Diss. ETH No. 18322
Detection of Pulsed Very High Energy Gamma-Rays from the Crab Pulsar with the MAGIC telescope using an Analog Sum Trigger
A dissertation submitted to the Swiss Federal Institute of Technology Zurich for the degree of Doctor of Natural Sciences
presented by Michael Thomas Rissi Dipl. Phys. ETH born August 31, 1979 citizen of Wartau (SG)
accepted on the recommendation of Prof. Dr. Felicitas Pauss, examiner Prof. Dr. Christoph Grab, co-examiner Dr. Adrian Biland, co-examiner
2009
Für Regina
Je mehr man kennt, je mehr man weiss, erkennt man: alles dreht im Kreis. (Goethe, Zahme Xenien VI)
Abstract
Pulsars (PULSating stARS) are strongly magnetized and fast spinning neutron stars emerg- ing from the massive core of a star after the supernova at the end of its lifetime. Their rotational frequency ranges from 0.1 Hz to nearly 1 kHz. In the 1960s, Pulsars were dis- covered at Radio frequencies. Until the mid 1990s, pulsating electromagnetic radiation was measured over the whole spectrum (radio, infrared, optical, ultraviolet, X-rays) from a few 1000s pulsars. Seven pulsars are even known to radiate pulsating γ-rays, being the photons with the shortest yet measured wavelengths and the highest energies ever observed.
Even though pulsars have been known for the last 40 years, the mechanisms leading to the emission of electromagnetic radiation is hardly known. The main models – the so-called polar cap and outer gap models – have in common that the emission of electro- magnetic radiation is related to relativistic electrons and positrons. These particles are accelerated by the electric field induced by the strong rotating magnetic field. Photons are emitted by those particles, e.g. by means of the synchrotron mechanism. The dif- ference between the two models lies in the region, where the acceleration of the charged particles takes place. The polar cap model assumes the acceleration in a region close to the neutron star above the magnetic poles, while in the outer gap model, the acceleration takes place in an area far out in the pulsar’s magnetosphere. The magnetosphere is the space in the vicinity of a pulsar, where a strong magnetic dipole field co-rotates with the pulsar. It is filled with a plasma. Due to different absorption mechanism for γ-rays, the two models predict different energy spectra for the pulsed radiation at the highest energies.
Gamma rays with an energy in the MeV to a few GeV range are usually called High Energy (HE) γ-rays and are measured by satellite experiments. Photons with energies above a few tens of GeV are called Very High Energy (VHE) γ-rays and can be detected from ground with Imaging Air Cherenkov Telescopes (IACT) such as the MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) Telescope. These kind of telescopes detect the Cherenkov flashes from electromagnetic atmospheric air showers initiated by a γ-ray hitting molecules or atoms in the upper atmosphere. Among all IACTs, MAGIC has the lowest energy threshold of 55 GeV. ≈ In the last 20 years since the emergence of VHE γ-ray astrophysics with ground based instruments, several unsuccessful attempts to detect VHE γ-rays from pulsars have been made. The reasons for the non-detection is the sharp cut-off of the energy spectra pre- dicted by the two pulsar models and the too high energy threshold of IACTs which did not allow to collect enough pulsating γ-rays. Following a hint for pulsed VHE γ-ray emission above 60 GeV from the Crab Pulsar from data taken with the MAGIC telescope in 2005, we developed a new trigger system for the MAGIC telescope: the sum trigger. The sum trigger allowed to reduce the energy threshold from 55 GeV to 25 GeV.
Between October 2007 and February 2008, we observed the Crab Pulsar with the MAGIC telescope using the sum trigger for about 22 hours under good weather conditions. The
V analysis of this data reveals pulsating VHE γ-radiation on a confidence level of 6.2σ.
In case of the Crab Pulsar, the two pulsar models discussed above both predict a cut-off of the pulsed γ-ray spectrum of exponential (outer gap) or super exponential (polar cap) shape in the range between a few GeV and some tens of GeV. For both cases, we calculated the cut-off energy to
Ecut = (17.7 2.8stat 5.0syst) GeV (exponential), and ± ± Ecut = (23.2 2.9stat 6.6syst) GeV (super exponential), ± ± respectively. Our measurements contradict the polar cap’s model predictions.
In a next step, the pulsed spectrum was determined in the cut-off region. I found that the pulsar still emits pulsed γ-rays above 60 GeV which is higher than predictions from the outer gap model indicate. The pulsed spectrum above 25 GeV rather follows a power law α (f(E) E ) with spectral index α = 3.1 0.6stat 0.5syst, than the steep exponential ∝ − ± ± cut-off.
VI Zusammenfassung
Pulsare sind stark magnetisierte, rotierende Neutronensterne, welche aus den massiven Kernen von Sternen nach der Supernova am Ende derer Lebenszeit entstehen. Ihre Rota- tionsfrequenz ist zwischen 0.1 Hz bis fast 1 kHz. Gepulste Radioemission wurde vom ersten Pulsar in den 1960er Jahren entdeckt. Gepulste elektromagnetische Strahlung wurde bis Mitte der 1990er Jahre über das gesamte Spektrum (von Radio über Infrarot, optischen Wellenlängen, Ultraviolett bis Röntgenstrahlen) von ein paar 1000 Pulsaren gemessen. Von sieben Pulsaren ist sogar bekannt, dass sie γ-Strahlung emittieren. Diese Photonen haben die kürzeste je gemessene Wellenlänge und die höchsten bisher beobachteten Energien.
Obwohl Pulsare seit 40 Jahren bekannt sind, wissen wir heute immer noch relativ wenig über deren Emissionsmechanismus. Die beiden Hauptmodelle (das “polar cap” und das “outer gap” Modell) haben gemein, dass die Emission der elektromagnetischen Strahlung mit relativistischen Elektronen und Positronen zusammenhängt. Diese Teilchen werden im elektrischen Feld, welches vom rotierenden Magnetfeld induziert wird, beschleunigt. Die Photonen werden dann zum Beispiel über den Synchrotron Mechanismus ausgestrahlt. Die beiden Modelle unterscheiden sich in der angenommenen Region, in der die Beschleunigung der geladenen Teilchen stattfindet. Das “polar cap” Modell nimmt an, dass die Beschleu- nigung oberhalb der magnetischen Polkappen nahe am Pulsar stattfindet. Im “outer gap” Modell dagegen findet die Beschleunigung weit aussen in der Magnetosphäre statt. Wegen unterschiedlicher Absorptionsmechanismen der hochenergetischen Gammastrahlung sagen die beiden Modelle unterschiedliche Energiespektren für die höchsten Energien voraus.
Gammastrahlen mit einer Energie zwischen MeV und wenigen GeV werden mit Satelliten- experimenten gemessen. Die Photonen mit Energien oberhalb ein paar Dutzend GeV kön- nen mit Experimenten auf der Erde nachgewiesen werden; zum Beispiel mit dem MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) Teleskop. Dieses Teleskop regi- striert die Cherenkov-Lichtblitze von elektromagnetischen atmosphärischen Luftschauern, die von einem Gammateilchen initiiert werden, welches Atome oder Moleküle der Atmo- sphäre trifft. Von allen existierenden Cherenkovteleskopen hat MAGIC die tiefste Energi- eschwelle von 55 GeV.
Seit den Anfängen der Gammastrahlen-Astrophysik mit erdgebundenen Instrumenten vor 20 Jahren wurde erfolglos versucht, gepulste hochenergetische Gammastrahlung von Pulsaren zu messen. Ein Grund für diese Nichtdetektion ist der von den Pulsarmodellen vorausgesagte starke “cut-off” (Abbruch) des Energiespektrums und die zu hohe Energi- eschwelle der Cherenkovteleskope, welche es verunmöglichte, eine genügende Anzahl gepul- ster Gammateilchen zu messen. Nachdem in Daten, die 2005 genommen wurden, mit dem MAGIC Teleskop ein Hinweis für gepulste hochenergetische γ-Strahlung oberhalb 60 GeV vom Krebspulsar gefunden wurde, haben wir ein neues Trigger-System1 für das MAGIC Teleskop entwickelt (der sogenannte Summentrigger, oder sum trigger). Dieser neue Trig-
1Ein Trigger-System ist ein Auslösemechanismus, welcher bewirkt, dass die gemessenen Daten gespeichert werden.
VII ger reduzierte die Energieschwelle von 55 GeV auf 25 GeV.
Zwischen Oktober 2007 und Februar 2008 beobachteten wir den Krebspulsar mit dem Summentrigger während gut 22 Stunden bei guten Wetterbedingungen. Die Analyse dieser Daten führte zur Entdeckung von gepulster hochenergetischer γ-Strahlung mit einer Sig- nifikanz von 6.2σ.
Die beiden obengenannten Pulsarmodelle sagen einen steilen cut-off des gepulsten Gam- maspektrums mit exponentiellem (outer gap) respektive super-exponentiellem Verlauf (po- lar cap) voraus. Für beide Fälle habe ich die charakteristische Energie, bei welchem das Spektrum abbricht, berechnet:
Ecut = (17.7 2.8stat 5.0syst) GeV (exponentiell), respektive ± ± Ecut = (23.2 2.9stat 6.6syst) GeV (super-exponentiell). ± ± Die hier vorgestellte Messung widerspricht den Voraussagen des polar cap Modelles und schliesst dieses daher aus.
In einem weiteren Schritte habe ich das gepulste Energiespektrum bestimmt und heraus- gefunden, dass der Pulsar Gammastrahlen sogar oberhalb 60 GeV aussendet; d.h. höher als das outer gap Modell voraussagt. Das gepulste Spektrum oberhalb 25 GeV folgt eher α einem Potenzgesetz (f(E) E ) mit spektralem Index α = 3.1 0.6stat 0.5syst, als ∝ − ± ± dem steilen exponentiellen Abbruch.
VIII Contents
Abstract V
Zusammenfassung VII
Introduction 12
1 Cosmic Rays 17
2 The γ–Ray Universe 21 2.1 Sources of γ-Rays...... 22 2.1.1 VHE γ-RaySources ...... 22 2.1.1.1 Extragalactic Sources ...... 24 2.1.1.2 Galactic Sources ...... 24 2.2 Production and Absorption Mechanism of γ-Rays...... 24
3 Pulsars 29 3.1 Introduction: The Crab Pulsar as a Canonical Pulsar ...... 30 3.2 Measurements of Pulsed γ-Rays from Pulsars before 2007 ...... 30 3.3 Emission of Electromagnetic Radiation from a Pulsar ...... 35 3.3.1 Polar Cap and Slot Gap Model ...... 38 3.3.2 OuterGapModel...... 40 3.4 Conclusion...... 41
4 Observation Technique and Data Analysis 45 4.1 Direct Measurement of γ-Rays with Satellites ...... 46 4.2 Imaging Air Cherenkov Telescopes (IACTs) ...... 46 4.3 TheMAGICTelescope...... 51 4.3.1 Mirrors, Frame and Drive ...... 51 4.3.2 Camera ...... 53 4.3.3 The MAGIC Standard Trigger ...... 54 4.3.4 The Data Acquisition System ...... 55 4.3.5 The Calibration System ...... 55 4.3.6 The Central Pixel ...... 58 4.3.7 Pyroscope...... 58 4.3.8 The Rubidium and the GPS Clock ...... 58 4.4 DataAnalysis...... 58 4.4.1 Extraction of the FADC Signals ...... 60 4.4.2 ImageCleaning...... 60 4.4.2.1 Standard Image Cleaning ...... 60 4.4.2.2 Sum Image Cleaning ...... 61 4.4.2.3 Calibration Image Cleaning ...... 63 4.4.3 Image Parameters ...... 66 4.4.4 Event Classification with Random Forest and Estimation of the Energy 67
IX 4.4.5 Determination of the Differential Flux ...... 68 4.4.5.1 Unfolding Methods ...... 70 4.5 Analysis of Periodic Signals from Pulsars ...... 71 4.5.1 Determination of the Cut-Off Energy of the Pulsed γ-Ray Emission . 72
5 The New Sum Trigger 75 5.1 Reaching the Design Goal of the MAGIC Telescope ...... 76 5.2 The Sum Trigger: The Basic Idea ...... 77 5.3 Photomultiplier Tubes Afterpulses ...... 79 5.4 Implementation of the Sum Trigger and Afterpulses into the Detector Simu- lation ...... 80 5.4.1 Afterpulse Simulations ...... 80 5.4.2 Sum Trigger Simulations: Topology, Thresholds and Shape ..... 81 5.5 Electronics and Installation on Site ...... 83 5.6 The Calibration of the Sum Trigger ...... 86 5.7 Comparison with the MAGIC Standard Trigger ...... 86 5.7.1 Homogeneity ...... 86 5.7.2 Energy Threshold ...... 86 5.7.3 Collection Area and Sensitivity for Low Energies ...... 88 5.8 Future Improvements ...... 88 5.9 Conclusion...... 91
6 Observation of the Crab Pulsar using the Analog Sum Trigger 93 6.1 Introduction...... 93 6.2 DataSample ...... 94 6.3 DataSelection ...... 100 6.4 Monte Carlo Simulations considering the Geomagnetic Field ...... 100 6.5 DataAnalysis...... 100 6.6 The Optical Lightcurve ...... 102 6.7 The Detection of Pulsed High Energy γ–Rays ...... 105 6.7.1 Number of Excess Events and Significance ...... 105 6.7.2 MC - Data Comparison ...... 106 6.7.3 Do P1 and P2 Follow a Different Spectrum? ...... 110 6.8 Cut-OffEnergy ...... 110 6.8.1 Exponential and Super Exponential Cut-Off ...... 110 6.8.2 Power Law Cut-Off ...... 114 6.8.3 Single Pulse Cut-Off Energy ...... 115 6.9 The Pulsed Spectrum above 25 GeV ...... 118 6.9.1 The Total Pulsed Spectrum in P1 and P2 ...... 119 6.9.2 Single Pulse Spectra ...... 122 6.9.3 Systematic Errors Influencing the Spectral Measurements ...... 124 6.10PhaseDiagram ...... 127 6.10.1 Arrival Time of Each Pulse ...... 127 6.10.2 Pulse Profile Morphology ...... 131 6.10.3 P2/P1 Ratio as a Function of Energy ...... 133 6.11 Measurement of High Energy γ-rays from the Crab Nebula at Low Energies 133
7 Summary, Conclusion and Outlook 137 7.1 Implications of our Measurements for Pulsar Models ...... 138
X 7.1.1 Conclusion derived from the Total and Phase Resolved Flux Mea- surements ...... 138 7.1.2 Conclusion Derived from the Pulse Profiles at Different Energies . . 143 7.1.2.1 The Phase Separation between P1 and P2 ...... 143 7.1.2.2 An Upper Limit for the Distance between the Production Regions of Optical and VHE γ-Ray Photons ...... 143 7.1.2.3 A Lower Limit on the Mass Scale of Quantum Gravity . . . 144 7.1.2.4 The P2/P1 Ratio: Comparison with the Predictions of a Multicomponent Model ...... 145 7.2 Outlook ...... 146
A Gamma/Hadron Separation Using Shower Autocorrelations 149 A.1 GeneralIdea ...... 149 A.2 Conclusion...... 151 A.3 Future Development: Implementation of the Algorithm using a GPU and CUDA...... 152
B List of Acronyms and Abbreviations 153
List of Figures 154
Bibliography 158
Acknowlegdement 169
XI
Introduction
Since human beings looked into the sky at night for the first time, they have been fascinated by the luminary’s illustrious equability. The majestic imperturbability of their movement in contrast to the unpredictable and chaotic life on Earth was interpreted by prehistoric peoples as divine signs. Consequently, they started to research the constellation’s periodic emergence and set the cornerstone of one of the eldest sciences: Astronomy. Observations of celestial objects were done at different time epochs in independent cultures, e.g. in ancient Egypt, where 2.000 BC the high correlation between the fruitful inundation of the Nile and the heliacal rising of Sirius was discovered, or in prehispanic Mexico, where the Maya predicted stellar constellations and calculated the duration of a tropical year to the very precise number of 365.2421 days. The methods to observe celestial objects and to predict their apparent movement were improved over the centuries. Until the beginning of the 20th century, all observations of celestial objects were performed by eye, using optical instruments, thus remaining con- strained to visible wavelengths. The predictions of electromagnetic waves by Maxwell in the middle of the 19th century, their experimental affirmation by H. Hertz in the 1880s and the understanding of Hertz that light behaves like the electromagnetic waves he measured (refraction, polarization and reflection), led to the conclusion that light is an electromag- netic wave as well. In 1895, an important discovery was made by Willhelm Conrad Röntgen, when he dis- covered a new kind of radiation which he called X-rays. He found that a running, but closed cathode ray tube was able to make a barium platinocyanide screen shimmer placed more than a meter away from the tube. In order to extent astronomical observations to the whole electromagnetic spectrum, huge technical advances had to be made. The first radio signals from a celestial body were measured by the engineer Karl Guthe Jansky in 1930, studying short wave transatlantic transmission. He noticed static noise on the transmission, correlated to the siderial rotation of the Earth. He concluded that the source had to be a celestial object, not the Sun, and could localize the source at the center of the Milky Way in the Constellation of Sagittarius. Unfortunately, the Earth’s atmosphere is impervious to most electromagnetic wave- lengths. Rayleigh scattering prevents e.g. the ultraviolet radiation to reach the surface of the Earth. To observe the radiation before being absorbed by the atmosphere, people have used balloon borne detectors and from the 1960’s on also experiments on satellites. The first cosmic X-ray source was detected by Riccardo Giacconi in 1962, with a X-ray detector on board the research rocket Aerobee. They failed to produce a X-ray image of the moon, but discovered a source of X-rays from the direction of Scorpius X-1. The photons with the highest energies and the shortest wavelengths are called γ-rays. They were discovered in 1900 by P. Villard who studied radioactive elements. He realized that one component of the radioactive radiation is not deflected by magnetic fields in con- trast to the charged α and β radiation and called them γ-rays. It was later found that γ-rays belong to the electromagnetic spectrum. In the interactions of γ-rays with matter, however, particle reactions like the photo effect dominates over coherent wave behavior. At the beginning of the 20th century, there was a mystery about an ubiquitous ionizing 14
radiation which caused electrometers to discharge without an apparent reason. It was first thought Earth itself emits this “Earth Radiation”, believed to be radiation from radioactive elements. If the Earth were the source, however, the radiation would become weaker with increasing height. Victor Hess tested this hypothesis in 1911, using electroscopes on a balloon. He found that the radiation became stronger the higher he flew. He concluded that the ionizing radiation has an origin in outer space. Robert Millikan confirmed this measurements and dubbed the radiation cosmic rays. He believed the cosmic rays to con- sist of γ-rays. Arthur Compton on the other hand was of the opinion that the cosmic rays are mostly charged particles like protons. Bruno Rhossi found in 1934 that the cos- mic ray rate depends on the Latitude. He concluded that cosmic rays are affected by the Earth’s magnetic field and must thus be charged. It took until 1948 when Melvin Gottlieb and James Van Allen found with balloon-borne emulsions chambers that the cosmic rays mostly consist of protons. Today it is known, that cosmic γ-rays contribute only to a small fraction of the cosmic rays of around 10 4 10 5. − − − In the 1960s, the first cosmic γ-ray source was discovered by a satellite borne gamma detector. The first ground based detection of cosmic γ-rays using the air shower technique (explained later) succeeded as late as 1989 when the Whipple collaboration discovered γ- rays from the direction of the Crab Nebula [1]. In figure 0.1, images of the Crab Nebula at Radio wavelengths to γ-rays are displayed. In this thesis, the Crab Pulsar, the highly magnetized and fast spinning neutron star in the center of the Crab Nebula, is established as an emitter of electromagnetic radiation, in particular at VHE γ-rays2. The Crab Pulsar spins with a high frequency of 33 Hz. Its ≈ strong co-rotating magnetic field of 8 1012 G induces an electric field which accelerates ≈ · particles. It is believed that electromagnetic radiation is emitted by relativistic electrons and positrons. Measurements of the pulsed γ-ray emission up to an energy of 10 GeV with satellite ≈ borne experiments revealed that the energy spectrum follows a power law f(E) E α, ∝ − with the spectral index α = 2.022 0.014 [2]. Until 2007, no instrument was sensitive ± enough to measure γ-rays between 10 GeV (the former flux sensitivity limit of space borne experiments) and 50 GeV (the lower energy threshold of ground based experiments like ≈ MAGIC). Above 50 GeV, no pulsed VHE γ-rays were detected before 2007.
This thesis is organized in the following way:
Chapter 1: The measured cosmic rays on Earth are described, including their energy spectrum, possible relation to cosmic γ-rays and their believed origin.
Chapter 2: An overview of HE and VHE γ-ray sources is given and possible emission mechanisms of VHE γ-rays are discussed.
Chapter 3: Pulsars are considered as emitters of electromagnetic radiation, in particular the HE and VHE γ-ray emission from young pulsars like Crab. The measurements of pulsed γ-rays from the Crab Pulsar before 2007 is discussed and the two current main theoretical models, the polar cap and the outer gap model is reviewed.
Chapter 4: In this chapter, I will explain the observation techniques used to measure HE and VHE γ-rays. The Imaging Air Cherenkov Telescope (IACT) MAGIC is illustrated and
2Note that “Crab” consists of two potential VHE γ-ray sources: the Crab Pulsar in the center and the Crab Nebula surrounding. They are separated in space by about 7 light years. 15
(a) Radio wavelengths (b) Infrared (c) Optical
(d) X-rays (e) γ-rays
Figure 0.1: The Crab Nebula as seen in radio, infrared and optical wavelengths, in X- and γ-rays. Note that the Nebula in X-rays is about 40% as large as the optical Crab Nebula, which is in turn about 80% as large as the Nebula at Radio wavelengths. The angular resolution of the γ-ray image (taken with the MAGIC telescope) is limited to some 0.1◦, while the optical image of the Crab Nebula has about a diameter of 0.01◦. Thus, the image in γ-rays cannot resolve any structure of the Crab Nebula. Image credit: NASA/CXC/SAO (X-ray), Palomar Obs (Optical), 2MASS/UMass/IPAC- Caltech/NASA/NSF (Infrared), NRAO/AUI/NSF: (Radio), MAGIC collaboration (γ-rays) [3, 4]. 16
the analysis of data taken with MAGIC is explained, where special emphasis will be put on the analysis of data close to the trigger threshold and to the analysis of data from sources, that are expected to show pulsation.
Chapter 5: The standard trigger of the MAGIC telescope provides an energy threshold of 55 GeV. To measure pulsed γ-rays from the Crab Pulsar, we realized that a lower ≈ threshold is mandatory. In 2006/07, we therefore designed a new trigger system, the sum trigger, which allowed to lower the energy threshold to 25 GeV. In this chapter, the new trigger is described.
Chapter 6: The new trigger system was used for the observations of the Crab Pulsar in the winter 2007/08. In this chapter, the analysis of this data is described, leading to the discovery of pulsed emission from the Crab Pulsar above an energy threshold of 25 GeV. The spectrum of the pulsed emission and the pulse profile morphology are studied.
Chapter 7: The results obtained in chapter 6 are reviewed and compared with theoretical predictions. An outlook on future observations of the Crab Pulsar is given. 1 Cosmic Rays
After their discovery by V. Hess in 1912 and their identification as mostly protons1 in the 1940s, cosmic rays were studied in great detail. The charged cosmic ray spectrum was measured over many orders of magnitudes in energy, from a few GeV energy to up to 1020 eV, a macroscopic energy of about 20 joules, corresponding to the kinetic energy of a tennis ball flying with 100 km/h. The cosmic ray spectrum measured by different experiments is shown in figure 1.1. For low energies < 1013 eV, charged cosmic rays can be directly measured with satellite- and balloon-borne experiments. For particle energies above 1013 eV, the small flux, however, makes the direct detection with the small space and air borne experiments difficult. In 1938, Pierre Auger found that the cosmic radiation arrives in short correlated bunches and concluded that a cosmic ray particle with a high energy (he estimated the energy to be above 1015 eV) hitting molecules of the Earth’s atmosphere initiates an extended air shower, where the energy of the incident cosmic ray particle is distributed over millions of secondary particles. To measure charged cosmic ray particles with energies above 1013 eV, ground based ex- periments are used which sample the secondary particles created in the shower. Based on these measurements, the energy, the incoming direction and the kind of the incident particle are inferred (figure 1.2). The small flux of cosmic rays at the highest energies of only 1 particle/km2 in a few hundred years requires experiments covering huge areas. The currently largest experiment is the AUGER array in Argentina covering an area of 3000 km2 and observing charged cosmic rays for energies above 1017 eV. ≈ Like the photons in optical astronomy, cosmic rays are messengers from distant objects. During their propagation through space, however, charged cosmic rays are randomly de- flected by galactic and extragalactic magnetic fields. Therefore, their incoming direction on Earth is randomly distributed and cannot be related with a known source observed e.g. at optical wavelengths. An exception might be the cosmic rays at the highest energies, for which the larmor radius2 extends the radius of our galaxy. In 2007, the AUGER collabo- ration found a first hint for a correlation of these events with nearby active galactic nuclei (AGN) [6]. Nevertheless, the origin of the cosmic rays is still not completely solved to this date. It is believed that the location where γ-rays are emitted and cosmic hadrons are accelerated are related, where in particular supernova remnants have been considered as accelerators of cosmic ray particles (e.g. [7, 8] and references therein). Thus, the observation of γ-rays can reveal details about the acceleration mechanisms and locations of the charged cosmic rays. A mechanism explaining the high energies of the cosmic rays and their power law spec- trum was proposed in 1949 by Enrico Fermi who postulated that charged particles which cross back and forth through moving and magnetized shock fronts would statistically gain energy. The higher the energy of a particle, the shorter the time while it is confined within
1The composition of cosmic rays at energies of a few GeVs is: 98% nuclei, where 87% are protons, 12% helium nuclei and 1% heavier nuclei, < 2% electrons and < 10−4 γ-rays. 2 p also called gyroradius: rL = |q|B with p the particles momentum, q its charge and B the magnetic field. 18 1. Cosmic Rays
Figure 1.1: The cosmic ray spectrum, measured by different experiments. Note that the flux at energies of 1019 eV is below 1 particle per km2 per year. Below 3 ≈ · 1015 eV (the so-called “knee”), the spectrum follows a steep power law dN/dE ∝ E α, with α 2.7, above it steepens to α 3. Image credit from [5]. − ≈ ≈ 1. Cosmic Rays 19
Figure 1.2: Illustration of an extended air shower initiated by a cosmic ray particle. The secondary particles created in the air shower are sampled with water filled tanks measuring the Cherenkov radiation of the relativistic particles passing through the water. The roundish detector in the middle registers the fluorescent light emitted by atmospheric molecules that were excited by the ionizing radiation within the air shower. (Image credit: AUGER collaboration) the front and the higher its escape probability. This naturally leads to a power law dis- tribution of the particle’s energies which leave the acceleration region [9]. The γ-rays are then emitted by the charged particles, either by electrons or positrons, by means of the synchrotron (in magnetic fields) and self compton mechanism, or by protons which may hit an atom from the denser matter surrounding the acceleration region and, in turn, produce neutral pions among others, which will then decay into γ-rays. More details are given in chapter 2. Due to their strong electric field induced by the spinning magnetic field, pulsars have also been considered as electrostatic particle accelerators contributing to the hadronic cosmic hadrons (e.g. [10]), to cosmic electrons (e.g. [11]) or to the cosmic positrons (e.g. [12]). This will be covered in chapter 3 in more detail. There are still many open questions about the details of the cosmic accelerators, the types of cosmic ray sources, the propagation through the interstellar medium or the cosmic ray composition at the highest energies. It is hoped that current cosmic ray experiments like AUGER, together with γ-ray experiments like MAGIC, H.E.S.S., VERITAS or FGST (see chapter 2), will help to shed light on the mystery of cosmic rays.
2 The γ–Ray Universe
Figure 2.1: A selection of scientific targets of very high energy γ-ray astronomy.
Gamma-rays are produced by the most energetic processes that occur in the universe, e.g. in jets emitted by AGNs, in supernova remnants or from the vicinity of pulsars with mag- netic fields that are 100 Million times stronger than the ones we can produce in laboratories on Earth. Scientific topics of γ-ray astrophysics include the understanding of the production mech- anisms of γ-rays in different sources or the correlation of the emission of γ-rays with the acceleration of cosmic rays, as well as fundamental physics questions, including the nature of Dark Matter, where γ-rays are potential annihilation products detectable on Earth or a possible vacuum dispersion due to quantum gravitational (QG) effects, causing time of flight delays of photons with high energies. A selection of scientific targets is displayed in figure 2.1. In this chapter, potential γ-ray sources and production mechanisms of high energy γ-rays 22 2. The γ–Ray Universe
Figure 2.2: The locations of the sources emitting γ-rays above 100 MeV detected with EGRET [13]. will be discussed. In chapter 3, pulsars as γ-ray sources will be discussed in detail.
2.1 Sources of γ-Rays
In the 20 years after the first detection of cosmic γ-rays with the Vela satellite in the 1960s, the satellite COS-B discovered 25 point-like sources in total. Due to the rather poor angular resolution, many sources could not be identified with known objects observed in radio and optical wavelengths or in X-rays. A large boost of the number of HE γ-ray sources was achieved with the Compton γ-ray satellite (CGRS), which started in 1991. The EGRET (Energetic Gamma Ray Experiment Telescope) experiment on board of this satellite performed a full scan of the sky. In total, γ-rays were detected from more than 200 sources. Amongst the galactic sources, EGRET detected HE γ-rays from pulsars, from a solar flare or from the large Magellanic cloud. From the extragalactic ones, HE γ-rays from AGNs and from one radio galaxy (Cen A) were discovered. Additionally, γ-rays were detected from several unidentified sources. The so called third EGRET catalog is a list of all those sources with their positions, fluxes and possible counterparts in other wavelengths (see figure 2.2) [13].
2.1.1 VHE γ-Ray Sources
In the VHE range, the first discovered source was the Crab Nebula, detected with the Whipple telescope in 1989 [1]. Until 2008, in total 25 extragalactic and 54 galactic sources were discovered by Imaging Air Cherenkov Telescopes (IACTs), see figure 2.3. In figure 2.4, the number of X-ray and γ-ray sources are displayed as a function of time. Among the individual VHE γ-ray sources are: 2. The γ–Ray Universe 23
VHE γ-ray sources o VHE γ-ray Sky Map +90 Blazar (HBL) Blazar (LBL) (Eγ>100 GeV) Flat Spectrum Radio Quasar Radio Galaxy Pulsar Wind Nebula Supernova Remnant Binary System Open Cluster Unidentified
+180o -180o
-90o 2008-10-29 - Up-to-date plot available at http://www.mppmu.mpg.de/~rwagner/sources/
Figure 2.3: The VHE γ-ray sources for energies above 100 GeV. From [14]
Figure 2.4: The known number of X-ray, HE and VHE γ-ray sources as a function of time (before 2007). [15] 24 2. The γ–Ray Universe
2.1.1.1 Extragalactic Sources AGN: Galaxies, which produce more (electromagnetic) emission than deduced from their stellar content, stellar remnants and interstellar medium are called Active Galactic Nuclei (AGN). It is assumed that they contain in their center a supermassive black hole with around 106 to 1010 M .1 If this black hole accretes matter from a surrounding accretion ⊙ disk, a jet can form perpendicular to this disk with an extension of up to 1024 cm. Within these jets, more radiation can be produced than in the whole galaxy. It is assumed that in jets charged particles can be accelerated up to the highest known energies. VHE γ-ray emission is measured from the direction of several AGNs. It is still unclear how VHE γ-rays are produced. There are leptonic or hadronic emission models (e.g. [16]), explained in section 2.2.
Gamma Ray Bursts: These are very bright and violent short term phenomena. The nature of these bursts is still not fully understood. In a few years, the γ-ray satellite Swift [17], dedicated to the measurement of gamma ray bursts, has detected several 100s of these most energetic objects. MAGIC has observed several Gamma Ray Bursts so far, but no VHE γ-ray emission has been detected.
2.1.1.2 Galactic Sources Supernova Remnants: A supernova may occur when a star at the end of its lifetime runs out of the fuel needed to provide the fusion. Stars that are massive enough will collapse and eject their outer shell. Depending on the mass of the progenitor star, a black hole, a neutron star or a white dwarf is formed in the center. The ejected material builds up a spherically shaped nebula, called supernova remnant. A shock is formed when the ejected material flows into the interstellar medium, where Fermi acceleration can take place. The large amount of relativistic particles may give rise to VHE γ-rays.
Pulsars: If the neutron star from a supernova explosion spins with a periodicity below a few seconds, it is called a pulsar. Due to their strong co-rotating magnetic field of > 1012 G, an electric field is induced, accelerating charged particles which will emit γ-rays. See chapter 3.
Pulsar Wind Nebulae: Most of the rotational energy lost by the pulsar is emitted in a relativistic particle wind or in a Poynting (radiation) flux. At some distance from the pulsar, a stationary shock is formed from where the VHE γ-ray emission originates.
γ-Ray Binary Systems: These objects consist of a compact object (i.e. a neutron star or a black hole) and a massive companion star. The compact objects accrete matter from the companion. In the binary systems called microquasars, a relativistic jet can be formed where particles are accelerated similar to AGNs [18, 19].
2.2 Production and Absorption Mechanism of γ-Rays
Photons with energies above 100 keV (wavelengths shorter than 10 10 12 m = 10 pm) · − are usually called γ-rays. Their interactions are dominated by particle like behavior, e.g.
1 30 M⊙ = 1.9891 · 10 kg, the mass of the sun. 2. The γ–Ray Universe 25
inelastic Compton scattering, the Photoelectric Effect or Pair Production2 and surmount wave behavior like coherent scattering by a large factor. Up to an energy of several MeV, γ-rays can be emitted by decaying radioactive nucleii. This emission comes from the relaxation of excited nuclei3 and from the annihilation of electron-positron pairs, where the positrons are produced in β+ decays. The energy features of this kind of emission is a sharp line at the relaxation energy or at 511 keV, respectively. In a few sources (e.g. Cas A: 1.157 MeV [20], Galactic Center: 511 keV [21]), line features were discovered. However, for most γ-ray sources the energy spectrum is continuous. For VHE γ-rays the spectrum often follows a power law f(E) E α with the spectral index ∝ − α. Thermal emission from a hot body can be excluded as a main production mechanism of HE and VHE γ-rays. The hottest measured structures in the universe are accretion discs around compact objects. Those objects have their thermal peak emission in X-rays and emit photons up to tens of keV. Furthermore, the black body spectrum does not follow a power law as it is observed from VHE γ-ray sources. In general, there are two concurring models trying to explain the HE and the VHE γ- radiation: Hadronic and leptonic γ-ray production mechanisms. In the following sections, these processes will be briefly discussed. Emphasis will be laid on the particle acceleration and VHE γ-ray emission mechanisms important in the vicinity of a pulsar.
Hadronic γ-Ray Emission The charged cosmic rays are dominated by hadronic particles (mostly protons). When these high energy particles hit cosmic matter, (neutral) pions can be produced. The main decay mode of π0 is into two γ-particles:
π0 γγ (98.798%) (2.1) → Assuming that a cosmic particle accelerator is surrounded by dense matter, a large amount of π0 are produced by the highly energetic protons. These pions will then decay into γ-rays. An overview over VHE γ-ray emission processes initiated by cosmic hadrons can be found in [22].
Leptonic γ-Ray Interactions Relativistic electrons and positrons in strong magnetic fields efficiently lose energy through synchrotron and curvature emission and through inverse Compton scattering that transmits the energy from high energy electrons to lower energy γ-rays, thus producing HE and VHE γ-rays. These mechanism are displayed in the follow- ing sections. Pulsars, as described in chapter 3, provide a strong electrostatic field needed to acceler- ate charged particles and a strong magnetic field needed for the observed synchrotron and curvature radiation and are thus considered as candidates of HE and VHE γ-ray emission. In figure 2.5, the leptonic interaction processes important for the production and ab- sorption of HE and VHE γ-rays in the vicinity of a pulsar are shown.
Synchrotron Emission: Electrons and positrons in magnetic fields efficiently lose • energy through synchrotron radiation. For small magnetic fields and electron energies Ee B 2 1, with the electron’s energy E , its mass m , and natural constant mec Bcr e e 2≪3 B = mec 4.4 1013 G, the synchrotron emission can be treated ignoring quantum cr e¯h ≈ · 2above 1022 keV − 3 60 β 60 ∗ − 60 ∗ 60 ∗ γ 60 For example: Co → Ni + e +ν ¯e. Ni relaxates under emission of two γ-rays: Ni → Ni + γ(1.332 MeV)+ γ(1.173 MeV) 26 2. The γ–Ray Universe
Curvature Radiation Synchrotron Radiation
γ γ
e B B e Magnetic Pair Production Photon Splitting
e+ γ γ γ 2 strong strong magn. magn. eld eld e- γ 1
Pair Production Inverse Compton Scattering γ γ + γ HE LE e LE
- γ e eHE eLE HE
Figure 2.5: Different interaction mechanism between γ-rays and leptons important in a pulsar’s magnetosphere. The index “LE” and “HE” indicates low energy and high energy, respectively. Note that in case of photon splitting and magnetic pair production, the recoil is absorbed by the strong (quantized) magnetic field. 2. The γ–Ray Universe 27
effects. In this regime, a particle with energy E and mass m emits synchrotron radiation with the power [22]:
2Ke2Γ4v4 P = , (2.2) 3c3r2 where K is the number of unit charges of the radiating particle, e the unit charge, Ee Γ= 2 , v c the electron’s velocity and r the radius of its trajectory. Depending mec ≈ on the magnetic field B perpendicular to the flight path of the electron, the peak ⊥ 9 2 energy of the emitted photons lies at Epeak(eV) = 5 10− B /1GΓ . · ⊥ In case of pulsars, magnetic fields can reach 1012 G. Thus, the classical treatment of synchrotron radiation is only possible for electron energies below 0.01 GeV. Above, the synchrotron emission has to be treated within quantum mechanics. This includes photon splitting [23, 24, 25]: Ee B 2 B 1 γ mec cr ≥ γγ (2.3) −−−−−−−→ and magnetic pair creation [24, 26, 27, 28]:
Ee B 2 1 mec Bcr ≥ + γ e e−. (2.4) −−−−−−−→ In strong magnetic fields, electrons will radiate γ-rays through synchrotron (and + curvature) radiation. Those γ-rays will create e e− pairs, either by magnetic pair production or by γγ e+e . By repeating this procedure, an electromagnetic → − cascade forms [22].
Curvature Radiation: In the strong and bent magnetic fields in the vicinity of • pulsars (e.g. [29]), an energy loss similar to synchrotron emission occurs to charged relativistic particles. The particles moving along the field lines rapidly lose their per- pendicular energy due to synchrotron radiation. The “spiraling” trajectory around the field line is treated within quantum mechanics - similar as a 2D harmonic oscil- lator. Due to synchrotron radiation the particle ends up in the ground state. Being in the ground state, the particle does not emit further synchrotron radiation. The trajectory of these particles can thus be treated quasi 1D and emission of γ-rays will only occur due to curvature radiation [30]. The energy loss of a particle emitting curvature radiation is similar to the loss by synchrotron radiation:
2Ke2Γ4c P = 2 , (2.5) 3rC
with rC the radius of the bent magnetic field line [31]. In common pulsar models (outer gap model and polar cap model), this is the most important VHE γ-ray emission mechanism [32, 33].
Inverse Compton Scattering: The upscattering of low energy photons with high • energy electrons (or positrons) is called Inverse Compton Scattering:
γLE + eHE γHE + eLE, (2.6) → an important process to transfer energy from particles to photons. Depending on the product of γ ray and electron energy, one distinguishes the following cases. In case 28 2. The γ–Ray Universe
of small energies ( E E m2c4), i.e. within the Thomson limit, the process can be e γ ≪ e described classically and the cross section becomes:
E σ = 8/3πr2 1 γ . (2.7) γe e − m c2 e For large energies (i.e. E E m2c4), i.e. the Klein-Nishina limit, quantum me- e γ ≫ e chanics effects have to be taken into account. The cross section then decreases with rising γ-ray energy: m c2 2E 1 σ = πr2 e ln γ + . (2.8) γe e E m c2 2 γ e Inverse Compton Scattering of photons emitted through synchrotron radiation by the same electrons (the so-called synchrotron self Compton process), is one of the mechanisms used to explain the VHE γ-rays from several source types. In pulsars, photons produced through synchrotron and curvature radiation are Compton scat- tered to TeV energies too. Due to efficient absorption mechanism in the vicinity of the pulsar, however, it is believed that these TeV γ-rays will not leave the pulsar’s magnetosphere.
Absorption: In the strong magnetic fields in the vicinity of a pulsar, magnetic pair • production and photon splitting play an important role in the absorption of γ-rays. Another important absorption mechanism is pair creation:
+ γγ e e− (2.9) → This process has the highest probability to happen if the mean photon energy lies at 511 keV. A detailed study of all emission and absorption mechanisms in the vicinity of a pulsar can be found in [34]. 3 Pulsars
Since their discovery at Radio wavelengths in 1967 by Jocelyne Bell [35] (see figure 3.1), pulsars have been observed in nearly the whole electromagnetic spectrum, from Radio waves to γ-rays. In 1934 already, Zwicky and Baade theoretically deduced that after a supernova explosion, the core of a star may remain as a dense neutron star. The discovery of pulsed radio emission from the Crab Pulsar in the center of the Crab Nebula in 1969 [36], which is the remnant of the known historic supernova in 1054, confirmed this theory. In the years after the discovery of pulsars, the observed periodic radio signal was explained due to the rotation [37] or the oscillation [38] of the neutron star. Because of emission of gravitational waves by the oscillation of the pulsar, however, the vibrational energy would be lost quickly [39]. Thus, the oscillation theory was dropped. Electromagnetic radiation is emitted in a (co-rotating) beam. The periodic crossing of the line of sight of the observer with this beam explains the observed pulsation. Today it is known that a pulsar is a fast rotating neutron star being the compact remnant of a star in a certain mass class1 after its supernova explosion at the end of its lifetime (e.g. [40, 41]). The size of the star is dramatically reduced during the collapse (from a radius of 1011 cm to 106 cm), reducing its moment of inertia by ten orders of magnitude, ≈ ≈ resulting in small rotational periods of down to fractions of a second. The star’s magnetic flux Φ = B n da is conserved during the collapse. To compute the pulsar’s surface · magnetic field, we assume that its progenitor had a surface (dipole) magnetic field strength R of B 102 G. During the collapse, the star’s surface area a is reduced by a factor 1010. ≈ ≈ Thus, the surface magnetic field strength B is increased by this factor to B 1012 G.2 ≈ Even though pulsars have been known for more than 40 years, the precise emission mechanism are still scarcely known. While the radio emission is believed to originate from above the magnetic polar caps emitted by coherent highly energetic electrons, there exist several theories about the location within the pulsar’s magnetosphere where the emission of the remaining electromagnetic emission occurs, displayed in figure 3.2. All theories assume that the emission is connected to electrons and positrons which are accelerated in the strong induced electric field. An overview in more details will be given later in this chapter. Before 2007, only seven pulsars (Crab Pulsar, PSR B1509-58, Vela, PSR B1951+20, Geminga, PSR B1055-52, PSR B1706-44) were known to radiate HE γ-rays above 1 GeV, and no pulsed VHE γ-radiation was detected. In the following sections, I will first expound the general phenomenology of young pulsars, where Crab is considered in particular. Then, an overview of the γ-ray measurements from pulsars before 2007 is given. In section 3.3, the mechanisms for the electromagnetic emission from pulsars is discussed. In the last sections, I will review the current main models explaining the γ-ray emission from pulsars: The polar cap (which was extended to the slot gap model) and the outer gap model.
1 The core mass of the progenitor star must be between 1.44 M⊙ and 3 M⊙ in order to form a neutron star. 2The energy density of such a magnetic field is ≈ 4 · 1020 Jmm−3. So in 10 mm3, the energy mankind uses in one year is stored. 30 3. Pulsars
Figure 3.1: The discovery plot of the first pulsar in 1967 by J. Bell [35]. The small peaks indicate the periodicity of the signal. J. Bell realized that the signal was cor- related with the siderial day (i.e. a day relative to the fix stars), indicating an extra-solar origin of the pulsating signal.
3.1 Introduction: The Crab Pulsar as a Canonical Pulsar
The Crab Pulsar is the most famous representative of a canonical pulsar, characterized by a mass of M 1.4 M , a diameter around 20 km (see figure 3.3) and a surface magnetic ≈ ⊙ field of B 1012 G. Canonical pulsars have rotation periods P between 0.01 - 8 seconds. ≈ ˙ dP 18 12 1 The rotation period derivative P = dt is within 10− - 10− ss− , shown in figure 3.4. In this diagram, pulsars start in the upper left corner, having a small rotational period and a large P˙ . They lose rotational energy by means of magnetic dipole radiation3 and thus slow down. While the surface magnetic field B P P˙ (see formula 3.5 below) stays constant, ∝ they “wander” during their lifetime diagonallyp down towards the lower right corner where they end up in the “graveyard”, where no more pulsed electromagnetic emission takes place. It is not known yet why the emission stops, but it is assumed that either the induced electric field is too weak to pull charges out of the pulsar’s surface or the acceleration of electrons to high enough energies to initiate pair creation (E > 511 keV) is prevented [42, 43, 44]. The Crab Pulsar is one of the youngest known pulsars and appears thus on the upper left corner.
3.2 Measurements of Pulsed γ-Rays from Pulsars before 2007
Today, more than 2000 radio pulsars are known. The first detection of pulsed HE γ-rays was in the 1990s, when the EGRET experiment onboard CGRS discovered pulsating HE γ-rays from 7 pulsars [45]. In figure 3.5, the pulse profile (also dubbed light curve, phaseogram, phase4 distribution) of those pulsars is shown. Four objects show distinct features: Two rather broad pulses are visible, with a phase separation ∆φ between 0.35 < ∆φ < 0.45. The first pulse is called main pulse (P1), the second one inter pulse (P2). The region in between the two pulses is called bridge.
3Other possible radiation mechanisms are gravitational waves or magnetic radiation of higher order. 4The phase φ corresponds to the rotational angle of the pulsar, divided by 2π. Within one rotation of the pulsar, φ goes from 0 to 1. 3. Pulsars 31
Rotation axis open eld lines
closed eld lines magnetic eld α symmetry axis
null charge polar cap surface
+ + + + + ------outer gap
Light Cylinder Light Pulsar
slot gap ------
+ + + + +
Figure 3.2: The polar cap, slot gap and outer gap regions are possible candidates for loca- tions within the pulsar’s magnetosphere where the acceleration of particles and emission of electromagnetic radiation might take place.
In case of the Crab Pulsar, another distinct feature can be observed: The pulses P1 and P2 appear at the same phase for radio waves, optical emission, X-rays and γ-rays. For energies up to 10 GeV, EGRET measured the pulsed γ-ray spectra for the 8 phase regions5:
Component Name Phase Interval φ Leading Wing 1 LW1 0.88 0.94 − Peak 1 P1 0.94 0.04 − Trailing Wing 1 TW1 0.04 0.14 − Bridge Bridge 0.14 0.25 − Leading Wing 2 LW2 0.25 0.32 − Peak 2 P2 0.32 0.43 − Trailing Wing 2 TW2 0.43 0.52 − Offpulse OP 0.52 0.88 − The measured lightcurve for energies above 100 MeV and the phase regions are displayed in figure 3.6. While the measured pulse profiles contain the information about the location of the emission region and the geometry of the emission beam, the energy spectrum also allows
5Measurements of the spectrum in phase regions are called “phase resolved” spectrum measurements. 32 3. Pulsars
Figure 3.3: A canonical pulsar like the Crab Pulsar has about the size of Zurich, but the mass of 1.4M and spins 33 times per second around its axis. (Map: Google ⊙ maps). to draw conclusions on the mechanisms within the pulsar’s magnetosphere that lead to the emission of the measured photons. The photons in different phase regions are believed to be produced in different locations, or the emission directions of the photons differ. Thus, the measurement of the spectrum in phase resolved bins (i.e. the spectrum of the photons whose phase lies within a certain range) yields more information on the emission and ab- sorption mechanisms within the pulsar’s magnetosphere. In figure 3.7, the phase resolved spectrum measurements of several γ-ray instruments are displayed. It was found that above an energy of 100 MeV, the spectrum follows a ≈ power law:
α dN E − f(E)= = f (3.1) dE dA dt 0 · E norm with the flux normalization f0, a fixed normalization energy Enorm and the power law’s spectral index α. For γ-ray energies between 100 MeV and 5 GeV, the spectral index of the γ-ray spectrum in each phase interval has a value of α = (2.022 0.014) [2]. Furthermore, ± the P1 spectrum at the highest energies shows a hint for a spectral turnover. Despite various attempts in the last 20 years, observations with ground based telescopes did not allow to detect pulsed γ-rays from any pulsar before 2007 [46, 47, 48, 49, 50, 51]. Studying the flux sensitivities of these instruments reveals that they would have detected pulsed emission from Crab if the spectrum followed the extrapolated EGRET power law up to the highest energies. Therefore, the spectrum must show a turn over at energies between 10 GeV and < 100 GeV. To account for this spectral change, the power law measured with 3. Pulsars 33
young pulsars
canonical pulsars
Figure 3.4: The pulsar period P and its derivative P˙ for the known radio pulsars. The dashed lines denote lines of constant characteristic age τ = P , see formula 3.7. C 2P˙ The hatched area in the upper left corner denotes pulsars with a characteristic age below 10-100 kyrs, dubbed “young pulsars”. The dot dashed lines are lines with constant surface magnetic field B P P˙ (depicted in formula 3.5). The ∝ reddish area denotes the canonical pulsars,p described in the text. During their lifetime, canonical pulsars decelerate. Given that their surface magnetic field is conserved, they follow the direction of the green arrow until they end up in the “graveyard”. For pulsars within this area, no more electromagnetic emission is observed. Image adapted from [40]. 34 3. Pulsars
Figure 3.5: The pulse profiles of the 7 pulsars detected with EGRET [45], at radio and optical wavelengths and for X- and γ-rays. On the x-axis of each pulse profile the rotational phase is given. The Crab, Vela, B1951+32 and Geminga pulsars show two distinct peaks in γ-rays with a phase separation of 0.4. In case of Crab, the two peaks are at the same phase for all energies.
350 TW1 LW2 TW2 LW1 TW1 LW2 TW2 LW1 P2 OP Bridge OP P1 Bridge P2 P1 300
250
200
150 counts [a.u.]
100
50
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Phase φ
Figure 3.6: The pulse profile of the Crab Pulsar measured with the EGRET experiments for energies above 100 MeV with the phase regions defined in [2]. For better visibility, two identical cycles are shown. 3. Pulsars 35
Figure 3.7: The phase resolved spectrum measurements of the Crab Pulsar [2] for γ-ray energies between 0.1 keV and 6 GeV. For energies above 100 MeV, the ≈ spectra in all narrow phase intervals follow a power law with spectral index α = 2.022, measured up to an energy of 6 GeV. This power law component ≈ is indicated by the dashed line.
EGRET is adjusted with a cut-off:
α β dN E − −E f(E)= = f e“ Ecut ” . (3.2) dE dA dt 0 · E · norm
Ecut denotes the cut-off energy and β the superexponential cut-off index. This steep turn over led to enhanced efforts to lower the energy threshold of the MAGIC telescope. This is described in the chapters 5 and 6.
3.3 Emission of Electromagnetic Radiation from a Pulsar
In a first approximation, the rotating neutron star – the pulsar – consists of a conducting rotating sphere with a co-rotating dipole magnetic field, inclined to the axis of rotation by the angle θ. The magnetosphere surrounding the pulsar is filled with a conducting plasma. A rotating conducting body in a magnetic field is called unipolar inductor, because an 36 3. Pulsars
electric field is induced between the rotation axis and a point on its surface. This was first measured by Faraday in 1831. He found that a spinning disk in a magnetic field induces an electric potential between a contact at the center of the disk and at its perimeter. This effect is described by Faraday’s induction law and included in Maxwell’s equations. An inclined rotating magnetic field is a Hertz Dipole and emits in vacuum the power [52]: 2 6 4 B0 r Ω 2 Lvacuum(θ)= sin θ (3.3) 6c3 with the magnetic field B0 on the pulsar’s surface and the pulsar’s radius r. The pulsar spins with frequency Ω. The spin down luminosity LSD is a function of the observed ˙ dP periodicity P and its derivative P = dt :
dE d 1 P˙ L = rot = IΩ2 = IΩΩ˙ = 4π2I , (3.4) SD dt dt 2 P 3 where I is the moment of inertia. We assume the pulsar’s mass to be mPulsar = 1.4M , its diameter d = 20 km and thus its moment of inertia I = 4.5 1038 m2 kg. For the Crab⊙ 13 · 31 Pulsar with P = 0.033 s and P˙ = 4.23 10 , a spin down luminosity of LSD = 4 10 W · − · is expected6. Only a small fraction of the total spin down luminosity goes in the pulsed radiation. Most of it is carried away in an ultrarelativistic particles and Poynting flux outflow. Combining equation 3.3 and 3.4, the surface magnetic field is found as a function of P and P˙ : B = 3.2 1019 P P˙ G (3.5) · The characteristic age of a pulsar is then computedp using the following expression:
τ τ τ P P P˙ 1 1 τ = dt = dt = P P˙ dt = P dP (3.6) P P˙ P P˙ P P˙ Z0 Z0 Z0 PZ0 with P dP = P P˙ dt and assuming that P P˙ ( B2) be constant over time. Integrating ∝ above equation and assuming that P 2 P 2, it follows: 0 ≪ P τC = , (3.7) 2P˙ For Crab, the surface magnetic field is then7: B = 1.8 1012 G and its characteristic age: · τC = 1240 years. As Crab is the remnant of the supernova in 1054, its real age is around 950 years. τC is an upper limit onto the lifetime of a pulsar, as the initial rotation frequency P0 is not known. It should be remarked that the derivation of equation 3.5 only makes sense if the spin down is dominated by magnetic dipole radiation. Nevertheless, there are other mechanisms for the pulsar to spin down:
1. Gravitational wave radiation.
2. Quadrupole magnetic radiation.
6The whole mankind needs around 1021J per year, so 1 second spin down luminosity could deliver power for about 20 billion years. 7More sophisticated methods (e.g. taking into account that the magnetosphere is filled with a plasma and not a vacuum) lead to a surface magnetic field of around B ≈ 8. · 1012 G [53] 3. Pulsars 37
3. Accretion of surrounding material, e.g. in binary systems.
These mechanisms predict different braking indeces n defined as:
Ω=˙ KΩn (3.8) − with Ω the rotation frequency and Ω˙ its derivative. K is an arbitrary constant, depending n 1 on the surface magnetic field. By differentiating equation 3.8 once and replacing Ω − by Ωn/Ω= Ω˙ /(KΩ), one finds: − ΩΩ¨ n = (3.9) Ω˙ In case of a spin down due to magnetic dipole radiation, n = 3 is expected. In case of the Crab Pulsar, a breaking index of nCrab = 2.51 0.01 is measured, with most young pulsars ± have a breaking index < 3 [54]. The consequences of this is that either
the spin down is not dominated by magnetic dipole radiation and there are additional • effects causing a torque onto the pulsar denoted above [54],
or the factor K in equation 3.8 is not constant due to a changing surface magnetic • field B0 with time or a change of the inclination angle α over time.
The precise way how the spin down luminosity is translated to the observed emitted radi- ation is not well known. The coherent radio emission is believed to originate from above the polar caps. Its production mechanism is thought to be generated by coherent rela- tivistic electrons, similar to a MASER [55]. For the electromagnetic emission of photons with wavelengths between infrared (IR) and X-rays, the emission is not coherent and the emission mechanism is hardly known [56, 57]. All theories about the emission of electro- magnetic radiation from a pulsar are based on charged particles being accelerated in the strong electric field induced by the rotating magnetic field. The electric field E and the electrostatic potential Φ induced by the rotating magnetic field in a pure vacuum is found by solving the Poisson equation ∆Φ=0 for the electric potential Φ within the pulsar’s light cylinder while assuming a vacuum outside and the magnetic field being a dipole co-rotating with the pulsar (e.g. [58]): B R5Ω Φ= s 3 cos2 θ 1 (3.10) 6cr3 − with the neutron star’s radius R and its surface magnetic field Bs. For the Crab Pulsar with B 1012G, R = d/2 10 km and P = 0.033 ms, a potential above the polar cap s ≈ ≈ of Φ 100 1012 V is induced. For particles with unit charge, this corresponds to field ≈ · energies of 100 TeV m c2, injecting electrons from the neutron star’s surface. Electrons ≫ e are accelerated by the electric field and start the particle-radiation cascade resulting in the magnetosphere being filled with a dense plasma. Plasma currents will screen the electric field parallel8 to the magnetic field and thus maintain the co-rotation condition E B = 0. · The γ radiation from pulsars is then produced by charges accelerated in the strong electric field induced by the rotating magnetic field. The main emission mechanisms are: Synchroton emission, curvature emission and inverse compton scattering. The main differ- ence between existing pulsar models consists of the location where the acceleration of the
8Acceleration of electrons and positrons is only possible parallel to the magnetic field lines. If the par- ticles are accelerated perpendicular to the magnetic field lines, they lose quickly their energy due to synchrotron radiation. 38 3. Pulsars
charged particles takes place. As mentioned above, the electric field parallel to the mag- netic field is screened in regions with a plasma density above the Goldreich-Julian (GJ) limit ρGJ(r) [42]: Ω B 1 E 1 ρGJ(r)= = ·Ω r (3.11) 4π ∇ · −2πc 1 | × | − c The screening does not allow particles to be accelerated. Nevertheless, if the plasma density is below the Goldreich-Julian limit, the screening is not effective enough and there is a component of E parallel to B. These regions with low plasma density – called gaps – are believed to exist either above the polar caps, extending to a few pulsar radii, or at large distances from the pulsar, close to the light cylinder at the radius: c rLC = . (3.12) Ω The region called outer gap extends between the null charge surface9 and the last open field line out to the light cylinder. An extension of the polar cap to the outer magnetosphere along the null charge surface – the slot gap model – was introduced later to overcome some of the shortcomings of the polar cap model (e.g. the small pulse width of the predicted pulse profile, which contradicts the observations). Figure 3.2 shows schematically these regions and the null charge surface in the co-rotating frame. Equation 3.13 (from [59]), which assumes a mostly model-independent relation derived from simulations of γ-ray absorption as a result of magnetic pair production in a magnetic dipole field, gives a relation between the pair creation cutoff energy Emax and the height of the emission above the pulsar’s surface r/R0 (with R0 the pulsar’s radius) for a pulsar with surface magnetic field B0 and period P :
3 r 0.1Bcrit r Emax 0.4 P max 1, GeV (3.13) ≈ R B R r 0 ( 0 0 ) 13 with the critical magnetic field Bcrit = 4.4 10 G. If one measures pulsating γ-rays with · an energy above Emax, one can thus derive a lower limit for the height r above the pulsar’s surface where the emission takes place. In chapter 7 this relation will be used to constrain the emission height. In the following sections, the main pulsar models will be presented.
3.3.1 Polar Cap and Slot Gap Model The polar cap and slot gap model are related, thus both will be discussed in the same section:
Polar Cap Model The region above the polar cap was first proposed in [43, 60, 61, 62] as a location of particle acceleration. A gap is formed, where the density is below ρGJ. Depending on the surface temperature of the neutron star, there are different mechanisms explaining the formation of the gap. Electrons are released from the surface of the neutron star if the surface temperature exceeds the electron thermal emission temperature and are accelerated by the electric field induced by the rotating inclined magnetic dipole. As derived above, in case of the Crab
9The null charge surface is the area for which is Ω · B = 0. It separates the positive and negative co-rotating charges. 3. Pulsars 39
Pulsar, potential drops of up to 100 1012V are induced in the polar cap region, accelerating · electrons to Γ-factors up to Γ= E/mc2 108. In these models (called space-charge limited ≈ flow models (SCLF)) (e.g. [63]), the charge density at the surface of the pulsar equals the 3 Goldreich-Julian one. The charge density ρ(r) decreases as r− . Thus, the accelerating electric field E is zero at the surface, but increases with larger radii and decreasing plasma k density ρ(r) < ρGJ(r) for r larger than the neutron star’s radius [63]. If the surface temperature is below the thermal emission temperature, a vacuum gap will be also formed. Thus, the parallel component of the electric field E is not short out in the plasma. Accelerated charged particles will start an electromagnetick pair cascade. In these so-called vacuum gap models as well as in the SCLF models, the accelerating electric field will be screened because of the charged particles produced in the onset of the electromagnetic pair cascade [63]. Absorption mechanisms like photon splitting and magnetic pair creation inhibit γ-rays with high energies to leave the polar cap area. This efficient absorption leads to a steep cut-off of the emitted γ-ray energy of super exponential shape. For the Crab Pulsar, the model predicted cut-off lies between 1-10 GeV [32]. In general, polar cap models predict rather narrow peaks in the γ-ray pulse profile [64], due to the small emission angles.
Slot Gap Model: An extension of the polar cap model model, the slot gap model, predicts wider emission beams, needed to match the wide pulse peaks observed in γ-rays. The polar cap model was extended to higher altitudes along the last closed field lines [65, 66]. Their potential as high energy γ-ray emission site, however, has only been explored recently [67]. The most recent slot gap models [32, 64, 68] account for caustic emission, which takes into account relativistic effects like aberration and consider time of flight and phase delays, leading to a staggering of γ-rays from different altitudes within the pulsar’s magnetosphere and thus forming the characteristic pulse profile. Also the initial frame dragging (Lense Thirring effect) is considered, leading to an increase of the size of the polar cap region and thus to wider peaks in the predicted pulse profiles.
For both models, the polar cap and the slot gap model, the observed emission is believed to be produced at one single pole. The main pulse P1 and the inter pulse P2 are observed when the co-rotating hollow cone beam enters the observer’s field of view and when it leaves again. The emission in between in the so called bridge comes from the insight of the cone. Due to the rotation, the absorption efficiency of the magnetic field is different for the main and the inter pulse [69], stronger for the leading peak forming the main pulse and weaker for the trailing peak forming the inter pulse. Therefore, the cut-off of the main pulse is expected to be at lower energies than the one of the inter pulse. Hints for this behavior was observed with EGRET in case of the Crab Pulsar [2]. In figure 3.8, recent flux predictions from K. Hirotani [53] and A. Harding [32] for the slot gap model are compared. The flux predicted in [53] has a flux peak value which is a factor 33 lower than the one predicted in [32] and is the same factor below the observed EGRET flux measurements [2]. The main differences between the two predictions lies in the derivation of the electric field E which accelerates the electrons. Harding finds a stronger k electric field component parallel to the magnetic field than Hirotani. The thus derived Γe factor10 of the primary electrons is about factor 33 larger and the derived spectrum fits the measured data.
10 E 2 Γe = mec 40 3. Pulsars
Figure 3.8: Slot gap model total pulsed spectrum predictions from Harding [32] (left) and Hirotani [53] (right). The dashed and solid lines in the later denote the flux predictions for different viewing angles ζ.
3.3.2 Outer Gap Model In the outer gap model, the acceleration of the charged particles takes place far out in the pulsar’s magnetosphere, between the null charge surface and the last open field line, out to the light cylinder, displayed in figure 3.2. It was first proposed in [70, 71] as a region within the pulsar’s magnetosphere where acceleration takes place. This gap is formed because of particles escaping through the light cylinder are not replaced fast enough by particles from below and the local plasma density falls below the GJ density ρGJ. For the Crab Pulsar, 8 1 the electric field parallel to the magnetic field can reach around E 2.55 10 V m− k ≈ · in this region, accelerating charged particles [53]. The γ-rays in the outer gap are either produced by the upscattering of softer photons (infrared/X-rays) or by curvature radiation. As in case of the polar cap model, the γ-rays above an energy threshold of some GeV will be absorbed, but not due to magnetic pair creation, because the magnetic field strength is not sufficient enough. In the outer gap, the absorption is caused by pair production with either infrared or X-ray photons:
+ γHE + γLE e e−. (3.14) → + The produced e e−-pairs are accelerated in the field again, and will upscatter softer pho- tons. The absorption results in a γ-ray spectral cut-off of exponential shape, with the cut-off energy at a few GeV or tens of GeV in case of the Crab Pulsar. The large emission angle of the outer gap has as a natural consequence the broad γ-ray pulses of the pulse profile. The photons in the main and the inter pulse originate from the same magnetic hemisphere. The main peak is produced when the hollow cone enters the line of sight, the inter pulse when it leaves the line of sight. Furthermore, the bridge emission comes from the inside of the hollow cone. Since the emission in P1 and P2 can originate from different regions within the outer gap, different spectra might be observed for P1 and P2. A tentative outer gap model spectrum of a young pulsar is shown in figure 3.9 [33]. It is composed of several components. At the lowest energies, the flux is dominated by the synchroton radiation of the electrons, only surmounted in a small energy region by the thermal emission from the pulsar’s surface. The main part of the γ-ray emission is due to curvature radiation. Another component is visible in the VHE γ-ray region: The inverse compton scattered γ-rays. It is debated whether these γ-rays escape through the light cylinder or if they are completely absorbed [53, 72]. From the experimental point of view 3. Pulsars 41
Figure 3.9: The theoretical phase-averaged spectrum for a typical young γ-ray pulsar de- duced for the outer gap model. Solid lines show the curvature spectrum (CR), the synchrotron emission (Sy) and the thermal radiation from the surface (kT). The dashed curve gives the TeV pulsed spectrum from inverse Compton Scat- tering (CS) of the synchroton photons on the primary e±. Figure and caption adapted from [33]. it should be remarked that no TeV observation has revealed a pulsating signal from pulsars in the last 20 years, indicating a strong absorption of the inverse Compton component. In case of the Crab Pulsar, flux predictions agree acceptably with measurements done with EGRET, even in phase resolved spectra. See figure 3.10.
3.4 Conclusion
Pulsars are laboratories where relativistic magnetohydrodynamics and huge magnetic fields can be investigated. Pulsating electromagnetic emission has been measured from a few thousands of pulsars in the last 40 years. Seven pulsars are even known to emit γ-radiation above 1 GeV. The mechanism leading to this emission is poorly known. Current theo- ries assume the radiation being related to relativistic electrons, accelerated by the induced electric field in so-called gaps within the pulsar’s magnetosphere. The two main model, the polar cap (extended to the slot gap) and the outer gap model assume different regions where the particle acceleration takes place. The measurement of gamma rays at the highest energies would allow to probe these pulsar models. Depending on the emission region, different fluxes, phase diagram mor- phologies and spectral cut-offs are predicted. Due to their particle nature, gamma rays are ideal messengers of the mechanisms within the magnetosphere leading to their emission: They do not coherently interfere and thus any reaction on their way from the pulsar to Earth would lead to their absorption. If one measures pulsating γ-rays from Crab, it is thus certain that they were produced within the pulsar’s light cylinder. 42 3. Pulsars
Figure 3.10: Phase-averaged (top left) and phase-resolved (others) spectrum of the pulsed emission from the Crab pulsar. The thin solid, dashed, and dotted curves denote the un-absorbed photon fluxes of primary, secondary, and tertiary components, respectively, while the thick red solid one presents the spectrum to be observed, including absorption along the line of sight. Interstellar absorption is not considered. Data points are from [2] http://www.sron.nl/divisions/hea/kuiper/data.html. In the top left panel, upper limits by ground-based observations are also plotted above 50 GeV. Figure and caption adapted from [53]. 3. Pulsars 43
The observation of pulsed γ-rays above a certain energy, however, turned out to be more difficult than expected. Satellite experiments were too small to measure the low expected fluxes and ground based experiments like MAGIC had their energy threshold on a too high level. In chapters 5 and 6, I will describe the observations of the Crab Pulsar with a new trigger that lowered the energy threshold of the MAGIC telescope by a factor of 2, resulting in the discovery of pulsed γ-rays above 25 GeV.
4 Observation Technique and Data Analysis
Figure 4.1: The MAGIC telescope during observations.
The first successful observation of cosmic γ-rays dates back to the 1960s when the Vela satellite1 measured γ-rays from gamma ray bursts. Direct measurements of γ-rays have to be performed from space because the Earth’s atmosphere will efficiently absorb γ-rays before they reach the ground. If the γ-ray energy is high enough, however, the incident particle will start an air shower in the atmosphere, with secondary particles and radiation even reaching the surface of the Earth. By measuring these secondary particles, γ-rays can be detected indirectly, using the atmosphere as a giant calorimeter. The following chapter is dedicated to the observational techniques used in the measure- ments of cosmic γ-rays. The first section includes the description of so-called direct mea- surements which are performed on board of satellite experiments like EGRET [73], AGILE (Astrorivelatore Gamma ad Immagini ultra LEggero) [74] or FGST (Fermi Gamma-ray Space Telescope, renamed from “Glast”) [75]. Then I will discuss the ground based indirect detection of γ-rays by measuring the Cherenkov light produced in the electromagnetic air shower induced by a γ-ray, in particular the imaging air Cherenkov technique, where the
1This military satellite was launched to monitor the “Treaty Banning Nuclear Weapon Tests In The Atmosphere, In Outer Space And Under Water”. 46 4. Observation Technique and Data Analysis
Cherenkov light is projected by a mirror on the focal plane, where the photons are registered by sensitive photodetectors (section 4.2). In the following section 4.3, the MAGIC tele- scope (shown during observation in figure 4.1) on the Canary Island La Palma is described, its set-up, its data acquisition, standard trigger2 and calibration system. Furthermore, I will describe the data analysis software in section 4.4. Special emphasis will be placed on a new image algorithms I developed and implemented as a part of this thesis, which allows to analyse shower images with the lowest yet measured energies down to 25 GeV. The new algorithm is more robust against fluctuations of the shower images induced by fluctuations of the night sky background (NSB) light. In the last section 4.5, the methods and algorithms used in the analysis of pulsed signals will be described.
4.1 Direct Measurement of γ-Rays with Satellites
Experiments measuring the primary γ-rays outside the Earth’s atmosphere generally use techniques known from particle physics. The experiments in space have to measure the energy of the γ-ray, its direction and have to distinguish the photon from other particles3. One technique used e.g. in the LAT detector [76] onboard of FGST is pair creation, illustrated in figure 4.2. The incoming γ-ray creates a pair in the thick pair creation foil. The traces of the electron and the positron are recorded by the particle tracking detectors, thus allowing a reconstruction of the incoming γ-ray direction. A calorimeter + at the bottom of the detector then measures the energy of the e e− pair and thus the γ-ray energy. An anticoincidence shielding prevents triggers from charged particles and thus suppresses the background denoted above. Their energy range starts from a MeV ≈ with a higher threshold at a few tens of GeV, overlapping with the lowest energy threshold 4 of the MAGIC telescope (see chapter 5). In case of FGST , the angular resolution is < 3.5◦ at 100 MeV and < 0.15◦ for energies above 10 GeV.
4.2 Imaging Air Cherenkov Telescopes (IACTs)
Cosmic ray particles like protons or γ-rays above a certain threshold of a few GeV hitting the Earth’s atmosphere start an air shower, similar to the cascade formed in a calorimeter in particle physics experiments. An electromagnetic shower (initiated by a VHE γ-ray or by a relativistic electron) shows a characteristic development: an exponential increase of the number of shower particles at the beginning, and an even faster decrease after reaching its maximum. At the beginning, secondary particles are created by pair production and bremsstrahlung, which will create further particles. If the energy of those particles falls below a critical limit, where ionization losses dominate over the creation of new particles, this multiplication process dies out and the shower development stops. Energy losses for charged particles include ionization, bremsstrahlung and to a small amount Cherenkov radiation. Photons on the other hand loose energy by the photoelectric effect, Compton scattering and pair creation at energies above 1 MeV. The particle-radiation cascade forms until the shower particles reach the critical energies. For charged particles in air, this energy is at 83 MeV/Z, with Z the charge of the particle, when the energy loss by ≈ 2The new sum trigger, which was developed as a part of this thesis, will be described in the separate chapter 5. 3For example charged cosmic rays, which are 104 − 105 times more abundant than γ-rays. 4FGST is able to measure γ-rays up to 300 GeV. Even though the detector is much more sensitive than EGRET, its detection area is around 1.3 m2. All known cosmic VHE γ-ray sources show a decreasing flux above 100 GeV. Thus, satellite experiments are flux-limited to measure γ-rays in the VHE range. 4. Observation Technique and Data Analysis 47
γ
Anticoincidence shield
conversion foil
particle tracking detector
e+ e-
calorimeter
+ Figure 4.2: The e e− pair creation technique used onboard the space borne FGST experi- ment to detect γ-rays. The incoming γ-ray creates in the conversion foil a pair + of e e−, which are tracked by the particle tracking detector. In the calorime- ter, their energy is measured. With this setup, one can reconstruct the γ-ray energy and its incoming direction. 48 4. Observation Technique and Data Analysis
ionization dominates the bremsstrahlung and the exponential growth dies out. In case of photons, the critical energy occurs at energies of 5 MeV when the Compton radiation ≈ starts to dominate over pair creation. In case a charged cosmic ray particle hits molecules or atoms in the atmosphere, a shower will develop as well. Most of the particles produced in this cascade are pions. Neutral pions will most probably decay into two γ-rays and thus initiate the above described electromag- netic cascade. Further shower particles are kaons and antiprotons as well as muons, which can reach the ground without decaying before. A hadronic air shower therefore consists of a shower core, built up from nucleons and mesons, of electromagnetic subshowers induced by neutral pion decays and of non-interacting muons (and neutrinos). A distinct feature of these hadronic shower is the large lateral distribution of the shower particles (due to the significant transverse momentum transfer in hadronic interactions) compared to the more compact electromagnetic showers. In figure 4.3, electromagnetic and hadronic air showers are schematically displayed. In figure 4.4, the traces of the simulated shower particles for γ-rays and protons at dif- ferent energies are shown. Gamma ray initiated showers show a smaller lateral distribution than hadronic showers. At the low energies simulated in these figures, hardly a shower particle reaches the ground level. Thus, the measurement of shower particles will only work for γ-rays with energies above a few hundreds of GeV. The particles in the shower, however, move with velocities faster than the speed of light c in the atmosphere vparticle > cn = n , with the refraction index n and thus emit Cherenkov radiation [77]. The light emission results from the re-orientation of the instantaneous electric dipoles induced by the particle in the medium. Because the particle passes "super- luminally" through the medium, the electromagnetic impulses originated in the different trajectory elements are in phase, and a net field can be produced at distant locations. The geometric picture for this follows from Huygens’ principle (see figure 4.5). A shock-wave is created behind the particle. The wavefront of the radiation propagates at a fixed angle θ, with 1 cos θ = . (4.1) βn
vparticle with β = c the relative velocity of the particle. Due to the change of the density of air with altitude the refraction index decreases with height h as:
h/h0 n(h)=1+ n0e− (4.2) with h 7.1 km and n 0.00029. According to equation 4.1, the Cherenkov angle 0 ≈ 0 ≈ changes as well. The higher the radiating particle, the smaller the angle. The Cherenkov light builds up a wave front in front of the particle with a thickness of only a few nanosec- 9 onds (10− s). The first measurement of Cherenkov radiation from an air shower succeeded in 1953 by using a mirror in a ton reflecting the Cherenkov light onto a photomultiplier tube (PMT) [78].
Today, in ground based VHE γ-ray astronomy, three main techniques dominate:
Sampling of the shower particles, e.g. in the TIBET [81] or MILAGRO [82] experi- • ments. To do so, water-filled pools or scintillators are used. If a relativistic shower particle hits the water, it irradiates Cherenkov photons which are measured by pho- tomultipliers on the ground of the pools. These experiments have large observation solid angles of nearly 2π and can be run day and night resulting in a duty cycle of 4. Observation Technique and Data Analysis 49
Primary γ Cosmic Ray (p, He, Fe,...)
γ
Atmospheric Nucleus e− πo γ EM Shower π+ e− + π+ e+ e γ −+ ν γ Nucleons, K, etc. µ e− Atmospheric Nucleus o e− π + − π− e e + γ e+ e γ µ+ e− EM Shower
+ γ e − + µ νµ e γ e− γ e+ EM Shower e− e− e+
EM Shower
(a) Gamma-ray initiated shower (b) charged cosmic ray initiated shower
Figure 4.3: Schematics of an electromagnetic (a) and a hadronic air shower (b). See text for details. Images provided by S. Commichau [79]
almost 100%. Nevertheless, their energy threshold is at several hundreds of GeV and the discrimination of γ-rays against the hadronic background is not very efficient.
Measuring the photons in the Air Cherenkov light cone, as it was done for instance • in the Celeste [49] or STACEE [83] experiments. These kind of experiments used modified solar towers at night to efficiently measure the Cherenkov photons sampled over a large area. They had a very low energy threshold of around 50 GeV. Nev- ertheless, the discrimination of γ-ray showers against the hadronic background was rather poor.
Imaging Technique, e.g. Whipple, MAGIC, H.E.S.S., VERITAS, CANGAROO. The • Cherenkov photons from the air shower are focussed by a mirror onto a camera con- sisting of light detectors, for instance PMTs or Geiger Mode Avalanche Photodiodes (G-APD). Thus, one achieves an image of the extended air shower. Particles hitting the atmosphere parallel to the telescope’s axis will point towards the center of the camera. Due to the changing Cherenkov angle θ with height, Cherenkov photons produced at higher altitudes will be imaged closer to the center than those produced at lower altitudes. As mentioned above, the duration of the air Cherenkov flash is 2 3 ns. Using fast PMTs and trigger electronics therefore allows to measure the − Cherenkov photons over the stable background light coming from stars and other NSB light sources. A schematics of this technique is displayed in figure 4.6. This technique allows better γ - background separation than the two above mentioned techniques, because with the imaging air Cherenkov method, one gains information about the development of the whole shower. The image of an air shower initiated by γ-rays differs in shape, extension and other parameters from the ones initiated by hadrons. The MAGIC telescope being the IACT with the lowest energy threshold, has a trig- ger threshold of 55 GeV, using its standard trigger system. This threshold is ≈ comparable with the ones from the non-imaging air Cherenkov telescopes. 50 4. Observation Technique and Data Analysis
(a) 50 GeV proton (b) 50 GeV γ-ray
25 km 100 GeV gamma-ray
0 -5 km 0 +5 km
(c) 200 GeV proton (d) 100 GeV γ-ray
Figure 4.4: The traces of the particles in air showers triggered by γ-rays and protons. The electromagnetic shower initiated by γ-rays is more compact than the hadronic shower and its lateral distribution is smaller. The red traces are from leptons and photons, the violet traces from hadrons and the green ones from muons. [80] 4. Observation Technique and Data Analysis 51
c ∆ n t wavefront
θ
electron
β c ∆t
Figure 4.5: Propagation of Cherenkov light, derived from Huygens’ principle. The electron moving horizontally polarises the crossed medium. If the electron moves with a velocity larger than the local speed of light, a coherent wave is emitted by the relaxating dipoles, called Cherenkov light.
In the following sections, the IACT MAGIC will be described in detail.
4.3 The MAGIC Telescope
The MAGIC telescope with its 17 m tessellated mirror is currently the largest single dish IACT in the world [3]. It was designed in 1998 to measure γ-rays in the previously un- explored energy region between 30 GeV and 300 GeV [84]. Engineering work started in 2001, commissioning in 2003 and regular data taking in fall 2004. A major upgrade of the readout system was performed in 2006/2007 when the sampling frequency was increased from 300 MHz to 2 GHz, see section 4.3.4. In autumn 2007, a new additional trigger system was installed, reducing the trigger threshold from 55 GeV to 25 GeV. This trigger will ≈ ≈ be described in chapter 5. The telescope is situated on the Roque de los Muchachos on the Canary Island La Palma at 2245 m above sea level (28◦45′N, 17◦53′W), which is considered as one of the best sites for night time observations. Because of the high altitude, the telescope is closer to the shower maximum and thus less Cherenkov photons are absorbed by the atmosphere. These specifications – large mirror, highly efficient photodetectors, fast electronics and high altitude – lead to the lowest energy threshold of all current IACTs.
4.3.1 Mirrors, Frame and Drive An important design goal of the MAGIC telescope is its light-weight structure needed for fast repositioning in case of Gamma Ray Burst (GRB) alerts, triggered by space exper- iments like Swift [17]. The low weight was achieved by building the frame from carbon fiber epoxy composite tubes. The resulting total weight is as low as 60 tons, while the frame weighs even only 25 tons. The telescope stands on horizontal rails and uses an altitude-azimuth (alt-az) mount. The three servo motors of the drive system [85] provide a repositioning of 180◦ in azimuth of less than 25 seconds [84], with a tracking accuracy of < 0.022◦. The maximal repositioning time between any two alt-az positions is < 40 seconds. To account for the bending of the light weight structure, a pointing correction model is used and regularly calibrated. To measure a possible mispointing, a so-called star guider camera is used, consisting of a CCD camera in the center of the mirror, measuring the 52 4. Observation Technique and Data Analysis
Primary particle (1 TeV) Top of atmosphere
First interaction with nuclei of atmosphere at about 20 km height
Cherenkov light emission θ = 0.29o under characteristic angleθ
Camera (cleaned event)
θ = 0.86o
~ 5 km
~ 20 m
θ = 1.03o ~8 km a.s.l. Camera
Cherenkov Telescope
Reflector
Figure 4.6: Schematics of the imaging technique. An image of the extended air shower is recorded by measuring the emitted Cherenkov light with an IACT. Image credits: S. Commichau. 4. Observation Technique and Data Analysis 53
direct light from a star and its reflection onto the camera plane, relative to 7 reference LEDs which are also located in the camera plane. This setup can also be used later in the analysis to correct a mispointing by software. The mirror of the telescope has a parabolic shape and consists of 964 49.5 cm 49.5 cm × mirror elements, with a total area of 236 m2. Dew and ice formation is prevented by equipping each element with an internal heating system. The averaged reflectivity in the wavelength range of Cherenkov light (300 nm – 650 nm) is about 85%. The parabolic shape (instead of a spherical shape used in smaller IACTs) of the mirror prevents the timing in- formation of photons arriving isochronously at the mirror plane. Thus, timing information of the Cherenkov light wave front is preserved, allowing for a short trigger coincidence window, which is important to increase the sensitivity to low energy γ-ray showers over the NSB, see chapter 5. Furthermore, the time development of the Cherenkov light can later be used in the analysis to distinguish between γ-ray and hadronic showers. To prevent the telescope to defocus due to bending, a so-called Active Mirror Control (AMC) [86] is used. The focussing is measured in terms of the Point Spread Function (PSF) which describes the defocussing of a point-like light source (e.g. a star or a distant flashlight). Using the AMC, a PSF of < 0.1◦ is achieved which is smaller than the size of a single PMT. To ensure a fast refocussing at different azimuth and altitude angles, look-up tables (LUT) are used, which are regularly calibrated using stars at different positions. Furthermore, the AMC allows different focal lengths. Because the shower maximum of γ-ray showers usually are at a height of 10 km above sea level, the telescope is in normal operation mode focussed to this distance.
4.3.2 Camera
As light detectors, the PMTs ET9116 are used. These devices have a quantum efficiency of nearly 25%, further enhanced by 20% (relative) by coating the surface with a wavelength shifting lacquer. The camera is located at the focus point of the telescope. It has a diameter of 1.5 m and consists of 577 pixels. The inner camera is built out of 397 smaller 25 mm diameter PMTs, the outer camera out of 180 larger 39 mm PMTs, respectively5. With the mirror’s focal length of 17 m, the camera covers a field of view (FOV) of ≈ 3.5◦, allowing the observation of modestly extended objects. The inner pixels have a FOV of 0.1◦, the outer ones 0.2◦ [87]. The finer pixelization of the inner camera was chosen because the images of low energy γ-rays are compact and close to the camera center (80% of the Cherenkov photons of a 25-35 GeV γ-ray shower lie on a ring between 0.25 0.8 , − ◦ see figure 5.3 in chapter 5). The shower of higher energy γ-ray showers, however, develop further down into the atmosphere. Thus, the Cherenkov photons from the showers tail are imaged at a larger distance from the camera center. To contain the full shower in the camera, the large diameter is needed. Among the inner pixels, the central one is not used for the measurements of Cherenkov light, but to record the optical signal of the source being observed. For the observation of pulsars, this has the advantage to co-measure their optical pulsation. The roundish PMTs are arranged in a hexagonal structure, see figure 4.7. The PMT tubes only cover 50% of the camera plane. To capture the light hitting in between pixels, so-called Winston cones (non-imaging light collectors) are installed. Next to their nearly perfect light collection efficiency for photons reflected by the mirror, they also prevent NSB photons with an incident angle > 35◦ to reach the PMTs. The signal leaving the PMTs are AC6 coupled preamplified. In the transmitter board
5In this work, “PMT” and “pixel” is used as synonyms. 6Capacitive coupling of the PMT signals, filtering the DC component out. 54 4. Observation Technique and Data Analysis
69cm
114cm
Figure 4.7: The layout of the MAGIC camera. The smaller PMT of the inner camera are used to get a better sampling of lower energy γ-ray shower images, which rather lie in the inner camera. within the camera, the signals are translated by means of a Vertical Cavity Surface Emitting Laser (VCSEL) into optical signal, then transmitted by optical fibers to the counting house. Using optical instead of analog transmission shields the signal against noise and prevents its dispersion. In the counting house, the signals are back-transformed into electrical signals by a photodiode and then split in two parts. One part is sent to the trigger system (section 4.3.3 and chapter 5), the other to the FADC (Flash Analog Digital Converter) system (section 4.3.4).
4.3.3 The MAGIC Standard Trigger Because it is not possible to register the complete data stream from the 577 pixels sampled at 2 GHz, a Cherenkov telescope needs a trigger. A trigger pre-selects images of extended air showers. Because the Cherenkov photons of γ-ray showers arrive in a short time window of 2-3 ns, an ideal trigger uses a coincidence window of this order of magnitude. The discrimination level should be higher than the possible fluctuations of the NSB to prevent accidental triggers. Furthermore, certain preselections on the shape of a shower can be applied to distinguish γ-ray showers from hadronic ones. Due to their greater abundance of 104 105, the great bulk of recorded events come from hadronic shower, however. − 4. Observation Technique and Data Analysis 55
The MAGIC standard trigger [88] consists of three Levels:
Level 0 (LT0): Uses the signals from the innermost 325 pixels (displayed in figure • 4.8). If the signal in a PMT reaches the discriminator threshold, a logical signal is produced.
Level 1 (LT1): In this step, a next neighbor (NN) logic is applied to the digital sig- • nals from LT0. This is done because images of γ-ray showers are rather compact. In the standard operation mode, 4 NN pixels above the LT0 discriminator threshold are required to fire LT1. Possible settings can be between 2NN and 5NN configurations.
Level 2 (LT2): Based on Field Programmable Gate Arrays (FPGA), the level • 2 trigger allows complicated pattern recognition algorithms. During standard data taking, LT2 is not being used, i.e. it consists of a simple OR between the different macrocells displayed in figure 4.8.
In this thesis, the term Standard Trigger refers to LT0 and LT1 with a 4NN configuration7. The discriminator thresholds are set at 6 photo electrons (phe) and the time window to 6 ns. The calibration of the trigger system is performed several times per year. In this procedure, the calibration pulses (see section 4.3.5) are used to calibrate the discrimination level in phe and to adjust the relative arrival times of neighboring pixels. Depending on the NSB, especially during observation in moonlight, twilight or in a FOV with bright stars, the LT0 discrimination thresholds are automatically adjusted by the Individual Pixel Rate Control (IPRC). Typical individual pixel rates (LT0 rates) are between 100 MHz and 500 MHz. The total standard trigger (LT1) rate in moonless clear nights is between 200-300 Hz.
4.3.4 The Data Acquisition System If the trigger fires, it will start the Data Acquisition Queue (DAQ). Since January 2007, the signals are digitized with a Multiplexed (MUX) FADC system, increasing the sampling frequency from 300 MHz to 2 GHz. Multiplexing is used to reduce the number of readout channels and thus provides a cost effective FADC system. It is possible because even at the highest possible trigger frequencies of 2 kHz, the duty cycle of the digitizer is still very low8 [90]. As described later in section 4.4, this allows to exploit the timing resolution provided by the PMTs of < 1 ns and increases the sensitivity of the telescope by about a factor of 2. In figure 4.9, the DAQ is schematically displayed.
4.3.5 The Calibration System The number of Cherenkov photons emitted by an air shower initiated by a γ-ray is propor- tional to the γ-ray energy. Thus, it is important to know the conversion from the number of Cherenkov photons hitting the mirror to the ADC counts recorded by the data acquisi- tion. In the MAGIC calibration system [91], three different methods are implemented to determine this conversion. All three make use of three very fast (3-4 ns) and high light output (109 photons per pulse) LEDs. For calibrating in different wavelengths, colored LEDs are used: 460 nm (blue), 370 nm (UV), 520 nm (green). They are situated in the
7In [89], 3NN was used as well. As we realized then, noise triggers coming from PMT after pulses (see section 5.3) will dominate the low energy events. Furthermore, with a 3NN configuration, roundish shower images are preselected, making γ-hadron separation less efficient. 8One event is 25 ns long, corresponding to 50 FADC slices 56 4. Observation Technique and Data Analysis
Figure 4.8: The trigger macro cells in the inner camera. The xNN groups used in LT1 lie each within the same macro cell. A trigger is raised if one xNN group within one cell reaches the trigger condition. middle of the reflector. Per pulse, each pixel receives between 50-400 phe, depending on the color of the LED. Because the light flux from the LEDs depends on the temperature and thus can vary, there are different calibration methods:
Blind Pixel Method: One PMT is being ’blinded’ with a foil which has a well known attenuation factor of around 1/1000 in order to attenuate the bright light from the LED pulser. Thus, one can determine the absolute LED light flux at the camera by recording the attenuated phe spectrum, identifying the peak coming from the Gaussian electronic noise and the first phe peak and its variance and performing a Poissonian fit to the phe
Winston Cones Receiver Board FADC Optical Optical splitter delay PMT Receiver Optical Link
Receiver MUX controller
Camera Receiver Trigger
Receiver
Figure 4.9: The readout scheme of the MAGIC telescope. The signals from Cherenkov photons measured with the PMTs are transmitted with optical fibers over 60 m to the counting house. The optical signals are split. One part of the signal goes to the trigger, the other to the FADC. 4. Observation Technique and Data Analysis 57
Figure 4.10: Calibration system of the MAGIC telescope. The pulsar box located in the center of the mirror contains fast and bright LEDs. The light current from the LED can be monitored by the PIN Diode or the “Blind Pixel”, where the latter is located in the camera plane. See text for details. Image credit: S. Commichau spectrum.
PIN Diode Method: With a calibrated PIN Diode at a distance of 1.5 m from the LED, the absolute light flux is measured.
Excess Noise Factor: In this method, the absolute light flux is not determined, but should be stable within the time the conversion is determined. The Excess Noise Factor (F-Factor) is defined as: σ2 σ2 F =1+ 1 − 0 , (4.3) µ2 µ2 1 − 0 2 2 where σi denotes the (Poissonian) variance of the ith phe peak, and µi its mean value in FADC counts. For i = 0, these are the values for the (Gaussian) electronic noise (pedestal) distribution. Using the relation Var(Q) = 1 F , as deduced in [92], with Q¯ the PMT’s Q¯ m¯ phe · anode output charge, Var(Q) its variance and m¯ phe the number of photoelectrons hitting the first dynode (all values are for N¯ number of photons hitting the photocathode), one can derive the following formula:
Q¯2 m¯ phe = F (4.4) σ2 σ2 1 − 0 Thus, one can determine the number of phe produced at the photocathode. Furthermore, if the photon detection efficiency p of the PMT is known, the number of incident photons ¯ m¯ phe is N = p . The first two methods provide a conversion from the light hitting the PMT to FADC counts, the third a conversion from phe produced at the first dynode of the PMT to FADC counts. Assuming that the light absorption of the winston cones and the plexiglass and the quantum efficiency (QE) of the PMT is constant, these procedures are equivalent. The set-up of the calibration system is schematically displayed in figure 4.10. In the current setup, all three methods are working. Nevertheless, in the further analysis (see section 4.4.1), only the F-factor method is used. 58 4. Observation Technique and Data Analysis
4.3.6 The Central Pixel The PMT in the center of the MAGIC camera is a standard MAGIC PMT, as they are used for the rest of the inner camera. However, its preamplifier is modified [93] to integrate visible light within 500 ns. In a further modification [94], the readout of the Central Pixel was changed such that the MAGIC readout system digitizes the signal of the Central Pixel each time the telescope is triggered. This allows to observe the optical emission from point-like objects (diameter < 0.1◦) in parallel to its γ-ray emission. If a pulsar with a known ephemeris is observed, this setup can be used to check the accuracy of the event time stamps [94]. During the observation of the Crab Pulsar, we recorded the signal from the central pixel as well. See chapter 6.6.
4.3.7 Pyroscope To measure the percentage of clouds covering the night sky, a pyroscope is used. This instrument measures the infrared radiation reflected by clouds between 8 14 µm. If the − infrared spectrum follows the Planck Spectrum, the temperature of the radiating body can be computed from the integral value measured by the pyroscope. It has a FOV of 2◦ and points to the same direction as MAGIC. If a cloud enters its FOV, the sky temperature changes by a small value (typically > 1 K). Thus, the measured sky temperature by the pyroscope can be used to determine the cloud coverage in the FOV. Unfortunately, the sky temperature also depends on zenith angle, air temperature and humidity. Using a calibration depending on these values, the so-called cloudiness is determined from the sky temperature, the zenith angle, air temperature and humidity during the observation. While a low value of cloudiness means good observation conditions, a high value does not necessarily mean bad conditions. However, a fluctuating cloudiness is a strong hint for clouds passing through. One can thus exclude data taken under suboptimal conditions.
4.3.8 The Rubidium and the GPS Clock
To measure pulsating γ-rays with periodicities around 30 Hz and the substructure of the pulse profile, the time stamp of each event has to be as precise as < 50 µs. This accuracy is easily achieved with a rubidium clock having a precision of 200 ns. Due to the unavoidable drift of the rubidium clock, it is synchronized with a GPS clock pulse. The time stamps (time and date) of the event is then recorded in UTC (universal time).
4.4 Data Analysis
The data being recorded by the DAQ at the telescope site in La Palma contains mainly the 50 recorded FADC slices of each PMT for each triggered event. Additionally, calibration and pedestal events are stored. These kind of events are each recorded at the beginning of a new datataking run and in addition interleaved with the data with 25 Hz. These interleaved events allow to adjust the calibration constants in the offline analysis, which can change due to temperature changes and other influences. Furthermore, technical information from the subsystems (AMC, drive system, camera, weather station, cloud monitor, star guider etc.) are stored in separate files. The recorded data is written to a local RAID system and to tapes to be shipped to the external datacenter, where the standard analysis chain described below is applied. This chain displayed in figure 4.11 consists of the following steps: 4. Observation Technique and Data Analysis 59
charge: 4phe, arrival time: 3.5ns PMT 1
charge: 1phe, arrival time: 5.5ns PMT 2 image cleaning and determination of image charge: 2phe, arrival time: 2.5ns PMT 3 parameters
charge: 2phe, arrival time: 6.5ns PMT 4
PMT 5 extraction signal charge: 3phe, arrival time: 4.0ns
PMT 6 charge: 3phe, arrival time: 3.0ns
Figure 4.11: Schematics of the analysis chain. The charge and the arrival time of PMT signals are extracted. In the second step, the image cleaning is performed, where PMTs containing only NSB noise are excluded from the further analysis. Then, the image parameters are determined. The red line denotes the shower image’s main axis.
Signal extraction: The PMT signals measured in FADC units are calibrated. • This includes the absolute calibration of the charge content measured in phe and the relative pulse arrival time calibration. In this step, for each pixel, the arrival time and the charge of the signal are stored for further analysis (section 4.4.1).
Image cleaning: Due to the NSB light, the recorded shower images are noisy. • The main task of the image cleaning step is to remove pixel signals containing only noise. To distinguish pixels with NSB signals from the ones containing also signals from Cherenkov photons, an image cleaning algorithm is applied, described in section 4.4.2. The cleaning algorithm takes advantage of the fact that the images of extended air showers are compact in extension and time distribution. The resulting images are parameterized. The most important parameters are the ones introduced by Hillas, see section 4.4.3, but also additional parameters are computed, for example those related to the time development of the shower image.
Gamma-Hadron separation and energy estimation: Nearly all events sur- • viving the image cleaning are those containing images of air showers. Nevertheless, a large fraction of these events are of hadronic origin. In the standard analysis, a Random Forest (RF) algorithm based on the image parameters is used to classify each event and a parameter, called HADRONNESS, is computed. This parameter is used to distinguish γ like events from hadronic ones, see section 4.4.4. In a further step, the energy of each event and its incoming direction will be estimated.
Flux determination: If a significant excess of signal events remains after the • classification, the γ-ray flux is derived. To do so, the dead time reduced effective observation time is deduced and the energy dependent collection area (see equation 4.12) is computed, using γ-ray MC simulations. The detector and analysis (cut) effi- ciencies are included in the calculation of the collection area. The detector efficiency below 300 GeV and thus the collection area are strongly energy dependent. The source γ-ray spectrum9 depends on the energy, often following a power law:
α dN E − f(E)= = f (4.5) dA dE dt 0 · E norm 9The spectrum corresponds to the number of γ-ray photons that arrive within a certain energy interval dE, area dA and time dt on Earth 60 4. Observation Technique and Data Analysis
with the spectral index α, f0 the flux normalization and Enorm an arbitrary normal- ization energy. Due to the energy resolution of below 40%, the determined spectra have to be unfolded. See section 4.4.5.
Additional analysis steps, software and algorithms I developed and used for the analysis of pulsars will be described in section 4.5. In the following sections, the standard analysis chain, the modifications done by me and those that were used in the presented analysis will be explained in greater detail.
4.4.1 Extraction of the FADC Signals In the standard analysis, the calibration program callisto first computes the conversion factor from FADC slices to the phe produced at the first dynode of the PMT photocathode, using the F-factor method. To do so, the recorded calibration pulses described in section 4.3.5 are used. They are stored as special events (“calibration events”). The electronic offset of the signal is computed from pedestal events, which are random triggers and contain only NSB. From the mean arrival time of the calibration pulses, the relative timing between different pixels is calibrated. To extract the digitized signal, several methods can be used [91]. In the standard analysis, signals are extracted using the digital filter method [90]. In this method, a pulse shape is assumed for cosmic rays, MC and calibration events. The extracted charge is then the sum of the FADC slices weighed with the pulse shape value. If one assumes that the shape stays constant for different signal amplitudes, one achieves a high signal/noise ratio and a low bias of the estimated charge content. Further details can be found in [91].
4.4.2 Image Cleaning In the signal extraction step, the following values are computed in each pixel: charge (in phe), the arrival time (in ns) and the root mean square (rms) of the pedestal distribution to estimate the noise. The task of the image cleaning is now to identify the images of the Cherenkov showers and thus distinguish them from signals coming from the NSB light. Several studies were made to improve the image cleaning [94, 95, 96]. An efficient algorithm is crucial if one is interested in γ-rays below 100 GeV, where the Cherenkov light output becomes small, or for the data taken in bright nights, where the NSB can become orders of magnitudes larger.
4.4.2.1 Standard Image Cleaning In the image cleaning, one distinguishes between shower core pixels and the ones from the shower boundary. Core pixel have to fulfill stronger criteria than the boundary ones, meaning for example that their charge content has to be above a threshold of 10 phe, while the charge in boundary pixels only has to be e.g. 5 phe. However, as their name says, boundary pixels have to be close to a core pixel or another boundary pixel to be considered as such. A group of core and boundary pixel belonging to the same connected group is called island. In general, the images of γ-ray showers are expected to consist of one single island, while the hadronic ones can also consist of several islands. This is explained by the formation of sub-showers in the development of the extended air shower. However, for low energies, the Cherenkov distribution on ground of a γ-ray shower will be inhomogeneous because of Poissonian fluctuations of the Cherenkov light output and due to the fact that in the shower there are only a few particles producing Cherenkov radiation. Thus, it is highly probable that those showers consist of several islands as well. 4. Observation Technique and Data Analysis 61
Before the installation of the MUX10 FADC system, the standard procedure was to use a threshold of 10 phe for core pixels, demanding that each core pixel has a neighbor fulfilling the same condition. Pixels close to a core or a boundary pixel with charge > 5 phe become boundary pixels. Furthermore, the number of cleaning rings can be chosen. In the standard analysis, the number of rings is set to 1, meaning that all pixels at a distance further than one pixel from a core pixel will be removed from the image. This setting provides a robust and stable analysis, well suited for the analysis of data taken under different conditions. However, the analysis threshold will be rather high at above 80 GeV, significantly higher than the trigger threshold of around 55 GeV. A major improvement of the image cleaning was achieved by [94] and [97] using the time information of the signals as well. Here, a pixel becomes a core pixel when its charge is above a certain threshold and its arrival time within a small time window defined by the arrival times of the signals in the neighboring pixels. Then, the mean arrival time weighed by the charge of all core pixels is computed. A boundary pixel will be accepted as such, if its charge is above the boundary pixel threshold and its arrival time within a small time window of the core pixel mean arrival time. Since the installation of the MUX FADC with its higher time resolution of 0.5 ns, the time information is used in one of the standard settings:
cleaning with the thresholds (10/5) phe (core/boundary) and no timing information • is used, or
cleaning with (6/3) phe and (4.5/1.5) ns time windows for core and boundary pixels, • respectively.
With these last settings, the analysis threshold approaches the standard trigger threshold. In case of data taken in sum trigger mode (see chapter 5), the analysis threshold is then around 45 GeV (for a trigger threshold of 25 GeV). In this case, a lower cleaning threshold is required. Unfortunately, the standard cleaning only allows cleaning levels of around (4.5/2) phe. Reducing the cleaning levels even further will increase the analysis threshold. This is due to the fact that for a too small cleaning level, the computation of the mean arrival time of the core pixels gets dominated by fluctuations of the NSB with an arbitrary time stamp. The tight time windows need to be increased, resulting in noisier images. The algorithm can be slightly improved by computing the mean arrival time only of the core pixel lying within the same connected cluster.
4.4.2.2 Sum Image Cleaning
The sum image cleaning algorithm also takes advantage of the fact that images of extended air showers are compact in time and extension. A pixel will be marked as core, if
it lies within a group of 2, 3 or 4NN with the clipped sum11 of the group’s pixel • signals is above the corresponding group’s threshold.
the arrival time of the pixel signal is within a small time window of the mean arrival • time of the corresponding group.
10multiplexed 11“Clipped” means here that the amplitude of the signal is limited at a certain threshold. This prevents large accidental signals (e.g. from afterpulses) to dominate a NN group. The clipping and cleaning levels were intensively tested. 62 4. Observation Technique and Data Analysis
Figure 4.12: A few of the NN groups used in the sum image cleaning. blue: 2NN, green: 3NN, red: 4NN. 4. Observation Technique and Data Analysis 63
The idea to form NN groups and to perform a correlated cleaning was already proposed and implemented earlier [97], see section 4.4.2.3. In figure 4.12, a few NN groups are displayed. In the new algorithm presented here, the clipped sum of the NN groups is formed. The following parameters (for x 2, 3, 4 ) can be set: ∈ { } sumthreshxNN: summed xNN cleaning threshold [phe] clipxNN: clipping level xNN [phe] fWindowxNN: xNN time window [ns]
For convenience, the parameters set by the user were changed to fSumThreshxNNPerPixel, where x is a value between 2 and 4. Together with the core pixel cleaning level (fCleanLvl1), the sum trigger threshold for each group is computed with:
sumThreshxNN = fSumThreshxNNPerPixel * fCleanLvl1.
This allows to set only the core and boundary cleaning levels and the sum cleaning levels will then be deduced with “reasonable” (default) settings for fSumThreshxNNPerPixel, without having to care for the details of the algorithm. An expert seeking to improve the xNN group cleaning levels, however, has all freedom to do so by varying fSumThreshxNNPerPixel. In figures 4.13 - 4.16, a comparison between the standard and the sum image cleaning is shown. Generally, the sum image cleaning recovers more pixels and thus the content of the shower, measured in phe and called SIZE (see also section 4.4.3), is larger. Figure 4.13 shows an example of an event, which the standard image cleaning fails to recover. Figure 4.17 shows that the energy threshold after cleaning12 for the sum image cleaning lies at 25 GeV, while the standard cleaning has a threshold of 40 GeV. The new sum image cleaning was successfully applied in the analysis of the Crab Pulsar, see chapter 6. A further analysis was applied to the Crab Nebula signal [98]. It was found that the sum image cleaning shows a better performance at low energies and the same performance as the standard cleaning at high energies. Furthermore, the after cleaning rate in nights with a large amount of NSB is more stable and more signal events can be recovered.
4.4.2.3 Calibration Image Cleaning A similar concept as the sum image cleaning was already described in [97]. In this algo- rithm, the extraction and the image cleaning is performed within the same step. Before a signal is extracted from the FADC signal, the algorithm searches for signals in the surround- ing pixels. Only if a signal in x neighboring pixels above a certain threshold depending on the number of pixels in the group is found, it will be extracted. This algorithm also takes full advantage of the fact that the images are compact and that the Cherenkov shower arrives within a small time window. The xNN thresholds were found by considering the probability to find an accidental trigger from NSB above the tested threshold for each group. As in the case of the sum image cleaning, the cleaning level per pixel can be dras- tically reduced. The sum image cleaning and the calibration image cleaning show a similar performance, considering random triggers from NSB and an analysis threshold (both 25 GeV for obser- vations with the sum trigger). A detailed description of the algorithm can be found in [97]. A direct comparison between the sum image cleaning and the calibration image cleaning
12The energy threshold is defined as the peak of the MC γ-ray energy distribution after image cleaning, for a γ-ray source following a power law spectrum with spectral index 2.6. 64 4. Observation Technique and Data Analysis
MHCamera MHCamera MHCamera Mean 1.529 Mean 4.945 RMS 1.286 Mean 0 RMS 2.002 RMS 0 9.4 9.4 8.8 8.8 8.3 8.3 7.7 7.7 7.1 7.1 6.5 6.5 5.9 5.9 5.3 5.3 4.7 4.7 4.1 4.1 3.5 3.5 2.9 2.9 2.4 2.4 1.8 1.8 1.2 1.2 0.6 0.6 ° ° 0.60 0.0 0.60 0.0 189mm 0.60 189mm 189mm
(a) MC, uncleaned image, (b) standard image clean- (c) sum image cleaning, energy: 33 GeV ing, no surviving pixel SIZE = 34 phe
Figure 4.13: An image of a MC γ-ray event with energy 33 GeV. While the standard image cleaning with cleaning levels (4.5/3) phe fails, the sum image cleaning recovers the image. Note that the red line in the cleaned image denotes the main axis of the shower image.
MHCamera MHCamera MHCamera Mean 1.627 Mean 8.876 Mean 7.882 RMS 1.807 RMS 5.544 RMS 5.68
21 21 21 20 20 20 19 19 19 17 17 17 16 16 16 15 15 15 13 13 13 12 12 12 11 11 11 9 9 9 8 8 8 7 7 7 5 5 5 4 4 4 3 3 3 1 1 1 ° ° ° 0.60 0 0.60 0 0.60 0 189mm 189mm 189mm
(a) MC, uncleaned image, (b) standard image clean- (c) sum image cleaning, energy: 35 GeV ing, SIZE = 106 phe SIZE = 110 phe
Figure 4.14: MC γ-ray, the energy is 35 GeV, about the same energy as the one displayed in figure 4.13. However, the measured phe content (called SIZE) is 110 phe. Thus, the standard and the sum image cleaning recover the image.
MHCamera MHCamera MHCamera Mean 1.054 Mean 9.633 Mean 8.052 RMS 1.268 RMS 3.538 RMS 4.473
15.2 15.2 15.2 14.2 14.2 14.2 13.3 13.3 13.3 12.3 12.3 12.3 11.4 11.4 11.4 10.4 10.4 10.4 9.5 9.5 9.5 8.5 8.5 8.5 7.6 7.6 7.6 6.6 6.6 6.6 5.7 5.7 5.7 4.7 4.7 4.7 3.8 3.8 3.8 2.8 2.8 2.8 1.9 1.9 1.9 0.9 0.9 0.9 ° ° ° 0.60 0.0 0.60 0.0 0.60 0.0 189mm 189mm 189mm
(a) data, uncleaned image (b) standard image clean- (c) sum image cleaning, ing, SIZE = 38 phe SIZE = 48 phe
Figure 4.15: An image of a recorded event. Both the standard and the sum image cleaning recover the image. 4. Observation Technique and Data Analysis 65
MHCamera MHCamera MHCamera Mean 1.096 Mean 5.543 Mean 4.65 RMS 1.132 RMS 1.521 RMS 1.757
7.0 7.0 7.0 6.6 6.5 6.5 6.2 6.1 6.1 5.7 5.7 5.7 5.3 5.2 5.2 4.8 4.8 4.8 4.4 4.4 4.4 4.0 3.9 3.9 3.5 3.5 3.5 3.1 3.1 3.1 2.6 2.6 2.6 2.2 2.2 2.2 1.8 1.7 1.7 1.3 1.3 1.3 0.9 0.9 0.9 0.4 0.4 0.4 ° ° ° 0.60 0.0 0.60 0.0 0.60 0.0 189mm 189mm 189mm
(a) data, uncleaned image (b) standard image clean- (c) sum image cleaning, ing, SIZE = 22 phe SIZE = 32 phe
Figure 4.16: A recorded event. Both the standard and the sum image cleaning recover the image. Due to the lower cleaning threshold of the sum image cleaning, it recovers more pixels and thus the phe content (SIZE) of the image is higher.
7000 standard image cleaning
6000 sum image cleaning
5000
4000 counts
3000
2000
1000 10 20 30 40 50 60 70 80 90 energy [GeV]
Figure 4.17: The energy distribution of the sum and the standard image cleaning for γ- ray MC and sum trigger simulations, see section 5.4. The energy threshold defined as the peak of the distribution of the sum image cleaning is at the trigger threshold of 25 GeV. The cleaning thresholds were chosen such that the number of pedestal event images surviving the image cleaning is below 1%. 66 4. Observation Technique and Data Analysis
in the analysis of the Crab Pulsar shows that both provide the same sensitivity towards low energy γ-rays. For the detection of pulsed γ-rays, both were used and compared. Similar results were achieved.
4.4.3 Image Parameters After the cleaning step, the image is parameterized, illustrated in figure 4.18. The so-called Hillas parameters [99] turn out to be a robust parameterization. They correspond to 1st, 2nd and 3rd moments along the main and minor axis of the image shower:
SIZE: The 1st moment of the shower image. It is the sum of the signals of the • surviving pixels. It can be computed from the main island of the image only, or also include other islands.
WIDTH: The 2nd moment of the image along its minor axis. It is a measure of • the transversal development of the shower.
LENGTH: The 2nd moment of the image along its major axis. It is a measure of • the longitudinal development of the shower.
M3LONG: The 3rd moment of the image along its major axis. Measures the • direction of the shower. This parameter is important to distinguish the shower head from its tail.
Further parameters were introduced. Those include:
MEANX, MEANY: The shower’s center of gravity. • CONC: The fraction of the charge contained in the two brightest pixels. • LEAKAGE: The fraction of the total charge that is contained within the outermost • ring of the camera. It is a measure for the amount of the shower not contained within the camera.
DIST: The distance between the center of gravity and the source position. It is • highly correlated with the impact parameter13 of the air shower.
ALPHA: The angle between the line connecting the center of gravity of the shower • with the source position and the major axis of the ellipse. The image of γ-ray showers coming from the source points towards the source position in the camera, thus having a small value of ALPHA. For the very low energy γ-ray showers analyzed in this thesis, this was the most important parameter to distinguish γ-rays from background.
Further parameters derived from the time information of the shower were introduced [100]. These are:
TIME GRADIENT: The change of the arrival time along the major image axis. • TIME RMS: The RMS of arrival times of the pixels belonging to the image after • image cleaning.
13The impact parameter is the distance between the telescope’s position and the penetration point of the incident γ-ray direction with the horizontal telescope plane. 4. Observation Technique and Data Analysis 67
32 30 28 26 ALPHA 24 22 20 18 center of LENGTH !eld of view 16 DIST WIDTH 14 COG 12 10 8 6 4 2 0
Figure 4.18: Definition of image parameters, defined for a moment analysis of a shower image in the camera plane.
4.4.4 Event Classification with Random Forest and Estimation of the Energy The great bulk of events triggering the telescope comes from cosmic hadrons. Efficient cuts are therefore needed to separate γ-rays and hadrons and thus to reduce the background. Usually, these cuts are based on the image (and time) parameters, because these parameters are rather robust under changing observation conditions (e.g. different NSB levels, weather changes, clouds) In order to obtain optimal results, these cuts have to be determined in a high dimensional parameter space. In the standard analysis, this task is accomplished by the RF algorithm, based on multidimensional decision trees. The RF is trained with MC γ-rays as signal events. As background, a measured data sample from a position pointing to a region in the sky where no γ-rays are expected (so-called OFF data sample) is used. Each event (background and signal event) is described by a set of (image) parameters forming a vector. A RF consists of a number of independent binary decision trees based on those parameters. The algorithm performs the following steps:
1. A sample of both, signal and background data, is drawn.
2. A random (image) parameter is chosen. The cut in this parameter that minimizes the Gini index14 is applied and thus the data sample is split into two sets, forming two nodes.
3. For each of the two subsets, another random parameter is chosen and the cut applied that minimizes the Gini index.
4. The above step is repeated (the tree is “grown”) until the remaining sample after the cut either only contains events of one kind (either background or signal), or the number of remaining events is below 10.
5. Steps 1-4 are repeated N times. Each repetition forms a random tree. All trees together build the random forest.
14The Gini index measures the node purity and is 0 if it contains only one kind of events and 1 if it contains from both the same amount. 68 4. Observation Technique and Data Analysis
This RF is then used to classify events from a sample containing γ-rays and background events. The classification is based on the HADRONNESS parameter, which is 0 if the event is γ-ray like and 1 for background like events. The HADRONNESS value for a given event is determined according to:
The parameters of the event are fed into the random tree i. • Nh The event ends up in a terminal node. The value hi is computed as: hi = , • Nh+Nγ with Nh and Nγ the number of hadrons and γs in the terminal node, respectively. Step 1 and 2 are repeated for all N trees. • The resulting HADRONNESS h of the event is then: 1 h = h (4.6) N i Xi In the following analysis, a cut in HADRONNESS h depending on SIZE15 is used to separate signal from background. If one is interested to discover a new source, the cut yielding the highest sensitivity should be chosen. A cut that maximises the Q-factor fullfills this condition. This factor is defined as: ǫ (h) Q(h)= γ (4.7) ǫbackground(h) p with ǫ = Nγ (h) the signal cut efficiency where N (h) the number of signal events γ Nγ (total) γ Nbackground(h) surviving the cut in h and ǫbackground(h) = the background cut efficiency Nbackground(total) with Nbackground(h) the number of background events surviving the cut in h. The higher the Q-factor, the better the separation between signal and background. In the standard analysis, the parameter ALPHA is not used in the RF, because the different ALPHA distribution of γ-rays (which are expected to peak at ALPHA= 0) and hadrons (flat distribution) are used to extract the excess events from the data. The energy of an event is also estimated from the image parameters. Here, the parameter SIZE and DIST are the most important ones. Furthermore, the light output of a Cherenkov shower depends on the zenith angle of the shower. Also the shape of the shower and its extension, and therefore WIDTH and LENGTH, change for different energies. To estimate the energy in the MAGIC standard software, a modified version of the RF is used. Instead of separating signal from background, this RF is used to determine the energy an event belongs to. With the optimal set of parameters, an energy resolution of 25% for high energies can be achieved. For the lowest energies at around 25-45 GeV, the energy resolution, however, gets worse and reaches values around 40-50%. Further details on the RF method can be found in [101, 102, 103].
4.4.5 Determination of the Differential Flux After applying the γ-hadron separation, the excess events are determined. To do so, the distribution of an image parameter (typically ALPHA) for data taken from the source (called ON region and containing signal and background events) and data taken from an
15The dependence on SIZE is chosen because for low SIZEs, the images from γ-ray showers and background nearly look the same, thus asking for softer cuts in HADRONNESS than for higher SIZEs where the events can be classified better. 4. Observation Technique and Data Analysis 69
21000 ON Data OFF Data 20500
20000
19500 entries
19000
18500
18000 region Signal Normalisation region Normalisation 0 10 20 30 40 50 60 70 80 90 ALPHA
Figure 4.19: Determination of the number of excess events from the ALPHA distribution. The ON data sample contains γ-rays and background, the OFF sample only background. For ALPHA> 30◦, the two distributions are normalized. The excess events are determined from the difference of the distribution in the signal region, ALPHA< 20◦.
OFF region (containing only background events) are drawn. From MC simulations, a parameter interval is chosen, where no signal is expected. For ALPHA, this is typically ALPHA > 30 . The distributions of ON and OFF events are normalized in this region | | ◦ (displayed in figure 4.19), and the excess events in the signal region defined before extracted according to: Nexcess = NON Fnorm NOFF (4.8) − · bg region NON with Fnorm = bg region the normalization factor in the background interval of the distri- NOFF bution. The significance of the detection can be computed using the assumption that ON and OFF data are independently measured data samples. Thus, the variance of the excess is: Nexcess Nexcess Nσ = = (4.9) 2 2 Vexcess NON + F NOFF norm · Since this formula overestimates the statisticalp significance of the number of excess events, the following formula is used (formula (17) in [104]):
1+ F N N N = √2 N ln norm ON + N ln (1+ F ) OFF σ ON F N + N OFF norm N + N s norm ON OFF ON OFF (4.10) Once the excess events are determined, a differential energy spectrum is computed: dN f(E)= (4.11) dE dA dt which describes the number of photons within the energy interval [E, E + dE] per time t and area A. 70 4. Observation Technique and Data Analysis
The spectrum cannot be determined directly. Thus, the data is binned in estimated energy and the number of excess events in each bin determined. This number is divided by the effective observation time teff (which is the observation time corrected for the dead time) and by the mean collection area in this bin. The collection area Aeff(E) is computed as:
2π rmax
Aeff(E,θ)= ǫγ(E,θ,r) r dr dφ (4.12) φZ=0 r=0Z with θ the zenith angle, r the impact distance of the incoming photon and φ its azimuth angle. The collection area is determined from MC γ-rays in bins of energy Ei and zenith angle θj: N after cuts Nγ (Ei,θj, rk) 2 2 Aeff(Ei,θj)= π total rk,max rk,min (4.13) N (Ei,θj, r ) − k=1 γ k X The resulting γ-ray flux in each energy bin Ei is then computed with:
Nexcess(Ei,θj) f(Ei)= f(Ei,θj)= (4.14) ∆Ej teff(θj) Aeff(Ei,θj) Xj Xj where the sum is performed over all observed θj bins.
4.4.5.1 Unfolding Methods
Due to the limited and biased energy resolution of the detector, the derived energy spectrum is generally different from the source spectrum. To correct for these effects, the spectrum needs to be unfolded. These effects are described by the migration matrix M which projects the original energy bins to reconstructed energy bins and is deduced from MC γ-rays:
Yi = MijSj (4.15) Xj where Yi is the number of measured events with an estimated mean energy in bin i and Sj the number of events in a true energy bin j. A simple deconvolution, meaning solving the linear equations given by equation 4.15 is not an ideal solution, because the energy bins of Y and S are strongly correlated and its values fluctuate, Y = Y +∆Y . Furthermore, in general cases, the number of estimated and true energy bins are not the same, and the matrix M therefore not square. The equations 4.15 are then solved by minimizing the summed squared differences χ0(S; Y ) between Y and MS, weighed by the covariance matrix of Y and S [105]. More sophisticated methods use regularization, meaning that certain constraints on the true distribution Sj are posed, e.g. that Sj or its derivative to be smoothly distributed. Minimizing w χ2(S; Y )= χ2(S; Y )+ Reg(S) (4.16) 2 0 2 with Reg(S) measuring the smoothness of S instead of χ0 alone, takes care of the regular- ization. The weights w are used to allow different relative weighs between the two terms. In the MARS package, several methods are implemented choosing different weights w and 4. Observation Technique and Data Analysis 71
regularizations Reg: Tikhonov [106], Bertero [107] and Schmelling [108]. In this work, the method of Tikhonov is used. The regularization in this method is given by:
d2S 2 Reg = 2 (4.17) dE j Xj d2S The derivative dE2 is either computed numerically or by using a spline interpolation be- 2 tween the points Sj = S(Ej). The χ (S; Y ) is minimized as a function of S, given the measurements Y .
Forward Unfolding Another approach is to assume a parameterized prior distribution Sj(θ1, ...θn) depending on a few parameters θ1, ...θn describing the assumed model and then minimize the squared difference between M S and Y . This method is called forward × unfolding and is used in this thesis to determine the cut-off value of the pulsed spectrum, described in section 4.5.1 and applied in section 6.8.
4.5 Analysis of Periodic Signals from Pulsars
In this work, signals from the Crab source which emits a periodic signal with a frequency of 30 Hz is investigated. The analysis of these periodic sources allow for additional analysis ≈ steps that are not included in the standard chain. An important new parameter is called PHASE φ and is assigned according to the arrival time of the γ-ray at the telescope. It describes the rotational phase of the pulsar, an observer at the position of the sun would observe at a certain time t. During one rotation of the pulsar, φ goes from 0 to 1. The position of the Sun and not the Earth is chosen as a inertial reference. Otherwise, the phase φ would not only depend on the rotation of the pulsar but also on the rotation of the Earth. The drawback of this definition is the need to transform the arrival times of the γ-ray candidates to the solar barycenter (the center of mass of the solar system). The phase of the rotating and decelerating pulsar is computed as: 1 φ(t)= ν (t t )+ ν˙ (t t )2 + ... (4.18) 0 · − 0 2 0 · − 0 where t0 denotes an arbitrary time with defined phase φ0 = φ(t = t0) = 0. In case of Crab, φ0 is defined as the arrival phase of the radio main pulse. ν0 is the rotational frequency of the pulsar at the time t and ν˙ = d ν(t) its derivative, needed due to the deceleration 0 0 dt |t=t0 of the pulsar’s rotation. Additional Taylor series terms can be included. For the Crab pulsar, where a monthly radio ephemeris listing the values for t0, ν0 and ν˙0 is available [109] and ν¨ and the following Taylor terms are small, this is not necessary. In this analysis, the program TEMPO [110] is used to perform the transformation from the telescope’s time frame tobs (measured in UTC times) to the solar barycentric arrival 16 time tb [111] : r n (r n)2 r 2 t = tobs + · + · − | | +∆tE +∆tS (4.19) b c 2cd with n the unit vector in the direction of the pulsar and r the vector connecting the solar barycenter with the telescope’s position. The first two terms perform the geometrical (Newtonian) transformation from the telescope system to the solar barycenter. ∆tE is the general relativistic (“Einstein”) delay caused by the gravitational redshift and time dilation
16The delay caused by dispersion used in [111] is for γ-rays naturally 0. 72 4. Observation Technique and Data Analysis
Component Name Phase Interval φ Leading Wing 1 LW1 0.88 0.94 − Peak 1 P1 0.94 0.04 − Trailing Wing 1 TW1 0.04 0.14 − Bridge Bridge 0.14 0.25 − Leading Wing 2 LW2 0.25 0.32 − Peak 2 P2 0.32 0.43 − Trailing Wing 2 TW2 0.43 0.52 − Offpulse OP 0.52 0.88 − Table 4.1: Crab Pulsar phase interval definition [112]. In figure 4.20, the phase regions are drawn.
mainly because of the motion of the Earth, and ∆tS the Shapiro delay, caused by the curved spacetime of the solar system. For Crab, the main and inter pulse P1 and P2 are for all energies, from Radio wavelengths to γ-rays at the same phase position. Thus, a sensitive test to decide if the measured phases φ are equally distributed or not, takes advantage of this fact by assuming that the two peaks are in VHE γ-rays at the same phase position as well. In [112], the phase regions denoted in table 4.1 and displayed in figure 4.20 were defined. Studying the light curve measured by EGRET at the highest energies shows that most of the emission lies within the phase regions defined as P1 and P2. If one assumes that this remains the same for the energy range of MAGIC, computing the significance of the excess found in P1+P2 together using formula 4.10 has a high sensitivity for pulsed emission. As ON phase region,
φON [0, 0.04] [0.94, 1] [0.32, 0.43] (4.20) ∈ ∪ ∪ is used, corresponding to the P1 and P2 phase regions in table 4.1 and in figure 4.20. As OFF phase region, it is reasonable to use the offpulse phase region (OP in table 4.1):
φOFF [0.52, 0.88] (4.21) ∈ The normalization factor is then computed from the ratio between these regions. This test is appropriate if one assumes that the positions of P1 and P2 do not change for different energies. As it can be seen in figure 3.5, this is the case for Crab for the whole electromagnetic energy range between Radio wavelengths up to the γ-rays measured by EGRET. This assumption was already made in [3, 94], where the upper limit on the pulsed VHE γ-ray emission was determined. Further periodicity tests are the H-Test [113], the Kuiper test [114], or a χ2-test of the pulse profile.
4.5.1 Determination of the Cut-Off Energy of the Pulsed γ-Ray Emission The total γ-ray flux in the phase region P1 and P2 as well as the phase resolved γ-ray flux in each phase region defined for the Crab Pulsar measurements by EGRET, follows a power law spectrum above 100 MeV - 6 GeV:
α dN E − f ,EGRET(E; f , α)= = f (4.22) γ 0 dE dt dA 0 E norm 4. Observation Technique and Data Analysis 73
350 TW1 LW2 TW2 LW1 TW1 LW2 TW2 LW1 P2 OP Bridge OP P1 Bridge P2 P1 300
250
200
150 counts [a.u.]
100
50
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Phase φ
Figure 4.20: The phase diagram of the Crab Pulsar measured by EGRET for energies above 100 MeV. The phase regions defined in table 4.1 are depicted. with spectral index α = 2.022 0.014. This spectrum is expected to turn over at an energy ± above a few or a few tens of GeV and to show a cut-off of exponential or super exponential shape, described by:
α β dN E − (E/Ecut) f (E; f , α, Ecut, β)= = f e− (4.23) γ 0 dE dt dA 0 E · norm is used. Ecut denotes the cut-off energy and the parameter β defines the shape of the cut-off. For β = 1, the cut-off is purely exponential. The measurements of EGRET do not allow to determine the cut-off energy and the shape of the turn over of the pulsed emission from Crab. However, these two parameters can be determined from the MAGIC data described in chapter 6. To achieve a good sampling of the cut-off shape, the MAGIC data were subdivided into exc bins of estimated energy. In each bin i, the number of excess events Ni with statistical exc error ∆Ni is derived from the data. Using MC γ-rays, the effective area Ai(E) (after all cuts) for each estimated energy bin i is determined. The number of excess events ˆ exc Ni (f0, α, Ecut, β), is estimated by folding the spectrum fγ(E; f0, α, Ecut, β) (equation 4.23) with the effective area in each bin i:
exc Nˆ (f , α, Ecut, β)= teff f (E; f , α, Ecut, β) A (E) dE (4.24) i 0 · γ 0 · i Z To determine the parameters f0, α, Ecut and β, the least squared difference between ˆ exc exc predicted number of excess events Ni (f0, α, Ecut, β) and Ni is minimized. In the fit, the spectrum points measured with EGRET and COMPTEL above 100 MeV are combined with the MAGIC measurements above 25 GeV: 2 2 N exc Nˆ exc(f , α, E , β) (f f (E ; f , α, Ecut, β) i i 0 cut χ2(f , α, E , β)= j − γ j 0 + − 0 cut (∆f )2 (∆N exc)2 HE j VHE i j,X i,X (4.25) with fj the measured flux at the energy Ej. The first sum goes over the HE flux points measured with COMPTEL and EGRET, the second sum over the VHE excess events in SIZE bins measured with MAGIC. The χ2 is minimized using ROOT’s17 TMinuit package. In chapter 6, f0, α, Ecut and β are determined. As one expects, the power law parameters
17ROOT is an objected oriented analysis framework, often used in high energy physics experiments. See http://root.cern.ch 74 4. Observation Technique and Data Analysis
f0 and α are mostly determined by the measurements of EGRET, while the cut-off para- meters Ecut and β by the measurements of MAGIC. The method described here to compute the cut-off energy of the pulsed spectrum has several advantages over the unfolding method described above in section 4.4.5.1. It is a robust method in terms of stability against statistical fluctuations. However, an important limitation is that for this method, the shape of the cut-off needs to be parameterized, here 2 by Ecut and β. From the χ value alone, it might be difficult to judge if the cut-off really has the assumed shape. Furthermore, this method is prone to possible systematic errors of the flux measurements by EGRET and to a mismatch of the energy scale calibration of MAGIC and EGRET. To overcome this disadvantages and for consistency checks, the spectrum of the pulsed emission is determined by the measurements of MAGIC alone, using the forward unfolding method with a power law and the unfolding method by Tikhonov. These methods are described in section 6.9. 5 The New Sum Trigger
Figure 5.1: The sum trigger as it is installed on place in the MAGIC counting house on the Roque de los Muchachos on La Palma. A large amount of cables was needed to adjust the relative time delay before summing the signals up. Image by Takayuki Saito.
Gamma rays from various cosmic sources have been measured with the MAGIC telescope above an (analysis) threshold of 80 GeV. One type of source – Pulsars – were not discovered before 2007, however. Even though the set-up described in chapter 4 provides the lowest trigger threshold of all current IACTs, the sharp predicted cut-off of the pulsed emission prevented to measure a significant amount of γ-rays from any pulsar. In this chapter, I will describe the idea of the sum trigger which is a new trigger system designed and installed by a small group within the MAGIC collaboration in 2006/07. As a main feature, the new trigger provides an energy threshold which is about a factor of 2 76 5. The New Sum Trigger
lower than the standard trigger. In section 5.1, I will depict several ideas of new trigger systems that could lead to a lower energy threshold. The basic idea of the sum trigger is explained in section 5.2. In section 5.3, PMT noise called afterpulses, which made the implementation of the sum trigger more difficult, are depicted. The simulations will be described in 5.4. Section 5.5 then covers the electronics built in Munich and installed on La Palma, and section 5.6 the calibration of the trigger threshold. In section 5.7, the performance of the standard trigger and the sum trigger will be compared. Figure 5.1 shows a part of the sum trigger installed in the counting house at the telescope site on La Palma. The sum trigger was successfully used in the observations of the Crab Pulsar that led to its detection in VHE γ-rays above 25 GeV. This will be described in chapter 6.
5.1 Reaching the Design Goal of the MAGIC Telescope
One of the main design goals of the MAGIC Telescope was to achieve an energy threshold as low as a few tens of GeV. Early plans even aimed at an energy threshold of 10 GeV [115], and thus have a sensitivity overlapping in energy with satellite experiments like EGRET. The components of the telescope were designed in order to reach an energy trigger threshold as low as possible (e.g. large mirrors, high QE PMTs, fast signal sampling). With the set- up described in chapter 4, however, the resulting trigger threshold is at a rather high energy of 50 60 GeV. One main point is that the MAGIC standard trigger as described in section − 4.3.3 is not sensitive enough for the low energy showers below 50 GeV. Reasons for this are the following: The standard trigger requests the signals from a group of compact pixels to be above • the trigger threshold. The Cherenkov light of low energy showers, however, is often distributed over more pixels which are not necessarily connected. The standard trigger uses rather large effective coincidence times between pixels of • 4-8 ns. This prevents the LT0 discriminator threshold to be lowered below 6 phe as otherwise triggers coming from Poissonian fluctuations in the NSB will dominate, resulting in huge trigger rates. The DAQ of the telescope, however, can only handle data rates below 1.4 2 kHz. − At low energies, roundish shower images have a higher probability to trigger the • standard trigger. These images have a random orientation image parameter ALPHA due to the compact next neighbor condition. Since this parameter is important to distinguish γ–rays from hadronic background events for low energies, the background discrimination is rather inefficient. It has already been tried at the beginning of the telescope operation to lower the energy threshold using special trigger configurations. The following ideas were proposed: Accept only triggers from events lying on a donut shaped ring around the center of • the camera between 0.2◦ and 0.8◦ [116]. This idea is based on the fact that more than 80% of the γ-ray Cherenkov shower images with energies below 50 GeV lie in this ring. The ring structure was implemented later in the topology of the sum trigger, see section 5.4.2. Use a 5NN trigger setting. This allows to lower the LT0 discrimination threshold. • MC simulations showed that the sum trigger finally implemented and described in this chapter, however, is more sensitive to low energy γ-rays. 5. The New Sum Trigger 77
Based on groups of several pixels (for example 8-16 pixels), a trigger is raised if at • least m out of the N pixel reach the discriminator threshold. This trigger (used for example in the H.E.S.S. experiment [117]) regards the variety of image shapes found for γ-ray showers. Sum trigger. This idea was first proposed in [118], but not consequently followed. • This trigger will be described in the next sections. Improvement of the analysis software, in particular the image cleaning. Add image • parameters that were deduced from the time information of the shower image. In the following sections, the basic idea of the sum trigger is explained, its features described and the problem of the intrinsic PMT noise (so-called afterpulses) discussed. Then, the performance of the sum trigger is compared with the MAGIC standard trigger.
5.2 The Sum Trigger: The Basic Idea
Studying images of low energy Monte Carlo γ–ray events (displayed in figure 5.2) reveals the following properties: the Cherenkov light arrives within a small time window of around 2 ns at the Camera • plane, the spatial distribution of the Cherenkov light has large fluctuations and is often • not distributed within only a few PMT, as it was assumed for the MAGIC standard trigger configuration and 85% of the Cherenkov light is distributed within a ring between 0.15 and 0.85 , • ◦ ◦ relative to the source position (figure 5.3). Based on these simulations, we decided to implement an analog sum trigger. The main component of this trigger is to sum up the analog PMT signals within one of a set of overlapping patches of N connected PMTs. The DAQ trigger is raised when the summed signal in one patch reaches the sum discriminator threshold. Compared to the standard trigger, this concept has the following features: There is a free choice on the shape or the distribution of the Cherenkov photons • within one patch. A small “natural” coincidence window of the order of a few ns. This can be changed • by varying the PMT signal’s full width half maximum (FWHM) before summing up the signals. Also small signals of a PMT below the standard trigger’s discriminator threshold • contribute to the trigger signal. Because the shower signal is distributed over several loosly connected PMTs, the • summed signal will show a better signal to noise ratio than a single PMT signal. A reduced sensitivity to Poissonian fluctuations of the NSB light. • As these are only qualitative arguments, I implemented the trigger simulation for different patch shapes and overlap regions into the existing detector simulation program. The different parameters (sum trigger discrimination level, patch shape, patch size and topology, signal shape and timing) were optimized with MC trigger simulations (see section 5.4). 78 5. The New Sum Trigger
49 22 46 21 43 19 40 18 37 17 34 15 31 14 28 12 25 11 22 10 19 8 15 7 12 6 9 4 6 3 3 2 ° ° 0.60 0 0.60 0 189mm 189mm
(a) 21 GeV γ-ray (b) 22 GeV γ-ray
28 26 25 23 21 19 18 16 14 13 11 9 7 6 4 2 ° 0.60 0 189mm
(c) 24 GeV γ-ray
Figure 5.2: The distribution of Cherenkov photons (black dots) of simulated γ-ray in the Camera of the MAGIC telescope. Note that the Cherenkov photons cover a large area containing several PMTs within the camera plane. 5. The New Sum Trigger 79
Figure 5.3: The radial averaged distribution of Cherenkov photons for simulated γ-ray showers with initial energy between 20 and 30 GeV. 85% of all Photons lie on a ring between 0.15◦ - 0.85◦. The trigger area therefore should cover this ring.
5.3 Photomultiplier Tubes Afterpulses
Compared to other photodetectors like Hybrid Photomultiplier Tubes (HPD) or G-APDs, PMTs show large intrinsic noise, called afterpulses. The origin of these pulses is not completely understood. They might originate in electrons accumulating at the first dynode. From time to time the electrons are released and thus generate a large signal by hitting the anode. Another reason for afterpulsing might be due to the imperfect vacuum sealing of the tubes. While producing the PMTs, water molecules may remain inside the vacuum tube. By the acceleration of the phe between photocathode and first dynode, they are able + to split the molecules and produce H and OH− ions. These ions are accelerated between first dynode and the photocathode. By hitting the photocathode, they can produce a large amount of phe amplified by the normal multiplication process within the PMT and thus produce large signals. The time delay of the afterpulses depends on the dimension of the tubes and on the voltage between the photocathode and first dynode, and is of the order of µs [119]. In figure 5.5, the measured and simulated rate as a function of the pulse height for a PMT exposed to NSB is displayed. The rate at pulse heights < 6 phe is dominated by NSB. Afterpulses become important above 6-7 phe, and have a rate of 100 Hz for a pulse height above 30 phe. The trigger rate of a “naive” sum trigger, which sums up the signals of a few PMTs without taking care for afterpulses, would be completely dominated by afterpulses. This could only be compensated by a rather high trigger threshold and thus reduce the sensitivity towards low energy γ-ray showers. Several ideas came up to prevent afterpulses from triggering. First we considered a veto for high pulses or demanding for at least 2 large pulses in one trigger patch. This turned out to be rather complicated and unpractical. In the end, a simple and effective solution to solve the afterpulse problem was found: Before 80 5. The New Sum Trigger
Figure 5.4: Strong signals are clipped before summed up. the summation, the analog PMT signals are clipped at a certain pulse height1, displayed in figure 5.4. This significantly reduces the contributions to the trigger signal of afterpulses. The sensitivity for γ–rays, however, will be reduced as well, in particular at the lowest energies.
5.4 Implementation of the Sum Trigger and Afterpulses into the Detector Simulation
The MC simulation software used in the MAGIC collaboration consists of three different programs. The extended atmospheric air showers are simulated with CORSIKA [121]. In the original CORSIKA code, detailed simulations of an air shower initiated by photons, protons or nucleii have been implemented. The program tracks all particles created in the avalanche, taking into account the reactions of the shower particles with the atmo- spheric molecules and atoms, the Earth’s magnetic field and also allows to apply different atmospheric models. In later versions of CORSIKA, the process of Cherenkov radiation emitted by relativistic charged particles (electrons, positrons, muons and hadrons) was im- plemented, but not the atmospheric scattering and absorption of the produced Cherenkov light. The detector simulation of MAGIC consists of the reflector and the camera program. The reflector program uses the simulated Cherenkov photons from CORSIKA and simu- lates the imaging of the produced Cherenkov photons by the mirror onto the camera plane, including aberration, reflectivity losses and scattering. Furthermore, it tries to adapt for atmospheric extinction and scattering of the Cherenkov light, which is not included in CORSIKA yet. The photons hitting the camera plane are then processed by the camera program. Based on the output of the reflector program, it simulates the PMT response, the electronic shap- ing of the signals, the standard trigger and the digitization by the FADC. Furthermore, the NSB is added to the Cherenkov signals. For the Crab observation regions, a value of 0.18 phe/ns in each pixel is used. The standard camera program did not include afterpulse simulations nor the sum trigger was set up.
5.4.1 Afterpulse Simulations The camera program uses a database in which typical NSB signals for different levels of background lights are stored. For each photon hitting the PMT, there is a small chance to
1The idea to limit the amplitude of one pixel was originally developed for trigger concepts for G-APDs, where similar large fake pulses can occur due to optical cross-talk. [120]. 5. The New Sum Trigger 81
layout pixels trigger thresh. collection area [m2] number per patch Vthreshold [mV] @10 GeV @20 GeV @30 GeV @40 GeV 3 32 (4 8) 35 151 2549 8394 18967 × 5 16 (2 8) 30 85.8 1783 6828 17287 × 6 14 (2 7) 26 264 3296 9876 20874 × 7 14 (2 7) 26 58 2929 10181 23626 × 8 14 (2 7) 27 102 1899 6938 16970 × 9 14 (2 7) 27 142 2324 8057 18979 × 10 15 (3 5) 27 150 2479 8558 20080 × 11 18 (3 6) 29 207 3054 10112 23032 × 12 18 (3 6) 29 316 5404 17134 32497 × 13 21 (3 7) 31 237 3230 10591 23991 × 14 21 (3 7) 31 263 2645 10184 22512 × Table 5.1: The collection areas at 10, 20, 30 and 40 GeV for different sum trigger layouts. produce an afterpulse of a certain height. The probability that an afterpulse is produced after a NSB photon hit the photocathode is given by:
0.25 A0 1 f(A > A ) = 0.0164 e− · phe− (5.1) 0 · with f(A > A0) the probability that an afterpulse is generated with amplitude A larger than A0 phe. In figure 5.5, the rate of signals with amplitudes larger than the discriminator threshold on the x-axis is displayed, when a PMT is exposed to NSB. The afterpulse rate depends on the photon intensity hitting the photocathode. The release of afterpulses will happen in the order of a few µs after the light reaches the cathode. Thus, afterpulses are mainly uncorrelated in time with the incident photon, but only dependent on the intensity of the NSB. As can be seen in figure 5.5, the rate is dominated by NSB below the kink at around 6 phe. Above this kink, afterpulses dominate. I simulated several clipping levels and found that a clipping level at around 5-7 phe discriminates the afterpulses efficiently enough. There is a trade off between the sensitivity to γ-rays, in particular at the lowest energies, reduced by the clipping and the maximum rate we can accept. As we aimed at a trigger threshold between 25-35 phe per shower, a trigger from afterpulses alone is highly improbable (corresponding to a 6 8σ effect). − We extended the existing NSB database with the afterpulse simulations. To achieve a good statistics of afterpulses, the total simulated NSB time was extended from 10’000 ns to 500’000 ns. The simulated database therefore includes afterpulses with a pulse height of up to 45 phe.
5.4.2 Sum Trigger Simulations: Topology, Thresholds and Shape The sum trigger simulation was added to the existing trigger simulations. Before the sig- nals are summed up, the AC coupling is simulated by first integrating the analog trigger signal and then subtracting the mean value. Several trigger configurations were simulated, with patch sizes between 8 - 32 PMTs and different overlapping regions. As most Cherenkov photons are projected on a ring between 0.15 0.85 in the camera, the whole trigger area covers only this ring. This structure ◦ − ◦ will already provide some hardware suppression of hadronic background events. To keep a rotational symmetric configuration, the patches were designed for one sector of the camera 82 5. The New Sum Trigger
Figure 5.5: The count rate above a discriminator threshold denoted on the x-axis for one MAGIC PMT exposed to NSB. The red crosses denote the simulation with a NSB level of 0.18 phe/ns, the black ones the measured spectrum. Note that above 6 phe, afterpulses dominate the count rate. 5. The New Sum Trigger 83
and then rotated 5 times each by 60◦. The trigger thresholds for each configuration was chosen such that random triggers from NSB and afterpulses were below 50 Hz. The clipping threshold was varied between 5 and 10 phe. It was found that for a clipping threshold between 5 and 7 phe, the resulting collection area was constant within errors. Thus, we decided to fix the clipping level at 6 phe. In the real setup, the discriminator and clipping levels fluctuate. To take this into ac- count, I added Gaussian fluctuations (σ = 1.5 phe) to the clipping and the discriminator thresholds. Since this did not affect the resulting collection trigger area, this feature was removed from the simulations. We also simulated different bandwidths of the sum trigger electronics and found that decreasing the analog PMT pulse width efficiently suppresses the NSB. Nevertheless, if the pulse width is too short (below 2 ns), the trigger efficiency decreases as well. This has a ≈ physical reason: The duration of a small energy γ–ray event is about 2-3 ns. By decreasing the analog pulse widths, one loses showers with slightly larger time spread. Furthermore, the electronic signals are expected to jitter in time at the order of < 1 ns. To assure that the whole γ-ray signal is contained within the trigger signal, we fixed the pulse width at 3.5 ns. We also examined the influence of the optical PSF on the trigger efficiency of the tele- scope. The idea was to defocus the mirror slightly. Thus, the Cherenkov light would be distributed over a larger area, resulting in less peaked single PMT signals. Thereby, the Cherenkov light would not be clipped, but it would still trigger the telescope. Using simu- lations, we realized that this method does not increase the sensitivity, and we dropped the idea. The final sum trigger layout is displayed in figure 5.6. The trigger area is contained within 0.26 0.83 and contains 216 PMTs. In table 5.1, the collection areas for a few ◦ − ◦ tested layouts are noted. It was found that an overlap factor of 2 (i.e. each PMT in the trigger area lies in two different trigger patches) increases the collection area significantly. An overlap factor of 3 would have increased the sensitivity even more, but hardware con- straints did not allow such a configuration. These hardware constraints also led to the choice of the somewhat strangely shaped sum trigger patches.
5.5 Electronics and Installation on Site
Parallel to the Monte Carlo simulations of the sum trigger, the necessary electronics was planned and designed at the electronics workshop of the MPI in Munich. To keep the design simple but flexible, the following boards, schematically displayed in figure 5.7, were chosen:
1. 35 type I boards with 8 channels each, where the clipping is done.
2. 40 type II boards. These boards can sum the signals of up to 8 pixels and form the so-called subpatches. They have 3 equal output lines, allowing each subpatch to lie within 1-3 patches.
3. 24 type III boards. These boards sum up the signals of up to 3 output signals from the type II boards
Additionally, an “OR board” was needed in order to run the sum trigger and the standard MAGIC trigger in parallel. The number and characteristics of these boards led to the following constraints: 84 5. The New Sum Trigger
8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 ° 0.60 0.0 189mm
(a) The sum trigger patches. (b) The subpatches of the final sum trigger layout, each consisting of 6 pix- els. Each subpatch belongs to two dif- ferent patches, resulting in a overlap factor 2.
Figure 5.6: The final configuration of the sum trigger. Displayed in (a) is the total trigger area (salmon) and the base sum trigger patches (reddish colors). This configu- ration contains 18 pixels per sum trigger patch and occupies in total 216 pixel. Each pixel within the trigger area is contained in exactly 2 different sum trigger patches. To get the total trigger layout, each base sum trigger patch has to be rotated 5 times by each 60◦ around the center of the camera. In (b), the subpatches are displayed. Each patch consists of 3 subpatches with 6 PMTs each. 5. The New Sum Trigger 85
input signals clipped output signals Clipping Board I 8 output channels 8 input channels to board II
clipped input signals
summed, clipped Summation output signal Board II 8 input channels 3 output channel to board III
summed, clipped output Summation signal from up to 3 subpatches Board III 1 output channel 3 input channels to discriminator
Figure 5.7: Schematics of the three sum trigger boards. Board I performs the clipping, board II sums the signals from up to 8 PMTs. This board defines the sub- patches, which can contain maximal 8 PMTs. The output signal from 3 board II types are then summed in board III, forming the full patches. A trigger is raised if the signal from one patch exceeds the discriminator threshold. In the final sum trigger layout, one patch consists of 3 subpatches, which sum the signal of 6 PMTs.
1. The number of pixels in the trigger area is smaller than 280 (35 8 clipping channels) ×
2. The total number of subpatches is smaller than 40 (i.e. 6 subpatches in each ≤ sector).
3. A subpatch can contain up to 8 pixels.
4. To provide an overlap between patches, each subpatch can be contained in up to 3 patches.
5. The number of patches is smaller than 24 (e.g. 4 patches per sector). ≤
All components were installed and tested at the MAGIC site at La Palma in October 2007. After the commissioning phase, regular data taking on Crab started by the end of October 2007. 86 5. The New Sum Trigger
5.6 The Calibration of the Sum Trigger
The trigger thresholds were set in mV. To calibrate the trigger threshold and the clipping level in phe, we used 3 different methods:
Using the calibration- and afterpulses. This was done after the installation of the sum • trigger. Afterpulses have a very short time spread and can be seen as δ-functions, compared to the time resolution of the MAGIC electronics [122]. Thus they show a ’perfect’ pile up of phe in time. The waveform of the afterpulses and the calibration pulses was measured with an oscilloscope. Using the F-factor method (see section 4.3.5), one can compute the average phe content of the calibration pulses. To compute the signal ratio between height (in mV) and phe content for afterpulses, one has to take into account the different time spread of both pulses. (The phe content is proportional to the area below the pulse). Thus one achieves the calibration:
C = (Vcalib[mV]/Nphe ) FWHMcalib/F W HMafterpulse 0.037[mV/phe] calib · ≈ Matching the measured NSB spectrum (i.e. rate vs. discriminator threshold) with a • simulated one. See figure 5.8. As the NSB can vary by a large factor depending on the sky region, this is not a very precise measurement.
Comparing the measured distribution of phe for cosmic ray events with the simulated • one. See figure 5.9.
The first and the second method resulted in a trigger threshold of 27 phe and a clipping level of 6 phe, while the third method showed a trigger threshold of 24 phe and a clipping level of 5.5 phe. As the first and the third method have an estimated systematic error of 10 15%, these measurements agree within the error. In the later analysis, a systematic − error for the threshold calibration of 10% was used.
5.7 Comparison with the MAGIC Standard Trigger
During each observation, the sum trigger was run in parallel to the MAGIC standard trig- ger. This allows to directly compare the performance of the sum trigger in comparison with the standard trigger, e.g.: the homogeneity of the COG distribution of the shower image, displayed in section 5.7.1, the energy threshold for γ-rays (section 5.7.2), the collection area in section 5.7.3, or the sensitivity towards a DC signal of the Crab Nebula for different SIZE cuts, illustrated in section 6.11.
5.7.1 Homogeneity By plotting the distribution of the COG for each shower image within the MAGIC camera, one achieves a visualization of the trigger homogeneity, see figure 5.10. While the standard trigger is expected to have a smooth distribution, the sum trigger shows a six fold structure due to the choice of the sum patches. For low SIZEs, the COG distribution is for the sum trigger more homogeneous than for the standard trigger.
5.7.2 Energy Threshold As defined above, the trigger threshold is the peak of the energy distribution for a γ-ray source with a spectral index of 2.6. Such a source was simulated with Monte Carlo γ-rays. 5. The New Sum Trigger 87
clipped NSB spectra
Measured NSB rates for 1 patch. Normalisation: 632mV = 27phe
Simulated NSB rates, clipping at 6.2 phe
rate [Hz] Simulated NSB rates, clipping at 6.5 phe 105 Simulated NSB rates, clipping at 7.0 phe
Simulated NSB rates, clipping at 7.25 phe
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Figure 5.8: The measured NSB spectrum (black markers) and the simulated spectrum (col- ored markers) for different clipping levels. Remark: The conversion factor computed here is 0.042 mV/phe, compared to 0.037 mV/phe using the after- pulse method. The flat tail to the right in the data is due to triggers from cosmic rays (mostly hadrons). This is not implemented in this simulations. 88 5. The New Sum Trigger
proton Monte Carlo Crab OFF 200
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Figure 5.9: The distribution of SIZE in phe for data taken from a OFF region (where no γ-rays are expected from) and for a proton Monte Carlo dataset. The distributions of data and simulations agree well for SIZE> 50 phe. For lower SIZEs, the distribution fit not ideally. This is due to the rather high level of NSB in the OFF region.
The energy distribution after trigger is plotted in figure 5.11. The energy threshold was lowered by about a factor of 2 from 50-60 GeV to 25 GeV. As the energy threshold of protons was reduced as well, this resulted in an estimated trigger rate of at least a factor 2.5 higher than by using the standard trigger. To reduce the energy threshold, we set the sum trigger discriminator to a rather low level, risking that Poissonian fluctuations of the NSB trigger the telescope. We estimated that thus about 50% of all trigger come from the NSB and not from cosmic rays. The total rate was increased from 200 Hz to 800-1’300 Hz, resulting in a total amount of 3.5 TB (raw) data for the 42 hours of Crab observation in sum trigger mode.
5.7.3 Collection Area and Sensitivity for Low Energies The energy dependent collection area (see section 4.4.5) characterizes the performance of an air Cherenkov telescope. Comparing the standard trigger with the sum trigger in figure 5.12 reveals an improvement of around one order of magnitude at 20-30 GeV.
5.8 Future Improvements
Even though the sum trigger shows a good performance, there is a lot of room for im- provement. There is no automatic setting of the trigger thresholds, resulting in a need to manually readjust the thresholds during data taking by one of the sum trigger experts us- ing screwdrivers, a voltmeter to read the thresholds and NIM scalers to check the resulting rate. Due to changing atmospheric conditions, frequent threshold readjustments during 5. The New Sum Trigger 89
COG, Lvl 1 400 1600 300 1400 200 1200 100 1000 [mm]
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(a) standard trigger - MC (b) standard trigger - data
(c) sum trigger - MC γ-rays (d) sum trigger - data
Figure 5.10: The distribution of the COG of the shower images within the MAGIC cam- era for the standard trigger and the sum trigger. Figure a) and c) shows the expected COG distribution gained from Monte Carlo simulations for the standard trigger (also dubbed Lvl1 trigger) and the sum trigger, respectively. Remark the six fold distribution which can also be seen in the data. The in- homogeneity in the lower right corner is due to a malfunctioning sum trigger board. 90 5. The New Sum Trigger
Monte Carlo energy distribution, after trigger for a power law with spectral index -2.6.
18000 std MAGIC trigger 16000
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Figure 5.11: The differential rate for MC γ-rays, following a power law with spectral index of 2.6 for the MAGIC standard trigger and the sum trigger. The peak of the distribution is a measure for the energy threshold. The standard trigger has a threshold of 55 GeV, while the sum trigger has a threshold energy of 25 GeV. The distributions were normalized for MC energies above 120 GeV.
Figure 5.12: The collection area for the MAGIC standard trigger and the sum trigger. The gain in sensitivity of the sum trigger at energies below 30 GeV is about 1 order of magnitude. Remark: For energies above 200 GeV, the standard trigger is more efficient than the sum trigger. The reason for this is the smaller trigger area within the camera. (Sum trigger: ring 0.26 0.83 , standard trigger: ◦ − ◦ full area 0 1.05 ) ◦ − ◦ 5. The New Sum Trigger 91
data taking were needed. To improve the handling, a computer controlled threshold steer- ing was installed in summer 2008 [123]. With the program SUMO, the single patch rates are checked and the thresholds adjusted, if the rate of one patch goes below or above a certain threshold. This window is 700-800 Hz for pulsars and 400-500 Hz for extragalactic sources. To increase the sensitivity, the trigger area can be enhanced and a larger overlap between neighboring pixels is provided. An enhanced trigger area will increase the effective area for large energies and thus yield a better sensitivity in this domain. The larger overlap will increase the sensitivity for lower energy showers.
5.9 Conclusion
As shown in this chapter, the sum trigger [124] is a simple, cost-effective and efficient trigger implementation for Cherenkov telescopes. Its installation at the MAGIC telescope site effectively reduced the trigger threshold by a factor of 2 from 55 GeV to 25 GeV and increased its collection area at 35 GeV by nearly an order of magnitude. At energies above 150 GeV, it is slightly less efficient than the standard trigger. This is due to the reduced trigger area. The sum trigger played a crucial role in the detection of the Crab Pulsar, described in the next chapter.
6 Observation of the Crab Pulsar using the Analog Sum Trigger
In this chapter the first detection of pulsed γ-rays from Crab will be described in detail. I will start with the description of the data sample (section 6.2) and the selection criteria that were applied to ensure that only data are analyzed that was taken under optimal observation conditions (section 6.3). The following section 6.4 covers the γ-ray simulations which are adjusted for the observation of Crab with the sum trigger. The applied cuts adjusted for this data sample and the reconstruction of the pulsar phase for each event is described in section 6.5. The optical data collected in the central pixel of the camera was analyzed as well and the optical pulsation of Crab determined. This is described in section 6.6. The optical data is recorded with the same DAQ system as the γ-ray data, and the conversion of the timestamps to phases is also the same. The analysis of the optical pulsation is therefore an important cross-check to ensure that the timestamps are treated correctly in the data taking and analysis chain. In section 6.7, the first detection of pulsed γ-rays above 25 GeV from Crab is described. The spectrum in the cut-off region is modelled with a power law spectrum with exponential and super exponential cut-off, taking into account the joint measurements of COMPTEL, EGRET and MAGIC (section 6.8). This modeling is done for the total pulsed flux of the main and inter pulse together, as well as separately for each pulse. In addition, the spectrum in the cut-off region is determined based only on the measurements of MAGIC in section 6.9, again for the total flux and for each pulse separately. The pulse profile itself contains physical information on the geometry of the emission region. In section 6.10, a closer look at the morphology of the pulse profile at different energies is therefore given. The data taken with the sum trigger can also be analyzed to search for an unpulsed signal. This is demonstrated in section 6.11, where the measurement of unpulsed γ-rays from Crab at energies around 50 GeV will be described. Note that this chapter contains a listing of all obtained results. An interpretation of these results, including the implications for current pulsar models, is given in chapter 7. The detection of the pulsed emission and the determination of the cut-off energy has been published [125].
6.1 Introduction
The γ-ray source candidate “Crab” contains two (potential) γ-ray sources: The Crab Pulsar and its surrounding Crab Nebula. The later is a bright and constant source of VHE γ-rays (e.g. [1, 3, 49, 126, 127, 128, 129]) and therefore taken as the VHE standard candle. The performance of an IACT is given in the percentage of the Crab flux the telescope can measure with a significance of 5σ within 50 hours. Furthermore, lacking a calibrated γ-ray test beam in the vicinity of the Earth, Cherenkov telescope have to rely on their simulations of air showers, the atmosphere, the local magnetic field and the detector. The energy spectrum from the Crab Nebula is therefore compared with measurements from 94 6. Observation of the Crab Pulsar using the Analog Sum Trigger
Figure 6.1: Measurement of pulsed VHE γ-rays from Crab with MAGIC using data taken in 2005. The excess in the marked phase region, which corresponds to the position of the two peaks in the pulse profile measured with the EGRET experiment, has a significance of 2.9σ. The (analysis) energy threshold was 60 GeV [3]. ≈ ≈ Figure provided by N. Otte [94] other instruments as a consistency check. Since the beginning of ground based VHE γ-ray observations more than 20 years ago, the Crab Pulsar in the center of the Crab Nebula has been a main target [46, 47, 48, 49, 50, 51]. Nevertheless, even the lowest energy threshold of above 50 60 GeV [3, 83, 130] − or higher [48, 131], achieved with Cherenkov telescopes, did not allow to detect pulsed emission from any pulsar. The analysis of data taken with MAGIC in 2005 using the standard setup, however, revealed a hint for a pulsed signal for γ-ray energies above 60 GeV [3], displayed in figure 6.1. The upper limits of the pulsed VHE γ-ray flux derived from different ground based observations are displayed in figure 6.2, together with the spectrum measurements from EGRET. It was found that the 2σ upper limit for the cut-off energy was 30 GeV, assuming an exponential cut-off shape. The sharp spectral cut-off in the energy range between a few GeV - tens of GeV requires thus a very low energy threshold at about the energy of the cut-off. Due to the steepness of the spectrum in the cut-off region, lowering a detector’s energy threshold results in a large increase of the number of measured γ-rays. After the layout design of the sum trigger and the construction of the electronic parts, the sum trigger was installed and commissioned in September 2007. Data taking on Crab Pulsar started at the end of September. By February 2008, we had observed Crab for about 40 hours.
6.2 Data Sample
Since the sum trigger operation was not automatized at that time, each observation was accompanied by one of the sum trigger experts to ensure a good performance under chang- 6. Observation of the Crab Pulsar using the Analog Sum Trigger 95
Figure 6.2: This figure shows on the left side (black circles) the EGRET spectrum mea- surements. On the right side, the flux upper limits (arrows) found with ground based Cherenkov telescopes are denoted. The dashed line denotes the fitted power law spectrum, adjusted with an exponential cut-off (see equation 3.2), where the power law part was derived for the EGRET points. For the cut-off energy, we found an upper limit of 30 GeV [3]. The red arrow denotes the energy threshold of the telescope using the standard setup. Figure provided by N. Otte [94] 96 6. Observation of the Crab Pulsar using the Analog Sum Trigger
2500
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accepted 1500 counts 1000
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Figure 6.3: The distribution of cloudiness for the whole observation period.
ing observation conditions. The single patch rates were counted by NIM scalers, and the thresholds of the 24 patches set by a screw driver. Because other sources were also observed with the sum trigger, the patch discriminator thresholds had to be changed within a few minutes when the telescope was moved from one source to the next. All data were taken at zenith angles below 20◦. At larger zenith angles, the shower develops further away and less Cherenkov light arrives at the telescope, resulting in an increased trigger threshold. During all observations, the standard trigger was run in par- allel to the sum trigger, connected by an OR-module. Every event was flagged with a bit pattern describing the type of event (calibration, pedestal, data) and which trigger fired (LT1, LT2, Sum). This allows to compare the performance of the sum and the standard trigger directly. Great care was taken to ensure that only data under optimal conditions was taken. Still, about 50% of all data did not fullfill the strong criteria depicted in the next section. To push the trigger threshold as low as possible, we lowered the discriminator thresholds to values such that the total trigger rate was at 800 1000 Hz, close to the maximal rate − of 1.4-2 kHz allowed by the DAQ system. The data taking in La Palma is subdivided into intervals of roughly 3 weeks, correspond- ing to the period when observation without moon is possible. We took sum trigger data between period 57 in October 2007 and period 63 in February 2008. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 97
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(e) Period 63 (f) Night 20071210
Figure 6.4: The figures (a) - (e) show the cloudiness curve as a function of MJD. As an example, figure (f) shows the detailed cloudiness for the night 20071210. The large fluctuations during this night indicate bypassing clouds or other chang- ing weather conditions, leading to the decision to remove this night from the analysis. 98 6. Observation of the Crab Pulsar using the Analog Sum Trigger
140 accepted 120
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Figure 6.5: The distribution of the event rates after cleaning and removal of nights not passing the cloudiness cut.
25 SIZE>200 100 15 accepted hour / σ 10 5 0 0 5 10 15 20 25 30 35 40 time bin [a.u.] Figure 6.6: The sensitivity for γ-rays from the Crab Nebula. Displayed is the significance per √hour for each time bin, for the data surviving the rate and cloudiness cut. Each time bin has a duration between 25 and 45 minutes. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 99 Figure 6.7: The track of Crab along the sky in Azimuth and Zenith distance. The center of the circle corresponds to Zenith, the observation direction is south. Note that the starfield is displayed as an illustration for the date 28/12/2007 at the time 23:12:58. 100 6. Observation of the Crab Pulsar using the Analog Sum Trigger 6.3 Data Selection A pyroscope installed at the telescope’s site is used to derive the cloudiness parameter, which roughly corresponds to the percentage of the FOV being covered in clouds and thus varies between 0 100%. Figure 6.3 shows the distribution of the cloudiness parameter − for the whole observation period. In figure 6.4, the cloudiness parameter for each period is displayed as a function of time and for one particular night. Note that the date of the night corresponds to the date of the end of the night, which is a definition used within the MAGIC collaboration. The night denoted as “20071211” stands for the night between the 10th and 11th December, 2007. Nights with high cloudiness > 30% or strong fluctuations of this value indicate the presence of clouds and thus suboptimal observation conditions. These nights were excluded from the analysis. Another quality check was performed using the trigger rates. Given the low zenith angle range of our data, the trigger rate is strongly correlated with the weather conditions (e.g. clouds or Sahara sand). Fluctuations of the trigger rate also indicate changing observation conditions. In the analysis, nights with low trigger rates R< 550 Hz are excluded. The image cleaning removes events triggered by NSB, the rates after the image cleaning are therefore dominated by hadronic background triggers. The proton flux is not expected to vary. So, this rate is also sensitive to changes in the atmospheric extinction. Nights with average event rates after cleaning below 450 Hz and single runs with cleaning rates below 420 Hz were excluded from the analysis (figure 6.5). A last quality check is based on the study of the steady (unpulsed, DC) signal from Crab. The data sample was subdivided in bins of 25 45 minutes. Using the standard − analysis, the significance per square root hour (Nσ,√h) for SIZE> 200 phe was determined for every bin. Time bins with a low Nσ,√h < 12 are removed (figure 6.6). After applying these strict observation cuts, in total 22.3 h of data taken under ideal conditions remained. 6.4 Monte Carlo Simulations considering the Geomagnetic Field As was shown in [79, 132], the Earth’s magnetic field has a strong influence on the shower images, depending on the observation direction (azimuth and zenith distance), γ-ray energy and shower location and is in particular important for low energy showers. The image parameter ALPHA can be distorted and pointing to a position different from the source position, introducing a broadening and a bias of the ALPHA distribution. Furthermore, depending on the influence of the magnetic field, the shower can have a greater transversal distribution leading to a broadening of the parameter WIDTH. To take into account the effects of the magnetic field, I simulated the γ-rays along the track of Crab in the sky, displayed in figure 6.7. The MC distribution in azimuth was weighed such that it coincides with the measured one. 6.5 Data Analysis The data obtained were calibrated and the images cleaned with the algorithm described in section 4.4.2.3. A quality cut in SIZE and CONC removed sparks known to be produced as a PMT feature: 1.5-4.*log10(CONC)>log10(SIZE) (6.1) 6. Observation of the Crab Pulsar using the Analog Sum Trigger 101 90 1 95% 80 0.9 70 85% 0.8 0.7 60 75% 0.6 50 65% ALPHA 0.5 40 55% 0.4 cut e!ciency 30 45% 0.3 20 35% 25% 0.2 10 15% 0.1 0 20 30 40 50 60 70 80 90 100 SIZE [phe] 1.6 1.4 1.2 Q - Factor 1 20 30 40 50 60 70 80 90 100 SIZE [phe] Figure 6.8: The upper panel shows the SIZE dependent cut efficiency in ALPHA. The val- ues denote the fraction of γ-rays surviving an upper cut in ALPHA and are displayed by the underlying reddish distribution. For constant cut efficiencies between 5% and 95%, dotted grey lines are drawn in steps of 10% of cut effi- ciency. The light blue crosses denote for each SIZE bin the optimal ALPHA cut that maximises the Q-factor (see text). The green dashed line shows the parameterized cut in ALPHA as a function of SIZE. The lower panel shows the corresponding Q-factor. 102 6. Observation of the Crab Pulsar using the Analog Sum Trigger In the next step, a parameterized cut in ALPHA was applied to the data to reduce hadronic background events. The cut in each SIZE bin was found by maximizing the Q-factor, defined as: ǫγ (tcut) Q(tcut)= , ǫbg(tcut) where ǫγ and ǫbg are the cut efficiencies for γp-rays and for background events. The γ-rays come from Monte Carlo simulations as described in section 6.4. As background sample, I used data taken from an OFF region, where no γ-rays are expected. The parameterized cut is displayed in figure 6.8 and is: |ALPHA| < 1.23265*1.0/(exp((log10(SIZE)+8.64083)/14.465)-1.97294)+8 (6.2) For the low SIZEs analyzed here, ALPHA has the best γ-hadron separation power, with a Q-factor of Q 1.16 at 30 < SIZE < 40. For cuts in other image parameters (LENGTH, ≈ DIST, WIDTH), the Q-factor is below or at 1 and thus no effective cut is possible. Due to the fact that MC and real γ-rays have to agree well to use the RF, no cut in HADRONNESS was used. Since for example the image parameter WIDTH strongly depends on the optical PSF of the telescope at low SIZEs, a precise monitoring of the PSF and fine tuning of the MC would be mandatory. By using only a SIZE dependent cut in ALPHA, the analysis is robust and no additional systematic uncertainties are introduced. In order to get rid of images with small SIZE mostly due to accidental triggers by NSB, a lower SIZE cut of 25 phe was used. This results in an analysis energy threshold after image cleaning and cuts of 25 GeV. The collection area after cuts and after trigger is displayed in figure 5.12. After the image cleaning, the event arrival times are transformed to the solar barycenter, as described in section 4.5. For each transformed event time, its phase φ is computed: 1 φ(t)= ν (t t )+ ν˙ (t t )2 + ... (6.3) 0 · − 0 2 0 · − 0 The ephemeris parameters for Crab (t0, ν0 and ν˙0) which are needed here are monitored by the Jodrell Bank Radio Observatory [109]. The monthly values covering our observations are displayed in table 6.1. The radio timing must be corrected for a radio frequency depending dispersion along the line of sight to Crab resulting in an estimated uncertainty of 160 µs for the Radio Ephemeris, corresponding to a phase uncertainty of ∆φEph. = 0.005, which I used in the later analysis as a statistical error on the phase determination. 6.6 The Optical Lightcurve As described in section 4.3.6, the optical light from a point source (i.e. extension < 0.1◦) in the center of the FOV is focused onto the central pixel. Using the data collected with the central pixel while pointing to the Crab pulsar, we measured its optical pulsation. To do so, the signal of the central pixel was integrated for each event, yielding a number proportional to the number of photons hitting the photomultiplier within 100 µs. The arrival phases were determined in the same way as for the γ-rays using formula 6.3, weighed by the number of photons and then filled into a fine binned histogram (figure 6.9). The optical lightcurve was used to check the accuracy of the barycentric correction, the timing of the telescope and the correctness of the used timing algorithms. We determined the arrival times of the two peaks relative to the radio peak at phase φ = 0 and compared 6. Observation of the Crab Pulsar using the Analog Sum Trigger 103 91.4 P1:91.2 90.6 91 90.5 90.8 90.4 91.4 90.6 90.3 91.2 90.4 90.2 90.2 90.1 91 90 90 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.35 0.4 0.45 0.5 0.55 counts [a.u.] 90.8 90.6 90.4 90.2 90 -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Phase φ Figure 6.9: The lightcurve for optical wavelengths as derived from the central pixel of the MAGIC Telescope. x10 3 622 621 620 619 counts 618 617 616 -1 -0.5 0 0.5 1 Phase φ Figure 6.10: The pulse profile for γ-rays above 25 GeV. The main pulse P1 at phase φ 0 ≈ and the inter pulse P2 at φ 0.35 are clearly visible. The signal region P1 ≈ and P2 is indicated by the yellow shaded area. The combined excess in the two pulses P1 and P2 has a significance of 6.2σ. Note that for better visibility, two identical phase diagrams are shown. 104 6. Observation of the Crab Pulsar using the Analog Sum Trigger ×103 1567 entries 1566 1565 1564 1563 1562 1561 1560 1559 -1 -0.5 0 0.5 1 phase φ (a) Phase diagram for inverted ALPHA cut. 8000 6 7000 5 6000 4 σ 5000 3 4000 2 3000 significance 1 number of excess events 2000 0 1000 -1 ×103 ×103 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 number of events number of events (b) Growth of excess events as a (c) Growth of the significance as function of the total number of a function of the total number of background events. background events. Figure 6.11: Figure (a) shows the pulse profile for the inverted cut in ALPHA, and thus selecting shower images which do not point to the center of the camera (no γ-events). In this case, the phase distribution is flat. Figures (b) and (c) show the growth of the excess events and the significance vs. the total number of events (for the non-inverted cut in ALPHA). In case the pulsed emission from Crab does not change over time and the observation conditions are stable over the whole observation period, the number of excess events are expected to grow linearly with the number of background events, while the significance is ex- pected to grow proportionally to the square root of the number of background events. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 105 date t0 [MJD] ν0 [Hz] ν˙0 [Hz/s] 15 OCT 07 54388.012919 29.7543867527 3.7224227 10 10 − · − 15 NOV 07 54419.001731 29.7533898037 3.7219617 10 10 − · − 15 DEC 07 54449.032240 29.7524250936 3.7217157 10 10 − · − 15 JAN 08 54480.016452 29.7514283219 3.7213776 10 10 − · − 15 FEB 08 54511.023052 29.7504316128 3.7210402 10 10 − · − Table 6.1: The ephemeris of the Crab pulsar used in this analysis. The second column t0 denotes the first arrival time of P1 after midnight of the corresponding day (in the time frame of the solar barycenter). Due to the small average value of ν¨0 and the short time interval of only one month between two ephemeres, ν¨0 was not used in the analysis. them with the optical measurements from other experiments. The position of P1 and P2 were determined by computing the mean value of the peaks between 0.1 <φ< 0.09 − (P1), and between 0.3 <φ< 0.45 (P2). The background was estimated from the off pulse region 0.52 <φ< 0.88 and subtracted before computing the mean. Using Gaussian error propagation, the error on the mean was computed. The position of the mean of the two peaks P1 and P2 are at phase φP1 = 0.0089 0.0051 (P1, optical) − ± (6.4) φP2 = 0.395 0.0057 (P2, optical) , ± corresponding to a radio – optical lag of ( 268 37) µs for P1. In [133], a radio – optical − ± lag for P1 of ( 255 21) µs was determined by simultaneously observing the Crab Pulsar − ± in optical and Radio wavelengths. The consistency of our result with other measurements thus shows that the arrival times were treated correctly, from the recording of the time stamps to the algorithms used in the analysis. 6.7 The Detection of Pulsed High Energy γ–Rays For each event surviving the cuts, the phase φ was computed according to formula 6.3. Assuming that no pulsation was observed, φ is expected to be distributed flat between 0 φ< 1. A detection of pulsed emission is achieved, if this hypothesis can be rejected on ≤ a level of typically 5σ. In the analysis of the Crab Pulsar data, I used the H-Test [113], the χ2 test applied to the pulse profile and the test based on the knowledge of the positions of P1 and P2 given by the measurements of EGRET (see section 4.5). For the χ2 test, the phase diagram was divided into 11 bins (per cycle) such that the position of P1 and P2 lie approximately in the center of a bin. All three tests yielded a significance above 5σ for our data. In figure 6.10, the pulse profile is shown. The profile has prominent peaks at the position of the main pulse P1 around φ 0 and at the position of the inter pulse P2 (around ≈ φ 0.35). ≈ 6.7.1 Number of Excess Events and Significance To compute the number of excess events and the significance, the phase regions defined in table 4.1 were used, assuming P1 and P2 as ON regions and the remaining regions as OFF. 106 6. Observation of the Crab Pulsar using the Analog Sum Trigger This results in total 8350 excess events with a significance of 6.2σ1. Applying a different unbinned test statistic, the H-Test [113], a test value of 38 is achieved, corresponding to a significance of 5.3σ. The χ2-test yields a significance of 5.8σ. In a similar analysis, only the region dubbed offpulse between P2 and P1 is used as background region, meaning that the bridge region is excluded from the estimation of the background. This is motivated by the optical and γ-ray measurements performed by EGRET where γ-rays are also measured in the bridge region, as well as from outer gap and slot gap models predicting γ-ray emission in the bridge region as well. The number of excess events and significance becomes2: N tot = 9230 490 (6.2σ) (P1+P2) (6.5) exc ± and for the individual pulses P1 and P2: N P1 = 3580 940 (3.8σ) (P1) exc ± (6.6) N P2 = 5650 990 (5.7σ) (P2) exc ± To ensure that the found signal is real, the phase diagram for an inverted cut in ALPHA was derived (inverted equation 6.11), thus excluding γ-ray candidates. As expected, the phase diagram is flat (figure 6.11a). In figure 6.11b and c, the growth of the excess and the significance, respectively, is shown as a function of the number of background events for the non-inverted cut in ALPHA. As expected, the number of excess events growths linearly, while the significance increases with the square root of the number of background events. Figure 6.12 shows the pulse profiles for data subdivided into 4 logarithmically equidistant SIZE bins (25 6.7.2 MC - Data Comparison It is important to check whether the MC simulations are reliable and in agreement with the real data. One possibility is to compare the SIZE distributions of the simulated hadrons with measured OFF data. Due to the large uncertainties on the primary hadron spectrum in the MAGIC energy range, the uncertainty of the hadron composition (H+, He2+,...) and further uncertainties, results derived from hadron shower simulations have to be handled with care. Figure 5.9 shows the agreement of the SIZE distribution between MC simulated protons and data, taken from an OFF position (pointing next to Crab). The agreement between data and simulations is good. In the case of γ-rays, the image parameter distribution for measured and simulated γ- rays can be compared with the ON-OFF method. Subtracting an OFF sample (containing only background) from the ON histogram (containing signal+background), where the OFF 1 The significance is computed with the formula 4.10, where Fnorm = 0.273 is the ratio between the ON and OFF region 2Even though the number of excess events is larger when estimating it with this new background region, the significance does not increase. This is because of the worse estimation of the background due to the smaller background phase region. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 107 ×103 250 249.5 249 248.5 counts 248 247.5 247 246.5 -1 -0.5 0 0.5 1 phase φ (a) 25 ×103 211.5 211 210.5 counts 210 209.5 209 208.5 -1 -0.5 0 0.5 1 phase φ (b) 51 ×103 129.5 129 128.5 counts 128 127.5 -1 -0.5 0 0.5 1 phase φ (c) 107 65800 65600 65400 65200 65000 counts 64800 64600 64400 64200 -1 -0.5 0 0.5 1 phase φ (d) 223 Figure 6.12: The pulse profiles in different SIZE bins used for the determination of the cut- off energy and the forward unfolded spectrum. In the two lower SIZE bins, the peaks P1 and P2 are of equal height, while in the 3rd and 4th SIZE bins (corresponding to energies above 60 GeV, the significance of the excess in ≈ P2 is above 2σ, it is below 2σ for the excess in P1. 108 6. Observation of the Crab Pulsar using the Analog Sum Trigger MC γ - rays 3000 MC γ - rays 3000 data γ -rays data γ -rays data, background 2500 data, background 2500 2000 2000 1500 1500 entries entries 1000 1000 500 500 0 0 0 5 10 15 20 25 30 0 10 20 30 40 50 60 WIDTH [mm] LENGTH [mm] (a) WIDTH (b) LENGTH MC γ - rays MC γ - rays 2500 data γ -rays 2500 data γ -rays data, background data, background 2000 2000 1500 1500 entries 1000 entries 1000 500 500 0 0 0 50 100 150 200 250 300 0 10 20 30 40 50 DIST [mm] ALPHA [°] (c) DIST (d) ALPHA 2000 MC γ - rays data γ -rays data, background 1500 1000 entries 500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 CONC (e) CONC Figure 6.13: Comparison of measured and simulated γ-rays. The solid blue histogram denotes the simulations, the red crosses the distributions for γ-rays derived from the data. The green histogram denotes the distributions for background events. The comparison was done for 25 < SIZE < 60. Note that the compar- ison was performed after the cut in ALPHA, resulting in a peaked ALPHA distribution of γ-rays and background. For this SIZE bin, background and γ-rays follow nearly the identical distributions. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 109 2000 γ MC γ - rays MC - rays 1500 data γ -rays data γ -rays data, background 1500 data, background 1000 1000 500 entries entries 500 0 0 -500 0 10 20 30 40 50 0 10 20 30 40 50 60 70 80 90 WIDTH [mm] LENGTH [mm] (a) WIDTH (b) LENGTH MC γ - rays MC γ - rays 1500 data γ -rays data γ -rays data, background 2000 data, background 1000 1500 500 entries entries 1000 0 500 -500 0 0 50 100 150 200 250 300 350 0 5 10 15 20 25 30 35 DIST [mm] ALPHA [°] (c) DIST (d) ALPHA MC γ - rays data γ -rays 1500 data, background 1000 entries 500 0 -500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 CONC (e) CONC Figure 6.14: Comparison of measured and simulated γ-rays. The solid blue histogram denotes the simulations, the red crosses γ-rays deduced from the data. The green histogram denotes the background distributions. The comparison was done for 60 < SIZE < 300. The agreement is good, but the low number of excess events prevents a detailed study of the image parameter distribution. 110 6. Observation of the Crab Pulsar using the Analog Sum Trigger sample is scaled with the ratio α between the ON and OFF sample, delivers the distribution of the measured γ-rays: N(γ)= N(ON) α N(OFF) (6.7) − · Assuming that the excess events in P1 and P2 in the pulse diagram is due to γ-rays, I used ON data events from the phase region around P1 and P2 and OFF data events from the phase region in the offpulse region. The scaling factor α is the ratio between the ON and the OFF phase region. The resulting distributions for simulated and measured γ-rays and for background are displayed in figures 6.13 and 6.14 for the image parameters ALPHA, DIST, WIDTH, LENGTH and CONC. Since the cut in ALPHA was applied beforehand, the OFF ALPHA distribution is also peaked. Note that at the low SIZE region where most of the excess events are found, the γ-ray and background distributions coincide. 6.7.3 Do P1 and P2 Follow a Different Spectrum? The disappearance of P1 at the highest energies indicates that P2 and P1 have different spectra in the VHE energy region. To test this hypothesis, I compared the number of excess events measured in SIZE bins for both peaks P1 and P2. To take into account that the flux in P1 and P2 might have the same shape but a different normalization, the χ2-test to the normalized excess events was applied. The large statistical errors (see figure 6.15) on the excess results in a high probability for the null hypothesis with χ2 = 1.1 for 4 degrees of freedom, corresponding to a probability of Prob(χ2) = 0.89. It can therefore not be decided whether P1 and P2 have the same spectral shape above 25 GeV. Theoretical models of the pulsed spectrum from Crab usually predict the total γ-ray flux as well as phase resolved in the phase regions P1 (main pulse), P2 (inter pulse), bridge region and in the leading and trailing wings of each peak. To compare our measurements with these predictions, I determined the total pulsed flux in P1 and P2 as well as the phase resolved flux in each peak separately. Due to the low excess in the remaining phase regions, no spectrum was determined for this data. 6.8 Cut-Off Energy The spectral turnover is determined in this section by a joint fit to the COMPTEL, EGRET and MAGIC measurements. The characterization is based on two different functions. In the first approach, an exponential or super exponential cut-off is assumed. In a second step, the cut-off is modelled as a smooth turnover from the EGRET power law spectrum with spectral index 2.022 to a power law spectrum with a larger spectral index. This results in a softer turn over than the exponential cut-off, and the spectrum will extend to higher energies. 6.8.1 Exponential and Super Exponential Cut-Off Both the outer gap and the polar cap models predict a cut-off of the pulsed spectrum in the energy range covered in our measurements. The cut-off spectrum follows an exponential or even super exponential shape. I determined the cut-off energy Ecut and the shape with the method described in section 4.5.1, using the following parameterization : α β dN E − (E/Ecut) f (E; f , α, Ecut, β)= = f e− (6.8) γ 0 dE dt dA 0 0.1 GeV · 6. Observation of the Crab Pulsar using the Analog Sum Trigger 111 0.6 normalised number of excess events in P1 0.5 normalised number of excess events in P2 0.4 excess 0.3 0.2 normalised N 0.1 0 50 100 150 200 250 300 350 SIZE [phe] Figure 6.15: The number of excess events in P1 and P2 normalized to the total number of excess events in each pulse. Due to the statistical uncertainties, it cannot be distinguished whether the excesses in P1 and P2 come from the same spectrum or not. The comparison between the two distributions was done with the χ2 test, yielding χ2 = 1.1 for ndf = 4. 3 4σ -1 3σ 10 2σ 10 -2 -3 2.5 1.5 σ 10 10 -4 probability probability -5 2 10 10 -6 -7 β 10 1.5 10 -8 10 -9 1 10 -10 10 -11 0.5 -12 10 10 -13 5 10 15 20 25 30 35 cut o [GeV] Figure 6.16: The probability of the fit to the measured EGRET, COMPTEL and MAGIC data, for different values of the cut-off energy Ecut and the parameter β de- scribing the shape of the cut-off. The red square denotes an exponential cut-off with β = 1, the blue triangle a super exponential cut-off with β = 2 and the green one the general super exponential case (β = 1.2). The black contour lines denote the regions that can be excluded at 1.5σ, 2σ, 3σ and 4σ levels. 112 6. Observation of the Crab Pulsar using the Analog Sum Trigger 5000 measured number of excess events excess events, exp. cut off (β=1) 4000 excess events, super exp. cut off (β=2) excess events, super exp. cut off (β=1.3) 3000 excess events 2000 1000 0 50 100 150 200 250 300 350 SIZE [phe] Figure 6.17: This figure shows the measured number of excess events (triangles) in each SIZE bin together with the predicted numbers of excess events assuming an exponential cut-off, super exponential cut-off with β = 2 and a super expo- nential cut-off with β = 1.2, yielding the best fit value. The power law parameters f0 and α are mostly determined by the fit to the EGRET and COMPTEL flux points for energies above 100 MeV, while the measurements by MAGIC determine Ecut and β. The MAGIC data was subdivided into 4 logarithmically SIZE bins displayed in figure 6.12 and table 6.2. With the method described in section 4.5.1, the cut-off energy of the spectrum measured with COMPTEL, EGRET and MAGIC was determined, using the spectrum parameterization given in equation 6.8. The cut-off energy Ecut and the parameter β describing the shape of the cut-off were scanned. For each pair 2 (Ecut, β), the χ (f0, α, Ecut, β) of the joint fit (see formula 4.25) was minimized as a function of f0 and α and the corresponding probability determined (figure 6.16). The highest probability (i.e. the smallest χ2) of the fit is achieved for Ecut = (20.4 3.9stat 7.4syst) GeV and β = 1.2 0.2, (6.9) ± ± ± where the subscripts stat and syst denote the statistical and systematic error. The deter- mination of the systematic error is described in section 6.9.3. For the conventional cases β = 1 (exponential cut-off) or β = 2 (super exponential), I found Ecut = (17.7 2.8stat 5.0syst) GeV for β = 1 ± ± (6.10) Ecut = (23.2 2.9stat 6.6syst) GeV for β = 2. ± ± In figure 6.17, the number of excess events measured with MAGIC for each SIZE bin are plotted together with the excess predicted for the 3 cut-off spectra denoted above. In table 6.3, the cut-off values, their errors, the χ2-values of the fits and their probabilities are summarized. The fit probabilities for all three spectra are good. Comparing the predicted number of excess events in each SIZE bin with the measured ones, it can be seen that the excess in 6. Observation of the Crab Pulsar using the Analog Sum Trigger 113 -1 s -2 10-4 MeV cm dF/dE 2 -5 E 10 MAGIC 2σ U.L. (Albert et al. 2008) Celeste (De Naurois 2002) Whipple (Lessard 2000) EGRET (Kuiper 2001) COMPTEL (Kuiper 2001) 17.7 GeV exponential cutoff -6 10 23.2 GeV superexponential cutoff (ν=2) 20.4 GeV superexponential cutoff (ν=1.3) Outer-Gap Model, Hirotani 2008 Slot-Gap Model, Harding 2008 Polar-Cap Model, Harding PC 10-7 1 10 102 103 104 105 106 Energy MeV β dN E α (E/Ecut) Figure 6.18: The joint fit f (E; f , α, Ecut, β) = = f − e to γ 0 dE dt dA 0 0.1 GeV · − the MAGIC, EGRET and COMPTEL data. The figure shows the three fitted models: β = 1 (red), β = 2 (blue) and β = 1.2 (green). The color shaded areas denote the systematical error region. The black triangles and circles denote the measured COMPTEL and EGRET flux points [2]. The arrows in the right part of the figure are the 2σ upper limits derived from previous measurements by MAGIC [3], Celeste [49] and Whipple [50]. Additionally, flux predictions for the polar cap model (light grey dashed line) [134], the slot gap model (dark grey dashed line) [32] and the outer gap model (light blue histogram) [53] are displayed. 114 6. Observation of the Crab Pulsar using the Analog Sum Trigger 6000 5000 4000 3000 excess events 2000 1000 0 30 40 50 60 70 100 200 300 400 SIZE bin [phe] Figure 6.19: The number of measured excess events (blue triangles) and the prediction based on the so-called power law cut-off (blue histogram). See text for details. the first two bins is well described by the models. For the 3rd and the 4th bin, however, the predicted excess is clearly below the measurements. This hints for a spectrum extending to higher energies with a less steep cut-off, yielding more excess events at higher energies. In section 6.8.2 and 6.9, this option will be reconsidered. In figure 6.18, the joint fitted spectral energy density (SED)3 to the COMPTEL, EGRET and MAGIC measurements is displayed, together with the theoretical predictions for the pulsed spectrum for the outer gap model [53], the polar gap [134] and the slot gap model [32]. 6.8.2 Power Law Cut-Off Due to the poor agreement between the number of excess events in the 3rd and 4th SIZE bin and an assumed exponential cut-off, I investigated a “power law” cut-off of the form: ǫ δ E − E − f (E; f ,ǫ,Ecut, δ)= f (6.11) γ 0 0 E + E · 0.1 GeV cut For E Ecut, this spectrum turns into a power law with spectral index δ. For E Ecut, ≫ ≪ the spectrum corresponds to a power law with spectral index α = ǫ + δ: ǫ δ α E− − = E− , for E Ecut fγ(E; f0,ǫ,Ecut, δ) δ ≪ (6.12) ∝ E− , for E Ecut ≫ By fixing α = ǫ + δ = 2.022 to the power law index determined by EGRET, the best fit is given for: 1 2 1 f = (20.4 0.7stat 0.4syst) s m GeV− , 0 ± ± − − Ecut = (5.8 1.9stat 4.1syst) GeV (6.13) ± ± δ = 3.2 0.3stat 0.2syst ± ± 3the SED is the spectrum multiplied by E2. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 115 SIZE bin excess in P1 excess in P2 background reduction 25 2 2 β Ecut χ /ndf Prob(χ ) 1 (17.7 2.8stat 5.0syst) GeV 27.3/23 24% ± ± 2 (23.2 2.9stat 6.6syst) GeV 27.8/23 22% ± ± 1.2 0.2 (20.4 3.9stat 7.4syst) GeV 26.6/22 23% ± ± ± Table 6.3: The cut-off values for the total pulsed flux in P1+P2, the statistical and the systematic error, the χ2 and its probability for the fit, assuming an exponential β = 1 or super exponential (β = 2 and β = 1.2) cut-off. The quality of the fit is χ2/ndf = 32/224. The power law spectrum measured by EGRET with spectral index 2.022 turns over into a power law with spectral index 3.2 0.3, de- ± scribing the VHE γ-ray flux. Even though the quality of the fit is worse than in the case of an exponential cut-off, the excess events in the higher SIZE bins are better described by a power law cut-off, which is displayed in figure 6.19. Later in section 6.9, the spectrum in the cut-off region measured by MAGIC will be de- termined without using the flux measurements by EGRET. Thus, one gets rid of a possible mismatch between EGRET’s and MAGIC’s flux and energy calibration and reduces the systematic errors, which influences the quality of the joint MAGIC-EGRET fit. 6.8.3 Single Pulse Cut-Off Energy The method used to determine the cut-off spectra of the total pulsed spectrum was also applied to the single pulse data P1 and P2. As mentioned above, P1 does not exhibit excess events with a significance > 2σ for the 3rd and 4th SIZE bin. All three models therefore agree equally well with the number of excess events: Ecut = (12.6 2.0stat 3.9syst) GeV for β = 1 ± ± Ecut = (17.3 2.0stat 3.7syst) GeV for β = 2 (P1) (6.14) ± ± Ecut = (13.5 2.8stat 4.6syst) GeV for β = 1.1 0.3 ± ± ± The results of the P2 fit is given as: Ecut = (20.3 3.0stat 5.9syst) GeV for β = 1 ± ± Ecut = (25.3 3.1stat 5.7syst) GeV for β = 2 (P2) (6.15) ± ± Ecut = (19.7 3.0stat 6.6syst) GeV for β = 0.9 0.3 ± ± ± 4 ndf denotes the number of degrees of freedom of the fit 116 6. Observation of the Crab Pulsar using the Analog Sum Trigger 2500 measured number of excess events (in P1) excess events, exp. cut off (β=1) excess events, super exp. cut off (β=2) excess events, super exp. cut off (β=1.1) 2000 1500 1000 excess events 500 0 50 100 150 200 250 300 350 SIZE [phe] (a) P1 measured number of excess events (in P2) excess events, exp. cut off (β=1) 2500 excess events, super exp. cut off (β=2) excess events, super exp. cut off (β=1.1) 2000 1500 excess events 1000 500 0 50 100 150 200 250 300 350 SIZE [phe] (b) P2 Figure 6.20: The measured (light blue triangles) number of excess events in P1 [figure (a)] and P2 [figure (b)] and the predictions for the exponential (red) and super exponential (blue, green) cut-off fit to the joint COMPTEL, EGRET and MAGIC measurements. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 117 6 10 -1 4σ 10 -3 5 -5 3σ 10 probability probability 4 10 -7 2σ 10 -9 β 3 10 -11 1.5 σ 2 10 -13 10 -15 1 10 -17 10 -19 5 10 15 20 25 30 35 cut o [GeV] (a) P1 6 -1 10 4σ -2 3σ 2σ 10 1.5 σ 5 10 -3 -4 10 probability 4 10 -5 10 -6 β 3 10 -7 10 -8 2 10 -9 10 -10 1 10 -11 10 -12 10 -13 5 10 15 20 25 30 35 cut o [GeV] (b) P2 Figure 6.21: The probability map in case of a spectral fit to the single pulses P1 (a) and P2 (b). The red square denotes the exponential cut-off with β = 1, the blue triangle the super exponential cut-off with β = 2 and the green one the general super exponential case. The black contour lines denote the regions that can be excluded at the 1.5σ, 2σ, 3σ and 4σ level. 118 6. Observation of the Crab Pulsar using the Analog Sum Trigger 2 pulse β Ecut χ /ndf [GeV] 1 12.6 2.0stat 3.9syst 22.7/23 ± ± P1 2 17.3 2.0stat 3.7syst 19.6/23 ± ± 1.1 0.3 13.5 2.8stat 4.6syst 19.5/22 ± ± ± 1 20.3 3.0stat 5.9syst 21.3/23 ± ± P2 2 25.3 3.1stat 5.7syst 20.9/23 ± ± 0.9 0.3 19.7 3.0stat 6.6syst 20.1/22 ± ± ± Table 6.4: The cut-off parameters Ecut and β derived for the pulses P1 and P2. . In table 6.4, the cut-off values for P1 and P2 and the fit probability is summarized. In figure 6.20, the number of excess events from the measurements and the model predictions are displayed. The corresponding probability map for different Ecut and β is shown in figure 6.21. Note that the cut-off energies for P1 and P2 are different. Using the simple exponential 5 model, the cut-off for P2 is by (7.7 3.6stat) GeV higher than P1’s . It can therefore be ± excluded on a 2σ level that P1 and P2 have the same cut-off energy and spectral shape in the cut-off region. This is in contradiction to the statement in section 6.7.3. The difference between these two methods is due to the inclusion of the EGRET flux measurements here. Studying the phase resolved spectrum at the highest EGRET energies < 10 GeV reveals that P1 already shows a hint for a cut-off. Together with our measurements, this hint is confirmed on a 2σ level. As it is the case of the total P1+P2 flux, the P2 excess events in the last two SIZE bins are well above the prediction. The excess events in P1, on the other hand, are very well described by all three models. Given only the χ2 from the fit, the flux in both phase regions are well described by an exponential cut-off shape with β = 1. 6.9 The Pulsed Spectrum above 25 GeV The method to determine the cut-off energy and the spectral shape used in the previous sections is rather robust against statistical fluctuations of the excess events measured by MAGIC. However, this method is strongly affected by a possible systematic mismatch be- tween the EGRET and MAGIC energy scales, resulting in a rather large systematic error. In this section, two ways to determine the pulsed spectrum without using the measure- ments by EGRET will be described. In the first method, a power law spectrum will be assumed. The flux normalization and the spectral index will then be determined by for- ward unfolding the excess events in the same SIZE bins as used previously. In the second method, the spectrum will be determined in bins of estimated energy. Then, the unfolding procedure by Tikhonov is applied to derive the spectrum in true energy bins. Both meth- ods, the forward unfolding and the unfolding method by Tikhonov are described in more detail in section 4.4.5.1. 5Note that the systematic error of the cut off energy in P1 and in P2 are correlated. By building the difference of the two energies, this error cancels out. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 119 6000 measured number of excess events 5000 predicted excess events, power law 4000 3000 excess events 2000 1000 0 30 40 50 60 70 100 200 300 400 SIZE bin [phe] Figure 6.22: The measured number of excess events in the main and inter pulse (P1 and P2, respectively) and the predictions from a power law fit to the MAGIC data. The spectral index is α = 3.0. See text for details. 6.9.1 The Total Pulsed Spectrum in P1 and P2 The methods to compute a pulsed spectrum from the data taken with MAGIC were in a first step applied to the total pulsed flux in the main- and inter pulse combined. Pulsed Spectrum derived with the Forward Unfolding Method As model function, a power law spectrum was used: α dN E − f(E; f , α)= = f (6.16) 0 dE dA dt 0 50 GeV with the flux normalization f0 and the spectral index α. The data was split in the SIZE bins denoted in table 6.2. Using the forward unfolding method (the free parameters are f0 and α), the spectrum for the combined P1 and P2 flux was determined. In the next section 6.9.2, the procedure is repeated for the individual pulses P1 and P2. In figure 6.22, the number of measured excess events and the power law predictions for P1 and P2 is displayed. The χ2 is minimized for: 8 2 1 1 f = (3.8 0.7stat 1.0syst) 10 m s GeV− 0 ± ± · − − − (6.17) α = 3.0 0.4stat 0.5syst. ± ± The probability for the derived χ2/ndf = 0.8/2 is 67%, implying a very good agreement between fit and measured data. In particular in the 3rd and 4th SIZE bin, the predicted and the measured excess events agree better than in case of the cut-off fit to the combined EGRET-MAGIC data. Comparing the spectral index found here with the one found for the power law cut-off in section 6.8.2 shows that both agree within the statistical error. 120 6. Observation of the Crab Pulsar using the Analog Sum Trigger 3 2.8 2.6 2.4 2.2 2 1.8 1.6 log10(rec. energy/GeV) 1.4 1.2 1 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 log10(original energy/GeV) Figure 6.23: The correlation between generated (original) γ-ray energy Eor and the re- constructed energy Erec. The energy was estimated using the parameters log10(SIZE), WIDTH, LENGTH, log10(SIZE/(WIDTH*LENGTH)). Above an energy of 30 40 GeV, the reconstructed and the original energy are in ≈ − good agreement. For small energies below 30 GeV, the reconstructed energy ≈ is overestimated due to the trigger threshold at 25 GeV. Pulsed Spectrum unfolded with the Method of Tikhonov The total pulsed spectrum in P1 and P2 was also determined with the more general unfolding methods described in section 4.4.5.1, without making assumptions on the spectral distribution as it is done in the method of forward unfolding. The program fluxlc.cc from the standard MAGIC analysis, which is used to determine an energy spectrum, was changed such that the excess events were derived from a (very fine binned) phase diagram. Thus, the same methods which determine a spectrum from the excess events found in an ALPHA plot could be used to find the pulsed spectrum. Due to the rather steep pulsed spectrum, the analysis close to the trigger threshold where the detector efficiency is strongly energy dependent and the energy resolution close or even above 40% (see figures 6.23, 6.24 and 6.25), the spectrum needs to be unfolded. The energy was estimated using the RF method based on the image parameters: log10(SIZE) • WIDTH • LENGTH • 6. Observation of the Crab Pulsar using the Analog Sum Trigger 121 1.2 1 0.8 0.6 or or - E 0.4 E rec E 0.2 0 -0.2 -0.4 20 30 40 50 60 70 80 90 energy E [GeV] or Figure 6.24: The bias of the reconstructed energy between 15 100 GeV. − 70 energy resolution, only SIZE 60 energy resolution, several parameters 50 40 rel. energy resolution [%] 30 20 30 40 50 60 70 80 90 100 energy [GeV] Figure 6.25: The energy resolution at low energies. The energy was estimated using only SIZE (blue circles), or with additional parameters denoted in the text (green circles) log10(SIZE/(WIDTH*LENGTH)) • Compared to the estimation of the energy from SIZE alone, this improves the energy resolution at 35 GeV from 45% to 38%, as shown in figure 6.25. The resulting spectrum (before unfolding) is given in figure 6.26, and after unfolding with the method of Tikhonov 122 6. Observation of the Crab Pulsar using the Analog Sum Trigger ] -1 10-8 s -2 cm -1 10-9 diff. flux dN/dE [TeV 10-10 20 30 40 50 60 70 80 100 200 estimated energy [GeV] Figure 6.26: The differential total pulsed spectrum in P1+P2 before unfolding. As bin center, the barycenter was chosen. 2 Method Pulse f0 α χ /ndf 8 2 1 1 [10− m− s− GeV− ] [] forward P1 1.3 0.6stat 0.9syst 3.5 0.7stat 0.8syst 0.6/2 ± ± ± ± Tikhonov P1 1.0 0.7stat 0.8syst 4.4 2.5stat 0.7syst 1.0/2 ± ± ± ± forward P2 2.5 0.4stat 0.9syst 2.6 0.5stat 0.8syst 0.9/2 ± ± ± ± Tikhonov P2 2.3 0.5stat 0.8syst 2.8 0.6stat 0.7syst 3.2/3 ± ± ± ± forward P1+P2 3.8 0.7stat 1.0syst 3.0 0.4stat 0.5syst 0.8/2 ± ± ± ± Tikhonov P1+P2 4.1 0.4stat 1.0syst 3.1 0.6stat 0.5syst 4.3/3 ± ± ± ± Table 6.5: The power law fit values: The flux normalization f0 at the energy 50 GeV and the spectral index α. The fits were derived from the spectra unfolded with the forward unfolding and the Tikhonov method. in figure 6.27. The correlated power law fit to the unfolded spectrum yields 8 2 1 1 f = (4.1 0.4stat 1.0syst) 10 m s GeV− 0 ± ± · − − − (6.18) α = 3.1 0.6stat 0.5syst. ± ± These results are consistent with the parameters found by the forward unfolding method. The quality of the (correlated) fit determined by χ2 = 4.3 for ndf = 3 was good. 6.9.2 Single Pulse Spectra The same methods used to derive the total pulsed spectrum were also applied to find the single pulse spectrum in the P1 and P2 phase region: The forward unfolding method and 6. Observation of the Crab Pulsar using the Analog Sum Trigger 123 10-7 ] -1 s -2 -8 cm -1 10 10-9 10-10 diff. flux dN/dE [TeV 10-11 20 30 40 50 60 70 100 200 300 400 estimated energy [GeV] Figure 6.27: The unfolded spectrum, using the method proposed in [106]. The power law fit yields a spectral index of α = 3.1 0.6stat 0.5syst. ± ± 3500 measured number of excess events measured number of excess events 3000 2500 predicted excess events, power law predicted excess events, power law 2500 2000 2000 1500 1500 1000 excess events excess events 1000 500 500 0 0 30 40 50 60 70 100 200 300 400 30 40 50 60 70 100 200 300 400 SIZE bin [phe] SIZE bin [phe] (a) P1 (b) P2 Figure 6.28: The predicted and measured number of excess events for P1 (a) and P2 (b), assuming a power law spectrum. Note that the excess events for two higher bins in P1 have both a significance below 1σ and are thus compatible with 0. 124 6. Observation of the Crab Pulsar using the Analog Sum Trigger the “direct” unfolding method by Tikhonov. As already mentioned, based on the excess events in P1 and P2 binned in SIZE, it cannot be distinguished whether P1 and P2 come from the same distribution and have the same spectral shape. Nevertheless, an independent spectrum for both pulses can be determined. The forward unfolding method was applied to the excess events binned in the same SIZE bins as for the total pulsed spectrum. In case of P1, the excess in the third and forth SIZE bin is not significant and well below 2σ. A power law fit is therefore mostly dominated by the excess events in the two first SIZE bins. The spectral index α thus has a somehow arbitrary value indicated by its large statistical error. The flux level f0, however, is still reasonable. The excess events and model fit are displayed in figure 6.28a, and the fit results are: 8 2 1 1 f = (1.3 0.6stat 0.9syst) 10 m s GeV− 0 ± ± · − − − (6.19) α = 3.5 0.7stat 0.8syst ± ± with χ2/ndf = 0.61/2, prob(χ2) = 74%. The P2 phase region is 0.32 <φ< 0.43 as defined in [112] and denoted in table 4.1. The number of excess events are given in table 6.2. As model spectrum, a power law spectrum (equation: 6.16) was used. The predicted and measured number of excess events are shown in figure 6.28b. The forward unfolding fit results are: 8 2 1 1 f = (2.5 0.4stat 0.9syst) 10 m s GeV− 0 ± ± · − − − (6.20) α = 2.6 0.5stat 0.8syst ± ± The quality of the fit was good (χ2/ndf = 0.86/2), corresponding to a probability of 65%. Both spectra were also determined without assuming an apriori spectral shape (figure 6.29) and unfolded with the method from Tikhonov (see figure 6.30). The data in the estimated energy range 20 300 GeV was subdivided into 6 bins. The unfolded spectra are − fitted with a power law. While the fit of the P2 spectrum works fine, the low significance of the spectral points of the P1 flux yields a large statistical error on its spectral index. The fit results are summarized in table 6.5. The values obtained for the flux normaliza- tion f0 and the spectral index α agree for the two different unfolding methods within the systematic uncertainty. 6.9.3 Systematic Errors Influencing the Spectral Measurements There is no γ-ray test beam to calibrate an IACT. Energy determination and detector effi- ciencies are therefore estimated from MC simulations. In addition, the Earth’s Atmosphere is not a high precision calorimeter, but prone to short and long term fluctuations. The detector itself is built from elements which may change over time (for example degradation of mirrors or PMTs). Even though the performance of the telescope is regularly monitored and the MC simulations adjusted accordingly, systematic errors cannot be excluded. As was shown in [3, 94], systematic errors affect the energy estimation and the flux level estimation. The energy estimation is e.g. affected by: varying atmospheric transmission, reflectivity uncertainty of the mirrors, uncertainty of the PMT’s quantum efficiency and their F-Factor and other influences. The biggest contribution comes from the uncertainty of the photo detection efficiency, which includes the transmission through the plexiglass in front of the camera and/or the PMT’s quantum efficiency. In total, the uncertainty in the energy scale sums up to 16%. The flux level uncertainty is influenced by e.g. dead ≈ channels, instable discriminator thresholds or temperature dependence of the trigger logic. This uncertainty is estimated to 11%. ≈ In the analysis presented, another systematic error was added: The uncertainty of the 6. Observation of the Crab Pulsar using the Analog Sum Trigger 125 10-8 ] -1 s -2 cm -1 10-9 10-10 diff. flux dN/dE [TeV 20 30 40 50 60 70 100 200 300 estimated energy [GeV] (a) P1 10-8 ] -1 s -2 cm -1 10-9 10-10 diff. flux dN/dE [TeV 10-11 20 30 40 50 60 70 80 100 200 estimated energy [GeV] (b) P2 Figure 6.29: The single pulse spectra of P1 and P2 before unfolding. See text for details. 126 6. Observation of the Crab Pulsar using the Analog Sum Trigger 10-7 ] -1 s -2 10-8 cm -1 10-9 10-10 diff. flux dN/dE [TeV 10-11 20 30 40 50 60 70 80 100 200 estimated energy [GeV] (a) (P1) 10-7 ] -1 s -2 10-8 cm -1 10-9 10-10 diff. flux dN/dE [TeV 10-11 20 30 40 50 60 70 100 200 300 400 estimated energy [GeV] (b) (P2) Figure 6.30: The unfolded single pulse spectra for P1 and P2 and the fit to the spectra. 6. Observation of the Crab Pulsar using the Analog Sum Trigger 127 sum trigger threshold calibration. In section 5.6, three methods used to determine the discriminator and clipping levels of the sum trigger are explained. They differ by around 10%. An additional uncertainty for the determination of the cut-off energy comes from the systematic uncertainty of the EGRET energy calibration for the highest energies. In [135], a possible explanation for the anomal flux of the diffuse galactic flux at GeV energies is addressed to a misscalibration of the EGRET detector at those energies. The measured Crab Pulsar flux points at energies above 1 GeV could also be affected by up to a factor 2 [135]. This consideration was taken into account in the joint fit to the EGRET and MAGIC points for the computation of the systematic error. 6.10 Phase Diagram In figure 6.31, the pulse profiles are displayed for optical wavelengths, HE γ-rays above 100 MeV and 1 GeV and for VHE γ-rays above 25 GeV and 60 GeV6. The phase diagram itself contains information on the region within the pulsar’s magnetosphere where the γ-ray production takes place. In the following section, I will describe the analysis of the phase diagrams at different energies, containing the MAGIC optical measurements, EGRET’s pulse diagram for energies above 100 MeV and 1 GeV and the MAGIC phase diagram above 25 GeV and above 60 GeV. By studying the pulse diagrams at different energies, it can be seen that the position of the main and the inter pulse do not dramatically change position. This is unusual, as most pulsars do show an energy dependence of the peak positions. In the following sections, I will discuss the arrival time and phase of the main and inter pulse relative to the radio main pulse for optical photons and for the γ-rays measured by EGRET and MAGIC. Then, the arrival phase differences for photons with different energies is studied. In the next step, a more detailed analysis of the pulse profile’s morphology will be presented. Then, the ratio of the flux in P2 to P1 is studied as a function of energy. 6.10.1 Arrival Time of Each Pulse The positions of the two peaks P1 and P2 were derived for the phase diagrams displayed in figure 6.31. By looking at the main peak of the optical pulsation in detail, it becomes evident that the pulse shape is not symmetric but has a complicated morphology. On the other hand, the phase resolution at the highest energies does not allow to distinguish if the pulse has a symmetric or an asymmetric shape. The peak positions P1 and P2 were therefore determined in a pulse shape independent manner: In the off pulse phase region (0.52 <φ< 0.88), the background per bin Nbg is computed. Then, the mean arrival φP1 and φ of the main and inter pulse is computed for the phase regions 0.1 <φ< 0.09 P2 − (P1) and 0.3 <φ< 0.45 (P2) from the histograms directly: 0.1<φi<0.09 0.3<φi<0.45 − − (N Nbg) φ (N Nbg) φ φ = φi − i , φ = φi − i (6.21) P1 (N N ) P2 (N N ) P φi bg P φi bg 0.1<φi<0.09 − 0.3<φi<0.45 − − P − P 6The energies 25 GeV and 60 GeV correspond to the peak of the MC γ-ray energy distribution after cuts for a spectrum with spectral index 3.1, as it was derived in section 6.9. The phase diagram above 25 GeV was derived with a lower SIZE cut of 25 phe, the one above 60 GeV for a lower SIZE cut of 107 phe. 128 6. Observation of the Crab Pulsar using the Analog Sum Trigger MAGIC, optical pulse pro!le 91.4 91.2 91 90.8 90.6 counts 90.4 90.2 90 -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 EGRET, E > 0.1 GeV 350 300 250 200 counts 150 100 50 -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 EGRET, E > 1 GeV 70 60 50 40 counts 30 20 10 0 -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1