Studies of the Influence of Moonlight on Observations with the MAGIC Telescope

Daniel Britzger

Munchen¨ 2009

Studies of the Influence of Moonlight on Observations with the MAGIC Telescope

Daniel Britzger

Diplomarbeit an der Fakult¨at fur¨ Physik der Ludwig–Maximilians–Universit¨at Munchen¨

vorgelegt von Daniel Britzger aus Marktoberdorf

Munchen,¨ den 30. Juni 2009 Erstgutachter: Prof. Dr. C. Kiesling Zweitgutachter: Prof. Dr. D. Schaile Zusammenfassung

Die hier vorgestellte Diplomarbeit behandelt ein Thema auf dem Gebiet der ergebunde- nen Gammastrahlenastronomie mit grossen Cherenkovteleskopen. Es geht dabei speziell um die Erweiterung der Messzeit durch Beobachtungen bei schwachem Mondlicht. Die ergebundene Gammastrahlenastronomie ist ein sehr erfolgreiches Teilgebiet der Hoch- energie Astroteilchenphysik, einem neuen und rasch expandierenden Bereich der Grund- lagenforschung. Nahzeu alle Resultate in der ergebundenen Gammastrahlen Astronomie wurden mit Cherenkovteleskopen erzielt. Mit diesen Teleskopen beobachtet man bei klaren, dunklen N¨achten das Cherenkovlicht das von Luftschauern in der Atmosph¨are abgestrahlt wird. Diese Luftschauer werden durch kosmische Teilchen, u.a. hochenerge- tische, kosmische Gammaphotonen beim Auftreffen auf die Atmosph¨are erzeugt. Eines der erfolgreichsten Teleskope auf diesem Gebiet ist das MAGIC Teleskop. Das MAGIC-I Teleskop auf der Kanareninsel La Palma hat eine parabolische Spiegelfl¨ache von 234 m2 und ist zur Zeit das weltgr¨oßte Teleskop mit der niedrigsten Energieschwelle. Die Ana- lyse von sehr schwachen und nur einige Nanosekunden (∼ 3 ns) dauernden Lichtblitzen, verursacht durch die Cherenkovstrahlung von Sekund¨arteilchen in einem ausgedehntem Luftschauer, erlaubt die Rekonstruktion der elektromagnetischen, bzw. hadronischen Kaskaden. So ist eine Klassifikation des Prim¨arteilchens, seiner Energie sowie der An- kunftsrichtung m¨oglich. Im Falle von Gammaquanten erlaubt dies auch die Zuordnung zu stellaren Objekten im Weltall. Die angewandte abbildende Luftschauer Cherenkovme- thode (englisch: imaging atmospheric Cherenkov technique) erm¨oglicht die Beobachtung von Gammastrahlung im Energiebereich von 30 GeV bis etwa 10 TeV und Flussen¨ von bis zu 10−12 pro cm2 und sec, da eine Detektionsfl¨ache von bis zu einigen 104 m2 zur Verfugung¨ steht. Dennoch wird selbst bei starken Quellen, wie etwa dem Krebsnebel, lediglich eine Gammarate von etwa 0.1 Hz und ein resultierender integraler Fluss von −10 −2 −1 FE>200GeV = (1.96 ± 0.05stat) × 10 cm s gemessen [1].

Im Gegensatz zu anderen Cherenkovteleskopen, wie dem High Energy Stereoscopic Sys- tem (H.E.S.S.) oder dem Very Energetic Radiation Imaging Telecope Array System (VE- RITAS), wurde das MAGIC-I Teleskop auch fur¨ Gammastrahlenbeobachtungen w¨ahrend Mondscheins geplant. Dies erm¨oglicht es, die bei anderen Teleskopen ubliche¨ Beobach- tungszeit von 1600 Stunden pro Jahr um etwa 30% auf uber¨ 2150 Stunden pro Jahr zu erh¨ohen. Das Mondstreulicht bildet einen erheblichen Untergrund bei der Aufzeichnung des Cherenkovlichts und fuhrt¨ damit zu einer m¨oglichen Verf¨alschung der Ergebnisse. Gegenstand meiner Arbeit ist die Untersuchung des Einflusses des Mondlichts auf die Messungen und die Verbesserung der Analysemethoden.

Um ein tieferes Verst¨andnis uber¨ den Einfluss des Mondlichts zu bekommen, wurde ein Modell zur Bestimmung der Lichtintensit¨at des Streulichts entwickelt. Dieses Mo- vi 0. Zusammenfassung dell wurde speziell an die Gegebenheiten von MAGIC-I angepasst. Insbesondere ist es das erste Modell dieser Art, das fur¨ kleine Mondphasen und fur¨ geringe Mondh¨ohen uber¨ dem Horizont (ab 1◦)Gultigkeit¨ hat. Es kann beispielsweise fur¨ automatisierte Monte Carlo Simulationen oder fur¨ einen otpimierten Beobachtungsplan verwendet wer- den. Neben den Modellentwicklungen wurden auch detaillierte Messungen bei Mondlicht durchgefuhrt,¨ um die Annahmen zu verifizieren. Anhand von Gammastrahlenbeobachtungen des Krebsnebels unter Mondlicht, welche von Februar 2007 bis Februar 2008 durchgefuhrt¨ wurden, werden die Auswirkungen eines erh¨ohten Nachthimmeluntergrunds auf einzelne Subsysteme der Datennahme un- tersucht und er¨ortert. Die bei der Standarddatenanalyse auftretenden aber bisher ver- nachl¨assigten Beitr¨age des Mondlichts fuhren¨ zu einer niedrigeren Gammarate und einer geringeren Sensitivit¨at. Dazu wurde eine Variante der Bildreinigungsmethode (englisch: image cleaning method) untersucht, die eine korrekte Datanalyse bei einem Mondlicht- hintergrund, der bis zu einem Faktor 10 - 15 uber¨ dem Nachthimmel Lichtuntgergrund in dunklen Himmelsregionen liegt, erlaubt. Im Bezug auf statistische Bildparameterver- teilungen wurden die ermittelten Ergebnisse mit Monte Carlo Simulationen best¨atigt.

Ich konnte zeigen, dass die Standardanalyse bei einem Mondstreulicht von bis zu einem 2.5-fachen Wert des Nachthimmeluntergrunds benutzt werden kann. Wird die ausge- arbeitete Empfehlung von ge¨anderten Bildreinigungsparametern befolgt oder werden angepasste Monte Carlo Simulationen verwendet, so kann mindestens bis zu einem 6.0- fachem Nachthimmeluntergrund beobachtet werden, ohne dass sich die Sensititv¨at des Instruments verringert. Dem entwickeltem Model zufolge entspricht dieser Hintergrund einem 70%-ig beleuchtetem Mond bei einem ausreichendem Winkelabstand zur Gamma- strahlenquelle von uber¨ 50◦. Die dabei gewonnene zus¨atzliche Beobachtungszeit fuhrt¨ zu einem wesentlich gesteigerten wissenschaftlichen Nutzen des MAGIC Teleskops, um bei- spielsweise neue Gammastrahlenquellen zu entdecken oder bisher unverstandene Gam- mastrahlenausbruche¨ zu erforschen. Contents

Zusammenfassung v

1 Introduction 1

2 Astroparticle Physics 5 2.1 History of γ-ray astroparticle physics ...... 5 2.2 Cosmic rays ...... 7 2.3 Very high energy gamma rays ...... 9 2.3.1 The electromagnetic spectrum ...... 9 2.3.2 Production mechanisms of VHE photons ...... 10 2.3.3 Absorption mechanisms and propagation of VHE photons . . . . . 12 2.4 Sources of very high energy γ-rays ...... 13 2.4.1 Galactic sources ...... 14 2.4.2 Extragalactic sources ...... 15

3 The MAGIC Telescope and the Imaging Atmospheric Cherenkov Technique 19 3.1 The Imaging Atmospheric Cherenkov Technique ...... 19 3.1.1 Extended air showers ...... 19 3.1.2 Cherenkov light emission ...... 22 3.1.3 The imaging atmospheric Cherenkov technique ...... 23 3.2 The MAGIC-I Telescope ...... 26 3.2.1 The structure and mirrors ...... 27 3.2.2 The MAGIC-I PMT-camera ...... 27 3.2.3 The trigger ...... 28 3.2.4 The data acquisition system ...... 29

4 The MAGIC Standard Analysis 31 4.1 Data selection ...... 31 4.2 Event reconstruction and shower parametrization ...... 31 4.2.1 Image cleaning ...... 32 4.2.2 Shower image parametrization ...... 32 4.3 Event classification (Gamma/hadron separation) ...... 33 4.4 Gamma-ray excess determination ...... 34 4.5 Energy estimation ...... 37 4.6 Spectrum calculation ...... 37 4.7 Significance of an excess being a signal ...... 38 4.8 Software framework ...... 38

5 Observations with the MAGIC Telescope during Moonlight 41 5.1 IACT observations under moonlight conditions ...... 41 viii Contents

5.1.1 Early Whipple observations ...... 41 5.1.2 Observations with the HEGRA CT1 ...... 41 5.1.3 H.E.S.S. Telescope array ...... 42 5.1.4 VERITAS ...... 43 5.1.5 MAGIC-I ...... 43 5.2 Observation time under moonshine ...... 44 5.2.1 Orbital parameters of the moon ...... 45 5.2.2 Xephem ...... 46 5.2.3 Observation time under moonlight conditions ...... 46 5.3 Considerations for observations with MAGIC during moonshine ...... 50 5.3.1 The photomultiplier tubes ...... 51 5.3.2 L0-Trigger ...... 51 5.3.3 L1-Trigger ...... 52 5.3.4 Pedestals ...... 53 5.3.5 Further motivation for studying moonlight observations ...... 55

6 A Model for Estimating the Brightness of the scattered Moonlight 57 6.1 Light of the night sky ...... 57 6.2 The anode current readout and data selection ...... 58 6.3 Theoretical assumptions ...... 59 6.4 The brightness of the moon ...... 63 6.5 Atmospheric attenuation of the moonlight ...... 66 6.6 Rayleigh and Mie scattering ...... 69 6.7 Result ...... 72 6.8 Discussion of the moon model ...... 74

7 Performance of the MAGIC Telescope during Moonlight Observations 77 7.1 Data selection and analysis approach ...... 77 7.1.1 Data selection ...... 77 7.1.2 Analysis approach ...... 78 7.2 Number of Islands ...... 79 7.3 Extraction of the γ-ray signal ...... 81 7.4 Sensitivity of MAGIC-I under moonlight conditions ...... 84 7.4.1 Significance of one hour of Crab Nebula observation under moon- light condition ...... 84 7.4.2 The sensitivity of MAGIC-I during moonlight observations . . . . 84 7.4.3 Crab observations at large zenith angles ...... 85 7.5 Monte Carlo simulations of γ-rays under moonlight conditions ...... 87 7.6 Effective collection area ...... 87 7.7 Study of the energy threshold during moonlight observations ...... 88 7.8 The Crab spectrum under moonlight conditions ...... 90

8 Conclusions and Outlook 93 8.1 Conclusions ...... 93 8.2 Outlook ...... 94

A Appendix 97 Inhaltsverzeichnis ix

A.1 Observations at small separation angles ...... 97 A.2 Additional figures and plots ...... 100

Acknowledgment 113 x Inhaltsverzeichnis 1 Introduction

This thesis deals with a topic in the research area of ground-based γ-ray astronomy with large Cherenkov telescopes. It elaborates especially the extension of the observation time under moderate moonlight. The ground-based γ-ray astronomy is a very successful branch in high energy astropar- ticle physics, a new and rapidly expanding area of fundamental research. Most of the results of ground-based γ-ray astronomy were achieved with Cherenkov telescopes. With such telescopes one observes during clear dark nights the Cherenkov light emitted by ex- tended airshowers in the atmosphere. These airshowers are induced by cosmic particles, among others also by γ-rays, impinging on the atmosphere. One of the most success- ful telescopes in this area is the MAGIC Telescope (Major Atmospheric Gamma-ray Imaging Cherenkov Telescope). The MAGIC-I telescope located on the Canary Island of La Palma at 2200 m a.s.l. has a parabolic mirror dish of 234 m2 and is currently the largest telescope worldwide with the lowest energy threshold. The analysis of the very faint and only few nanosecond (∼ 3 ns) light flashes, induced by Cherenkov radi- ation, permits the reconstruction of the electromagnetic or hadronic cascades. Hence, the classification of the primary particle can be performed, as well as the primary par- ticles energy and its arrival direction can be determined and for the case of a γ-ray also the allocation to stellar objects in outer space is possible. The applied imaging atmospheric Cherenkov technique allows the possibility for observations of γ-rays in the energy region from 30 GeV up to 10 TeV and of fluxes of 10−12 per cm2 and sec, since a detection area up to some 104 m2 is available. However, even for strong sources like the Crab Nebula, only a gamma-rate around 0.1 Hz and a resulting integral flux of −10 −2 −1 FE>200GeV = (1.96 ± 0.05stat) × 10 cm s is measured [1].

Contrary to other Cherenkov telescopes, like the High Energy Stereoscopic System (H.E.S.S.) or the Very Energetic Radiation Imaging Telescope Array System (VERI- TAS), the MAGIC-I telescope was already designed to perform γ-ray observations dur- ing moonlight. This allows to extend the typical observation time of 1600 hours per year of around 30% up to 2150 hours per year. The scattered moonlight builds a sub- stantial background during the record of Cherenkov light flashes and thus might lead to a possible falsification of the results. The subject of my thesis is the investigation of the influence of moonlight on observations and the improvement of the analysis methods.

In order to obtain a deeper understanding of the influence of moonlight, a model to estimate the light intensity of scattered moonlight was developed. The model was es- pecially adapted to the conditions of MAGIC-I. It is in particular the first model of this kind, which holds for small moon phases and low moon altitudes above the horizon (above 1◦). It can be used for automated Monte Carlo simulations or for an optimized 2 1. Introduction source scheduling. Besides the model development, also detailed measurements during moonlight were performed to verify the assumptions.

On the basis of γ-ray observations of the Crab Nebula under moonlight conditions, which were performed from February 2007 to February 2008, the effect of an increased night sky background on single subsystems is investigated and discussed. The so far neglected effects, appearing during the standard analysis, are resulting in a decreased gamma- rate and sensitivity. I have investigated an alternative image cleaning method, which allows a correct analysis under moonlight background conditions, up to a factor 10 - 15 above the night-sky background level of a dark sky region. On the level of statistical image parameter distributions the achieved results were confirmed with Monte Carlo simulations.

I was able to show, that the standard analysis can be used under moonlight observation up to a level of 2.5 times the night sky background of the Crab Nebula region. If the elaborated recommendation of changed image cleaning parameters is followed, or dedi- cated Monte Carlo simulations are used, it can be observed up to a 6.0 times increased night sky background without loosing sensitivity. According to the developed model, this background level corresponds to a 70% illuminated moon at a minimum angular distance to the gamma-ray source of above 50◦.

The following overview of this thesis provides a guideline for the reader

Chapter 2: This chapter gives a short introduction into the field of astroparticle physics with em- phasis on very high energy (VHE), ground-based gamma ray (γ-ray) astronomy. Some recent research goals are pointed out. In the second part of this chapter a detailed in- troduction to VHE γ-ray physics astronomy is given. The production for VHE γ-rays, as well as the absorption mechanisms during their long journey through the universe are discussed. The chapter closes with an overview of γ-ray source types that can be studied by MAGIC.

Chapter 3: The Imaging Atmospheric Cherenkov Telescope (IACT) technique is explained: the evo- lution of airshowers, the physics of Cherenkov radiation and the working principle of IACTs. Then, the technology and construction of the MAGIC-I telescope are explained in more detail, already with an emphasis on key parts for observations under moonlight.

Chapter 4: This chapter introduces the analysis method for data recorded with the MAGIC tele- scope. The description starts from the recorded FADC signal, elaborates in particular the γ/hadron-separation issue and the energy estimation and extends up to the calcula- tion of the γ-ray energy spectra and fluxes. 3

Chapter 5: The observation strategies of several leading Cherenkov telescopes are summarized. It is explained why MAGIC is suitable for observations under moonlight conditions and what necessary hardware requirements had to be fulfilled. The orbital parameters of the moon are described and new calculations for the estimation of extended observation times are performed. Furthermore, a detailed discussion of all relevant components of MAGIC which are affected by moonlight is performed.

Chapter 6: A model for estimating the background light contribution from the moon is derived. The assumptions are shown to be reasonable and the development of the model is explained. It is the first model of this type being also relevant for very low moon altitudes and low moon phases.

Chapter 7: This chapter deals with the performance of the MAGIC telescope when observing in the presence of moonshine. The influence of moonlight on the image cleaning and parametrization level is depicted. The impact on the γ/hadron separation is investi- gated, as well as that on the source allocation. New methods to improve the analysis and, as well, the limitations caused by too high moon brightness are presented. Monte Carlo simulations were performed to confirm the assumptions. Those were later also used for recovering the differential energy spectra for data recorded in the presence of moonlight.

Chapter 8: The most important results from moonlight observations are summarized and a recom- mendation for analyzing moonlight data is given.

Appendix: Additional data from observations at very small angular distances to the moon are added to the moon model and are discussed in the appendix. Furthermore, it holds several plots, which are not necessary in the previous chapters for a full understanding, but might serve the interested reader for a more comprehensive insight. 4 1. Introduction 2 Astroparticle Physics

High energy astroparticle physics, is a rapidly expanding field of fundamental research. One of the most successful sections of this field is ground based very high energy (VHE) γ-ray astronomy. The starting point of high energy astroparticle physics can be set to 1911/12, when during balloon flights Victor Hess detected traces of cosmic rays [2]. Since then, cosmic particles, their composition and possible sources are under investigation. More recently, direct measurements could be performed by means of satellite borne detectors and many new questions about the origin of cosmic (γ-)ray particles appeared. Because γ-rays fly straight through the universe they act as cosmic “messengers” of high energy processes in stellar environments.

2.1 History of γ-ray astroparticle physics

In 1911/12 Victor Hess performed pioneering balloon flights to investigate the until then mysterious ionizing radiation measured at ground. It was speculated that this ionizing radiation was emerging from ground and it was assumed that during balloon flights the radiation should disappear at high altitudes. By using an electroscope, Hess measured the ionizing radiation as a function of height up to 5.3 km. The electroscope showed that at 5 km height the level of radiation was trice that at sea level, although at first it decreases within the first 1 km. He finally concluded that there is ionizing radiation coming from outer space. R. A. Millikan confirmed his discoveries in 1925, and named this radiation “cosmic rays”. Victor Hess was awarded the Nobel Prize in 1936 for his pioneering work.

In 1948 P. M. S. Blackett pointed out, that approximately 1/10, 000 of night-sky light should actually be contributed by cosmic rays [3]. This light could be Cherenkov light produced in the corresponding air showers, although Cherenkov light had been detected in liquids and solids. Already in 1953, Galbraith and Jelley postulated that Cherenkov light might be detectable as a light pulse from cosmic-ray induced air showers [4]. They set up a simple optical detector in a garbage can at Harwell, UK, and detected Cherenkov light pulses from air showers. In 1960 Chudakov and Zatsepin set up the Crimea experiment. This was actually the first dedicated gamma-ray telescope. Already, they recorded an increased signal from the Crab Nebula region, but it was not significant. The first dedicated gamma ray experiment then was set up by T. Weekes at Whipple Observatory in 1967/68. The 10m Whipple telescope is still under operation today. With its initial camera of only 37 pixels, it was not yet able to detect gamma ray 6 2. Astroparticle Physics

Figure 2.1: Photograph of Victor Hess starting to one of his pioneering balloon flights (1911). He could prove, using an electrometer, that from 1 km above sea level, the ionizing radiation increases. He correctly concluded, that the increase in ionization is caused by some type of radiation coming from outer space (later called cosmic rays).

Figure 2.2: The first detection of Cherenkov light from extended air showers was performed by Galbraith and Jelley in 1952 with the detector shown in the photograph. sources until 1977, and there was only a phantom detection of binary sources until 1984. Nevertheless, the fundamental ideas for the Imaging Atmospheric Cherenkov (IAC) technique were developed during this time. The key to the success was the ability to enrich γ-ray induced showers against the many orders more frequent hadronic showers, i.e. the gamma/hadron separation, inspired by A. M. Hillas in 1985 [5]. Finally 1989, Whipple detected TeV gamma radiation from the Crab Nebula [6] and thus opened the “window” of VHE gamma ray astronomy using the imaging atmospheric Cherenkov technique. 2.2 Cosmic rays 7

During the next decade, a number of second generation telescopes and telescope arrays were set up like HEGRA, Cangaroo, CAT or TA. Those experiments improved the techniques and detected some more VHE γ-ray sources. In the first decade of 2000, the third generation of telescopes were built, like MAGIC, VERITAS, H.E.S.S. and CANGAROO-III. Today, 27 extragalactic sources and 54 galactic sources, emitting VHE γ-rays, have been discovered [7]. Crucial discoveries for γ-ray astronomy were also contributed by satellite experiments, in particular the Compton Gamma Ray Observatory (CGRO) with four independent instruments. This satellite was operational from 1991 to 2000. The Energetic Gamma Ray Experiment Telescope (EGRET) instrument detected 271 sources emitting γ-rays between 100 MeV and about 1 GeV energy (Recently an article revised this number to only 188 [8]). The Burst and Transient Source Experiment (BATSE) recorded more than 2000 gamma ray bursts, uniformly distributed over the complete sky. Furthermore, it could be shown, that blazars are one of the main sources of high energetic gamma rays. The follow up satellite FERMI (formerly called GLAST) was launched in 2008 and studies γ-ray sources in the energy range from 30 MeV to hundreds of GeV. The now achieved overlap with the IAC technique will close the long term observational gap in the electromagnetic spectrum. The gamma ray burst monitor instrument, installed also on FERMI, has the ability to detect in real time GRBs and thus can be used to trigger the MAGIC GRB follow-up observations.

2.2 Cosmic rays

The general term for all types of energetic, outer space particles impinging on earth’s atmosphere is cosmic rays. Although the term “rays” herein is basically a misnomer, it is an established definition for all cosmic particles. The energy of cosmic rays is usu- ally described in units of electron Volts (eV). A handy classification of energy regions is given in [9], mostly motivated by flux sensitivities of different space- and ground-based instruments.

designation abbreviation energy range

low energy region LE Eγ ≤ 30MeV high energy region HE 30MeV ≤ Eγ ≤ 30GeV very high energy VHE 30GeV ≤ Eγ ≤ 30T eV ultra high energy UHE 30T eV ≤ Eγ ≤ 30P eV extremely (high) energy EHE, EE 30P eV ≤ Eγ

The all-particle spectrum of charged cosmic rays is shown in 2.3. The flux from 109eV up to 1021eV is given in units of numbers of arriving particles per unit area, per solid angle, per unit time ((m2 s sr GeV )−1). The spectrum is rather smooth (featureless) and is rapidly dropping with energy, see figure 2.3. Three regions can be distinguished: • The first region extends from about 10 MeV up to the so-called knee at around 1015 eV. A power law with a spectral index of E−2.7 is a good description for the energy spectrum in this range. 8 2. Astroparticle Physics

Figure 2.3: All particle cosmic ray energy spectrum. The “knee” and the “ankle” indicate a change in the spectral slope and thus different physical origins.

• Above the knee, 1015, the spectrum falls with a spectral index of E−3.0 up to the so-called ankle at around 5×1018 eV.

• Above around 5×1018 eV, the spectrum changes again. No particles with an energy > 3×1020 eV have been observed up to now. It is generally assumed that cosmic particles above the ankle are of extragalactic origin.

The composition of the charged cosmic rays is comparable with the chemical composition of the solar system, with only remarkable differences for lithium, beryllium and boron (Z = 3 − 5). The dominant cosmic particle is the proton, forming ≈ 85% of the overall composition, followed by α particles with ≈ 12%. Heavier nuclei account for only 3% of the cosmic ray flux while electrons and γ-rays add up to less than 1%. The flux of cosmic neutrinos is unknown but dominated by solar neutrinos.

Charged nuclei are one of the main research interest for astroparticle physicists. For relatively low energies (below a few 1012 eV), direct measurements of the composition can be performed with balloon or satellite experiments. Current detectors allow one to determine the nucleon number. The relative abundance of lithium, beryllium and boron 2.3 Very high energy gamma rays 9 can be explained with secondary processes, when primary heavier nuclei interact with interstellar matter and decay into lighter nuclei. It is assumed that galactic cosmic rays have to pass a column density of ≈ 6g/cm2 in the intergalactic media. Low energetic primary cosmic rays (< 1GeV/nucleon) are deflected by earth and solar magnetic field and therefore cannot be measured on earth. Direct measurements of cosmic rays above several hundreds GeV run out of statistics. Therefore, the indirect detection of primary and secondary particles by means of the Cherenkov technique or the measurement of extensive air showers via air fluorescence or by detecting showers from ground by scintillator arrays, is becoming crucial.

2.3 Very high energy gamma rays

Within the cosmic ray composition, gamma rays are somehow exceptional, because they have no charge and fly with the speed of light, i.e. the time structure of a cosmic process is conserved even after many billions years of flight time through the universe. They are not deflected by magnetic fields and are pointing back to the point of their creation. VHE γ-rays are the so-called messengers of ultra-relativistic processes in our universe. Because of their very high energy, thermal creation processes are excluded. VHE γ- rays can only be produced in non-thermal processes of at least an energy exceeding the observed γ-ray energy. From the astronomers’ point of view, they are the last “open window” to observe the universe. At the very highest energies of γ-rays a non-negligible cross-section with background photons in the IR-region and microwave region (of the 2.7◦ background radiation) has to be considered, and thus, no γ-rays above several hundred TeV are expected from outside of our galaxy. Therefore γ-ray astronomy for high redshift sources is only possible below 100 GeV to a few TeV (z-dependent). In principle, also cosmic neutrinos can act as messenger particles but it is extremely difficult to detect them, because of the weak interaction process requiring enormous detectors (Ice Cube, KM3NET, ...). Up to now only high energy neutrinos from the sun and SN 1987A have been observed. Due to the weak interaction, neutrinos would be basically not be absorbed during their long journey through the universe. It should therefore in principle be possible to observe cosmic processes very shortly after the Big Bang. Because of the neutrino detection difficulties γ-ray astronomy is the only tool to observe distant high energy processes in our cosmos. An important difference between γ-rays and neutrinos is also that neutrinos are only produced in hadronic processes while γ-rays can originate both from leptonic and hadronic processes (see later for more details).

2.3.1 The electromagnetic spectrum

Today, astronomical observations extend over many magnitudes in photon energy, start- ing from radio frequencies (∼10−6 eV), over infrared, visible, UV, X- and γ-rays up to VHE γ-rays of at least to ∼1014 eV. Ground-based experiments are strongly affected by the atmosphere: while in the IR- and UV-wavelength part of the spectrum direct 10 2. Astroparticle Physics observations are impossible because of absorptions lines of air molecules, photons above X-ray energies are absorbed by particle interactions (see fig. 2.4). In the energy range from GeV to TeV, only indirect measurements are possible either by high flying balloon borne instruments or on ground using the imaging atmospheric Cherenkov (IAC) tech- nique. The IAC technique is described in detail in chapter 3. The radiation emitted by stars follows Planck’s radiation formula with temperatures

Figure 2.4: Atmospheric windows for electromagnetic radiation to observe the universe [10]. In green and blue the photon energy and the corresponding wavelength is written. The continuous blue line indicates the height above sea level, where a detector can detect half of the incident radiation. In the VHE regime, this is schematically for the first interaction of a photon with earth atmosphere. from 3000K to 50000K, i.e. to photon fluxes peaking in the visible to the ultra-violet, re- spectively. The highest thermally generated photons in universe reach up X-ray energies of a few keV. Higher energetic photons, usually called γ-rays, are created in non-thermal processes, especially in π0-decays and through inverse Compton scattering (IC) pro- cesses. Of certain interest is the modeling of complete spectra from a source. Hereby it is reasonable to investigate possible connections of different energy bands, i.e. optical with γ/X-rays [11] or radio with γ/X-rays. Especially very precise optical and radio flux changes may allow triggering γ/X-ray observations of cosmological events like AGN flares, gamma-ray bursts (GRBs) or periodicity studies in pulsars and binary systems.

2.3.2 Production mechanisms of VHE photons

The production of very high energy γ-quanta can not be explained with thermal pro- cesses. Already in the case of 1 MeV γ-rays (five orders of magnitude below the MAGIC 2.3 Very high energy gamma rays 11 energy threshold) one would need temperatures of at least 107 K. Therefore, only par- ticle physics reactions can be the source of VHE γ-rays. The most relevant elementary processes are highlighted in [10].

Hadronic production: Charged protons gain energy in acceleration processes like shock wave acceleration (Fermi acceleration, first or second order). If such relativistic protons interact with cosmic particles or gas in stellar environments (or rarely interstel- lar dust), short-lived hadrons are created. Most secondary particles are mesons with about a third being π0s, which decay nearly instantaneously (τ ≈ 10-16 sec) into nearly 99% into 2 γ. The π0-mesons decay like:

π0 → γ + γ (branching ratio 98.8 %) and π0 → e+ + e− + γ (branching ratio 1 %). The π±-mesons have to conserve charge and therefore are decaying like:

± ± π → µ + νµ, while the muons decay again into an electron and two neutrinos.

Inverse Compton scattering: Relativistic electrons (or positrons) scatter via the Compton mechanism off low energy photons and transfer part of their energy to these photons. Depending on the electron-photon energy (EeEγ), one distinguishes three cases with different cross-sections [12].

2 4 8 2 • EeEγ  mec : σT = 3 πre (Thomson cross-section) 2 4 • EeEγ ≈ mec : σKN (Exact Klein-Nishina cross-section)

2 • E E  m2c4 : σ = πr2 m2c (ln 2 + 1 ) (The Klein-Nishina approximation) e γ e KN e Eγ 2 It can be shown, that the maximum energy gain is described by

4 Emax ≈ 4γ Eγ, for Lorentz-factors γ ≈ 102 − 103. Therefore, seed photons are upscattered into the GeV-TeV domain. Those cross-sections σ are the mechanisms work in the SSC models. For the Klein-Nishina regime, the resulting spectrum has a sharp cut-off, which is de- termined by the participating electrons.

Bremsstrahlung: When charged particles like electrons or protons are deflected in electric fields they lose energy while radiating bremsstrahlung. The resulting photon spectrum has a power law form with the same spectral index as the primary particle. Bremsstrahlung of UHE cosmic rays can reach TeV energies, though photons typically serve as seed photons for IC scattering. 12 2. Astroparticle Physics

Besides, bremsstrahlung is the most important photon production phenomenon in the development of air showers in the atmosphere.

Synchrotron radiation: Relativistic charged particles emit synchrotron radiation in the presence of magnetic fields. Cosmic magnetic fields are often connected to regions with acceleration processes. Synchrotron radiation of accelerated electrons is one of the most important processes for non-thermal radiation in the universe. Synchrotron radia- tion is believed to be the usual process for the generation of seed photons for the inverse Compton scattering process. However, UHE cosmic rays can also emit synchrotron ra- diation directly in the VHE range.

Non-standard processes: There are some more “exotic” processes discussed. For example, dark matter annihilation from SUSY particles could produce γ-rays, as well as exotic top-down scenarios. So far, none of those have been observed.

2.3.3 Absorption mechanisms and propagation of VHE photons

The propagation and possible absorption losses of VHE photons in the universe are crucial issues in VHE γ-ray astronomy. The universe is not empty but filled with a diversity of low energy photons, such as from the 2.7 K microwave background, radio waves, IR photons or visible starlight. All these photons can interact with the VHE γ-ray on their long journey through the universe. The interaction of photons is well understood theoretically. Of course photons can be absorbed by interstellar dust, but this is very unlikely except in galaxies. However, in the VHE regime there is a non- negligible QED cross-section of photons with low energy photons resulting in e+e− pair creation provided the cm energy is above 1 MeV. VHE photons interact with infrared photons from the extragalactic background light like

+ − γVHE + γEBL → e + e if 2 2 EγVHE + EγEBL > 2(mec ) . (2.1) When traveling cosmological distances, the attenuation of VHE photons can affect and deform observed spectra. Already at energies above 300 GeV, γ-rays from sources with z > 0.2 suffer absorption. This implies that most of the up to now extragalactic sources show spectra with cutoffs between 10 GeV and 300 GeV. This absorption practically limits the observable distance of extragalactic objects. For energies above 30 TeV the cross-section with cosmic microwave background photons (CMB; λ > 300µm) is no longer negligible and leads to very strong absorptions. For the blazar Mrk 501, a cutoff in the spectrum is observed at E ≈ 10 TeV [13] as measured by HEGRA [14] and Whipple. On the other hand, cutoff studies of sources at different z allows one to study the evolution of EBL. Two main contributions to the EBL spectrum are relic emission of galaxies/star-forming systems and re-emitted light from dust. The wavelength part of 2.4 Sources of very high energy γ-rays 13

-1 -9 10 TeV -1 s

-2 -10 10 cm

-11

dN/dE 10

-12 10

-13 10

-14 10

-15 10 -1 2 10 1 10 10 E TeV

Figure 2.5: The energy spectrum of Mrk 501 as measured by HEGRA IACT array (open circles) and by the Whipple group (closed circles) (from [13]). The “de-absorbed” HEGRA data are shown together with a power law fit (solid line). the EBL which is sensitive on VHE γ-rays from sources between a z of 0.05 to 1 is between 0.1 and 2 m wavelength. Therefore EBL models and the γ-ray horizon can be tested using blazar emission as “testbeams”.

2.4 Sources of very high energy γ-rays

The field of VHE γ-ray astronomy is still a quite young field. The detection of a new source is a matter of long observation, sometimes exceeding more than 100 hours. Also many (extragalactic) sources show flux variability and can only be detected with some luck during an outburst. The sensitivity of IACTs is usually defined as a flux level, which can be significantly detected after 50h of observation with a significance of 5σ respectively more than 10 excess events in case of satellite observation. A sky map of all detected sources for Eγ > 100GeV is shown in fig. 2.6 (status: spring 2009). The grey shaded areas show the accessible zenith angle ranges for the MAGIC 14 2. Astroparticle Physics telescope in La Palma. Observations with IAC instruments at large zenith angles are affected by different air shower development and Cherenkov light absorption in the at- mosphere, which increases the telescope trigger threshold (≈ (cos θ)−2.7, θ being the zenith angle). Basically, there are two classes of sources: galactic and extragalactic ones. In fig. 2.6 a

VHE γ-ray sources o VHE γ-ray Sky Map +90 Blazar (HBL) 1218+304 Blazar (LBL) Mkn 421 (Eγ>100 GeV) M87 Flat Spectrum Radio Quasar Radio Galaxy 1011+496 1426+428 W Comae Pulsar Wind Nebula 3C 279 Mkn 180 Supernova Remnant Binary System 0806+524 1553+113 Mkn 501 Open Cluster S5 0716+71 1101-232 0710+591 Unidentified

1959+650 Cen A SN 1006

Cygnus X-1 HESSHESS J1837-069 J1834-087 MAGIC J0616+025 LS I+61 MGROTeVMGRO 2032+4130 J2031+41 J2019+37 HESSHESS J1825-137 J1813-178G0.9+0.1 HESSHESS J1640-465 J1616-508 o HESSMGROHESS J1912+101 J1908+06 J1857+026HESSHESS J1809-193 J1804-216HESS J1713-381HESSHESS J1634-472 J1632-478PSRHESS 1509-58 PSRHESSJ1418-609J1420-607 1259-63 J1303-631Westerlund 2 HESS J0832+058 o +180 Cas A HESS J1357-645 Vela HESS J0632+057-180 2344+514BL Lac Kes 75 W 28Sgr A* G21.5-0.9LS 5039 RX J1713 RCW 86 PSR 1706 MSH 15-52 3C 66A HESS J1841-055HESS J1809-193HESSHESS J1745-303HESSHESS HESSJ1731-347 J1718-385 J1708-410 HESSJ1702-420HESS J1626-490 J1614-518HESS J1427-608 2005-489 0548-322 Crab/Crab Pulsar

0229+200 Min. ZA for MAGIC 2155-304 ° 0347-121 θ ≤ 30 ° 0152+017 θ ≥ 30 2356-309 ° θ ≥ 60 o ° θ ≥ -90 90 2009-02-25 - Up-to-date plot available at http://www.mppmu.mpg.de/~rwagner/sources/

Figure 2.6: A sky map of VHE γ-ray sources in galactic coordinates as of February 2009 from [7]. The accumulation of galactic sources can be seen. The grey shaded areas show the accessible zenith angle ranges for MAGIC for different limits of the zenith angle. band of sources in the galactic plane can be seen. Extragalactic sources are distributed homogenously over the sky map as the standard assumption of cosmology suggests. In the following a brief overview over known γ-ray sources is given.

2.4.1 Galactic sources

Supernova remnants and plerions A final stage of stellar evolution is reached when a star runs out of “fuel” necessary for the fusion reaction. Then the dropping radiation pressure can no longer counteract the gravitational pressure and the star collapses. Depending on the initial mass of the star, a neutron star or a black hole is formed. During the collapse, some material is ejected. This expanding structure is called a nebula. If a neutron star (pulsar) remains it is referred to as a plerion or a pulsar wind nebula. The forming shocks can cause particle acceleration leading to a steady VHE γ-ray emission. The best known system of this type is the Crab Nebula. It emits a steady emission and is visible from the northern as well as from the southern hemisphere under a large zenith angle. It was the first detected VHE source in 1989 [6]. Because of its high and steady γ-ray flux it serves as a standard candle for VHE γ-ray astronomy. In this thesis, the Crab Nebula was used for testing the performance of the MAGIC-I telescope when recording data under the influence of moonlight.

Pulsars Pulsars are highly magnetized, rotating neutron stars of the order of 1.44 solar masses 2.4 Sources of very high energy γ-rays 15 and are found in the centers of supernova remnants. They have a very short rotation period down to milliseconds and very intense magnetic fields of the order of 1012 G. Pulsed VHE emission was recently detected by MAGIC above 25 GeV from the Crab Pulsar [15]. This observation of high energy γ-rays is important for the understanding and testing of different pulsar emission models.

Microquasars and binary systems Microquasars and (X-ray) binaries are astronomical systems composed of two objects: one very compact object like a black hole (microquasar) or a neutron star, and a second (massive) star rotating around each other. They are gravitationally locked. Often, the dense object accretes matter from the accompanying star. Since there are some similar characteristics to quasars (see below) such as accretion and optical behavior, they are named microquasars. The compact object sometimes emits a jet of particles, respectively plasma bubbles in which shock fronts can be formed and particles be accelerated, similar to some active galactic nuclei. Microquasars are especially interesting to compare phe- nomena similar in AGNs on much shorter timescales due to its small dimensions. One prominent system of this type is LS I +61 303 [16]. It is likely, that charged particles in the accretion process are accelerated and entering a shock region between the two objects. VHE γ-rays are then created via IC scattering of relativistic particles with CMB photons. Sources of this type usually emit variable radiation, depending on the phase of the system.

The galactic center The galactic center has been found to emit a steady VHE γ-ray signal up to 30 TeV [17]. The interpretation of this emission is very difficult since the region is packed with poten- tial sources. With current instruments it is not (yet) possible to disentangle the exact location of the emission. Some scenarios involve emission from pulsar wind nebulae or a SNR remnant. Other scenarios include the central supermassive black hole as an accel- erator. Also dark matter annihilation processes are discussed close the black hole which could emit VHE emission.

The galactic center region and galactic plane Notably, one has observed diffuse gamma-ray emission correlated spatially with the central 200 parsecs of the Milky Way as reported by H.E.S.S [18]. A likely scenario would be a hadronic collision of cosmic rays with dense molecular clouds or dust in the central part of the galactic plane. Also EGRET observed a diffuse γ-ray excess in the HE regime in the galactic plane [19].

2.4.2 Extragalactic sources

Active Galactic Nuclei An active galactic nucleus (AGN) is an active region in the center of a galaxy. Often, the the center of galaxies host a supermassive black hole (SMBH) with a mass around 106 − 1010 solar masses [20]. Material close to the central black hole forms an accretion disc and heats up to a hot plasma. The gravitational potential of the SMBH energy is 16 2. Astroparticle Physics the source of power to “drive” a cosmic accelerator. If the accretion rate is high enough, two strongly collimated ultra-relativistic plasma outflows, so called jets, are observed perpendicular to the accretion disc. The length of a jet can exceed the size of the host galaxy and can reach lengths sometimes 104 light years. The jet formation mechanism is not fully understood so far. Particle acceleration takes place throughout the jet. There are also shock regions de- tected. A very good object to study the mechanisms of jets is the nearby radio galaxy M87. M87 is often referred to a “misaligned” blazar, and thus the regions of the jet can be resolved in some wavelengths. VHE γ-ray emission is supposed to be mostly emitted in the jet region close the supermassive black whole. AGNs are classified basically by their line of sight towards the earth, initially from op-

Figure 2.7: Schematic drawing of an AGN. The major regions are label in white. Some typical classifications are written in yellow. tical and radio observations. Some prominent representatives, BL Lac objects, Seyfert 1 and 2 galaxies defined by their observation angle, are shown in fig. 2.7. BL Lacs have their jet aligned close to the line of sight of the observer, as well as Flat Spectrum Radio Quasars do. Those two classes are jointly called “blazars”. One prominent representative of this source type is Markarian 421 (Mrk 421), which was also analyzed in this thesis. Mrk 421 was the first extragalactic source observed by the Whipple telescope [21]. All so far detected extragalactic sources are TeV blazars. The 2.4 Sources of very high energy γ-rays 17 exception is the already mentioned M87 radio galaxy at a redshift of z = 0.0044. The farthest source detected so far is 3C 279 [22] at a redshift of z = 0.536, which already leads to restrictions on EBL models [23]. The study of correlations of VHE emissions and other wavelengths are an important tool to understand high energy reactions in AGNs. For example for Mrk 501, correlations with high significance have been observed, while also an orphan γ-ray flare without a optical or X-ray counterpart was observed in 1ES1959+650. Optical-TeV correlations have still to be studied. However optical-GeV correlations were reported for 3C 279. Therefore, optical flares are of great interest as triggers for VHE observations. Correla- tion studies are mentioned here because they are difficult to coordinate beacause of the short observation time with IACTs. Therefore, any extension of the observation time into periods of moonlight, like investigated in this thesis, is a big bonus for correlation studies.

Gamma Ray Bursts Gamma Ray Bursts (GRBs) are among the most violent processes in the universe and can be observed as a short event from seconds to minutes. They can be observed quite frequently (1-2 per day) with current instruments. During their outbursts, they out- shine all other sources in the universe, mostly in γ-rays. The origin of GRBs is still not clear. A focus of MAGIC is the observation of GRBs. It is therefore designed to point very fast to the region, where a GRB was observed (e.g. by satellite or neutrino experiments) [24]. Detecting the afterglow of a GRB with MAGIC would give very in- teresting insights on the processes of GRBs. Within the last years, several GRBs were observed, some only seconds after the alert, but no significant VHE signal (σ > 5) was detected so far. On 23rd April 2009 the so far farthest GRB has been detected by the Italian optical telescope Telescopio Nazionale Galileo (TNG) at a redshift z = 8.1 [25]. Although a number of 1-2 GRBs per day look like a large number, the chance to observe one from a given location and during clear dark nights is very low. For MAGIC only at most one per month lay in the favorable zenith angle range below 60◦. Only a fraction of these GRBs should be detectable by MAGIC because most of the GRBs are at very high redshift and in turn their upper spectral end is strongly affected by the absorption of γ-rays by the EBL. By also carrying out observations during dusk or dawn, where one has similar enhanced night sky light background as during moon shine, one would enhance the chance for detection by < 50%. 18 2. Astroparticle Physics 3 The MAGIC Telescope and the Imaging Atmospheric Cherenkov Technique

Very high energy γ-rays can not be detected directly with ground based telescopes, since a) they are absorbed by the atmosphere and b) their flux is so low that it is impossible to build sufficiently large detectors for a direct hit. A very successful observation technique is the Imaging Atmospheric Cherenkov Technique, which is for example used with the MAGIC telescope. In this chapter an introduction to the Imaging Atmospheric Cherenkov Technique is given. The MAGIC-I telescope setup and the analysis technique is explained. Some key parts are discussed in more detail, which are relevant for observations under moonlight conditions.

3.1 The Imaging Atmospheric Cherenkov Technique

The Imaging Atmospheric Cherenkov (IAC) Technique is a very successful observation method for cosmic particles of very high energy γ-rays from ∼50 GeV to ∼100 TeV. Also cosmic ray hadrons in the same energy range produce air showers of similar light intensity, such as protons, helium nuclei or iron nuclei. Further, studies of electron and positron fluxes can be performed with the IAC technique. Unfortunately, the charged components cause a more than 1000 times higher background rate than the γ-ray flux. The cosmic ray flux above 10 GeV is, nevertheless, generally very low. Satellite borne detectors have at most an area of 1 m2 and are therefore unsuited for the detection for γ-ray sources. On the other hand, the ground-based IAC technique offers the possibility for a detection area above a few 104 m2 using an indirect detection principle becuase air showers spread the Cherenkov light nearly uniformly1, but with sizeable fluctuations, over a large area.

3.1.1 Extended air showers

When relativistic cosmic particles impinge on earth’s atmosphere, they interact with nuclei of air molecules, and secondary particles are produced. The first interaction pro- cesses are sketched in Fig. 3.1. One distinguishes two types of extended air showers (EAS), motivated be the evolution of the cascade caused by the primary particle.

1Above a few TeV the distribution becomes more and more non-uniform, peaking close to the shower principal axis. 3. The MAGIC Telescope and the Imaging Atmospheric Cherenkov 20 Technique

Photons and leptons (electrons/positrons) only emit (> 99%) further photons and elec- tron/positrons via QED interactions in the EAS. The first interaction of a γ-ray is within the electromagnetic potential in the vicinity of air molecules. The resulting secondary particles from primary photons and leptons only consist of electrons, positrons and pho- tons. This is referred to as electromagnetic cascades. Hadronic cosmic rays (like protons, He-nuclei or heavier ions) instead will interact strongly with air nuclei, initiating a hadronic cascade, with a more complex evolution. Prominent particles from hadronic cascades are pions and and heavier mesons, such as for example kaons. Charged pions and kaons can either interact again or decay, most frequently into muons and their correlated neutrinos. Muons were first detected by Carl D. Anderson in 1936 in such secondary processes. Neutral pions from hadronic cascades decay in two photons which can initiate an electromagnetic subshower, similar to an electromagnetic cascade from primary photons or electrons. In the energy region accessible by IAC telescopes, the first interaction typically takes

Primary Cosmic Ray (p, , Fe ...)

Atmospheric Nucleus

e+ e- EM Shower e+ Nucleons, K , etc. e- Atmospheric Nucleus EM Shower e+ e+ e- e+ e- Nucleons, e- K , etc. e- + e+ e + e- EM Shower

Figure 3.1: Schematic drawing of an electromagnetic extended airshower, as induced by a pri- mary photon (left) and a hadronic cascade, induced by a primary hadron (like p, α, Fe, ...). Electromagnetic subshowers are scetched as blue cones. place at heights around 10-30 km depending on the primary particles energy and type while the shower maximum is typically around 6-8 km above sea level for vertical showers of 100 GeV - 10 TeV. For single IAC telescopes like MAGIC-I, this shower maximum parameter is difficult to estimate, but stereo systems are capable of measuring it. Fig. 3.2 shows the simulated shower evolution of a 100 GeV photon and a 100 GeV proton. The total vertical extension is around 20km. Within an electromagnetic cascade a number of elementary processes contribute to the shower evolution:

Pair production: In the presence of the Coulomb field in the vicinity of a nucleus, a 3.1 The Imaging Atmospheric Cherenkov Technique 21

Figure 3.2: Simulated longitudinal development of a 100 GeV γ-ray induced (left) and a 100 GeV proton induced EAS (from [26]). The particle traces are color coded for the particle type: red=e±/γ, green=muon, blue=hadron. The vertical scale is from zero to 30 km height, while the first interaction is assumed to take place at 30 km height.

relativistic photon undergoes pair production:

γ → e+ + e−.

The energy threshold for the pair production process is at twice the rest mass of an electron (Eγ > 1.022MeV ). Pair production is also the first interaction process of an VHE γ-ray in the atmosphere.

Bremsstrahlung: Charged particles emit bremsstrahlung in Coulomb fields of an atmo- spheric nucleus. Bremsstrahlung is emitted when the charged particle is deflected. Bremsstrahlung is also be referred to as free-free radiation.

Photoproduction: In the photoproduction process a photon interacts with an atmo- spheric nucleus and produces hadronic particles via photoproduction, such as for example a % or Ω meson.

γ-rays above the critical energy of 20 MeV undergo pair production in the presence of an air nucleus. Secondary electrons and positrons produce high energy photons via bremsstrahlung above the so-called critical energy of ∼80 MeV, i.e. an energy, where the ionization losses are about the same as the bremsstrahlung losses. A cascade is formed with an exponentially increasing number of particles after the first interaction. A maximum number of secondary particles in this avalanche like process 3. The MAGIC Telescope and the Imaging Atmospheric Cherenkov 22 Technique is reached when the average energy of the electrons/positrons drops below the critical energy at which ionization losses start to prevail losses due to bremsstrahlung. In fig. 3.5, the number of shower particles as a function of height are simulated for different primary γ-ray energies.

3.1.2 Cherenkov light emission

Most of the secondary particles within an extended airshower are ultrarelativistic and thus emitting Cherenkov radiation. If a particle moves with a speed v > c0, which is faster than the speed of light in the medium c0 = c/n, where n is the refraction index of the medium, than the spherical electromagnetic waves are propagating slower than the particle itself. The individual waves interfere, as shown in fig. 3.3, at an angle θC , which is the so-called Cherenkov angle.

c0 1 cos θ = = (3.1) C n βn

with: β = v/c Following this condition, an electromagnetic radiation is emitted in a cone at the angle θC , called Cherenkov radiation. A common analogy is the sonic boom of a supersonic object, like an aircraft or a bullet. The sound waves generated by the supersonic body can not move faster than the body itself. Hence, the sound waves “stack up” and form a shock front. All charged particles in an extended airshower, fulfilling v > c0, emit Cherenkov radia- tion. Due to the exponential change of the atmospheric density as a function of altitude, the Cherenkov angle for β = 1 particle varies typically between 0.3◦ and 1.4◦ (at sea level). The Cherenkov light spectrum is affected by atmospheric extinction and peaks at 2200 m altitude around 320 nm, but mainly ranges from 300 to 500 nm as a function of zenith angle. Charged particles stopping higher up in the atmosphere, illuminate a “donut ring” on ground. This donut ring is not even illuminated uniformly because the air density increases towards the ground, which also increases the refractive index n and thus the Cherenkov angle θC and, in turn, some modest focusing occurs.

In case of an electromagnetic shower, the cumulated Cherenkov light typically illuminates a disk with a slightly enhanced rim. The photon density at ground is much more uniform than in case of light of heavier particles because the electrons/positrons undergo much larger multiple scattering and magnetic field deflections as well as much more frequent bremsstrahlung deflections. At 2200 m asl the majority of the Cherenkov photons from an electromagnetic cascade arrive within a radius of 120 m from the impact point. Inside this circle, the Cherenkov photon density is almost constant at e.g. 15 photons per m2 for a 100 GeV γ-ray induced shower and the photons arrive within some nano seconds only. Fig. 3.4 shows the simulated Cherenkov light distribution on ground for a 300 GeV γ-ray and a 1 TeV proton. Several small electromagnetic subshowers (from π0 decays) can be identified in the Cherenkov light distribution of the proton simulation. However, the distribution is different from a γ-ray induced shower. This provides the possibility of γ/hadron separation. 3.1 The Imaging Atmospheric Cherenkov Technique 23

Figure 3.3: Cherenkov emission of a charged particle moving ultrarelativistic in a medium. The speed of light c0 in a medium with refraction index n is c0 = c/n. The emitted spherical electromagnetic waves superimpose to a cone with an opening angle of θC . ◦ The mean value of θC in the atmosphere would be around ∼ 1 .

photon/(5 5 m2) photon/(5 5 m2) 500 500 500 500 Y[m] Y[m] 400 450 400 450

300 400 300 400 200 350 200 350 100 300 100 300 0 250 0 250 -100 200 -100 200 -200 150 -200 150 -300 100 -300 100 -400 50 -400 50 -500 -500 -500 -400 -300 -200 -100 0 100 200 300 400 500 -500 -400 -300 -200 -100 0 100 200 300 400 500 X[m] X[m]

Figure 3.4: Simulation of the Cherenkov light pool on ground level (500×500m2 area) emitted by an extended airshower of a 100 GeV γ-ray (left) and a 300 GeV proton (right) impinging perpendicular on the atmosphere (taken from [27]). The light content is comparable, while the Cherenkov light distribution is very different.

3.1.3 The imaging atmospheric Cherenkov technique

Using the Imaging Atmospheric Cherenkov Technique, Cherenkov photons in the visible to near UV range from extended airshowers are recorded. Like other optical telescopes, Cherenkov telescopes consist of three basic elements: a mechanical tracking system, a large area focusing mirror and a camera of a few degree diameter in the focal plane. The 3. The MAGIC Telescope and the Imaging Atmospheric Cherenkov 24 Technique mechanical tracking counteracts the earth’s rotation and allows to continuously follow an astronomical object. The mirror surface is optimized to focus on the mean shower height and to reflect the fraction of the Cherenkov light pool falling onto the mirror surface onto the camera. The Cherenkov light pool has a typical radius of 120 m, which leads to an effective detection area in the order of 104m2. The camera in the focal plane is a matrix of up to a few hundreds of very fast photomultiplier (PMTs) sensitive to single photons and covers typically a field of view (FoV) of a view degree. The very fast PMTs allow one to record the light flashes of the Cherenkov light and to obtain a simplified “photo” of the shower. It has to be mentioned that due to the directional emission of the Cherenkov light only photons within a small angle w.r.t. the shower axis are recorded. The telescope is blind to view a Cherenkov light emitting shower under large angles, thus it is quite different to, for example, air fluorescence detectors which can view showers even at 90◦ angle. The Cherenkov telesopes are also blind if outside a 120 m impact distance2 except to Cherenkov light from large angle scattered particles. Fig. 3.5 shows “Cherenkov light pictures” recorded by the MAGIC camera. A schematic picture of the Imaging Atmospheric Cherenkov Technique is shown in fig. 3.5. The very faint Cherenkov light implies, that Cherenkov telescopes must have a large optical reflector and a very sensitive camera with highest efficiency between 300 and 500 nm wavelengths. The short shower duration implies a very fast detection, which currently only photomultipliers and very fast readout electronics can provide. The Cherenkov technique takes advantage of the shower development information in the image of the telescope camera. Some shower events taken by MAGIC-I is shown in fig 3.6. Using the image of the Cherenkov radiation, many parameters of the primary particle can be determined from the shower image. The total light intensity is a measure of the primary particle energy. The orientation of the shower picture is correlated with the arrival direction of the primary, and the shape provides information on the primary particle type. All image parameters provide only indirect information on the primary particle. For a precise estimation of relevant information (energy, γ/hadron, arrival di- rection) the recorded pictures are “compared” with those of Monte Carlo simulations to achieve best estimates of the parameters of the incident particle. Hadronic showers dominate electromagnetic showers by more than a factor of 1000. The hadronic showers form therefore a huge an unwanted background, which has to be sup- pressed as much as possible to detect VHE γ-rays or electons/positrons. In early times of VHE γ-astronomy ne had no tool to the hadronic background except to search for “hotspots” in the sky map, and therefore no sources could be detected. The so called γ/hadron separation based on analyzing differences in the shower images, allowed one to reject a large number of hadronic showers. Also, the image technique allowed one to improve the resolution and restrict the origin of the cosmic particle on the sky map to a much smaller spot. Therefore, a small excess originating from a γ-source would be much more peaked on a uniform hadronic background in the sky map. Furhtermore, these not rejected and diffuse showers could be statistically subtracted. In practice, this is performed, with quasi-simultaneous recording of background events nearby the source location (called OFF-source measurement). Either, during same atmospheric conditions, an “OFF-sample” is recorded at a celestial position where no source is present, or by using the so-called wobble-observation [28] technique. During wobble observations, the

2The distance limit changes with the zenith angle. 3.1 The Imaging Atmospheric Cherenkov Technique 25

Figure 3.5: Schematic drawing of the imaging atmospheric Cherenkov technique. The first in- teraction of a VHE γ-ray is around 20 km height with an atmospheric nuclei. The number of secondary electrons in the induced extended airshower depending on the energy and height is sketched. The charged secondary particles emit Cherenkov light. A telescope located within the Cherenkov light pool can record an image of the electromagnetic cascade.

35 41 29 33 38 27 30 36 25 28 33 23 26 30 21 24 28 19 21 25 17 19 23 16 17 20 14 15 17 12 12 15 10 10 12 8 8 9 6 6 7 5 3 4 3 1 2 1 ° ° ° 0.60 -1 0.60 -1 0.60 -1 189mm L 189mm L 189mm L

Figure 3.6: Shower images as recorded by MAGIC-I during Crab Nebula observations. Color coded is the measured charge in phe. The left image shows a γ-candidate, the middle an hadronic event, the right a muon ring event. 3. The MAGIC Telescope and the Imaging Atmospheric Cherenkov 26 Technique source position is not centered in the telescope, but displaceed 0.4◦ away from the center. Hence, an artificial OFF-position is recorded simultaneously on the opposite site of the the displaced source. Even more control regions can be found along the circle defined by the displacement from the center. To reduce effects from camera inhomogeneities, the wobble switches every 20 minutes, and also the source moves during observations as a consequence of the telescope mount. The wobble observation technique is the standard observation method for MAGIC.

Also the zenith angle of the source has an important influence on VHE γ-ray observa- tions. When observing at large zenith angles, the shower development increasingly takes place only in upper layers of the atmosphere and is further away. This leads to a different Cherenkov light development such as a lower light production due to a higher threshold, an on average smaller Cherenkov angle emission (which nevertheless collimated more the light cone and partially offsets the 1/r2 reduction in light flux) and a larger Cherenkov photon absorption in the atmosphere. This implies a higher trigger threshold and more compressed images. A positive effect of large zenith angle observations is the increased collection area from the larger Cherenkov light pool on ground.

3.2 The MAGIC-I Telescope

Figure 3.7: A picture of the MAGIC-I telescope during sunset on the Roque de Los Muchachos on the Canary Island of La Palma (28.8◦ N, 17.9◦ W) 3.2 The MAGIC-I Telescope 27

3.2.1 The structure and mirrors

The MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) Telescope located on the Canary Island of La Palma (28◦4504300N 17◦5302400W) at 2225 m above sea level, is currently the largest single dish IACT worldwide. The 17m parabolic mirror surface is approximated by 234 one m2 panels composed each of four small spherical mirrors with curvature radii from 36.6 to 34.1m. Each mirror panel can be adjusted individually with an automated mirror control. The diamond turned, all-aluminum lightweight sandwich mirrors are quartz-coated and have an initial reflectivity of ∼85% in the wavelength range from 350 - 650 nm. Heating wires are implemented into the mirror elements to de-ice and to remove dew from the surface. The mirror support structure is a four-layer space frame and built out of a lightweight carbon-fiber-epoxy tubes. This low weight design allows fast repositioning of the tele- scope within 20s for GRB follow-up observations. The overall weight is only 70 tons.

3.2.2 The MAGIC-I PMT-camera

The MAGIC camera (see fig. 3.8) is equipped with 576 6-dynode compact photomulti- pliers with a field of view of 3.5◦. The camera is divided into an inner hexagon with 396 photomultiplier tubes (PMTs) with a diameter of 0.1◦ each and an outer region equipped with 180 PMTs of 0.2◦ diameter each. The 6-dynode electron multiplier chain has an amplification factor of 3-5×104. This is a small value compared to commonly used PMTs with amplification factors of the order of 106. However, low gain amplification PMTs were chosen on purpose to allow observations under comparatively high background lev- els, like under moonlight. This prevents the last dynodes from damage from large anode currents from the diffuse background light. The schematics if the readout circuit of the PMTs is shown in fig. 3.8. A connected preamplifier guarantees an overall amplification of the photoelectron signal of a factor of 106. Besides the capacitive coupling of the preamp to suppress the dc component of the

Figure 3.8: Left: A picture of the MAGIC-I camera with open lids during daytime. Right: A schematic drawing of the photomultiplier readout circuit with the anode direct current readout and the AC-coupled fast preamplifier making up for the low gain of the 6 dynodes. 3. The MAGIC Telescope and the Imaging Atmospheric Cherenkov 28 Technique steady night sky background flux, also a parallel, but slow resistive readout with 100 kΩ in installed. This allows to monitor the PMT anode currents (DC ). The anode currents are recorded for each photomultiplier using an ADC with an integration window of a few µs and sampled with ∼ 3 Hz frequency. The DCs are a direct proportional measure of the night sky background and will be used frequently in the following chapters. As sketched in fig. 3.9, the fast signal transmission from the camera to the readout at

optical optical optical fibers splitters receiver PMT transmitter

receiver PMT transmitter

receiver PMT transmitter

receiver optical fibers receiver

receiver

Figure 3.9: A schematic drawing of the readout circuit of three channels. 16 channels are mul- tiplexed into one 2 GHz FADC unit. Pixels, which are not included in the trigger are delayed accordingly and directly connected to the mulitplexer controler. (Taken from: [29] the 80 m away counting house is performed via optical fibers. In the camera the signals are converted by Vertical Cavitiy Surface Emitting Laser Drivers (VCSELs) back into optical signals and injected into 60/125 micron step index optical fibers. In the counting house the fibers are split into two branches. One branch is routed to the trigger circuit, while the second one is connected to the digitization system.

3.2.3 The trigger

The trigger region of the MAGIC-I camera is composed of 19 overlapping macro cells of 37 pixels each at the inner part of the camera. The pixels of each macro cell are con- nected in one trigger logic. The analog optical signal is received and transformed back into an analog electric signal which has to pass the trigger levels. The Magic trigger system has two trigger levels:

Level-0 (Discriminator Thresholds (DT)): If the pulse height exceeds a certain threshold, a ∼ 6ns logic output signal is created. The discriminator thresholds can be adjusted individually for each pixel. This limits the frequency especially for pixels having a star in the FoV, which is e.g. the case for ζ-Tauri, a star close to the Crab Nebula. The discriminator thresholds are discussed in more detail in chapter 5. The discriminator thresholds are typically adjusted such that the data are read out at a frequency of 200 Hz. 3.2 The MAGIC-I Telescope 29

Level-1 (nn-trigger): The signals from Level-0 are grouped into 19 overlapping cells of 36 pixels each. The currently employed standard trigger is a topological four next neighbor-trigger logic in each trigger cell. If four close packed neighboring pixels receive a signal from the level-0 trigger within the integration window of 2-5 ns, the trigger sends a signal to the DAQ. The event is read out.

Alternatively: Level-1 (Sum-trigger): An alternative trigger logic is available and is used for pulsar observations where low energy thresholds are needed and the 4nn is not fulfilled. Eight patches of 18 or 24 pixels are connected in an analog sum logic. The signal of all channels herein is summed up. If exceeding a threshold of 26 coinciding photoelectrons in the full patch, the DAQ is triggered. To prevent accidental triggers from frequent large afterpulses, the signal of each pixel is clipped at the 6 photoelectron level. The sum trigger logic achieves higher sensitivity for low energy γ-rays around ≈30 GeV.

3.2.4 The data acquisition system

The second optical fiber after the signal splitter is connected to the DAQ unit. To reduce costs of the very expensive FADC system, 16 channels are multiplexed into one FADC unit. Therefore the channels are optically delayed with successively elongated fibers, according to the required time span. Upon arrival of a trigger signal, the FADC system is thus reading out successively the signals of 16 pixels. A commercial 2 GHz Flash ADC system from Aquiris is used. For each pixel it writes out 20 slides of 0.5 ns width containing the charge information. In addition the time and the trigger information is recorded for each event. The fast readout allows the use of a relative timing difference of fired pixels, which allows one to improves e.g. the γ/hadron separation. This system is often referred to as MUX-FADC. In order to convert from FADC counts back to the physical unit of phe (photoelectrons), the channels have to be calibrated. Gain variations of the PMTs and the VCSELs are calibrated using an optical calibration system. Differently colored LEDs of 370, 460 and 520 nm illuminate the camera uniformly with different intensities. The DAQ system records those dedicated calibration runs. Also interleaved calibration events during regular data taking are recorded. 3. The MAGIC Telescope and the Imaging Atmospheric Cherenkov 30 Technique 4 The MAGIC Standard Analysis

With imaging atmospheric Cherenkov telescopes, the primary cosmic particle can not be detected directly, but instead, Cherenkov light emitted by secondaries within the extended airshower. The signal, recorded with the MAGIC telescope, is at the earliest stage of the analysis consisting out of digitized counts of the FADC readout for each pixel. The reconstruction of physical parameters of the primary γ-ray therefore needs a comprehensive treatment. Furthermore, the γ/hadron separation has to be performed to extract the γ-ray signal. Here, only the basic steps of the data analysis are summarized. The effects of moonlight are discussed whenever necessary.

4.1 Data selection

The first step is the data selection and data quality check. Generally, the weather con- ditions and also the subsystem reports for the selected data have to be checked. A weather station provides the necessary information on temperature and humidity and a pyrometer determines the “cloudiness”. For the dark-night analysis, constant L1-trigger rates around 200 Hz are usually a good indicator for stable weather conditions. During moonlight observations the discriminator thresholds are permanently adjusted by the individual pixel control to limit the accidental trigger rate. While this algorithm is not optimized for moonlight, the L1-trigger shows high fluctuations during moonshine and thus is no reliable parameter for clear weather conditions. However, the L1-trigger rate should be checked if there is no rapid change of the rate, which might indicate a cloud or problems with the DAQ system. A slight cloud cover is expected to create more unstable rates. During moonlight condition, an extra quality indicator for the weather conditions are the anode currents. If clouds are present in the field of view, the anode currents fluctuate significantly in time.

4.2 Event reconstruction and shower parametrization

The first steps in the analysis are signal extraction and the calibration of the events. Therefore, calibration runs of 5000 events are taken, when the camera is illuminated artificially with light of different wavelengths. The calibration run is used to determine the conversion factor from FADC counts into photoelectrons (phe). Then a signal is extracted from the pedestal-subtracted FADC slices using a cubic spline extractor. Bad 32 4. The MAGIC Standard Analysis pixels, which are either “hot” or “dead”, are interpolated with the charge of the neigh- boring channels.

4.2.1 Image cleaning

To isolate the shower in the recorded image before parametrization, an image cleaning is applied according to [30]. The employed image cleaning algorithm uses two parameters, one for core and one boundary pixels, and additionally, timing constraints for neighbor- ing pixels are applied. The image cleaning used in the standard analysis keeps core pixels with charge ≥ 6 phe

24 24 22 22 20 21 19 20 17 19 16 18 14 17 12 15 11 14 9 13 7 12 6 11 4 9 3 8 1 7 6 0.60° -1 5 189mm -2

Figure 4.1: A image recorded by MAGIC of an extended airshower before (left) and after (right) image cleaning. Color coded is the charge within the integration window in phe. The resulting fitted Hillas ellipse with the axis directions is drawn as red lines. and a maximum spread of 4.5 ns plus boundary pixels with a charge ≥ 3 phe and max- imum of 1.5 ns delay from the neighboring core pixel. All pixels not fulfilling these constraints are set to zero charge. This standard image cleaning will be referred to 6-3 ” later. A shower image before and after image cleaning is shown in fig. 4.1. It is shown later in chapter 7, that the choice of image cleaning parameters is basically one of the most important parts when analyzing data recorded under moonlight conditions.

4.2.2 Shower image parametrization

The cleaned shower images are parameterized using a method which was proposed by A. M. Hillas [5]. This method supposes, that γ-ray induced showers have an elliptical shape different from hadronic background events. Therefore, a so-called Hillas ellipse is fitted into the cleaned shower image and several Hillas parameters are determined. The major axis of the Hillas ellipse is connected to the shower direction. An example of a fitted Hillas ellipse can be seen in fig. 4.1. From this Hillas parametrization, following parameters can be derived: 4.3 Event classification (Gamma/hadron separation) 33

• Size: The overall light content of the image after image cleaning in phe. Size is approximately proportional to the energy of the primary particle if the impact parameter is below ∼120 m (i.e. about a DIST of 1.2◦ - 1.4◦).

• Length: The RMS value of the charge distribution along the major image axis.

• Width: The RMS value of the charge distribution along the minor image axis. The length and the width describe the vertical and lateral development of the EAS, respectively.

• CONCn: The fraction of the charge distribution contained in the n brightest shower pixels.

• M3Long: The 3rd moment of the charge distribution along the major axis of the shower image.

• Leakage: Ratio of charge contained in the outer pixel ring of the camera to the total amount of photoelectrons. Leakage is used to estimate the energy of high energy showers, which often leak out of the camera boarder.

• Number of islands (NoIsl): Number of separated signal areas in a cleaned image. The number of islands actually is no traditional Hillas parameter.

The parameters Size, Length, Width and CONCn, describe the shape and charge content of the showers. Two additional parameters parameterize the orientation and position of the shower in the camera.

• Alpha: The angle between the major axis of the shower ellipse and the connection line from the source position to the “center of gravity” of the image. Gamma- induced events from the source have a small angle |Alpha|. Thus this parameter is a powerful parameter for the background rejection from hadrons.

• Dist: Distance from the image center of gravity to the position on the camera of the candidate source.

An additional parameter Theta2 can be defined as the angular distance between the source position and the reconstructed source position, but it is not used in the here performed Alpha analysis.A θ2-analysis is a source-independent analysis method and is particularly suitable for extended sources and sky scans.

4.3 Event classification (Gamma/hadron separation)

Hadron induced showers are the main background of the measurement of VHE γ-rays. Even for a strong source like the Crab Nebula, the ratio of hadron triggered showers and γ-ray triggers is roughly 1/1000. Also muons and diffuse electrons contribute to the background. The energy distribution of the hadronic background follows a power law distribution dN/dE = E−2.7 in the VHE energy region (see fig. 2.3). In order to suppress the background showers, reasonable cuts in the multiparameter space of the Hillas parameters and the arrival time characteristics have to be found. 34 4. The MAGIC Standard Analysis

ALPHA

DIST WIDTH

LENGTH

Figure 4.2: Illustration of the Hillas parameters. The Hillas ellipse is drawn in green on top of a cleaned shower image (from [31]).

Fig. 4.3 shows exemplarily the Hillas parameters size, CONC1, width and length for a data sample and for a Monte Carlo γ-sample. Although the simulated γ-sample has a very different spectrum as the hadron sample in here (as the size distributions indi- cates), the parameters length, width and CONC1 do not suggest a reasonable cut for the γ/hadron separation on these normalized plots.

Within the MAGIC standard analysis, the γ/hadron classification is performed with statistical training methods. The used random forest method [32, 33] is a collection of decision trees. As γ-ray examples for the statistical training, Monte Carlo simulated events are used, while as hadron examples, real data events, either from an OFF-position observation or from observations of a weak source are used. The random forest takes several Hillas parameters and the shower arrival time simultaneously into account. Here the parameters size, zenith angle, width, length, size/(width·length), CONC1, Dist, M3Long, RMS of time and time gradient are used. The random forest algorithm calcu- lates one decision parameter 0 < h < 1, called hadronness for each event. Fig. 4.4 shows the normalized hadronness distribution for a Monte Carlo γ-ray test sample and for real data.

4.4 Gamma-ray excess determination

In order to determine the γ-ray excess, the (hadronic) background has to be suppressed. Therefore a cut in hadronness, here h ≤ 0.1, is applied (see fig. 4.4). The remaining background is discriminated by a source dependent cut on |Alpha| < 8◦ as shown in 4.4 Gamma-ray excess determination 35

Size Conc1 0.07

0.1 0.06

0.05 0.08

0.04 0.06 0.03 0.04 0.02

0.02 0.01

0 0 1 2 3 4 5 6 7 0 0.05 0.1 0.15 0.2 0.25 0.3

Length Width

0.08 0.1

0.07 0.08 0.06

0.05 0.06

0.04

0.03 0.04

0.02 0.02 0.01

0 0 0 50 100 150 200 250 300 350 400 0 20 40 60 80 100 120 140 160 180 200

Figure 4.3: Exemplarily comparison of Hillas parameters between real, hadron dominated data (black line) and γ-ray Monte Carlo simulations (high energetic MC sample) (blue dashed line). Clear cuts to distinguish both particle types cannot be found easily, especially since hadrons dominate over γ-rays with a factor of 1000.

fig 4.5. In the further analysis, throughout additional quality cuts on size < 220 phe and the Number of Islands NoIsl ≤ 2 are applied. Images with small size are likely accidentally triggered events, have further a bad γ/hadron separation capability and have further a large uncertainty in their energy estimation. Images with large number of islands are supposed to be most likely hadron showers1, and are therefore commonly rejected with a cut on this parameter.

The following table gives a short overview of the background rejection power for all types of cosmic particles in case of Crab Nebula observations. The second column is valid for all observations, although, the numbers strongly depend on the applied cuts. The “overall cut efficiency” is basically the cut on |Alpha| and thus dependent on the γ-ray flux and the spectrum of the source.

1An islands is supposed to represent a subshowers from an hadronic EAS. 36 4. The MAGIC Standard Analysis

500 Hadrons Counts Gammas 400

300

200

100

00 0.2 0.4 0.6 0.8 1 Estimated Hadronness

Figure 4.4: The scaled “hadronness” distribution of a Monte Carlo sample (red) and a real data set (black). The defined signal region is h < 0.1 and is blue shaded.

2000

1800 Alpha, ON

# Events Alpha, OFF 1600

1400

1200

1000

800

600

400

200

0 0 10 20 30 40 50 60 70 80 90 |Alpha|

Figure 4.5: A typical |Alpha| plot of a strong γ-ray source. Here, ∼8 hours of Crab Nebula observations under moderate moonlight are shown. ON-events (black) peak signifi- cantly in the signal region, which is here defined as |Alpha| <8◦ (blue shaded region) over OFF-events (red).

cosmic particle Hadronness rejection Overall cut efficiency Proton p >99 % > 99.9 % α, ions >99 % > 99.9 % e± ≈20 % > 30 % Diffuse γ-rays ≈20 % ≈30 % ν, WIMP, DM – – Muon ≈100 100 % γ-rays (MC) ≈20 % ≈30 % 4.5 Energy estimation 37

4.5 Energy estimation

The energy of the primary particle is in first order proportional to size. Additional dependencies exist on the zenith angle, the impact parameter and the atmospheric ex- tinction. The energy estimation is performed with a regression tree algorithm, which takes Monte Carlo γ-ray samples as training examples. The quality of the energy estima- tion has to be checked carefully when analyzing data. A deviation in energy estimation has to be unfolded, before calculating a physical parameter like the spectrum. The mi- gration matrix derived from Monte Carlo simulations which include moderate moonlight is attached in the Appendix (Fig. A.5).

4.6 Spectrum calculation

The spectrum of a γ-ray source is defined as the differential γ-ray flux dF dN (E) = γ (4.1) dE dEdAeff dteff with the effective collection area Aeff and the effective observation time teff [34] (Nγ are the numbers of measured γ-ray events per (estimated) energy E). The effective ob- servation time is determined by fitting the distribution of time differences of consecutive events (hadron dominated) by an exponential function

dn = n · λ · e−λt, (4.2) dt 0 where λ is the event rate. If one multiplies the inverse event rate with the number of events, one yields the effective observation time: n t = . (4.3) eff λ

For example, from fig. 4.6 the effective observation time was determined to be teff = 39.7 hours for the selected Crab Nebula data sample, which was used in this thesis. The effective collection area Aeff (E), which depends on the energy E, can be calculated by simulating Monte Carlo γ-rays on a well-defined area A0 and counting the events surviving the cuts N [35]. N(E) Aeff = A0 · (4.4) N0(E) Calculations of the effective collection area are shown for moonlight Monte Carlo simu- lations in fig. 7.13 and fig. A.12. 38 4. The MAGIC Standard Analysis

Total effective observation time Entries 4195708 2 / ndf 7371 / 198 Counts [#] 5 Constant 12.62 0.00 10 Slope -28.97 0.02

104

103

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time Delay between two events [s]

Figure 4.6: Determination of the effective observation time by a fit to the distribution of the event time differences.

4.7 Significance of an excess being a signal

The significance, in units of one standard deviation, of a γ-ray signal is calculated by counting the number of ON events in the expected signal region (NON) and the number of OFF events (NOFF) and using equation 17 in Li and Ma (1983)[36]:

s       √ 1 + α NON NOFF S = 2 NON ln + NOFF ln (1 + α) α NON + NOFF NON + NOFF (4.5) Here, α is a scaling factor of the observation times α = TON or respectively the inverse TOFF 1 number of used wobble positions (ω) in wobble mode (α = ω ). The sensitivity F of a VHE γ-ray instrument is commonly defined as the minimum flux, normalized to the Crab flux that can be measured with a 5σ significance within 50 hours of observation. Thus r T 1 Ω50h = 5 · obs · (4.6) 5σ 50h S Here, S is the significance, defined as S = √ Nexcess . Nbackground

4.8 Software framework

The data analysis is performed in the standard MAGIC Analysis and Reconstruction Software (”MARS”) [37], a ROOT based C++ collection of programs and scripts. A 4.8 Software framework 39 comprehensive sketch of the analysis pipeline is shown in fig. 4.7 taken from [34] for all three types of data sets: ON-data, OFF-data and the Monte Carlo γ-samples, while ON and OFF data is recorded simultaneously, using the wobble-observation technique.

Figure 4.7: The MAGIC analysis chain from raw data up to flux/spectrum and lightcurve cal- culation, illustrated for the MC γ-ray sample, the OFF-data and the ON-data set in parallel. 40 4. The MAGIC Standard Analysis 5 Observations with the MAGIC Telescope during Moonlight

Ground-based searches for very high energy γ-ray emission are normally carried out during clear, dark, moonless nights. During moonshine, the very faint Cherenkov light flashes from extended airshowers have to be detected under high background conditions. Also, possible damage of the PMTs from the increased background light can lead to restrictions. In this chapter, the different approaches by several IACTs for observations under moon- light conditions are summarized, and also the approach of MAGIC-I to observe un- der moonshine is discussed. New calculations for the extension of observation time for MAGIC on La Palma, taking reasonable assumptions into account, are performed. Furthermore, the influence of moonlight on single subsystems of MAGIC-I is discussed.

5.1 IACT observations under moonlight conditions

5.1.1 Early Whipple observations

The first observations of VHE γ-ray observations under moonlight conditions were car- ried out by the Whipple collaboration. Their approach was based on restricting the PMTs sensitivity to the UV range by using solar-blind PMTs, or by using UV bandpass filters in front of standard PMTs, blocking light from 300 - 500 nm [38]. The approach proved successful on Mrk 421 [39] and the Crab Nebula, but the threshold energy was increased by a factor of 3.5 with respect to measurements with normal PMTs during dark night conditions. This lead to an energy threshold estimated to be 1.1 TeV. This solution was quite demanding in additional work as the experimental conditions had to be changed in half of the nights per month. Furthermore, the need of high precision filters proved to be very expensive given the size of a camera of ∼1 m diameter.

5.1.2 Observations with the HEGRA CT1

First regular observations under moonlight conditions were performed by the HEGRA CT1 telescope [40] by lowering the PMT high voltages by 6%, 9% and up to 13% depend- ing on the level of moonshine. TeV γ-ray signals from the Crab Nebula and Mrk 501 were detected with the HEGRA CT1 telescope during moonshine [41, 42]. Also obser- vations during twilight conditions were performed with HEGRA CT1. In contrast to 42 5. Observations with the MAGIC Telescope during Moonlight the Whipple approach, no filters were used. In 1997 several flares from Mrk 501 were successfully recorded under moonlight conditions [42]. During 2001 the AGN Mrk 421 was flaring at a flux level exceeding 1 Crab unit. The HEGRA CT1 telescope could record the lightcurve and spectrum, while performing 30% of those observations under moonlight conditions [43]. Fig. 5.1 shows the lightcurve recorded by HEGRA CT1 of Mrk 501 in 1997 at an energy ]

16 -1 s -2 14 Mkn 501, 1997 = HEGRA CT1 (no moon) = HEGRA CT1 (moon) cm o o

-11 12 11 < Θ < 58.9 = HEGRA CT2 = HEGRA CT System 10 [ 10

8 1.5 TeV) > 6

4 Flux (E 2

0

-2 50520 50540 50560 50580 50600 50620 MJD ]

16 -1 s

-2 14 cm

-11 12 10 [ 10

8 1.5 TeV) > 6

4 Flux (E 2

0

-2 50640 50660 50680 50700 50720 MJD

Figure 5.1: γ-ray observations performed under moonlight conditions are combined with mea- surements during dark nights. Measurements of the different HEGRA telescopes and different observation conditions are shown. Red triangles represent moon- shine/twilight observations whereas blue triangles represent dark night measure- ments. threshold of 1.5 TeV. Data taken under moonshine is combined with data taken during dark-night conditions. Furthermore, also the measured spectra, which were recorded during moonlight conditions, are in excellent agreement with the measurements from dark night conditions (see [44]).

5.1.3 H.E.S.S. Telescope array

The H.E.S.S. IAC Telescope array does not observe during moonlight [45, 46] because H.E.S.S. uses high gain PMTs. The PMTs from the H.E.S.S. telescopes have an intrinsic amplification of 2×105 [47], which is ∼10 times higher than that of the MAGIC-PMTs. Therefore, the anode currents are already comparably high during dark-night observa- tions. Higher anode currents, like occurring during moonshine observations, would result in very fast ageing and damage of the PMTs. 5.1 IACT observations under moonlight conditions 43

5.1.4 VERITAS

No detailed reports about observations under moonlight could be found for the VER- ITAS array. Like in MAGIC, the use of low gain PMTs allows the extension of the duty cycle by a factor of two compared to Whipple [48]. However, it was reported, that LS I +61 303 was observed in 2007/08 partly under moonlight conditions and combined with dark night data [49]. Reputedly, the VERITAS cameras are also equipped with low gain PMTs with an intrinsic amplification of ∼ 3 × 104.

5.1.5 MAGIC-I

The MAGIC-I telescope is the only IACT, whose design and observation strategy is based on the extension of the duty cycle into moonshine times. Therefore, many obser- vations have already been performed during moonlight conditions and several important results and discoveries were obtained, such as for example the following objects:

Cassiopeia A Cassiopeia A (Cas A) is a prominent shell type supernova remnant (SNR) and a bright source of synchrotron radiation observed at radio frequencies and in the X-ray energies. This source was scheduled to be observed for 86% of the scheduled time under moderate moonlight illumination, because Cas A was predicted to have a hard spectrum. Depend- ing on the different moonlight levels, the resulting PMT anode currents ranged between 1 µA and 6 µA [50].

LS I +61 303 LS I +61 303 is a very interesting microquasar system with an expected orbital period

Figure 5.2: A smoothed sky map around the position of LS I +61 303. Left: Observations around periastron. Right: observation around apostron. The bottom right circle shows the size of the point spread function of MAGIC (from [51]). of ∼ 27 days. Thus LI I is an excellent laboratory to study the VHE γ-ray emission and 44 5. Observations with the MAGIC Telescope during Moonlight absorption processes taking place in massive X-ray binaries. LS I +61 303 was observed during 54 hours during good weather conditions between October 2005 and March 2006 by MAGIC. In particular, 22% of the data used in this analysis were recorded under moonlight. An observation during moonshine is vital to cover the entire periodicity of the flux curve. A skymap including observational data under moonlight conditions is shown in fig. 5.2 for two orbital periods, with and without γ-ray excess [51].

Observations of variable emission from Mrk 501 Mkn 501 is a nearby TeV blazar at a redshift of z = 0.034 [52]. The total observation

-9 -9 ] ] 10 10 -1 -1 s s -2 -2 2 2

1.5 1.5

1 1 F (0.15-10 TeV) [cm F (0.15-10 TeV) [cm

0.5 0.5

Crab Nebula Crab Nebula 0 0

15 Bkg Rate [counts/min] = 9.9 0.2 (Chi2/NDF = 32.5/30) 15 Bkg Rate [counts/min] = 9.4 0.2 (Chi2/NDF = 17.1/21) 10 10 5 5 Counts/min Counts/min 0 0 21:50 22:00 22:10 22:20 22:30 22:40 22:50 21:50 22:00 22:10 22:20 22:30 Time Time Figure 5.3: Important Mrk 501 flares were recorded under moonlight conditions. The integrated flux lightcurves of Mrk 501 for the flare nights of June 30 and July 9 2005 are shown. time for Mrk 501 by MAGIC between May and July 2005 was 54.8 hours. This includes 34.1 hours of moon-time observations, i.e. 62% of the total observing time. Remarkable are the nights of June 30 and July 9 2005, when Mrk 501 was flaring and these observa- tions had to be performed under moonlight conditions [53].

Discovery of the most distant AGN 3C279 The AGN 3C279 was discovered as a flaring γ-ray source in 2007. The discovery was achieved during a time with about 25% under moonshine.

5.2 Observation time under moonshine

The main motivation for observations under moonlight condition is of course the exten- sion of the observation time. Previous reports differ a lot in their calculation for the prediction of additional observation time for moonshine observations. The VERITAS collaboration reports an extension of 100% compared to Whipple, when observations under moonlight are performed [48]. In [54], the extended observation time for MAGIC is expected to be 50%, namely 1500 hours per year compared to 1000 hours of dark time observations. In this section, the additional observation time is calculated, and the particularities are 5.2 Observation time under moonshine 45 discussed under which those observations can be carried out and bare the promise to yield better results.

5.2.1 Orbital parameters of the moon

In order to calculate the correct observation time, one first has to get familiar with the orbital parameters of the moon. The moon is the only natural satellite of the earth. Its orbit is gravitationally locked to the earth, thus always the same side of the moon is seen from earth. The moon circulates around the earth in a synchronous orbit, although the main gravitational potential is given by the sun. The center of gravity of the moon-earth system is still within earth’s radius. As seen from earth, the inclination of moon’s orbit is at 5.145◦ against the ecliptic inclination. Small variations, the so-called libration in the angle from which the moon is seen from earth, together with the inclined orbit, allow to see about 59% of its surface. The moon’s orbital eccentricity is 0.0549 at a mean distance of 384.4 × 103 km. The minimum distance of the moon w.r.t. to the earth is 363.3 × 103 km at perigee and its maximum distance at apogee is 405.5×103 km, which leads to a change of the brightness of up to 20%. The Moon’s diameter is 3,474 km, which corresponds to a diameter of ∼ 0.5◦ in the celestial sphere [55]. One astronomical year, which is one orbital period of the earth(/moon-system) around

Figure 5.4: Left: Illustration of moon phases as illuminated by the sun (inner circle) and cor- responding moon phases as seen from earth (outer circle). Right: Orbit of earth around the sun and the inclined moon orbital plane around earth. the sun, is 365.25 days. One orbital period of the moon is 27.3 days (which is one com- plete orbit around the earth). Thus one synodic period is 29.5 days. Taking the ecliptic inclination of the moon’s orbit into account, the sun-earth-moon system cannot be in the same constellation after one year. A good coincidence is found after one Saros-cycle: 1 this is a period of 18 years, 11 days and 8 hours (approximately 6585 /3 days). The moon does not emit radiation/light by itself, but only reflects light, mostly from the sun. As seen from earth, the moon has therefore phases, although the same side of the moon always points to the earth. A schematic drawing of lunar phases is shown in fig. 5.4. Those orbital parameters lead to some correlations of the moon phase and the moon celestial position as it is seen by an observer on earth. For example during new moon, 46 5. Observations with the MAGIC Telescope during Moonlight when the back-side of the moon is illuminated, the moon is only visible during daytime, but is never visible during night. Whereas around full moon, the moon is at the opposite site than the sun, as seen from earth, and thus a full moon is always in the sky during night. According to this, a first/last quarter moon can not reach highest altitudes during night, but only during daytime. Since the lunar orbital plane is inclined within 5.5% towards the ecliptic, and the moon altitude during night depends also on the observers position on earth, the maximum altitude the moon can reach during night at La Palma, is even the zenith during winter.

5.2.2 Xephem

XEphem is a free interactive astronomy program for UNIX-based systems and is dis- tributed with several linux distribution. Xephem stands for “X Window System + Ephemeris” and provides very precise ephemeris and permits simulations of almost all astronomical objects. In this thesis, Xephem is used for calculating the observation time under moonlight conditions. Also, the angular distance between the Crab Nebula and the moon was calculated for special constellations.

5.2.3 Observation time under moonlight conditions

Using the Xephem ephemeris package, a time period of one Saros-cycle was calculated. The position on the earth was set to the coordinates of the MAGIC experiment on the Roque de los Muchachos on La Palma at 28◦4504300N 17◦5302400W at an altitude of 2200 m above sea level. The starting time was set to January 1st 2001, 00:00 UCT. Every 5 minutes the moon altitude and phase, as well as the sun altitude is calculated. Night time is defined as the astronomical night, when the sun is below −18◦ altitude. The result of those calculations is shown in fig. 5.5, where the altitude of the moon is shown versus its phase and color coded is the corresponding cumulated time for each 2-D bin. One can see that the moon can not reach all positions, since some constellations are non-physical. An early moon cannot reach high altitudes during night.

A very conservative approach for calculating the observation time is illustrated in fig. 5.6. It is assumed that:

• One can always perform observations while the moon is below the horizon: in particular until the moon phase < 85%.

• Observations under moonlight conditions, i.e. the moon is above the horizon, are possible until(from) first(third) quarter moon, thus for moon phase < 50%.

• A “moon-break” is performed if the moon phase is > 85%.

Taking these assumptions into account, one first can calculate the total dark-night ob- servation time tDN. This is the period, when there is no moon present in the sky and 5.2 Observation time under moonshine 47

Moon Celestial Position at Night (Sun < 18deg) 90 180 80 160 70 140 Altitude [deg] 60 120

50 100

40 80

30 60

20 40

10 20

00 10 20 30 40 50 60 70 80 90 0 Phase of the Moon [%]

Figure 5.5: Moon altitude depending on the moon phase. Color coded is the time in 5 minutes per Saros-cycle (∼18 years) per 2D-bin. The moon can not reach the white area, since the phase and the maximum altitude per night are not independent. sun is below −18◦ altitude. Also a “moon-brake” is respected, when the moon phase is > 85%. This time can be used e.g. for maintenance, since there would be only very few observation time anyhow accessible. The total dark-night observation time per year is calculated to be tDN = 1600 h.

The moon-time observation time tMoon is defined as the time, when the moon is above the horizon, so the moon altitude is > 0◦. A conservative restriction to a moon phase < 50% is reasonable since a quarter moon has only ∼10% of the brightness of the full moon, and it will be shown in this thesis, that this will be accessible for γ-ray observations. The calculated moon-time per year is

tMoon = 300 h.

This corresponds to an extended observation time of 18% per year. If one takes more challenging assumptions into account, one can even reach more obser- vation time. It will later be shown, that observations under moonlight conditions are still possible up to an anode current of 6 µA. This is e.g. the case if the moon phase is at 70% and the angular distance from the moon is below 55◦. If one assumes, that observations until < 70% are possible, one calculates a moon-time of

tMoon = 550 h per year. This corresponds to an extension of the observation time of more than 30% as compared to the dark-night observation time. 48 5. Observations with the MAGIC Telescope during Moonlight

Figure 5.6: An assumed scenario for moonlight condition observations to calculate the address- able observation time. The small moon icons illustrating the corresponding moon phase shall guide the reader.

During twilight, when sun rises or sets down, also some extension of the observation time is possible, although the background light increases/decreases very rapidly. One can estimate, that around 10 minutes would be accessible for twilight observations. This results in a twilight observation time tTwilight of approximately

tTwilight = 80 h hours per year. The very rapidly changing background level during twilight would prob- ably lead to difficult observation conditions, different from slowly changing moonlight intensity. Especially the pedestal estimation and the correct setting of the discriminator thresholds could lead to difficulties. Altogether one would calculate therefore a maximum observation time of

tTotal = 2230 h per year. Of course, the above mentioned calculated observation time is normally re- duced by bad weather conditions or maintenance down time. During MAGIC observation cycle III, from May 2007 to May 2008, 350.1 hours of moon-time and 1109.4 hours of dark-time observations were performed. The scheduled dark-time observation time for 5.2 Observation time under moonshine 49 this cycle was 1650 hours, which resulted in an observation efficiency of 67.2%. The calculated results for the observation times are in excellent agreement with [56].

An interesting fact of moon-time observations can be seen in fig. 5.7. In this figure, the time period of the moon is shown depending on its altitude until a moon phase of 50%. Up to a moon altitude of zero degree moon is below the horizon and it is dark-night. But if the moon is above the horizon, the moon is for 80% of the time below 30◦ altitude and only for 20% of the moon-time the moon is at an altitude above 30◦. If the moon is at low altitudes, then the moonlight suffers from high atmospheric ex-

Moon below Moon above horizon horizon

80% 20%

Figure 5.7: The cumulated time per year of the moon position during night as a function of altitude. The moon phase is restricted to < 50%. If the moon is above horizon, it is for 80% of the time even below 30◦ altitude, which, in addition, implies strong attenuation of the moonlight by the atmosphere. tinction. In first order, the atmospheric density follows like 1/cos2φ, where φ being the zenith angle. This concludes that even less background light from moonlight is expected for most of the moon-time observations. Furthermore it motivates to understand the moonlight intensity under low altitudes. Following this idea, a model describing the stray light from the moonlight was developed, where a certain focus was set to early lunar phases and low moon altitudes. This model is presented in chapter 6.

With the calculated numbers from Xephem, also a moon “calendar” can be created. Fig 5.8 illustrates the time period from January 11 to May 08 2009. The moon calendar shows the moon phase, the maximum moon altitude and the predicted brightness of the moon during nights and for the location of the MAGIC telescope. 50 5. Observations with the MAGIC Telescope during Moonlight

One can see, that around new moon, the moon is never in the sky, while during full

Phase of the Moon [%] 100 Maximum Altitde of Moon per Night [deg] Altitde of Moon if above horizon [deg] Maximum Brightness of moon per Night [scaled] Brightness of moon [scaled] 80

60 Various (see legend) 40

20

0 22/01 05/02 19/02 05/03 19/03 02/04 16/04 30/04 Date 2009

Figure 5.8: “Moon calendar” for spring 2009. The red line shows the phase of the moon [%]. The black line/counts indicate the maximum altitude of the moon per night [deg] and thus the minimum atmospheric attenuation. The green counts indicate the moon altitude every 10 min [deg]. The maximum brightness of the moon per night according to [57] and taking the lowest atmospheric attenuation into account [scaled: full moon = 100%] is shown in violet. moon the moon is always above horizon. In “between”, the moon does not reach high altitudes during night. Furthermore one can see, that a quarter moon only has 10% of the brightness of full moon and atmospheric extinction further decreases the brightness of the moon. In Appendix A, the moon calendars for 2009 and 2010 are attached.

A practical application for the moon calender is e.g. the optimization of the “shadow” of the moon. For observations of the moon shadowing of charged cosmic ray particles, particularly, electrons and positrons, e.g. for dark matter studies as proposed in [58], one needs to know the maximally possible observation time for quite small lunar phases, but also high altitudes. Since the MAGIC energy threshold increases with larger zenith angles an altitude of ≤ 40◦ would be desirable. The almost exponential rising brightness according to the moon phase would on the other hand strongly recommend very small moon phases. Using the moon calendar, one can now estimate the possibility for such observations and also calculate the possible observation time. First calculations with the assumptions of a minimum moon altitude of 40◦ and a maximum phase of 50%, gives the maximum addressable observation time in 2009 of only 29.5 h and in 2010 of only 27.2 h for “moon shadow” observations. Those calculations are performed in more detail, taking also the predictions of the “moon model” into account.

5.3 Considerations for observations with MAGIC during moonshine

Several hardware components are affected when performing observations under moon- light conditions. Throughout the signal chain, changes may appear or have to be consid- ered. Some components already are designed to allow for observations under moonlight 5.3 Considerations for observations with MAGIC during moonshine 51 conditions. Here the influence of increased background is discussed for relevant telescope subsystems.

5.3.1 The photomultiplier tubes

The camera was designed specifically to perform observations under moonlight condi- tions. For the camera low gain PMTs are selected. The 6-dynode design of the PMTs prevent the last dynode from too much damage in case of a large light level such as observing the galactic center or observing during moonshine or dusk or dawn. The spectral sensitivity is optimized for blue wavelengths. It is not necessary to reduce the high voltage except during bright moonlight or observations close to the moon. The PMT anode current is directly proportional to the number of photoelectrons produced by the night sky background, i.e. the anode current is a measure of the night sky light background multiplied by the quantum efficiency (QE) of the photocathode (corrected by the spectral parameters of the mirror, the camera window and the reflectivity of the light catchers in front of the PMTs). The allowed threshold for observations is currently at a DC value of 8 µA. Only at prolonged currents far above 50 µA permanent damage of the PMTs is expected. In MAGIC, PMTs with currents higher than 30 µA are auto- matically switched off. As noted, the low gain of the PMTs is recovered by AC (=capacitative) coupled pream- plifiers to be raised to close to 106 gain. The AC coupling suppresses the DC component of the steady signal from the flux of the night sky light background1, thus only the fluc- tuations, proportionally to the square root of the flux, are coupled to the discriminator inputs to generate a trigger signal. It is therefore obvious that increased moonlight will nevertheless increase the probability to accidentally “fire” the discriminators and in turn start the event recording. In case of very high background levels the accidental trigger rate might rise well above the maximally allowed trigger rate and eventually completely “choke” the readout system. Therefore, the trigger thresholds must be increased even if some good low energy events are lost.

5.3.2 L0-Trigger

The discriminator thresholds are adjusted by the so-called IPR (individual pixel rate) control. This circuit loops continuously over all channels and registers the individual pixel rate after the discriminator thresholds (DT). If this rate is too high, the DT for any individual pixel is increased to set back the L1-trigger rate to around 200 Hz. This algorithm was initially developed to decrease accidental triggers in channels with a bright star in the field of view. A prominent example is“ζ Tauri” (B magnitude: 2.8 [59]), at around 1◦ angular distance from the Crab Nebula, e.g. still in the trigger area when observing the Crab. By chance, the IPR control also adjusts the DTs during moonlight to a reasonable level

1Here I add in the following discussions the contribution of the moonlight to the night sky light back- ground. 52 5. Observations with the MAGIC Telescope during Moonlight that a L1-trigger rate of 200 Hz is guaranteed.

5.3.3 L1-Trigger

The currently used L1-Trigger logic in MAGIC is a “four next-neighbors”-trigger (4nn). If four close packed next-neighbors have a coincident L0-signal within a time window of ∼5 ns, the DAQ is triggered. Furthermore, a 3nn and a 5nn trigger logic is also in the hardware trigger logic and can be used on demand. However, the 3nn-logic trigger is difficult to adjust and is normally triggering too frequent and is therefore not used, while the use of the 5nn trigger logic is still under discussion. The difference of the 4nn and a 5nn trigger logic under moonlight conditions were

105

4nn Trigger

104 L1-Trigger rate [Hz]

5nn Trigger 103

max. DAQ rate

102

5 10 15 20 25 30 Level-0 | Discriminator Treshold [mV]

Figure 5.9: The L1 trigger rate [Hz] depending on the discriminator threshold settings DT [mV] under moonlight conditions (DC = 2.3 µA). The blue line shows the standard 4- next-neighbor trigger logic. The red line shows the 5nn trigger. The maximum DAQ frequency of 200 Hz is marked with a green dashed line. measured by T. Schweizer. Fig. 5.9 shows the L1-trigger frequency depending on the DT thresholds during moonlight observations (a mean anode current of DC = 2.3 µA was measured) for the 4nn-logic and the 5nn-logic. A change of the slope of both curves sets in at a certain DT level when the accidental triggers start to dominate. An optimal trigger should be set to this “kink”. The DTs are set correctly, either at the kink (if one puts priority in preventing accidental triggers) or preferable at the maximum DAQ rate of 200 Hz. Nevertheless, for both nn-logics the amount of triggered showers are on a comparable level. 5.3 Considerations for observations with MAGIC during moonshine 53

5.3.4 Pedestals

In the following I want to mention a problem linked to the baseline of the F-ADC readout when observing in the presence of moonshine. As one can see in fig. 5.10 the baseline amplitude in the absence of any signal is not at zero. This shift is called pedestal and is normally adjusted on purpose in the construction in order to allow also small negative fluctuations below the zero value. Under moonlight conditions, it is expected, that the fluctuations of the pedestal, the so-called pedestal RMS, increase (in first order with the square root of the anode currents). On the other hand the peak value of the averaged pedestal is slightly dropping because

Figure 5.10: Contributions to pedestal RMS in a pixel. During dark night observations, the NSB pulses lead to a low pedestal RMS level, while high background light levels, e.g. under moonlight, lead to a high pedestal RMS in each pixel. of the distribution of the pedestal values in all the consecutive time slices is asymmetric due to a Poisson distribution of the night sky photon arrival. The situation might become more complex. As the night sky photons might be so frequent that they follow within the system time resolution a Gaussian distribution and the averaged pedestal value ap- proaches the same value as if the PMTs are switched off. If the night sky light flux increases further the fluctuations might become larger than the preset pedestal value. As a consequence the averaged pedestal values shift upward because of the truncated negative fluctuations. Normally, the preset pedestal values can drift; therefore they have to be monitored constantly by taking so-called pedestal runs. The MAGIC DAQ sys- tem makes use of pedestal runs and of interleaved pedestal event triggering. During a pedestal run, events are triggered by a random signal and contain no Cherenkov pulses. The interleaved pedestal events, i.e. events without Cherenkov light, are triggered au- tomatically with a frequency of 25 Hz (50 Hz) and are written also onto disk. After 500 pedestal events, thus after 40 s (20 s) the resulting pedestal is calculated for each channel. Fig. 5.11 shows the pedestal and the pedestal RMS for each single pixel, while observing under bright moonlight conditions. The blue dashed line indicates dark night pedestal RMS level. Inner and outer pixels have different reference values, due to lower gain but larger collection area of the outer pixels. Three components sum up in one channel: pulses from Cherenkov light, NSB pulses (single photoelectron pulses) and electronic 54 5. Observations with the MAGIC Telescope during Moonlight noise. During moonlight observations, the pedestal does not increase according to the NSB level because of the AC coupling of the preamp. Actually, the mean pedestal level will drop a bit because of the asymmetric distribution (Poission distribution) except at very high background levels, as shown in the picture, where the fluctuations become symmetric and Gaussian. The determination of the pedestal ensures, that the resulting “size” ( = amount of

Mean Pedestal 500 Pedestal RMS 3500 Dark night 450 Dark night 400 3000 350 2500 300 250

2000 [cts/slice] 200 P [cts/slice] rms

P 150 1500 100 1000 50 0 0 100 200 300 400 500 0 100 200 300 400 500 Pixel Index Pixel Index

Figure 5.11: The mean pedestal (left) and the pedestal RMS (right) of all pixels in the MAGIC-I camera under bright moonlight conditions. The dotted line indicates the common dark-night level. The mean pedestals are comparable to dark night observations, while the pedestal RMS increases during moonshine observations due to the in- creased NSB rate. photoelectrons ) of the Cherenkov light pulses is not affected by moonlight, and thus in principle the Hillas parameter size holds:

hsizedarknighti = hsizemoontimei.

This assumption is also confirmed later in this thesis, using Monte Carlo simulations (see fig. 7.11, though there are analysis cuts applied). This further implies, that the same procedure for the energy estimation of the primary particles can be used during moonlight observations like under dark conditions, since the energy is in first order pro- portional to the size.

Actually, the pedestal RMS would also be in zeroth order an excellent measure for the night sky background level, provided that the spectral shape does not change. This is, of course, not true when comparing the dark night light flux form the galactic plane and outside the galactic plane and the scattered light from the moon. The former differences are small while the scattered moonlight is quite frequent. The dark night increases dramatically in the “red” and IR and has even some line enhancement (sodium line), while, as already mentioned, the sky light during full moonshine is strongly blue- enhanced like during a sunny day. This is the consequence of Rayleigh scattering. While the “blue” night sky is not visible for the human eye, one nevertheless observes a red colored moon close to the horizon, similarly as for the sun during sun setting. The pedestal RMS is proportional to the anode currents like √ pedrms ∝ DC. 5.3 Considerations for observations with MAGIC during moonshine 55

Fig. 5.12 shows this square root proportionality for an already increase background level measured during two nights.

5

4 Median Ped RMS 3

2

1

0 0 1 2 3 4 5 6 MedianDC [µA]

Figure 5.12: The pedestal RMS as a function of the median DC current [µA] during moonlight observations.

5.3.5 Further motivation for studying moonlight observations

Besides the increased observation time of steady state sources and to enhance the chances to observe rapid flares or rare GRBs, there are also further reasons, which motivate the study of moonlight on observations with MAGIC.

Light of the night sky A comprehensive understanding of the light of the night sky is of certain physical inter- est. Besides some well understood phenomena like aurorae and zodiacal light, I think that also the moonlight deserves some attention in this context.

Data analysis The study of the influence of moonlight on VHE γ-ray observations, further provides the opportunity for a better understanding and a possible improvement of dark night observations. Although this was not the aim of this thesis, there can be a method de- rived for lowering the energy threshold during dark night observations.

Physics results There were already many physics results published with data taken under moonlight conditions so far. It is of great importance, that the past applied analysis methods for those results have to be proven to be correct (or not). 56 5. Observations with the MAGIC Telescope during Moonlight 6 A Model for Estimating the Brightness of the scattered Moonlight

In this chapter a model for estimating the diffuse background light from moonlight is pre- sented. It is inspired by the model presented by Krisciunas and Schaeffer in 1991 [60], but includes several improvements. Besides the atmospheric attenuation, the moon phase and the angular distance, it also takes into account the moon distance from earth. The atmosphere was comparably thinner than in the above mentioned paper, but still around 5 times denser than expected from optical measurements. Furthermore it is the first model holding already for a moon altitude > 1◦ and was proven work for small moon phases. For the brightness of moonlight at small phases, no reliable data could be found since this is highly dominated by atmospheric extinction at small altitudes. The model takes Rayleigh and Mie scattering into account, while for small separation angles ρ < 10◦, probably also reflections from the telescope structure become significant and must be taken into account in future improvements. The model can be used for an optimized schedule or for automated Monte Carlo simu- lations. It is further an interesting and new study for extreme conditions (small moon phases and very small altitudes), which have concrete scientific applications. E.g. [42] took advantage of such predictions according to Krisciunas and Schaeffer. This model calculates the anode currents for given moon phase, moon zenith angle, moon distance from earth and the separation angle from the pointing position. The DCs are proportional to charge recorded by the PMTs (phe/ns/pixel).

6.1 Light of the night sky

The night sky light background (NSB) is one of the main factors limiting the threshold of large atmospheric Cherenkov telescopes [61]. In the literature one finds two different abbreviations for the night sky background (NSB) light, respectively, the light of the night sky (LONS), I will use both abbreviations, but I will refer to night sky background (NSB) light if the detection of Cherenkov light is the aim. LONS has several components [62]:

• Zodiacal light

• Direct star light

• Airglow

• Aurorae 58 6. A Model for Estimating the Brightness of the scattered Moonlight

• Diffuse galactic star light

Here, also following components are added to LONS:

• Moonlight

• Direct and backscattered man-made artificial light

While zodiacal light is very weak or even negligible during astronomical quality nights and aurorae are rare phenomena, the main components of NSB is direct and scattered starlight and airglow. Many publications measure the LONS intensity for a limited spectral range, e.g. [63] reports an intensity of 6.4×1011 ph/m2/sr/s for a limited spectral band of 430 - 550 nm. The spectral sensitivity of the used PMTs in MAGIC ranges from 200 - 700 nm with a peak sensitivity around 380 nm. The maximum quantum efficiency is 30% [64]. PMTs are basically only counting the number of photoelectrons (phe) converted from photons. It is not physical to calculate any number of photons per m2/sr/s since there is no reliable information about the incident spectrum. Following the advice from [61], ”It is probably best to measure the intensity of LONS directly for a given detector at the site where it is operated”, an intensity is not unfolded from the measured data, but only the appearing background for the (given) detector is determined. For moonlight this is in particular reasonable, since the spectrum changes with altitude, because of the strong wavelength dependence of the atmospheric scattering. This is well known from daily life, when seeing red moon rising (low altitudes) while seeing a very bright, almost blue, moon at high altitudes. However, a value for the intensity of LONS around the order of

LONS ∼ 2 · 1012ph/m2/sr/s. has been measured for dark sections of the night sky after subtracting direct starlight on La Palma and in the spectral range of 300 - 600 nm [61].

6.2 The anode current readout and data selection

The anode currents (DCs) are monitored throughout the measurements, as described in section 3.2. Only the inner pixels with a field of view of 0.1◦ are used to measure the background level. To neglect impacts from hot pixels, or stars, or different gains, the median out of all 396 pixels is calculated, and to suppress impacts from car light flashes, airplanes or satellites, the mean over one minute is determined. This mean anode current value serves as the direct measure of the LONS/NSB including the scattered moonlight. The anode current can be converted to the number of recorded photoelectrons per pixel since both values are proportional. The PMTs have a typical amplification gain of K ≈ 3 · 104. The electron carries a charge of

1e = 1.602 × 10−19C. 6.3 Theoretical assumptions 59

Hence, one can calculate the relation between photoelectrons per nanosecond and the anode current I to: I 0.208 I ≈ 1.0µA = · 10−9 ≈ . (6.1) K · 1.6 · 10−19C ns

For the data selection it was tried to include as much data as possible, from galactic and from extragalactic observations. Also very different moon phases and angular distances from the moon were selected. As a representative for a galactic source, the Crab Nebula was chosen. A typical extragalactic source that was observed for a long time under moonlight conditions is the AGN Mrk 421. Hence, data from 27 nights of Crab Nebula observations and 17 nights of Mrk 421 observations between February 2007 and May 2008 were investigated. The selected data is summarized in the following table:

Analyzed Data Crab Nebula Mrk 421 Total observation time under moonshine 38.6h 37.7h from Feb 2007 until May 2008 (source Zd < 45◦) After bad weather and twilight cuts 36.2h 34h Direct currents (DC) (median of all inner pix- 0.8-5.7µA 0.6-8.1µA els, mean value of one minute) Moon phase F 5% − 53%(80%) 13% − 78%(94%) Separation angle ρ 25◦ − 130◦ 30◦ − 113◦ Moon altitude 0◦ - 55◦ 0◦ - 65◦

6.3 Theoretical assumptions

A full theoretic modeling of the illumination from the moon has to take many pa- rameters into account. At first, the spectrum and the intensity of the moonlight with changing moon phases must be known. Then, the atmospheric properties (like density and composition) should be well known to take all possible single and multiple scatter- ing cross-sections for different wavelengths correctly into account. Furthermore, also the properties of the measurement instrument must be considered, here, the spectral mirror reflectivity, light catchers, and the PMTs spectral sensitivity. The measured number of photoelectrons is the result of a multidimensional integration over local scatterings in the atmosphere over the viewcone of the telescope and the mir- ror are, multiplied by the initial intensity folded by various loss mechanisms. Fig. 6.1 shows the sketch of the analytic calculation of the scattered light if multiple scattering processes are excluded. The moon is assumed as a point source at an infinite distance.

Starting with a differential scattering volume (at R) at a distance h away from the position on ground. In this volume dV light from the moon is scattered. This light is the remaining light after scattering losses along the path through the atmosphere (along MR) before entering the differential scattering volume. Because of the large distance of the moon the scattering angle is always the same, i.e. independent of the height. 60 6. A Model for Estimating the Brightness of the scattered Moonlight

Moon

M

R ε1 dV h ρ ε2

G Ground

Figure 6.1: Calculation of the intensity of scattered moonlight if multiple scattering is excluded. See the text for a detailed description.

The scattering process in the differential volume at the position x = h can be either Rayleigh or Mie scattering. By using the appropriate differential cross sections

dσ(x, λ) dσ (x, λ) dσ (x, λ) = M + R , (6.2) dΩ dΩ dΩ the density %(x) at x and the angle of observation ρ w.r.t. the incident moonlight direction one can calculate the scatter probability into the direction of the pixel.

• Firstly, an incident illumination is supposed with an intensity I0(λ),

• then atmospheric attenuation takes place before reaching the differential scatter volume dV at point h (at R), resulting in a reduced intensity

−1 Ih(h, λ) = I0(λ)e , (6.3)

where Z R Z dσ(x, λ) 1 = %(x)dΩdx. (6.4) M 4π dΩ

• Then, with a certain probability a scattering process (Rayleigh or Mie scattering) occurs in dV into the direction of the telescope with the differential cross section dσ(x,λ) dΩ . Only the light which is scattered into the direction of the mirror area AM has to be considered. Therefore, the differential cross-section has to be integrated over the solid angle Ω depending on h and AM which can be estimated roughly by

2 Ω ∼ AM /h (6.5) 6.3 Theoretical assumptions 61

. This multiplies the intensity Ih with a factor of Z dσ(h, λ) %(h)dΩ. (6.6) Ω dΩ

• Then, the scattered light suffers a certain probability of scattering between (R) and (G) before reaching the camera, which gives a factor of e−2 , with

Z G Z dσ(x, λ) 2 = %(x)dΩdx (6.7) R 4π dΩ

• The product of all those processes gives now the number of photons from a small volume at h and atmospheric density %(x) with the differential cross-section dσ dΩ (x, λ) scattered onto the instrument. • Next, it has to be integrated over the atmospheric volume V along the line of sight.

• Finally, the intensity has to be folded by the spectral performance of the mir- ror, camera window and light catcher and the spectral sensitivity of the PMTs1, which is here all called together collection efficiency C(λ), and integrated over the sensitivity range of the PMTs (300 - 700 nm).

The measured intensity in number of photoelectrons reads:

Z Z Z dσ(h, λ) I = C(λ) %(h) · I (λ) · e−1 e−2 dΩdV dλ (6.8) dΩ 0 λ V Ω where, λ must be integrated over 300 - 700 nm. Correctly, the attenuation parameters 1 and 2 should take, besides the scattering cross-sections, also the possible absorption into account. Very forward scattering which would lead to higher absorption factors  could be considered in the appropriate differential cross sections.

There exists now a fundamental problem: not all parameters of the incident light (like the spectral distribution, or moon albedo variations) and the scattering process (for ex- ample the Mie scattering process or the atmospheric density distribution) are precisely known. Therefore I tried to replace the multidimensional integration, whenever possible, by constants fitted from some observation data. For example to avoid the integration over the roughly exponential atmospheric density distribution, I replace the atmosphere by a constant density homogenous layer of air of 40 km height. In the following I will discuss the different components and approximations.

Restrictions on the atmospheric modeling and the atmospheric scattering have to be introduced for simplicity reasons. The measured data is recorded over more than one year, therefore short-term variation of atmospheric conditions and also “exotic” effects like calima are neglected. Therefore, it is assumed, that the atmospheric conditions are

1Correctly the PMT photon detection efficiency 62 6. A Model for Estimating the Brightness of the scattered Moonlight constant. For the modeling of the scattering of the moonlight the following basic and reasonable assumptions are made:

1. Light is scattered only once inside the atmosphere (at least for larger scattering angles > 10◦).

2. Only light, which is scattered in the view cone of the telescope, is recorded by the camera.

3. The opening angle of the field of view of the PMT (0.1◦) can be neglected.

4. The source position is preferably at small zenith angles.

5. Only light between 300 and 700 nm is considered.

If light would scatter multiple times in the atmosphere, we probably could not do astron- omy, since the scattering cross-sections in the atmosphere must be much larger. Only for short wavelengths and small scattering angles this assumption is not completely ful- filled. The second assumption is just a result from simple geometry and optics. The telescope only focuses light inside the view cone to the camera. The third assumption is introduced mainly for simplicity reasons, but leads to the fact, that the scattering angle is equal to the separation angle, which is the angle between the pointing position and the moon ρseparation angle = ρscattering angle ≡ ρ. The forth assumption for this model comes from the IAC technique, since large zenith observations increase the energy threshold and makes the energy estimation more dif- ficult. However, this ensures that the line of sight, thus the scatter volume V , where scattering might take place, is not changing significantly. This means, that the integra- tion over the scatter volume always lead to a similar constant value.

Following the above assumptions, the problem can be divided into a few independent parts as illustrated in fig. 6.2. It was tried, to find a very simple formula, which still is capable of describing the problem in a comprehensive way. The ansatz for the brightness of the scattered light from the moon, which is measured with the anode currents of the PMTs reads then:

IDC (Zm, F, d, ρ) = NSBg/eg + c · B(F, d) · E(Zm, β) · R(b, g, ρ) (6.9) where NSBg/eg is the dark-night background light level without the scattered moon- light in the direction of the observed γ-ray source, Zm is the zenith angle of the moon (Zm = 90◦ − altitude), B is the incident brightness of the moon, dependent on moon phase F and its distance d from the earth, as it would be measured in a direct mea- surement and the moon being always at the zenith. The atmospheric attenuation E is dependent on the zenith angle of the moon and has in the chosen atmospheric model only one parameter, the atmospheric height h2, that has to be determined. Here, also the important assumption is included, that all the extenuated light does no longer contribute

2The parameter h is here different from before, where it was the height where the scattering takes place. 6.4 The brightness of the moon 63

Source Moon B(F,d) NSB

R(ρ;b,g) E(Zm;β) ρ

Ground

Figure 6.2: Schematic drawing of the moon model. The moon “emits” light depending on lunar phase and the distance from earth (B). Then, the light is absorbed in the atmosphere depending on moon altitude but independent on atmospheric changes (E). The residual light is scattered in the line of sight of the telescope (R). Mie and Rayleigh scattering is taken into account and the scattering angle is equal to the angular distance of the pointing position and the moon. to the finally measured scattered light, since it is assumed, that light is only scattered once in the atmosphere. Furthermore, it is important to mention, that also the extinc- tion that takes place between the differential scattering volume and the ground is also included in this parameter E. This is reasonable, since the volume of the view cone is almost constant, since the observation is restricted to small zenith angles. The scatter- ing process in the scatter volume takes two scattering mechanisms, namely Rayleigh and Mie scattering, with simplified formulae into account and is dependent on two constants (b, g), which have to be determined, as well as on the scattering angle ρ. Also one free scaling constant c has to be determined, which respects all the effects from the parameter C(λ). Besides the to determined (atmospheric) parameters, some input for modeling the scat- tering from moonlight have to be known before. The zenith angle of the moon, as well as the moon phase and the distance d for the time of the observation have to be known and are the input to fix B(F, d). Therefore the model finally only depends on the date of the observation and the source position in the sky.

6.4 The brightness of the moon

The brightness B of the moon depends in first order on its phase F . Throughout this thesis, the moon phase is defined as its illuminated fraction. In astronomical publica- 64 6. A Model for Estimating the Brightness of the scattered Moonlight tions, often the phase angle is used. This is the angle between the earth and sun, as seen from the moon center. On the contrary, some publications prefer the elongation, which is the angle between the moon and the sun as seen from the center of the earth. Fig. 6.3b shows the correlation between those three factors. The illuminated fraction (the moon phase), is defined as 1 ± cos φ F = , (6.10) 2 where φ is the phase angle or the elongation, respectively, and is mostly given in units of % of full moon. The brightness further depends on the moon distance d from earth. This is calculated

×103 450 100

400 90 Phase angle as seen from the moon 80 350 Elongation | Angle seen from earth' center

Distance [km] 70 300 60 250

Illuminated Fraction (%) 50 200 40 150 30 1-cosφ 1+cosφ F = F = 100 20 2 2

50 10

0 22/01 05/02 19/02 05/03 19/03 02/04 16/04 30/04 00 20 40 60 80 100 120 140 160 180 Date 2009 [Day/Month] Angle (deg)

Figure 6.3: Left: Distance of the center of the moon to an observer on La Palma during spring 2009. Right: The moon phase is defined in this thesis as the illuminated fraction of the moon. The correlation of the moon phase to the “phase angle” (red) and the elongation (green), which is the angle between moon and sun as seen from earth is plotted here. for spring 2009 in fig. 6.3a. The very small changes in this picture belong to the rotation of the earth. This distance changes the brightness like 1 B ∼ . (6.11) d2

Only two references for the brightness of the moon for low moon phases could be found. A widely used polynomial of 4th order can be found in [57]. The second reference is of tabulated form by Bond and Henderson [65]. There, two different values for the waning and the waxing moon was measured. This is due the to moon’s different albedo in the range from 0.04 to 0.14 for different regions on moon’s surface [66]. Both measurements are shown in fig. 6.4a. The formula given by [57] is expressed in V-magnitudes m. According to [68], this is converted to footcandles like:

−0.4(m+16.57) BAllen = e (6.12) where e = 2.7182 is euler’s number and m is the V-magnitude from [57]:

m = −12.73 + 0.026|φ| + 4.0 · 10−9.0φ4. (6.13) 6.4 The brightness of the moon 65

1

0.9 Allen (polynomial fit) Bond Henderson for Waxing Moon 0.8 Bond Henderson for Waning Moon Applied brightness model 0.7

0.6

0.5

0.4 Brightness (scaled to full moon) 0.3

0.2

0.1

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Moon Phase

Figure 6.4: Left: Brightness of the moon depending on the moon phase scaled to full moon. Two models are shown here [57, 65]. In this thesis an adapted model is used and the brightness is scaled to the quarter moon (red dashed line). Right: A very precise measure out of over 40,000 pictures adapted from [67]. A scaling to full moon is difficult, since the opposition effect takes place. Reliable data on irradiance for low moon phase (F<50%) is difficult to measure. The calibration of the instrument is very complicated since for low altitudes the attenuation is non-negligible and the moon spectrum is different compared to most star spectra.

Here, exceptionally the phase angle φ is used. φ is calculated depending on moon phase as equation (6.10) implies: φ = arccos (2 · F − 1). (6.14) However, I recognized, that this formula underestimates the brightness specially for low moon phases and thus a scaling of this formula is introduced, which adapts the brightness to the parameters as measured by [65]. Formulae 6.12 is adapted, using a parameter α like α·(−0.4)·(m+16.57) B1 ∝ e , (6.15) while this also changes the constant c, however, that will be estimated later when the absolute scaling is performed. The rather ad hoc estimation of the scaling parameter lead to a factor of α · 0.4 = 0.85 and thus α = 2.125 (6.16) and leads to the (scaled to full moon) brightness as shown in fig. 6.4. Thus, the incident illumination depending on lunar phase is:

−0.85·(3.84+0.026φ+4.0·10−9.0φ4) B1(φ = arccos(2 · F − 1)) = e (6.17)

The index ”1” indicates, that this brightness is already measured on ground, i.e. passing one airmass.

Differently to both brightness models the brightness in this study is scaled for consistency to the quarter moon (i.e. differently to fig. 6.4) which only changes the yet to determined constant c. This prevents unphysical scaling in some extreme cases. As fig. 6.4b shows, because an additional effect is contributing to the brightness of the moon, which is not 66 6. A Model for Estimating the Brightness of the scattered Moonlight included in above mentioned models. Close to full moon, the so-called opposition effect takes place. This means, that e.g. from a phase angle of 4◦ to 0◦, the brightness increases by 40% [69, 70]. This effect must not be considered here, since γ-ray observations are only performed under moderate moonlight, i.e. well below full moon. The very precise measures from fig. 6.4b also show, that it is indeed very hard to perform reliable mea- surements of the moon brightness for small moon phases. Also the different brightness of the waning and the waxing moon can be recognized in this figure, which confirms the measurements by Bond and Henderson that lead to my brightness estimation.

6.5 Atmospheric attenuation of the moonlight

As I could not find in the literature any direct measurements of the altitude dependence of the attenuation of the moonlight a well-measured star light attenuation was used. The atmospheric attenuation is the extinction of light in the atmosphere resulting from scattering and absorption processes. The atmospheric attenuation is derived from mea- surements of the star Vega which has in first order a similar specrum as the moon light and does not change from day to day. The mean visible extinction in magnitudes is given by [71]: E(Zm, β) = β · (X(Zm) − 1). (6.18) Where X(Zm) is the zenith angle dependent airmass, which is the relative integrated density of the atmosphere and it is defined to be unity at zenith. The atmospheric parameter β depends on the atmospheric conditions and is wavelength dependent, but according to the assumptions, this parameter has to be determined as a constant. Transferring equation (6.18) from magnitudes to linear units, the atmospheric attenua- tion reads: −β·(X(Zm)−1) E(Zm, β) = 10 2.512 . (6.19) The horizontal airmass in the visible spectrum is around 38. At small zenith angles, the airmass up to the top of the atmosphere evolves like 1/cos2(Zm), but since most of the observation time is at low moon altitudes, the atmospheric attenuation for the moonlight has to be ascertain very precise. A slightly different airmass model of a different density distribution as a function of height affecting optical (or V-band) measurements is ex- pected, since the PMTs are most sensitive in the blue wavelength region. In literature, several airmass models are discussed. Some interpolative formulae are derived from the “plane parallel” model, which is X(Zm) = cos−2(Zm), which can be found for example in [72] or [73]. For compari- son, those models are also shown in fig. 6.5. However, those atmospheric models did not lead to good results and thus, a different approach, namely the assumption of a homogenous spherical atmosphere is followed. This model can be analytically calculated very easily from geometrical considerations and one free parameter for the atmospheric height has to be determined. The airmass formula for a homogenous atmosphere reads: s  2 Rearth 2 h h Rearth Xh(Zm) = · cos (Zm) + 2 + − cos(Zm) (6.20) h Rearth Rearth h 6.5 Atmospheric attenuation of the moonlight 67

The estimation of the parameter h was performed in a quite experimental way, but this value will be discussed later and will show up to be quite precise.

Airmass models Atmospheric Attenuation | Scattering 40 Rozenberg Young and Irvine 0.9 35 Plaine-parallel Atmosphere | 1/cos(x) Krisciunas Schaefer (simplified Garstang) Analytic Model, 8.65km LaPalma density 0.8 30 Analytic Model, 40km LaPalma density Analytic Model, 100km LaPalma density 0.7 Bemporad 25 0.6 Attenuation to Zenith 20 0.5 Airmass scaled to Zenith

15 0.4 beta = 0.080 0.3 beta = 0.120 10 beta = 0.160 0.2 5 beta = 0.200 0.1 0 60 65 70 75 80 85 90 60 65 70 75 80 85 90 Zenith Angle (deg) Zenith Angle (deg)

Figure 6.5: Left: Different discussed airmass models of integrated density distributions as a function of the zenith angle. Most observations under moonlight conditions with MAGIC take place, when the moon is at low altitudes (here high zenith angles). The model with the best results is the analytic model with 40 km homogenous densitiy (pink dashed). Right: Different atmospheric attenuation parameters. Since regular observations with MAGIC usually take place during clear night, the parameter could be determined to be constant at β = 0.145.

Firstly, the dark-night NSB background NSBe/eg was determined by fitting a gaussian to the anode current data, when there was no moon present. The night sky background was found to be NSBgalactic = 1.05µA (6.21) and NSBextragalactic = 0.67µA (6.22) for the galactic and extragalactic data sample, respectively. Those values are subtracted in the following, since one is only interested in the moonlight intensity. The widely accepted height of the atmosphere is ∼100 km, but with an exponential den- sity distribution. One now can integrate over the so-called US-standard atmosphere [74] at the MAGIC site, i.e. which is also used for the Monte Carlo simulation, from an altitude above 2200 m. This would result in a homogenous atmosphere with a height of 8.65 km. However, since the spectral sensitivity of the PMTs peaks in the blue wave- lengths3 and also attenuation between the actual scatter process and the ground has to be considered in this term, a higher value than 8.65 km is expected, but still lower than 100 km. Following the experimental approach, the idea to determine the atmospheric height is shown in fig. 6.6. For all the 44 nights of observation, the expected atmospheric attenua- tion is re-calculated. Thereby, many parameters between 8.65 - 100 km were tried. The region one has to focus on to determine the best parameter h, is especially the resulting value at low altitudes. If a wrong atmospheric density is assumed, the “zenith corrected data” shows an extreme value for small altitudes, especially very different from the value

3The Rayleigh scattering cross-section is proportional to the light frequency like σ ∝ ω4. Therefore, light with shorter wavelengths is more likely absorbed. 68 6. A Model for Estimating the Brightness of the scattered Moonlight

Zenith Moon, CrabNebula 02.11.2007 5 A] Monitored DC Data 4.5 Zenith dependence corrected data DC [ NSB Galactic 4 Zenith Attenuation [#]

3.5 Zenith corrected data

3

2.5 monitored DC data

2

1.5 subtracted NSB level 1 atmospheric attenuation 0.5 different scale: [ratio] 0 30 40 50 60 70 80 90 Moon Zenith [deg]

Figure 6.6: Crab Nebula observations during November 2nd 2007 and rising moon (moon phase = 48%). The recorded anode currents [µA] depending on the moon zenith angle is plotted in blue. A change of the order of some percent is observed. This is the consequence of the change of the wobble position every 20 minutes. The zenith correction according to the model is sketched in green, an applied on data in black. The atmospheric attenuation model is valid up to almost 90◦. of higher altitudes, where the atmospheric attenuation is not so strong. One value for the atmospheric height h was found to lead to good results. This best value was

h = 40 km, (6.23) where the data could be corrected up to the horizon for almost the full data. This precision can be seen in fig. 6.9 and is discussed later in more detail. The influence of the parameter h on the atmospheric attenuation is also shown for three values (h = 8.65, 40, 100 km) in fig. 6.5.

Once the atmospheric height is determined, also the atmospheric parameter β can be determined. This was performed, by fitting the expected curve to the measured anode currents. The effect of different parameters β is sketched in fig. 6.5. All the parameters β for the best fit are shown in fig. 6.8 separately for the Crab Nebula and the Mrk 421 data set. Not from all nights, reliable fits for the atmospheric parameter β could be determined, since at least an observation of more than one hour is necessary for a reliable fit. However, from fig. 6.8, it can be seen, that the parameter β best fits around:

β = 0.145 (6.24) 6.6 Rayleigh and Mie scattering 69

Atmospheric Attenuation 1

0.9

0.8

0.7

0.6 Attenuation to Zenith 0.5

0.4 Rozenberg 0.3 Young and Irvine Plaine-parallel Atmosphere | 1/cos(x) 0.2 Krisciunas Schaefer (simplified Garstang) Analytic Model, 8.65km LaPalma density Analytic Model, 40km LaPalma density 0.1 Analytic Model, 100km LaPalma density 0 60 65 70 75 80 85 90 Zenith Angle (deg)

Figure 6.7: Atmospheric attenuation for the Johnson V-band light for different airmass models. The model that gives the best description of the data, is shown pink dashed.

Figure 6.8: Best fit of the atmospheric attenuation parameter β of the direct moonlight using measured anode currents. Crab Nebula (left) and Mrk 421 (right) sample peak around 0.145.

6.6 Rayleigh and Mie scattering

The main atmospheric scattering processes are Rayleigh and Mie scattering. The Rayleigh scattering is the dominating scattering process for large scattering angles, while Mie scat- tering is the dominating process for small scattering angles, if aerosol particles or ice, is assumed to be present in the scatter volume. One of the main problems in atmospheric light scattering studies is that the part due to Mie scattering is quite variable due to the weather changes. For example high haze layers or thin fog layers can completely alter the scattering. While Rayleigh scattering is well predictable, Mie scattering is not. Normally it would need LIDAR studies to de- 70 6. A Model for Estimating the Brightness of the scattered Moonlight termine the atmospheric scattering and transmission losses, but these are not available (yet). Therefore, I assume a Mie scattering during clear nights in first order not varying and small compared to Rayleigh scattering. This assumption is normally justified for the upper layers of the atmosphere in places like La Palma.

Rayleigh scattering is the elastic scattering by particles which are much smaller than the wavelength of the light. The Rayleigh cross-section is proportional to the frequency of the 4 light like σRay ∝ ω . The angular distribution of the scattered light is symmetric in the plane normal to the incident direction of the photon. It can be described theoretically in an electrodynamic framework as an excited electromagnetic dipole absorbing and reemitting the photon [75]. The angular intensity distribution of Rayleigh scattering is 3 I(ρ) ∝ (1 + cos2 ρ). (6.25) 4

Mie scattering describes the scattering of light at aerosol particles which are larger than the wavelength of the light. The Mie theory is originally derived by an analytical solution of Maxwell’s equations found by G. Mie, for electromagnetic radiation scattering off spherical particles. Mie scattering is mostly a forward scattering, depending on the aerosol shape and size and on the incident light wavelength. In atmospheric physics, Mie scattering is often approximated by Henyey-Greenstein phase functions [76]

2 ∞ 1 − g X l PHG(cos ρ; g) = = (2l + 1)g Pl(cos ρ) (6.26) 2 3 (1 + g − 2g cos ρ) 2 l=0 where Pl(x) is a Legendre polynomial. The parameter g in (6.26) is an asymmetry factor, which scales the intensity towards the forward direction. To describe Mie-scattering also for the forward and the backward direction, commonly two Henyey-Greenstein functions are used like P (cos(ρ)) = bPGH (cos ρ; g1) + (1 − b)PGH (cos ρ; g2) (6.27) with a ratio factor b. For this study, the backward region can not be investigated, since the source position was restricted to high zenith angles4. Therefore, only one Henyey- Greenstein function is used, which restricts the model to forward scattering regions. The full scattering term R sums the two intensity distributions for Rayleigh and Mie scattering, with one scaling parameter b. Also, the left over absolute scaling constant c is included here. The yet to determine term reads: 3  R = c · (1 + cos2 ρ) + b · P (g, ρ) . (6.28) 4 HG The free parameters can now be fitted to the normalized data. Therefore, the cor- responding NSB level is subtracted from the measured DC data, and the atmospheric attenuation is scaled to unit airmass applying the atmospheric attenuation (6.19) and

4The full sky spans only over an angle of 180◦. Furthermore, only sources are observed under large zenith angles, that never can reach high altitudes. Therefore those large zenith angle observations are at very different azimuth angles (north/south) than the moon (around ecliptic (east/west)) and thus also the angular distance diminishes. 6.6 Rayleigh and Mie scattering 71 A] 8 2 / ndf 2085 / 2157 c 1.467 0.02563 7 bHG/Ray 0.535 0.01669 g HG 0.6396 0.008813 6

5

4

3

DC (scaled to half moon and Zm=0) [ 2

1

0 20 40 60 80 100 120 Scattering angle [deg]

Figure 6.9: Scaled anode currents due to atmospheric scattering of moonlight using observed Crab Nebula (blue) and Mrk 421 (red) measurements. The recorded anode currents (DC [µA]) are scaled to the quarter moon value, the mean moon distance from earth and the atmospheric attenuation of one airmass. The black line is the best fit of the moon model using the above noted ansatz for the Rayleigh and Mie scattering part. The region beyond >100◦ is not included in the Mie scattering formula of the model. The source zenith position was restricted to < 45◦ altitude.

the incident brightness is scaled to quarter moon. Fig. 6.9 shows the normalized data with the corresponding fit parameters. The black counts are Crab Nebula data, the red counts are Mrk 421 data points. The best fit determines the still free parameters of the model to:

c = 1.467 (6.29) b = 0.535 (6.30) g = 0.640. (6.31) 72 6. A Model for Estimating the Brightness of the scattered Moonlight

6.7 Result

The complete model for estimating the background light from scattered moonlight reads

IDC (Zm, B, ρ) = NSBg/eg (6.32) −0.145 (X40(Zm)−1) +BN (F, d) × 10 2.512 (6.33) 3 ×1.47 · [ (1 + cos2 ρ) + 0.54 · P (ρ, 0.64)], (6.34) 4 HG where X40(Zm) is the spherical homogenous airmass model from equation 6.20 with h = 40 km and PHG is the Henyey-Greenstein phase function from equation 6.26. The NSB term is the dark night background level in the observed region and BN is the brightness of the moon from equation 6.35, relative to half illuminated moon (quarter moon F = 0.5) and mean distance d = 384.4 × 103 km:

 3 2 B1(F ) 384.4 × 10 km BN (F, d) = · (6.35) B1(0.5) d The model is capable of estimating the DC currents of the MAGIC-I camera and thus

120 7

6 100 5

80 4 Separation Angle [deg]

3 60

2

40 1

20 0 10 20 30 40 50 60 70 80 90 100 Moon Phase [%]

Figure 6.10: Prediction of the anode currents as a function of the moon phase and the an- gular separation between source and moon using the moon model. The expected background from moonlight depending on the separation angle and the moon phase, calculated for the highest possible zenith angle of the moon per night. The expected background increase in µA is color coded. To make the plot better readable, all values above 7 µA are set to 7 µA. According to the observed source, a galactic (1.05 µA) or extragalactic (0.67 µA) NSB level has to be added. the night sky background level resulting from scattered moonlight. It is optimized for 6.7 Result 73 small lunar phases and is the first model dealing with low moon altitudes, almost until 0◦. This was possible, since the atmospheric conditions on the MAGIC observation site is of excellent and constant atmospheric conditions.

An exemplary application of the moon model is performed in fig. 6.10. Depending on the moon phase and the separation angle, the resulting anode currents from equation 6.32 are shown using a color code (in µA). Also the atmospheric attenuation is considered. Here, the values are calculated for the highest possible moon altitude per night, which depends on the moon phase (see chapter 5). In order to compare the model values with real data, a dark-night NSB-level has to be added according to the observed γ-ray source.

Another result can be obtained, when looking at the final scattering function. This can 2

3 4 4

0

7 5 4 4 2 3

Figure 6.11: The scattering phase function for Rayleigh and Mie scattering as a polar plot. The red line is the Rayleigh scattering and the blue line is the Mie scattering function. The dashed line indicates the mathematical functions, but in regions, where the model is not valid. 0◦ is forward, and 180◦ is backward scattering. No backward scattering function is included in the used model. be plotted individually for the Rayleigh and the Mie scattering, from which basically some atmospheric properties, like aerosol sizes and density, could be estimated. Fig. 6.11 shows the polar plot of the scattering phase functions for the valid angular range from 74 6. A Model for Estimating the Brightness of the scattered Moonlight

20◦ - 120◦ and the analytic formulae for the not accessible region. The Henyey-Greenstein function (blue) is the overall Mie scattering for all wavelengths and all aerosol sizes. The backward scattering contribution is not included, since this region was not measured.

6.8 Discussion of the moon model

The developed model for the scattered moonlight, which predicts the anode currents of the PMTs, is a very good description of the problem of moonlight for IACTs. This can basically be seen already in the scattering plot (fig. 6.9). However, there are several remarks, that still have to be discussed. Especially, there is one peculiarity that showed up during the development, which restricts the valid range of the model.

It has to be mentioned, that the measured background light evolves slightly differently than the moon model would predict, if the source travels through its culmination, namely the measured anode currents are higher than it is expected. This effect can also be seen in the scattering plot (fig. 6.9) when regarding nights, where the normalization is not precisely to same value for the complete one-night data. This is mostly the case for higher separation angles, or for brighter moon phases. There are now some remarks in place. On the one hand, the explanation for this is simply, that the volume of the view cone gets larger and therefore it is more likely that moonlight is scattered into the direction of the camera. Nevertheless, this effect is quite small, especially close to the culmination, and on the other hand, γ-ray observations with such constellations are not performed very often. If such an increase of the scatter volume would be considered correctly, one would have to integrate over the actual scatter volume, and therefore, the model would be quite more complicated.

Also the applied scattering terms can be discussed. Here, only one term for the Mie scattering is applied, although this is a very complex and widely discussed process. The actual Mie scattering formalism respects the size and the shape of aerosol particles as well as the incident wavelength. Therefore, it is expected, that with changing atmo- spheric conditions the scattering is changing. This was already seen when there were very faint clouds in the field of view, as it was measured by the pyrometer, and the DC currents were fluctuating very much. Also the calima, or simply industrial air pollution, might increase the background level significantly more. However, one can take advantage out of a changing Mie scattering part, and could use this effect for a quality check. If the anode currents under moonlight are significantly higher than the model would predict, it is very likely, that the atmospheric conditions are worse than during clear conditions. This would also influence the Cherenkov spectrum and thus the Monte Carlo simulations would have to be adapted in order to perform a correct energy estimation of the measured γ-rays. 6.8 Discussion of the moon model 75

I claim here, that this model can predict the anode currents for very low altitudes, al- ready from above > 1◦. This can be seen in the scattering plot in fig. 6.9. Almost all investigated nights were measured either during a moonrise or a moonset. Therefore, very much data is taken under small moon altitudes. In the scattering plot, this data then is normalized to a quarter moon, but also specially to only one airmass absorption. If the applied atmospheric attenuation term would not be the correct description, each measured night would “spread out” (like for the measurement above ρ > 120◦). One can see in the scattering plot, that each single night is almost precisely on one DC-value, which means, that the re-calculated atmospheric attenuation is correct up to very low moon altitudes, and thus the validity of the moon model is also given up to a moon altitude >1◦.

In this model, all spectral properties of the moonlight were ignored. For the description of the anode currents this was not necessary. However it would be of interest to calculate a photon flux or maybe a spectrum from the model results. This might be possible, if one assumes that the moon has a similar spectrum than the sun. The measured photon spectrum would then show the same characteristics than the sky-blue. For the sky-blue, there are for sure many very precise measures and thus a photon flux could be estimated.

γ-ray observations under small separation angles ρ < 20◦ to the moon are usually not performed. However, there are ideas for the measure of the moon shadowing of electrons and positrons. A discussion about this is performed in the Appendix. The model has also problems in describing the measured NSB for large separation angles as it is the case for ρ > 110◦. This might be due to the fact, that scattered moonlight hits the PMT directly.

There is no perfectly flat countryside in La Palma, but a volcano present. The Roque de Los Muchachos has a height of 2426 m and is roughly in the southeast, as seen from the telescope site. Therefore, also this mountain can be considered when observing under moonlight, although the effect is very small, almost negligible. However, during one night, which was taken under very bright moonshine for only a short time, it could be seen, that the Roque de Los Muchachos has an altitude of ∼ 10◦ as it can be seen from the MAGIC site. 76 6. A Model for Estimating the Brightness of the scattered Moonlight 7 Performance of the MAGIC Telescope during Moonlight Observations

In this chapter, the analysis of Crab Nebula data, which was taken under different moon- light conditions between February 2007 and February 2008, is described. The impact from moonlight on airshower images is shown, especially the role of the image cleaning is investigated. The hadronness and |Alpha| distributions are calculated for different moon illuminations and compared with Monte Carlo simulations. The impact on the γ-ray spectrum is investigated. The sensitivity of the telescope under different night sky background levels is studied.

The underlying background from photons from the night sky (background light) as mea- sured with MAGIC-I is found to be at 0.12 phe/ns/pixel (photoelectrons per nanosecond per 0.1◦ diameter photomultiplier pixel) for an extragalactic field of view and around 0.18 phe/ns/pixel for a galactic area. Here an NSB unit is defined as the background level, which MAGIC-I records while pointing to a galactic celestial field comparable to the Crab Nebula region. The definition reads for

1.0 NSB ≡ 1.0 µA (7.1) anode current at a gain of 3×104. It is directly proportional to ≈ 0.18 phe/ns/pixel [77], or with a square-root proportion to the pedestal RMS at 0.8 phe/pixel/event (dependent on the width of the readout windows).

7.1 Data selection and analysis approach

The Crab Nebula is a classical object for studying the performance of an imaging at- mospheric Cherenkov telescope. The source is always emitting a constant and high flux and is observable both from the northern and southern hemisphere; therefore the Crab Nebula is often referred to as the standard candle of γ-ray astronomy.

7.1.1 Data selection

The used data from Crab Nebula observations are summarized in the following table. A large dark night data sample is also included to the data set, to have a fundamental comparison level to moonlight night observations. 78 7. Performance of the MAGIC Telescope during Moonlight Observations

Analyzed Data Crab Nebula Observation period February 07 until February 08 Total observation time 50.3 hours Observation mode wobble-mode Zenith angle range 5◦ < Zd < 45◦ Effective observation time for Zd < 30◦ after bad 39.7h weather cuts Effective observation time 30◦ < Zd < 45◦ 8.7h Direct currents (DC) (median of all inner pixels, 0.8 - 5.8 (7.0) µA mean value of one minute) Discriminator thresholds (DT) 14-30 mV Moon phase 5% − 53%(80%) Separation angle ρ 25◦ − 130◦ Moon altitude up to 55◦

Cuts on bad weather conditions are applied by checking the humidity to be within the limits and also the pyrometer data was checked, that the parameter “cloudiness” is always < 30. If the anode currents under moonlight conditions show up fluctuations & 20%, this data is also excluded from data analysis, since clouds are assumed in the field of view, which scatter additional moonlight and which also attenuate Cherenkov light. No cuts on twilight conditions were applied, since the same effects for twilight and moonlight observations are expected. The zenith range is restricted to zenith angles below 30◦, in order to have a comparable airmass for the full data set. However, a high zenith angle data set from 30◦ < Zd < 45◦ was also analyzed separately and is used in section 7.4.

7.1.2 Analysis approach

The PMT anode currents are used as a direct measure for the night sky background level according to sections 6.2 and 3.2.2 and are converted to NSB-units according to equation 7.1. Data was taken up NSB levels of 7.0 NSB, however, high statistics are only available up to ∼ 6 NSB. Fig. 7.1 shows the total observation time as a function of the NSB. For a separate analysis of different background levels, the data is split up in NSB bins of 0.5 width. However, if necessary the samples are combined again to provide higher statistics and better readable plots. The effective observation times for the four later used NSB bins are shown here:

NSB level Effective observation time 0.8 < NSB < 2.0 26.9 hours 2.0 < NSB < 3.0 7.5 hours 3.0 < NSB < 4.5 3.9 hours 4.5 < NSB < 6.0 2.2 hours

Along the description in [1] and chapter 4 an analysis of the γ-ray data is performed. It was found, that the image cleaning is of key importance in analyzing moon data 7.2 Number of Islands 79

600

Total Observation Time 500

400

Observation Time [min] 300

200

100

0 0 1 2 3 4 5 6 7 NSB [NSB]

Figure 7.1: Total observation time [min] of the investigated Crab Nebula data sample depending on NSB. For comparison, a large dark night data sample was added. correctly. To investigate this behavior, a second image cleaning parameter set was investigated in addition and compared to the standard analysis method. The standard analysis is in this context referred to as 6-3 cleaning according to the cut values for core and boundary pixels (see section 4.2.1). The second image cleaning parameter set applies the same timing constraints like the standard method, but requires 8 phe for core pixels and 4 phe for boundary pixels (referred to as 8-4 ). Again, pixels not fulfilling these constraints are excluded from the image parametrization.

7.2 Number of Islands

An island is defined as a group of pixels detached from another group in a shower image after image cleaning is performed. The choice of the image cleaning parameters can be seen throughout the analysis chain. More islands usually point to a more hadron-like event and thus the event is rejected in the further analysis. Exemplarily, the impact of image cleaning with two different parameter sets (e.g. 6-3 and 8-4 ) for a real event recorded under high background light level is shown in fig. 7.2. There, the left image illustrates too low image parameters for the high background level. Hence, additional islands, which do not come from the air show but from the high back- ground level, are left after the image cleaning is performed. This leads to complications when fitting the Hillas ellipse. The MAGIC standard analysis takes all residual pixel information for the fitting into account. Very high image cleaning parameters would lead to an higher energy threshold, since low energy showers do not surpass the level of the cleaning parameters. Also the residual image is getting very small, which might lead to difficulties in the Alpha-parameter estimation. 80 7. Performance of the MAGIC Telescope during Moonlight Observations

24 24 22 22 21 21 20 20 18 18 17 17 16 15 14 14 13 13 12 11 10 10 9 8 8 7 6 5 5 4 3 3 0.60° 0.60° 2 1 189mm S [au] 189mm S [au]

Figure 7.2: Example of the impact on image cleaning on a shower image recorded under moon- light conditions (γ-candidate). Left: 6-3 timing image cleaning. Right: 8-4 timing image cleaning. Too low image cleaning parameters lead to additional islands. Also the Hillas ellipse does not point to the source position. Hence, this image would be rejected.

3

2.8 Mean number of islands Number of Islands | 6-3 Timing Image Cleaning 2.6 Number of Islands | 8-4 Timing Image Cleaning 2.4

2.2

2

1.8

1.6

1.4

1.2

1 0 1 2 3 4 5 6 7 NSB [NSB units]

Figure 7.3: Number of Islands for the two investigated image cleaning levels and for an increased NSB from moonlight (For events with a size > 100 phe). A significant deviation from dark night level is recognized at 2.0 NSB for the 6-3 cleaning and for around 4.5 NSB for the 8-4 cleaning.

A quality parameter, which is introduced here and will show up to be an important indicator (e.g. for the sensitivity during moonlight), is the mean number of islands de- pending on the NSB and the applied image cleaning level. It can be seen in fig. 7.3, that for increased NSB, the mean number of islands stay constant at the dark night level up to a certain amount of NSB. A significant deviation from the dark night level is observed at 2.0 NSB for the 6-3 image cleaning parameters, and around 4.5 NSB for 8-4 cleaning. 7.3 Extraction of the γ-ray signal 81

7.3 Extraction of the γ-ray signal

A first comparison of the data from different NSB levels is the size distribution. Only very loose cuts on size > 30 phe and the number of islands ≤ 3 are applied to this data. The calculated size distributions after image cleaning for four different NSB levels and for both image cleaning parameters, normalized to one hour of observation, are shown in fig. 7.4. One can see, that there is a decrease rate for higher NSB levels, although there are only very loose cuts applied. For the further analysis a size cut of size > 220 phe and a cut on the number of islands

Size Distribution | 0.5 < DC < 2.0µA Size Distribution | 0.5 < DC < 2.0µA

Size Distribution | 2.0 < DC < 3.0µA Size Distribution | 2.0 < DC < 3.0µA

4 Size Distribution | 3.0 < DC < 4.5µA Size Distribution | 3.0 < DC < 4.5µA 10 104 Size Distribution | 4.5 < DC < 6.0µA Size Distribution | 4.5 < DC < 6.0µA Counts per hour [#] 3 Counts per hour [#] 10 103

102 102

10 10 2.5 3 3.5 4 4.5 5 2.5 3 3.5 4 4.5 5 Size [phe] Size [phe]

Figure 7.4: Size distribution for size > 30 phe and four different background levels, normalized to one hour. (Left: cleaning level 6-3, right: 8-4 ; both using also timing constraints.).

≤ 2 for the is applied. Those are common quality cuts. Showers with a small size are likely accidentally triggered events, have further a bad γ/hadron separation capability have a large uncertainty in their energy estimation. Images with large number of islands are under dark-night observations supposed be most likely hadron showers.

Within the MAGIC standard analysis a γ/hadron separation is performed using the random forest decision tree algorithm as described in chapter 4. For the training of the decision trees, dark night Monte Carlo simulations of γ-examples and real data from dark night observations as hadron-examples are used. Independent of the NSB level, identical decision trees are used for event classification. However, for both image clean- ings separate random forests have to be trained. Fig. 7.5 shows the resulting hadronness excess, distributions for an NSB level of 4.0 < NSB < 4.5 compared to dark night for both investigated image cleanings. The number of excess events is calculated by subtracting the OFF-events1 from the ON-event distri- bution. During dark night observations the hadronness-excess shows a large excess of gamma like particles. While for an NSB between 4.0 and 4.5, the separation power in 8-4 cleaned data is almost the same as in dark night data, one observes an apparent decreased hadronness excess in the the 6-3 cleaned data set.

The Hadronness distributions for all NSB levels and for both image cleanings are at- tached in the appendix (Figs. A.6 and A.7).

1Here, the OFF event distribution is calculated as the mean of three (wobble) OFF positions. 82 7. Performance of the MAGIC Telescope during Moonlight Observations

100 100

80 80

Counts per hour 60 Counts per hour 60

40 40

20 20

0 0

-20 -20 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 Hadronness Hadronness

Figure 7.5: The Hadronness-excess distribution of Crab Nebula observations for two exemplarily chosen background levels (normalized to one hour observation time). Black counts are no-moon level (1.0 < NSB < 1.5) and grey counts are from data recorded during moonlight (4.0 < NSB < 4.5). The left plot is for 6-3, and the right one is for 8-4 image cleaning. When applying higher cleaning level parameters, the hadronnness distribution is still “dark-like” under strong moon conditions. A size cut of size > 220 phe is applied.

As the next step in the analysis the |Alpha|-distributions are studied. A cut in hadron- ness of h < 0.1 is applied, and the |Alpha| excess is calculated by subtracting the OFF- event distribution from the ON-events. The |Alpha|-excess plots for dark-night and for one NSB level of 4.0 < NSB < 4.5 are shown for both image cleaning samples in fig. 7.6. The |Alpha|-excess distribution for the higher NSB level is still comparable to the dark-

200 200

150 150 Counts per hour Counts per hour

100 100

50 50

0 0

0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 |Alpha| [deg] |Alpha| [deg]

Figure 7.6: |Alpha|-excess distribution for two exemplarily chosen background levels (normalized to one hour of data taking). Black counts are no-moon level (1.0 < NSB < 1.5) and grey counts are during moonlight (4.0 < NSB < 4.5). Again, the left plot is for 6-3, and the right one is for 8-4 image cleaning. Here, a cut on hadronness h ≤0.1 was applied. Thus, the 6-3 distribution at high NSB is mainly affected by the lower hadronness significance. night distribution if the 8-4 image cleaning is used. On the other hand, the |Alpha|- excess is less significant in the signal region for high NSB levels, if the 6-3 image cleaning is used. This excess is mostly affected by the fact, that for the |Alpha|analysis already an hadronness cut is applied beforehand.

In order to calculate the γ-excess distribution, the already used cuts on size and the 7.3 Extraction of the γ-ray signal 83 number of islands, as well as cuts on hadronness and |Alpha| have to be applied. The following table summarizes all (common) applied cut values:

Parameter Cut value Number of Islands NoIsl ≤ 2 Size size >220 phe Hadronness h ≤ 0.1 Alpha |Alpha| ≤ 8◦

The integrated size distributions of the excess events are shown in fig. 7.7. One can see ] ] -1 -1

10-1 10-1

Integrated gamma rate [s -2 Integrated gamma rate [s -2 10 integrated γ excess rate | 0.8 < NSB < 2.0 10 integrated γ excess rate | 0.8 < NSB < 2.0 integrated γ excess rate | 2.0 < NSB < 3.0 integrated γ excess rate | 2.0 < NSB < 3.0 integrated γ excess rate | 3.0 < NSB < 4.5 integrated γ excess rate | 3.0 < NSB < 4.5 integrated γ excess rate | 4.5 < NSB < 6.0 integrated γ excess rate | 4.5 < NSB < 6.0

-3 -3 10 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 10 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 log10(Size) [phe] log10(Size) [phe]

Figure 7.7: Integrated γ-excess distribution for 6-3 image cleaning (left) and 8-4 image cleaning (right) and for four different NSB levels from moonlight. Cuts on hadronness h ≤ 0.1, |Alpha| ≤ 8◦ and the number of islands NoIsl ≤ 2 are applied. from those γ-rate plots that for the 6-3 cleaning set, the integrated size distribution is significantly lower for night sky background levels above 3.0 NSB, while for the same data, but cleaned with 8-4 cleaning parameters, it is still dark-like until 4.5 NSB.

Differently from [54], where it is reported that a loss of events is given mainly for low energy values whereas there would be no significant difference for high values, there is a comparable loss in the event rate independently from the gamma-size/energy under moonlight conditions. The only reasonable explanation for the loss of high energy events with the same ratio that low/medium energy events suffer, is connected to the appear- ance of additional islands. If additional islands show up, the event is rejected due to the cut on this parameter. Hence, the γ-rate drops accordingly to the increase in the number of islands, comparable as fig. 7.3 indicates. Also the size distributions for both image cleaning levels are comparable to the dark night ones, as long as the number of islands is constant with that seen during dark-nights.

The differential size distributions for four different background bins are appended in fig. A.10. The interested reader can also look at the integrated size distribution for a more detailed NSB level binning in the appendix (Fig. A.11). 84 7. Performance of the MAGIC Telescope during Moonlight Observations

7.4 Sensitivity of MAGIC-I under moonlight conditions

It is of great interest to calculate the sensitivity of the MAGIC telescope during moon- light observations. In the following not the significance of the overall γ-ray signal during the moon-time observations is in the focus, but the comparison of the sensitivity of the instrument during observations under different moonlight intensities. It is common, to use tighter cuts compared to γ-ray measurements for defining the signal region in order to optimize the sensitivity of the instrument.

7.4.1 Significance of one hour of Crab Nebula observation under moonlight condition

The significance of a γ-ray signal is calculated by counting the number of OFF events (NOFF) and the number of ON events (NON) in the expected signal region, subtracting them from each other, and calculating essentially the probability that the resulting excess is a statistical fluctuation using formula 17 from [36]. In order to increase the significance of the γ-ray signal, tighter cuts than for the measurement of the γ-rate are applied. For MAGIC-I, the highest integral sensitivity is obtained for energies above 250 GeV [1]. This corresponds to a value for size of above 400 phe. Here, the cuts recommended by [78] are used:

Parameter Cut value Number of Islands NoIsl ≤ 1 Size size > 400 phe Hadronness h ≤0.05 Alpha |Alpha| ≤ 6◦

The number of ON events and OFF events for different NSB levels normalized to one hour of observations are shown in fig. 7.8, separately for 6-3 image cleaning in the upper row and 8-4 in the lower row. The number of found ON excess events decreases rapidly for the 6-3 data set at NSB values above 2.5 NSB, while the 8-4 cleaning shows an almost constant level of ON excess events up to an NSB level of 4.5 NSB. The resulting significance according to formula 17 from [36] (see section 4.7) is calculated in the right plot. The√ typical significance of MAGIC-I during dark night observations is around S =∼ 16σ/ h. Using the 6-3 cleaning, this value can be achieved up to 2.5 NSB, while using the 8-4 cleaning, the dark night significance can be achieved up to 4.5 NSB.

7.4.2 The sensitivity of MAGIC-I during moonlight observations

√ The sensitivity S to detect a γ-source is calculated in units of σLiMa/ h [36]. The sensitivity of an IACT is usually expressed as the minimum flux, normalized to the Crab 7.4 Sensitivity of MAGIC-I under moonlight conditions 85

400 ] 20 σ

350 18 16 300 14 Count per hour 250 Significance [ 12

200 10

150 8 6 100 4 50 2 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 NSB [NSB units] NSB [NSB units]

400 ] 20 σ

350 18 16 300 14 Count per hour 250 Significance [ 12

200 10

150 8 6 100 4 50 2 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 NSB [NSB units] NSB [NSB units]

Figure 7.8: Crab excess rates and significances as a function of NSB. Above: 6-3 cleaning. Bot- tom plots: 8-4 image cleaning. The left plots show the ON-event counts (blue) and OFF-event counts (red) nor- malized to one hour effective observation time. The right plots show the calculated LiMa-significance [σ] [36], as a function of the NSB level.

flux that can be measured with 5σ significance (calculated as √ Nexcess ) within an Nbackground observation period of 50 hours [79]. Hence, r p T Nbkg Ω = 5 · obs · . (7.2) 50h Nexcess E phe 1 C.U. = 6.0 · 10−10( )−2.31−0.26log(E/300GeV ) (7.3) 300GeV cm2 · s · T eV The sensitivity for an IACT is usually given in so called Crab units (C.U.). One Crab unit measured with the MAGIC telescope corresponds to [1]: One can see from fig. 7.9 that the MAGIC standard analysis provides the same level of sensitivity up to ∼ 3.5 NSB for an energy above 200 GeV, while the 8-4 cleaning level provides even a dark like sensitivity for higher NSB (for energies > 250 GeV).

7.4.3 Crab observations at large zenith angles

Besides the “main” data set, which was restricted to zenith angles < 30◦, also an high zenith angle data set was investigated from zenith angles 30◦ < Zd < 45◦. For this data sample, only the 6-3 timing image cleaning was studied. The effective observation time was calculated to be 8.7 hours, while for higher moon illuminations only 0.4 hours 86 7. Performance of the MAGIC Telescope during Moonlight Observations

5 6-3 timing image cleaning 4.5 8-4 timing image cleaning 4

3.5

3

2.5

Sensitivity [% Crab units] 2

1.5

1 0 1 234 5 6 NSB [NSB units] Figure 7.9: Optimized sensitivity in Crab units of MAGIC-I for the standard analysis (grey) and for the exemplarily applied 8-4 timing image cleaning (black) depending on the NSB. at an NSB around NSB ≈ 3.5 and another 0.7 hours between 5.0 < NSB < 5.5 were recorded. For the γ/hadron separation there were two random forests trained according to the zenith angle range from 30◦ − 40◦ and from 40◦ − 45◦. As it can be seen in

5

4.5

4

3.5

3 Sensitivity [% Crab units]

2.5

2

1.5

1 0 1 2 3 4 5 6 NSB [NSB units]

Figure 7.10: Sensitivity of MAGIC-I under moonlight conditions. The grey solid markers indi- cate the standard analysis, the black counts are for 8-4 image cleaning. The grey dashed counts are from high zenith angle observations (30◦ < Zd45◦), using the standard analysis.

fig. 7.10, the sensitivity for high zenith angle observations is comparable to low zenith angle observations at least until 3.0 NSB. Unfortunately there is no data for large zenith 7.5 Monte Carlo simulations of γ-rays under moonlight conditions 87 angles in the interesting region from 3.0 − 5.0 NSB.

7.5 Monte Carlo simulations of γ-rays under moonlight conditions

Monte Carlo simulations for four different NSB levels, namely 1.0 NSB, 2.5 NSB, 3.75 NSB and 5.5 NSB, were performed, using the CORSIKA framework [80] and the MAGIC re- flector, camera and readout codes [81]. The resulting pedestal RMS was crosschecked to be consistent with real data around these background levels. The simulated trigger threshold (DT) was also adjusted to data recorded at the corresponding NSB. Fig. 7.11 shows the differential size distribution of the MC simulated events. Almost independent of the size/energy of the γ-rays, one can recognize a loss of events. This loss is consistent with that observed in presence of moonlight and shows that the conclusion from [54] are wrong about energy dependent losses. If one performs the same analysis (especially the same cuts) with Monte Carlo simula-

Figure 7.11: Differential size distributions of Monte Carlo simulated Crab events for four differ- ent NSB levels and the two applied image cleaning levels (left: 6-3, right: 8-4 ). tions as with data, the excess distributions of the data can be compared to the Monte Carlo simulations. The hadronness and |Alpha|-distributions of the MCs are included into the data shown in fig. 7.5 and fig. 7.6. The normalization of the event rate to the data is done in the signal region. One can see in the plot, that the data and the MC simulations are in good agreement. However, it must be mentioned, that the MCs are simulated for NSB = 3.75 NSB, while the data in these plots is for 4.0 < NSB < 4.5.

7.6 Effective collection area

Using the Monte Carlos simulations, the correct effective area for different NSB levels can be calculated. Therefore, the same cuts on size, NoIsl, hadronness and |Alpha| are applied to the Monte Carlo sample as to the data in section 7.3. According to equa- tion 4.4 the effective collection area for different NSB levels is estimated. The resulting 88 7. Performance of the MAGIC Telescope during Moonlight Observations

100 6-3 cleaning dark-night 8-4 cleaning dark-night 80 4.0

Counts per hour per Counts 20 0 -20 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Hadronness Hadronness 200 6-3 cleaning dark-night 8-4 cleaning dark-night 4.0

100

Counts per hour per Counts 50

0 0 5 10 15 20 25 0 5 10 15 20 25 |Alpha| [deg] |Alpha| [deg]

Figure 7.12: Hadronness-excess (upper plots) and |Alpha|-excess (lower plots) for two different cleaning parameters (left: 6-3 ; right: 8-4 ). Black markers indicate dark night data, while the grey markers are for 4.0 < NSB < 4.5. Dotted markers are corresponding MC simulations. A size cut of 220 phe was applied. effective collection areas after cuts are shown in fig. 7.13. While for the 6-3 image cleaning, the effective collection area Aeff is roughly compa- rable to the dark-night values until NSB ≤ 2.5, it is still compatible with dark night up to an NSB = 3.75 for the 8-4 image cleaning. The dark-like collection area also shows up to which NSB level the standard dark-night MCs can be used. This means, that the MAGIC standard analysis, i.e. the 6-3 timing image cleaning with the use of only dark-night Monte Carlo simulations, permits a stable analysis up to . 2.5 NSB. If the 8-4 image cleaning is applied, but still only dark-night Monte Carlo simulations are used, then the analysis is correct until NSB < 4.5. More detailed plots of the collection area, also before cuts, can be found in the Ap- pendix (Fig. A.12). Also, the measured spectrum using only dark-night Monte Carlos are appended in the Appendix.

7.7 Study of the energy threshold during moonlight observations

The effect of the NSB on the energy threshold is calculated with Monte Carlo simulations, by applying the used cuts on the simulated events. Here, the analysis threshold is defined as the peak of the simulated energy distribution after all cuts. The simulated energy 7.7 Study of the energy threshold during moonlight observations 89

5 ]

2 10

104 Collection Area [m 103 2 3 4 10 10 10E [GeV] 5 ]

2 10

104 Collection Area [m 103 2 3 4 10 10 10E [GeV]

Figure 7.13: Effective collection area after cuts for (a) 6-3 and (b) 8-4 timing image cleaning for four simulated background levels. Solid lines represent for dark night MCs (1.0 NSB), dashed lines correspond to 2.5 NSB, dotted lines to 3.75 NSB, and dash- dotted lines to 5.5 NSB. spectrum follows a power law ∼ E−Γ with the spectral index of the Crab Nebula of Γ = 2.6. To determine the peak of the observed energy distribution a gaussian fit to the energy distribution after cuts is applied in the expected region. The energy threshold is of course very dependent on the size cut. Here, a size cut of size > 120 phe was set. Fig. 7.14 shows the results for both image cleanings. The analysis energy threshold shows no dependence of the NSB level and is independent from the image cleaning. For the size cut of 120 phe the analysis energy threshold was determined to be 164 GeV for the 6-3 image cleaning and 170 GeV for the 8-4 image cleaning. The results are summarized in the following table

Energy threshold NSB 6-3 timing image cleaning 8-4 timing image cleaning 1.00 164.0 ± 1.8 GeV 171.5 ± 1.5 GeV 2.50 163.3 ± 1.9 GeV 168.9 ± 1.7 GeV 3.75 164.8 ± 2.6 GeV 169.9 ± 1.6 GeV 5.50 180.7 ± 9.7 GeV 170.4 ± 3.0 GeV 90 7. Performance of the MAGIC Telescope during Moonlight Observations

MC energy distribution | NSB = 1.0 0.7 MC energy distribution | NSB = 1.0 0.7 MC energy distribution | NSB = 2.5 MC energy distribution | NSB = 2.5

Counts Counts MC energy distribution | NSB = 3.75 MC energy distribution | NSB = 3.75 0.6 0.6 MC energy distribution | NSB = 5.5 MC energy distribution | NSB = 5.5

0.5 0.5 0.4 0.4 0.3 0.3

0.2 0.2

0.1 0.1 0 0 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 Energy [GeV] Energy [GeV]

Figure 7.14: The determination of the energy threshold. The peak of the size distribution of Monte Carlo simulations is found by using a gaussian distribution. The energy distribution peaks around 165 GeV for all four different simulated NSB levels and the two image cleanings (left: 6-3, right: 8-4 ).

The analysis energy threshold for the size cut of 220 phe, which is applied for the spec- trum and flux calculations, was determined to be at ∼190 GeV for all NSB levels, using the same technique.

7.8 The Crab spectrum under moonlight conditions

The differential energy spectrum of the Crab Nebula taken under moonlight conditions can now be determined. For the energy estimation, one “dark night” random forest according to chapter 4 is used for the full data set, i.e. for all different NSB level. This is reasonable, since no changes on the Hillas parameters are expected and also the size distributions do not change with NSB. An independent test in a small size-region from 280 < size < 330 phe was performed, which confirmed, that all NSB levels show the same energy distribution than dark-night.

Using the estimated effective collection area Aeff from fig. A.12 and the differential gamma rate, the spectum can be calculated. The resulting differential energy spectra for the four different NSB levels are shown in figs. 7.15 and 7.16 for the two investigated image cleanings.

For fitting of an analytic formula, an exponential spectrum is assumed from 200 GeV to 2 TeV according to: dF  E Γ  phe  = Φ × (7.4) dE TeV cm2 · s · TeV The following tables show the results for the four different NSB levels each. 7.8 The Crab spectrum under moonlight conditions 91

Differential energy spectrum; 6-3 timing image cleaning NSB Φ Γ 0.8 < NSB < 2.0 (3.22 ± 0.23) × 10−11 2.32 ± 0.09 2.0 < NSB < 3.0 (3.28 ± 0.23) × 10−11 2.34 ± 0.09 3.0 < NSB < 4.5 (3.09 ± 0.27) × 10−11 2.39 ± 0.11 4.5 < NSB < 6.0 (7.44 ± 0.93) × 10−11 2.85 ± 0.17

Differential energy spectrum; 8-4 timing image cleaning NSB Φ Γ 0.8 < NSB < 2.0 (2.93 ± 0.20) × 10−11 2.38 ± 0.01 2.0 < NSB < 3.0 (3.05 ± 0.23) × 10−11 2.34 ± 0.11 3.0 < NSB < 4.5 (3.00 ± 0.25) × 10−11 2.34 ± 0.11 4.5 < NSB < 6.0 (2.68 ± 0.28) × 10−11 2.58 ± 0.13 ] -1

s Zenith range 5-30deg -2 NSB = 1.0 -9 NSB = 2.5 cm 10

-1 NSB = 3.75 NSB = 5.5

10-10 dN/dE [TeV

10-11

-12 10 2 3 10 10Estimated Energy [GeV]

Figure 7.15: Differential energy spectrum of Crab Nebula for the 6-3 timing image cleaning and for four different moonlight illuminations. The continuous line represents the dark night spectrum derived from teff =26 h effective observation time. The dashed curve is derived for 2.0

First it has to be mentioned, that the results of the two different image cleanings for dark night observations are well consistent within the errors. This was of course to be expected, since different image cleaning levels should not influence the spectrum of the same data. Comparing the data taken under moonlight with the dark-night data, it can be seen, that the recovered spectrum is consistent with that taken during dark night until 4.5 NSB if the 6-3 image cleaning is used, and for the 8-4 image cleaning parameters even for all the analyzed data. However, it is remarkable, that the spectrum for NSB > 4.5 is not correctly measured 92 7. Performance of the MAGIC Telescope during Moonlight Observations ] -1

s Zenith range 5-30deg -2 NSB = 1.0 -9 NSB = 2.5 cm 10

-1 NSB = 3.75 NSB = 5.5

10-10 dN/dE [TeV

10-11

-12 10 2 3 10 10Estimated Energy [GeV]

Figure 7.16: Differential energy spectrum of Crab Nebula for 8-4 timing image cleaning and for four different moonlight illuminations. The same line coding as in fig. 7.15 is used. with the standard image cleaning, although appropriate Monte Carlo simulations were used. The higher measured flux is basically a consequence from an underestimated ef- fective collection area. As it can be seen in fig. 7.13 the assumed collection area is of a factor 6 - 10 smaller than during dark-night observations. Also fig. 7.14 shows that for the simulated NSB = 5.5 only very few MC events are fulfilling the applied cuts. Hence, it is assumed, that the MCs were not simulated correctly, but most probably with a too high NSB level. Furthermore, the simulated NSB is at 5.5 NSB, while the data in this NSB-bin from 4.5 - 6.0 is only at 5.4 NSB, but this would probably not be a suffi- cient explanation. It is more likely, that at those extreme conditions, the Monte Carlo simulations are not yet tuned perfectly to match the reality, and thus would probably need some fine-tuning. This also influences the spectrum at high NSB levels for the 8-4 image cleaning, and thus might also be the reason for the different spectral index there. Although the spectral index is almost consistent with dark-night values within the errors.

The question might arise, up to which NSB level the spectrum can be recovered correctly without taking dedicated Monte Carlo simulations into account. This analysis approach would correspond exactly to the standard analysis, which is also used in the online analysis and might also be interesting for a fast or simplified analysis, if moonlight data has to be included. However, this only affects the calculation of the collection area and is equal to the question, up to which NSB level the effective collection area is still in agreement with dark night values. Hence, this question is answered in section 7.8 (see fig. 7.13), while the corresponding spectra can be found in the Appendix. 8 Conclusions and Outlook

8.1 Conclusions

The scope of this thesis is the study of the influence of moonlight on observations with the MAGIC-I telescope. While besides VERITAS, other γ-ray observatories only ob- serve during dark-night, i.e. when there is no moon present in the sky, MAGIC can also perform γ-ray observations during moonlight conditions. This is achieved by a specially designed camera, using low gain photomultiplier tubes, and increasing the discriminator thresholds automatically to run at an almost constant DAQ-rate.

Several separate investigations were performed to achieve a fundamental understanding of the given problem. The orbital parameters of the moon were investigated in detail. This lead to new calculations of the useful observation time. With reasonable assump- tions, the observation time can be extended under moonlight conditions by 30% or 550 hours, from 1600 hours to 2150 hours per year. Additional extension to twilight is pos- sible adding around additional 80 hours per year. For future instruments like CTA [82] this should be taken into account.

For a comprehensive understanding of the brightness of the moonlight, a compact model for estimating the increased background light level from scattered moonlight was de- veloped. It is the first model of this kind, holding especially for extreme conditions like very low moon altitudes already above 1◦ and early moon phases. It takes the lunar phase, the moon altitude, the moon distance and the separation angle into ac- count and calculates the estimated background increase for a MAGIC-I camera pixel. It can be used for automated Monte Carlo simulations or for optimized source scheduling. Together with the orbital calculations, the predictions of the moon model are used to schedule so-called “moon shadow” observations of charged cosmic rays in the near future.

The main part of this thesis deals with the analysis and treatment of data taken un- der moonlight conditions. Crab Nebula data recorded under different NSB levels were analyzed and compared with dark night data. The impacts of an increased night sky background level on all subsystems was explained. The impact of moonlight on shower images was studied in detail. It was found that the main influence is on the image cleaning if low cleaning levels are used. In turn, hadronness and |Alpha|-distributions are biased. The higher fluctuations in each pixel from the increased night sky light background result in artifacts in the shower image, which basically lead to the loss of quite some γ-ray shower images, looking like hadronic shower images. This blurring of 94 8. Conclusions and Outlook images is mostly energy independent. However, the problem can be handled by using higher cleaning parameters. Applying these cuts one loses very small size events but at higher energies one obtains basically the same image quality and in turn the same spectra. This behavior could be confirmed by Monte Carlo simulations. With those Monte Carlo simulations also the appropriate collection area could be calculated. This permits to recover the correct spectrum up to even higher NSB levels. The three analysis approaches results are: • The standard analysis procedure: 6-3 timing image cleaning and dark-night Monte Carlo simulations lead to correct results up to 2.5 NSB. • Different image cleaning parameters: The analysis with the exemplarily ap- plied 8-4 cleaning parameters with timing constraints, but using dark-night simu- lated Aeff , lead to a robust analysis up to 4.5 NSB. • Moonlight Monte Carlo simulations: Using the appropriate Monte Carlo simulations to estimate the effective collection area, correct results are achieved until 4.5 and even above 6.0 NSB for the 6-3 and the 8-4 cleaning, respectively. In order to provide a correct analysis for data taken under moonlight condition I would therefore recommend, that always data with a higher image cleaning (e.g. the here stud- ied 8-4 timing image cleaning) is provided by the data center. This already allows to perform a correct and easy analysis, since no dedicated Monte Carlo simulations have to be created. Also the online analysis could probably be done with higher image cleaning parameters, in order to treat all recorded data in the same way.

The sensitivity of the MAGIC-I telescope during moonlight observations is constant and comparable to that of dark nights up to 3.5 NSB using the standard analysis, and until 4.5 NSB for the investigated 8-4 image cleaning. Some of the results are in contradiction to [54], but are proved to be related to the different analysis approach. An MAGIC internal refereed conference contribution, with a more detailed description on the different analysis and changes in the hardware, com- pared to [54], was already submitted as a conference contribution [83].

8.2 Outlook

Within this thesis, the problem of moonlight on γ-ray observations using the imaging atmospheric Cherenkov technique was studied. The brightness of the moon for the MAGIC-I telescope could be characterized. Also it was shown, that observations un- der moonlight with the current MAGIC-I setup is possible, even without any residual negative effects provided that one observes during a “clear” atmosphere, i.e. a low con- centration of Mie scattering objects, such as haze or fain fog. Although quite a few problems could be solved successfully, while during this study some thoughts came up, which could be studied in the future to improve further the analysis. Image parametrization It was shown that additional islands, as the artifacts of a too low image cleaning, cause 8.2 Outlook 95 the main problems to select genuine γ-ray showers. Hence, it could be investigated to parameterize only the main island to calculate the Hillas parameters. One may spec- ulate, that this leads to a decreased γ/hadron separation capability, or otherwise, this approach could probably lead to some improvements for data recorded in the presence of moonlight. Even more ambitious could be an improved analysis of the FADC slices. Here, it might be possible, to find additional parameters that could be used for an im- proved image cleaning, which prevents the creation of islands. A possible direction might be to study in more detail the time spread between the pixels belonging to an island as well as to tighten more the time correlation between the main shower cluster and the islands. As the pixel signals originate from random noise fluctuations, the time corre- lation should be significantly lower than in genuine islands from subshowers. A similar argument should hold for the fluctuations of the amplitudes and time structure of pix- els belonging to the same island. For such a characterization of the events, one could apply a random forest decision tree algorithm. It was already suggest by [84], that an improved shower characterization could be performed with a decision tree taking single pixel information into account.

Stereoscopic observations together with MAGIC-II A second telescope with the same structure has been built at 85m next to MAGIC- I [85]. It is currently performing the first observations and stereo-mode observations are approaching soon. The MAGIC-II telescope allows stereo observations together with MAGIC-I, which lead to improvements in sensitivity, a lower energy threshold, better energy estimation and γ/hadron classification. Due to the increased number of pixels in the MAGIC-II camera one might expect more islands just from statistical reasons. Hence, it would be necessary to loosen the island cut, set the number of necessary core pixels to a higher value or use only the main island for parametrization. So, running the telescopes in stereoscopic mode, as planned, this will give an improvement in the shower reconstruction. The improved shower reconstruction lead to a better discrimination of the background from the scattered moonlight. However, the impacts of moonlight on the MAGIC stereoscopic system should be studied carefully. 96 8. Conclusions and Outlook A Appendix

A.1 Observations at small separation angles

During December 2008 and January 2009, there was dedicated data taken to measure the background light during observations at very small separation angles, so called close moon observations. This data was taken without observing a VHE γ-ray source. The angular distance of the moon was changing from 6.0◦ up to only 3.5◦. The outer pixels were switched off during those close moon observations to prevent them from damage. Furthermore, during March 31st and April 1st 2009, there was a quite special constella- tion. The Crab Nebula was only 7◦ − 8◦ far away from the moon during two days, while the moon phase was at 31% and at 42% respectively. This data can also be included into the model presented in chapter 6. Fig. A.1 shows the resulting scattering plot for anode currents (normalized to mean moon distance, moon phase F = 50% and one airmass attenuation) where the same Rayleigh and Mie scattering formula is assumed to determine the free parameters from equation 6.28.

80

A] 2 28

µ 10 χ2 26 / ndf 4476 / 2372 24 b 23 ± 21 Ray 2.36 0.01188 A] 70 b P 19 HG 0.1273 ± 0.003663 17 g 16 HG 0.889 ± 0.002821 60 14 12 10 9 7 50 5 3 2 10 0.60 0 40 189mm I [PA]

30

20

10 Scattering Function (scaled to halfmoon) [ Scattering Function (scaled to halfmoon) [ 1 0 0 20 40 60 80 100 120 0 246810 Separation Angle [deg] Separation Angle [deg]

Figure A.1: Left: Scattering plot including close moon observations with exponential vertical axis. Green markers are from dedicated NSB measurements during December 2008. Pink markers are from Crab Nebula observations at 8◦ distance. The solid grey curve is the best fit including Rayleigh and Mie scattering as presented in chapter 6. The resulting function gives no proper description of the data. Right: The black dashed line indicates the model presented in chapter 6. The solid black line adds an exponential term, probably from backscattering effects from ground or the telescope structure, to this moon model. The inhomogeneity in the camera at a very small separation angle of 3.5◦ is shown to scale.

Differently from fig. 6.9 (mind the exponential vertical axis), the fit has a worse χ2 and 98 A. Appendix it does not seem to be a comprehensive description of the data. Focussing on the “close moon” region, the normalized anode currents evolve more like an exponential function, instead of the supposed to be dominant Mie scattering function. Fig. 6.9 shows this assumption with a fitted additional exponential function (black line). The field of view of the MAGIC camera is shown to scale. At the most extreme condition at 3.5◦ close to the moon, the camera is already illuminated very inhomogeneously and the anode currents range from 8 µA up to 28 µA. It is supposed, that an additional effect takes place at close moon observations. Either, A]

10

Scattering Function (scaled to halfmoon) [ 1

0 20 40 60 80 100 120 Separation Angle [deg]

Figure A.2: Scattering plot including close moon observation data. The green counts are from NSB measurements at close distances. The pink counts are from Crab Nebula obser- vations at 8◦ close to the moon. Red markers are regular Crab Nebula observations and blue markers are from Mrk 421 observations. The black dashed line indicates the model presented on this thesis 6. The solid black line adds an exponential term to this moon model. it could be an additional effect in the atmospheric scattering, like a small angle scatter- ing on comparably large aerosol particle. Such a contribution to the scattering can be assumed with a second, very forward oriented, Henyey-Greenstein functions. However, it is also discussed and seems to be quite likely, that there is a diffuse backscat- tering from parts of the telescope structure or from ground. Nevertheless, I personally think, that atmospheric scattering contributes the most to the region of small scattering angles. If an exponential function is assumed to describe this backscattering effect, additional to equation 6.28, the scattering can be well parameterized (see fig. A.2), well knowing, that this exponential function is not an adequate phase function to describe a scattering effect. A.1 Observations at small separation angles 99

The resulting scattering function reads:

IDC = NSBg/eg (A.1) −0.145 (X40(Zm)−1) +BN (F, d) × 10 2.512 (A.2)  3  × 1.56 · [ (1 + cos2 ρ) + 0.48 · P (ρ, 0.67)] + 102.57−ρ/3.07 (A.3) 4 HG

The functions BN (F, d),X40(Zm) and PHG are the same as in formula 6.32. This formula gives a good description of the scattered moonlight, including small separation angles. Especially, the pink points were originally predicted beforehand, using this formalism with a precision of some percent.

This extended model can be used, for estimating the background especially for close moon observations. As proposed in [58], observations of the moon shadow are planned to measure the diffuse electron and positron flux. The energy threshold of IACT rises strongly with the distance to zenith. In order to keep an energy threshold below 300 GeV with MAGIC, the zenith angle must be less than 50◦. The typical deviation angle from the geomagnetic field for a 500 GeV electron/positron is around 3◦ - 4◦. The dis- crimination between electrons, positrons and diffuse γ-rays is achieved by deviation into opponent directions. The addressed energy range is in particular interesting, since the PAMELA reported an increased e+/e− ratio above 10 GeV [86], which is in agreement with previous mea- surements by HEAT [87] and AMS-01 [88]. Fermi measured the all-electron spectrum following a power-law with a spectral index of −3.0 [89]. ATIC reported a even harder spectrum with a bump between 300 GeV and 700 GeV [90]. At around 800 GeV, both ATIC and HESS [91] measure a break in the spectrum, which physical nature is still not yet solved. This energy region of interest is at a well measurable energy range for MAGIC and it is planned to perform those observations in late 2009. The physical and technical restrictions on those observations are quite close. In order not to damage the PMTs, and further allowing a stable analysis, the background level must be at least below DC < 20µA. Hence, the observation possibilities can be calculated. For the upcoming observation cy- cle from July 2009 to July 2010 following observation times are possible for observations dependent on the angular distance of the moon shadow position.

angular distance observation time 3.5◦ 21.83 hours 4.5◦ 60.17 hours 5.5◦ 103.3 hours 6.5◦ 1109 hours

At the optimal distance of 3.5◦, the maximum observation time is only 21.8 hours. If the background level can not be handled up to 20 µA, the possible observation time decreases very rapidly. 100 A. Appendix

A.2 Additional figures and plots

Phase of the Moon [%] Maximum Altitde of Moon per Night [deg] Altitde of Moon if above horizon [deg] 100 Maximum Brightness of moon per Night [scaled] Brightness of moon [scaled]

80

Various (see legend) 60

40

20

0 31/12 02/03 02/05 02/07 01/09 31/10 Date 2009

Figure A.3: “Moon calendar” for 2009. The red line shows the phase of the moon [%]. The black line/counts indicate the maximum altitude of the moon per night [deg] and thus the minimum atmospheric attenuation. The green markers indicate the moon altitude every 10 min [deg]. The maximum brightness of the moon per night according to [57] and taking the lowest atmospheric attenuation into account(scaled to full moon = 100%) is shown in violet.

Phase of the Moon [%] Maximum Altitde of Moon per Night [deg] Altitde of Moon if above horizon [deg] 100 Maximum Brightness of moon per Night [scaled] Brightness of moon [scaled]

80

Various (see legend) 60

40

20

0 31/12 02/03 02/05 02/07 01/09 01/11 Date 2010

Figure A.4: “Moon calendar” for 2010. A.2 Additional figures and plots 101

Migration Matrix (GeV) 4 true 10 E

103

102

10

10 102 103 104 Eest (GeV)

Figure A.5: The migration matrix as calculated by the random forest. A strong deviation Etrue = Eest would require urgently an unfolding of the spectrum.

Hadronness OFF 0.0 < DC < 0.5 µA Hadronness OFF 0.5 < DC < 1.0 µA Hadronness OFF 1.0 < DC < 1.5 µA Hadronness OFF 1.5 < DC < 2.0 µA 200 200 200 200

180 180 180 180 Counts Counts Counts Counts 160 160 160 160

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0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness Haddronness

Hadronness OFF 2.0 < DC < 2.5 µA Hadronness OFF 2.5 < DC < 3.0 µA Hadronness OFF 3.0 < DC < 3.5 µA Hadronness OFF 3.5 < DC < 4.0 µA 200 200 200 200 180 180 180 180 Counts Counts Counts Counts 160 160 160 160

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20 20 20 20 0 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness Haddronness

Hadronness OFF 4.0 < DC < 4.5 µA Hadronness OFF 4.5 < DC < 5.0 µA Hadronness OFF 5.0 < DC < 5.5 µA Hadronness OFF 5.5 < DC < 6.0 µA 200 200 200 200 180 180 180 180 Counts Counts Counts Counts 160 160 160 160

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0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness Haddronness

Hadronness OFF 6.0 < DC < 6.5 µA Hadronness OFF 6.5 < DC < 7.0 µA Hadronness OFF 7.0 < DC < 7.5 µA 200 200 200 180 180 180 Counts Counts Counts 160 160 160

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0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness

Figure A.6: The hadronness distribution of Crab Nebula observations, resulting from 6-3 image cleaning, for 15 different NSB levels, normalized to one hour. The black counts are the ON-position, the red counts are the OFF-position. A size cut of size > 220 phe is applied. 102 A. Appendix

Hadronness OFF 0.0 < DC < 0.5 µA Hadronness OFF 0.5 < DC < 1.0 µA Hadronness OFF 1.0 < DC < 1.5 µA Hadronness OFF 1.5 < DC < 2.0 µA 200 200 200 200

180 180 180 180 Counts Counts Counts Counts 160 160 160 160

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0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness Haddronness

Hadronness OFF 2.0 < DC < 2.5 µA Hadronness OFF 2.5 < DC < 3.0 µA Hadronness OFF 3.0 < DC < 3.5 µA Hadronness OFF 3.5 < DC < 4.0 µA 200 200 200 200

180 180 180 180 Counts Counts Counts Counts 160 160 160 160

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0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness Haddronness

Hadronness OFF 4.0 < DC < 4.5 µA Hadronness OFF 4.5 < DC < 5.0 µA Hadronness OFF 5.0 < DC < 5.5 µA Hadronness OFF 5.5 < DC < 6.0 µA 200 200 200 200 180 180 180 180 Counts Counts Counts Counts 160 160 160 160

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0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness Haddronness

Hadronness OFF 6.0 < DC < 6.5 µA Hadronness OFF 6.5 < DC < 7.0 µA Hadronness OFF 7.0 < DC < 7.5 µA 200 200 200 180 180 180 Counts Counts Counts 160 160 160

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0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Haddronness Haddronness Haddronness

Figure A.7: The hadronness distribution of Crab Nebula observations, resulting from 8-4 image cleaning, for 15 different NSB levels, normalized to one hour. The black counts are the ON-position, the red counts are the OFF-position. A size cut of size > 220 phe is applied. A.2 Additional figures and plots 103

Alpha ON 0.0 < DC < 0.5 µA Alpha ON 0.5 < DC < 1.0 µA Alpha ON 1.0 < DC < 1.5 µA Alpha ON 1.5 < DC < 2.0 µA 300 300 300 300

250 250 250 250

200 200 200 200 Counts per hour [#] Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 150 150

100 100 100 100

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00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à] Alpha [à]

Alpha ON 2.0 < DC < 2.5 µA Alpha ON 2.5 < DC < 3.0 µA Alpha ON 3.0 < DC < 3.5 µA Alpha ON 3.5 < DC < 4.0 µA 300 300 300 300

250 250 250 250

200 200 200 200 Counts per hour [#] Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 150 150

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0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 0 Alpha [à] Alpha [à] 0 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à]

Alpha ON 4.0 < DC < 4.5 µA Alpha ON 4.5 < DC < 5.0 µA Alpha ON 5.0 < DC < 5.5 µA Alpha ON 5.5 < DC < 6.0 µA 300 300 300 300

250 250 250 250

200 200 200 200 Counts per hour [#] Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 150 150

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00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à] Alpha [à]

Alpha ON 6.0 < DC < 6.5 µA Alpha ON 6.5 < DC < 7.0 µA Alpha ON 7.0 < DC < 7.5 µA 300 300 400

350 250 250 300 200 200 250 Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 200

150 100 100 100 50 50 50

00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à]

Figure A.8: The |Alpha|-distribution of Crab Nebula observations, resulting from 6-3 image cleaning, for 15 different NSB levels, normalized to one hour. A cut in hadronness h ≤ 0.1 is applied The black counts are the ON-position, the red counts are the OFF-position. 104 A. Appendix

Alpha ON 0.0 < DC < 0.5 µA Alpha ON 0.5 < DC < 1.0 µA Alpha ON 1.0 < DC < 1.5 µA Alpha ON 1.5 < DC < 2.0 µA 300 300 300 300

250 250 250 250

200 200 200 200 Counts per hour [#] Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 150 150

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00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à] Alpha [à]

Alpha ON 2.0 < DC < 2.5 µA Alpha ON 2.5 < DC < 3.0 µA Alpha ON 3.0 < DC < 3.5 µA Alpha ON 3.5 < DC < 4.0 µA 300 300 300 300

250 250 250 250

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00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à] Alpha [à]

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200 200 200 200 Counts per hour [#] Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 150 150

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00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à] Alpha [à]

Alpha ON 6.0 < DC < 6.5 µA Alpha ON 6.5 < DC < 7.0 µA Alpha ON 7.0 < DC < 7.5 µA 300 300 300

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200 200 200 Counts per hour [#] Counts per hour [#] Counts per hour [#] 150 150 150

100 100 100

50 50 50

00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 90 Alpha [à] Alpha [à] Alpha [à]

Figure A.9: The |Alpha|-distribution of Crab Nebula observations, resulting from 8-4 image cleaning, for 15 different NSB levels, normalized to one hour. A cut in hadronness h ≤ 0.1 is applied The black counts are the ON-position, the red counts are the OFF-position.

Size Distribution -Candidates | 0.5 < DC < 2.0 A Size Distribution -Candidates | 0.5 < DC < 2.0 A

Size Distribution -Candidates | 2.0 < DC < 3.0 A Size Distribution -Candidates | 2.0 < DC < 3.0 A

Size Distribution -Candidates | 3.0 < DC < 4.5 A Size Distribution -Candidates | 3.0 < DC < 4.5 A 10 Size Distribution -Candidates | 4.5 < DC < 6.0 A Size Distribution -Candidates | 4.5 < DC < 6.0 A 10 Counts per hour [#] Counts per hour [#]

1 1

10-1

10-1

2.5 3 3.5 4 4.5 5 2.5 3 3.5 4 4.5 5 Size [phe] Size [phe]

Figure A.10: The differential size distribution of gamma candidates during Crab Nebula obser- vations under four different NSB levels. (left: 6-3, right: 8-4 image cleaning) A.2 Additional figures and plots 105 ] ]

-1 Gamma Rate ExcessEvents dependend on size cut | 0.5 < DC < 1.0 µA -1 Gamma Rate ExcessEvents dependend on size cut | 0.5 < DC < 1.0 µA Gamma Rate ExcessEvents dependend on size cut | 1.0 < DC < 1.5 µA Gamma Rate ExcessEvents dependend on size cut | 1.0 < DC < 1.5 µA Gamma Rate ExcessEvents dependend on size cut | 1.5 < DC < 2.0 µA Gamma Rate ExcessEvents dependend on size cut | 1.5 < DC < 2.0 µA -1 Gamma Rate ExcessEvents dependend on size cut | 2.0 < DC < 2.5 µA Gamma Rate ExcessEvents dependend on size cut | 2.0 < DC < 2.5 µA 10 Gamma Rate ExcessEvents dependend on size cut | 2.5 < DC < 3.0 µA -1 Gamma Rate ExcessEvents dependend on size cut | 2.5 < DC < 3.0 µA Gamma Rate ExcessEvents dependend on size cut | 3.0 < DC < 3.5 µA 10 Gamma Rate ExcessEvents dependend on size cut | 3.0 < DC < 3.5 µA Gamma Rate ExcessEvents dependend on size cut | 3.5 < DC < 4.0 µA Gamma Rate ExcessEvents dependend on size cut | 3.5 < DC < 4.0 µA Gamma Rate ExcessEvents dependend on size cut | 4.0 < DC < 4.5 µA Gamma Rate ExcessEvents dependend on size cut | 4.0 < DC < 4.5 µA Gamma Rate ExcessEvents dependend on size cut | 4.5 < DC < 5.0 µA Gamma Rate ExcessEvents dependend on size cut | 4.5 < DC < 5.0 µA Gamma Rate ExcessEvents dependend on size cut | 5.0 < DC < 5.5 µA Gamma Rate ExcessEvents dependend on size cut | 5.0 < DC < 5.5 µA Gamma Rate ExcessEvents dependend on size cut | 5.5 < DC < 6.0 µA Gamma Rate ExcessEvents dependend on size cut | 5.5 < DC < 6.0 µA 10-2

10-2

10-3 Integrated Gamma Rate [s Integrated Gamma Rate [s

10-3 10-4

2.5 3 3.5 4 4.5 5 2.5 3 3.5 4 4.5 5 log10(Size Cut [phe]) log10(Size Cut [phe])

Figure A.11: Integrated size distributions of γ-excess events for both image cleanings (left: 6-3, right: 8-4 ) and 11 different background levels.

Figure A.12: Effective collection area before and after cuts for both image cleaning levels (left: 6- 3, right: 8-4 ). The marker style indicate the simulated background level. Circle corresponds to 1.0 NSB, a square is 2.5 NSB, a up-pointing triangle is 3.75 NSB and a down-pointing triangle is 5.5 NSB. 106 A. Appendix ] -1

s Crab Nebula Differential Spectrum | Zenith range 5-30à -2 Differential Spectrum | 0.8 < NSB < 2.0 [NSB units]

cm Differential Spectrum | 2.0 < NSB < 3.0 [NSB units] -1 10-9 Differential Spectrum | 3.0 < NSB < 4.5 [NSB units]

Differential Spectrum | 4.5 < NSB < 6.0 [NSB units] dN/dE [TeV 10-10

10-11

10-12 103 Estimated Energy [GeV] ] -1

s Crab Nebula Differential Spectrum | Zenith range 5-30à -2 Differential Spectrum | 0.8 < NSB < 2.0 [NSB units]

cm Differential Spectrum | 2.0 < NSB < 3.0 [NSB units]

-1 -9 10 Differential Spectrum | 3.0 < NSB < 4.5 [NSB units]

Differential Spectrum | 4.5 < NSB < 6.0 [NSB units] dN/dE [TeV 10-10

10-11

10-12 103 Estimated Energy [GeV]

Figure A.13: Calculated spectra of Crab Nebula under four different NSB levels for two image cleaning levels (up: 6-3, below: 8-4 ) calculated with dark night Monte Carlos. The effective collection area is not calculated correctly, and the spectrum is not reliable. The left plot corresponds to the MAGIC standard analysis. Here one can see, that the standard analysis gives the correct result compared to dark-night results until 2.5 NSB. Bibliography

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The first person I would like to thank is Professor Masahiro Teshima. I am deeply grate- ful for giving me the opportunity to write my diploma thesis in his group. Over the past year, he always supported me with helpful suggestions. Special thanks go to my adviser Robert Wagner. I want to express my gratitude for the time he spent on dis- cussions with me. His comments and ideas play a crucial role in the results of this thesis.

Furthermore I also want to acknowledge Professor Christian Kiesling for supervising my thesis and thus giving me the possibility to work on this great subject. I also want to thank Professor Otmar Biebel for supporting me several times during my complete study.

I like to thank my room mates, Julian Sitarek and Ching Cheng Hsu for discussions and a lot of help on many technical problems. My thanks also go to all members of the group, who create a friendly and productive atmosphere. Here, I want to give especially thousands ”Thank you” to Eckart Lorenz for the very detailed reading of my thesis and the discussions about my topic. Special thanks go also to Nikola Strah for several inspi- rations on the moon model.

I especially want to acknowledge my colleagues Florian Abicht, Jan Heyder and Anna Melbinger for supporting me and always beeing friends to me. They helped me out every way they could.

I like to thank my family and friends. My parents, Brigitte and Hermann Britzger and my brother Michael who always supported me during the whole period of studying. They always believed in the success of this work and encouraged me in cumbersome times. Last, I want to thank my girlfriend Lisa for loving me and beeing with me. Without her this work had not been possible.

Ich versichere, die Arbeit selbstst¨andigangefertigt und dazu nur die im Literaturverzeichnis angegebenen Quellen benutzt zu haben.

M¨unchen, den 30. Juni 2009