Search for Variability of the VHE Γ-Ray Source HESS J1745-290 in the Galactic Center

Search for variability of the VHE γ-ray source HESS J1745-290 in the Galactic Center

Dissertation

zur Erlangung des akademischen Grades

doctor rerum naturalium

(Dr. rer. nat.)

im Fach Physik

Spezialisierung: Experimentalphysik

eingereicht an der

Mathematisch-Naturwissenschaftlichen Fakultät

der Humboldt-Universität zu Berlin

von

Philipp Wagner Präsidentin der Humboldt-Universität zu Berlin: Prof. Dr.-Ing. Dr. Sabine Kunst

Dekan der Mathematisch-Naturwissenschaftlichen Fakultät: Prof. Dr. Elmar Kulke

Gutachter:

1. Prof. Dr. Thomas Lohse 2. Prof. Dr. Elisa Bernardini 3. Prof. Dr. Markus Böttcher

Tag der mündlichen Prüfung: 2.5.2017

Abstract

This work presents a detailed study on the very-high-energy (VHE) γ-ray source HESS J1745-290 in direction of the Galactic Center using 10 years of data from the H.E.S.S. array of Cherenkov telescopes from 2004 to 2014 with the objective to search for variability of the γ-ray fux of this object. The question if HESS J1745-290 shows variability is of special interest, since the source is located at the same direction as the super-massive black hole Sgr A*. From the vicinity of this black hole variable radiation has been reported for diferent wavelength bands. The detection of a variability of the VHE γ-ray fux of HESS J1745-290 would favor the hypothesis of a connection of this object and Sgr A* which could not be confrmed so far. The search for variability was performed for diferent timescales from minutes to years and indeed revealed evidence for variability in diferent statistical tests which will be discussed in detail together with systematic cross-checks. The study focuses on both variability with and without periodic character. While there is evidence for a long- term fux modulation with a period of 110 d at the 4.1σ signifcance level, the χ2 ft of a H.E.S.S. run-wise light curve from 2004–2014 shows variability at the 6.1σ level, which reduces to 4.5σ after adding a 10% systematic error to each fux measurement. Also signs of variable behavior at a timescale of minutes were found at the 3.1σ level. This tentative VHE short-term variability also shows quasi-periodic behavior as it was reported during infrared and X-ray observations of Sgr A*. Such a tentative long-term fux modulation with a period of 110 d has previously also been reported for the radio band. Due to the similarity of time structure of the variability, which is reported for HESS J1745-290 in this thesis to observations of Sgr A* at other wavelength bands, the thesis will close with the discussion if these results can be considered to be frst evidence for a link between HESS J1745-290 and Sgr A*.

Kurzzusammenfassung

Die folgende Arbeit beschäftigt sich mit der Quelle hochenergetischer Gammastrahlung HESS J1745-290, welche in Richtung des galaktischen Zentrums liegt und präsentiert die Analyse eines Datensatzes, der von den H.E.S.S. Teleskopen zwischen 2004 und 2014 aufgezeichnet wurde. Ziel der Untersuchung war es, eine zeitliche Variabilität des beobachteten Flusses festzustellen. Die Frage ob der Fluss von HESS J1745-290 variables Verhalten zeigt stellt sich, da sich die Quelle in der gleichen Richtung wie das supermassive schwarze Loch Sgr A* befndet, aus dessen Umgebung bereits variable Strahlung in verschiedenen Frequenzbereichen detektiert wurde. Die Beobachtung einer Variabilität des hochenergetischen Gammastrahlenfusses von HESS J1745-290 würde die Hypothese eines Zusammenhangs zwischen diesem Objekt und Sgr A* stützen, welche bis dato nicht bestätigt werden konnte. Die Suche nach Variabilität wurde für verschiedene Zeitskalen von Minuten bis hin zu Jahren durchgeführt, wobei Hinweise für Variabilität in verschiedenen statistischen Tests gefunden wurden. Die Suche konzentriert sich auf Variabilität ohne periodischen Charakter sowie auf Periodizität. Es wurden Hinweise auf eine Periode von 110 Tagen bei einem Signifkanzniveau von 4.1σ gefunden und auch der χ2 Fit einer H.E.S.S. Lichtkurve, die von 2004–2014 reicht, zeigt Variabilität bei einem Signifkanzniveau von 6.1σ, welches sich nach Anwendung eines systematischen Fehlers von 10% auf 4.5σ reduziert. Auch Anzeichen für Variabilität auf einer Zeitskala von Minuten wurden gefunden. Diese Variabilität auf einer Zeitskala von Minuten zeigt quasi-periodischen Charakter, ähnlich derer, welche während Infrarot- und Röntgenbeobachtungen von Sgr A* festgestellt wurde. Die Möglichkeit einer Verbindung zwischen HESS J1745-290 und Sgr A* und ins- besondere auch die Fragestellung, ob die hier präsentierten Ergebnisse als erster Hinweis auf solch einen Zusammenhang gewertet werden können, werden Thema der Diskussion am Ende der Arbeit sein.

Contents

Contents7

1 Introduction9 1.1 Astroparticle Physics: Studying Cosmic Accelerators ...... 10 1.2 The non-thermal Milky Way and the Galactic Center Region ...... 11

2 The High Energy Stereoscopic System 13 2.1 Air Showers and Cherenkov Light Cones ...... 14 2.1.1 The Cherenkov Efect ...... 14 2.1.2 Diferent Types of Air Showers ...... 15 2.2 The H.E.S.S. Experiment: Science and Detector ...... 17 2.2.1 The H.E.S.S. Site ...... 17 2.2.2 H.E.S.S. Phase I ...... 19 2.2.3 H.E.S.S. Phase II ...... 19 2.2.4 The diferent Subsystems of the H.E.S.S. Detector ...... 20 2.2.5 Calibration and Detector Simulations ...... 24 2.2.6 Detector Simulations ...... 25 2.3 Reconstruction and Particle Identifcation ...... 25 2.3.1 The Standard Hillas Reconstruction ...... 26 2.3.2 Particle Identifcation: Moving towards Pattern Recognition . . . 28

3 The Galactic Center Source HESS J1745-290 35 3.1 Variability of Sgr A*: multi-wavelength Results ...... 36 3.1.1 A Periodicity at about 110 Days ...... 36 3.1.2 Short and weak Flares during Infrared and X-Ray Observations . 38 3.1.3 The G2 Gas Cloud ...... 43 3.1.4 Giant X-Ray Flares ...... 44 3.1.5 Estimates of the Frequency of Galactic Center Flares ...... 44 8 Contents

3.2 Summary of H.E.S.S. I Results from 2006 ...... 45 3.3 Summary ...... 47

4 Search for Variability of HESS J1745-290 49 4.1 Methods: Variability and Periodicity Tests ...... 49 4.1.1 Light Curves: A Defnition ...... 49 4.1.2 Periodicity Tests ...... 50 4.2 Data Analysis ...... 64 4.2.1 The Dataset, Cuts and Background Method ...... 65 4.2.2 Skymap of the Galactic Center Region ...... 67 4.2.3 The Spectrum of HESS J1745-290 with Loose Cuts ...... 69 4.2.4 Search for a long-term Variability ...... 73 4.2.5 Search for a Variability at a Timescale of Minutes ...... 98 4.2.6 Run-wise χ2 Test of the post-cut Event Rates ...... 117

5 Summary and Outlook 127 5.1 Summary ...... 127 5.2 Comparison to MWL Observations ...... 128 5.3 Cross-Checks and External Data ...... 131 5.4 Candidate Mechanisms explaining the observed Variability ...... 133 5.5 Conclusion and Outlook ...... 134

Bibliography 139

A Simulated Monte Carlo Event Displays for gamma-like Events 153

B Studies with respect to Broken Pixels 155 Chapter 1

Introduction

The cosmic rays (CRs) were discovered by Victor H.E.S.S. in August 1912 during a balloon fight from Aussig to Pieskow which was preceded by several other measurements. His important discovery, which was awarded with the Nobel Prize in physics in 1936, can be considered to be a mile stone on the way towards modern particle physics and also the starting point of a new discipline: The astroparticle physics which needed about 60 years after the discovery of cosmic radiation to emerge as independent discipline next to the classical accelerator based particle physics. Today the astroparticle physics studies the most violent phenomena in the universe and particles reaching energies that no accelerator on earth has reached so far. While the Large Hadron Collider (LHC) in Geneva reaches a center of mass energy of 13 TeV since 2015, modern γ-ray detectors measure particles at several 10 TeV. Even so-called PeVatrons, accelerators reaching energies in the petaelectronvolt (PeV) range are in sight now. While the majority of CRs reaching the atmosphere of the earth consists of protons and heavier nuclei, there are also highly energetic electrons (positrons) and photons. There should be a correlation between regions of CR production and the direction of high energy photons which are emitted due to the interaction of CRs with magnetic felds and matter in their environment. An important hadronic production mechanism of high energy photons is via the production of secondary π0 mesons which decay into photon pairs afterwards. Photons with an origin in the π0 decay usually have larger energies than those which are produced via synchrotron emission. Their minimum energy is half the mass of the π0 in the rest frame which implies that photons which are produced via the π0 decay have energies of at least ∼ 70 MeV. In general photons with energies ≥ 1 MeV are called γ-rays. Next to these hadronic production mechanisms γ-rays can also be produced by leptons. While at MeV energies the synchrotron emission is the dominant process, for the γ-ray production in the GeV and TeV range Inverse Compton (IC) 10 Introduction scattering where γ-rays (which could be produced as synchrotron radiation before) gain energy from an interaction with relativistic electrons is the most important mechanism. The photons produced by these diferent mechanisms cover a large energy range up to 100 TeV. Due to the fact that γ-rays are not bent by magnetic felds like electrons and protons they form an excellent tool to observe the universe at high and very high energies (VHE, E > 0.1 TeV). From the 70ies of the last century onwards systematic eforts were undertaken to study γ-rays and the γ-ray astronomy was born as a new discipline. While the γ-ray sky at energies of about 100 MeV is dominated by Galactic and extragalactic difuse emission, more and more point like sources were discovered in the GeV and TeV range. Since photons with energies larger than 10 eV do not pass the atmosphere of the earth there are only two methods to observe them: The frst strategy is to go to space and observe with a satellite experiment. Prominent detectors of this type are the Energetic Gamma Ray Experiment Telescope (EGRET) [102] and its successor the Fermi Large Area Telescope (LAT) [36]. On the other hand, there is a ground-based approach using so-called Imaging Atmospheric Cherenkov Telescopes (IACTs) which use the earth’s atmosphere as calorimeter and detect cosmic γ-rays indirectly using the Cherenkov light of the showers which the initial particles create by their interaction with the atmosphere. The concept of IACTs to observe cosmic γ-rays was introduced at the Fred Lawrence Whipple Observatory [78] in the late 1960s with a single 10 m diameter Cherenkov telescope and led to a successful series of discoveries which is continued by recent projects like the High Energy Stereoscopic System (H.E.S.S) [107] among others which will be used in Chapter 2 to illustrate the concept of IACTs in more detail. Although signifcant progress in understanding the origin of CRs was made during the last decades, it is still not fully understood. Concerning the highly energetic γ-rays, several categories of objects emitting such radiation could be identifed some of which will be shortly explained in the next section. The last section of this introductory chapter is dedicated to the central region of the Milky Way from the VHE γ-ray perspective with focus on the central γ-ray source HESS J1745-290 which is the main subject of this thesis.

1.1 Astroparticle Physics: Studying Cosmic Accel- erators

One of the key science targets of astroparticle physics is studying cosmic accelerators and mechanisms producing the high energy particles arriving at earth. Although this mission is far from being fnished at the time of this writing, there are several successful models 1.2 The non-thermal Milky Way and the Galactic Center Region 11 explaining parts of the phenomena. The most prominent acceleration mechanism is the so-called Fermi or difusive shock acceleration [68] which charged particles experience when they are refected at so-called magnetic mirrors. These magnetic mirrors can be formed by magnetic inhomogeneities which are related to shock-waves for example. By repeated downstream to upstream refections the particle gains energy and the resulting spectral distribution created by this process can be approximated by a power-law. This process is also called frst order Fermi acceleration. Shocks which are strong enough for a signifcant acceleration are produced in violent astrophysical processes like supernova explosions which attain velocities of the order of 104 km s−1 [69] or during jet- like outbursts close to super-massive black holes, mostly located within so-called active galactic nuclei (AGNs) which can be found in the center of many galaxies. Furthermore, charged particles can also undergo second order Fermi acceleration which takes place in case they interact with randomly moving magnetic mirrors (e.g. magnetized gas clouds). Whenever such a mirror is moving towards the direction of movement of the refected particle it will gain energy by the refection. For the γ-ray astronomy this means that the observed HE and VHE emission is expected to be associated with supernova explosions and their leftovers and pulsar-wind nebula (PWNe) and their corresponding pulsars on the one hand and super-massive black holes on the other hand. Indeed many of these objects have been detected as γ-ray sources meanwhile and form an important component of our picture of the non-thermal universe and our galaxy.

1.2 The non-thermal Milky Way and the Galactic Center Region

The discoveries made during the last 20 years dramatically changed the non-thermal picture of our own galaxy, the Milky Way. While at the beginning of this century only a couple of γ-ray sources like the famous Crab Nebula [48] were known, until 2015 more than 150 individual TeV sources could be identifed, whereby H.E.S.S. and Fermi LAT made a signifcant contribution. Most γ-ray sources within our galaxy could be identifed as SNRs or PWNe but there are several γ-ray sources the nature of which has not yet been revealed. An especially interesting point-like source of this kind is located right in the direction of the center of our galaxy where also the prominent black hole Sagittarius A* (Sgr A*) can be found. Sgr A* was discovered as a strong radio source in 1974 at the National Radio Astronomy Observatory (NRAO) [51] and its mass could be determined to be (4 31 0 06 0 36 ) 106 solar masses ( )[91]. It is located at a distance . ± . |stat ± . |R0 × MSun 12 Introduction of about 8.5 kpc. The discovery of this VHE γ-ray emission from the direction of the Galactic Center (GC) by CANGAROO-II [27] and H.E.S.S. [51] in 2004 triggered many speculations about its origin. The corresponding source is called HESS J1745-290 [10] in the following since due to the complexity of the GC region there are diferent sources and processes which could contribute to the observed signal. Despite the positional coincidence of HESS J1745-290 with Sgr A* within the angular resolution of the H.E.S.S. detector it could not be proven so far that the GeV and TeV emission from the GC is connected to this object. While the supernova-remnant (SNR) Sgr A East [92] could be ruled out to coincide with HESS J1745-290, the nearby pulsar wind nebula (PWN) G359.95-0.04 [109] is still a candidate to cause the VHE γ−ray emission from the direction of the GC. Also exotic explanations like dark matter could play a role, although no evidence for that has been found so far. Furthermore, in 2013 the Nuclear Spectroscopic Telescope Array (NuSTAR) [1] discovered a new magnetar only 2.8′′ away of Sgr A* which pulsates with a period of 3.76 s and showed an increased activity in 2013 [105]. The pulsed fux was observed at keV energies. A possible approach to understand the γ-ray emission from the GC is to search for a variability in time. While the difuse emission, PWNe or a hypothetical Dark Matter (DM) halo produce a constant fux, the environments of black-holes are usually highly variable at all energies. This could be shown for many AGNs so far. For a better understanding of HESS J1745-290 it is essential to investigate if this source shows a constant γ-ray fux like a typical PWN or SNR or indeed shows signs of variability which would support the hypothesis of a link between Sgr A* and HESS J1745-290. The main objective of this thesis is to perform such a study with the full H.E.S.S. dataset available by the time of writing and shed some light on this interesting question. After a short description of the H.E.S.S. experiment in Chapter 2 there will be an introduction to the data analysis techniques and statistical tests which are used in Chapter 3 and 4, followed by a discussion and interpretation of the results presented there. Chapter 2

The High Energy Stereoscopic System

The H.E.S.S. experiment, which is located in the Khomas Highland in Namibia, is an array of 4+1 IACTs and has been inaugurated in 2003. During its frst phase (H.E.S.S. I) it consisted of four Cherenkov telescopes of the same type with a diameter of 12 meters. In 2012, the array was extended by another, larger telescope starting the second phase of the H.E.S.S. project (H.E.S.S. II). The H.E.S.S. array can be operated in diferent setups either combining all 5 telescopes (stereo or hybrid mode) or using the large telescope (CT5) in stand-alone mode while operating the four small telescopes (CT1 - CT4) in a diferent sub-array. The full H.E.S.S. array with its fve telescopes is shown in Fig. 2.0.1. The following sections will present an overview on the principles of Cherenkov astronomy together with an introduction to the available methods of event reconstruction and data analysis. In order to be able to detect cosmic γ-rays at the earth’s surface, the use of Cherenkov telescopes is necessary since high-energy γ-rays cannot penetrate the earth’s atmosphere without interaction and can only be detected indirectly from the ground level via the Cherenkov light cones, the secondary shower particles produce on their way through the atmosphere. In order to defne the requirements for such a detector, one needs a detailed understanding of these Cherenkov air-showers. The design of the H.E.S.S. detector has been optimized with respect to being as sensitive as possible and also providing a relatively large Field of View (FoV) with a diameter of 5°. The angular resolution of the detector is better than 0.1° and its energy resolution is about 20%. Like that, it is possible to detect a γ-ray source with 1% of the fux of the Crab Nebula (which can be considered to be a standard-candle in γ-ray astronomy) at the 5σ level in only about 25 hours (with the H.E.S.S. I sub-array at low zenith angles ≤ 20°). An important challenge 14 The High Energy Stereoscopic System

Figure 2.0.1: The H.E.S.S. Array with its 5 telescopes. The large telescope CT5 is surrounded by the four telescopes from H.E.S.S. I. Image: The H.E.S.S. Collaboration. in Cherenkov astronomy is to distinguish the showers which are induced by primary γ- rays from a huge number of background showers, which are triggered by hadrons and also by electrons. Furthermore, light cones by muons contribute to the background. The diferences of showers with a γ-ray as primary particle and those having a diferent origin will be discussed in this chapter. The background suppression especially gets very important when CT5 is operated in mono-mode at energies below 100 GeV where the background contribution increases dramatically.

2.1 Air Showers and Cherenkov Light Cones

The following paragraphs give an overview of the characteristics of the diferent shower types which are relevant for Cherenkov astronomy after a short defnition of the Cherenkov efect.

2.1.1 The Cherenkov Efect

The Cherenkov efect was discovered by the Russian physicist Pawel Alexejewitsch Tscherenkow and refers to the electromagnetic radiation which is emitted whenever a charged particle moves in a dielectric medium with a velocity which exceeds the speed of light in that medium. A prominent example of this radiation is the bluish light which is emitted by a nuclear reactor operated under water. The cone-like light emission is 2.1 Air Showers and Cherenkov Light Cones 15 created by a polarization of the surrounding medium in combination with a constructive interference of the electromagnetic waves which are created during that process. This constructive interference only takes place when the velocity of the particle is greater than the speed of light in the medium the particle is crossing, otherwise the elementary waves created during the interaction of the particle with the surrounding medium interfere destructively and do not form a coherent wave. The Cherenkov light is emitted in a cone with a characteristic opening angle with cos( ) = 1 where is . Only θ θ nβ β v/c particles with β > 1/n where n is the refractive index of the medium emit Cherenkov radiation and low mass particles dominate the emission. Considering the fact that the refractive index of the atmosphere varies as a function of the altitude, a shower on its way to the ground experiences diferent Cherenkov angles between 0.5° and 1.4°. The wavelength of the Cherenkov light of an air-shower varies between 250 nm (blue) and 700 nm (red).

2.1.2 Diferent Types of Air Showers High-energy particles interacting with the atmosphere always induce cascades of secondary particles which form an air-shower. It can either be triggered by electrons positrons or γ-rays with only electromagnetic interactions being present or by hadronic particles like protons or heavy nuclei, where the strong interaction is dominant and induces more heterogeneous cascades. During the development of such a shower the number of particles increases with each interaction or radiation length until the shower maximum is reached. At the same time, the energy per particle decreases, which results in the shower fading away after reaching its maximum.

2.1.2.1 Electromagnetic showers

For Cherenkov astronomy the electromagnetic showers are the most interesting class of showers since they allow the observer to detect VHE γ-rays. For this class of showers a combination of pair production and bremsstrahlung are the most important energy loss mechanisms. Ionization of molecules in the air only plays a role when the average particle energy reaches the critical energy of about 81 MeV in air where those losses are comparable to those by bremsstrahlung. At this point the shower development stops due to the electrons and positrons not being able to produce secondary photons any more. The frst interaction for primary particles with energies > 10 GeV, which is shown schematically in Fig. 2.1.1, typically takes place at a height of several 10 km above the sea level. The depth of the shower maximum is approximately proportional 16 The High Energy Stereoscopic System

Figure 2.1.1: The typical start of an electromagnetic shower. The initial γ-ray triggers a cascade of secondary particles via pair production. to the logarithm of the energy of the primary particle (a fact which also can be used for the energy reconstruction of the initial particle). While the pair production and bremsstrahlung processes are strongly forward-directed in the laboratory frame due to the large boost of the primary particle, the lateral shower development is dominated by elastic collisions of the shower particles with air molecules. An important quantity describing the transverse extension of the shower is the Moliere radius, which is the radius of a cylinder containing on average 90% of the shower particles. A typical Moliere radius of an electromagnetic shower at sea level is about 60 m to 90 m, which means that these showers are rather narrow and give a good guideline for the dimension of a telescope array together with the Cherenkov angle of the shower. Although showers induced by γ-rays and electrons are dominated by the same processes, there is a slight diference between these two shower types: For primary γ-rays the frst interaction is a pair-production process while electrons (positrons) undergo bremsstrahlung frst. Since the mean free path length for pair production at high energies is larger than the radiation length for bremsstrahlung, the height where the frst interaction takes place slightly difers for the two types. Therefore, also the height of the shower maximum for electron- and γ-induced showers difers by about 5%. This is the only diference between these two classes of showers, which makes it difcult in practice to distinguish between them.

2.1.2.2 Hadronic showers Hadronic showers show a completely diferent behavior than the electromagnetic showers due to the fact that weak and strong interaction processes are involved. This leads to hadrons and leptons as secondary particles. During the frst interaction of cosmic ray hadrons with nuclei in the atmosphere, secondary pions (and also protons and kaons) 2.2 The H.E.S.S. Experiment: Science and Detector 17 are produced which then induce the secondary cascades. Since strong inelastic scattering takes place, the fnal state mesons usually have sizable transverse momenta which results in a large lateral extension of hadronic showers in comparison to the narrow electromagnetic showers. While the neutral pions, which are produced in the initial reaction decay into two photons, induce an electromagnetic sub-shower, the charged pions (π+, π−) have muons and neutrinos as fnal states after their decay. While the neutrinos obviously escape without an interaction, the muons often reach the ground level without further interactions emitting a ring-like cone of Cherenkov light. In the same way, the hadronic showers give a heterogeneous picture in the camera and show larger fuctuations across the telescope array: While a particular telescope sees a sub-shower which has been induced by a γ-ray from the pion decay a second telescope may see a clear muon ring. Also the shower width of hadronic showers is larger. That way they can be identifed relatively easily by combining the information from several telescopes (in mono mode this is more complicated of course). Also the integrated pixel intensity measured in a specifc telescope fuctuates stronger between the diferent telescopes for hadronic showers. The intensity maximum of hadronic showers is located deeper in the atmosphere than for γ-induced showers due to a larger free mean path lengths of hadrons.

2.2 The H.E.S.S. Experiment: Science and Detector

The next sections will describe the H.E.S.S. experiment in more detail and give an overview of past and ongoing science projects at H.E.S.S. Relevant sub-systems and data taking procedures will be introduced together with references providing further information.

2.2.1 The H.E.S.S. Site

H.E.S.S. has been built in the southern hemisphere in order to be able to observe the Galactic plane and especially the Galactic Center region at high elevations. The telescope array is located in Namibia, about two hours south-west of the capital Windhoek at the exact position with the coordinates 23°16’18” S, 16°30’00” E at an altitude of 1800 m above the sea level. The site was chosen due to its excellent climatic conditions for astronomical observations. 18 The High Energy Stereoscopic System

Figure 2.2.1: The inner Galactic plane as seen in the H.E.S.S. Galactic Plane Survey, where the color scale describes the statistical signifcance for an excess within a 0.22° radius at each position. Figure from Ref. [53]. 2.2 The H.E.S.S. Experiment: Science and Detector 19

2.2.2 H.E.S.S. Phase I The H.E.S.S. experiment was operated as four-telescope array from 2004 until 2012 and is considered to be the most successful ground-based γ-ray observatory, achieving many high impact results like the H.E.S.S. Galactic Plane Survey (HGPS), which revolution- ized our image of the Galactic plane in the TeV range revealing an unexpectedly large and diverse population of over 60 TeV γ-ray sources. An excerpt of the result of the HGPS is shown in Fig. 2.2.1. Before this scan, less than 10 sources where known at TeV energies. Further highlights of Phase I were the stringent upper limits on the velocity- weighted dark matter (DM) annihilation cross-section for the Galactic Center halo, frst evidence for a difuse large scale emission in the Galactic plane or the frst detection of a pulsar wind nebula in the Large Magellanic Cloud (LMC). Furthermore, shell-type SNRs could be identifed as γ-ray sources. Some extragalactic highlights are the discovery of VHE γ-ray emission from the star burst galaxy NGC 253 or an upper limit on the extragalactic background light at optical/near-infrared wavelengths which, implies that the intergalactic space is more transparent to γ-rays than expected. Analyzing the full dataset of the Galactic Center region, H.E.S.S. recently found hints for Pevatrons (acceleration mechanisms reaching the PeV range) by showing that the difuse emission close to the Galactic Center does not have a cut-of. The search for pulsed emission from γ-ray pulsars in data from the four telescope array did not lead to any conclusive results, which put high expectations on Phase II [5, 11, 52, 60, 89, 100].

2.2.3 H.E.S.S. Phase II In 2012 the new telescope in the center of the array was inaugurated. With its large mirror area (diameter 28 m) it is the largest optical telescope in the world at the time of this writing. The new telescope was built to lower the energy threshold of the array by almost an order of magnitude from 100 GeV to about 10 GeV, which gives an excellent overlap with the Fermi LAT for this energy range, which is a satellite experiment. The low threshold was motivated by diferent physics objectives: • Pulsed emission: Fermi LAT observed many γ-ray pulsars in this energy range the most promising of which being the Vela pulsar. First H.E.S.S. II results from 2015 confrmed the pulsations of the Vela pulsar seen by Fermi LAT at energies > 20 GeV [34].

• Gamma Ray Bursts (GRBs): So far no ground-based γ-ray telescope ever managed to detect a GRB. Due to its large efective collection area and its fast drive system CT5 is an ideal telescope to search for such GRBs. 20 The High Energy Stereoscopic System

• Dark Matter: The search for an annihilation signature of Weakly Interacting Massive Particles (WIMPs) or other exotic dark matter particles still is a hot topic. In 2012 there has been a promising signature in Fermi LAT data at 130 GeV close to the GC, which would have been an ideal target for H.E.S.S. II. However, this signal could be ruled out by the Fermi Collaboration before H.E.S.S. II could collect sufcient statistics to make a statement on this topic.

• The Galactic Center region: Due to its good angular resolution CT5 would be the ideal telescope to study the Galactic Center region and fnd unresolved sources in that region.

The list above shows that there is a diverse spectrum of science targets for H.E.S.S. II some of which still are waiting to be exploited.

2.2.4 The diferent Subsystems of the H.E.S.S. Detector The diferent subsystems of the H.E.S.S. detector will only be mentioned very briefy here since a good overview can be found in the references quoted at the end of each paragraph. An exception here is the Data Acquisition System (DAQ), since the author has been working as an expert for this system from 2012 to 2015. The focus here will be especially on the steps which were necessary to prepare the system for the integration of CT5.

2.2.4.1 The Cameras of CT1 - CT4 The telescopes CT1 to CT4 are all equipped with cameras of the same type. Each camera in total contains 960 photo-multipliers (PMTs), whereby each PMT covers a solid angle of 0.16° in diameter. This gives a total feld of view of 5° when the sub-array CT1 - CT4 is operated in a stand-alone mode. The PMTs are grouped in so-called drawers which contain 16 pixels each and contain the electronics which is needed for triggering and data-acquisition along with the power supplies for the PMTs. The PMTs have very short reaction times of a few nano-seconds and are sensitive in a wavelength-range of 300–700 nm which perfectly fts the Cherenkov light-spectrum created by an air-shower [50, 108].

2.2.4.2 The CT5 Camera The CT5 camera mimics the design of the H.E.S.S I cameras with the diference of providing considerably more PMTs in order to achieve a better angular resolution and 2.2 The H.E.S.S. Experiment: Science and Detector 21 a lower energy threshold. The total number of PMTs used for the CT5 camera is 2048. CT5 is the frst telescope in the world where the camera can be automatically removed from the telescope and put into a shelter in case of bad weather conditions or if maintenance is needed. In total the process of loading or un-loading the camera takes about 45 minutes [56].

2.2.4.3 The Trigger The H.E.S.S. trigger system consists of two levels. The frst level is installed directly at the individual telescopes. An individual telescope triggers when a threshold of 5.3 photo- electrons is exceeded for at least 3 PMTs within a sector of 64 PMTs in a time window of 1.5 ns. The Central Trigger forming the second level is combining the signals from the diferent telescopes and requires that at least two telescopes have triggered within a time window of 80 ns. In case an event is accepted by the Central Trigger, an event number is assigned together with a GPS time-stamp and distributed to all telescopes, which were involved in the trigger. Then the data is read out from the analogue ring bufers in the telescopes where it is temporarily stored and sent to the DAQ computing cluster where it is ultimately written to disk [90].

2.2.4.4 Data Acquisition, Run Control and Monitoring In contrast to other Cherenkov telescope systems like VERITAS [81] and MAGIC [24], H.E.S.S. uses a combined system for Data Acquisition, Run Control and Monitoring which is referred to as DAQ in the following. It was designed to meet all science requirements of the H.E.S.S. array: An important factor here is the dead-time of the array which may not be increased artifcially by the DAQ. Therefore, the system has to be able to deal with a data rate of at least 50 MB/s where the four H.E.S.S. I telescopes contribute 900 Hz with an event size of 4.5 kB and CT5 up to 3.4 kHz with an event size of 10 kB. In order to have some tolerance also with respect to possible further H.E.S.S. upgrades at least 80 MB/s are required for the whole system. Furthermore, sufcient storage capacities in Namibia are needed in order to store the data until it has been safely transferred to the European data centers in Lyon (France) and Heidelberg (Ger- many). For the transfer to Europe the data are written on tapes, which are shipped via airplane to the two European data centers each of them receiving its own copy. From the hardware perspective the H.E.S.S. DAQ during H.E.S.S. I consisted of 5 servers and 10 worker nodes. These are linked via optical 1 Gigabit/s connections to the telescopes via two main network switches. Furthermore, there is an internal, independent network for the communication between the diferent servers and nodes. A sketch of the 22 The High Energy Stereoscopic System

Figure 2.2.2: Schema of the network layout and storage units of the H.E.S.S. DAQ system. The telescopes are linked to the worker nodes and data servers in the control room building (upper part of the fgure) via two main switches. All connections work at the gigabit/s level. The green lines illustrate a physically separated networks for the internal communication between data servers and worker nodes, while the black lines indicate the connections from/to the telescopes. The fgure was taken from Ref. [3]. 2.2 The H.E.S.S. Experiment: Science and Detector 23 system layout can be found in Fig. 2.2.2. The task of the worker nodes is to receive the data from the telescopes and to write it to the actual storage space via a network fle system (NFS). The nodes do not provide any facilities for long-term storage in contrast to the servers. Initially, only one of the servers was dedicated to storage providing 12 TB for data, while the remaining four servers were used for diferent tasks like hosting the H.E.S.S. database or user home directories and virtual machines which are needed by the cameras. Like that the initial DAQ system had 12 TB for storage while the rest of the available disk space was dedicated to other tasks. During H.E.S.S. I this was sufcient, however, to meet all requirements of a full hybrid system the H.E.S.S. DAQ system needed to be upgraded in 2013: Considering the rate of the full system, under good instrumental and weather conditions one would expect a data rate of about 10 TB/months during the winter time when the nights are long. Therefore, 12 TB clearly were not sufcient to guarantee to store the data from at least three months on site which is also a design requirement. Furthermore, the data rates were limited by the fact that all the data had to be written via a single network interface to the same hardware RAID (RAID stands for Redundant Array of Inexpensive Disks, self-explaining) by both network transmission and the I/O rate of the RAID controller. In order to increase the bandwidth and storage capacity for H.E.S.S. II (and further upgrades), two more data servers were integrated into the system together with an upgrade of the disks forming the hardware RAID: For the two new servers 3 TB disks were used instead of 1 TB disks which were used before (the diference in price is only marginal). Furthermore, a third machine (the previous data server) was also upgraded with 3 TB disks. Like that there are three servers with a capacity of 36 TB each which could be mounted to a single virtual storage unit using GlusterFS [87], which is a network fle system allowing parallel I/O operations in contrast to NFS, which is a serial flesystem. This allows a signifcantly higher bandwidth since the workload is distributed between the three physical servers in terms of disk usage and network bandwidth. In total the new storage units provide a volume of 108 TB for data only. Although this number may appear large it is justifed for multiple reasons:

• Redundancy: The current size of the system allows one of the data servers to fail without the storage capacity of the system dropping below an acceptable size.

• Readiness for the H.E.S.S. I upgrade: The current setup will also provide sufcient bandwidth and storage capacity after an upgrade of the H.E.S.S. I cameras end of 2016.

• Delays in tape writing: Due to occasional delays in the tape writing procedure 24 The High Energy Stereoscopic System

temporarily up to 60 TB of disk space were used (about 5 months) since before deleting the data in Namibia it has to be verifed that it has correctly arrived in Europe.

In a second step an additional GlusterFS partition was created combining two of the 12 TB servers as backup space and also for the system log-messages. It was not possible to create a merged volume of all fve servers since the version of GlusterFS, which is used in Namibia, only supports equally sized backends for a particular volume. A further important feature of the H.E.S.S. DAQ system is its ability to respond fully automatically to target of opportunity (ToO) alerts like GRBs. Information from the Gamma Ray Burst Coordinates Network (GCN) can be fed directly into the H.E.S.S. DAQ system and a dedicated process, the GCNAlerter, reacts to the input automatically in case such an event occurred at coordinates which are observable. The observation starts automatically and no human input is needed, which signifcantly reduces the reaction time to the system for GRB observations to a range from only 30 seconds to 1 minute. More information about the H.E.S.S. DAQ can be found in Ref [3].

2.2.5 Calibration and Detector Simulations The calibration and detector simulation are essential for dealing with the data recorded by the telescopes and producing solid analysis results. In the following a very short overview on the calibration procedure and the available simulation packages is given.

2.2.5.1 Calibration Since the quality of the data taken with H.E.S.S. depends on both environmental and instrumental conditions, the data need to be calibrated before an actual analysis can be performed. For that purpose calibration runs are taken at regular intervals (see Ref. [9]). During the calibration the ADC values of the PMTs are converted to intensity maps in units of photo electrons (pe). For the ADC values there are two channels available: The low gain channel is used for strong signals which range up to 1600 pe while the high gain channel covers signals up to 200 pe. The calibrated intensities Ii can be obtained via the formula I (A − P ) i = i i × F (2.2.1) pe γi where Ai are the ADC values for the channel i, which can either be low or high gain,

Pi is the pedestal value for a PMT, γi the electronic amplifcation factor of the channel and F the fat-felding coefcient. The pedestal is an additional signal which is caused 2.3 Reconstruction and Particle Identifcation 25 by electronic noise without light input. Furthermore, the night sky background (NSB) can cause noise at usually 1 pe level. Both efects have to be subtracted from the actual ADC value. The time dependence of the pedestal of each PMT can be extrapolated from the average value of the frst two minutes of an observation run. The electronic amplifcation factor is measured every two days with a dedicated calibration run, the SinglePE run. The fat-felding coefcients correct for inhomogeneities of diferent PMTs and are obtained by exposing the camera to a uniform illumination. At H.E.S.S. there are currently two diferent calibration chains in use, one being maintained by the MPIK in Heidelberg and the second one independently maintained by the French institutes of the collaboration.

2.2.6 Detector Simulations

Another crucial requirement for an actual data analysis are the detector simulations, which are referred to as Monte Carlo (MC) simulations in the following. Like for the calibration there are two independent MC simulation packages available in H.E.S.S. The frst, mainly maintained by MPIK is based on the CORSIKA package [49] for the shower simulations, while the French based counterpart is using CASCADE [2]. Both of these tools can be used to simulate showers induced by γ-rays and also other particles like protons. Models for the diferent interaction types are implemented. A full set of simulations covers a wide range of zenith angles, source ofsets from the center of the camera and azimuth angles. For the simulation of the instrument response to these showers there are again two packages: For the Heidelberg chain simtelarray [23] is used, while in the French MC chain the response of the detector is simulated with SMASH [57]. Hereby the behavior of the full H.E.S.S. array is mimicked by simulating the two- level trigger system and taking into account properties of the mirrors (e.g. refectivity) or the quantum efciencies of the PMTs and also the detector electronics. The output from these simulation chains can be processed by the analysis software as if it was real data.

2.3 Reconstruction and Particle Identifcation

At H.E.S.S. there is a large variety of tools available which facilitate the analysis of the calibrated data. For briefness, the following section only focuses on those methods which are relevant for the actual data analysis in Chapter 4 together with the presentation of promising ideas which emerged during attempts of improving the current data analysis 26 The High Energy Stereoscopic System

Figure 2.3.1: The defnition of the Hillas parameters (Figure from Ref. [31]). methods.

2.3.1 The Standard Hillas Reconstruction

The classical method of shower reconstruction and particle identifcation in γ-ray astronomy is the Hillas method, which is well explained in Ref. [31]. It is a geometric approach simplifying the recorded image to an ellipse in the camera plane, which can be described by few parameters, which are discussed in the following. On these parameters box cuts can be applied.

2.3.1.1 Hillas Parameters The so-called Hillas ellipses (shown in Fig. 2.3.1) are characterized by the following parameters:

• Length L and width W of the ellipse.

• The so-called size which is equivalent to the total image amplitude.

• The nominal distance d which is defned as the distance of the center of the camera and the center of gravity of the image.

• The azimuthal angle φ of the image main axis and the orientation angle α. Since the stereoscopic reconstruction approach was introduced by HEGRA and followed up by H.E.S.S. and later also MAGIC, the direction of the initial particle can be simply 2.3 Reconstruction and Particle Identifcation 27

Confg. ¯ min ¯ max min¯ max¯ 2 pe d Ws Ws Ls Ls θ STD -2.0 2.0 -2.0 2.0 0.0125 70 2.0 Loose -2.0 2.0 -2.0 2.0 0.04 40 2.0

Table 2.1: The H.E.S.S. I STD cuts versus the Loose cuts. reconstructed by the intersection of the main axis of the ellipses observed by the dif- ferent telescopes, which are projected into a common plane. The reconstructed energy is proportional to the signal amplitude measured in all telescopes. For the background suppression also a simple concept is used: For the so-called scaled cuts technique the width and length of the ellipses are compared to their expectation value and variance obtained from simulations, as a function of impact distance and charge. The scaled width and scaled length can be defned as:

W − < W > L− < L > Ws= ,Ls= , (2.3.1) σW σL For more telescopes involved these parameters can be easily combined to obtain the mean scaled parameters

P P ¯ Ws ¯ SL Ws = √ , Ls = √ (2.3.2) ntel ntel It could be shown from simulations that these mean scaled parameters are uncorrelated for γ-like events. Therefore, simple box cuts on these parameters can be applied as most simple discriminator between γ-like and hadron-like events since the distributions ¯ ¯ for hadron-like events show a tail towards large values of the Ws and Ls which is not present for γ-like events.

2.3.1.2 Hillas Cuts during H.E.S.S. Phase I: The standardized Hillas cuts defned for H.E.S.S. Phase I are summarized in Ref. [8]. From the cuts which are summarized here mainly the Loose cut confguration is relevant for the analysis presented in this thesis. The Loose cuts were chosen since they provide the lowest energy threshold and largest integration radius of the ofcial cuts for point like sources. In Table 2.1 the Loose cuts are compared to the STD cuts.

2.3.1.3 Hillas Cuts for H.E.S.S. Phase II: In order to be able to analyze H.E.S.S. II data, the author adapted the Hillas analysis which is implemented in the Heidelberg software to be operative for H.E.S.S. II data 28 The High Energy Stereoscopic System

min¯ max¯ ¯ min ¯ max 2 pe CT 1 4 pe CT5 d Ls Ls Ws Ws θ − -2.0 1.4 -2.2 1.0 0.0132 30 50 2.0

Table 2.2: The H.E.S.S. II Hillas low energy cuts for the stereo mode. as well. To reach this goal the lookup table scheme for the scaled parameters had to be adapted by introducing a new telescope type for CT5. This was necessary in order to correctly account for the larger mirror area of CT5 in comparison to CT1 - CT4. This modifed Hillas analysis was the frst analysis chain to be operative for H.E.S.S. II data within the HD software and has been used for the web summary in Namibia, which automatically analyzes the data from the last night on site as a frst quality check. Furthermore, it was used for the training of other software chains like Impact [84]. Meanwhile, Impact is considered to be the standard method to analyze H.E.S.S. II data within the HD software, however the available confgurations use an amplitude cut of 70 photo electrons for CT1 - CT4, which leads to an energy threshold similar to that of the H.E.S.S. I STD cuts when CT5 is used in combination with CT1 - CT4. In order to have a cut confguration with a comparable energy threshold to the H.E.S.S. I Loose cuts, a custom Hillas low energy cut confguration was defned for CT1 - CT5 which will be used in the following. The exact defnition of these cuts can be found in Table 2.2.

2.3.2 Particle Identifcation: Moving towards Pattern Recog- nition During the last years methods based on multivariate statistics have been used for various reconstruction and analysis tasks in diferent felds of physics ranging from energy reconstruction and particle identifcation at LHC experiments [114] to γ/hadron separation at H.E.S.S. [80]. This development was fostered by the TMVA software package, which has been developed at CERN [54]. The main advantage of these multivariate analysis (MVA) methods is that they are able to model non-linear correlations between the input variables. The following section summarizes the studies which have been performed by the author with the intent of improving the current efciency of γ/hadron separation at H.E.S.S. This initiated the promising approach of using state of the art pattern recognition algorithms for particle identifcation tasks in ground based γ-ray astronomy. Only the basic ideas leading to this idea, which were considered to be worth to be put on record, are sketched here with the intention of not discussing them in too much de- 2.3 Reconstruction and Particle Identifcation 29 tail. A frst implementation of the approach of reducing the γ/hadron separation to a pure pattern recognition problem has been realized in a master thesis where they are described in all detail (see Ref. [103]). The idea of applying pattern recognition technologies for γ/hadron separation tasks at H.E.S.S. emerged from studying the distribution of pixel clusters in H.E.S.S. event displays, especially for low-energetic events with the intention of improving the separation power of the existing chains. In Fig. 2.3.2a a typical simulated γ-like 4 telescope event with a reconstructed energy of 200 GeV is shown and in Fig. 2.3.2b the event display of a typical hadronic shower with a reconstructed energy of 300 GeV can be found (also a 4 telescope event). For these event displays the information of all telescopes was projected into the same camera plane since this approach turned out to be very helpful when trying to distinguish between γ-like events and hadron-like events by eye. Self- experiments done by the author showed that doing a γ/hadron separation by hand for a region of interest using this representation one reaches an accuracy which is comparable to chains like TMVA. The quality factor or Q-Factor is the standard tool to quantify the performance of a set of cuts which is defned as:

ε Q = γ εBG

ni where εi = . Ni

The quantity εi defnes the cut efciency where ni is the number of events which pass the cuts. Ni stands for the number of pre-cut events. In case the analysis chain has a large separation power, the ratio ni/Ni is close to 1 for γ-like events, since most of them should be correctly identifed as signal and small for the background, since the background should be rejected efciently. The quality factor reached when doing the γ/hadron separation by hand is about 1.3 at zenith angles of 20° versus 1.2 for the simple Hillas chain. The study on manual γ/hadron separation showed that the event displays carry suf- fcient information to successfully complete the task without additional information. An interesting question is upon which information a human event selector looking through thousands of event displays is relying in order to be able to quickly categorize an event. An important role for the decision plays the distribution of pixel clusters in the camera together with the distance between these clusters. The γ-like events ideally only show one cluster per camera, which is describing the Hillas ellipse, while for hadron like events multiple clusters per camera are expected. A second important criterion for the human 30 The High Energy Stereoscopic System event selector is the implicit information of the direction of the shower which is encoded in the event display when projecting all ellipses in a common camera plane. As soon as a human identifes ellipses which are pointing towards an intersection point of their axis he will classify the event as γ-like event. It should be easily possible to train a good pattern recognition algorithm on this behavior. During intents to quantify the distribution of clusters throughout the camera two quantitative discrimination variables were defned:

1. The frst was the ratio of the number of pixel clusters observed in an event divided by the number of telescopes which participated in recording the event. This ratio is expected to be close to 1 for γ-like events.

2. Another variable is the maximum distance between two pixel clusters in a telescope.

Attempts were made to introduce these new variables into the existing framework of TMVA chains at H.E.S.S. Although these new discrimination variables lead to a 10% improvement in sensitivity during MC simulations, the improvement could not be stably reproduced when applying the classifer to real data. This is likely related to the robustness of diferent types of classifers in case there are diferences of quality between training and application data. So far so-called boosted decision trees (BDTs) are the only MVA method which has been used for particle identifcation tasks at H.E.S.S. [80, 84], however, in terms of performance they are comparable with artifcial neural networks. Therefore, the question arises which of the two methods suits better for this particular use case application. The main advantage of BDTs is that their decision can be retraced in principle, while NNs behave as black boxes which do not ofer this transparency. For their traceability BTDs are the preferred choice in the analysis of fnancial markets and in some countries even required by law in that feld. However, for the use in counting experiments with large statistics this advantage vanishes in practice, since it is not possible to trace the decisions. On the other hand, in Ref. [98] the authors conclude that one of the advantages of neural networks over other MVA methods (including BDTs) is that they could be shown to be more robust against deviations in data quality between training and test samples. Taking this as given, neural networks seem to be a good choice for astroparticle physics: The quality of observation data is subject due to dif- ferent external systematic efects like light pollutions, changing atmospheric conditions or broken pixels and therefore a considerable deviation between MC data and real data conditions can be expected. These studies with additional discrimination variables were briefy mentioned here for completeness, although in the end they were considered to be not sufciently robust with respect to varying systematic conditions like broken pixels or missing drawers: 2.3 Reconstruction and Particle Identifcation 31

(a) A 4 telescope γ-like event at a reconstructed energy of 200 GeV.

(b) A 4 telescope hadron-like event at a reconstructed energy of 200 GeV. Figure 2.3.2: Typical H.E.S.S. event displays where the information from all telescopes is projected into a common camera plane. 32 The High Energy Stereoscopic System

Broken pixels can afect the number of clusters in a camera and therefore afect the sensitivity of a method, which relies on such information in a negative way (e.g. a Hillas ellipse is split into two by a string of broken pixels). However, taking into account the overall distribution of pixels showing an intensity over the camera could be helpful for the discrimination task. For example, a human event selector would not get tricked by a string of missing pixels in case the event display still contains implicit direction information. Therefore, the approach of counting clusters was discarded in favor of the completely new idea of applying pattern recognition software for particle identifcation tasks to the whole event. Thereby the information from all pixels of an event is taken into account by projecting the intensities of all pixels into a common plane instead of reducing this information to certain discrimination variables. From all available technologies so-called Convolutional Neural Networks (CNNs) were considered to be the most suitable approach to process large numbers of H.E.S.S. event displays. Meanwhile, applications based on this new type of neural networks have sur- passed all previous methods of computer vision and current software implementations considered to be advanced enough to be applied to complex problems in research. Like Multi Layer Perceptrons (MLPs), these CNNs are trained via back propagation [98] but unlike classical NNs they consist of groups of neurons which are arranged in a way that they focus on overlapping sub-groups of the input data. By this overlap in combination with diferent layer types the networks reach a certain level of invariance regarding shifting, scaling and distortion of the shapes in the images which makes them superior to classical MLPs. This robustness could be of advantage in situations where the observation data difers from the simulation quality e.g. due to broken pixels. One of the most advanced software frameworks supporting CNNs is called Cafe and was created by Yangqing Jia [58]. It consists of C++ and CUDA libraries with Python and Matlab wrappers. Therefore, Cafe supports modern GPUs guaranteeing fast image processing times (as fast as 2.5 ms per second at a state of the art GPU). So far, this type of pattern recognition technology has not been used in high energy physics due to the short time since the software packages providing methods for training and application of these CNNs are available and their still very experimental state. Since the performance of these networks is known to scale with their complexity, there still is huge potential for further improvements. An example where the technology of CNNs performed better than the human mind was the solution of so-called CAPTCHAs which are commonly used across the world-wide web as reverse Turing test to prevent all kind of automatized requests [43]. The NN implementation for solving these puzzles reached an accuracy of 99.8%, whereas humans only reached an accuracy of 94% on 2.3 Reconstruction and Particle Identifcation 33 average. The authors attribute their success to the level of complexity used in the networks and hypothesize that especially the depth of the network architecture was crucial to reach such a high accuracy. Their network implementation used 11-layers representing more than 5.0 × 107 parameters. This example shows the huge potential of this technology. The frst application of this technology at H.E.S.S. in Ref. [103] already has reached a separation power comparable to that of a typical Hillas chain with a limited training sample in a limited hardware environment. Since the performance of the setup is expected to rise with complexity there should also still be a potential of improvement for the γ/hadron separation at H.E.S.S. or for future observatories of ground based γ-ray astronomy.

Chapter 3

The Galactic Center Source HESS J1745-290

It is well known that the vicinity of the super-massive black hole Sgr A* in the center of the Milky Way is emitting radiation at many wavelengths from sub-millimeter to hard X-ray and across this huge frequency-range Sgr A* is also known as a highly variable source. For the energy band from 200 MeV to 100 GeV, which is covered by Fermi LAT so far no evidence for a variability for the GC has been published, which may be due to the limited angular resolution of that instrument at low energies where one obtains sufcient statistics for a search for variability in combination with the complexity of the Galactic Center region. The angular resolution of Fermi LAT at 200 MeV is about 10°. Since the VHE γ-ray source HESS J1745-290 is located in the same direction as Sgr A*, there is the hypothesis of a connection between these two objects, which could not be proven so far. The detection of a variability of HESS J1745-290 in H.E.S.S. data would be the frst evidence for a connection between Sgr A* and HESS J1745-290. Of course, variability alone would not prove such a link, since there is always the possibility that it is caused by an unknown source close to Sgr A*. For example, in 2013 the magnetar SGR J1745-2900 [61, 62] was discovered at an angular distance of only 2.8” of Sgr A*, which is often also called the GC magnetar. However, so far no magnetar has been detected at GeV or TeV energies. In case the search for a variability of HESS J1745-290 in fact fnds evidence for a variable γ-ray fux, a comparison of the timescale of the efect to the behavior of Sgr A* at other wavelength bands can help to distinguish between Sgr A* and the GC magnetar. In the end, a possible variability would not exclude that the observed signal from the direction of HESS J1745-290 is a superposition of a contribution of Sgr A* with the DC fux of the PWN and the difuse emission or the GC magnetar but it would still be sufcient to claim the detection of 36 The Galactic Center Source HESS J1745-290

VHE γ-ray emission from Sgr A* in case it shows a time structure or even a periodicity, which is similar to that which was observed for other wavelengths. The following section summarizes what was found out so far about the variability of Sgr A* at diferent wavelengths and also addresses some of the numerous open issues and questions about the properties of this interesting object. Furthermore, recent results about the GC magnetar are briefy summarized, followed by the discussion of a frst published H.E.S.S. search for a variability of HESS J1745-290 from the year 2006.

3.1 Variability of Sgr A*: An Overview of multi- wavelength Results

During the last ten years, several multi-wavelength campaigns have collected substantial evidence that the black hole Sgr A* shows variability at timescales of years, hours and also even at a timescale of minutes. While there are indications for a periodicity with a period in the order of 110 days in radio data, various infrared (IR) experiments and X-ray observatories found fares with durations from minutes to hours.

3.1.1 A Periodicity at about 110 Days In 2005 evidence for a long-term modulation of the radio signal from the direction of Sgr A* with a period of about 100–120 days was found in data from the Very Large Array (VLA) in New Mexico. The period could be observed across a large range of frequencies. The amplitude of this reported periodicity increases with decreasing wavelength. The efect is not yet fully confrmed, but there are various hypotheses which let it appear consistent in the context of expected properties of the black hole Sgr A* [71]. For the analysis nearly 20 years of monitoring data from the VLA were taken into account at wavelengths of 1.3 cm, 2.0 cm, 3.6 cm, 6.0 cm and 20 cm. The analysis shows a clear peak in the measured power-spectrum which ranges from 100 –120 days. The authors claim that they have shown with the help of Monte Carlo studies that the probability of obtaining this signal by random processes is less than 5%, which means that their result is not very signifcant and the efect is rather weak. An independent confrmation of the efect would be helpful. There are various scenarios which could explain such an efect like a companion on a close orbit or the precession of the black hole’s accretion disk. Since in terms of period this 110 days periodicity is 4 orders of magnitude larger than the known inner disk movement of Sgr A* the latter is unlikely to be related to that tentative long-term 3.1 Variability of Sgr A*: multi-wavelength Results 37

Figure 3.1.1: Here the geometry of Sgr A* is shown including an inner non-thermal halo and the accretion disk. The precession of the accretion disk might cause a periodic variation of the fux, which can be observed from earth. In this model d is the distance to the GC, Rh denotes the radius of the inner non-thermal halo of Sgr A* and Rd the radius of the accretion disk. S is the spin vector of the black hole, while L is the angular momentum vector of the accretion disk. The angle γ between L and S causes a periodical eclipse of the emission from the non-thermal halo towards an observer on earth. The fgure was taken from Ref. [71]. 38 The Galactic Center Source HESS J1745-290 variability. Also the presence of a companion is not the best candidate for an explanation for this phenomenon following a simple reasoning: An object orbiting around Sgr A* with such a period would be found on an orbit with a radius of about 60 AU. The VLA would easily have been able to resolve such an object. In case of an object rapidly circulating around Sgr A* the black hole would also show a characteristic proper motion which could not be observed so far. Liu & Melia [65] proposed a mechanism in 2001 which could account for the observed modulation without the assumption of a companion: In the Kerr Metric each gravitational acceleration acquires a dependence on the poloidal angle relative to the black hole’s spin axis, which means that matter orbiting around a black hole below and above the equator is subject to a force towards the black hole’s equator. That way the angular momentum vector may start to precess around the black holes rotation axis. As shown in Fig. 3.1.1, the spinning angular momentum vector of the disk results in the disk periodically, shielding parts of the emission from the non-thermal halo of relativistic particles in the vicinity of Sgr A* from an observer on earth. Thereby highly relativistic particles on our line of sight, which are created around the black hole close to the event horizon, are absorbed. This can lead to the observed periodic signal modulation. Therefore, the tentative radio-variability of Sgr A* could be caused by a simple combination of a periodical disk precession and the presence of a non-thermal halo close to the horizon of Sgr A*. A disk precession at a timescale larger than 100 days can also be observed for other black holes and black hole candidates like the Galactic Center micro quasar 1E1740.7-2942 [96]. Theoretically, such a precession can also afect the inner dynamics of diferent sections of the accretion disk which may connect it to the observed short-term variability which is described in the following sub-sections. In case Sgr A* shows such a non-thermal halo of relativistic particles, also a possible VHE γ-ray emission from the vicinity of this object could be afected by the disk modulation which makes it appear interesting to search for this tentative 110 days period also in the γ-ray regime.

3.1.2 Short and weak Flares during Infrared and X-Ray Ob- servations

During the last 10 years a large number of weak and short fares have been reported for Sgr A* and their frequency has been estimated to reach up to several fares per day. For the infrared (IR) band the Adaptive Optics Imager NACO 9, which is part of the Very Large Telescope (VLT) in Chile [42], among others, repeatedly reported fares. Further- 3.1 Variability of Sgr A*: multi-wavelength Results 39 more, the Chandra X-ray observatory [112], which is operated by the National Space Agency (NASA) and several other X-ray satellite experiments like the Swift/BAT Hard X-ray Transient Monitor [63], or XMM-Newton [113] which is operated by the European Space Agency (ESA) and also the Nuclear Spectroscopic Telescope Array (NuSTAR) [47] detected Sgr A* fares. It can be stated that the emission mechanism of these fare events is expected to be non-thermal but is yet undetermined. Possible underlying processes are synchrotron radiation induced by relativistic electrons with cooling break or synchrotron self-Compton scattering [73]. The fares reaching the highest energies were observed by NuStar [20]. A promising model for explaining these X-ray fares will be summarized at the end of this section. The short-term variability of Sgr A* is a complex and dynamic feld and we are only at the beginning of understanding the mechanisms which could lead to such a behavior. So far no short-term variability at a timescales of minutes and hours has been reported for the GeV and TeV energy range from the position of Sgr A*. Finding hints here would be another interesting piece in the whole puzzle. Concerning the variable fux from the vicinity of Sgr A* in the X-ray band, there is evidence for quasi-periodic oscillations (QPOs) during Sgr A* fares: An analysis by Aschenbach et al. [16] has shown an interesting feature of two rather luminous X-ray fares of Sgr A* observed by XMM-Newton on October 3, 2003 and Chandra on October 26, 2000: The two fares (shown in Fig. 3.1.2) seem to have comparable power spectra with peaks at periods of about 100 s, 219 s, 700 s, 1150 s, and 2250 s. Furthermore, two noticeable periods at 370 s and 850 s were reported for X-ray data during a Sgr A* fare in 2004 [21]. Assuming that these fares occur in the inner region of the accretion disk, these events may help to derive properties of the black hole. Aschenbach et el. associate the periods with characteristic orbits around the black hole i.e., the Lense-Thirring precession, Kepler orbital motion and the vertical and radial epicyclic oscillation modes which allows them to estimate the black hole mass MBH = 6 (2.72+0.12−0.19)×10 Msun (a value slightly difering from the literature) and also the black hole angular momentum = 0 9939+0.0026. The large angular momentum might a . −0.0074 have some characteristic implications on the properties of Sgr A*. Mueller & Camenzind [74] have shown that boost factors from general relativity have a large impact on an observed emission due to beaming efects. Along with the well-known shift in frequency, the fux density in the observer’s frame is boosted downwards compared to the rest frame of the black hole. These efects become even stronger for accretion disks observed face- on. Accordingly, the observation becomes more difcult when the angular momentum gets larger or the inclination angle decreases. Therefore, the large angular momentum 40 The Galactic Center Source HESS J1745-290

Figure 3.1.2: Light curves of the Sgr A* fares observed by XMM-Newton on October 3, 2003 (left) and Chandra on October 26, 2000 (right). The arrows in the left fgure show peaks with a quasi-periodic pattern. The plot was taken from Ref. [16]. 3.1 Variability of Sgr A*: multi-wavelength Results 41 might be one of the factors contributing to the fact that Sgr A* is rather faint compared to AGNs. Also in the IR band such periods or quasi-periods have been observed including a 1008 ± 120 s period, which is consistent with a X-ray period within errors [39]. The QPOs in IR observations have been observed with NACO during X-ray fares at June 15 and 16 in 2003. The frst fare showed a pattern of 3 peaks with a spacing from 840 s to 1020 s while the second fare involved 5 distinct sharp peaks with a spacing from 780 s to 1020 s. Within errors, these periods are consistent with the larger X-ray periods 700 s and 1150 s. The authors of Ref. [39] locate the origin of these fares in the innermost region of the accretion disk and hypothesize that they either could be caused by hot gas or highly relativistic electrons. Finally in 2004 the frst simultaneous X-ray and IR fares were reported by Eckart et al. [32]. The authors were able to give a conservative estimate for an upper limit of a time lag between the ends of the fares in the order of 15 minutes. Due to the fact that the fares coincide, it is possible that the same population of electrons causes both the IR and X-ray fare but to confrm this more knowledge about the population of IR and X-ray fares and systematic correlation studies are needed. Concerning their energy release, these typical X-ray and IR fares are rather weak: Peak X-ray luminosities between 1033 erg/s and 1034 erg/s are obtained for a typical 10 mJy coincident near-infrared fare [110]. In Fig. 3.1.3 the typical light curve of an IR fare with a quasi-periodic sub-structure consisting of two weak sub-fares within a time interval of 15 minutes followed by a more luminous main fare after another 15 minutes is shown [25]. The two sub-fares have durations ≤ 10 minutes. There is no generally accepted explanation for the short-term faring behavior of Sgr A* at the time of this writing. One possible mechanism is that the fares are caused by stars getting tidally disrupted by the black hole but following the argumentation in Ref. [13] these events are way to rare to explain the frequent short fares observed for Sgr A*. They occur as seldom as ∼10−5 yr−1 which makes it utterly unlikely to observe such an event in our galaxy anytime time soon, although such events have been reported for neighboring galaxies already [33]. However, the efect may be less enigmatic than expected. In Ref. [33] asteroids or even planets which are torn apart by tidal forces are given as the most likely explanation for the short X-ray fares of Sgr A*. The fact that there are more asteroids available than stars to fuel these fares would explain their occurrence at a daily basis and also account for their relatively short duration. Within this framework the most prominent models are synchrotron emission by either thermal or power-law distribution of electrons for the near infrared fares, together with 42 The Galactic Center Source HESS J1745-290

Figure 3.1.3: Light curve of an IR fare which is reported in Ref. [116], where also this light curve was taken from, in order to illustrate the time structure of a typical IR fare. the inverse Compton or self-Compton emission at X-ray energies. Again power-law synchrotron emission for all the components is possible. The end of an asteroid, which gets tidally disrupted, can be sketched as follows: When vaporized tail particles of the asteroid get mixed with particles forming part of the accretion fow of Sgr A*, plasma instabilities in the fow are expected when the ions and the electrons of the vaporized material are assimilated into the accretion fow of Sgr A*. Models of γ-ray bursts [83] suggest that non-thermal electrons in their interaction with shocked ions could reach relativistic γ-factors in the order 0.1 mi , where m and m are the ion and electron me i e mass respectively. Even for mi = mp where mp stands for the proton mass this factor exceeds 100. The resulting population of non-thermal electrons should at least produce synchrotron emission in the presence of magnetic felds. In this simple model the frequency of fare occurrence is simply given by the rate at which asteroids from the so-called Super-Oort Cloud [75] within the inner parsec are defected onto low angular momentum orbits that bring them close enough to the central object to undergo tidal disruption. The expected peak luminosity of the fares produced by this mechanism is in the order of 1039 erg/s for asteroids which are larger than 10 km. Further possible approaches to explain the fares are accretion instabilities or orbiting 3.1 Variability of Sgr A*: multi-wavelength Results 43

Figure 3.1.4: The trajectory of the G2 gas cloud around Sgr A* is shown here schematically in arbitrary coordinates from the years 2006 to 2014. The position of the black hole is marked by a red cross. In September 2014 the gas cloud was still existing after its closest approach to Sgr A* [106]. The fgure was taken from Ref. [15].

hot spots. Detailed explanations of these models can be found in Refs. [25, 66].

3.1.3 The G2 Gas Cloud

In 2012 Gillessen et al. [41] discovered a gas cloud (G2) with nearly 3 earth masses which was moving on a radial orbit towards Sgr A*. It was predicted to get tidally torn apart with the consequence of the material ultimately falling into the black hole. Models gave a well constrained orbit reaching a predicted pericenter in spring 2014. However, the VLT could show that these predictions fnally turned out to be wrong and G2 survived the passage and did not get absorbed by the black hole, continuing on a stable orbit instead [106]. In Fig. 3.1.4 the elliptical orbit of the G2 gas cloud around Sgr A* is shown schematically from the year 2006 until September 2014. The gas cloud was still existing in September 2014 after its closest approach to Sgr A*. 44 The Galactic Center Source HESS J1745-290

3.1.4 Giant X-Ray Flares

In 2012 and 2013 the strongest X-ray fares of Sgr A* so far were measured by Chandra. The 2012 fare was exceeding the usual fux level by a factor of about 200 while the 2014 fare was even twice as powerful exceeding the quiescent fux by a factor 400. It is not yet clear what caused these fares. Although one might assume a connection to the G2 gas cloud, this is rather unlikely since the gas cloud was expected to be closest to the black hole in spring 2014 and not in autumn where the fares took place. In any case for the 2012 fare the distance of the gas cloud and Sgr A* was too large to see any causal connection between G2 and this particular fare event. Also for these giant fare events one of the most popular explanations is that an asteroid or planet in an unstable orbit got torn into pieces by tidal forces and these pieces got entirely absorbed by Sgr A* after circulating around the black hole for several hours. This hypothesis is similar to the explanatory approach for the regular short-term variability, which has been discussed previously. The model would also be consistent with the fare duration of several hours which was measured [77, 85].

3.1.5 Estimates of the Frequency of Galactic Center Flares

There are various estimates of the frequency of X-ray fares for Sgr A* due to regular monitoring programs like those of Swift and Chandra. Swift recently published an estimate for the recurrence time of 5–10 days which means a frequency of 0.1–0.2 X-ray fares per day. Another census of Sgr A* fares which was performed using Chandra data claims roughly one fare per day. The average duration of an X-ray fare has been given with 2600 seconds [35] which is a bit longer than a H.E.S.S. run. Assuming that these processes also reach the VHE γ-ray regime, one can obtain two insights for planning a study based on H.E.S.S. data from these numbers when assuming that the underlying mechanism also causes VHE γ-ray emission: Taking into account that the whole usable dataset is about 350 hours at the moment (including 250 hours from H.E.S.S. I) one would expect that H.E.S.S. has observed about 1.5 to 15 of these fares by chance during its lifetime. The lower limit is based on the Swift population estimate, while the upper limit uses the population estimated by Chandra. More details about the H.E.S.S. dataset follow in Chapter 4. An important point here is that one would expect a variability at a timescale of H.E.S.S. runs (28 minutes) and below due to the average duration of these X-ray fares which is in the order of the duration of H.E.S.S. runs. Therefore, it is important to focus also on such short timescales in an analysis of H.E.S.S. data. IR fares even occur with a larger frequency: A census by Genzel et al. gave an estimate 3.2 Summary of H.E.S.S. I Results from 2006 45 of as much as 2–6 near-infrared fares per day [40] which is confrmed independently in Ref. [110].

3.2 Discussion of H.E.S.S. I Results on the Search for a Variability of HESS J1745-290 from 2006

In 2009 the H.E.S.S. Collaboration published a study on the spectrum and the variability of the source HESS J1745-290 using the dataset from the GC campaign from the years 2004, 2005 and 2006. The total livetime taken into account for this analysis was 48.7 hours in the “wobble observation mode”. With respect to a possible variability of Sgr A*, the study could not reveal any hint for an efect. It included a search for QPOs at frequencies ranging from 100 s to 2250 s which are known from X-ray observations [16] and a χ2 ft of a night-wise light curve with a constant. This ft with a constant shown in Fig. 3.2.1a gave a χ2 of 233 for 216 degrees of freedom (d.o.f.) which corresponds to a signifcance for variability of less than 1σ. Concerning the search for a periodicity, the distribution of the mean Rayleigh power as a function of time was investigated. As one can see in Fig. 3.2.1b all values are close to one, which means that also here no evidence for a variability could be found [101]. The theory behind the Rayleigh test will be explained in more detail in Sec. 4.1.2.2. Although the frst search for variability of HESS J1745-290 using H.E.S.S. data did not lead to a positive result it is not yet ruled out completely for various reasons:

1. Observation time: The dataset taken into account for the published analysis was only 3 years of the 10 years which are available now. If the variability is a weak efect more data is required in order to fnd a hint for it.

2. Occasional fares: There will always be the possibility that Sgr A* undergoes occasional fares reaching the GeV and TeV regime, which is difcult to rule out without permanent monitoring of this source.

3. QPOs: In X-ray and IR data QPOs only have been observed during fare activity. Even if there had been such a fare in the dataset which was taken into account for the analysis it would not afect the distribution of the mean Rayleigh powers signifcantly if the remaining runs do not contain fares.

4. Cuts and statistics: For the analysis the STD cuts were used, which lead to relatively low statistics compared to the Loose cuts and an energy threshold of 46 The Galactic Center Source HESS J1745-290

(a) A three years light curve of the integrated fux > 1 TeV using the H.E.S.S. GC data taken until 2006 and STD cuts for the analysis.

(b) The mean Rayleigh power as a function of frequency. Figure 3.2.1: Light curve and mean RL Power from the analysis of the H.E.S.S. 2004- 2006 dataset with the STD cuts. The two plots were originally published in H.E.S.S. paper about the GC from 2006 (Ref. [101]). 3.3 Summary 47

300 GeV. Especially for the search for variability at the timescale of minutes, this lack of statistics could be a problem, since it implies large statistical errors. On the other hand if the γ-ray signal observed from the direction of Sgr A* is a superposition of constant contribution of a DC source (e.g. the pulsar wind nebula) and a variable part from the black hole itself this might be leptonic process with a cut-of at some 100 GeV, which would mean that the variability would not have been detected in the previous study. Although this is somewhat speculative, it is possible.

5. Binning of the light curve: The light curve for this analysis was created on a night-wise base. In case the variability of Sgr A* takes place at a shorter timescale, it would get lost with such a binning.

In summary one can say that a variability of the GC source could not entirely be ruled out by this study due to the reasons above and therefore a (re-)analysis of the complete H.E.S.S. dataset, which consists of about 250 h of H.E.S.S. I observations and about 350 h in total, may still give interesting insights.

3.3 Summary

The faring behavior and tentative long-term variability of Sgr A* from the radio to the hard X-ray band have already given some interesting insights into the nature of Sgr A* and started a discussion about the origin of the frequent and short fares. The fares vary dramatically in their characteristics like luminosity and duration. Therefore, it is unlikely that they are produced by a single efect but rather an interplay of diferent mechanisms should be expected. Their similar time structure over diferent wavelength bands and some synchronous IR and X-ray fares, which have been observed, indicate that there might be a common underlying mechanism for IR and X-ray fares but this needs more detailed investigation. This assumption is further backed by reports of similar QPOs seen for both types of fares. Since none of the current models is completely excluding that these efects also reach the VHE γ-ray band, further searches and studies are urgently needed. Although a frst search for variability of HESS J1745-290 with H.E.S.S. data for diferent timescales lead to a negative result, the presence of such an efect could not yet be fully excluded for the reasons discussed above. Therefore, it is necessary to repeat this study with the full dataset available to date, including all the information collected by other experiments during the last 10 years.

Chapter 4

Search for Variability of the Galactic Center Source HESS J1745-290

The following chapter is dedicated to the search for variability of the γ-ray source HESS J1745-290. While the frst part is explaining the methods in use, the second part presents the results of their application to the available HESS J1745-290 dataset. The analysis takes into account data which were taken between 2004 and 2014.

4.1 Methods: Variability and Periodicity Tests

First the methods, which will be used for the data analysis, are presented and tested with toy data. Since the χ2 ft of a H.E.S.S. light curve with a constant is a rather common method the focus here was set to the periodicity tests which will be used later, namely the Lomb-Scargle (L-S) test and the Rayleigh (RL) test.

4.1.1 Light Curves: A Defnition Light curves are a common tool to investigate the fux or intensity of an astronomical object as a function of time. Most light curves refer to a certain energy range. By applying diferent statistical tests to a light curve, one can investigate if the object has a constant fux, is variable or even shows periodic behavior. A prominent use case of light curves is the search for extrasolar planets: There the variation of the brightness of a star can give hints for orbiting planets, which periodically absorb a fraction of the light emitted by their parent star. Furthermore, light curves are a useful tool for studying systems with periodic behavior like binary systems or black holes with a rotating accretion disk. Their periodicity usually can be observed across a large range 50 Search for Variability of HESS J1745-290 of wavelengths.

4.1.2 Periodicity Tests

Since Sgr A* has shown periodic and quasi-periodic behavior in radio, X-ray and IR data it is an interesting question if such periodic behavior is also observable for the VHE γ-ray source HESS J1745-290. In order to answer this question, the L-S test and the RL test will be applied to the HESS J1745-290 dataset after a brief introduction and discussion of these two periodicity tests. While the L-S test can be applied to the fux values of a light curve with irregular sampling, the RL test is an event-wise periodicity test, which will be used for the search for a short-term variability during single runs.

4.1.2.1 The Lomb-Scargle Test

The L-S test is a powerful statistical test to fnd weak periodic signals within unevenly sampled datasets, which for example could be time series with variable gaps due to irregular observations. The method ignores the non-equal spacing and calculates the regular Fourier power spectrum as if the data had an equal spacing [44, 55]. Furthermore, it gives a solid statistical signifcance in case a signal is present. The formalism of this test has been developed by Barning [19] and Lomb [67] who added the correct normalization. Scargle [93] gave a statistical interpretation in 1982 and found a way to calculate the signifcance of a signal if present. Alternative methods to search for a periodic signal within a dataset are the classical Fourier Transform (FT) or Fast Fourier Transform (FFT) algorithms. The problem with these methods is that periodic gaps in time often produce large powers for periods comparable to these gaps. The L-S method is an extension of these classical periodograms, which is able to minimize these undesired efects by evaluating the data only for time-windows during which the measurements actually took place and in principle is equivalent to a ft with sine and cosine functions.

The L-S power is defned as follows: In case one has a series of N data points hi = h(ti), ¯ which were actually measured at times ti, one can calculate a mean h and the standard deviation σ by the classical formulas

1 1 N−1 ¯ = (X ) and 2 = X ( ¯)2 (4.1.1) h hi σ 1 hj − h . N i N − i=0 4.1 Methods: Variability and Periodicity Tests 51

The normalized L-S power can then be defned as

1 [P (h − h¯) cos ω(t − τ)]2 1 [P (h − h¯) sin ω(t − τ)]2 P (ω) = j j j + j j j . (4.1.2) h 2 2 (P cos2 ( )) 2 2 (P sin2 ( )) σ j ω tj − τ σ j ω tj − τ

The constant τ is called time-ofset and is defned as

P sin(2ωt ) tan(2 ) = j j (4.1.3) ωτ P cos(2 ) j ωtj and makes the obtained L-S power independent from shifting all the tis by an arbitrary constant. Therefore, time translation invariance is a useful property of the L-S periodogram. The time ofset has to be calculated for each investigated angular frequency ω. As shown by Lomb, the time ofset makes the expression for the normalized L-S power equivalent to a linear least square ft with the function

h(t) = A cos(ωt) + B sin(ωt) (4.1.4) which is an estimate of the harmonic content of the dataset under consideration. The maximum L-S power occurs exactly at the period which minimizes the sum of squares of a ft of Eq. 4.1.4 to the data. In case the data are evenly sampled Eq. 4.1.2 reduces to the classical periodogram which is directly derived from the discrete FT.

4.1.2.1.1 The Statistical Interpretation Considering the null distribution of L-

S powers which are obtained by chance, it can be shown that Ph(ω) for any given frequency ω is following an exponential distribution. One can write down the cumulative distribution function (CDF) of the Ph(ω):

F (z) = Prob[Ph(ω) <= z] = 1 − exp(−z). (4.1.5) This means it gets exponentially unlikely to obtain a power like the observed one or a larger one by chance. However, this holds in the case of scanning a single frequency only. In case more frequencies are scanned the probability of obtaining a large Ph(ω) by chance increases and the statistical signifcance has to be corrected accordingly. For strictly uncorrelated periods the false alarm probability for getting the observed or a larger L-S power by chance can be written as

p = 1 − (1 − exp(−z))N (4.1.6) 52 Search for Variability of HESS J1745-290 where N is the number of frequencies which were scanned. From this formula the detection threshold z0 for a certain p-value p0 can be derived as

1 z0 = − log[1 − (1 − p0) N ]. (4.1.7)

In case one wants to detect a periodic signal at the 5σ level doing 10 trials one would need to observe a peak with Ph(ω) larger than 17.32. The classical L-S method does not take any statistical measurement errors into account. However, one can assume that in case of large statistical measurement errors a weak signal would rather be destroyed than artifcially added to the dataset.

4.1.2.1.2 Application to Toy Monte Carlo Data In order to test the implementation of the L-S method, it was frst applied to toy MC data. Diferent sets of random data were simulated with and without the superposition with a sinusoidal signal. For the test a toy light curve covering 1000 days was created which contains 200 measurements with uneven spacing and gaps. Fig. 4.1.1a shows the noise-only light curve and periodogram where the red line marks the 5σ detection threshold for the number of trials in the test. The L-S powers which were encountered in this test, stay below the detection threshold as one would expect. In Fig. 4.1.1b a weak periodical sinusoidal signal with a period of 40 days was added which is optically not visible in the light curve. Its amplitude was chosen to be in the same order of magnitude as the standard deviation of the Gaussian noise. The distribution of the L-S powers for the noise-only case also correctly showed the expected mean value of one.

4.1.2.1.3 Application to Data from the Swift X-Ray Telescope The L-S test has also been applied to data from Swift BAT, which is publicly available. As example for a source with known periods the Galactic Center microquasar 1E 1740.7-2942 [97] was chosen, which is also known under the popular name “Great Annihilator” and is the brightest electron (positron) source in the sky. In order to test the L-S method, the data of a day wise Swift light curve were used which were taken from February 2004 until December 2014. The result of this frst application of the analysis code to real astronomical data is presented in Fig. 4.1.2a where the L-S power is plotted versus the period in days. The resulting power spectrum shows 5 signifcant peaks for 1E 1740.7- 2942 at frequencies of 140 d, 360 d, 500 d, 710 d and 1010 d and one slightly crossing the 5σ detection threshold at 420 d. The 5σ threshold is marked by a red line, taking into account the correct number of trials which was 221 for the analysis: Periods from 100 d to 1200 d were investigated with a step-width between neighboring periods of 5 d. 4.1 Methods: Variability and Periodicity Tests 53

(a) A toy Monte Carlo light curve containing Gaussian noise only (left) with the resulting L-S periodogram (right).

(b) A toy Monte Carlo light curve with a sinusoidal signal (left) with the resulting L-S periodogram (right). At the simulated period of 40 days a clear and signifcant peak can be observed. Figure 4.1.1: Test of the L-S method with toy MC data. The red lines in the periodograms mark the 5σ detection threshold for the number of trials which were used to create the power spectrum. 54 Search for Variability of HESS J1745-290

(a) The L-S periodogram for 1E 1740.7- (b) The LS-periodicity test applied to a 2942 is showing fve clear peaks at periods scrambled light curve of 1E 1740.7-2942. of140 d, 360 d, 500 d, 710 d and 1010 d. Figure 4.1.2: The L-S periodicity test applied to a light curve of the “Great Annihilator” 1E 1740.7-2942. Both fgures plot the L-S power versus the period in days.

In order to rule out that the periodic behavior is produced by sampling efects (this should not be the case since the LS test is designed to be robust to that but in any case it is better to test) the fux values of the light curve of 1E 1740.7-2942 were exchanged in a random fashion keeping the time stamps untouched. The L-S periodogram obtained with that manipulated light curve is shown in Fig. 4.1.2b: Exchanging the fuxes makes the periodic behavior disappear completely, which rules out that sampling efects are fooling the L-S test here for the original light curve. The method of randomizing the fuxes, which was successfully tested here, will also be later applied for the H.E.S.S. GC data analysis.

Both the period at around 140 days and the very large period around 1010 days have not been found in the literature and therefore seem to be unpublished at the time of this writing. Although not being directly part of the topic of this thesis, this is certainly the most interesting side result of this thesis. There is no room for further investigation here but these periods seem to be an interesting topic for further studies. Another test with a Swift light curve of the object IGR J17475-2822 [88] which is a molecular cloud shows a stable zero result as expected. The L-S periodogram obtained in this second test with real X-ray data can be found in Fig. 4.1.3. These additional tests show that the method works also with real data and only detects periodic behavior where it is present. 4.1 Methods: Variability and Periodicity Tests 55

Figure 4.1.3: L-S periodogram of the molecular cloud IGR J17475-2822. As expected all L-S powers stably stay below the 5 sigma detection threshold which is indicated by the red line.

4.1.2.2 The Rayleigh Test

The RL test is a powerful event-wise periodicity test, which can easily be applied to a series of event arrival times for example. It is the special case = 1 for the 2 statistics n Zn which is defned as

2 n 2 = X([X cos( )]2 + [X sin( )]2) (4.1.8) Zn jθi jθi N j=1 i i and is summing over the frst n Fourier components of the series. The θi are the event phases, which are taken from the interval [0, 2π) and are calculated using an assumed period T. The index i runs from 1 to N, which is the number of events. For the simplest Z2 case setting n = 1 the variable 1 is equivalent to the normalized RL power : 2 P

Z2 1 ! = 1 = [X cos( )]2 + [X sin( )]2 (4.1.9) P 2 θi θi . N i i The overall distribution of normalized RL powers follows an exponential distribution with mean equal to one in the absence of a signal, therefore the false alarm probability for a power obtained can be calculated in the same way as discussed previously for the L-S test (Eq. 4.1.5 - Eq. 4.1.7). Applying the RL test to data one has to be careful to apply it to a sample which has a length of an exact multiple of the length of the period of interest, which means that for most applications of the test the sample needs to be truncated. Otherwise the result will be biased towards larger powers. The RL test is 56 Search for Variability of HESS J1745-290 very sensitive for simple sine waves. For more complex pulse shapes the 2 statistics Z2 could be taken into account [95].

4.1.2.2.1 The Distribution of Rayleigh Powers As mentioned before the pure background distribution of the normalized RL powers S is equivalent to an exponential with mean one and slope minus one. In case one is searching for a weak signal which may be only present in parts of the dataset Ref. [59] gives a good overview how one could do so taking into account the shape of the distribution of all RL powers obtained when applying the test. The basic idea here is that the presence of a weak, periodic signal would slightly change the shape of the whole distribution of RL powers from the theoretical distribution. A possible way to quantify the diference from the theoretical exp(−P ) distribution is the following: In case one has N data segments, e.g. H.E.S.S. runs, one can calculate the sum over all RL powers for a particular period over all segments. This sum is called Ptot in the following and can be defned as:

k=nseg X Ptot = Pk (4.1.10) k=1 where nseg is the total number of data segments. It can be easily shown that for the pure background 2 follows a 2 distribution (the index in subscript stands for the Pk χ2 number of degrees of freedom) and therefore 2 follows a 2 distribution for the Ptot χ2nseg background scenario: Since the distribution of RL powers in case of the pure background scenario is dN = exp(−P ) (4.1.11) dP the quantity y = 2P is distributed according to

dN y = exp(− )/2. (4.1.12) dy 2

The latter is the χ2 distribution for two degrees of freedom. Therefore, the resulting quantity 2 automatically follows a 2 distribution when summing over the for Ptot χ2nseg yi all runs. Therefore, the signifcance for a given period can be calculated by a comparison between the experimental distribution and the theoretical distribution which can be done quantitatively by summing over the normalized RL powers for all data segments. This principle can also be extended to the more general question of quasi-periodicities. If an object shows quasi-periods these not necessarily need to be identical for diferent data segments. In that case one is rather interested in the question if the number of local 4.1 Methods: Variability and Periodicity Tests 57 efects obtained for diferent data segments at diferent periods form a globally signifcant efect or can be attributed to noise. Thereby none of these local periods needs to be globally signifcant on its own. The question to be answered by this approach is rather if the number of xσ efects, which were found in the dataset, is compatible with the background expectation or not (x stands for an arbitrary signifcance level here). The important assumption here is that in case of the pure-background scenario all periods which are scanned independently follow an exponential distribution and are not correlated. Further studies at the end of this section discuss when this assumption is ap- propriate. In case neighboring periods can be considered to be statistically independent it is allowed to integrate over all Ptot obtained from single frequencies. The quantity Pint can be defned as

i=np = X (4.1.13) Pint Ptoti i=1 where np is the number of frequencies which were scanned for each segment. In the pure-background case where no signal is present, the quantity 2 will follow a 2 Pint χ2nsegnp distribution then. However, the assumption of neighboring periods being statistically independent is expected only to be true for large datasets with an infnite number of events. Since the literature about the RL test, which has been consulted, is not conclusive about this important criterion, namely what infnite statistics means in practice, toy MC simulations have been performed to test whether it is possible to defne a robust null-hypothesis when applying this method to H.E.S.S. data. During these tests a sample of pseudo H.E.S.S. runs with the following characteristics was simulated: A simulated run shows the typical statistics of a Galactic Center run at low zenith angles < 10° analyzed with the Loose cuts, which is 200 events per run. These events were distributed uniformly over the duration of a H.E.S.S. run, which is 28 minutes. It is important to mention that these simulated runs do not include any systematic efects like the detector dead time or efects which could be caused by the trigger and therefore this study only serves to investigate the statistical applicability of the method but does not take into account any systematic efects. Due to the fact that the RL test can only be applied to datasets having a length which is an exact multiple of the period of interest, for each period which is tested a certain fraction of events at the end of the run needs to be skipped. The larger the period duration, the larger this fraction gets. In the following, the RL test was applied to diferent period ranges for samples containing 400 of these toy MC H.E.S.S. runs each. Thousands of these samples were 58 Search for Variability of HESS J1745-290 simulated and for each of them the signifcance for variability was calculated assuming that 2P really follows a χ2 distribution. In the background-only scenario one int 2(nseg∗np) would expect the resulting distribution to be a Gaussian with mean and 0 and σ equal to 1 in case neighboring periods are uncorrelated. For all simulations which follow the RngStream software package was used which is recommended for verifying periodicity tests, since it guarantees independent, non- overlapping sub-streams of random numbers [30]. Standard random generators could produce sequences of pseudo random numbers which might be too correlated for the verifcation of periodicity tests. During these simulations the following scenarios were investigated where the step-width stands for the distance between two neighboring periods which were considered :

1. Periods from 1 s to 10 s with a step-width of 1 s using 50 000 samples of 400 pseudo runs.

2. Periods from 50 s to 150 s with a step-width of 1 s using 20 000 samples.

3. Periods from 350 s to 450 s with a step-width of 1 s using 20 000 samples.

The resulting signifcance distributions from this study can be found in Fig 4.1.4 for all three scenarios. For scenario (1) the signifcance distribution in Fig. 4.1.4a results into a perfect Gaussian with mean 0 and standard deviation 1. This means that for periods < 10 s the statistics at H.E.S.S. is sufcient to consider neighboring periods statistically uncorrelated when using a scan interval of 1 s. A frst important criterion for a stable null-hypothesis seems to be the number of events per period: Since the RL test in principle is equivalent to the ft of a histogram where all entries are folded to a single period with a sine, for a large number of events statistical fuctuations will average out when folding the events to a common period T0 and also when folding them to a neighboring period T0 + ε. However, in case of limited statistics this may not be the case. From the particular example of scenario (1) it follows that if the number of events per period is ≳ 20 at a step-width ε = 1 s, the assumption that neighboring periods are uncorrelated holds and the deviation of an empirical distribution from the theoretical prediction can be quantifed using the method of simply summing over all RL powers obtained in the test. However, the situation is a diferent one for larger periods. Further simulations for period ranges from 50 s to 100 s and 350 s to 450 s showed a deviation from the expected Gaussian for the background. The signifcance distributions obtained for these two period ranges are shown in Fig. 4.1.4b where one can observe that the 4.1 Methods: Variability and Periodicity Tests 59

Fit χ2 / ndf 66.98 / 76 Constant 2346 ± 11.8 Mean 0.0004893 ± 0.0041236 103 Sigma 0.9978 ± 0.0029 Entries per 0.1 Sigma 102

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(a) The signifcance distribution for the deviation of the empirical RL power distribution from the theoretical prediction for the period range from 1 s to 10 s.

Period Range from 350 s to 450 s

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(b) The signifcance distributions for the period ranges from 50 s to 100 s and 350 s to 450 s. Figure 4.1.4: Signifcance distribution when comparing the shape of the entire RL power distribution to the theoretical prediction. The distributions correspond to the diferent period ranges which have been investigated. 60 Search for Variability of HESS J1745-290 disagreement of the signifcance distributions with the expected Gaussian increases as a function of the mean value of the period range under consideration: The larger the periods under investigation, the less the signifcance distribution is compatible with the expected Gaussian. Both distributions show that for these period ranges it is not possible to derive a proper Gaussian signifcance with the method of summing over all RL Powers (The sharp cut at -9σ is an artifact of the function used to translate χ2 and d.o.f. into a p-value and is returning zero for p-values corresponding to signifcances < −9σ ). When only increasing the statistics of the simulation for periods from 350 s to 450 s by a factor of 10 but keeping the step-width of 1 s, the signifcance distribution still disagreed from the expected Gaussian. However, when increasing also the step-width ε from 1 s to 10 s again a stable null-hypothesis could be constructed (The plot for this result is not shown here since it closely resembles Fig. 4.1.4a and therefore does not carry any new information). On the other hand, also using a step-width of 10 s with the actual statistics of 200 events per run also did not result into the expected background distribution. Therefore, with respect to its application to a typical region of interest at H.E.S.S. it has to be concluded that the method of summing over all RL powers cannot safely be used to quantify the signifcance level of a possible efect, when combing the information from neighboring periods for period durations > 10 s. For the interesting X-ray periods of Sgr A*, which reach from ∼ 100 s to ∼ 2000 s, this approach cannot be used. However, the previous study also showed that under certain conditions neighboring periods can be considered to be statistically independent, namely when having sufcient statistics and using a proper step-width. In that case the shape of the whole RL Power distribution can be used to quantify the signifcance level of an efect. Simulations for the particular use case can clarify, if the method is suitable. In case one intends to scan a large range of periods, it should also be possible to increase the step-width as a function of the period. Furthermore, it is also important to mention that these complications do not occur when investigating a single period over diferent data segments. In this case problems due to correlations are not expected, since the diferent data segments are statistically independent. Due to these complications in obtaining a quantitative result here the shape of a RL power distribution has also been investigated from a qualitative point of view to test whether it is at least suitable to detect weak transient periodic signals in a large dataset. In a frst step diferent types of periodic signals were simulated based on a statistics of about 200 events per run. These simulations may appear arbitrary, however the number of pulsed events and the uniform background level are typical for the statistics of H.E.S.S. 4.1 Methods: Variability and Periodicity Tests 61 runs at post-cut level when the Loose cuts were used for the analysis (The average is 30 excess events per run but there are runs with up to 80 excess events in the dataset). The idea behind these examples was to design scenarios showing local 3–4σ efects in the RL test for periods which are in the order of those of the known X-ray periods of Sgr A* which are accessible by the test during a H.E.S.S. run (∼ 100 s, 220 s, 370 s). Also pulsed signals were simulated in order to investigate how the RL test behaves in case of the presence of possibly repeating short-lived fares in the data. The RL power spectra for the following four simulated scenarios can be found in Fig. 4.1.5:

1. In Fig. 4.1.5a the RL power spectrum for a truly sinusoidal event distribution with a period of 290 s based on a statistics of 150 events is shown.

2. In Fig. 4.1.5b the RL power spectrum of a simulated uniform event distribution which was superimposed with a simulated pulsed signal is shown. In total 150 uniform background events were simulated and superimposed with 3 simulated Gaussian peaks with a width of 20 s and containing 10 events each. The distinct peaks are separated by a time interval of 400 s. The number of pulsed events corresponds to a pulsed fraction of 20%.

3. The plot in Fig. 4.1.5c shows the RL power spectrum of a uniform distribution of 160 events, which was superimposed by equidistant δ-like peaks consisting of 1–2 events with a spacing of 150 s. In total 35 pulsed events were added to the sample which also gives a pulsed fraction of 22%.

4. Finally, the RL power spectrum in Fig. 4.1.5d is based on a single Gaussian pulse with a width of 20 s, consisting of 20 events on top of 180 uniformly distributed background events, which is giving a pulsed fraction of 10%.

During these simulations it could be shown that the RL test is sensitive to both a sinusoidal fux modulation and a uniform background event distribution, which was superimposed with Gaussian or δ-like peaks with an approximately equal distance in time. Even the presence of a single pulse at 10% level of the total statistics of a typical H.E.S.S. run also has an efect on the overall shape of the RL power distribution. This implies that the RL test can be used to detect both truly sinusoidal fux modulations and also quasi-periodic behavior represented by short pulses on top of a uniform background. When adding runs with a simulated signal to a background sample based on uniform event distributions one will obtain a RL power distribution with a large-power tail as shown in Fig 4.1.6, where the RL power distribution for a period range from 60 s to 600 s which was scanned with a step-width of 1 s. In total 150 toy MC runs with the event 62 Search for Variability of HESS J1745-290

10 8

8 Normalized RL Power Normalized RL Power 6

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0 0 100 200 300 400 500 600 100 200 300 400 500 600 Period in Seconds Period in Seconds (c) (d) Figure 4.1.5: Comparison of the RL power spectrum of simulated runs containing diferent types of a periodic signal. Both a sinusoidal event distribution and diferent pulsed signals were simulated. 4.1 Methods: Variability and Periodicity Tests 63

Simulated Signal Background

104 Number of Entries 103

102

0 2 4 6 8 10 12 14 Normalized RL Power

Figure 4.1.6: The RL power distribution for a simulated uniform dataset (blue) and a uniform dataset containing 5 runs which are containing a simulated weak periodic signal (red). arrival times following a uniform distribution were simulated with 150 to 200 events each. This fgure was created for illustration purposes only in order to show how the presence of several data segments showing a weak periodic behavior in a large dataset would qualitatively modify the overall shape of the RL power distribution. The frst simulated sample (blue histogram) only contains uniform event distributions, while the second sample (red histogram) also contained 5 runs with a simulated periodicity similar to the simulations in Fig. 4.1.5. All other runs of the second sample also are following a uniform event distribution. The main diference between these two samples is the tail for RL powers > 9. This simple study shows that a large-power tail can be interpreted as a qualitative hint for the presence of data segments showing variability. In summary it can be concluded that it was shown that the method for quantifying the diference between a theoretical and an empirical RL power distribution which was presented above is applicable only in a strictly quantitative fashion for periods < 10 s for H.E.S.S. runs due to the limited statistics. However, it was also shown that the 64 Search for Variability of HESS J1745-290 shape of the RL power distribution can be used in any case to identify data segments with periodic behavior qualitatively within a large dataset: If an efect is present in the dataset the corresponding RL power distribution will show a tail at large RL powers. Although it is not possible to estimated the signifcance level of such a tail by simply summing over all RL powers, it is still possible to estimate the signifcance level by brute force simulations which will be discussed in Sec. 4.2.5. An important question before applying the method to data is also how a trial can be defned when the observable is the overall shape of the RL power distribution in order to avoid the trial factor to be unnecessarily large. Since the test variable here is the shape of the distribution of all normalized RL powers and not the value of the RL power of any particular period, every change in the experimental setup which modifes this shape can be considered to be an independent trial. In order to create such a distribution one has to adjust the following parameters beforehand:

1. A set of event selection cuts like the θ2 cut, the MSW and MSL cut or additional quality cuts like on the ofset or zenith angle.

2. A previously defned frequency range to be scanned.

3. The step-width ε between neighboring periods which is used for the scan.

Since these parameters defne the exact shape of the RL power distribution a set of these parameters can be considered to be sufcient to defne one trial. If any of these ingredients is changed one has to count the resulting distribution as a new trial. After this discussion of methods which may be helpful for the search for a variability of HESS J1745-290 and their possible caveats, the next section is dedicated to the actual data analysis.

4.2 Data Analysis

After a defnition of the dataset under consideration, the main topics covered by this section are searches for both a long-term and a short-term variability of the GC source HESS J1745-290. Short-term refers to a timescale of minutes in this context, while long- term means timescales from days to years. A discussion of the results which are obtained in this section and an outlook to possible interpretations can be found in Chapter 5. 4.2 Data Analysis 65

4.2.1 The Dataset, Cuts and Background Method

For this analysis in total about 300 hours of H.E.S.S. data from the years 2004 to 2014 were analyzed in total. While the dataset from 2004 until 2012 only includes the telescopes CT1 - CT4, the 2013 and 2014 datasets also include CT5 in stereo mode which means that only events were used for the analysis where CT5 recorded an event in combination with at least two other telescopes. Due to the diferent experimental conditions, the years from 2004 –2012 are referred to as Subset A in the following, while the years 2013 and 2014 are labeled as Subset B. For Subset A a maximum ofset of the source position from the pointing position of 2.0° was allowed, while for Subset B a smaller ofset of 1.5° was chosen due to the reduced FoV in stereo mode which is about 3.2°. In comparison the four telescope array consisting of CT1 - CT4 has a FoV of 5°. Furthermore, the spectral data quality criteria [46] were applied for the run selection. A summary of the dataset parameters is presented in Table 4.1. From the H.E.S.S. I GC dataset, which has a total livetime of 298 h and consists of 678 runs, a total of 517 runs passed the spectral selection criteria which is equivalent to an exposure of 237.3 h. For H.E.S.S. II 70.8 h of data were used for the analysis. The entire analysis was done with data from the HD calibration chain under application of the HD analysis software. In a frst step a set of cuts had to be selected. For Subset A the selection was made in favor of the H.E.S.S. I Loose Hillas cuts: If one wants to detect variability at timescales of minutes, one should use cuts providing a large efective area for γ-like events. Although the standard cut confgurations available at H.E.S.S. do not contain dedicated transient cuts for transients with a duration < 200 s like those provided by the Fermi LAT software [29], the Hillas Loose cuts were considered to be the cut confguration which is meeting these requirements best due to their large efective area for γ-like events: The efective area of these cuts at a true energy of 200 GeV is 105 m2, while the STD cuts are not sensitive at this energy any more. Despite the existence of loose cut confgurations for other data analysis chains like TMVA, the Hillas Loose cuts are the ones which ofer the largest statistics of γ-like events, being more transmissible for γ-like events by a factor of two at post-cut level at an energy of 200 GeV than other chains. Therefore, the Hillas Loose cuts were selected for the analysis. The IMPACT reconstruction [84] did not ofer a comparable cut confguration in production quality at the time this analysis was done. A further advantage of the simple Hillas chain is that it is less susceptible to qualitative and quantitative discrepancies between MC data and observation data, especially close to the energy threshold in contrast to simulation based high-level chains like Model++ or IMPACT, since the Hillas chains only use the simple MSW and MSL cuts 66 Search for Variability of HESS J1745-290 for γ/hadron separation. Since Hillas chains do not ft entire events against models derived from simulations, they can be considered to be more robust in the case that the simulations which are used to optimize the analysis chain and the actual data samples the chain is later applied to are not exactly of the same quality and show systematic diferences. Robust in this context means that the simple Hillas chains in combination with the Loose cuts is expected to reject γ-like events which slightly difer from simulated events at low energies with a lower probability, which is expected to result in a larger efective area for γ-like events when the chain is applied to real data. A similar argument has already been brought in the discussion of possible advantages of neural networks in comparison to BDTs where the conclusion was that neural networks may be more robust in the case of quality diferences between diferent training and application data samples. Close to the energy threshold where only little information about the events is available, quality diferences between training and application data might have a larger impact on the performance of simulation based chains than for a simple Hillas chain. Of course the high-level chains are still expected to perform better with respect to background suppression and sensitivity for the detection of DC sources. However, for transient searches the detection sensitivity for steady-state sources should not be the decisive criterion for the selection of an analysis method. The transmissibility for γ-like events is the more important criterion. In case the background rates can be shown to be stable by cross-checks with control regions one should choose cuts which are optimized for large γ-like event rates. Concerning systematic efects of the MC simulations, it was for example shown that close to the energy threshold the efective areas for H.E.S.S. II between the French and HD MC pipeline difered at a level of one order of magnitude at the time of this writing [38], which implies that there were unresolved problems with the MC simulations of low-energetic γ-like events. Also the H.E.S.S. I analysis chains show a diference in the nominal energy threshold which is about 50 GeV between the French and HD software chain. While the French analysis chains have a mean energy threshold at a true energy of 50 GeV [72], the energy threshold for the HD part of the Software is at 100 GeV. These examples were mentioned to illustrate possible systematic issues of simulations close to the energy threshold. The author expects simple Hillas chains to show less dependence on possible issues of the simulations than high-level chains which may be an advantage to be sensitive for low-energetic γ-like events when searching for rapid variations of the rates of such events. For a better control of possible background systematics of the Loose cuts, diferent 4.2 Data Analysis 67

Subset Instrument Years Max Ofset Exposure #Runs Selection A H.E.S.S I 2004-2012 2.0° 237.3 h 517 spectral B H.E.S.S II 2013,2014 1.5° 70.8 h 145 spectral

Table 4.1: Parameters of the dataset used for the variability search. control regions have been taken into account in order to cross-check the GC results against them during the whole analysis. Wherever a background was needed during the analysis for the spectral reconstruction, it was retrieved with the refected background method [22].

4.2.2 Skymap of the Galactic Center Region

In a frst step of this data analysis H.E.S.S. skymaps of the Galactic Center region are discussed, which were created with both reconstruction chains (H.E.S.S. I and H.E.S.S. II) which will be used for the variability search later.

4.2.2.1 A Skymap based on H.E.S.S. I Data with Loose Cuts

The signifcance map, which was created for the GC region, uses a correlation radius of 0.1° and the Galactic coordinate system. It is based on the ring background method [22] and uses the standard exclusion regions for the known sources and the difuse emission in the GC region, which were also used for previous GC analysis at H.E.S.S. like the search for a dark matter annihilation signal from the GC halo [100]. These exclusion regions will be used in all parts of the analysis which follows. The resulting skymap is shown in Fig. 4.2.1. A point-like source is located in the GC at the position of HESS J1745-290 at a signifcance level of 40σ. Furthermore, other known objects like HESS J1745-303 [18] and the SNR G 0.9+0.1 [6] together with the expected band of difuse emission along the Galactic plane are clearly visible. HESS J1745-303 and the difuse emission of the GC ridge are marked by 5σ contours. In summary all expected objects and structures (and only those) could be correctly detected with the Loose cuts and there are also no signifcant holes or gaps in the map, which can be seen as a frst successful test of the Loose cuts: The skymap shows that the background rates of these cuts are stable and do not introduce artifcial objects where no objects are expected. 68 Search for Variability of HESS J1745-290

Figure 4.2.1: Skymap of the GC region based on H.E.S.S. I data using the Loose cuts. The skymap is using the Galactic coordinate system in degrees.

4.2.2.2 A Skymap based on Stereo Data

For comparison a skymap of the same region was created using H.E.S.S. II stereo data which is including CT5 and using the same cuts that will be used for the variability search afterwards. Due to the relatively small FoV in stereo mode of about 3.2° the template background method [22] was used for this H.E.S.S. II skymap. The resulting skymap is displayed in Fig. 4.2.2a. It closely resembles the skymap which was produced with H.E.S.S. I data before (Fig. 4.2.1) but shows a more extended difuse emission than the H.E.S.S. I skymap. At the frst glance it is difcult to judge if this is a systematic artifact of the H.E.S.S. II data and reconstruction or if it can be interpreted as evidence for the difuse large scale emission reported in Ref. [4]. In this H.E.S.S. publication an extension of the difuse emission for the GC region from −1◦

4.2.3 The Spectrum of HESS J1745-290 with Loose Cuts Another important test before going ahead with the actual variability search is to investigate if the spectral reconstruction is working as expected with the applied cuts, since the light curves which will be used later are based on it. The safe energy threshold of the spectrum with the Loose cuts where the energy bias stays below 10% is at 160 GeV for a 0.5° ofset at 10° zenith angle and is therefore signifcantly lower than with the STD cuts which have a threshold of about 300–350 GeV. A possible complication for a spectrum of an object in the GC region is the presence of the difuse emission. When creating a spectrum for a point-like source, one also contaminates the region of interest with an additional difuse component which is proportional to the integration radius. Therefore, a larger fux normalization is expected for the Loose cuts than for the STD cuts due to their integration radius being larger by a factor of 2. The spectrum of HESS J1745-290 which was created with the Loose cuts and is shown in Fig. 4.2.3a indeed fulflls this prediction: It shows a fux normalization of 5.28 × 10−12 ± 0.01stat × 10−13 TeV−1 cm−2 s−1 and a spectral index of 2.34 ± 0.02 stat ± 0.12 syst while the index which was published in Ref. [101] is 2.10 ± 0.04 stat ± 0.10 syst in combination with a fux normalization of 2.57 ± 0.07 × 10−12 TeV−1 cm−2 s−1 (no systematic error on the normalization was given in Ref. [101]). Within the standard systematic error on the spectral index at H.E.S.S. which is defned as 5% in Ref. [8] for the Crab Nebula, the spectral index of the GC spectrum with the Loose cuts does not agree with the spectral index which was previously published. but it agrees within a 10% systematic error. A possible explanation for the additional 5% of systematic error is the contamination of the region of interest by the difuse emission due to the larger integration radius. The assumed dependence of the fux normalization on the integration radius can easily be made plausible by a simple test: In case an integration radius which is comparable to that of the STD cuts is used in combination with the remaining parameters of the Loose cuts, the normalization should be similar to the value obtained with STD cuts, since using a tighter integration radius one would reduce the additional fux by the 70 Search for Variability of HESS J1745-290

(a) This plot shows a skymap obtained from the H.E.S.S. II dataset.

(b) A second version of the H.E.S.S. I skymap with the signifcance scale ending at 5σ in order to also visualize 3σ efects which are not visible in Fig. 4.2.1. Figure 4.2.2: A H.E.S.S. II skymap in comparison to a H.E.S.S. I skymap with a color scale which is highlighting hidden structures of difuse emission beyond the classical GC ridge at the 3–5σ signifcance level. Both plots are using the Galactic coordinate system in units of degrees. 4.2 Data Analysis 71 difuse emission. Therefore, one should get a comparable fux normalization in that case. Of course the PSF of the Loose cuts is not the same like the PSF of the STD cuts due to low-energetic events for which the direction can only be reconstructed with less precision. However, when reducing the integration radius one would exclude a large fraction of these low-energetic events along with the additional difuse emission. Therefore, one should obtain a fux normalization similar to that obtained with the STD cuts: Indeed the normalization obtained in this test was 2.81±0.01 stat±0.28 syst×10−12 TeV−1 cm−2 s−1 which agrees with the published H.E.S.S. I result of 2.57±0.07±0.26 syst×10−12 TeV−1 cm−2 s−1 within a 10% systematic error, which is reasonable to assume for the fux normalization with the Loose cuts due to the fact that also low-energetic events with little information for the energy reconstruction are included in the analysis. The previous study shows that the spectral reconstruction is working as expected for the Loose cuts within systematic errors. The larger fux normalization is likely due to the larger integration radius which adds an additional contamination of difuse emission to the region of interest. A comparison of diferent confgurations and the resulting fux normalizations and spectral indices is shown in Table 4.2. Comparable integration radii in the order of ∼ 0.1° for the GC source lead to comparable fux normalizations and spectral indices which agree within a 10% systematic error. Furthermore, the spectrum shows a structure in the residuals between 800 GeV and 2 TeV. The residuals are at 3σ level only which could be just statistical fuctuations or a systematic efect of a superposition of diferent spectral components (e.g. HESS J1745-290 and the difuse emission) which is due to the large integration radius. The fact that there is no sign of a high-energy cut-of in this spectrum supports this assumption since H.E.S.S. recently discovered multi-TeV γ-ray emission from the central 10 parsecs of the Galaxy [52], which is evidence for the presence of PeV protons, so-called PeVatrons. In any case these systematic efects of the HESS J1745-290 spectrum presented here are not expected to have an efect on the behavior of a light curve with respect to variability between diferent runs, although they may cause a constant systematic shift of the fux values. Due to the fact that the fux of the difuse emission is expected to be constant, also an additional difuse component due to this larger integration radius is not expected to interfere with the planned search for variability.

Also a spectrum with the Subset B was created. The spectral index of 2.06 ± 0.03 stat ± 0.1 syst agrees within a 5% systematic error with the literature value. For the fux normalization of 2.15 ± 0.06 stat ± 0.24 syst × 10−12 TeV−1cm−2s−1 one reaches an agreement with the two H.E.S.S. I cut confgurations using an integration radius of ∼ 0.1° within a systematic error of 10%. In contrast to the H.E.S.S. I spectrum, 72 Search for Variability of HESS J1745-290

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10-14

) 1 10 σ 2 Energy (TeV) 0

Residual ( -2 1 10 Energy (TeV) (b) Spectrum with the H.E.S.S. II low energy cuts. Figure 4.2.3: Spectra of HESS J1745-290 with the H.E.S.S. I Loose cuts and a H.E.S.S. II stereo cut confguration. 4.2 Data Analysis 73

Cuts Radius [°] Index Norm [TeV−1 cm−2 s−1] STD 0.125 2.10 ± 0.04 stat ± 0.10 syst 2.57 ± 0.07 ± 0.51 syst × 10−12 Loose 0.2 2.34 ± 0.02 stat ± 0.20 syst 5.28 ± 0.1 stat±0.52 syst × 10−12 Loose 0.1 2.29 ± 0.01 stat ± 0.20 syst 2.81 ± 0.01 stat ± 0.28 syst × 10−12 H.E.S.S. II 0.1 2.06±0.03 stat±0.20 syst 2.15 ± 0.06 stat ± 0.24 syst × 10−12 Table 4.2: The fux normalization and spectral indices obtained with diferent cut confgurations. the spectrum based on H.E.S.S. II data does not show a signifcant fux point at energies > 10 TeV which may be due to both the lower level of statistics and the tighter integration radius which is used by the H.E.S.S. II cuts (0.13°). Due to the diferent fux normalizations for the H.E.S.S. I and H.E.S.S. II dataset which can be explained by the diferent integration radii, independent light curves were created for Subset A and Subset B in the next step of this analysis.

4.2.4 Search for a long-term Variability When searching for a long-term variability at a timescale larger than the duration of a H.E.S.S. run, which is ∼ 28 minutes, two questions arise: The frst is if there is a long-term variability at all and in case hints for such an efect are found the second question would be if it is rather a random efect like irregular fares or if it also shows a recurring or even periodic pattern. For answering the frst question a simple χ2 ft with a constant can be applied to the HESS J1745-290 light curve and in case evidence of a variability is found, the L-S test is the correct tool to test whether a possible efect also shows periodic behavior. Therefore, after discussing the application of the χ2 ft with a constant to the H.E.S.S. I and H.E.S.S. II light curves the L-S test will be applied to search for a possible periodicity in the next step. The search for a long-term variability contains all runs which passed the spectral data quality selection criteria. No additional selection criteria were introduced at this point.

4.2.4.1 Analyzing the run-wise Light Curve of HESS J1745-290

Two independent run-wise light curves of HESS J1745-290 were created for the integrated fux above 100 GeV using the standard method for light curves at H.E.S.S. which is implemented within the HAP data analysis software package for both the H.E.S.S. I and the H.E.S.S. II dataset. This procedure requires the spectral index to be set as input parameter. For the H.E.S.S. I light curve which will be discussed in this section, 74 Search for Variability of HESS J1745-290 the empirical index of 2.3 ± 0.2 syst, which was derived with the Loose cuts before, was used but it will also be shown that the level of variability of the integrated fux does not depend on a 10% variation of the spectral index. The χ2 ft of the light curve was performed separately for the H.E.S.S. I light curve including the years 2004 to 2012 and H.E.S.S. II using data from the years 2013 and 2014. There are two possible ways of combining these two independent results: The frst is directly combining the light curves (by scaling them to a comparable level of integrated fux) and ftting the resulting combined light curve with a constant. A second approach is to simply combine the results of the independent fts by adding the χ2 and d.o.f. of the two independent fts according to the theorem of additivity of χ2 variables [86]. In the following the second approach will be used.

4.2.4.1.1 Light curve from H.E.S.S. Phase I The light curve derived from the H.E.S.S. I dataset is shown in Fig. 4.2.4a. It was created using an integration radius of 0.2°. Although the light curve does not show any obvious fares which could be detected “by eye”, the χ2 ft with a constant shows evidence for variability. The ft resulted in a χ2 of 693.1 which was obtained for 516 d.o.f. This corresponds to a p-value of only 2.8 · 10-7 in favor of the null-hypothesis of the light curve being fat, implying a signifcance level for variability of 5.0σ for the H.E.S.S. I light curve. As a control source, which is located in the same FoV, the SNR G 0.9+0.1 was used to cross-check the result for HESS J1745-290. The G 0.9+0.1 data were taken exactly under the same instrumental and atmospheric conditions like the HESS J1745-290 data. The χ2 ft of the G 0.9+0.1 light curve with a constant did not show any sign of a signifcant variability with a p-value of 0.19 which implies that the G 0.9+0.1 fuxes are in good agreement with the null-hypothesis of a fat light curve. Comparing the integrated fux > 100 GeV for the integration radius of 0.2° HESS J1745-290 shows an integrated fux of 4.9 ± 0.1 · 10−11 cm-2 s−1 while G 0.9+0.1 only has an integrated fux of 1.3 ± 0.1 · 10-11 cm−2 s−1, which means that the integrated fux of G 0.9+0.1 is only 26% of that of HESS J1745-290. In order to investigate if the observed variability is a methodical artifact of the algorithm which is used to create H.E.S.S. light curves, several parameters were varied during a cross-check. For example one could argue that the lower integration threshold for the light curve of 100 GeV was chosen too low, since the mean energy threshold of the Loose cuts is at about 150 GeV, although the algorithm for the light curve at H.E.S.S. should extrapolate the integrated fux correctly to the given integration threshold. The spectral index which also needs to be set as parameter for creating a H.E.S.S. light curve 4.2 Data Analysis 75

Light Curve of HESS J1745-290 −9 ×10 χ2 / ndf 693.1 / 516 Integrated Flux > 100 GeV Prob 2.8e−07 0.2 p0 4.985e−11 ± 9.877e−13 Fit with a Constant ] -1

s 0.15 -2

0.1

0.05

− Integrated Flux > 100 GeV [cm 0.05

−0.1

53000 53500 54000 54500 55000 55500 56000 56500 Date in MJD

(a) χ2 ft of the run-wise fuxes of HESS J1745-290 with a constant.

Light Curve of G 0.9+0.1 −9 ×10 χ2 / ndf 467.8 / 442 Integrated Flux > 100 GeV Prob 0.1912 0.2 p0 1.316e−11 ± 1.108e−12 Fit with a Constant ] 0.15 -1 s -2 0.1

0.05

−0.05

−0.1 Integrated Flux > 100 GeV [cm

−0.15

−0.2 53000 53500 54000 54500 55000 55500 56000 56500 Date in MJD

(b) χ2 ft of the run-wise fuxes of the SNR G 0.9+0.1 with a constant. Figure 4.2.4: Fit of the run-wise fuxes with a constant using H.E.S.S. I data only. The ft was applied to a light curve of HESS J1745-290 and also to a light curve of G 0.9+0.1 as a control source from the same FoV. 76 Search for Variability of HESS J1745-290

Source θ Eth α p σ HESS J1745-290 0.15 100 2.1 3.0 · 10−6 4.5 HESS J1745-290 0.15 100 2.3 2.6 · 10−5 4.1 HESS J1745-290 0.15 300 2.3 1.5 · 10−5 4.2 HESS J1745-290 0.2 100 2.1 7.9 · 10−8 5.2 HESS J1745-290 0.2 100 2.3 2.8 · 10−7 5.0 HESS J1745-290 0.2 300 2.3 2.6 · 10−5 4.1 G 0.9+0.1 0.15 300 2.3 0.14 1.1 G 0.9+0.1 0.2 100 2.3 0.16 1.0 G 0.9+0.1 0.2 100 2.1 0.16 1.0

Table 4.3: The ft results in terms of p-value p and signifcance for variability σ of the χ2 ft of diferent HESS J1745-290 light curves, which were built based on diferent spectral indices α, diferent energy thresholds Eth and integration radii θ. might also have an efect on the behavior of the light curve with respect to variability. In order to rule out systematic efects due to these parameters the light curve was created and ft assuming two diferent spectral indices, two diferent energy thresholds and also using diferent integration radii. The results of these cross-checks can be found in Table 4.3. By this cross-check it could be shown that the variability for HESS J1745-290 can be observed independently of the input parameters for the light curve at a signifcance level between 4.1σ and 5.2σ which mainly depends on the integration radius. On the other hand, G 0.9+0.1 shows a zero result for all parameter settings. Therefore, the efect can be considered not to be an artifact of the method or its predefned parameters respectively. In order to investigate if the variability is only observed for certain pointing positions which would be a hint for a systematic efect, which could be introduced by particular, problematic background regions, the light curve was also split into two diferent subsets with respect to the pointing position. The frst partial curve only consists of pointings in the north of the Galactic plane (b > 0), while for the second partial curve only pointings below the Galactic plane with b < 0 were taken into account. The pointings with b > 0 take the background mainly from the north of the GC while the pointings with b < 0 take the background mainly from the south. This is due to the radial symmetry of acceptance and the fact that the background regions are located along circles with a constant radial acceptance. Since the Galactic plane itself is excluded for the background, for pointings north (south) of the GC the northern (southern) part of this circle is taken into account for the background, since its segments in the south (north) of the GC (if geometrically 4.2 Data Analysis 77

Figure 4.2.5: The NSB level along the Galactic plane. The position of the GC is marked by a red dot. possible) are mostly excluded. One could argue that the variability is caused by the NSB, a light pollution caused by bright stars etc. which is at a diferent level in the south of the GC than in the north as shown in Fig. 4.2.5 where the NSB along the Galactic plane is plotted. The GC is marked by a red dot in this plot. If one were to observe a signifcant diference of the mean fux between the two light curves or the variability were only be observed for one of them one could argue that the variability is likely to be a systematic artifact, which is either introduced by the NSB or problematic background regions in a particular region of the sky. On the other hand, if the fux level and the level of variability are comparable between the two partial light curves it is unlikely that such systematic explanations can account for the observed variability. The frst observation from this cross-check was, that the number of pointings in the south of the GC is larger than the number of pointings in the north of the GC with 290 versus 227 pointings. The mean integrated fux > 100 GeV for the pointings in the north of the GC is 4.90 ± 0.15 × 10−11 cm−2 s−1 while for the pointings in the south of the GC it is 5.06 ± 0.14 × 10−11 cm−2 s−1. This implies that the mean fux values of the two independent partial light curves agree within statistical errors. The diference of the mean values is only 3%. With respect to variability, the northern pointings show a χ2/d.o.f. of 300.1/226 in a χ2 ft with a constant corresponding to a p-value of 7.0·10−4, while the pointings in the south show a χ2/d.o.f. of 392.4/289 which is equivalent to a p-value of 4.8·10−5. When combining the ft results for the two independent light curves again, one obtains a χ2/d.o.f. of 692.5 to 515. The p-value corresponding to this result is 2.6 · 10−7 or 5.0σ in units of sigma. Both independent fts show signs of variability and the combined p-value is comparable to that which was obtained from the ft of the full light curve which was 2.8 · 10−7. The two diferent values for the signifcance level can be explained by the fact that performing the ft two times to independent, partial light curves introduces an additional degree of freedom since the mean fux may difer for each of the independent fts. By this cross-check it could be shown that the observed signs of variability are inde- 78 Search for Variability of HESS J1745-290

−12 ×10 χ2 ] / ndf 14.51 / 9 -1 s

-2 60 p0 5.061e−11 ± 9.837e−13

50 Integrated Flux > 100 GeV [cm 45

2 4 6 8 10 Subset Index

Figure 4.2.6: The mean integrated fux > 100 GeV for 10 subsets of the H.E.S.S. I light curve consisting of 50 consecutive runs each. pendent of pointings north and south of the GC. Therefore, it is unlikely that the NSB or a problematic background region are causing the observed variability. After it was shown that the long-term variability of the integrated fux > 100 GeV is observed independently of the Galactic latitude where the background is taken from, another type of possible systematic efects was investigated: The H.E.S.S. I light curve was built upon 8 years of GC observations. It is possible that changes in the performance of the detector, aging of the mirrors of the telescopes or an increasing number of broken pixels have an efect on the integrated fux, although some of these efects like the decrease of the mirror refectivity are corrected in the calibration. If such systematic efects infuence the integrated fux, one would observe an increase or decrease of the integrated fux as a function of the time. Of course, such an increase could also be due to physics but it is worth studying if it is present in the data at all. In order to investigate if the integrated fux changes as a function of the time, the mean fux was calculated for 10 subsets of 100 consecutive fux points. The values which were obtained for the mean fux of each sub-set in this test are plotted in Fig. 4.2.6. It could be shown that the mean fux does not change signifcantly between the 4.2 Data Analysis 79

subset p-value σvar 1 9.9 · 10−3 2.3 2 2.1 · 10−4 3.5 3 3.5 · 10−2 1.8 4 1.9 · 10−1 0.85 5 5.1 · 10−3 2.6 6 7.8 · 10−1 -0.78 7 3.6 · 10−1 0.36 8 4.7 · 10−1 0.05 9 7.1 · 10−3 2.45 10 8.2 · 10−2 1.39

Table 4.4: The p-values and signifcance levels for variability for subsets 1–10. diferent subsets by ftting the 10 data points with a constant. The χ2/d.o.f of 14.5/9 corresponds to a 1.3σ signifcance level for variability. Furthermore, the last data point from the year 2012 shows a comparable fux level like the frst data point from 2004. This implies that the variability is likely not to be caused by aging efects of the detector. Another interesting question is which of the subsets show an internal variability by discussing the p-values of the ft for each of the subsets. These p-values and their corresponding signifcance levels for variability can be found in Table 4.4. Although the mean signifcance level for variability of the frst 5 fts (2.2σ) is larger than that of the last 5 fts (0.7σ), the signifcance for variability shows a tendency of an increase for the subsets 9 and 10. The lesson which could be learned from these cross-checks is that the mean fux for subsets of 50 runs does not vary signifcantly as a function of time and systematic efects related to the age of the detector are unlikely to afect the integrated fux since the mean fux value of the frst subset agrees with that of the last subset within statistical errors. Furthermore, the observed variability seems to occur on a timescale of a few runs rather than a timescale > 50 runs since it averages out when ftting the mean values of the 10 subsets with a constant. However, particular subsets still show signs of variability internally when they are ft with a constant. Since the sampling in this test is not correlated with the calender date, it is not possible to make a strict statement about the development of the observed variability as a function of time.

4.2.4.1.2 Light Curve from Phase II In the following also a H.E.S.S. II light curve based on Subset B is analyzed. Since the data quality of the H.E.S.S. II data from 2013 and 2014 cannot be considered to be at the same level than that of the H.E.S.S. 80 Search for Variability of HESS J1745-290

Light Curve of HESS J1745-290 −9 ×10 χ2 / ndf 211.4 / 141 0.1 Integrated Flux > 100 GeV Prob 0.0001149 p0 2.607e−11 ± 9.61e−13 0.08 Fit with a Constant ] -1 s -2

0.06

0.04

0.02

Integrated Flux > 100 GeV [cm 0

−0.02

56400 56500 56600 56700 56800 Date in MJD

(a) The χ2 ft of the run-wise fuxes of HESS J1745-290 with a constant.

Light Curve of G 0.9+0.1 −12 ×10 χ2 / ndf 171.1 / 168 60 Integrated Flux > 100 GeV Prob 0.4198 p0 7.218e−12 ± 6.819e−13 Fit with a Constant ] -1 s

-2 40

0 Integrated Flux > 100 GeV [cm −20

56400 56500 56600 56700 56800 Date in MJD

(b) The χ2 ft of the run-wise fuxes of G 0.9+0.1 with a constant. Figure 4.2.7: Fit of the H.E.S.S. II run-wise fuxes with a constant for both HESS J1745-290 and G 0.9+0.1. 4.2 Data Analysis 81

I, dataset this part of the analysis rather has the character of a cross-check in order to investigate if the tendency observed for the H.E.S.S. I light curve is also continuing for the H.E.S.S. II data. For the ft with a constant shown in Fig. 4.2.7a the χ2 is 211.4 for 141 d.o.f. corresponding to 3.7σ in terms of a Gaussian signifcance. The mean integrated fux of (2.6 ± 0.1 · 10−11) cm-2 s−1 > 100 GeV difers from the value which was obtained from the H.E.S.S. I dataset. As discussed previously this diference can be accounted for by the diferent integration radii which are used by the H.E.S.S. I and H.E.S.S. II confgurations. This implies that there also is evidence for a variability of the HESS J1745-290 fuxes in the H.E.S.S. II dataset. The cross-check with data from G 0.9+0.1 which can be found in Fig. 4.2.7b did not show any signs of variability confrming the H.E.S.S. I data.

4.2.4.1.3 Combining the Results from H.E.S.S. I and H.E.S.S. II Summing over the χ2 from the two independent fts of the H.E.S.S. I and H.E.S.S. II data sample one obtains a χ2 of 904.5 at 657 d.o.f, which is corresponding to a p-value of 1.1 · 10−10 . In terms of a Gaussian signifcance this is equivalent to 6.1σ. The variability which was observed in the χ2 ft of the light curve is a promising result which requires a careful discussion of systematic efects. Previously it has already been shown that the efect for the H.E.S.S. I dataset does not depend on the spectral index and the energy thresholds which were used as input parameters for the light curve. Also using a tighter integration radius of 0.15° did not reduce the efect for the H.E.S.S. I light curve. Furthermore, the cross-check with G 0.9+0.1 can be used to estimate possible systematic efects. The constant γ-ray fux of G 0.9+0.1 still rules out most of the possible systematic efects which could cause the observed variability of HESS J1745-290, since the two sources are located in the same FoV at a distance of only 1.0°. If problems with the background rates caused the variability, this efect would have afected both regions with the same probability due to diferent pointing ofsets which were used for the observations. If such an efect existed on average both regions should be afected with the same probability. Also possible gradients in the background are unlikely to cause the observed variability, since in case such gradients caused the variable fux which was observed for HESS J1745-290 there would also be an efect for an object at 1° ofset. Also taking the background only from the north or only from the south of the Galactic plane did not eliminate the observed variability. Therefore, efects induced by the background can be most likely excluded as systematic origin of the variability, since the G 0.9+0.1 fuxes do not fuctuate beyond noise level. On the other hand, due to the diferent fux levels of both sources systematic vari- 82 Search for Variability of HESS J1745-290 ations of the rates of γ-like events by atmospheric irregularities cannot be entirely excluded. However, the systematic infuence of variations of the atmosphere on the integrated fux at H.E.S.S. is only at the 5% level [45]. Diferent systematic errors on the integrated fux will be discussed later in this section.

4.2.4.1.4 The Excess Variance The normalized excess variance is often used to characterize the variability of light curves of astronomical sources [14]. It is defned as

1 N σ = X[(x − x¯)2 − σ2] NXV ¯2 i i Nx i=1 where N stands for the number of fux measurements and x¯ is the unweighted arithmetic mean of the fux values of the light curve. The quantities and 2 are the fux value xi σi and variance of a particular data point. In case a light curve shows variability beyond the noise level, the quantity σNXV is expected to be > 0. The normalized excess variance is often given in population studies, for example, to compare diferent AGNs. It cannot be translated directly into a signifcance level for variability, since it also depends on parameters like the length of the light curve. In order to translate it into a signifcance, detailed simulations of the light curve under consideration are necessary. Nevertheless, it will be given here for completeness and as a further cross-check for the previous results, since obtaining a normalized excess variance which is < 0 would contradict the variability which was revealed in the χ2 ft of the light curve with a constant. The excess variance was calculated for both the H.E.S.S. I and the H.E.S.S. II light curve separately again. For the H.E.S.S. I light curve an excess variance of 0.097 was obtained, while for the H.E.S.S. II light curve this quantity could be determined to be 0.063. As expected both values are > 0 and furthermore of the same order like excess variances which were quoted for several low mass X-ray binaries in Ref. [82]. Although one has to be careful with such comparisons, the excess variance > 0 which was found during this cross-check is consistent with the variability, which was reported for the χ2 ft.

4.2.4.1.5 A Systematic Error on the Flux Values In order to further investigate the robustness of the result, diferent systematic errors in percent have been added to the data points of the light curves. The systematic error was increased in steps of 5% up to 15%. Figure 4.2.8 shows the development of the signifcance level for variability from the χ2 ft of the light curve with a constant as a function of the systematic error in percent. The initial signifcance level for variability drops from 6.1σ to 2.9σ after applying a 4.2 Data Analysis 83

HESS J1745-290 6 5 σ level 5.5

5 Significance on Variability

4.5

3.5

0 2 4 6 8 10 12 14 16 Systematic Error in Percent

Figure 4.2.8: The dependence of the signifcance level for variability as a function of the systematic error on the fuxes in percent.

15% systematic error, which is the systematic error which was given for the integrated fux of the Crab Nebula when comparing the fuxes between diferent nights [8]. The question is if this systematic error of 15% also correctly accounts for the systematic diference of the integrated fuxes from two diferent runs of the HESS J1745-290 light curve. There are several reasons for the full 15% error being in fact be too large for the GC region:

• Humid and unstable weather conditions during the summer time on the southern hemisphere where the Crab Nebula is observable by H.E.S.S. should introduce additional atmosphere-related systematic efects. Furthermore, the humidity also afects the detector electronics, which might introduce additional instrumental efects. The GC region on the other hand is usually observed from March to September where the weather conditions are dry and stable.

• The G 0.9+0.1 light curve, which was created under identical systematic conditions, does not show any variable fux.

In opinion of the author, the arguments above justify the assumption that the systematic error on the HESS J1745-290 between two diferent runs is in fact smaller than 15%: For example it was shown before that the mean integrated fux changes by only 3% when comparing pointings which are taking their background from regions with b > 0 to such 84 Search for Variability of HESS J1745-290 with a background from regions with b < 0. The level of variability was still comparable for both subsets. When talking about systematic errors it is also important to discuss which kind of systematic efects actually can introduce an artifcial variability, since there are also systematic efects which afect all integrated fuxes the same way shifting them upwards or downwards. Such a constant shift is not expected to introduce a variability between diferent runs or nights. An example of an efect which causes a constant shift of all integrated fuxes would be a bias of the energy reconstruction. Further efects causing a shift of the entire are light curve could be induced by the spectral index or the energy threshold which is used to calculate the integrated fux. It could be shown before that these efects do not afect the level of variability of a light curve. On the other hand, efects which are related to the background regions which are used for particular pointings could cause a variability between diferent runs. However, such efects were shown to be less than 5% on average. Also changes in the transmissibility of the atmosphere cannot be excluded to cause a change of the integrated fux between diferent nights. However, such efects due the atmosphere are not expected to exceed the 5% level. Since none of these efects is larger than 10%, adding a systematic error of 10% to the HESS J1745-290 integrated fux was considered to be sufcient. The signifcance level for variability which is corresponding to this systematic error is 4.5σ.

4.2.4.1.6 Discussion of a MSH 15-52 Light Curve As additional cross-check a light curve of the SNR MSH 15-52 [94] was taken into account, which is a supernova remnant with a comparable fux level like HESS J1745-290. Furthermore, the source is observed under comparable zenith angles like the GC. For MSH 15-52 a constant fux level is expected. The analysis was done with the same setup like HESS J1745-290 analysis. The mean integrated fux of (4.1 ± 0.1) × 10−11 cm-2 s−1 MSH 15-52 is at a comparable level to that of HESS J1745-290 which is (4.9 ± 0.1) × 10−11 cm-2 s−1. Unfortunately, the size of the MSH 15-52 dataset is not comparable to the GC dataset. A light curve based on 200 runs of MSH 15-52 data has been created and was ft with a constant using a χ2 ft (under application of the 10% systematic error). For MSH 15-52 the ft does not show any hints for variability resulting in a p-value of 0.11 which corresponds to 1.3σ. Due to the diferent statistics for MSH 15-52 and HESS J1745-290 one can compare the signifcance for variability with respect to the livetime: For MSH

15-52 this quantity is in the order of 0√.1σ while for HESS J1745-290 it is by a factor of 3 h larger with 0√.3σ . Both quantities were calculated after application of the 10% systematic h error. Therefore, also with respect to the livetime, HESS J1745-290 shows more evidence for variability than MSH 15-52. 4.2 Data Analysis 85

Light Curve of MSH 15-52 −9 ×10 χ2 / ndf 224.1 / 199 Integrated Flux > 100 GeV p0 4.045e−11 ± 1.3e−12 0.15 Fit with a Constant -1

s 0.1 -2

0.05

Flux > 100 GeV cm 0

−0.05

53000 53500 54000 54500 55000 55500 Date in MJD

Figure 4.2.9: χ2 ft of a run-wise light curve of the SNR MSH 15-52.

4.2.4.2 Applying the L-S Test to the H.E.S.S. Dataset In the following the application of the L-S test to a combined run-wise light curve based on H.E.S.S. I and H.E.S.S. II data will be discussed in order to study possible long-term periodicities of HESS J1745-290. In order to build this combined light curve for the L-S test, the H.E.S.S. I light curve with the 0.15° integration radius and an energy threshold of 100 GeV from Table 4.3 was used because the diference of the mean fux level between the H.E.S.S. I and the H.E.S.S. II curve which is depending on the integration radius for the GC region due to the difuse emission was the lowest for this combination: The mean fux of the H.E.S.S. I light curve is 3.2 ± 0.06 · 10-11 cm-2 s−1 while the H.E.S.S. II light curve shows a mean fux level of 2.7 ± 0.1 · 10−11 cm-2 s−1. Scaling the H.E.S.S I fuxes with a constant factor to the level of the mean H.E.S.S. II fux by applying a factor of 0.84 did not change the results which are discussed in the following. The resulting L-S periodogram for the combined light curve in Fig. 4.2.10a shows a peak reaching a normalized L-S power of 10.8 which translates into a 4.1σ signifcance level for a period of 110 days. Since a hint of this 110 days period has been found in the literature [71] before it can be considered to be free of trials. This is a tempting ad hoc result, since it would be the frst independent confrmation of the tentative radio period 86 Search for Variability of HESS J1745-290 which has been reported for Sgr A* radio data. Although the L-S method has been carefully tested beforehand, additional systematic studies are performed in the following in order to rule out a possible systematic origin of the observed 4.1σ efect.

4.2.4.2.1 Discussion of systematic Efects The frst question that arises whenever a periodicity test returns a positive result is if the signal simply could be induced by sampling efects. Although the L-S test can be considered to be robust against sampling efects if the sampling is not too regular, it is necessary to investigate if the sampling contributes to the peak observed at 110 days. Therefore, the following cross-checks were performed:

• Randomizing the fuxes: For this test the x-values of the light curve (time stamps) were kept static but the y-values (fuxes) were replaced by random numbers. These random numbers were based on the fux level of the HESS J1745-290 light curve.

• Permuting the fuxes: A second test was permuting the original fuxes from the light curve in a random fashion, keeping the time stamps constant. This procedure can be repeated in a systematic way multiple times in order to gain a deeper understanding of the empirical background PDF for the sampling of the observations.

• Using a control source: The test was also applied to the light curve of the SNR G 0.9+0.1 which is part of the same FoV like HESS J1745-290.

None of these tests revealed any hint for a feature at 110 days like observed for the original dataset. The corresponding periodograms are shown in Fig. 4.2.10. In order to perform these cross-checks in a more quantitative fashion the light curve was created 10 000 times with exchanged fuxes but static time stamps. For each of these 10 000 light curves the normalized L-S power for a period at 110 days was calculated in order to test if any of these L-S powers obtained for a randomized light curve exceeds the observed value of 10.8 which was obtained for the original HESS J1745-290 light curve. The distribution of these L-S powers can be found in Fig. 4.2.11 where the theoretical expectation for the background distribution is indicated by a red line. For this cross-check the empirical L-S power distribution is in excellent agreement with the theoretical background distribution which is an exponential with mean 1 and slope -1. There is no L-S power close to the observed value of 10.8. By this cross-check it was shown empirically that the signifcance level is > 3.7σ since the probability to obtain 4.2 Data Analysis 87

12 12

10 10

8 8

6 6 Normalized Lomb-Scargle Power Normalized Lomb-Scargle Power

4 4

2 2

0 0 100 105 110 115 120 125 130 100 105 110 115 120 125 130 Period (days) Period (days) (a) The L-S periodogram for HESS J1745-290. (b) All fuxes replaced by random fuxes.

12 12

10 10

8 8

6 6 Normalized Lomb-Scargle Power Normalized Lomb-Scargle Power

4 4

2 2

0 0 100 105 110 115 120 125 130 100 105 110 115 120 125 130 Period (days) Period (days) (c) Scrambled fuxes: The fux values were ex- (d) The L-S test applied to a light curve of G changed keeping the time stamps of the runs 0.9+0.1. constant. Figure 4.2.10: L-S periodograms around 110 days which were obtained during the cross- checks. None of the three methods shows a signal at the expected period of 110 days. The normalized L-S power is plotted versus the period in days here. 88 Search for Variability of HESS J1745-290

3 10 LS Power at 110 Days

Theoretical BG Expectation

Number of Entries 102

0 1 2 3 4 5 6 7 8 Normalized LS Power

Figure 4.2.11: The distribution of L-S powers calculated for a period of 110 days which was obtained for 10 000 randomized light curves with an identical time structure like the actual HESS J1745-290 dataset. 4.2 Data Analysis 89

Lomb-Scargle-Periodogram 12 HESS I Dataset

10 HESS I + II Dataset

8 Lomb-Scargle Power

0 106 108 110 112 114 Period (days)

Figure 4.2.12: This plot compares the L-S power spectrum of the H.E.S.S. I dataset with the combined analysis. The blue curve shows the L-S powers versus the period in days applied to the H.E.S.S. I dataset only. The red curve stands for the L-S powers corresponding to the combined H.E.S.S. I and H.E.S.S. II light curve . 90 Search for Variability of HESS J1745-290 the observed or a more extreme result by chance could be shown to be ≦ 10−4 by the application of the test to the 10 000 randomized light curves. However, the signifcance level of 4.1σ, which was given before, can be considered to be justifed due to the fact that the background distribution is in agreement with its theoretical expectation.

4.2.4.2.2 Analyzing H.E.S.S. I Data and H.E.S.S. II Data separately To further investigate this tentative periodicity at 110 days, the dataset has been split up into a H.E.S.S. I and a H.E.S.S. II sub-sample. In case the efect is real, the signifcance level for periodicity of the peak at 110 days should increase when the H.E.S.S. II data is added to the H.E.S.S. I sub-sample. In Fig. 4.2.12 the result of this cross-check is shown: The blue curve refers to the L-S power spectrum, which is based on the H.E.S.S. I sub- sample only, while the red curve represents the L-S power for the combined light curve. The L-S power for the peak at 110 days indeed increases after merging the two samples, which means that an efect is present in both datasets. The fact that the signifcance level periodicity increases after adding the statistically independent H.E.S.S. II dataset to the H.E.S.S. I light curve supports the assumption that one has to deal with a real property of the light curve and not just a statistical fuctuation.

4.2.4.2.3 The Amplitude of the Flux Modulation Since the L-S test showed evidence of a fux modulation with a period of 110 days an interesting question is of which order of magnitude the amplitude of this fux modulation is. In order to obtain an estimate for this amplitude, the H.E.S.S. light curve from Fig. 4.2.4a was ft with a simple model based on the following assumption: Since the efect observed in the L-S test is weak, the HESS J1745-290 fux certainly consists of a DC component which is superposed with a variable component. Therefore, the light curve was ft with the following function to get an estimate of the amplitude of the variable fux component which was assumed to be sinusoidal:

2π f(t) = A · sin( · (t − t )) + c (4.2.1) T 0

The parameter of interest in this ft is the amplitude A, t0 stands for an arbitrary time ofset, T is the period, which was set to 110 days for the particular application of the ft and c is the parameter for the constant fux component. The ft result can be found in Fig. 4.2.13 where the light curve is only displayed partially for a better visibility. The modulus of the amplitude, which was obtained here, is (6.48 ± 1.48) × 10−12 cm−2 s−1. Therefore, the diference between the minimum fux and the maximum fux level with respect to this sinusoidal modulation is of the order of (1.30 ± 0.27) × 10−11 cm−2 s−1, 4.2 Data Analysis 91

Light Curve of HESS J1745-290 −9 ×10 χ2 / ndf

] 623.2 / 516 -1 s Prob 0.0008149 -2 0.2 A −6.481e−12 ± 1.476e−12 t0 19.84 ± 4.312 0.15 c 4.714e−11 ± 1.105e−12

0.1

0.05 Integrated Flux > 100 GeV [cm 0

−0.05

−0.1

53400 53600 53800 54000 54200 54400 Date in MJD

Figure 4.2.13: The ft of the H.E.S.S. I light curve with the function ( ) = sin( 2π f t A · T · (t − t0)) + c. The plot does not show the full light curve for a better visibility. which is 26.5% of the total integrated fux of (4.9 ± 0.1) × 10−11 cm-2 s−1. This number can be read in a way that the fux of HESS J1745-290 is variable at a level of at least 26.5%. A further observation is that the function from Eq. 4.2.1 gives a better ft to the light curve than a simple constant: While the ft with a constant gave a χ2/d.o.f. of 693.1/516, the ft with Eq. 4.2.1 resulted in a ratio of 623.2/516. Although the ft with Eq. 4.2.1 performs better than the ft with a constant, the model of a constant, which is superposed with a sinusoidal fux modulation, alone is not sufcient to explain the observed variability of the light curve. Various reasons could play a role here: The presence of an additional irregular variability, which is not connected to the fux modulation, is one possibility. Furthermore, it is possible that the amplitude of the periodic fux modulation shows a time dependence, which was not taken into account by the simple model, which was used here.

4.2.4.2.4 Attempt of a MWL Study with public Data from Fermi LAT and Swift In order to further investigate the situation from a MWL point of view also data which were publicly provided by external observatories have been analyzed. While the Fermi LAT collaboration made their whole dataset available to the public, Swift 92 Search for Variability of HESS J1745-290 provides light curves of selected objects like Sgr A*, which are updated on a daily basis. The analysis with these external data has been restricted to the long-term variability and the L-S test since it did not make sense to consider smaller timescales due to the limited efective area of these two experiments.

4.2.4.2.5 Fermi LAT Data The Fermi LAT Data Analysis Tools [29] ofer two approaches to produce light curves. The simplest way is to use the Aperture Photometry (AP) technique, which is very straight forward in its application but has some caveats: First of all no background is subtracted when this method is applied. Furthermore, one has to expect a contamination from nearby sources which makes the analysis less precise. The second approach is the Likelihood Method, which requires a detailed modeling of all known sources and the difuse emission in the region of interest. For simple regions this is a viable approach. For the GC region this technique is not realistic due to the large number of unknown sources which are expected to be present in this region in the energy range which is covered by Fermi LAT (100 MeV to 500 GeV). However, one can still try to obtain a rough estimate using the simpler AP technique in combination with a scan along the Galactic plane: This was done by defning diferent circular regions of interest with the size of the Fermi LAT PSF at an energy of 500 MeV which is about 5°. In total 10 of these regions were distributed along the Galactic plane at Galactic longitudes from -8° to 8°. The exact pointings are indicated in Fig. 4.2.14 by dots. For each of these regions of interest one can create a photometric light curve and perform a χ2 ft with a constant. Plotting the signifcance level for variability of these fts along the Galactic plane can give a hint for a variability in case it is peaking around a certain position, e.g. the position of Sgr A*. In case there is a variable source at this position one would expect a peak with a full width at half maximum (FHWM) of roughly the Fermi LAT PSF. In Fig. 4.2.14 the result of this scan along the Galactic plane is shown. The x-axis stands for the Galactic longitude at which the particular pointing was centered in the Galactic plane (the latitude of all pointings was zero). The y-axis stands for the signifcance level for variability. The scan indeed gave the expected result: The signifcance distribution in Fig. 4.2.14 shows a peak around the position of the GC, which could be interpreted in a way that there is a variable source at this position, which is contributing to the signifcance beyond the expected level of systematic efects. Of course this plot should be read in a qualitative way rather than a quantitative way since the AP approach is subject to a large background systematics. There is also the possibility of other variable objects like the magnetar SGR 1745-2900 or the GC microquasar 1E 1740.7-2942 contributing to an 4.2 Data Analysis 93

20 Significance on Variability

−8 −6 −4 −2 0 2 4 6 8 Galactic Longitude of the Pointing

Figure 4.2.14: Signifcance distribution of the χ2 ft of Fermi LAT photometric light curve with a constant for the diferent pointings along the Galactic plane. efect which cannot be excluded with this method. Nevertheless, there is a local maximum of variability at the position of the GC in combination with a correlated series of points with signifcances > 18σ. There seems to be another local signifcance maximum at a Galactic latitude of about 4.0° which coincides with the position of the low mass X-ray binary GRS 1758-258 [64] but seeing a correlation here is very speculative and would require more detailed studies to be justifed. Therefore, the discussion will focus on what can be learned from these observations with respect to the GC and Sgr A*. There is a series of correlated signifcance values for variability from -4° to 2° (or 4° when attributing the outlier at 4° to GRS 1758-258) which is peaking at the GC. The FHWM of the Gaussian one can ft to this peak is in the order of 5° which is equivalent to the Fermi LAT PSF at an energy of about 500 MeV. This series of correlated points around the GC at least gives a hint for a variable source and therefore does not contradict the result obtained with H.E.S.S. data. A second study was repeating the L-S test with the Fermi LAT AP light curve, which was produced before. Dealing with Fermi LAT light curves one has to expect the presence of several artifcial periods induced by diferent systematic efects. The periods related to systematic efects are [79]:

• 96 minutes: This is the orbital period of the satellite.

• 3.2 hours: The duration of a survey period after which the setup of the satellite maybe modifed.

• 27.3 days + harmonics: The moon contaminates Fermi LAT data when it passes 94 Search for Variability of HESS J1745-290

near sources due to the fact that CRs which are interacting with the moons surface can produce γ-rays.

• 53.4 days: This is the precession of the spacecraft’s orbit and the strongest systematic period.

• 1 year: For sources observed close to the trajectory of the sun, γ-rays emitted from the sun may produce an efect.

Since a period range of 100-120 days is not among the problematic periods there are no systematic objections against applying the L-S periodicity test also to a Fermi LAT light curve. The test was applied to the light curve for the pointing directly at the GC and the resulting L-S periodogram can be found in Fig. 4.2.15a. It indeed shows a L-S power for the period range of interest which is slightly higher than one would expect from noise level. The periodogram shows a maximum at 120 days with a normalized L-S power of 6.1. This corresponds to a pre-trial signifcance of 2.8σ. Applying 5 trials which were needed to scan the full width of the radio peak from 100 days to 120 days this signifcance reduces to 2.3σ. An important point which should be discussed here is that the L-S power is not maximal at T=110 days where the maximum for the H.E.S.S. light curve could be observed. A possible interpretation is that one of these peaks or even both of them are just due to statistical fuctuations. On the other hand, in case one assumes that there is an efect behind those peaks one could argue the following way to resolve the discrepancy. The radio period for Sgr A* which was discussed in Sec. 3.1.1 was given for a range from 100-120 days. For the analysis of the H.E.S.S. light curve the mean value of this interval was used which is 110 days. However, the period does not need to be exactly at 110 days and it may even change with the time in case it is really related to the disk movement of Sgr A* as it is claimed for the modulation observed in radio data. In that case the exact position of the peak would also depend on the length of the dataset, the time frame of the observations and the sampling. The light curves discussed here do not cover exactly the same time windows.

4.2.4.2.6 Swift Data The ft of the daily fuxes with a constant, which were moni- tored by SWIFT BAT, will not be performed here since Sgr A* is well know as variable source in the X-ray band. However, it is more interesting to ask the question if one also fnds a hint of the tentative period around 110 days in Swift data. As shown during tests in Sec. 4.1.2.1 this method turned out to be robust when applying it to Swift light curves. The light curve used for this analysis covers an energy range from 15–50 keV. Applying the L-S test to a Swift daily light curve from the years from 2004 to 2014 4.2 Data Analysis 95

8 8

7 7

6 6

5 5 Lomb-Scargle Power Lomb-Scargle Power

4 4

3 3

2 2

1 1

0 0 95 100 105 110 115 120 125 95 100 105 110 115 120 125 Period (days) Period (days) (a) L-S periodogram derived from a Fermi (b) L-S periodogram derived from a Swift LAT light curve. light curve of the daily fuxes. Figure 4.2.15: L-S periodograms for the Swift and Fermi light curves. one obtains a double peak around 110 days which has its maximum at 100 days with a normalized L-S power of 7.4 and a second peak with a L-S power of 6.2 at 120 days. The period of 110 days does not show up among the signifcant periods. The test results are shown in Fig. 4.2.15b. The pre-trial signifcance of the peak at 100 days is 3.2σ, which reduces to 2.8σ at post-trial level. Of course these two results, which were obtained with Fermi LAT and Swift data, cannot be considered as an independent confrmation of the tentative 110 days period due to low signifcance levels which were obtained and also the fact that the peak positions do not agree exactly. However, it can be stated that these cross-checks at least point into a similar direction like the H.E.S.S. and radio data and therefore do not provoke an unresolvable contradiction between the diferent wavelength bands. In order to further investigate this efect, the L-S power spectra of Fermi, Swift and H.E.S.S. were plotted in a common coordinate frame as shown in Fig. 4.2.16. All of them show L-S powers > 6 within the range from 100–120 days while the period where all three power spectra seem to be most correlated is 120 days which may account for the larger error on the time ofset. In case the three light curves really show a correlated fux modulation for a period from 100–120 days, the time ofset t0 which is obtained when ftting the light curves with Eq. 4.2.1 is expected to be identical for the most simple case of a common origin of the modulation at diferent photon energies. If the observed fux modulation is due to a more complex interplay of diferent processes also a correlation of the light curves with a fxed time delay is possible. To test this the ft with Eq. 4.2.1 was performed with two 96 Search for Variability of HESS J1745-290

SWIFT Fermi 12 H.E.S.S.

6 Normalized Lomb-Scargle Power

0 100 105 110 115 120 125 130 Period (days)

Figure 4.2.16: L-S periodograms of Swift, Fermi and H.E.S.S. diferent periods: First the period of 110 days which shows the largest signifcance level for periodicity for the H.E.S.S. dataset and second a period of 120 days was used, where the L-S periodograms have correlated peaks. The ft functions for all three light curves were normalized and plotted into a common coordinate system afterwards. While the time ofset t0 disagrees for the ft with a period of 110 days in Fig. 4.2.17a, the ft with a period of 120 days which can be found in Fig. 4.2.17b shows comparable time ofsets for the three ft results.

The exact numbers for t0 for the period with 120 days are t0Swift = (−13.10±4.94) d days, t0F ermi = (−12.44 ± 10.25) d and t0H.E.S.S = (−18.45 ± 11.76) d. The error of the time ofset is in the order of 5-10% of the period. While the Fermi and Swift light curves provide a measurement for nearly every day and only show few gaps due to detector downtimes, the sampling of the H.E.S.S. light curve is irregular and shows only observations at about ∼ 250 days in 10 years.

4.2.4.2.7 Summary Both the χ2 ft of the run-wise light curve with a constant and the L-S test showed evidence that HESS J1745-290 shows a variable γ-ray fux at a timescale larger than the duration of a run. The signifcance level of the periodicity at 110 days which was detected applying the L-S test was 4.1σ. MWL studies with public data from Fermi LAT and Swift also showed a hint into this direction although the result not being very conclusive due to the low post-trial signifcance levels, which were found for the period range from 100–120 days only are at the 2.3σ (Fermi LAT) and 2.8σ (Swift) level. Nevertheless, the MWL studies did not contradict the H.E.S.S. result, since the period range of interest from 100–120 days showed a hint for an efect 4.2 Data Analysis 97

SWIFT 3 Fermi H.E.S.S.

1 Normalized Amplitude

−1

−2

−3 −150 −100 −50 0 50 100 150 Time (Days)

(a) Fit with a period of 110 days.

SWIFT 3 Fermi H.E.S.S.

1 Normalized Amplitude

−1

−2

−3 −150 −100 −50 0 50 100 150 Time (Days)

(b) Fit with a period of 120 days. Figure 4.2.17: Normalized ft results of the fts of the Fermi, Swift and H.E.S.S. light curves of the Galactic Center with Eq. 4.2.1. 98 Search for Variability of HESS J1745-290 which is further supported by the comparable time ofsets which were found during the ft of the light curves with Eq. 4.2.1. Also the χ2 fts, which were performed here with H.E.S.S. light curves from 2004 until 2014, gave evidence for variable behavior of HESS J1745-290 at the 4.5σ level after the application of a 10% systematic error on the fux values. Furthermore, it can be stated that the tentative period of 110 days is not in contradiction to the discussion in Sec. 4.2.4.1.1 where subsets of 50 consecutive runs were studied. Since these subsets were not chosen to be in phase with the period, the efect is expected to average out over the diferent subsets.

4.2.5 Search for a Variability at a Timescale of Minutes After the discussion of the long-term behavior of HESS J1745-290 in the next step the short-term behavior at timescales shorter than the duration of a H.E.S.S. run (∼ 28 min) will be investigated. In this part of the analysis a simple event analysis approach was used applying the RL test and a χ2 ft to the arrival times of all events from a circular region of interest around HESS J1745-290 with a radius of 0.15°. This radius difers from the default integration radius of the Loose cuts which is 0.2°. Since no efective areas were needed for this event wise analysis, it was possible to tighten the integration radius in order to minimize a possible infuence of other potentially variable objects in the HESS J1745-290 region of interest like the GC magnetar or undiscovered sources which might be hidden in the difuse emission and perform the analysis with setting the focus on Sgr A*. Thereby an integration radius of 0.15° was used as compromise between the rather tight radius of the STD cuts (∼0.1°) and the generous integration radius of the Loose cuts. MC simulations showed that a radius of 0.15° contains more than 75% of the events of a γ-ray point source observed at 10° zenith angle and 0.5° ofset which means that the default integration radius of the Loose cuts (0.2°) is covering more than the 68% containment radius, which is usually used for defning the integration radius. Reducing it to 0.15° was considered to be a good compromise between the goal of including as many events as possible from the direction of Sgr A* and avoiding an unnecessary contamination of the dataset by the difuse fux. Furthermore, an additional cut on zenith angles < 40° was introduced in order to minimize the efect of variations of the event rate during a run, which occur at zenith angles > 40°. Furthermore, for the search for a short-term variability only runs were included in the analysis for which at least 3 telescopes participated in the observations. The data were analyzed in a run-wise fashion with the focus on detecting possible QPOs and short-term variations of the GC event rates at timescales of minutes. The 4.2 Data Analysis 99

RL test was chosen for this purpose. Furthermore, a χ2 ft was applied to the photon rates in a run-wise fashion in order to search for short fux variations without a periodic pattern. It is also possible to ask the question if the VHE γ-ray source in the direction of the GC shows a permanent periodicity at timescales of the order of minutes. This efect is not expected since it has not been reported for any other wavelengths band, yet it is still important to rule out this behavior also for the VHE γ-ray regime. Therefore, also a search for global periods was performed after investigating the overall distribution of RL powers for the H.E.S.S. GC dataset. The search for a short-term variability presented here is limited to H.E.S.S. I data only. Due to the more complex systematic situation and unresolved issues with the CT5 camera and calibration at the time of this writing, H.E.S.S. II data was considered not to be reliable enough for a variability search at this short timescale with the method chosen here. An example for an unresolved issue which could be critical with respect to the search for a short-term variability are the pedestals of the CT5 camera, which are changing in a rapid and unpredictable way during a run. This efect should not be crucial for the search for a variability at a timescale larger than the duration of a run but might afect a search at timescales of minutes. With respect to these problems the H.E.S.S. II data was not used for the search for short-term variability in order to keep the dataset for an independent cross-check when all these issues are fully understood and resolved during the calibration.

4.2.5.1 The Distribution of Rayleigh Powers of the H.E.S.S. Dataset The frst step of this study was to investigate the overall shape of the distribution of all RL powers, which was obtained by testing periods from 60 s to 600 s for all runs of the previously defned dataset with a step-width of 1 s. In case HESS J1745-290 shows fares with a similar timescale and fare population like in the X-ray band one would expect a tail at large RL powers to be present in the resulting RL power distribution. For the H.E.S.S. dataset one would expect 1–10 γ-ray fares (Sec. 3.1.2) when assuming that such fares exist and furthermore, that the fare population of the γ-ray and the X-ray band are comparable. Due to this low number of expected fares, their efect on the overall shape of the distribution will be weak in case an efect is present in the data. As shown in Sec. 4.1.2.2 the shape of the RL Power distribution is likely to give at least a qualitative hint in case of variability being present in the data. Before discussing the RL power distribution for HESS J1745-290 the background from the refected background method and the G 0.9+0.1 signal region were studied, in order to obtain a deeper understanding of possible systematic problems. The resulting 100 Search for Variability of HESS J1745-290

Background G 0.9+0.1 104 Background Expectation Number of Entries 103

102

0 2 4 6 8 10 12 14 Normalized RL Power

Figure 4.2.18: The distribution of RL powers for the background from the refected background method (blue histogram) and the SNR G 0.9+0.1 (green histogram). distributions of RL powers can be found in Fig. 4.2.18 where the theoretical expectation of entries is indicated by a red line. Both distributions show a good qualitative agreement with the theoretical background expectation for large RL powers > 10. The RL power distribution of the G 0.9+0.1 region even shows a defcit with respect to the theoretical expectation for large RL powers: No entries with RL powers > 10 are observed. Simulations which will be discussed later in this section showed that the probability of obtaining zero entries for RL powers > 10 is about 20% (Fig. 4.2.20a) for the particular sample size of this analysis in case of the pure-background scenario and under the assumption that the events of H.E.S.S. runs are distributed uniformly. These two tests showed that there are no instrumental efects for the fnalized run list which cause a large-power tail for the RL power distribution at post-cut level. The step-width between neighboring periods and the period range which were investigated for the background are identical to that of the analysis of HESS J1745-290. Before proceeding with the discussion of the actual HESS J1745-290 analysis it is worth mentioning that within the history of this analysis the application of the RL 4.2 Data Analysis 101

Background Expectation

105 HESS J1745-290 G 0.9+0.1

104 Number of Entries

103

102

0 2 4 6 8 10 12 14 Normalized RL Power

Figure 4.2.19: The distribution of RL powers for HESS J1745-290 and the corresponding background from the refected background method. The blue line shows the theoretical expectation for the background. 102 Search for Variability of HESS J1745-290 test was the very frst step revealing a possible variability of HESS J1745-290. Initially the author planned to study another object with respect to possible variable or faring behavior, namely the Galactic Center microquasar 1E 1740.7-2942. Although the object is not visible as a signifcant DC source in H.E.S.S. data there still is a possibility of transients emerging from this object, which could take place during some runs and reach the VHE γ-ray range without causing a globally signifcant signal. In order to detect such a hypothetic variability during single runs the RL test can be used. Since HESS J1745-290 was always considered to show a constant γ-ray fux since frst H.E.S.S. results were published in 2006, the object seemed to be a good candidate to verify the method. Therefore, a RL power distribution for periods from 60 s to 600 s which is shown in Fig. 4.2.19 was created with a step-width of 1 s showing an unexpected large-power tail for RL powers > 10. Considerable efort was invested into understanding the obtained shape of the RL power distribution, which is summarized in Sec. 4.1.2.2. The lesson learned from these simulations was that there is no simple way of quantifying the signifcance level of the large-power tail of this particular RL power distribution apart from performing simulations. In the following an estimate for the signifcance level for variability corresponding to the RL power distribution in Fig. 4.2.19 will be obtained by such simulations. From the insights, which were obtained when studying the shape of a RL power distribution, two important characteristics could be derived for a RL power distribution that is likely to be built upon data segments which contain an efect: First it is expected to show a tail for large RL powers. For the RL power distribution which was obtained from the HESS J1745-290 dataset this can be converted into a quantitative condition by the statement that the number N of entries with RL powers > 10 is 104. The threshold to determine N was motivated by the observation that G 0.9+0.1 does not show any RL powers > 10 and only about 5 entries are expected for this range from the theoretical prediction. However, the empirical distribution is above the background expectation for RL powers from 8–9. Therefore, the threshold was chosen in a somewhat arbitrary fashion and mainly is justifed by the observation that G 0.9+0.1 did not show any entries for this RL power range. Furthermore, in case an efect is present in some data segments, which is afecting the shape of the entire distribution, one would also expect the quantity EP = Pint − Ndof to be ≫ 0, which should be close to zero in the case of noise. This condition is closely related to the fact that 2P follows a χ2 int 2(nseg∗np) distribution under certain conditions when neighboring periods can be considered to be statistically independent but also holds if this statistical independence is not given. For the RL power distribution in Fig. 4.2.19 this “excess RL Power” EP could be calculated 4.2 Data Analysis 103 to be 4658. The two conditions can be combined to a simple hypothesis test which can be summarized to the question: What is the probability to obtain a distribution (or even a more extreme one) by chance which

1. shows an excess RL Power ≧ 4658 and

2. shows a large-power tail with N (Entries with RL powers > 10) ≧ 104?

A combination of these two criteria is expected to be sensitive to cover two possible scenarios:

1. It is possible that the empirical distribution only disagrees at low RL powers from the theoretical expectation if several data segments contain a weak efect, which is not sufcient to produce an obvious large-power tail.

2. Furthermore, the method ofers an approximation to quantify the probability to obtain a large-power tail like the one observed for HESS J1745-290 by chance.

In simulations with the objective to estimate the probability to get the observed distribution or a more extreme one by chance, both quantities (N and EP ) were calculated 10 000 times for toy MC samples containing 500 simulated H.E.S.S. runs each. One can count the number of RL power distributions for which the conditions above are exceeded and derive an estimate for a p-value based on this number. Although these simulations do not include possible systematic efects like the detector deadtime or changes of the zenith angle within a run, they can be used to estimate the statistical signifcance level of the obtained RL power distribution. Due to the fact that the RL power distributions of G 0.9+0.1 showed a good agreement with the theoretical expectation, such instrumental efects are expected to play a negligible roll: The RL power distribution of G 0.9+0.1 does not show any entries for RL powers > 10 and leads to an EP of −7105, which means that no signs of variability or periodicity could be observed for this control region. In the 10 000 simulated datasets exactly 9 results were found which were exceeding both criteria, which means that the probability of obtaining the observed result by chance is ≤ 9×10−4 . This p-value corresponds to a signifcance level of 3.1σ in Gaussian units. The obtained distributions for N and EP are shown in Fig. 4.2.20 where the vertical red line indicates the empirical value which was found for HESS J1745-290. Under the assumption that the H.E.S.S. events are approximately uniformly distributed during a run, these 3.1σ can be considered to be a good approximation of the probability of obtaining the RL power distribution in Fig. 4.2.19 or a more extreme one by chance. 104 Search for Variability of HESS J1745-290

103

Frequency of Occurrence 102

0 20 40 60 80 100 120 140 160 Number of Entries for a RL Power > 10 (a) The simulated distribution of the number of entries for RL powers > 10.

350

300

250 Frequency of Occurrence

200

150

100

0 −40000 −30000 −20000 −10000 0 10000 20000 30000 EP (b) The simulated distribution of the excess RL power EP. Figure 4.2.20: The simulated distributions for the number N of entries for RL powers > 10 and the excess RL power EP. 4.2 Data Analysis 105

Run Date Zenith Periods [s] 22278 Fri 3 Sep 18:31:39 2004 15° 360-400 22279 Fri 3 Sep 19:01:50 2004 20° 550 26085 Sat 4 Jun 23:35:12 2005 6° 90 27569 Fri 29 Jul 19:49:49 2005 6° 82 74371 Fri 20 Jul 18:21:30 2012 30° 142-148 75001 Sat 11 Aug 19:01:05 2012 6° 420-500

Table 4.5: List of runs showing RL powers > 9 where no or few entries are expected from the pure background assumption.

In total six runs are contributing to the large-power tail in Fig. 4.2.19, which are listed in Table 4.5. Removing these runs from the dataset makes the observed large- power tail completely disappear and therefore makes the empirical RL power distribution compatible with the background expectation. Identifying these runs was done in an empirical fashion. The result can be summarized by the quantitative condition that all runs with normalized RL powers > 9 were selected, which is a slightly looser criterion than considering only runs with RL powers > 10, which was used during the previous study. The looser cut has the advantage of returning a sample which is large enough for follow-up studies like the search for correlations with MWL data or a study if the runs with large RL powers are correlated with a fux increase.

4.2.5.1.1 An Overview of the Runs forming the Tail of the RL Power Dis- tribution The six runs which show RL powers in a range where no or few entries are expected when the background hypothesis holds, are compared in Table 4.5 with respect to observation date, zenith angle and (quasi-)periods encountered. The corresponding power spectra are displayed in Fig. 4.2.21. All these runs were taken at zenith angles ≤ 30◦ and fve out of six of them were even taken at zenith angles ≤ 20◦. There are only the years 2004, 2005 and 2012 present in the list, which can be explained by the fact that the GC was regularly observed during these years, while during other years only few GC observations took place. Another interesting observation is that there is a pair of consecutive runs taken on Friday, 3 September 2004 in the list. A combined analysis of these runs allows a search for periods larger than 600 s which is interesting since there are known X-ray periods at 700 s, 1150 s and a IR period of 1008 ± 120 s respectively. Another remarkable observation is that there is a coincidence of Run 27569 with a Chandra X-ray fare. Further correlations with MWL observations could not be found. This rises the question how it can be shown that none 106 Search for Variability of HESS J1745-290 of these runs which were selected as “special” is not just a statistical fuctuation. It is not possible to investigate this analytically since such fuctuations always can happen. However, 4 out of the 6 runs are characterized by either a correlation with an X-ray fare or show periods similar to such which were observed in the X-ray band, supporting the assumption that these runs contain an efect related to a similar underlying mechanism than the X-ray fares.

4.2.5.1.2 Power Spectra An interesting question is if the power spectra in Fig. 4.2.21 which were created for these candidate runs are similar to those which are known from other wave length bands. For the X-ray and IR band the following periods are known: 100 s, 219 s, 370 s, 700 s, 1150 s and 2250 s for the X-ray band and 1008 ± 120 s for IR band. Although there are periods in the order of 100 s among these 6 runs there is one exact match with the X-ray periods: The 370 s X-ray period fts well with the peak from Run 22278, which is reaching from 360–400 s. The 3 large X-ray and IR periods > 600 s were included into the search when investigating single H.E.S.S. runs due to the fact that only periods up to 600 s were scanned.

4.2.5.1.3 Combined Analysis of Run 22278 and Run 22279 Since there were two consecutive runs showing unexpectedly large RL powers (Run 22278 and Run 22279 combined), these two runs have also been analyzed in combination, whereby the tran- sition gap between the runs is flled randomly with simulated events at the level of the mean event rate. For the combination of the two runs periods from 60 s to 1200 s have been investigated. The power spectrum (Fig. 4.2.22) has been produced with both the HD software and calibration chain (red curve) and the French calibration chain, using the French Hillas analysis with Loose cuts (green curve). The GC power spectra show a period around 400 s at a pre-trial signifcance level of 4.0σ and a wide region of increased RL power ranging from 800 s to 1000 s which is reminding of the 1008 ± 120s QPO reported in X-ray data and is at the 2.5σ level locally. Another feature which is slightly exceeding the noise level locally at the 2.3σ level can be found at 200 s, where also a period has been reported in X-ray observations. From the technical point of view this direct comparison shows that the HD and French software and calibration chain are clearly correlated and deliver comparable results. The main peak at 400 s is more signifcant in the Heidelberg software version of the curve but it is also clearly present in the version produced with the French calibration and analysis chain. In Ref. [21] two noticeable periods at 370 s and 850 s were reported for a X-ray fare on 31 August 2004. The two consecutive H.E.S.S. runs were taken only 3 days later 4.2 Data Analysis 107

12 12

10 10 Normalized RL Power

8 Normalized Power RL 8

6 6

4 4

2 2

0 0 100 200 300 400 500 600 100 200 300 400 500 600 Period (s) Period (s) (a) Run 22278 (b) Run 22279

12 12

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Normalized Power RL 8 Normalized Power RL 8

6 6

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2 2

0 0 100 200 300 400 500 600 100 200 300 400 500 600 Period (s) Period (s) (c) Run 26085 (d) Run 27569

12 12

10 10

Normalized Power RL 8 Normalized Power RL 8

6 6

4 4

2 2

0 0 100 200 300 400 500 600 100 200 300 400 500 600 Period (s) Period (s) (e) Run 74371 (f) Run 75001 Figure 4.2.21: Power spectra of the six runs which are forming the tail of the RL power distribution. 108 Search for Variability of HESS J1745-290

Heidelberg Software

10 French Software

8 Normalized RL Power

200 400 600 800 1000 1200 Period in s

Figure 4.2.22: Combined analysis of Runs 22278 and 22279 searching for periods from 60–1200 s. at 3 September, showing a periodogram with a very similar time structure having a peak ranging from 350–450 s and a second one from 700–1000 s. However, when comparing the combined analysis in Fig. 4.2.22 with the individual power spectra of Run 22278 (Fig. 4.2.21a) and Run 22279 (Fig. 4.2.21b) one encounters some discrepancies:

• Run 22278 shows a period of 360 s while Run 22279 shows a period at about 550 s, which deviates from the period from the frst run by 35%.

• When combining the two runs, the signifcance level of the peak at 300 s decreases instead of showing an increase, which one would expect intuitively.

• Run 22279 shows an additional peak reaching a normalized RL power of 8 when it is analyzed in a standalone fashion. This peak is also less signifcant in the combined power spectrum.

In case one is searching for an exact period, these fndings are certainly problematic. However, it was shown in Sec. 4.1.2.2 that the RL test also is sensitive to a series of (more or less) equidistant short-lived pulses. In fact the power spectra of the two runs rather resemble the simulated pulsed scenario in Fig. 4.1.5b than the exact sinusoidal fux modulation in Fig. 4.1.5a with respect to their shape: The peak which was simulated for the pulsed pattern shows a FWHM which is about twice as large as the one of the exact sine. The peak in the RL power spectrum of the simulated pulsed signal is also more asymmetric than that of the sinusodial signal. 4.2 Data Analysis 109

IR/X-ray H.E.S.S. H.E.S.S Run(s) Ref.

∼ 100 s 82 s,90 s,150 ± 10 s 26085, 27569,74371 [17] 370 s 400 ± 50 s 22278,75001 [21] 850 s 850 ± 150 s 22278 and 22279 [21] 1008 ± 120 s 850 ± 150 s 22278 and 22279 [39]

Table 4.6: Comparison of the H.E.S.S. periods with published periods from X-ray and IR observations.

In case the observed signs for variability are rather due to event distributions which contain short pulses, there is no reason to assume that these pulses have to be exactly equidistant and therefore it could be possible that the observed periods are changing when combining diferent runs with respect to the original pattern when the runs are analyzed separately. It is admittedly hard to imagine which mechanism could cause pulses of a duration of ∼ 30 s or less, despite the fact that this is the typical duration of long-lived GRBs [99]. In fact there are theories which connect micro tidal disruption events like the disruption of asteroids, which was discussed before, to GRBs with a relatively low luminosity [33]. Since these theories are still lacking a confrmation, it would be purely speculative to claim a connection between the tentative short-term variability reported here and such events at this point. In any case the fact that the combined analysis of the two runs showed that there is no constant period across both of the runs rather points into the direction that the short-term variability has a pulsed character instead of that of a genuine sinusoidal modulation. Pulses which are not equidistant or have a changing time structure in principle could resolve the contradiction, the period is not constant over the two runs. A comparison of the H.E.S.S. candidate quasi-periods with published X-ray periods can be found in Table 4.6.

4.2.5.1.4 A Coincidence with a Chandra Flare: Run 27569 While for 5 out of the 6 runs no MWL counterpart could be found, Run 27569 was taken synchronously with an X-ray fare which was reported by Chandra [37, 115]. H.E.S.S. Run 27569 started on Friday, 29 July 2005, 19:50:07, while the reported X-ray fare took place during a Chandra observation, which also started on Friday, 29 Jul 19:49:49, 2005. The X-ray fare started only about 8 minutes before the end of the H.E.S.S. run, which means that the overlap between the H.E.S.S. and Chandra observations is rather short. The Chandra fare showed an X-ray luminosity of 0 64 1034 erg . . × s The H.E.S.S. RL power spectrum corresponding to this fare can be found in Fig. 110 Search for Variability of HESS J1745-290

4.2.21 (d). It shows a sharp peak at 80 s, which reaches up to a normalized RL power of 9 and translates into a local pre-trial signifcance of 3.7σ. The efect is not globally signifcant, since the run was found in a scan over the whole dataset which means that the trial factor reduces the signifcance to the 1σ level from a global perspective. In fact it does not make much sense to quote the individual signifcance level for periodicity of a particular run which was identifed in the RL test, since all these runs were identifed in a test which was taking into account the overall shape of the RL power distribution. None of the runs contributing to the change of this shape towards large RL powers shows a globally signifcant efect on its own due to the trial factor. However, it is possible that these runs form a globally signifcant efect in combination, although the signifcance level of 3.1σ, which was reached during this particular analysis, was not sufcient for claiming detection. In case there was a parallelism of the time structure of Run 27569 and that of the Chandra fare, this correlation could be used to quote a reduced trial factor for this particular run in principle, since it could have been identifed before testing all other runs by the additional information. However, unfortunately there is no further information about the Chandra fare available publicly. It would be interesting to study if it shows a similar time structure as the H.E.S.S. event in order to prove or rule out a connection between the two events.

4.2.5.1.5 Results from the Search for a short-term Variability The main observations of the study of the shape of the RL power distribution were:

1. The shape of the empirical RL power distribution resembles the shape of a simulated RL power distribution which is containing a weak periodic signal in less than 5% of the data segments.

2. The probability of obtaining a distribution as extreme as or more extreme than the observed one by chance is ≦ 9·10−4, which corresponds to a global signifcance level of 3.1σ. This number was derived assuming that H.E.S.S. runs follow truly uniform event distributions. Possible systematic efects were not taken into account during the simulations.

3. The time structure of the QPO-like behavior is similar to the time structure which is known from X-ray observations.

4. Cross-checks with the background and G 0.9+0.1 show a defcit at large RL powers in contrast to the HESS J1745-290 dataset. 4.2 Data Analysis 111

−1

−2 Significance of a global Periodicity in Units Sigma

100 200 300 400 500 600 Period in Seconds

Figure 4.2.23: The signifcance for global periodicity as a function of period for periods between 60 s and 600 s.

Although it was shown to be difcult to quantify the efect observed for the GC region, the reasons listed above support the assumption that there might be HESS J1745-290 runs with quasi-periodic behavior in the H.E.S.S. dataset.

4.2.5.2 Search for a Global Periodicity

After this frst discussion of the possibility of a transient variability of HESS J1745-290, a search for exact global periods was performed. The search interval was 60 s to 600 s again (with a step-width of 1 s). During this analysis the RL test was applied for each period separately, integrating over the results for all runs being part of the data set in the following way: For each run a RL power P was calculated independently for a certain P period under consideration. The quantity 2Ptot where Ptot = Pi, which stands for the sum of RL powers for a frequency over all runs exactly follows a χ2 distribution with 2 degrees of freedom ( 2 ), which was shown in 4.1.2.2. As expected, the result nruns χ2nruns of this study did not reveal any signifcant global period. In Fig. 4.2.23 the signifcance for periodicity plotted versus the period duration in seconds is shown. The values with a negative signifcance correspond to p-values > 0.5. The fact that there is no global period present in the data set does not exclude that there are local QPOs hidden in the data set, as it has before. 112 Search for Variability of HESS J1745-290

35 French Calibration 30 HD Calibration

Number of Events 25

0 0 200 400 600 800 1000 1200 1400 1600 1800 Time in Seconds from the Beginning of the Run

Figure 4.2.24: Comparison of the event distributions from the French and HD Hillas analysis chain for Run 22278. The dashed red line marks the bin where the event displays discussed in Sec. 4.2.5.3 were taken from.

This result perfectly agrees with the frst published H.E.S.S. analysis presented in Ref. [101] which also did not report an exact periodicity for this frequency range. Comparing these periods of the QPOs which were found in the previous section with Fig. 4.2.23 one observes a loose correlation with the local signifcance peaks from the search for a global period: In the map there are 1–2σ efects for periods around between 70 s and 200 s and for large periods > 400 s. These are consistent with the peaks of the power spectra in Fig. 4.2.21.

4.2.5.3 Event Displays and Broken Pixels

It is difcult to imagine a mechanism connected to broken pixels which could cause the observed short-term variability, since the number of broken pixels usually does not change during a run. Instead, pixels stay switched of during the whole run. As a further cross-check, the runs showing variability in the RL test have been compared to runs without any hints of variability from the same night with respect to their patterns of broken pixels and no correlation could be found here. The broken pixel map for CT1 - CT4 for this run (and also for Run 22279) can be found in AppendixB and shows that only few pixels of the camera were deactivated during this run. No entire drawers are missing. 4.2 Data Analysis 113

(a) (b)

(e) (f)

(g) (h)

(i) (j) Figure 4.2.25: Sample event displays from Run 22278 which correspond to the peak at 750 s from the histogram in Fig. 4.2.24. 114 Search for Variability of HESS J1745-290

Furthermore, Fig. 4.2.24 compares the photon rates of Run 22278 from the French and HD Hillas chain and shows that they are clearly correlated for this run, which illustrates that the Hillas analysis produces comparable results independently of the calibration chain in use. Also the actual event displays from a particular bin in Fig. 4.2.24, which shows more events than the average, were investigated in order to further exclude technical problems with the camera. Therefore, the bin at 750 s (marked by a dashed red line in Fig. 4.2.24) with a bin content of 20 events was chosen randomly from all bins showing more events than the average. The event displays were created with the HD calibration. Taking into account the background level of 8 ± 3 events per bin for this run, one would expect at least 9–10 γ-like events for this particular bin given the fact that it contains 20 entries in total. The corresponding event displays where the images from all 4 telescopes were projected into one camera plane for a better illustration are shown in Fig. 4.2.25. In fact at least 10 events, which were found within this bin, could be perfectly be caused by γ-like showers. These events are characterized by ellipses which are pointing to the position of the GC with respect to the camera plane which is located in the lower left quarter of the camera for this run. The 10 best candidate events for γ-induced showers are shown in Fig. 4.2.25. As reference γ-like events from MC simulations are shown in AppendixA, which were created to illustrate that these event displays closely resemble γ-like events. The fact that the ellipses are rather small means that during this bin a bunch of low-energetic events was recorded showing energies < 400 GeV. By this “by-eye” cross-check it could be shown that the observed variability is plausible from the reconstruction and camera side and the event displays causing the efect for this run resemble low-energetic γ-like events. Of course, it only considers a random sub-sample of one run, but it could be shown that for this run the variability is not caused by obvious problems at the camera and calibration level.

4.2.5.4 PKS 2155-304 In order to obtain a deeper understanding of how the RL test behaves for an object with a known short-term variability, it was also applied to the PKS 2155-304 dataset in an additional cross-check. Like for the GC a period range from 60 s to 600 s was scanned with a step-width of 1 s. Runs passing the spectral quality selection criteria were used with an additional cut on zenith angles < 40°. The results which are shown in Fig. 4.2.26 cannot be discussed in the same detail as the HESS J1745-290 analysis, since this would exceed the margin of this thesis. However, already just studying the RL power distribution in Fig. 4.2.26a it shows an obvious large-power tail of RL powers 4.2 Data Analysis 115

105 PKS 2155-304

Background Expectation 104 Number of Entries

103

102

1 0 5 10 15 20 25 30 35 Normalized RL Power (a) The RL power distribution for the H.E.S.S. PKS 2155-304 dataset.

−1 Significance for a global Periodicity in Units of Sigma −2

100 200 300 400 500 600 Period in Seconds (b) The signifcance distribution for a global period from 60–600 s. Figure 4.2.26: The RL test applied to the H.E.S.S. PKS 2155-304 dataset. 116 Search for Variability of HESS J1745-290

> 10, which reaches up to a normalized RL power of 34. The tail contains 394 entries in total. This large number of entries in the tail of the distribution is expected to form a signifcant efect. From the simulations in Fig. 4.2.20a it can be concluded that this number of entries was not reached in 10 000 trials during the toy MC simulations (the statistics of the GC and PKS 2155-304 dataset are comparable at H.E.S.S. and these simulations can be used for an estimate). This means a upper limit for the p-value for reaching this distribution by chance can be given with p ≤ 1·10-4 corresponding to 3.7σ. Simulations to prove the 5σ level here were too time consuming to be realized within a reasonable time frame. Also, the search for a global period over all data segments was repeated for the same period range as for the HESS J1745-290 data applying the same search strategy as before. The result can be found in Fig. 4.2.26b. The obtained signifcance distribution shows a global period which reaches the 5σ level at 500 s. Statistical problems like those which were observed when studying neighboring periods within the same run due to correlations of neighboring periods within a particular run, which were discussed in Sec. 4.1.2.2, cannot be held responsible for this peak since when investigating one period over diferent runs the individual runs are statistically independent data segments. Also, a systematic efect for large periods is not plausible, since the signifcance level is decreasing again for periods > 500 s. In case of such an efect one would not expect a peak of correlated points around a period as it was observed here but rather a continuous increase towards large periods. Furthermore, the exceptional fare of PKS 2155-304 which was observed by H.E.S.S. [7] shows a sub-structure with quasi-periodic peaks at a time interval of 8–10 minutes, which shows that the time structure observed for PKS 2155-304 here with the RL test is completely realistic. The fare runs were part of the dataset. With respect to the HESS J1745-290 analysis, this fnding is interesting since for HESS J1745-290 evidence for quasi-periods in the order of 400–500 s was reported for six runs. Comparing this with PKS 2155-304, it is possible to hypothesize that the variability of both objects is of a similar time structure but the efects are present at a weaker level for HESS J1745-290. Considering the fact that PKS 2155-304 is expected to contain (at least one) super-massive black hole such a reasoning of seeing a fainter version of PKS 2155-304 in HESS J1745-290 is not completely unrealistic. In any case, it was shown by this cross-check that the RL test can be used to correctly reveal a short-lived variability at a timescale of minutes. Although the efect observed for HESS J1745-290 is weak compared to PKS 2155-304, the RL power distribution of HESS J1745-290 shows a tendency towards a large-power scale similar to that observed 4.2 Data Analysis 117 for PKS 2155-304.

4.2.6 Run-wise χ2 Test of the post-cut Event Rates In case HESS J1745-290 shows a short-term variability at a timescale of minutes, also the time dependence of the post-cut event rates should show hints for variability during a run-wise χ2 ft with a constant. Hereby the data are again split into diferent segments (runs), each of which is treated independently. The χ2 test was performed for each run separately since the mean event rates for a particular run depend on quantities like the zenith angle or the source ofset from the pointing positions. In order to combine the ft results from diferent runs, the following steps were performed:

• First the χ2 of the ft with a constant and the number d.o.f. was obtained for each run.

2 • Then Sχ2 , the sum over all χ and Sdof , the sum of all d.o.f. were calculated following the theorem of additivity of χ2 variables.

2 The obtained quantity S 2 is expected to follow a χ distribution in case of no ef- χ Sdof fect being present in the dataset. In case Sχ2 signifcantly difers from the background expectation one can claim that the post-cut rates show variable behavior. The main advantage of just investigating the event distributions on a run-wise basis is that one avoids additional systematic efects due to varying observation conditions between the diferent nights. Concerning a single run, zenith-angle induced rate changes within a run can be neglected for zenith angles < 40◦ at post-cut level. The exact binning in time may vary between diferent runs when applying this method due to variations of the length of a run. However, this is also the case for all control regions, which are used to cross-check the analysis, and therefore efects due to such a variation of the run duration would immediately attract attention. There are two possible approaches to realize this test, which may be subject to diferent biases. The frst method is to perform a classical χ2 ft with a constant, which is minimizing the sum of squared errors

ν (O − E )2 2 X i i (4.2.2) χ ≡ 2 . i=1 σi

In this defnition Oi is the observed number of entries for a particular bin i with the variance 2. The quantity is the expectation value for the bin from the underlying σi Ei model. The diferent Oi are assumed to be normally distributed random variables here. 118 Search for Variability of HESS J1745-290

Within the ROOT data analysis software [26], which is widely used in high-energy physics, the χ2 ft is defned according to Eq. 4.2.2. When applying the ft to binned √ data, the errors for each bin are defned as σi = Ni with Ni being the number of entries in the bin i by ROOT. When performing the χ2 ft, the algorithm is simply minimizing Eq. 4.2.2 by demanding ∂χ2 = 0. ∂E

In case the ft function is a constant which is equivalent to the condition Ei = E = const, it follows immediately for the ft result that

P Oi σ2 = i (4.2.3) E P 1 2 σi which is exactly the weighted mean of the Oi over all bins. Based on this result for E, the sum of squared errors can be calculated and used to determine the goodness of the ft. However, an important implicit assumption here is that the number of entries per bin is large enough that the fuctuation of this number can be approximated by a Gaussian. A common rule for the applicability of the χ2 ft to binned data, which can be found in the literature, is that the sample size should be at least 4 to 5 times the number of bins [76], which means that at least 140 events per run are required in the case of 28 bins. Another common rule of thumb is that at least 5 to 10 entries per bin are required. For H.E.S.S. runs the number of 28 bins corresponds to a timescale of about 1 minute per bin. The average number of events for the GC region is about 200 events per run, which means that the criterion above can be expected to be fulflled for 28 or fewer bins. In order to investigate if the goodness of ft can be obtained in a statistically robust way with the ROOT implementation of the χ2 ft when it is applied in the planned way, uniform toy runs with diferent event numbers per bin were simulated. During these simulations 4 diferent sets of 500 uniform toy H.E.S.S. runs were simulated. The set with the lowest statistics contains 200 events per run or 7 events per bin on average, whereas for the set with the largest statistics, 5000 events per run or 179 events per bin were used. Furthermore, sets with 500 and 1000 events per run were simulated. For each of these sets of toy runs a χ2 ft using the defnition in Eq. 4.2.2 was applied in a run-wise fashion. The resulting distributions of p-values for the diferent simulated sets of runs are shown in Fig. 4.2.27.

From these simulations it is immediately clear that the χ2 ft according to the defnition in Eq. 4.2.2 is biased when it is applied to a binned histogram in case the statistics 4.2 Data Analysis 119

200 Events per Run 70 500 Events per Run 1000 Events per Run 5000 Events per Run 60

50 Simulated Runs per 0.01

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P-Value

Figure 4.2.27: Distributions of p-values for diferent sets with 500 runs. The number of events per run was varied from 200 events per run to 5000 events per run. per bin is too low: For an unbiased ft one would expect a fat distribution of p-values. Although this is the case for the simulated uniform runs with a statistics of 1000 and 5000 events per run, the low statistics samples with 200 (red) and 500 (blue) events per run show a clear bias for p-values < 0.01. While one would expect about 5 entries for p-values < 0.01 the low statistics sample with 200 events per run shows 73 entries in this bin and the sample with 500 events per run still shows 20 entries for p-values < 0.01. The simulation with 200 events per run is equivalent to ∼ 7 events per bin, whereas the 1000 events per run scenario is equivalent to ∼ 36 events per bin. The lesson learned from this study is that the χ2 ft as it is defned in Eq. 4.2.2 can only safely be applied to binned histograms with a statistics of O(30) and more events per bin. Otherwise one has to expect a bias which overestimates the signifcance level obtained by the ft or mimics an efect where no efect is present. Therefore, the method as it is implemented in ROOT cannot be applied safely to a typical region of interest at H.E.S.S. in order to search for a short-term variability at timescales below the duration of a run. However, this problem can be neglected for the run-wise light curves which were discussed previously, since the error on the excess which is used to calculate the integrated fux depends also on the background statistics. Due to the fact that the refected background method is used in combination with the Loose cuts, the background statistics is large enough that the excess fuctuates according to a Gaussian in case of no variability being present in 120 Search for Variability of HESS J1745-290 the data. Apart from the classical χ2 ft, which is minimizing the χ2, there is also the possibility of a maximum likelihood approach. When applying this approach in case of a uniform background distribution, the number of events in the bin i can be assumed to fuctuate according to a Poisson distribution, which is the correct model for a low statistics per bin: exp(−E) Oi P (Oi) = E . (4.2.4) Oi! When integrating over all bins, the total number of events per run can be described by the likelihood function N Y Ptotal = P (Oi|E) i=1 where N stands for the total number of bins. By maximizing the corresponding log- likelihood function one obtains

N 1 X NEvents E = Oi = (4.2.5) N i=1 N 2 where NEvents stands for the total number of events in a run. For the χ which is needed later to calculate a combined signifcance level for variability for all runs Eq. 4.2.2 can be written as

ν (O − E)2 χ2 ≡ X i (4.2.6) i=0 E since for the underlying Poisson distribution both the mean value E and the variance σ2 are equal to E. When defning the χ2 according to Eq. 4.2.5 and Eq. 4.2.6 the distribution of p-values could be shown to be fat in simulations, even in the case with 200 events per run. Therefore, the defnition of the χ2 derived from the maximum likelihood approach is considered to be applicable also in the low statistics case. When having enough statistics, both the classical minimization of the χ2 and the maximum likelihood approach should have comparable results. However, in the low statistics case the maximum likelihood approach is considered to be more robust. In a next step, also the signifcance distribution for variability based on the previously defned quantity Sχ2 was simulated for 5000 complete analyses for the background-only scenario. Each simulated complete analysis consists of 500 runs again and Sχ2 was calculated for each set of 500 runs. The resulting signifcance distribution is shown in Fig. 4.2.28: Since the resulting signifcance distribution is compatible with a Gaussian with mean and standard deviation equal to one, the quantity Sχ2 can be used to estimate 4.2 Data Analysis 121

Significance Distribution Significance Distribution Entries 5000 200 Mean −0.01274 RMS 1.007 180 χ2 / ndf 45.52 / 65

Entries per Bin ± 160 Constant 197.7 3.5 Mean −0.01318 ± 0.01430 140 Sigma 1.001 ± 0.010

120

100

0 −5 −4 −3 −2 −1 0 1 2 3 4 5 Significance in Units of Sigma

Figure 4.2.28: Simulated signifcance distribution for variability based on the quantity 2 2 Sχ2 when calculating the sum of χ for diferent runs according to Pearsons χ test as defned in Eq. 4.2.6. the signifcance level for variability of the dataset. The previous simulations have shown that the χ2 test as it is defned in Eq. 4.2.6 can be safely applied to binned data at a level of statistics like it is typical for the planned analysis. When using the defnition of the χ2 for a bin given in Eq. 4.2.6, also the applicability rule of 5–10 events per bin can be considered to be valid. For completeness it has to be mentioned that the study again was performed under the assumption that the distributions of the event arrival times at H.E.S.S. can be approximated by a uniform distribution. It would be an interesting follow-up study to quantify the agreement of these distributions with a truly uniform distribution, which would go beyond the range of this work. For such studies a infrastructure to produce run-wise MC simulations would be helpful, which is planned but not available at the time of this writing. Since Pearson’s χ2 test as defned in Eq. 4.2.6 in connection with MC simulations did not show any systematic problems or biases during the toy MC simulations which were done here, it will be used for the analysis of the H.E.S.S. I dataset in the following. In order to obtain a result which is robust against possible binning efects, diferent binnings were used from 3 bins per run to 28 bins per run. This corresponds to timescales from about 10 minutes per bin to 1 minute per bin. The signifcance level for variability as a function of the binning is shown in Fig. 4.2.29. In total 10 signifcance values for binnings from 3 to 30 bins were calculated with a step-width of 3 bins. 122 Search for Variability of HESS J1745-290

2.5

1.5

1 Significance for Variability in Units of Sigma

0.5

0 0 5 10 15 20 25 30 Number of Bins

Figure 4.2.29: Here the global signifcance level for variability in terms of σ is shown as a function of the number of bins per run from 3 bins to 28 bins.

The mean signifcance level for all bins is 1.9 ± 0.2σ while the maximum signifcance of 3.2σ was found for 3 bins corresponding to a timescale in the order of ∼ 10 minutes per bin. The latter signifcance level reduces to 2.5σ when applying the trial factor. The observation that the signifcance level decreases as a function of the binning is likely due to the fact that the method loses its sensitivity when the number of events per bin is getting too low. The conclusion here is that with the χ2 test no signifcant short-term variability could be detected. For completeness, the method was also applied to the G 0.9+0.1 and PKS 2155-304 data: G 0.9+0.1 showed a mean signifcance level of −1.2±0.2σ which is below the value found for HESS J1745-290, while PKS 2155-304 is variable at the 10.5 ± 0.6σ level. The cross-check with G 0.9+0.1 showed that possible changes of the event rates within a run do not have a signifcant efect in this test at post-cut level. The signifcance level for variability found with the χ2 test is lower than the signifcance level for variability estimated by simulations for the RL test in the previous section, which is 3.1σ. This may be due to both the fact that the RL test also takes into account information about periodic or quasi-periodic behavior, which is ignored by χ2 test. Also, binning efects and trial factors due to the binning, which exist for the binned χ2 test, play a role here, while the RL test is performed in an unbinned fashion. Therefore, the RL test is expected to be more sensitive. Since the RL test gave a more obvious deviation from the theoretical background distribution, which made it easier to identify runs with signs of variability, the next section will only investigate if there is a correlation between the tentative short-term variability which was found in the RL test and the integrated fux. 4.2 Data Analysis 123

The results from the χ2 test were not taken into account for this study, since no runs with obvious signs of variability could be identifed here.

4.2.6.1 Short-term Variability and Flux

In case the physics phenomena behind the runs showing hints for a short-term variability are weak fares with a duration shorter than the length of a run, one would expect an increased integrated fux for such runs which were identifed to show large RL powers in the RL test. Another mechanism causing such a short-term variability is difcult to imagine. The mean integrated fux > 100 GeV which could be derived from the H.E.S.S. I light curve is (4.99 ± 0.10) × 10−11 cm−2 s−1. In order to investigate if there is a correlation between short-term variability and a fux increase, the sub-sample of six runs which was identifed to form the large-power tail in the RL test was ft with a constant. The mean fux which was calculated for this sub-sample of the light curve is (5.87 ± 0.71) × 10−11 cm−2 s−1, which corresponds to a −11 −2 −1 fux increase of △Φγ = (0.88 ± 0.72) × 10 cm s or 17.6% at the 1.2σ signifcance level with respect to the mean fux of the whole dataset. Since the two consecutive runs which were identifed in the RL test have been discussed in all detail, it was also investigated if their mean fux shows an increase with respect to the rest of the dataset. In combination Run 22278 and Run 22279 show a mean fux of (8.0 ± 1.2) × 10−11 cm−2 s−1. This corresponds to a fux increase −11 −2 −1 △Φγ = (3.0 ± 1.2) × 10 cm s or 60.0% at the 2.5σ signifcance level. Although the signifcance level of the fux increase is low with only 1.2–2.5σ, a tendency of a correlation between variability and a fux increase could be shown to be present for runs with signs of a short-term variability. Observing a mean fux which is lower than the average for such runs would have been problematic for the interpretation of the tentative short-term variability. Also the energy release which is corresponding to such a fux increase will be calculated in the following. The luminosity L in units of erg/s as a function of γ-ray fux increase △Φγ can be calculated as

α − 1 erg L = △Φ · 0.1 TeV · 4πd2 · 1.6 (4.2.7) γ α − 2 TeV where d is the distance between the observer and the Galactic Center (8.5 kpc) and α the spectral index which was used for the light curve. Given the large statistical error of the obtained fux increase △Φγ and a further systematic uncertainty introduced by the spectral index, the uncertainty of the energy release has to be assumed to be large. In 124 Search for Variability of HESS J1745-290 the following a spectral index of 2.3±0.2 was used. For the whole sub-sample of six runs the luminosity L could be calculated to be 5.3 ± 5.1 × 1034 erg/s while L for Run 22278 and Run 22279 is in the order of 1.8±1.2×1035 erg/s. The errors of the fux increase were calculated according to the standard error propagation, taking into account the errors of △Φγ and α. Based on these numbers, the following limit can be given for the increase of luminosity of runs with signs of variability: 2 × 1033 erg/s ≦ L ≦ 3.0 × 1035 erg/s. This fux increase is of the same order of magnitude like that which was observed for IR and X-ray fares of a comparable duration. In Ref. [111], it is reported that peak luminosities between 1033 erg/s and 1034 erg/s are attained for a 10 mJy near-infrared fare, which was coincident with a X-ray fare of the same strength. This means that tentative short-term variability found in H.E.S.S. data is of the same order of magnitude as the energy release reported for other wavelength bands. A last observation, which was made when comparing the integrated fux > 100 GeV of runs with RL powers > 9 to the mean value of all runs, was that all but one of these runs showed an integrated fux which was larger than the mean fux of all runs. Only Run 26085 showed a mean fux of 3.8 ± 1.6 × 10−11 cm−2 s−1, which is below the mean value of the light curve of 4.99 ± 0.10 × 10−11 cm−2 s−1. When trying to interpret the runs showing signs of variability in the RL as weak fares, this particular run does not ft the picture since it is lacking the fux increase which one would associate with a fare. This makes it appear likely that the increased RL power observed for this run is due to a statistical fuctuation. Therefore, the runs which will be referred to as “fare candidates” in the following do not include this particular run. The term as it is used in the following refers to runs which show RL Powers > 9 and an integrated fux > 100 GeV, which is larger than the mean value of the light curve.

4.2.6.2 The Zenith Angle Distribution and Energy Thresholds of Runs with Hints of Variability In order to investigate if there is a correlation between the tentative short-term variability and the energy threshold, the distributions of the mean zenith angle and the safe energy threshold of the sub-sample of runs, which were identifed in the RL test, were compared to the whole dataset. The energy threshold of H.E.S.S. can be considered to be proportional to the zenith angle. The safe energy threshold is defned as the value of the reconstructed energy where the bias of the reconstructed energy becomes > 10%. The absolute energy threshold as a function of the true energy is about 50 GeV lower than the safe energy threshold. The comparison of the zenith angle distributions can be found in Fig. 4.2.30a. The 4.2 Data Analysis 125

0.5 Runs with RL Powers > 9

All Runs 0.4 Percentage of Runs

0.3

0.2

0.1

0 0 5 10 15 20 25 30 35 40 Mean Zenith Angle in Degrees

(a) The zenith angle distribution of the six runs with RL Powers > 9 versus the zenith angle distribution of all runs used for the search for a short-term variability.

0.35 Runs with RL Powers > 9

0.3 All Runs

0.25 Percentage of Runs

0.2

0.15

0.1

0.05

0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Safe Energy Threshold in TeV

(b) The energy threshold of the six runs with RL Powers > 9 versus the distribution of the energy threshold of the whole dataset. Figure 4.2.30 126 Search for Variability of HESS J1745-290 blue distribution represents the whole dataset, while the red distribution stands for the runs with signs of variability. The mean zenith angle of all runs is 17.6°, while the runs with signs for variability show a mean zenith angle of 13.5°. It is worth mentioning that 3 out of the 6 runs were taken at zenith angles < 10◦. The comparison of the energy thresholds of runs with signs of variability with all runs can be found in Fig. 4.2.30b. In total 5 out out of six have a safe energy threshold < 250 GeV, while for all runs the safe energy threshold is < 350 GeV. This means that all runs showing signs of variability reach energies where the STD cuts are not sensitive due to their larger energy threshold, which is in the order of 350 GeV. The tendency observed here shows a correlation between short-term variability and low energies, which fts the overall picture which has been elaborated so far. If the short-term variability was also observed for runs with an energy threshold > 500 GeV it would have been difcult to argue why it was not seen with the STD cuts before. Chapter 5

Summary and Outlook: Putting the Results into Context

The results of a variability search for the VHE γ-ray source HESS J1745-290 at the direction of the Galactic Center based on 10 years of H.E.S.S. data have been presented. In this search various hints for a variable fux were found at diferent timescales from minutes to days and even months (a ∼ 110 days periodicity). After a brief summary of all efects which were found in this study, the fndings are compared to MWL observations of the black hole Sgr A*. Furthermore, possible candidate explanations and the implications of this work for our understanding of the nature of HESS J1745-290 will be discussed.

5.1 Summary

Several tests were performed to search for variable behavior of the VHE γ-ray source HESS J1745-290. In order to detect a possible long-term variability frst a H.E.S.S. light curve containing the integrated fux values > 100 GeV was ft with a constant applying a χ2 ft. Also the L-S test was applied to this light curve to search for periodicities. In a second step the short-term behavior at the timescale of minutes was investigated by applying the RL test and ftting the post cut event rates with a constant using a χ2 ft again. While there is evidence for a variability at timescales larger than the duration of a run at the 4.1σ level in form of a periodic fux modulation with a period of ∼ 110 days, which was found applying the L-S test, the ft of the light curve with a constant gave a signifcance level for variability of 6.1σ without any systematic error. This signifcance reduces to 4.5σ after adding a 10% systematic error on the integrated fux. It was dif- 128 Summary and Outlook

Analysis Signifcance Result Counterparts Data set Fit of the LC 4.5σ Variability Radio to X-ray H.E.S.S. I+II L − S test 4.1σ 110 d period Radio H.E.S.S. I+II RL test 3.1σ QPOs IR, X-ray H.E.S.S. I

Table 5.1: Comparison of the signifcance levels ≥ 3σ obtained in the diferent analysis approaches. The signifcance levels given here take into account the systematic errors which have been explained in the particular section. fcult to quantify the systematic variation of the integrated fux between two diferent runs. However, a systematic error of 10% was considered to be sufcient to account for such systematic variations, since the SNR G 0.9+0.1 did not show any signs of variability even without systematic error, and also taking the background only from certain Galac- tic latitudes did not rule out the efect, which is speaking against background-related systematic efects as cause for the observed variability. Studying the short-term behavior of the GC source no globally signifcant efect at the 5σ level was found. However, when applying the event wise RL test to the dataset six runs showed evidence of quasi-periodic behavior with the following periods: O(100 s), 350–450 s and 800–1000 s, which are similar to published periods from IR and X-ray data. Run 27569, which is showing quasi-periodic behavior, has a fare counterpart in Chandra X-ray data. A summary of the studies which were performed during this thesis giving a signifcance level for variability ≥ 3σ can be found in Table 5.1. The analysis was done mainly with the Heidelberg calibration and reconstruction chain. However, the author showed that the event distributions of the French and HD Hillas chain are correlated and show a comparable statistics for the Run 22278 which showed an efect in the RL test.

5.2 Comparison of the H.E.S.S. GC Results to Sgr A* MWL Observations

In combination the short-term variability and the 110 days periodicity, which were reported for HESS J1745-290 for the VHE γ-ray band, very closely mimic the known MWL behavior of Sgr A* in terms of the frequency of occurrence of the fare events, their time structure and their energy release. The most plausible phenomena behind the short-term variability are weak fares with a short duration, which show a repeating pattern and have a leptonic origin. Flares with similar properties are also known from 5.2 Comparison to MWL Observations 129 other wavelength bands like the X-ray or the IR band. The short cooling timescales, which are needed explain a rapid variability at timescales of minutes, exclude a hadronic origin of the observed short-term variability. Concerning the frequency of occurrence of Sgr A* fares the following can be stated:

• As discussed in Sec. 3.1.5, Sgr A* is faring in the X-ray band from 0.1 times per day up to 1 times per day. Under the assumption that X-ray fares and fares in the VHE γ-ray band take place due to the same underlying mechanism one would expect 1 to 10 fares in the H.E.S.S. I dataset. In fact during the analysis of H.E.S.S. I data 5 runs were found which were showing large RL powers > 9 in combination with a fux increase with respect to the mean fux of the HESS J1745-290 light curve. This observation fts well into the predicted window of 1 to 10 expected fares. Therefore, the population found in the RL test is neither too large and nor too small to be compatible with the fare frequency which was predicted based on the X-ray fare population.

• For the IR band the estimated population of fares is larger than for the X-ray band, reaching from 2 up to 6 fares per day. These limits were derived in Ref. [40] after measuring 4 fares per day and assuming an underlying Poisson statistics. In case the mechanism which is responsible for the IR fares also reaches VHE band one would expect 20 to 60 runs with signs of variability in the H.E.S.S. I dataset. These numbers are larger than the observed number of fare candidate runs from the RL test.

It was shown that the population of H.E.S.S. GC runs with signs of variability fts well with the predicted fare population from the X-ray band. The question if X-ray and IR fares of Sgr A* are linked in general is still under discussion, although occasionally such a coincidence has been reported but there are also fares of each kind missing a counterpart in the other wavelength band [70]. Alone from the numbers above one could argue that the short-lived variability observed by H.E.S.S. is rather linked to the X-ray band than to the IR band. However, such correlation studies may be misleading since they could be biased due to the limited statistics and irregular observation campaigns, which not always took place in a synchronized manner. Nevertheless, it is an interesting observation that the frequency of occurrence of the H.E.S.S. “GC fare events” perfectly fts the existing fare population of Sgr A* in the X-ray band. Also the internal time structure (QPOs) of the runs which showed an efect in the RL test and the timescale of the long-term variability is in agreement with MWL observations: 130 Summary and Outlook

• With respect to the short-term variability for the X-ray and IR band, QPOs were reported for certain frequencies (see Sec. 3.1.2). The periods reported in this H.E.S.S. data analysis are similar to the IR and X-ray periods within their errors.

• Concerning the long-term behavior, radio observations gave hints of a periodicity around 110 days. The LS periodicity test applied to a H.E.S.S. light curve gave a signal at the 4.1σ level for this known period. This allows the conclusion that HESS J1745-290 shows typical behavior of Sgr A* with respect to the time structure of the variability reported here. The luminosity increase for energies > 100 GeV for the runs with signs of short-term variability was estimated to be in the order of 2 × 1033 erg/s ≦ L ≦ 3.0 × 1035 erg/s and therefore is in a comparable order of magnitude like the average increase of the luminosity during X-ray and IR fares, which is 1033–1034 erg/s. Recently an upper limit on the Sgr A* fare luminosity of 5.5 × 1038 erg/s for an energy range from 100 − 200 GeV has been published based on Fermi LAT data [104]. The luminosity reported for the H.E.S.S. analysis is 3–4 orders of magnitude below this upper limit. Although the energy range considered in the H.E.S.S. analysis is a diferent one than for the Fermi LAT analysis, the H.E.S.S. results do not contradict this upper limit due to the lower luminosity which is claimed here for H.E.S.S. data. The Fermi LAT limit refers to the luminosity of isolated fare events and does not make any statements about a possible long-term variability. Although in Ref. [12] the possibility of a γ-ray emission of Sgr A* for the GeV and TeV energy bands with a leptonic origin is discussed, no quantitative prediction for its luminosity is given since it depends too much on the fne tuning of the model parameters like the magnetic felds in the Sgr A* region. The authors hypothesize that the origin of a possibly variable emission would be located within a very compact production region in the vicinity of Sgr A* which is implying short acceleration and radiative cooling times in the order of minutes like those which are reported in this thesis. The fndings presented in this thesis could be the frst evidence for such a predicted rapid variability of Sgr A* and therefore put this source into the focus again as a candidate for the origin of the VHE γ-ray emission from the direction of the Galactic Center. In any case the GC magnetar which is located in the same region of interest like Sgr A* or another possibly unknown object within this region are considered to be unlikely to cause the observed variability due to the similarity of the properties of the HESS J1745-290 data to known behavior of Sgr A*. The similarity of the efects found during this analysis to MWL results for Sgr A* in terms of time structure and energy release is probably the best argument against a systematic origin of the observed variability. Nevertheless, the question if this behavior could be an interplay of systematic efects 5.3 Cross-Checks and External Data 131 and what has been done to get control of systematic efects will be shortly discussed in the next section.

5.3 Summary of Cross-Checks and the Analysis of External Data

The data analysis presented here has been using data from H.E.S.S. I, which is well understood on the systematic side and partially included data from H.E.S.S. II for variability searches at timescales larger than the duration of a run. For shorter timescales H.E.S.S. II data has not been taken into account for unresolved systematic issues. The analysis was performed entirely with the Heidelberg software and calibration chain and the Hillas Loose cuts, which hardly have been used for data analysis before. Therefore, diferent control sources were analyzed in parallel to track possible systematic issues like unstable pedestals. They did not give indications of problems with the cuts in use. Whenever possible, control sources which were observed under the same conditions like the GC such as G 0.9+0.1 were analyzed as a cross-check. However, a full comparison of G 0.9+0.1 and HESS J1745-290 was not possible due to the fact that G 0.9+0.1 only shows about 25% of the fux level of HESS J1745-290. With respect to the long-term variability, the HESS J1745-290 data were found to be more variable in the χ2 ft with a constant than G 0.9+0.1 and MSH 15-52. Fluctuations by the background are therefore unlikely to cause the observed variability since if this were the case an efect would also have been observed in these cross-checks. Furthermore, it was shown that the variability could also be observed when pointings with a Galactic latitude b > 0 and such with b < 0 were analyzed separately. This cross-check makes it appear unlikely that the NSB level which varies as a function of the Galactic latitude in the GC region or a particular problematic background region cause the observed variability. Systematic changes of the rates of γ-like events could not fully be excluded by this cross-check but since MSH 15-52 has a comparable γ-ray fux like HESS J1745-290 and did not show signs of variability also this systematic origin of the efect is unlikely. The signifcance level for the variability of the light curve is 6.1σ without systematic error and reduces to 4.5σ when adding a 10% systematic error. A further, qualitative argument against a purely systematic origin of the observed long-term variability is its time structure: The fact that evidence for a known period was found at 110 days supports the assumption that the observed long-term variability is at least partly linked to physics. The period is present in both the H.E.S.S. I and the H.E.S.S. II data sample and the signifcance level for variability increases when merging 132 Summary and Outlook the two datasets. Also the variability searches with X-ray data from Swift and a Fermi LAT photometric light curve show a hint of a periodicity for the period range of interest (from 100 to 120 days). Although none of these cross-checks is exceeding the 3σ level they also do not contradict the H.E.S.S. result. Furthermore, the time ofsets agree within errors when ftting the 3 light curves with a constant plus a sine with a period of 120 days, which can be read as a hint that in fact the same modulation has been observed for the three light curves.

With respect to the short-term variability at the 3.1σ level the main reason, which is speaking in favor of a true signal rather than a systematic efect, is the similarity of the periods which were found in H.E.S.S. data to known X-ray and IR periods. Furthermore, there is a correlation between the observed variability and a fux increase at a 15% level for all six runs of interest as one would expect in case of an additional variable fux component was present during those runs. Also the number of excess events, which are available with the Loose cuts at post-cut level, is sufcient to produce such quasi- periodic behavior as shown in Chapter 3. In summary it can be stated that during the cross-checks and tests no obvious problems or unresolvable contradictions could be found.

Of course there is still the possibility that a set of hidden systematic efects which have not been found during these cross-checks causes the observed variable behavior of the HESS J1745-290 dataset. Assuming such efects poses the question why these systematic efects are causing physical reasonable behavior, which shows parallels to observations at other wavelength bands and is of the expected order of magnitude rather than orders of magnitude away which usually is the case for systematic artifacts.

Although it is impossible to fully rule out the case of an unknown systematic efect, the similarity to observations from other wavelengths favors the following hypothesis: The VHE γ-ray source at the position of the Galactic Center is in fact identical with Sgr A* (probably in combination with other fux components like the difuse emission) and shows a similar variability like in other wavelength bands. If the VHE γ-ray GC source is (at least partly) identical with the black hole Sgr A* the question arises which is the emission mechanism causing the variability. This question will briefy be treated in the next section. 5.4 Candidate Mechanisms explaining the observed Variability 133

5.4 Candidate Mechanisms explaining the observed Variability

In Sec. 3.1.2 possible mechanisms for explaining both the long-term and short-term variability of Sgr A* have been discussed, presenting various explanatory approaches for the diferent efects. The intention of this section is to discuss if the H.E.S.S. results presented in this thesis ft the framework of existing candidate mechanisms explaining the variability of Sgr A*. While there is a convincing model for the long-term variability at the time of this writing, the situation is more enigmatic for the short-term behavior.

A Review of the long-term Variability

A mechanism to explain the tentative period from 100 to 120 days in radio data was presented in Sec. 3.1.1. The efect could be caused by the precession of the accretion disk of the black hole and the presence of a non-thermal particle population close to the horizon of Sgr A* which is partially shielded from an observer on earth by the precessing disk. In case relativistic particles from the non-thermal halo of Sgr A* also reach the HE and VHE γ-ray regime, it is possible or even likely to observe this efect also at those energies if it is present at other wavelengths since also particles from the VHE γ- ray range would be partially shielded by the disk. A model describing the absorption of GeV γ-rays by an accretion disk can be found in Ref. [28] for the microquasar Cygnus X- 3. In this model GeV γ-rays are signifcantly absorbed by soft X-rays which are emitted from the inner parts of the accretion disk. This absorption is following a complex and anisotropic absorption pattern. It is also stated that even photons from the outer parts of the disk, which are expected to be from the IR band, even could pair-produce with TeV γ-rays. Although it is not clear at which level the accretion disks of Cygnus X-3 and Sgr A* are comparable, the study showed that an absorption of HE and VHE γ-rays by an accretion disk in principle is possible and could be used as a starting point for a further modeling of the situation for Sgr A*. Measuring the disk precession of Sgr A* by the detection of a periodic fux modulation of the VHE γ-ray fux would be the frst independent confrmation of this radio period. Since the signifcance of this periodicity does not reach the 5σ detection threshold, further data taking and monitoring campaigns are needed to obtain a clear answer here. The topic is promising and should be followed up with H.E.S.S. and future observatories like CTA, which is scheduled to start construction in 2016 or 2017. 134 Summary and Outlook

Preferred Candidate Explanation for the short-term Variability There is no commonly accepted candidate explanation for the short-term variability of Sgr A* for diferent wavelength bands at the time of this writing. Previously (Sec. 3.1.2) several possible candidates and scenarios for an explanation have been discussed. The G2 gas cloud does not seem to be a good candidate here since there is no correlation between the pericenter passage of the G2 gas cloud and the occurrence of the fares during MWL observations. Although there were two extraordinarily bright X-ray fares of Sgr A* in 2012 and 2013, they took place well before the epicenter of the G2 trajectory in spring 2014. For VHE γ-ray regime no signifcant fares were detected in the H.E.S.S. II light curve reaching from 2014 to 2013. Therefore, a diferent efect is likely to be responsible for these tentative, rather short and weak fare events. A more promising explanatory approach here is the tidal disruption of asteroids which are getting too close to Sgr A*, which has been discussed in Chapter 3. The process is expected to take place at a regular basis with at least one event per day. The estimated luminosity of the γ-ray fare candidates in the order 1033–1035 erg/s is comparable to the predicted strength of an efect in this scenario and well below the expected peak luminosity of 1039 erg/s (see Sec. 3.1.2). Obtaining a fux increase larger than this limit would rule out the asteroids model as an explanation for the variable VHE γ-ray emission. Furthermore, as shown in the previous chapter the efect seen in H.E.S.S. data may be limited to low energies. The presence of a cut-of would support the assumption of a leptonic scenario being responsible for the short-term variability in favor of a hadronic origin. This agrees with a population of highly relativistic electrons which is predicted in the asteroids model. For the moment a connection between the short-term variability and the asteroids scenario is at a speculative level of course but the H.E.S.S. results presented here in combination with further H.E.S.S. observations may help to confrm or rule out this interesting model. In any case a hadronic origin of the short-lived variability can be likely ruled out due to the short cooling times which are need to produce a rapid variability at timescales of minutes.

5.5 Conclusion and Outlook

The main question asked at the beginning of this thesis was: Is the VHE γ-ray source at the direction of the Galactic Center variable and at least partially linked to the black hole Sgr A* ? It would be daring to answer this question with a clear yes since the analysis performed here was at the limit of what was doable with H.E.S.S. from the systematic and statistical perspective. However, several observations, which were 5.5 Conclusion and Outlook 135 presented in this work favor the scenario that at least one component of the signal from HESS J1745-290 is in fact connected to Sgr A*. Further components could still be from the PWN G359.95-0.0 and the difuse emission in the Galactic plane. Although the signifcance levels, which were found during this analysis, were too low to claim a detection of a variability of HESS J1745-290 at the 5σ level, this work revealed evidence for both a short-term variability of HESS J1745-290 at timescales of minutes and also for a long-term variability of this source. These observations clearly support the assumption of a link between the GC VHE γ-ray source HESS J1745-290 and Sgr A*, since the only known objects to show variable behavior at timescales like the observed ones are black holes. Furthermore, the fndings presented here are similar to the known behavior of Sgr A* in terms of time structure for both the short-term variability and the long-term variability. When putting them into a common context, the H.E.S.S. results ft well into the overall picture of Sgr A* and might give a new insight into the nature of this black hole at so-far unreached energies from the VHE γ-ray range. It is hard to imagine that all the efects which are reported here are due to an unknown systematic origin, although this cannot fully be excluded at the time of this writing. However, the parallelism to MWL observations of Sgr A* disfavors the systematic explanation since the efects observed here have counterparts at diferent wavelength: Both the long-term fux modulation which is of the order of 110 days and the hints of quasi-periodic behavior have counterparts from the radio band (long-term behavior) to the X-ray band (quasi-periodic) behavior. Furthermore, control sources like G 0.9+0.1 did not show any comparable efects. There is no plausible explanation why systematic efects should mimic known behavior with respect to the time structure of the variability only at the position of Sgr A* but nowhere else in the FoV. The assumption that HESS J1745-290 and Sgr A* are linked raises the question how large the contribution of Sgr A* to the overall fux of HESS J1745-290 is. From the studies, which were summarized in this thesis, the following limits can be given: Concerning the short-term variability which appears to be present in less than 10% of all runs a luminosity of 1033 –1035 erg/s could be derived which on average is corresponding to a −11 −2 −1 fux increase of △Φγ = 0.88±0.72×10 cm s which is 17.6% of the total integrated fux > 100 GeV and implies that the contribution of Sgr A* to the HESS J1745-290 fux is ≥ 17.6% during runs showing a short-lived variability. In case the reported long-term variability is caused by the precession of the accretion disk of Sgr A* there should also be a steady VHE γ-ray fux component from the vicinity of Sgr A*, which is partially shielded by the disk precession. This steady fux component should be larger than the fux modulation. Therefore, a lower limit for the expected 136 Summary and Outlook

VHE γ-ray fux can be derived from the result of the ft of the Sgr A* light curve with Eq. 4.2.1 in Sec. 4.2.4.2.3. About twice the amplitude of the sinusodial component of the ft function should be equivalent to the maximum fux which is shielded by the preceding disk. This value was calculated to be 1.29 ± 0.24 · 10−11 cm−2 s−1 for energies > 100 GeV which corresponds to 26.5% of the total integrated fux of HESS J1745-290. This allows the conclusion that the fux component which Sgr A* is contributing to the HESS J1745-290 fux is ≥ 26.5%. Trying to give a detailed, quantitative model explaining the VHE γ-ray emission would go beyond the scope of this thesis and requires further combined eforts by theorists and experimentalists. In order to confrm the VHE γ-ray variability of Sgr A*, which was reported in this thesis at the 5σ level, follow-up observations and dedicated MWL campaigns are needed. Therefore, the Galactic Center remains an extremely interesting target for H.E.S.S. II and of course also future observatories like CTA may play a crucial role here. The results on a VHE γ-ray variability of Sgr A* presented in this work may already now be helpful for theorists in fnding the correct model for the not yet fully understood variability of Sgr A* at diferent wavelengths bands, which from now on are also expected to include the VHE γ-ray range. Acknowledgements

There are many people who were important for realizing this work and it is certainly not possible to mention them all. However, there are some people I would like to thank in particular: First of all I would like to mention Professor Thomas Lohse for giving me the opportunity to do my PHD in his working group. I really appreciated the inspiring atmosphere and also the good conversations about scientifc and non-scientifc adventures at lunch. The work certainly would not have been possible without the input by Ulli Schwanke who always had time to discuss any doubts. Furthermore, I would like to thank Loise Oakes for the good collaboration and the cross-check analyses. Also many thanks to Veronika Schneider for being patient when handing in my travel expense reports late and Tim Holch for proof-reading some chapters and also buying an excellent cofee machine for the ofce - better late than never. Not to forget about the numerous discussions with Gerrit Spengler about physics and systematics at H.E.S.S. and the good collaboration in the beginning of my PHD when I was working at indirect Dark Matter searches. There were also many people who indirectly supported me during this work and made the past four years unforgettable experience in my life. Many thanks to my parents and brother, my grand parents and of course also my friends Andres, Andrew, Clara, Elias, Johannes, Letizia, Laia, Robin for the great time. Also not to forget about Sven, Michael, Lars and the other guys for some inspiring weekends and everybody else I forgot to mention here. Last but not least I would also like to thank Professor Elisa Bernardini and Professor Markus Böttcher for volunteering to review this thesis.

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Simulated Monte Carlo Event Displays for gamma-like Events

In order to illustrate that the event displays, which were projected in one camera plane from Sec. 4.2.5.3, resemble low energetic γ-like events, in Fig. A.0.1 a series of low energetic γ-like events from MC simulations with energies < 400 GeV is presented. In contrast to the events in Sec. 4.2.5.3, which were all taken from the GC region and therefore show ellipses pointing to the same direction in the camera, these MC events were simulated using difuse MC runs and therefore the ellipses do not point into a preferred direction. Nevertheless, these event displays can be used to make it somewhat plausible that the events, which were selected in Sec. 4.2.5.3, were caused by primary γ-rays due to their similar appearance to the events from the GC region. Of course, this cannot be considered to be a full prove that the GC events are in fact caused by γ-rays but at least the similar appearance supports this hypothesis. 154 Simulated Monte Carlo Event Displays for gamma-like Events

(a) (b)

(e) (f)

(g) (h)

Figure A.0.1: Sample MC event display for low-energetic γ-like events at energies < 400 GeV. Appendix B

Studies with respect to Broken Pixels

In order to investigate if there is a correlation between the tentative short-term variability within certain runs and the number of broken pixels in the cameras, the total number of broken pixels of four runs showing signs of variability in the RL test (Run 22278, Run 22279, Run 26085 and Run 27569) was compared to the distribution of broken pixels of runs which did not show any signs of variability. The distribution of the number of broken pixels for the background sample without signs of variability can be found in Fig. B.0.1 where the four runs with hints for variability are marked by vertical lines. The mean number of broken pixels for the background sample is ∼ 30. The four runs with large RL powers do not signifcantly exceed this number. Since Run 22278 and Run 22279 were discussed in most detail due to the fact that they were consecutive and showed a 60.0% fux increase at the 2.5σ level, their patterns of broken pixels were studied in more detail: The broken pixels for these two runs are distributed uniformly over the diferent cameras. Furthermore, there are no complete drawers missing for any of these two runs. Another observation was that some runs from the same night, which did not show any signs of variability, had a larger number of broken pixels than Run 22278 and Run 22279. These observations make it appear unlikely that there is a correlation between the number of broken pixels and the reported short-term variability. 156 Studies with respect to Broken Pixels

Figure B.0.1: Distribution of broken pixels for a background sample of runs without signs of variability in comparison to particular runs showing large RL powers. 157

(a) CT 1 (b) CT 2.

(a) CT 1. (b) CT 2.

Berlin, den 15.8.2016

Hiermit erkläre ich, dass die Dissertation selbstständig und nur unter Verwendung der gemäß Paragraph 7, Absatz 3 der Promotionsordnung Nr. 126/2014 angegebenen Hilfen und Hilfsmittel angefertigt worden ist.

Philipp Wagner