observation mode. The trigger ofthe detectabel shower is lower in stereoscopic mode than for a single IACT,which makes detections of weak gamma-ray sources possible. The surface ofeach telescope consists of several hundred panels of aluminium and glass mirrors,which are continuously aligned by an Active Mirror Control system to a parabolicmirror. 1039 photomultiplier tubes (PMTs) with 0.1∘ diameter in the camera ofeach telescope convert the measured light into electronic pulses for the analysisof the air shower.Mirror and camera are mounted on a frame made of light-weight carbon fibre,which allows fast reorientation of the telescopes to quickly followup transientevents, for example in the case of GRB alerts. The reorientation of the telescopesto different positions in the sky takes less than 25 s for a 180∘ radiation in azimuthangle [Ale+16a; Dor+08].The readout electronics of the MAGIC telescopes are DRS4-chips (Domino RingSampler 4), where further details about the readout electronics are provided in[Ale+16a].

ObservationThe telescopes can observe typically in two different modes: the so-called ON/OFFmode and the wobble mode. In the ON/OFF mode, the telescope is pointettowards the source (ON) or towards a region without a known gamma-ray sourcefor the background (OFF) observation. In the wobble mode, a source is observedwith a fixed offset of 0.4∘ to the source position, which combines the ON andOFF observation and increases the effective observation time. Furthermore, itensures that the ON and OFF events are recorded under the same observationalconditions, so that the observed OFF events can be used for an estimation ofthe cosmic ray background. Therefore, the data are taken by default with thewobble mode. A detailed information about the different Observation methodscan be found in [Fom+94b] and [Fom+94a].

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3.2 The MAGIC Analysis Chain


The analysis of data taken with the MAGIC telescopes is performed by defaultwith the MAGIC Analysis and Reconstruction Software (MARS), which hasbeen developed within the collaboration [Mor+09]. The aim of data analysisis, for example, to detect a gamma-ray signal from a source, to study of theextragalactic background light or models for the explanation of jet emissionmodels. This requires the identification of the primary particle inducing the airshower, its energy and its arrival direction. The most important Hillas parametersfor the MAGIC data analysis are described in further detail [Hil85; GM08] inthe following.Length and Width describe the semi-axes of the shower-ellipsis. The lateraland longitudinal developments of a gamma-ray induced air shower are typicallysmaller than for hadron induced shower.Size is the amount of light of the shower, which is dependent on the energy ofthe primary particle and therefore important for the energy estimation.Alpha is the angle between the shortest connection of the centre of gravity(COG) of the shower image to source position and the major axis of the shower.Conc is the fraction of the charge concentration in the brightest pixels of theshower. This parameter is important for the gamma-hadron separation, since itis higher for gamma-ray induced shower.Dist describes the distance of the COG of the shower to the source position inthe camera.

3.2.1 Calibration, Parametrisation and Stereoscopic Reconstruction

The raw data of the MAGIC observations are preprocessed automatically intothree different states, which are available for the analyser: calibrated, star andsuperstar files.Raw data contain the digitised signal pulse from each PMT in the camera. Thefirst step is the calibration and signal extraction of the raw data with the MARSprogram sorcerer. A signal extraction means to obtain the charge of eachpixel in photoelectrons and the time at which the signal for each pixel arrivedin a certain time window around the trigger signal. The extraction requiresinformation about the cosmic ray background noise and the absolute measuredbrightness of the light. This information is obtained by performing pedestaland calibration runs. Pedestal runs prepare an estimation of fluctuations, likeafter-pulses in the PMTs and electronic noise within the readout electronics andthe determination of the night sky background (NSB). Calibration runs provide

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the conversion factors of the signal amplitude to the number of photoelectrons(phe) for each pixel [GM08; Mor+09].The MARS program star provides an image cleaning for the calibrated files inwhich each pixel containing only NSB noise is removed in order to receive onlythe shower image pixel after the cleaning. A cleaning can be executed by anabsolute or a time cleaning. A more detailed description of the cleaning procedurecan be found in [Ali+08]. The surviving pixels after the cleaning correspond toa 𝛾-ray event, which further includes electronic noise and NSB, and the imagecan be characterized by the Hillas parameter. The automatically provided dataare available with a default cleaning, but a different cleaning for the analysis ofcertain source data depending on the light conditions is possible.Superstar is used for the stereoscopic reconstruction of the events producedby star. Since MAGIC observes in a stereoscopic system, a reconstruction ofgeometrical parameters and Cherenkov light parameters is needed. Geometricalparameters are the shower axis direction, the shower core impact on the ground,the impact parameter and the height of the shower maximum. The shower axisdirection is reconstructed by the projection of the shower image of both telescopesas it is seen by one telescope, where the crossing point is the initial direction ofthe primary gamma-ray. This geometrically reconstruction performs a geometricimage of the shower in 3D, which makes it possible to calculate the Cherenkovlight parameters, such as the Cherenkov radius and the density. Superstarcalculates the impact parameter, estimate the energy of the primary particle andobtains the height if the shower maximum. The resulting parameters are storedinto the superstar files [Mor+09].

3.2.2 Direction Reconstruction, Hadroness and Energy Estimation

The number of gamma-ray signal events is usually significantly less than hadronicbackground events, which constitutes in a large background [Wee03]. Therefore,a separation of the gamma and hadron events is needed, since the aim of theanalysis is to investigate only the gamma-ray events. As well as a sepatationof the events, the energy has to be estimated and the direction of the primaryparticle need to be reconstructed. Coach obtains a model for the gamma-hadronseparation, the reconstruction of the direction and the estimated enery, for whichsamples of 𝛾-ray and hadron induced air shower are nessecary. Observationcharacteristics like the zenith-range, the weather conditions and light have to bethe same for off-data and source data, while the zenith-range of MCs have to bethe same as well.

14


Off-sourcesFor the characterisation of an observed event, a sample of background eventsis required to estimate how image parameter of hadronic events look like. Thebackground data will be provided by so-called Off-sources, which are distinguishedby their less emission of gamma-ray photons so that they constitute a suitablebackground sample [Mor+09].

MC SimulationMonte Carlo (MC) simulations provide standardized gamma-ray photon inducedair showers with a certain energy and direction. In general, they are stochasticprocesses created on a basis of predetermined probability distributions [GM08].The interaction models of different particles, the geometry of the telescopes andan estimation of the night sky background (NSB) is taken into account in thesimulation of an air shower. Furthermore, geometry and functionality of themirror and the camera influence the measured data as well and therefore theyare needed to be simulated during the MC production.In order to train the gamma-hadron separation with machine learning meth-ods, a pure gamma-ray shower sample is required to estimate how the Hillasparameter look like for signal events. Since the background rate is always muchhigher, these pure gamma-ray events can just be produced via MC simulations.Cherenkov telescopes can not be calibrated like other detectors and therefore thecharacteristics such as the effective detector area and the angular and energyresolution are obtained via the comparison with MC simulations.One half of the MCs, which are called Train-MC, are used for the trainingand the other half, which is called Test-MC, is used for the characterization.More information about the Monte Carlo simulation by MAGIC are provided in[Car+07].

Gamma-hadron separationCoach obtain a model for the gamma-hadron separation with a Random Forests,which provides the calculation the hadroness of an event. The hadroness ofan event describes the probability for an event to be a hadron induced shower.Random Forests are based on an ensemble of decision trees, which has randomlychosen image parameter for the separation at each knot of the tree. Figure 2.4provides an insight into differences like the shape and the development of hadronand gamma-ray induced air showers. Since gamma-ray induced shower has onlyan electromagnetic component, the shape of the shower image is less wide andhave a lower transverse momentum than hadronic events. Therefore image pa-rameter can be used for the characterization of the hadroness of each event.Melibea applies the trained model to the source data and assigns the hadronness

15


value to each event. For the removal of probable hadron events, the strength ofthe cuts in this parameter is needed to be adjusted [Alb+07a].

Energy estimationThe energy of the primary particle is correlated to the number of Cherenkovphotons and therefore to the Hillas parameter Size. In addition, Size itselfdepends on the zenith range, the location of the shower in the camera, the impactdescribing the distance between the shower core and telescope and the showerheight maximum, which is the height with the highest emission of Cherenkovlight [Hil85].Based on these dependencies, a multidimensional table, the so-called Look UpTable (LUT), is created, where the correlation between each parameter and theenergy based on the MC simulations is written down. Accordingly, the estimatedenergy is assigned to a real event based on the determined parameters and theadjustment to the table. Melibea applies this estimated energy to the sourcedata during the execution [Col+09].

Direction reconstructionFor the reconstruction of the source position the DISP method [SS09] is used,which uses the different Hillas parameter to perform a calculation of the estimatedsource position. DISP means here the distance between the COG of the imageand the source position, where it is reconstructed by using another RandomForest. Mainly the Hillas parameter Size, Width, Length and Leakage are usedfor a model to estimate the source position, where the Leakage of an eventspecifies the ratio between photoelectrons in the outermost pixels and the size.An estimated source position of the gamma-ray is obtained along the main imageaxis at the calculated distance DISP from the COG, where the distance betweenthe expected source position and the estimated source position 𝜃 is estimated.This parameter is needed for the calculation of the significance of the sourcedetection.

More details about the described methods above are provided in [Alb+07a;SS09].

3.2.3 Skymaps and Signal Detection

For the detection of a 𝛾-ray signal from a source the number of background andsignal events need to be estimated for any sky coordinate, where the regions fromwhich ON and OFF events are collected is illustrated in Figure 3.2. In case thatthe estimated position of an event belongs to the background region, it is defined

16


as a background event. In the other case, the event belongs to the ON region, itis assigned to an ON event of the source. The signal of the source is related to

Figure 3.2: Principle of the estimated number of background and ON events.The event on the left side is assigned to the number of ON events, where the eventon the right side is assigned to the background events [Maz07].

the number of excess events, which is given by the difference of the number ofOFF events and ON events:

𝑁ex = 𝑁on − 𝛼 ⋅ 𝑁off, (3.1)

where 𝑁on describes the number of gamma-ray events from the signal and 𝑁off isthe number of events from the background. The scaling factor 𝛼 is the reciprocalvalue of the number of background regions.Finally, the significance of the detection of the source data is calculated by thefollowing equation, which is given in [LM83],

𝑆 =√

2 (𝑁on ln [1 + 𝛼

𝛼( 𝑁on

𝑁on + 𝑁off)] + 𝑁off ln [(1 + 𝛼) (

𝑁off𝑁on + 𝑁off

)])12

.

(3.2)

A source is considered to be detected when the estimated significance exceedsthe limit of 5𝜎. A hint of a signal is defined to exceed a significance of 3𝜎.

Skymaps of the source region, plotted by Caspar, show the reconstructedarrival direction of all 𝛾-ray events in a histogram in equatorial coordinates (rightascension and declination). Caspar produces various types of Skymaps, where therelative flux map shows the relation of the excess events map to the backgroundmap and presents the luminosity of the source. The TS (test statistic) value iscalculated by a gaussian regression of the number of excess events to the number

17


of bins for the background data. The deviation of a pixel from the regressionis the test statistic value, which roughly corresponds to the formula of Li&Main Equation 3.2. The TS value is applied to the estimated background map byCapsar, which is generated through a very high random oversampling of theexposure model.The scaling factor between the ON and OFF events is

𝛼 = 1/𝑁resample (3.3)

with 𝑁resample = 200.

3.2.4 Energy Spectrum and Lightcurve

Flute (FLUx vs. Time and Energy) extracts the lightcurve and the energyspectrum of a gamma-ray source.A lightcurve of a source is the time evolution of the integral flux in a given energyrange, wherein the integral flux for a particular energy range is described by

𝐹 = ∫u�max

u�min

d𝐹d𝐸

d𝐸 = 𝑁ex𝐴eff ⋅ 𝑇eff

. (3.4)

𝐴eff is the effective collection area of the observation and describes the acceptanceof the measuring process. It is obtained from the Train-MC sample and calculatedby the collected events in the given area folded with the efficiency. 𝑇eff is theon-source time-range of the measurement and 𝑁ex is the number of excess events.

The energy spectrum shows the source flux as a function of the gamma-ray energyand is defined as:

d𝐹d𝐸

= d𝑁exd𝐸d𝐴effd𝑇eff

. (3.5)

It represents the estimated energy of the 𝛾-ray events as a histogram. Since theestimated energy is unequal to the true energy, the energy spectrum has to beunfolded.

The spectral energy distribution (SED) of the source is given by

𝐸2 ⋅ d𝐹d𝐸

𝑣𝑠.𝐸, (3.6)

which shows the energy and flux distribution of the particles and presents directlythe radiated energy at a given wavelength [Col16].

18


Unfolding of the energy spectrumOne aim of the analysis of sources is to get the true energy, but determining theenergy spectrum suffers from several properties. The differential energy spectrumas a function of the estimated energy produced by flute is not equal to the trueenergy, since Cherenkov telescopes measure only indirectly as already outlined insection 2.3. In addition to that, the energy resolution falsifies the measured energyspectrum. Therefore the direct measurement of the true energy is not possible,a preliminary energy spectrum of the primary gamma-ray photon is obtainedfrom image parameters of the shower in the camera in flute. Only a part of thegamma-rays entering the Earth’s atmosphere will be detected by the MAGICtelescopes, since the acceptance of the detector is limited and energy-dependent,where the limited energy resolution of the detector leads to a migration of events.Migration means that an event is classified through the reconstructed energy intoanother bin, than the real energy would have been. A two-dimensional histogramwith the estimated energy plotted against the true energy shows a smearedout correlation, which is described by the migration matrix. Furthermore, anundesirable background distorts the measurement [BL13; Blo02].The mathematical description of the problem is given by the Fredholm integralequation [BL13; Fre03]:

𝑔(𝑦) = ∫u�

u�𝑀(𝑥, 𝑦)𝑓(𝑥)d𝑥 + 𝑏(𝑦), (3.7)

where g(y) is the measured distribution of parameter like the estimated energyor size and f(x) is the distribution of the sought parameter (true energy). Themigration matrix M(x,y) represents the probability to obtain the estimatedenergy, if the true energy is given. The background estimation is represented byb(y).The equation can analogously be written in matrix form

⃗𝑔 = M ⋅ ⃗𝑓 + ⃗𝑏, (3.8)

since the components are parametrized in binned histograms. In the following ⃗𝑔is replaced by ⃗𝑔- ⃗𝑏.Finding a solution of the sought distribution of ⃗𝑓 , the first idea is matrixinversion, but due to the fact that the matrix is not quadratic, the invasion isnot a possible solution. Therefore the equation can be solved by minimization ofthe least-squares expression, defined by:

𝜒20 = ( ⃗𝑔 − M ⋅ ⃗𝑓)u� ⋅ 𝑉u� ⋅ ( ⃗𝑔 − M ⋅ ⃗𝑓), (3.9)

with 𝑉g as the covariance matrix of measured distribution. The minimizationobtains the solution of the sought distribution of ⃗𝑓 , which agrees best with the

19


source data.The solution is often subjected by strong fluctuations, due to insignificant entriesin the migration matrix, which are enhanced during the unfolding process. Addinga regularization term to the expression of the least-square fit the fluctuations canbe controlled:

𝜒2 = 𝑤2

𝜒20 + 𝑅𝑒𝑔( ⃗𝑓) (3.10)

where the weight of the strength of the regularization is given by 𝑤. The strengthof the regularization has to be controlled, because too strong regularization leadsto a loss of important information and too weak regularization leads to too manynon-physical fluctuations.The Mars program CombUnfold provides different approaches for the regulariza-tion: Tikhonov uses for the regularization the minimization by MINUIT. Themethod of Schmelling is divided into two different types: one with minimizationby Gauss-Newton method and one with minimization by MINUIT. Regular-ization with the Bertero-method is appropriate for under-constrained and forover-constrained cases. An alternative approach is the forward unfolding methodwith an assumed function of the sought distribution. Details about the algorithmsand their implementation in Mars can be found in [Alb+07b; AW06].

EBL correcionGamma-ray photons are scattered by the extragalactic background light (EBL)during the propagation trough earth, which causes in a possible cascading of thephotons. A correction of the differential spectrum necessary. The spectrum ofthe observed source is attenuated by the scattering of the photons which can bedescribed as the following:

d𝐹measd𝐸

= d𝐹intd𝐸

⋅ 𝑒−u�u�(u�,u�), (3.11)

where 𝜏 is the strength of the EBL correction for the given energy E at a givenredshift z. The higher the redshift, the higher number of photons is attenuatedby the EBL. In addition, the attenuation is energy dependent, but finally, notmonotonous as the redshift. In MAGIC different models for the EBL correctionare developed such as Franceschini [FRV08], which are not described in furtherdetail here. The used EBL correction model is applied within CombUnfold to thedata.

20

4 Analysis of the FSRQ 3C 279 data from 2015and 2016

Figure 4.1: The source position of 3C 279 (red dot in the left figure) [WH16], as wellas measured in gamma-rays (right). The source position is RA=12ℎ56u�11.1u� andDEC=−05u�47u�22u� [Ta07]. The gamma-ray recordings are provided by EGRETin the Compton Observatory by NASA [EGR16].

Despite its large redshift of 𝑧=0.536, 3C 279 is one of the brightest gamma-rayemitter in the sky, which makes the flat-spectrum radio quasar one of the mostinteresting targets for MAGIC [Ta07]. In Figure 4.1 the source position of 3C 279is shown, as well as measured gamma-rays from the source.

FSRQ are a particular subgroup of blazars, since they belong to a very variablegroup of sources with broad emission lines, which is called type 0. Active galacticnuclei are subdivided into three classes of objects based on the emission lines:type 1 are AGNs with broad emission lines caused by the high velocity of hotgases, whereas type 2 have narrow emission lines, due to the low velocity of thehot gases. Flat-spectrum radio quasars belong to the special type 0 of activegalactic nuclei, which are characterized by the small angle between jet and theobserver. Type 0 objects have broad emission lines like type 1 AGN [UP95].Therefore 3C279 belongs to an interesting type of AGN to study of differentSED models, the emission of AGNs and EBL absorption.

In 1992, 3C 279 was discovered for the first time by the Compton Gamma-RayObservatory [Har+92] and was discovered by the single MAGIC-I telescope as

21

4 Analysis of the FSRQ 3C 279 data from 2015 and 2016

a very high energy (VHE) gamma-ray emitter in 2006 [Ta07]. The detection of3C 279 took place in February 2006 with a significance of 6.2𝜎 and in January 2007with a significance of 5.4𝜎 by MAGIC-I [Ta07; Ber+11]. At that time, 3C 279was the most distant very high gamma-ray source detected. For more informationabout previous MAGIC observations have a look at [Ale+11a; Ale+14; Ae08].

This chapter is structured according to the individual analysis and processingsteps presented in section 3.2. To ensure no problems during the processingof the 3C279 data, the analysis of Crab Nebula data is needed as a referenceor pre-analysis with the same conditions as for the analysis 3C 279. The CrabNebula is a so-called standard candle of the gamma-ray astronomy, since itcontinuously emits gamma-rays in VHE. Therefore the analysis results of theCrab Nebula, especially the spectrum and spectral energy distribution, are wellknown and some parameters can be optimized by the analysis of this data.

4.1 Selected Data Samples for Analysis

Prior to the analysis itself, the initial set of MAGIC data from 3C279 needs tobe selected according to several criteria, which are presented in Table 4.1. Theselected cuts are applied to the data by the MARS executable quate (QUalityTEster), but also a manual selection is used.First of all, a data selection is needed to exclude too bright sky. Car flashesand bright sky are recorded by the night shifters in runbooks in each night. Toprecisely check the observation conditions subrunwise, the analysis of this thesisstarts at star level. Therefore the data need to be processed by superstar afterthe quality selection.

The Observation method is already mentioned in section 3.1 and since all of thedata of 3C 279 were taken in wobble mode in the analysis period, this is also acriteria for the Crab Nebula to ensure the same observation conditions of thesedata. 3C 279 is observed in May/June 2015 and April 2016 and therefore theanalysis period lies between the 24th November 2014 and 28th April 2016, whereanalysis periods are divided by hardware changes of the telescopes. Therefore,all taken Crab Nebula and background data need to be taken from the sameanalysis period. The set of 3C 279 data contains all observations with excellentweather conditions and with zenith angles between 34∘ and 48∘.Weather conditions of MAGIC observations are characterized by the transmissionof the sky. Four different weather conditions are distinguished: Excellent qualitywith a transmission above 0.85, acceptable quality with a transmission between0.7 and 0.85, bad quality with a transmission between 0.55 and 0.7 and worse

22


Table 4.1: The applied quality cuts for the MAGIC data in the analysis of datafrom November 2014 till April 2016. The observables and the conditions for themare given.

Time range 24th November 2014 to 28th April 2016Observation mode wobble modeZenith range 34∘ ≤ Zd ≤ 48∘Cloudiness ≤ 20%Direct Current ≤ 3000 nATransmission ≥ 0.85Size in a given range around the median

data with a transmission below 0.55. Excellent and acceptable quality can beused for MAGIC data analysis, however acceptable quality need corrections dueto possible fluctuations. Finally, these limits are roughly specified and can beadjusted accordingly. The transmission is measured by the LIDAR system ofMAGIC, which uses the reflection of laser shots by the clouds to get informationabout the cloudiness. For more details have a look at [DNB09; Fru+13]. Thecloudiness of the data needs to be less than 20%, since all 3C 279 data are takenwith a cloudiness less than this value. Therefore all Crab Nebula and backgrounddata need a transmission greater than 0.80.

The direct currents need to be chosen to ensure a cut in the light backgroundintensity of the signal. The value below 3000 nA is given by default by thecollaboration and defines dark conditions for the observation.The cut in the Hillas Parameter Size is assumed to exclude an increased lightamount by the background. This cut is done by the calculation of the median ofthe entire data sample. Data is excluded, if it is outside of a certain number ofstandard deviations, which is fixed here at a value of three.

The final inputcard for the quality selection with quate can be found in section A.4.In the following chapter observation dates of 3C 279 and Crab Nebula are shown,as well as the selected off-sources for the analysis and the MC simulations.

3C 279

3C279 was observed in 11 nights in the analysis period from November 2014to April 2016, where two nights in May 2015 were available with worse qual-ity weather conditions and therefore they were excluded. Finally 9 nights ofobservation with overall 6.6 hours remain, which are listed in Table 4.2. The

23


Table 4.2: Available observation dates of 3C 279 taken with the MAGIC telescopesbefore quality cuts. The total observation time before quality cuts is 6.6 hours ofobservation.

Year Month Day2015 June 16., 17., 18., 19.2016 April 07., 10., 11., 12., 13.

selection cuts mentioned above are chosen in agreement with the given quality ofthe observations of 3C 279, to ensure that a large part of the data survives afterthe applying of the quality cuts. Finally 6.5 hours of observation remain afterapplying the cuts.

Crab Nebula

Crab Nebula was observed in 194 nights in the wobble observation method in theperiod from November 2014 to April 2016, which is listed in Table 4.3. Finally,the initial set of Crab Nebula data includes 69.2 hours in the given analysis period.To ensure that the reference analysis for the optimization of cuts and parameterof the Crab Nebula is made under the same conditions as the analysis of 3C 279,the quality cuts mentioned above need to be applied to the Crab Nebula data aswell. After the application of the quality cuts, 3.9 hours of observation remain.Most of the Crab Nebula files are available at a large zenith range between 5∘and 70∘ and only subruns with observations in the given zenith range remainafter the selection. Therefore, most of the observation time is excluded throughthe zenith range and a cloudiness above 20%.

Table 4.3: Available observation dates of Crab Nebula taken with the MAGICtelescopes before quality cuts. The total observation time before quality cuts is69.2 hours.

Year Month Day2014 November 25., 26.

DECember 13., 14., 15., 18., 19., 20., 21., 25.2015 January 11., 16., 17., 18., 23., 24.

February 07., 12.March 12., 13., 14., 15.

24


April 10., 11., 12.August 17.September 12., 13., 14., 15., 16., 17., 19., 21., 26.November 07., 06., 07., 08., 09., 20.DECember 03., 04., 09.

2016 January 01., 02., 10., 12., 13., 27., 28.February 10., 11.March 01., 05., 07., 10., 11., 27.

Off Sources

Background data are needed for the hadroness estimation of the 3C279 data,as already mentioned in subsection 3.2.2. Therefore, it is necessary, that thesamples are taken in the same analysis period under the same weather and zenithrange conditions as the data of 3C 279.

Table 4.4: Chosen off sources for the analysis. For each off-source, the source-name,the year of observation and the number of days in the analysis period is given.

Source Year # Days Source Year # Days1ES 0229 +200 2014 8 4C55.17 2014 2

2015 30 2015 22BZBJ0809+345 2014 2 Dragonfly 2014 1

2015 10 2016 2HESE-37 2016 10 HESE-38 2016 5M15 2015 24 RBS0921 2016 12Perseus‐MA 2014 4 UrsaMajor II 2014 7

2015 7 2015 142016 2 2016 28

MOLA (MAGIC OnLine Analyis), which is a MARS program for the real-timeanalysis of data taken by MAGIC, provides a tool to find matching off-sources.The condition of an OFF source to be weak enough in the period is fulfilled,

25


if the combined MOLA output for all observation dates of one source shows asignal below 2𝜎 in low energy and high energy. With this tool and a databaseof available data, the off-sources in Table 4.4 were chosen for the analysis inthis thesis. The number of observation dates in each year for the backgroundsources is given, where a full overview over single days is given in Table A.1. Anoverview over the combined MOLA output of the off-sources can be found insection A.1.

Monte Carlo Simulations

For the analysis of 3C 279 the standard MAGIC Monte Carlo simulations, whichare produced at the TU Dortmund, will be used. Monte Carlo simulations areadapted to the geometry and the current hardware of the MAGIC telescopes.As already mentioned above, the analysis periods of the MAGIC telescopes aredivided by hardware changes of the telescopes. Therefore, for each analysisperiod different MC simulations with the current changes are produced, since itis needed that the simulations are as close as possible to the real measured data.

The MC simulations, which are used in this analysis are simulated with, initially,around 10 million events in a zenith range between 5∘ and 50∘ for the givenanalysis period. MC simulations are provided as superstar or star files. Sincethere are no changes in the MC simulations necessary, the superstar files arechosen.

4.2 Gamma-Hadron Separation, Energy Estimation andDirection Reconstruction

As already mentioned in subsection 3.2.2, this part is needed to estimate thehadroness of events, as well as for the estimation of the energy of gamma-raysand for the direction reconstruction of the origin of the observed gamma-rays.

The training is performed with the Train-MCs and the selected off-data presentedabove in a zenith range of 5∘ to 50∘. The zenith range is chosen to ensure, thatall gamma-ray events in the MC data can be used for the training described inthe following. Finally, the trained methods are applied zenith dependent to thesource data. In the random forest 100 trees are used for the training by default,but in this thesis 150 trees are used to ensure an even more precise training.As every MARS program, coach uses cuts in different parameters during theexecution. The general cuts are in the Hillas parameter Size and the Leakage.

26

4.2 Gamma-Hadron Separation, Energy Estimation and Direction Reconstruction

For the training only data with a Size above 50 phe and below 50000 phe areused, since 50 phe is the threshold of the telescopes and the MCs are simulatedonly up to 50000 phe. The Hillas parameter Leakage is directly correlated to theSize and therefore a cut in this parameter is useful as well. The Leakage of anevent characterizes how much the image leaks outside of the camera during themeasurement by the fraction of the signal light amount in the last pixel ring ofthe camera to the amount inside. Therefore the higher the Leakage is, the less ofthe shower is outside of the camera, for which reason only events with a leakageabove 0.15 are used for the training.

Coach calculates the three different parts independent of each other:

Gamma-hadron separation: The separation is trained with the help of therandom forest method. For the training, it is necessary that the whole zenithrange of the 3C279 data is covered to ensure that the estimated hadroness iscalculated reliably. Figure 4.2 shows the distribution of the events of MC files andbackground data per bin in cosine of the angle. Since the program excludes theincreased number of events of each zenith bin, the number of background eventsneeds to be larger than the number of MC events, so that enough gamma-rayevents can be used for the training. Furthermore the number of bins in the zenithrange is chosen as a value of 22, so that for each zenith bin enough events areavailable for the training.For the training of the gamma-hadron separation coach uses the primary parti-cle dependent Hillas parameter Size, Width, Length, Impact, MaxHeight andTimeFit. The trained hadroness estimator is saved in a root file called RF.root.This file can be applied to the data by melibea, so a hadroness value can beassigned to each event.

Energy estimation: The energy estimation in coach is made through the setup of so-called LUTs (look up tables). As mentioned in subsection 3.2.2, theLUTs are created by the Hillas parameter Size, Impact, Leakage and the zenithangle, since the energy depends on this parameter. The look up tables are storedin a root file named as Energy_Table.root. The readout of this multidimensionaltable and the application to the data is performed during the execution of melibea.Thereby, the estimated energy, based on the obtained parameters of the event, isassigned to this event of the source data.

Direction reconstruction: The direction reconstruction is based on anotherrandom forest, the so-called DISP-RF. For the training of the DISP (Distancebetween the Image centroid and the Source Position) parameter for the directionreconstruction, coach uses the Hillas parameter Size, Impact, MaxHeight, Width,Length and Dist, as well as the zenith angle. The estimated source position is cal-

27


Figure 4.2: Zenith angle distribution of the MC files (blue) and the off data (red).In the histogram is the number of events per bin in cosine of the angle is outlined,where the number of bins is 22.

culated for each telescope separated and is stored in two files called DispRF.root,which are applied to the data during the melibea execution.

The final files after the processing with melibea are used for the production ofscientific results in the following. The used settings for coach and melibea canbe found in section A.4.

4.3 Signal Detection

The signal detection of an observed source is made by the MARS program odie,as already mentioned in subsection 3.2.3. A detection plot shows the number ofevents for the ON and the OFF region is shown for the squared distance betweenexpected and estimated source position 𝜃2.

To estimate the signal and background regions, a cut in 𝜃2 is assumed, whichrepresents the so called signal cut. A standard default signal cut is defined bythe collaboration. In this thesis the results with a custom cut in LE and HE arepresented for 3C 279. The default cut for FR is the optimal cut and therefore nocustom cut is shown. For LE the signal cut is set at 𝛩2 = 0.021 and for HE at0.009, which are selected by optimization of parameter during the pre-analysis ofthe Crab Nebula. One aim of this thesis is to reach a higher significance than 5𝜎in a good agreement with a low sensitivity, which depends on the signal cut. Theoptimization of the signal cut will be described in further detail in section 4.3.

28


The arrival direction of each photon in reconstructed with a certain accuracy,hence, a point source measured with the telescopes shows a minimal extension.This resolution is called the point spread function (PSF). The values for thePSF is given for each energy range by default in the MAGIC collaboration. Incase of no extended sources just like 3C279 and Crab Nebula, this standardvalues for each energy range can be used.The zenith range is the same as outlined in the data selection, which is neededfor the normalisation by the effective on-time (see Equation 3.4). Possible cutsin the Hillas parameter can be assumed for the optimization of the Sky maps.In this thesis no custom cuts in the Hillas parameter are used, since the defaultcuts show the best significance of the signal detection here. For LE the hadronessneeds to be less than 0.28 and the Size needs to be higher than 60 phe. HEpresupposes a hadroness less than 0.1, a Size larger than 400 phe and an energylarger than 1TeV and FR needs a hadroness less than 0.16 and a Size higherthan 300 phe.As already mentioned in subsection 3.2.3, the number of the OFF regionscan be chosen by the analyser. Finally the background regions and the on regionneed to be symmetrically distributed in the camera, to compensate fluctuationsand inhomogeneities. The OFF regions also may not overlap, because events cannot be assigned to a particular off region and it could be that they are calculateddouble. Taking these conditions into account, the number of background regionsis set to three.

In the following the signal detection for the pre-analysis of the Crab Nebula andfor 3C 279 are presented. The final inputcard for signal detection with Odie canbe found in section A.4.

Crab Nebula

The signal detection for the Crab Nebula pre-analysis are given in all energyranges in Figure 4.3, in which the optimal cuts are applied.

The sensitivity of the detection plot is defined by the flux of the Crab Nebulaby the given data sample, which can be significantly detected within 50 hoursof observation. For example, the sensitivity of the data sample is 1.14%, whichmeans that a source with a flux of 1.14% of the Crab Nebula flux can be detectedwith a significance above 5𝜎 in 50 hours of observation. Therefore the sensitivityis calculated for the Crab Nebula data, so that the custom cuts can be chosen onlyin the pre-analysis. If a good agreement of the highest possible significance witha low sensitivity for the applied signal cut and the number of background regions

29


is found, the cut is optimal for the given analysis. By default, the sensitivity hasto be around 1.2% for LE, about 1.0% for HE and around 0.7% for FR.

The presented signal detection for the Crab Nebula are in a good agreement withthe given sensitivities, whereat the significance of LE is 67.86𝜎, for HE 28.72𝜎and for FR 47.42𝜎. Therefore the cuts can be applied to the 3C 279 data.

3C 279

The signal detection of 3C 279 for all energy ranges with the optimal cuts outlinedabove are presented in Figure 4.4. The significance of HE and FR are with 2.74𝜎and 1.71𝜎 below the significance value of a hint of a signal. The less number ofON events for higher energies represent that, the higher the energies, the lessnumber of gamma-rays reach the earth, as outlined before. The significance

Table 4.5: Significance and effective on time of the day-wise and full analysis of3C 279 for LE, HE and FR. Negative significances arise from a higher number ofbackground events than ON events, since the significance is multipied with thesign of the excess events.

Day Eff. Time[h] Sign. LE[𝜎] Sign. FR[𝜎] Sign. HE[𝜎]20150616 0.83 3.33 1.96 1.4720150617 0.83 1.70 -0.30 -0.4920150618 0.55 1.53 -0.46 -1.0720150619 0.32 -0.63 -0.60 1.5220160407 0.72 2.22 2.18 0.020160410 0.62 1.91 -0.12 0.020160411 0.58 2.44 -0.80 1.5220160412 0.55 3.43 0.32 1.5220160413 1.20 2.41 1.46 1.80Total 6.20 6.41 1.71 2.74

for low energies above 100GeV is about 6.41𝜎 and the number of ON events isestimated at 2801 during the observation. Finally, the results of the full analysisshow a significant detection of the source during the analysis of the data of 2015and 2016 for LE. Therefore, it can be seen that most of the gamma-ray events of3C 279 belong to energies between 100GeV and 250GeV, but the few gamma-raysof higher energies show that even high energy photons are emitted from 3C279.

30


The effective on-time of the full analysis is 6.20 hours of observation and thereforethe effective on-time is a bit lesser than the observation time given in section 4.1.This occurs, amongst other, due to a dead time of the detector in which it isunavailable for recording events.

Furthermore, significance is also calculated for the daily observations, which canbe found in Table 4.5. The daily significances show a hint of a signal for the 16thof June in 2015 and for the 12th of April in 2016 for LE. There is no hint of asignal in the daily and total significances of HE and FR. Negative significancesarise, if the number of background events is higher than the number of ON events.

31


Figure 4.3: Signal detection for Crab Nebula for all energy ranges. The numberof ON events (blue) and OFF events (red) is given for the 𝜃2 parameter for LE(top), HE (middle) and for FR (bottom). The vertical line shows the signal cutapplied to the data. The data are given for bins in 𝜃2, which are presented by thehorizontal bars.

32


Figure 4.4: Signal detection for 3C279 for all energy ranges. The number ofON events (blue) and OFF events (red) is shown for the 𝛩2 parameter for LE(top), HE (middle) and for FR (bottom) and the vertical line shows the signal cutapplied to the data. The data are given for bins in 𝜃2, which are presented by thehorizontal bars. 33


4.4 Sky Maps

Sky maps produced with the MARS program Caspar are briefly described insubsection 3.2.3 and show the two dimensional arrival direction of the gamma-raysafter the subtraction of background events. Here relative flux maps and TS valuemaps are presented.

Sky maps depend on different parameters for the optimization, which are describedin the following. The program can be executed in three default energy ranges:low energy (LE), high energy (HE) and full range (FR). LE describes energiesabove 100GeV, HE is energies above 1TeV and the FR shows energies above250GeV. To estimate in which energy range the most gamma-rays of the sourcereach earth, the Sky map needs to be produced for each energy range.The zenith range, the energy ranges and the PSF are finally described insection 4.3. In this thesis no custom cuts in the Hillas parameter are used, sincethe creation of Sky maps is only for the purpose, to fit the source position and tohave a look at the strength of gamma-ray sources in the near surrounding fieldof the source.

In the reference analysis of the Crab Nebula, only Sky maps for low energies areshown here, since Sky maps for higher energies do not contribute any relevantconclusions for this analysis here. The Sky maps (TS value and relative fluxmap) for 3C 279 are shown in all three energy ranges, since the relative flux isdifferent for each energy range. Relative flux maps can be presented with theestimated source position and the significance, which is represented by contours,starting at 3𝜎 for weaker sources and at 5𝜎 for strong sources. A source positionfit can be compared to the known source position and gives information aboutthe accuracy of the origin of the measured gamma-rays. Sky maps are very usefulfor very weak sources or for extended sources. The TS value map shows mainlythe significance of the data. The final inputcard for the Sky map productionwith Caspar can be found in section A.4.

Crab Nebula

The TS value map and the relative flux map of the pre-analysis of the CrabNebula for low energy are presented in Figure 4.5, whereat the results for HEand FR can be found in section A.2.

In the relative flux map, the estimated source position of the given data sample,as well as the significance of the source is shown in contours. The steps betweenthe contours is larger the stronger the source, in this case the contour start at 5𝜎

34

4.4 Sky Maps

and the steps are 12𝜎. The final significance is calculated in the previous chapter.Crab Nebula is positioned at RA=05h34m31.1s and DEC=+22d 00m52.1s [Aha+04]

Figure 4.5: Sky map as a test statistic value map (left) and a relative flux map(right) of the Crab Nebula for LE. In both maps a two dimensional hostogram ofthe right ascension (RA) and the declination (DEC) is shown, where on both mapsthe source position of the Crab Nebula is marked with an blue empty cross. Theestimated source position is marked with a red star (right) and the contours of thesignificance start at 5𝜎. The size of the PSF is given by the white circle.

and the position fit of the given Crab Nebula data by Caspar is estimated atRA=(05h34m33.92s ± 0.324s) and DEC=(+22d01m5.45s ± 4.36s). Thereby, theestimated positions are nearly the same, since the deviations are within theuncertainty.Crab Nebula belongs to one of the strongest gamma-ray emitter in the sky andtherefore in the surrounding field, no other gamma-ray source emits such a highnumber of gamma-rays. The crosscheck on Crab Nebula data shows that theanalysis chain works well, since the estimated position is nearly equal to the trueposition and that Crab Nebula is the only visible source with such a high numberof gamma-rays in the relative flux map. Therefore, the cuts can be applied tothe data of 3C 279.

3C 279

The Sky maps of 3C 279 for LE (TS value map and relative flux map), HE andFR are shown in Figure 4.6. A relative flux map for HE and FR are not shown

35


here, since there is no significant flux at higher energies.

For weaker sources the contour on the relative flux map starts at 3𝜎 and thesteps are 1𝜎 each time. The maximal significance in the TS value map andthe relative flux map is higher than around 5𝜎, though the final significance isalready presented in section 4.3.3C 279 is positioned at RA=12h56m11.1s and DEC=-05d47m22s, as outlined inchapter 4, whereas the estimated position for each energy range by Caspar isgiven in Table 4.6. As it can be seen, the estimated position for LE is more

Table 4.6: The estimated source position for 3C 279 at LE, HE and FR. For eachenergy range the estimated position in RA and DEC is given with the estimateduncertainty during the fit.

LE RA [hh mm ss] 12 56 15.94 ± 00 00 3.49DEC [dd mm ss] -05 47 54.34 ± 00 00 49.18

HE RA [hh mm ss] 12 56 7.32 ± 00 00 4.788DEC [dd mm ss] -05 49 17.44 ± 00 03 34.99

FR RA [hh mm ss] 12 56 10.14 ± 00 00 4.28DEC [dd mm ss] -05 53 59.21 ± 00 02 12.77

consistent with the given source position, since the position deviates less fromthe real source position. The deviation is equally small for each energy range,however the deviation for DEC in HE and FR are slightly worse than for LE.The main reason for the higher deviation at higher energies is, that the higherthe energy the less number of gamma-ray photons reach the earth.Furthermore, the Sky maps show for LE fluctuations up to 4𝜎, where thefluctuations of HE and FR are only 2 to 3𝜎, which also takes account of the lownumber of high energy gamma-rays.

36

4.5 Energy Spectrum and Lightcurve

Figure 4.6: The test statistic value maps of 3C 279 data for LE (top left), HE(bottom left) and FR (bottom right) and the relative flux map for LE (top right).All maps show a two dimensional hostogram of the right ascension (RA) and thedeclination (DEC) is shown, where on all maps the source position of 3C 279 ismarked by an white or blue empty cross.The flux-map with contours (top right)shows the estimated source position for LE with a red star. The size of the PSF isgiven by the white circle.


The estimation of the energy spectrum, the spectral energy distribution (SED)and the lightcurve (LC) are produced by the MARS program flute, which is

37


already outlined in subsection 3.2.4. A energy spectrum is presented as the energyweighted flux for the energy, whereat the SED shows the energy flux for theenergy. The lightcurve shows the flux per observation date. The Test-MC sampleis needed here for the characterization of the collection area and the energyresolutions, so that the number of excess events can be used for an estimation ofthe flux.

There are some parameters, which can be optimized by the pre-analysis of theCrab Nebula data, where two parameters need to be adjusted for the source.The optimization of flute differs from those previously, since the values areconsidered for weaker sources and then they are applied to the Crab Nebula data.The zenith range is the same as for the previous analysis steps. In agreementwith the signal detection in section 4.3, the size of the data needs to be largerthan 60 phe, since most of the data belongs to low energies, the cut is selected bythe odie cuts for LE. In addition to that, below this value the reconstruction ofthe events is not accurate anymore.For the optimization the binning of 𝜃2 and the binning of the energy areneeded to be chosen. In this thesis no custom value for the 𝜃2 binning is chosen,since the value of 40 bins is already optimal for the analysis here. The number ofenergy bins in an energy range of 5GeV till 50TeV is chosen by analysing 3C 279data, because it is trying to get not only upper limits in the estimated spectrum.If there is no significant excess of events in a given bin, Flute calculates upperlimits for the estimated spectrum, LC and SED. Therefore, this value should beselected so, that as many real data points are generated as possible. This valueis tested for the 3C 279 data and was selected as a number of 20 bins.Finally, the energy spectrum and the lightcurve ought to contain mostly truegamma-ray events, which leads to cuts in the hadroness and in 𝜃2. These cuts canbe chosen as a fixed cut by the analyser for each bin, but it could be chosen byflute itself by a given efficiency for each parameter. These cuts are chosen bythe optimization with the given Test-MC distribution, so that the given fractionof gamma-ray events, which survive after the cut. The chosen values for theefficiencies are for 𝜃2 0.7 and for the hadroness 0.9, to get a preferably clean datasample in a larger signal area.For the estimation of the lightcurve an energy threshold is needed to be set.This is done by applying size and hadroness cuts to the energy distribution ofthe Test-MC sample with a spectral index of 𝛼=-2.6, which can be found inFigure 4.7. The cuts are chosen in agreement with the cuts for LE in section 4.3,where the hadroness needs to be less than 0.28 and the size needs to be largerthan 60 phe. The estimated energy threshold is around 127GeV and since this isonly an approximation as there is a known discrepancy between MC simulations

38


and real gamma-ray events, a bit larger threshold of 150GeV is chosen.An assumed spectrum needs to be given by the analyser for the estimation

Figure 4.7: The calculated energy threshold for the lightcurve estimation of theenergy distribution of MCs. The number of events of the Test-MC data sample(blue) with the applied cuts is shown for the energy bins. The red line represents afit to estimate the maximum of the distribution.

of the source spectrum in flute, which shows a possible spectral shape of thesources given for example in previous analyses. The assumed spectrum for thepre-analysis of the Crab Nebula is given by default as:

d𝐹d𝐸 u�u�

= ( 𝐸300.

)−2.31−0.26⋅log10(u�/300.)

, (4.1)

whereat the assumed spectrum of 3C279 is given by a previous analysis of thesource from 2011 in [Ale+14]:

d𝐹d𝐸 3u� 279

= ( 𝐸300.

)−2.37

. (4.2)

The last parameter, which is needed to be given by the analyser is the redshiftof the source, since it affects the energy spectrum. 3C379 is positioned at aredshift of z=0.536 [Ta07] as outlined above and the redshift of the Crab Nebulais given by default at z=0.0.

In the following the energy spectrum and the spectral energy distribution for the

39


pre-analysis of the Crab Nebula is presented. The lightcurve of the Crab Nebulais not relevant for the optimization of the parameters and therefore not presentedhere. The results of 3C 279 are presented afterwards. The final inputcard for theproduction of the energy spectrum with Flute can be found in section A.4.

Crab Nebula

The spectral energy distribution of the Crab Nebula is a good indicator tooptimize the parameters, since they are estimated by many analyses before. In

Figure 4.8: The spectral energy distribution of the Crab Nebula. The data points(blue) of the SED and the assumed spectral shape (red) are shown for each energybin. The black line is the SED of the Crab Nebula from [Alb+07c] and the yellowdotted lines show an analysis of the Crab Nebula by HESS in [Aha+06]. The morethe shape of the analysed data matches with this data, the better the optimizedparameters are.

Figure 4.8 the SED of this pre-analysis is presented. The lightcurve and theenergy spectrum are presented in section A.3, since they contain non relevantinformation for the analysis of 3C 279.A reference shape of the SED of the Crab Nebula of a previous analysis (see[Alb+07c]) is given as a black line in the plots to assume, whether the optimizedcuts fit with this referenced distribution. Another reference from the analysis ofthe Crab Nebula by HESS in [Aha+06] is given as a yellow dotted line.It can be seen that the assumed spectral shape, the data points and the givenspectrum match very well for the energy spectrum and the SED of the Crab

40


Nebula. Therefore, it can be concluded, that the chosen parameters are optimizedfor the analysis at the given time of November 2014 till April 2016. The sameparameters are applied to the spectral analysis of 3C 279 in the following.

3C 279

The estimated lightcurve for an energy above 150GeV compared to the given fluxof the Crab Nebula and only for 3C 279 are presented in Figure 4.9. Compared tothe lightcurve of the Crab Nebula reference with a flux of 3.2327 ⋅10-10 [Alb+07c],the LC of 3C279 shows mainly upper limits. Therefore the flux of 3C279 ispresented separately in the bottom figure. 3C 279 is detected by the MAGICtelescopes, because of a higher flux compared to the normal state. It can be seen,that two days - June 16th, 2015 (MDJ=57189) and April 12th, 2016 (MDJ=57726)- show a higher flux than the remaining days. To get an idea of the magnitudeof the flux, these two days and the total flux are compared to the Crab Nebulaflux by the unit of CU. The crab units (CU) describe the fraction of the sourceflux to the Crab Nebula flux. The flux of the total analysis is calculated by

Table 4.7: The flux of 3C 279 compared to the Crab Nebula flux. The used unitCU is the percentage of the Crab Nebula flux, which is f=3.2298 ⋅ 10-10 cm-2s-1 forthe energy range between 150GeV and 50TeV [Alb+07c]. The percentage and theestimated flux for the two days with the highest flux are given as well as the totalflux of all days.

Day Flux [cm-2s-1]⋅10-11 Flux[CU]20150616 2.2667 ± 1.0410 0.070220160407 2.6717 ± 1.1954 0.0827total 1.31336 ± 0.349 0.0407

a constant fit of the data points, whereas the flux of the days with the higherflux is read from the data. Considered over the whole period, 3C 279 reachesa flux of 0.0407CU, whereas the highest flux at the 12th of April 2016 with aflux of 0.0827CU corresponds to a level twice the average flux. The smallestflux, besides the days of upper limits only, at the 18th June 2015 shows a flux of0.0140CU, therefore the flux of 3C 279 between this value and 0.0826CU.

The energy spectrum and the spectral energy distribution of 3C 279 are presentedin Figure 4.10 and Figure 4.11. A basis for the spectral analysis of 3C 279 isprovided by the assumed spectral shape and the redshift given above. In both

41


Figure 4.9: The estimated lightcurve for energies above 150GeV of 3C 279 com-pared to the Crab Nebula reference flux (top) and only the flux of 3C 279 (bottom)in the given time. The black line in the upper plot shows the flux of the CrabNebula in [Alb+07c] and the blue dots and arrows show the flux from 3C279 foreach day. The plot in the bottom presents the flux of 3C 279 (blue) for each day in2015 and 2016.

plots the calculated data points, the assumed spectral shape and the givenreferences are shown. The deabsorbed spectrum shows a possible EBL correctionof the spectrum during the execution of Flute. Since the EBL correction is made

42


Figure 4.10: The estimated energy spectrum of 3C 279 for the given data in 2015and 2016. The spectral energy of 3C 279 (blue) and the assumed spectral shape(red) are presented for each energy bin. The black line is the reference of the CrabNebula analysis with MAGIC and the yellow dotted line is the reference of theanalysis with HESS as outlined above. The assumed spectral shape of 3C 279corresponds to the given spectrum in Equation 4.2

during the unfolding, the deabsorbed spectrum is not relevant here.Since the calculated flux of 3C279 is very weak, only 4 real data points areobtained for the spectrum of 3C 279. The given fit of the assumed spectral shapethrough the data-points is in a good agreement with three data-points, but thelowest one point spreads from the function. Sine the spectral index of this fit isfixed by the given assumed spectrum, the probability is not as well as with nonfixed parameters.

At this point of time, no real conclusion about the energy spectrum can be drawn,since the spectrum is very steep and thus the smearing by the energy resolutionaffects the energy spectrum even more. Therefore the estimated energy spectrumof 3C 279 needs to be unfolded.

Unfolding of the energy spectrumThe unfolding of the energy spectrum of 3C 279 produced previously with fluteis made with the MARS macro CombUnfold. Due to the fact, that the energyspectrum of the Crab Nebula is totally sufficient as a sanity check of data in thegiven time range, no unfolding of this spectrum is accomplished.

43


Figure 4.11: The spectral energy distribution of 3C 279 of the given data in 2015and 2016. The spectral energy of 3C 279 (blue) and the assumed spectral shape(red)

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