Measurement of the cosmic ray flux with H.E.S.S

Transcription

1 Measurement of the cosmic ray flux with H.E.S.S DIPLOMARBEIT zur Erlangung des akademischen Grades Diplom-Physiker eingereicht von Arne Schönwald geboren am 9. Februar 1982 in Berlin HUMBOLDT-UNIVERSITÄT ZU BERLIN Mathematisch-Naturwissenschaftliche Fakultät I Institut für Physik 1. Gutachter: Prof. Dr. T. Lohse 2. Gutachter: Prof. Dr. H. Kolanoski Berlin, den 28. August 2008

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3 Abstract The High Energy Stereoscopic System (H.E.S.S.) is an experiment which observes sources in space which emit high energy γ-rays like neutron stars, supernova remnants and galactic nuclei. This work is the first attempt to measure the flux of cosmic rays with H.E.S.S. A stand-alone analysis chain for the energy reconstruction of showers measured with H.E.S.S. and for the flux measurement was developed with the help of proton Monte Carlo data. The quality of the energy reconstruction method was tested with proton Monte Carlo data. In order to check the flux measurement method as well as the whole stand-alone analysis the index of the power law spectrum of the Monte Carlo data was determined and compared to the known one. Thereafter real measured data from H.E.S.S. was used for a determination of the cosmic ray flux. Moreover the spectrum of the cosmic ray proton flux was derived with an approximation and compared with a measurement from the KASCADE experiment. The calculated differential flux of the cosmic ray proton spectrum (dφ/de)(e) = (0.227 ± stat ± sys ) /(TeV s m 2 sr) (E/1 TeV) ( 2.931±0.023stat±0.219sys) is compatible to the result measured by KASCADE. iii

4 Contents 1 Cosmic Rays Discovery The Energy Spectrum Current Experiments The Imaging Atmospheric Cherenkov Technique Particle Shower Interaction Mechanisms Electromagnetic Showers Hadronic Showers Cherenkov Radiation The Cherenkov Effect The Cherenkov Effect in Air Showers Air Shower Monte Carlo Simulation Software CORSIKA The hadronic interaction models QGSJET-II and SIBYLL 19 3 The High Energy Stereoscopic System The H.E.S.S. Experiment The Site Weather and Atmospheric Monitoring The Telescopes Mount and Tracking The Optical System The Cameras The Trigger The Camera Trigger The Central Trigger Shower Reconstruction Mapping of the shower into the camera Image parameters i

5 Contents 4 Analysis Algorithm Monte Carlo Samples Cuts The Shower Direction The Impact Parameter The Energy Reconstruction Muon Correction Bias and Resolution of the energy The Energy Threshold Effective Area Flux Measurement Algorithm of the Flux Measurement Selection of the Energy Range for the Fit of the Flux Test on the Monte Carlo Data Index Flux of Cosmic Rays Proton Flux of the Cosmic Ray Systematic Studies Analysis of the Influence of the Energy Bias, the Energy Resolution and the Effective Area on the Index Determination Energy Discretization Bibliography 80 ii

6 List of Figures 1.1 Differential flux of cosmic rays over the energy (taken from [7]), the dotted line shows a power law E 3 for comparison Feynman graph for bremsstrahlung Feynman graph for pair production Electromagnetic shower model by Bethe & Heitler Different interaction parts of a hadronic shower Simulated longitudinal shower developments for a 300 GeV photon and a 1 TeV proton (taken from [6]) Polarization of a medium by a charged particle with v < c n (a) and v > c n (b), where c n is the speed of light in the medium (taken from [14]) Geometry of the Cherenkov effect Cherenkov light pool of a vertical electromagnetic shower Cherenkov light distribution on the ground of simulated air showers (300 GeV γ-ray (left) and 1 TeV proton (right) taken from [6]) Position of the H.E.S.S. site in Namibia The four H.E.S.S. telescopes on the site One of the four H.E.S.S. telescopes on the site Dish and mirror facets of a H.E.S.S. telescope. In the middle between the center and the left edge of the dish, the sky CCD can be seen A H.E.S.S. camera. One can see the 960 photomultipliers A sketch of the mapping mechanism of the H.E.S.S. telescopes Hillas parameter of the camera image of an air shower The angular direction resolution in degrees against the true energy (black = QGSJET-II, red = SYBILL) Figure of the impact parameter d Distribution of δd/d in the interval 40 m d true 80 m Bias of the impact parameter (QGSJET-II) Bias of the impact parameter (SYBILL) iii

7 List of Figures 4.6 Resolution of the impact parameter (QGSJET-II) Resolution of the impact parameter (SYBILL) Relative number of events against d true (black line) and of d reco (red line) (QGSJET-II) Relative number of events versus d true (black line) and of d reco (red line) (SYBILL) Ratio of the number of events N reco /N true against impact parameter (QGSJET-II) Ratio of the number of events N reco /N true versus impact parameter (SYBILL) Plot of the lookup: One can see the energy value in TeV (in a colour scale) against the true impact parameter and the amplitude (QGSJET-II) Plot of the lookup: One can see the energy value in TeV (in a colour scale) versus the true impact parameter and the amplitude (SYBILL) Bias of the energy (QGSJET-II) Bias of the energy (SYBILL) Resolution of the energy (QGSJET-II) Resolution of the energy (SYBILL) Relative number of events against E true (black line) and of E reco (red line) (QGSJET-II) Relative number of events versus E true (black line) and of E reco (red line) (SYBILL) Ratio of the number of events N reco /N true against the energy (QGSJET- II) Quotient of the number of events N reco /N true versus the energy (SYBILL) Number of events per bin over the reconstructed energy E reco (QGSJET-II) Number of events per bin over the reconstructed energy E reco (SYBILL) Plot of the effective area (QGSJET-II Monte Carlo) Plot of the effective area (SYBILL Monte Carlo) Plot of the effective areas from the two interaction models Plot of the ratio A eff (QGSJET-II)/A eff (SYBILL) of the two fit functions Comparison of the tree methods of calculating the flux Fit of the QGSJET-II Monte Carlo data from 5 TeV to 30 TeV Fit of the SYBILL Monte Carlo data from 5 TeV to 30 TeV iv

8 List of Figures 5.4 Fit of the QGSJET-II Monte Carlo data from 5 TeV to 40 TeV Fit of the QGSJET-II Monte Carlo data from 5 TeV to 80 TeV Number of events per bin over the reconstructed energy E reco, using the lookup of the QGSJET-II Monte Carlo data Number of events per bin over the reconstructed energy E reco, using the lookup of the SYBILL Monte Carlo data Fit of the flux of cosmic rays using effective area and the energy lookup table from the QGSJET-II Monte Carlo data Fit of the flux of cosmic rays using effective area and the energy lookup table from the SYBILL Monte Carlo data Total flux of the cosmic rays and proton flux of cosmic rays against the energy, taken from [5] Fit of the fraction of protons in the flux of cosmic ray Fit of the proton flux of the cosmic rays using the effective area and the energy lookup generated with the QGSJET-II Monte Carlo data Fit of the proton flux of the cosmic rays using the effective area and the energy lookup generated with the SYBILL Monte Carlo data Fit of the proton flux of the cosmic ray using the effective area and the energy lookup generated with the QGSJET-II Monte Carlo data Fit of the proton flux of the cosmic ray using the effective area and the energy lookup generated with the QGSJET-II Monte Carlo data 69 v

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10 List of Tables 4.1 Overview over the used Monte Carlo files Used cuts Number of events before and after the cuts quality properties of the energy reconstruction Comparison of the fit results for the flux index for both Monte Carlo data sets Comparison of the fit results from the QGSJET-II Monte Carlo data for different energy ranges Overview over the used data set Comparison of the results of the flux of cosmic rays Comparison of the results of the proton flux of cosmic rays Comparison of the fit results for the proton flux of cosmic rays for different energy ranges using the QGSJET-II Monte Carlo for the generation of the energy lookup and the effective area vii

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12 Chapter 1 Cosmic Rays 1.1 Discovery After Henri Becquerel had discovered radioactivity in 1896, most of the scientists of this era thought that the ionization of the air was only caused by the radiation of radioactive terrestrial elements. Domenico Pacini noticed changes around the same time of the ionization rate over the sea and over a lake in From this measurement he reasoned that there have to be also other sources of radioactivity than radioactive elements in the ground or radioactive gases. Also 1912 Victor Hess did a balloon flight up to the altitude of 5000 m. He took some electrometers with him and observed that the ionization rate at the maximal altitude of his flight was four times higher than the one on the ground. He concluded from this result that a radiation of a huge penetrating power seems to enter the atmosphere from space. For this measurement Hess received the Nobel Prize in Some years later from 1913 until 1914 Werner Kolhörster was able to confirm the measurements by Hess due to measuring the ionization rate at 9 km altitude. After believing for years that the cosmic rays were mainly gamma rays new experiments in the time from 1927 to 1937 showed that the cosmic rays are primary massive particles with a positive charge Gottlieb and Van Allen showed that the primary particles are mainly protons, some helium nuclei and a few heavier nuclei. They also used ballon experiments which used emulsions for the measurement near the top of the atmosphere. 1.2 The Energy Spectrum Figure 1.1 shows the differential spectrum of the cosmic rays. Up to an energy of ev the particle flux is big enough to measure single nuclei with either satellites or experiments carried by balloons. With such direct experiments one can measure the relative amount of different particles and the energy spectra of 1

13 Chapter 1. Cosmic Rays Figure 1.1: Differential flux of cosmic rays over the energy (taken from [7]), the dotted line shows a power law E 3 for comparison electrons, positrons, protons and of diverse nuclei. Furthermore one can measure the energy, intensity and spatial distribution of X-rays and γ-rays. One could imagine the sun as a source of cosmic rays but measurements of energy and isotropy have shown, that the sun is not the main source. But the solar wind can shield cosmic ray particles with a kinetic energy less than 100 MeV from outside the solar system. Only therefore the sun dominates the proton flux in this energy range. For energies in the order of ev the flux becomes so low that one needs ground-based experiments with large apertures and long exposure times in order to measure a significant number of events. One can say that these experiments use the atmosphere as a huge calorimeter to measure the properties of the cosmic ray flux. If particles with these high energies hit the atmosphere they produce 2

14 1.3 Current Experiments extensive air showers (EASs). These showers can spread over large areas. Already in 1938 Pierre Auger reasoned from the large size of EASs that the spectrum extents up to and perhaps even beyond ev. Today there is made enormous progress measuring the very low flux (about 1 event km 2 yr 1 ) in the energy region above ev. The spectrum of the cosmic rays above 10 9 ev can be described by multiple power laws. At the energy of about ev, the so called knee, the spectrum steepens from E 2.7 to E 3.0. Until today this feature is still not consistently explained. At the energy of about ev, which is called the dip, the index changes to E 3.3. The spectrum flattens to E 2.7 at the so called ankle, which lies approximately at ev. A possible interpretation of the ankle is that beyond the energy of ev the flux is dominated by cosmic radiation with extragalactic origin while before the flux is dominated by the cosmic rays with galactic origin (see [11]). This idea is supported by the measurements of the Akeno Giant Air Shower Array (AGASA) experiment, which found that around ev the angular distribution of the cosmic rays correlates with the Galactic center and is furthermore compatible with a Galactic origin. At higher energies this correlation vanishes (see [15]). 1.3 Current Experiments Current experiments which measure the flux of the cosmic radiation are for example BESS, Tibet ASγ Experiment, KASACADE-Grande and Pierre Auger Observatory. BESS (Balloon-borne Experiment with a Superconducting Spectrometer) is a balloon experiment which measures the flux of the cosmic ray in the atmosphere. Its energy range is from 1 GeV to 120 GeV for protons or from 1 to 54 GeV/nucleon. It can reach an altitude of 37 km. The Auger observatory is a ground based experiment which searches for the most highly energetic particles from the flux of cosmic ray. In order to detect protons with an energy of about ev (that is the same kinetic energy a tennis ball traveling with 85 km/h has) one needs a huge detector because protons with this energy only have an estimated arrival rate of just 1 per square kilometer per century. Thus Auger has a detection area which is a little bit larger than the area of the country of Luxembourg. It is located in the southern hemisphere in the Pampa of Argentina. The experiment uses two types of detectors, on the one hand it uses water tanks for the measurement of the interaction of the high energy particles with the water and on the other hand it measures the fluorescence light from the interaction of the cosmic ray particles with the atmosphere. The Tibet ASγ experiment is an air shower observation array which is built in Yangbajing (Tibet) and is run by a collaboration of China and Japan. The air- 3

15 Chapter 1. Cosmic Rays shower array is not only designed for the measurement of the nuclear component of the cosmic rays but also for the detection of high energy gamma rays. Today it consists of 761 fast timing counters and 28 density counters around them. It has an energy range from ev to ev. The KASCADE-Grande (KArlsruhe Shower Core and Array DEtector-Grande) is a scintillator array with 252 detectors which form an array of 200 m times 200 m. It consists of ionization chambers and multi-wire proportional chambers for measuring extensive air showers of cosmic rays in the energy range from ev to ev. The experiment is located on the area of the research institute Karlsruhe, in Germany. 4

16 Chapter 2 The Imaging Atmospheric Cherenkov Technique Due to the atmosphere a direct detection of very high energy (VHE) γ-rays on the ground is not possible. One can use satellite experiments to detect VHE γ-rays outside the atmosphere. The problem with satellite experiments is, that a satellite only has an effective area (A eff ) in the order of square metres. The relation between the differential rate dr/de and the differential flux dφ/de is dr dφ (E) = de de (E) A eff (E). If the differential flux dφ/de is small, one needs a big effective area to get an acceptable rate R. For energies above some 10 GeV the flux of γ-rays becomes too small to detect enough γ-rays in an acceptable time. Therefore one uses Imaging Atmospheric Cherenkov Telescopes (IACT) which provide an effective area in the order of > 10 5 m 2. If a particle with high energy hits the atmosphere it generates a particle shower. Some of the particles in the shower produce Cherenkov radiation which is detectable with telescopes on the ground although often the shower dies out before it can reach the ground. In the following section the generation of particle showers and Cherenkov light by some of the shower particles is explained. 2.1 Particle Shower If a VHE particle from space hits the earth s atmosphere it can generate secondary particles. In general the first interaction takes place at an altitude of km above sea level. If after the interaction the secondary particles still have enough energy they can also interact in the atmosphere and generate again secondary particles. This goes on until the energy of the secondary particles becomes too 5

17 Chapter 2. The Imaging Atmospheric Cherenkov Technique small to generate new particles. This evolution of the shower mainly depends on the altitude the first interaction takes place, the energy of the primary particle and the type of the primary particle (γ, electron, proton or nucleus). The most important interaction mechanisms are discussed briefly in the following section Interaction Mechanisms The following interaction mechanisms of particles or photons with matter are important for the understanding of the shower evolution. Ionization: Heavy charged particles with moderate kinetic energy mainly lose energy by ionization and excitation (of the electrons) of atoms or molecules in the traversed matter. If a massive particle of the charge ze flies through a medium of atomic number Z and atomic mass A with the velocity β = v/c the mean rate of the energy loss is given by the Bethe-Bloch equation de dx = 2πN Lrem 2 2 ec 2 ρ Z A z 2 β 2 [ log ( ) 2me c 2 β 2 γ 2 T max 2β 2 δ 2 C I 2 Z For minimum ionizing particles is de/dx min = 1.8 MeV cm 2 /g in air. Due to ionization loss a minimum ionizing particle would lose 2.2 kev/cm on sea level. The formula for the energy loss of electrons as ionizing particles differs slightly from the Bethe-Bloch equation due to the interaction of quantum mechanically identical particles. Bremsstrahlung: A charged particle travelling through matter can be deflected in the Coloumb field of a nucleus. This deflection, which is an effective acceleration of the particle, leads to the emission of electromagnetic radiation, the particle emits bremsstrahlung in the form of photons. The cross section for emitting bremsstrahlung is σ r 2 e = (e 2 /mc 2 ) 2. Therefore the cross section for muons (the next lightest charged lepton after the electron), which have a mass of about 200 times of the electron mass, is already smaller by a factor of Thus only electrons and positrons emit a reasonable amount of bremsstrahlung. The mean energy loss is de dx = N ( ) Lρ r 2 4Z2 e 183 A 137 log E. 6 Z 1 3 ].

18 2.1 Particle Shower After the distance of one radiation length x = x 0 the particle has on average emitted 1/e of its starting energy in form of bremsstrahlung. Bremsstrahlung leads to an exponential decay of the initial energy with the flight path E = E 0 e x x 0. One distinguishes between the flight path x, and the grammage X which is related to the flight path via X = ρ x. In air the radiation length is X 0 = 36.7 g/cm 2. For standard pressure at sea level this corresponds to a flight path of 306 m. The photons are emitted in a cone around the forward direction. The average emission angle Θ is related to the Lorentz factor γ via the equation Θ = 1/γ, therefore for electrons or positrons with high energy all photons are mainly emitted along their flight direction. For particles with higher energies the energy loss due to bremsstrahlung becomes more and more important in comparison to ionization effects. This is due to the fact that the energy loss by ionization is proportional to Z log E while for bremsstrahlung it is proportional to Z 2 E. Figure 2.1 shows the Feynman graph of bremsstrahlung. Figure 2.1: Feynman graph for bremsstrahlung Pair production: Pair production is the most effective way of particle production at high energy. If a photon has an energy of at least twice the mass of an electron (or another charged particle), particle-antiparticle pairs can be produced. Due to the conservation of the four momentum this is only possible in the Coloumb field of a nucleus or an electron. The mean free path length λ 0 is related to the mean free path length of the bremsstrahlung by the relation λ 0 9/7 x 0. The average opening angle under which the electron-positron pair is emitted, follows the same relation as for bremsstrahlung. Figure 2.2 shows the Feynman graph of pair production. Hadronic interaction: In hadronic interactions of a nucleus with nuclei of the atmosphere often 7

19 Chapter 2. The Imaging Atmospheric Cherenkov Technique Figure 2.2: Feynman graph for pair production the nucleus is excited or even destroyed and jets of particles are generated. Some typical hadronic reactions are: p + nucleus π + π π nucleus nucleus nucleus 1 + n + p + α +... Hadronic cross sections are proportional to the geometrical size of the nucleus and therefore σ A 2/3. The interaction length for hadronic interactions is also related to the atomic number: λ int A 1/ Electromagnetic Showers An electromagnetic shower is formed whenever a particle with enough energy interacts electromagnetically with atoms or molecules from the atmosphere. After the first interaction a cascade of secondary particles is produced mainly via pair production and bremsstrahlung. If the energy of the secondary particles is sufficient, they can again interact in the atmosphere and produce new particles. The number of particles in this process grows exponentially. The particle cascade dies out, when the critical energy per particle is reached. The critical energy E C is reached, if de dx = de bremsstrahlung dx. ionisation This means that the loss of energy per unit length of the particle due to bremsstrahlung becomes equal with the loss of energy due to ionization (Bethe-Bloch formula). A good approximation for the critical energy is given by E C 800 MeV Z In air this leads to a critcal energy E C 80 MeV. With decreasing energy per shower particle the generation of new bremsstrahlung photons becomes more and more unlikely and all shower particles only react via ionization and the shower dies out because the generation of new secondary particles by bremsstrahlung or pair production is not longer possible. 8

20 2.1 Particle Shower The lateral development of the shower is determined by elastic multiple Coulomb scattering of electrons. The mean scattering angle for electrons with energy close to the critical energy is small, therefore the lateral size of the shower is smaller than the longitudinal one. While the longitudinal size of a shower is described by the radiation length x 0 the lateral size is described by the Molière radius R Mol R mol = x 0 mec 2 4π/α E c = x MeV E c. For a critical energy about 80 MeV the Molière radius is R mol 1/4 x 0. A simple shower model which can explain the basic properties of the electromagnetic shower development is the one of Bethe & Heitler. It relies on a few very basic assumptions. The first one is, that the energy loss due to ionization is neglected, which is a good approximation for particles with very high energy. As discussed above the average length for the generation of a electron-positron pair λ 0 (by pair production) differs by the factor 7/9 from the radiation length of bremsstrahlung x 0. The second assumption is to set this factor to one, so that for both processes the radiation length is x 0. That leads to the following simple model: If the primary particle, which hits the atmosphere, is a γ then it generates at the point of first interaction (after the first radiation length) an electron-positron pair. The electron and the positron each get half of the energy of the primary γ. The electron and the positron both generate after one radiation length x 0 a photon, which gets half the energy of the electron or positron. In the next step after the third radiation length the photons generate again electron-positron pairs and the electrons or positrons new bremsstrahlung photons. This process goes on and after each radiation length the number of particles doubles and the energy per particle is divided by two (see figure 2.3). After n = x/x 0 interaction lengths, the shower consists of N(x) = 2 x/x 0 particles each with an average energy of E(x) = E 0 2 x/x 0. The maximal shower depth x max in the atmosphere is reached, if the average energy per particle is or becomes smaller than the critical energy E c E 0 2 xmax/x 0 = E c x max = log E 0/E c log 2 x 0. With these relations one can rewrite the the maximal particle number in the shower depending on the primary energy N max = 2 xmax/x 0 = E 0 E c. Thus one can see that the Bethe & Heitler model predicts an exponential growth of the particle number in the shower development as long as the average energy 9

21 Chapter 2. The Imaging Atmospheric Cherenkov Technique Figure 2.3: Electromagnetic shower model by Bethe & Heitler per particle is higher than the critical energy. Furthermore the maximal number of shower particles is proportional to the energy of the primary particle and the maximal shower depth grows logarithmically with the primary energy. For example a γ photon with a primary energy of 1 TeV would generate a maximal number of secondary particles. For air the radiation length x 0 is 36.7 g/cm 2. This leads for γ-photon with an energy of 1 TeV to x max 500 g/cm 2. Using the barometric formula as an approximation for the density of the air as function of the height (which is not a perfect approximation due to the fact that the atmosphere is not isothermic), the shower maximum is reached in a height about 6 km above sea level Hadronic Showers Hadronic showers are generated by protons and nuclei which hit the atmosphere and the shower development of a hadronic shower differs a lot from electromagnetic showers. This is due to the fact, that the reactions are more complex and also that nuclei of atoms or molecules of the atmosphere can be exited or even destroyed in strong interactions with the primary particle or even secondary particles. In hadronic showers there can evolve electromagnetic subshowers, too. If a proton or nucleus hits the atmosphere mainly pions (π +, π, π 0 ) are generated but also kaons (K +, K, K 0 ), nucleons (protons and neutrons) and hyperons. Due to the fact that these secondary particles also interact strongly a hadronic 10

22 2.2 Cherenkov Radiation cascade is generated. While the charged pions have a relatively long life time in the order of 10 8 s the neutral pion decays in 98.8 % of all cases very quickly after the short time of s into two photons. This reaction is mainly responsible for the generation of electromagnetic subshowers due to the interaction effects from γ-photons with the atmosphere which were described above. Figure 2.4 shows some different interactions in a hadronic shower. The charged pions live long enough to interact with the nuclei of the atmosphere before the decay into muons and neutrinos π + µ + + ν µ π µ + ν µ π 0 γ + γ. Since muons are long-lived and do not suffer considerable energy losses due to bremsstrahlung or ionization some of them can reach the ground before they decay. The ones that decay do it in the following way µ + e + + ν e + ν µ µ e + ν e + ν µ. The interaction length for nuclear interactions λ int in air is about λ int 90 g/cm 2. This is much bigger than the radiation length in air (x 0 37 g/cm 2 ) and therefore the hadrons penetrate deeper into the atmosphere. In strong hadronic interactions a lot of kinetic energy is lost by the generation of new particles or secondary hadrons. Furthermore the secondary particles receive a larger transverse momentum in the production (due to the transverse momentum being proportional to the mass of the decaying particle) compared to the ones in electromagnetic showers. In consequence the lateral extension of handronic showers is much larger than that of electromagnetic showers. The structure of hadronic showers is in addition much more complex, because in hadronic interaction multiple particle processes are involved. In particular, hadronic showers generally contain very compact electromagnetic subshowers. This complexity makes hadronic showers less regular and they exhibit larger fluctuations. Figure 2.5 shows the difference between a photon and a proton shower. 2.2 Cherenkov Radiation The Cherenkov Effect If a charged relativistic particle travels through a medium - which can be polarized - it moves other charged particles in the medium out of their rest position. If 11

23 Chapter 2. The Imaging Atmospheric Cherenkov Technique Figure 2.4: Different interaction parts of a hadronic shower these particles fall back to their rest position the second derivative of their dipole moment doesn t vanish and due to this they emit electromagnetic radiation (see Figure 2.6). In general all these elementary waves interfere destructively. However, if the speed of the charged relativistic particle becomes bigger than the speed of light in the medium, the elementary waves interfere constructively and Cherenkov radiation is emitted. The angle Θ c under which the Cherenkov radiation is emitted is given by (see als Figure 2.7) cos Θ c = c n t v t = c n v = c n v = 1 β n, where n is the refractive index of the medium and β is the velocity of the particle in units of the speed of light in vacuum. Since cos Θ c 1, the particle velocity has to fulfill β 1/n for emission of Cherenkov radiation to become possible. The Cherenkov angle Θ c grows with increasing β, until for ultra-relativistic particles with β 1 the maximal Cherenkov angle Θ c,max is reached Θ c,max = arccos 12 ( ) 1. n

24 2.2 Cherenkov Radiation Figure 2.5: Simulated longitudinal shower developments for a 300 GeV photon and a 1 TeV proton (taken from [6]) In the atmosphere the refractive index varies with the height and becomes bigger for smaller altitudes. For example, in the atmospheric model which is used for the H.E.S.S. experiment the Cherenkov angle Θ c,max for ultra-relativistic particles (β 1) at 10 km hight is Θ c,max 0.8 and at ground level Θ c,max The minimum energy E min that a charged particle traveling in a medium must have to emit Cherenkov radiation, corresponding to the threshold velocity β min = 1/n reads E min = m 0 c 2 1 ( ). 1 2 n For example in the height of 10 km the minimal Lorentz factor γ min is about 72 and the minimal energy for an electron about 37 MeV. On the ground the γ min is about 43 and the minimal energy for an electron about 22 MeV. The emitted number of Cherenkov photons per length and per wavelength interval by a particle with charge Z can be calculated with the Frank-Tamm formula (α is the fine structure constant, α 1/137) 13

25 Chapter 2. The Imaging Atmospheric Cherenkov Technique Figure 2.6: Polarization of a medium by a charged particle with v < c n (a) and v > c n (b), where c n is the speed of light in the medium (taken from [14]) Figure 2.7: Geometry of the Cherenkov effect d 2 N dx dλ = 1 ( ) 1 2παZ2 1. λ 2 β 2 n 2 (λ) Due to the factor 1/λ 2 the maximum of the distribution d2 N is reached for dx dλ smaller wavelengths. Strong absorption processes in the atmosphere in the UV region shift the maximum number of detected Cherenkov photons to the blue region of the electromagnetic spectrum. If one neglects the dependence of the refraction index n on the wavelength λ and integrates over the bandwidth of the electromagnetic spectrum in which the absorption in the atmosphere is small and which is detectable by the H.E.S.S. experiment (from 300 nm to 600 nm), one gets 14

26 2.2 Cherenkov Radiation dn λ2 dx = λ 1 d 2 N dx dλ dλ = 1 2παZ2 λ with λ 2 = 600 nm and λ 1 = 300 nm ( = Z ) 1 β 2 n 2 [m]. λ 2 λ 1 ( 1 1 ) β 2 n 2 By an ultra-relativistic particle (β 1) with charge Z = 1 close to the ground (using again the values for the refraction index n from the model atmosphere which is used for H.E.S.S.) about 42 Cherenkov photons are on average emitted on a 1 m flight path The Cherenkov Effect in Air Showers Cherenkov light from a vertical electromagnetic shower creates a circular light pool on the ground with a fairly sharp boundary (see figure 2.8 ). Figure 2.8: Cherenkov light pool of a vertical electromagnetic shower The relation between the radius on the ground r, the emission height h and the Cherenkov angle Θ c is r = tan Θ c (h) h. Due to the fact that the Cherenkov angle Θ c depends on the height of the emission one can understand qualitatively that there must exist a maximal radius on the ground. To get a large radius r on the ground either the Cherenkov angle Θ c must be big, which corresponds to a small emission height or the emission height must be in the early atmosphere but there the Cherenkov angle Θ c is 15

27 Chapter 2. The Imaging Atmospheric Cherenkov Technique small. With a simple toy model of the refractive index n as function of the height h n(h) = 1 + n 0 exp ( h/h 0 ), where H 0 is the scale height from the barometric formula and about 8.33 km and n 0 is about , one can calculate the maximal radius on the ground. r = tan Θ c h cos Θ c = 1 nβ sin Θ c = r = n 2 β 2 1 h = 1 1 (nβ) 2 tan Θ c = (1 + n 0 exp ( h/h 0 )) 2 β 2 1 h 1 1 (nβ) 2 1 (nβ) 2 Neglecting higher orders of n 0 and using β 1 (ultra-relativitic particles), one gets r(h) n 0 exp ( h/h 0 ) 1 h = 2 n 0 exp ( h/h 0 ) h dr dh 2 n 0 exp ( h/h 0 ) h 2 H 0 2 n0 exp ( h/h 0 ) + 2 n 0 exp ( h/h 0 ) = 1 2 H 0 2 n0 exp ( h/h 0 ) h + 2 n 0 exp ( h/h 0 ) dr dh = 0 h + 1 = 0 h e = 2 H 0. 2 H 0 One can see easily that at the extremal value h e there is a maximum of the function r(h). One gets a maximal radius on the ground of about 148 m, which is compatible with the one from much more complex Monte Carlo simulations and more complex atmosphere models (see figure 2.9). While in general electromagnetic showers which consist of electrons, gammas and positrons generate circular homogeneous light pools on the ground, hadronic showers create light pools which are much more irregular and have a larger lateral extension (see 2.9). While traveling through the atmosphere some of the Cherenkov photons are scattered or absorbed. The main processes are Rayleigh scattering (scattering on polarize-able particles whose size is much smaller than the wavelength of the Cherenkov photons), Mie scattering (scattering on aerosols whose size is compatible with the wavelength of the Cherenkov photons) and absorption by ozone (via photo dissociation of ozone). 16

28 2.3 Air Shower Monte Carlo Simulation Software CORSIKA Figure 2.9: Cherenkov light distribution on the ground of simulated air showers (300 GeV γ-ray (left) and 1 TeV proton (right) taken from [6]) 2.3 Air Shower Monte Carlo Simulation Software CORSIKA CORSIKA (COsmic Ray SImulations for KAscade) is a highly developed Monte Carlo program to simulate the development of extensive air showers (EAS) in the atmosphere of the earth. The showers can be initiated by photons, protons, nuclei or a lot of other Standard Model particles. Its energy range for air shower simulations starts at Cherenkov telescope experiments (E ev) and goes up to the highest observed energies (E 0 > ev). The further development of CORSIKA is driven by the idea not only to get the correct mean values of observables with the CORSIKA package code, but also to predict the correct fluctuations around the mean value. Therefore all known processes of EAS interaction with the atmosphere are taken into account, like interactions with air molecules as a target but also the transport of particles through the earth s atmosphere. All secondary particles are followed up along their trajectories and all their parameters are saved, when they reach an observation level. It is possible to simulate the further shower development of various primary particle species within an air shower as well as the production of Cherenkov radiation. Furthermore the chemical composition of the earth s atmosphere is included. Another included feature is the density variation with altitude for some different seasonal days. A lot of international collaborations use CORSIKA to try to understand and interpret their cosmic ray experiment results (see [1] and [2]). Parameters 17

29 Chapter 2. The Imaging Atmospheric Cherenkov Technique like particle numbers for muons, electrons and hadrons and their distribution in energy and lateral space extension, arrival times and lots of other parameters have been simulated with CORSIKA and have been compared with the data from experiments. The good agreement between both the simulation and the data from experiments (within systematic errors in the order of 20 %) gives the confidence that the CORSIKA simulation package works fine. The CORSIKA package knows 50 elementary particles, which are γ, e ±, µ ±, π 0, π ±, K ±, KS/L 0, η, the baryons (plus the corresponding anti-baryons) p, n, Λ, Σ ±, Σ 0, Ξ 0, Ξ, Ω, the mesons (plus the corresponding anti-mesons) ρ ±, ρ 0, K ±, K 0, K 0 and the hyperons (plus the anti-hyperons) ++, +, 0,. Furthermore nuclei until A = 56 can be simulated, which are identified within the program by their numbers of protons and neutrons. All these particles can be pursued through the atmosphere, are able to either interact or annihilate or decay and therefore generate secondary particles. They are described completely in the software via their kind of particle, their Lorentz factor, their azimuth and zenith angle of their flight path, the time since the first interaction of the primary and their three spatial coordinates x,y and z. Of course, the Monte Carlo method is highly dependent on pseudo random numbers and the uniformity and and randomness of these numbers. The random numbers for CORSIKA are generated with RANMAR (see [13]) like it is implemented in the CERN program library (see [10]), which stands for the state of the art in computational physics. It has the ability to produce at the same time up to independent sequences of random numbers each with a sequence length of It passes very strict randomness tests and also tests on the uniformity of the pseudo random numbers and it is quick enough. CORSIKA takes into account the following effects, while it simulates the path of a particle through the atmosphere: Energy loss: Particles lose energy by ionization, for particles with high energy the processes of bremsstrahlung and pair production are also taken into acount. If after the energy update of a particle its Lorentz factor is below a certain threshold, the particle is dropped from the calculation. Multiple Coulomb scattering: Charged particles are scattered in the Coulomb field of the nuclei of the air in the atmosphere. In CORSIKA the process of Coulomb multiple scattering is only regarded for muons and electrons, because due to the fact that the nuclei are much more massive than the scattered particles, the flight direction may change but not the energy. For heavy particles like protons or nuclei at high energy the process of Coulomb multiple scattering is negligible. 18

30 2.3 Air Shower Monte Carlo Simulation Software CORSIKA Deflection in the earth s magnetic field: Due to the Lorentz force charged moving particles are deflected in the magnetic field of the earth. The magnitude of the Lorentz force depends on the strength of the magnetic field and therefore the geographical coordinates and the velocity of the particle, which is deflected. Mean free path: The distance which a particle travels before it undergoes its next inelastic scattering or even decays is given by the cross section for a hadronic reaction and atmospheric density distribution on the trajectory of the particle and the probability to decay (of course stable particles can only be scattered). The decay length and the interaction length are calculated independently of each other at random. The shorter length of both path lengths is used as the path length of the particle. Via this mechanism it is also distinguished whether the particle interacts or decays. More details about CORSIKA can be found in [8] The hadronic interaction models QGSJET-II and SIBYLL At very high energies there exist no perturbative solutions for hadronic interactions, for example hadronization or fragmentation. Therefore one has to use models. Two of the models which CORSIKA uses are the QGSJET-II model (see [19]) and the SYBILL model (see [22]). 19

31

32 Chapter 3 The High Energy Stereoscopic System 3.1 The H.E.S.S. Experiment H.E.S.S. (High Energy Stereoscopic System) is a third generation project of IACTs (Imaging Atmospheric Cherenkov Telescope) designed for the observation of cosmic VHE (Very High Energy) γ-rays by detection of the Cherenkov light of their air showers. The name of the experiment reminds of Victor Hess, who discovered the cosmic radiation in H.E.S.S. uses stereoscopic observations of air showers, like introduced by the HEGRA (High Energy Gamma Ray Astronomy) collaboration. Its energy range goes from 100 GeV to several tens of TeV. It consists of four telescopes, a fifth larger telescope is intended for the near future (H.E.S.S. 2). H.E.S.S. (1) was built by an international collaboration of 19 institutes from European and African countries and was completely operational in the beginning of Former important experiments were the Whipple telescope with an energy threshold of about 350 GeV and the HEGRA experiment. After the introduction of stereoscopic observation by HEGRA, in which showers are watched simultaneously by two or more Cherenkov telescopes, this new technique has led to significant improvements in the measurement of the shower parameters such as shower direction and energy The Site H.E.S.S. is located in southern Africa in the Khomas Highland of Namibia. Its accurate position is southern longitude and eastern latitude 1800 m above sea level (see Fig. 3.1). The region around the site is only sparsely inhabited, thus there are no artificial light sources which could influence the mea- 21

33 Chapter 3. The High Energy Stereoscopic System surements. Furthermore the clean and dry air reduces the light absorption due to aerosols in the atmosphere to a minimum. Apart from the rain season from January until March most nights are clear and cloudless, which allows observations with high efficiency. The location on the southern hemisphere makes it possible to observe the central part of the Galactic Plane which contains many highly interesting objects. A lot of these objects culminate directly at zenith in the Namibian autumn and winter, which facilitates their observation. Figure 3.1: Position of the H.E.S.S. site in Namibia Weather and Atmospheric Monitoring For the correct data analysis it is highly important to know a lot of parameters of the atmosphere and the weather. Therefore the H.E.S.S. site is also equipped with a fully automatic weather station, which records wind speed, wind direction, air temperature, atmospheric pressure, relative humidity and rain fall over 24 h a day. 22

34 3.2 The Telescopes Radiometer Radiometers are used for the detection of clouds. They measure the radiant flux in the infrared part of the electromagnetic spectrum in the atmosphere. This flux can be compared to a black body spectrum and a so-called radiative temperature can be derived. This temperature is neither the temperature of the clouds nor the temperature of the air in the atmosphere. But clouds reflect the ambient light and therefore they have a higher radiative temperature than the clear night sky. The radiometer readings of clear night sky may change on timescales of hours due to variations of the temperature and the humidity in the atmosphere. Each of the telescopes of the H.E.S.S. experiment has its own radiometer parallel to the observation direction. Thus the radiometer looks in the same direction of the sky like the telescope. Due to this it is possible to detect clouds in the field of view. If clouds pass the field of view they decrease the trigger rate of the telescope or lead to an unstable trigger rate. Therefore these runs are excluded from further analysis. Another radiometer is located on site, which can scan the whole sky during day and night and thus give an immediate overview about the presence of clouds and approaching weather fronts. Details about the radiometer can be found in [12] Ceilometer The ceilometer measures the transmissivity of the atmosphere. A ceilometer is a LIDAR (LIght Detection And Ranging), which fires a laser pulse into the atmosphere and measures the laser light which is backscattered by the atmosphere. The amount of backscattered light is related to the portion of aerosols in the atmosphere. If one measures the time of flight of the laser pulse (via the backscattered light) one gets an atmospheric profile up to the height of 7.5 km. Details about the ceilometer can be found in [4]. 3.2 The Telescopes The four H.E.S.S. telescopes are arranged in a square with a baseline of 120 m. The diagonals of this square are parallel to the north-south direction and to the east-west direction, respectively. The baseline was chosen to have the best chance to observe an air shower by several telescopes simultaneously. Figure 3.2 shows a picture of the four telescopes on the site. Some of the most important features of the H.E.S.S. telescope system are the relatively large field of view, its diameter of 5, the large number of pixels of the H.E.S.S. cameras, which allows an improvement of of the image parameters of the air shower images (in comparison with former Cherenkov telescopes) and the low energy threshold of 100 GeV for observations at zenith. 23

35 Chapter 3. The High Energy Stereoscopic System Figure 3.2: The four H.E.S.S. telescopes on the site Mount and Tracking To minimize the effects of bending and tilting of the telescope due the drag of wind and the weight of the camera, each one is supported by a steel structure, which has a high rigidity. To allow to rotate the telescope parallel to the horizon it is placed on a rail with a diameter of 13.6 m. The spherical dish with a focal length of 15 m can be turned orthogonally to the horizon. In the focal plane of the dish the camera is mounted on four supporting steel masts. Figure 3.3 shows a picture of a single H.E.S.S. telescope. Figure 3.3: One of the four H.E.S.S. telescopes on the site Positions in the sky are described in the local horizon system with the azimuth angle and the altitude angle. The azimuth angle is counted clock-wise from north to the direction of the telescope direction in the plane parallel to the horizon. The 24

36 3.2 The Telescopes altitude is the angle from the horizon to the direction of the telescope. One often also uses the zenith angle, which is 90 minus the altitude. Due to the rotation of the earth a permanent tracking of the observed source is necessary. The tracking is done by friction drives acting on 15 m drive rails with an angular velocity of 100 /min. With digital shaft encoders which have a digital step size of 10 the position of the telescope is controlled. The accuracy of the position of the target in the camera is about 30. To control the pointing direction of the telescope a small optical telescope with a CCD camera is mounted on the dish. With this CCD camera stars in the field of view of the source can be observed. The information of the positions of these stars in the CCD camera can be used to correct mis-pointing of the dish due to wind drag, for example The Optical System Every telescope consists of 380 round mirror facets each with a diameter of 0.6 m. They are arranged in a hexagonal dish with a flat-to-flat width of 13 m. The dish as well as the mirror facets are spherical with a focal length of 15 m, which is the so-called Davies-Cotton design. The advantages of this design are the costefficiency and the relatively small time dispersion of about 5 ns. Thus the design allows a nearly point-like focus for rays parallel to the optical axis. Figure 3.4 shows a picture of the dish and the mirror facets. Figure 3.4: Dish and mirror facets of a H.E.S.S. telescope. In the middle between the center and the left edge of the dish, the sky CCD can be seen. To reduce costs round mirror facets are used instead of hexagonal ones, which would have covered the dish completely. The facets are made of aluminized optical glass. To protect them for outdoor use, they are coated with quartz. Due 25

37 Chapter 3. The High Energy Stereoscopic System to dust, sand and other interactions with the environment the mirrors loose bit by bit their reflectivity. This loss is taken into account for the energy calibrations of H.E.S.S. The reflectivity of the facets in wavelength window from 300 nm to 600 nm is about 80%. The entire reflecting area is about 107 m 2, but it is reduced by shadows of the camera support structure and the camera itself to about 95 m 2, depending a little bit on the angle of incidence. More details on the optical system of H.E.S.S. can be found in [17]. For alignment reasons the mirror facets are fixed on three points on the dish. At two of these three points there are actuators, with which every single mirror can be tilted individually. To align all the single mirrors a CCD camera - called the Lid CCD - is mounted in the centre of the dish, that observes the light of a star. Before the alignment of the mirrors the star images were spread out to about 1 but after it 80% of the star s light is focused into a circle with a radius of about 0.02 a little bit in dependence of the observation altitude and the incidence angle. The mirrors of the dish reflect the incoming Cherenkov light into the focus of the dish, into the camera. More about the dish and the mirror alignment can be found in [21] The Cameras Each camera has a mass of about 900 kg and is contained in a body of a length of 2 m and a width of 1.6 m. In the camera body there are also the power supplies and the electronics for triggering, signal processing and digitization. Due to the sensitivity of the camera a lid which is shielding the camera pixels from daylight, is in front of each camera. Each camera can be parked in a shelter to protect it from environmental effects. Each of the four H.E.S.S. cameras consists of 960 pixels and has a field of view with a diameter of 5. The pixels of the cameras are round photomultiplier tubes (PMT). In order to close the gap between the round PMTs Winston cones are used, which are hexagonally shaped light guides. Due to this design every pixel, which is not located at the edge of the camera, has six neighbours. Each pixel has a size of 0.16, which is small enough to resolve the details of shower images. The PMTs have a quantum efficiency of about 30%. Figure 3.5 shows a picture of the opened camera and its pixels. Every PMT runs with high voltage, which is provided by a PMT base. The PMTs are calibrated to generate a signal of electrons for every photo electron (p.e.). To achieve a large dynamical range, the pulse from each PMT is divided into a high-gain channel and a low-gain channel which have different amplifications each. A drawer is formed by 16 PMTs, which also contains two data acquisition cards for 8 PMTs each, the power supplies for the PMTs and 26

38 3.3 The Trigger Figure 3.5: A H.E.S.S. camera. One can see the 960 photomultipliers. three temperature sensors. Each drawer can be extracted easily from the body and replaced if necessary. The camera readout is done by an Analogue Ring Sampler (ARS) chip, which was first developed for the ANTARES experiment (see [9]). This chip samples the signal at 1 GHz and saves it in a memory of 128 cells until the trigger decision. If an event is triggered it will be read out from a time window of 16 ns. To digitize the signal with an analogue-to-digital converter (ADC) it is integrated over the whole time window into ADC counts. The integration window of 16 ns is large enough to contain the time spread of the cherenkov pulse 6 ns and the dispersion time due to the design of the reflector of about 5 ns. The data acquisition system of each camera has its own GPS card, which provides the exact arrival time for each event. The central data acquisition, which gets the images and data of all triggered cameras, runs on a Linux PC farm. 3.3 The Trigger H.E.S.S. has a three-level trigger. The first one acts on the level of single pixels of a single telescope, the second one is the so called sector trigger, which acts on groups of pixels in a single telescope and the third one is the central trigger system 27

39 Chapter 3. The High Energy Stereoscopic System (CTS), which is a multi-telescope coincidence trigger. Due to the camera sector trigger random triggers by the night sky background are already reduced at the hardware level. Due to this the trigger thresholds for the cameras can be reduced, which leads to lower energy thresholds of the H.E.S.S. experiment. Furthermore the CTS provides the dead-time measurement and the event synchronisation The Camera Trigger A single pixel in the camera is triggered, if the number of photo electrons (p.e.) reaches a threshold, typically 4 p.e. during normal observations. The camera array contains 38 overlapping sectors, each one formed by 64 PMTs. A homogeneous efficiency over the whole camera array is guaranteed by the sector overlap. A sector will be triggered, if the number of triggered single pixels in this sector exceeds a threshold, normally three. This sector trigger is highly important for the reduction of the night sky background (NSB) because air showers form images of clusters of pixels, while the photons of the NSB are randomly distributed over the whole camera The Central Trigger The telescope multiplicity for the CTS is selectable. At least a coincidence of two telescopes is required to get a stereoscopic view of the air shower. In general a higher multiplicity increases the resolution of parameters like energy, shower direction and so on. Single muons are a major part of of the background in the telescopes. Due to the fact that muons only trigger a single telescope, they are rejected nearly completely by the CTS. 3.4 Shower Reconstruction Due to the shower reconstruction from the telescope images, it is possible to obtain the shower parameters like the energy of the shower and therefore the energy of the primary particle and the shower direction Mapping of the shower into the camera All the Cherenkov light from an air shower which hits the telescope is mapped isogonically into the camera plane. This means that all the parallel Cherenkov light which hits the dish is mapped into one point in the camera. Cherenkov light which is emitted under a small angle is mapped close to the camera center while the one emitted under bigger angles is mapped closer to the edge of the camera. Figure 3.6 shows a sketch of the mapping mechanism. 28

40 3.4 Shower Reconstruction Figure 3.6: A sketch of the mapping mechanism of the H.E.S.S. telescopes Image parameters The camera image of the Cherenkov light of an electromagnetic air shower has an elongated, roughly elliptical shape. Thus it can be parametrized by an ellipse like suggested by Hillas (see [16]). Before the parametrization takes place, the camera image is cleaned from noisy pixels that are caused by the night sky background or by PMT noise. After that, the ellipses are parametrized according to the Hillas parameters. Figure 3.7 shows the Hillas parameters of a camera image of an air shower. Beside the Hillas analysis there are also other methods of the shower reconstruction. The major axis of the ellipse is related to the shower length respectively the longitudinal dimension of the shower, while the minor axis is related to the lateral dimension of the shower. The distance between the center of the camera and the centre of gravity of the ellipse is correlated to the distance between the shower and the telescope. This distance is also called impact parameter. The amplitude of the whole ellipse, given by summing over every pixel amplitude inside the ellipse, together with the impact parameter is a measure for the shower energy respectively for the energy of the primary particle. Furthermore the major axis of the ellipse points in the direction where the shower came from. If at least two telescopes observe the shower simultaneously one can 29

41 Chapter 3. The High Energy Stereoscopic System Figure 3.7: Hillas parameter of the camera image of an air shower derive the position of the source in the sky from the intersection of the two major axes of the ellipses. If more than two telescopes detect the shower, the resolution of the source position will increase. 30

42 Chapter 4 Analysis Algorithm At the very beginning of a cosmic ray flux measurement one has to reject all measured showers which are badly reconstructed for example showers whose image in the camera lies at or on the camera boundary, whose shower image in the camera consists only of very few pixels or whose camera image has only a very small amplitude. In order to keep only well reconstructed showers one has to develop cuts. They are developed with Monte Carlo data, which contains information about the properties of the simulated showers (the so called true showers) as well as about the properties of the reconstructed showers (the so called reconstructed showers). The reconstructed showers whose properties (like their energy and their shower direction) differs very much from the properties of their true showers have to be cut away by the cuts. In principle the camera images of the showers are measured with H.E.S.S.. With the help of the Hillas Analysis (see section 3.4.2) these camera images are parametrized. With this parametrization and the condition that at least to telescopes have seen the same shower, basic properties of the shower can be derived. These basic properties (for example the reconstructed shower direction and the reconstructed impact parameter, which will be explained in detail later in this chapter) are saved in a special data format and form the reconstructed shower of the observation. To be able to measure the cosmic ray flux one needs the energy of the measured showers. Therefore an energy reconstruction for every measured shower is necessary because the reconstructed showers do not contain the energy of the shower, but they contain some parameters which one can use to reconstruct their energy. Therefore a so called energy lookup is used. In dependence of some parameters (the amplitude and the impact parameter of a shower) which are contained in the true shower as well as in the reconstructed shower, the energy value of each true shower is filled in a lookup table. With the help of the reconstructed parameters (the amplitude and the impact parameter) on can look up the energy 31

43 Chapter 4. Analysis Algorithm in the lookup table which belongs to the reconstructed parameters. The quality of this energy reconstruction is tested with Monte Carlo data, with whose help one can compare the reconstructed energy of a shower with the true energy of this shower. Furthermore with the help of the Monte Carlo data one has to calculate the effective area, which is in principle the area around the telescopes in which they are sensitive for showers. The effective area is needed for the measurement of the cosmic ray flux, too. In order to study systematic effects two different Monte Carlo models (QGSJET- II and SYBILL) for the interaction of protons from the cosmic ray flux with the atmosphere and therefore for the shower development in the atmosphere are used. In the following sections the Monte Carlo samples, the cuts, the impact parameter and the energy reconstruction are described in detail. Furthermore the quality of the reconstruction of important parameters, like the impact parameter or the energy are studied. 4.1 Monte Carlo Samples For the following analysis proton Monte Carlo files are used. The zenith angle of the simulated protons is 20 (the zenith angle is counted from the zenith to the horizon, that means that it is zero at zenith and 90 degree at the horizon). This zenith angle is chosen due to the fact that for higher zenith angles the energy threshold is higher and the reconstruction of showers is more complicated since their path through the atmosphere is longer. The simulated protons come from the south direction. Due to the interaction of charged particles with the earth s magnetic field there are slight differences in Monte Carlo simulations depending on whether the protons come from the south or the north direction. The protons are simulated in a cone of 2.2 opening angle around the zenith angle (that means from 17.8 until 22.2 ). The angle between the observation direction and the shower direction is called Θ. In the next section is will be seen that this is an important cut parameter. In this case the maximal Θ would be 2.2. The spectral index γ of the proton Monte Carlo data is 2. Table 4.1 shows the used interactions models, the used Monte Carlo files, their energy range and the number of events in the files. 4.2 Cuts Table 4.2 shows the cuts which were applied to both the Monte Carlo events and the data events. The number of telescopes which must have seen the event is determined by the 32

44 4.2 Cuts interaction model QGSJET-II SIBYLL-Extended used files proton_20deg_180deg_run_1000 _3_112_phase1_desert.dst.root.. proton_20deg_180deg_run_1639 _3_112_phase1_desert.dst.root proton_20deg_180deg_run_1000 _3_112_phase1_desert.dst.root.. proton_20deg_180deg_run_2000 _3_112_phase1_desert.dst.root number of events in the files energy range TeV TeV Table 4.1: Overview over the used Monte Carlo files multiplicity 4 local distance 1 minimal amplitude p.e. maximal amplitude p.e. Θ 2 (1 ) 2 Table 4.2: Used cuts multiplicity cut. The Hillas parameters (see Chapter 3) are calculated for every single telescope which has seen the shower. The more telescopes view a shower the better is the extrapolation of the shower direction and therefore the shower direction resolution. As will be seen later the energy resolution is correlated via the impact parameter resolution with the direction resolution. Therefore it is necessary to have a good direction resolution. The local distance cut is a cut on the distance of the centre of gravity of the event from the centre of the camera. The reconstruction of the Hillas ellipses of events near or at the boundary of the camera can be determined wrongly due to the fact that only a part of the ellipse is seen in the camera and the rest is outside of the boundary of the camera. That leads to a wrong direction reconstruction and also to a too small reconstructed energy because only a part of the ellipse is seen and therefore the amplitude of the event is underestimated. The higher the cut on the minimal amplitude (in photo electrons (p.e.)) the bigger are the images which pass this cut. Bigger images result in a more precise determination of the orientation of the Hillas ellipses and therefore parameters like the direction resolution and the energy resolution are determined better. The Θ 2 cut is a cut on the maximal angular difference between the observation position of the telescope and the shower direction. A Θ 2 cut of 4 square degree 33

45 Chapter 4. Analysis Algorithm Interaction model QGSJET-II SIBYLL-Extended triggered events events after cuts % after cuts 1.68 % 1.67 % Table 4.3: Number of events before and after the cuts would mean that all showers that have an angular difference to the observation position which is larger than 2 are cut away. Due to the fact that within the Monte Carlo data the showers are only simulated in a cone of 2.2 around the zenith angle, the Θ 2 cut has to be at least (2.2 ) 2 =4.82 square degree. Otherwise one could have measured data with angular differences between the shower direction and the observation position for which no Monte Carlo data representation exists. Due to the fact that the acceptance of the camera decreases with increasing Θ 2 the Θ 2 cut is set to 1 square degree. Table 4.3 shows the number of events which pass the cuts. The percentage of events which pass the cuts is in the same order like the one for γ events, which lies in the order of 0.1 % to 1%. 4.3 The Shower Direction One important parameter for extensive air showers is their reconstructed shower direction. This is due to the fact that H.E.S.S. is an astroparticle project and one wants to know the positions of sources of highly energetic γ-radiation as accurately as possible to be able to compare them with known sources in different wavelengths. But furthermore the shower direction is also important for the reconstruction of the shower energy respectively the resolution of the shower direction is correlated with the resolution of the reconstructed energy (this will be shown later). To get an impression how well the shower direction is reconstructed within the Hillas analysis of H.E.S.S. for protons the angular direction resolution δ is studied within the proton Monte Carlo data. It describes how precisely the source of an event in the sky can be determined. Within the H.E.S.S. group its exact definition is that 68% of all events have an angular direction resolution which differs by less than δ from the true direction. For comparison reasons this definition was used is in this work, too. Figure 4.1 shows the angular direction resolution as function of the true energy E true from the Monte Carlo data for both interaction models. The difference between the two interaction models QGSJET-II and SYBILL is quite small. Furthermore one can see that for true energies of 1 Tev E 5 TeV the angular direction resolution is about 0.3 and from 10 TeV to 50 TeV 34

46 4.4 The Impact Parameter Figure 4.1: The angular direction resolution in degrees against the true energy (black = QGSJET-II, red = SYBILL) it is even smaller than The angular direction resolution from H.E.S.S. for γ showers (air showers that were produced by gamma rays) is about 0.1. Due to the fact that air showers which are generated by protons are more irregular and have more fluctuations (than the ones generated by gamma rays) it is easy to understand that they have an angular direction resolution which is worse than the one of γ events. 4.4 The Impact Parameter Together with the amplitude the impact parameter is an important parameter for the energy reconstruction for every telescope. Figure 4.2 shows a sketch of the definition of the impact parameter. If one imagines that the primary particle, which has induced the air shower, would reach the ground, then the point where it would hit the earth is called the shower core. If one takes the flight path of the primary particle and extends this line a little bit beyond the shower core (into the ground) then the shortest distance (which may run through the earth) from a telescope orthogonal to this line is called the impact parameter d (see also 4.2). The impact parameter has no sign. From the sketch one can also see that the impact parameter d depends on the shower direction in the following way 35

47 Chapter 4. Analysis Algorithm Figure 4.2: Figure of the impact parameter d d = D cos α. As already mentioned before the impact parameter is highly important for the energy reconstruction. To determine values like the bias or the resolution of the impact parameter the value δd d = d true d reco d true = 1 d reco d true, where d true is the true impact parameter from the Monte Carlo and d reco is the reconstructed one from the Hillas analysis (also included in the proton Monte Carlo data), is calculated. The values δd/d are calculated for all values of d true within a given interval. Figure 4.3 shows an example distribution of δd/d in the interval 40 m d true 80 m. As one can see already from the definition of δd/d the distribution is asymmetric. For the smallest value of δd/d, which is reached if d reco d true, there exists no limit. On the other hand the maximal value of δd/d is 1, which is reached if d reco d true. Due to the asymmetry it is not possible to fit the distribution with a Gaussian thus the bias B and the error of the bias B of the impact parameter d are defined as the mean and the error of the mean of the distribution δd/d ( ) δd B(d) = Mean = 1 d n [ ( δd B(d) = Var Mean d n i=1 )] ( ) δd d i = σ(d) n. In the same manner the error σ respectively the resolution and the error of the resolution σ of the impact parameter d are defined as the RMS and the RM- 36

48 4.4 The Impact Parameter Figure 4.3: Distribution of δd/d in the interval 40 m d true 80 m SError of the distribution δd/d ( ) δd σ(d) = RMS = 1 d n 1 σ(d) = Var [ RMS ( )] δd = d n i=1 ( B(d) σ(d) 2(n 1). ( ) ) 2 δd d i In the example of figure 4.3 the bias B(d) is about and the resolution σ(d) is about 0.4. The calculation of the bias and the resolution is done for every interval of d true. Plotting the bias over all intervals of d true leads to figure 4.4 for the QGSJET-II interaction model and to figure 4.5 for the SYBILL interaction model. The black crosses show the bias of the impact parameter B(d) versus the true impact parameter d true. The red curve shows the relative number h i of proton Monte Carlo events with h i = n i ni as function of the reconstructed impact parameter d reco. One can see that for most events the absolute value of the bias B(d) is smaller than 10%. Events with a small value of true impact parameter d true are reconstructed with too large reconstructed impact parameter d reco, which leads to the strong negative bias in the first bin. Furthermore there exist no significant difference between the two interaction models. 37

49 Chapter 4. Analysis Algorithm Figure 4.4: Bias of the impact parameter (QGSJET-II) Figure 4.5: Bias of the impact parameter (SYBILL) 38

50 4.5 The Energy Reconstruction Figure 4.6 shows the resolution of the impact parameter against the true impact parameter d true for QGSJET-II. The same plot for SYBILL is shown in figure 4.7. The black crosses show the resolution of the impact parameter σ(d) versus the true impact parameter d true. The red curve shows again the the relative number h i of events as function of the reconstructed impact parameter d reco. One can see that for both interaction models the resolution of the impact parameter in the first bin, that means for impact parameter smaller than 50 m, is quite bad. But this is only the case for about 10% of all reconstructed impact parameters. For impact parameters 50 m d 100 m the resolution is about 40% and for d > 100 m the resolution is about 30%. Figure 4.8 shows the relative number of events as function of d true (black line) and of d reco (red line) for the QGSJET-II Monte Carlo and figure 4.9 for SYBILL. The ration of the number of events against the reconstructed impact parameter d reco and the number of events versus the true impact parameter d true is shown in figure 4.10 (QGSJET-II) and 4.11 (SYBILL). One can see that in the first three bins, which correspond to the impact parameter interval from 0 to 120 m, the number of reconstructed events is larger than the number of true events in this interval. That means that some events with larger true impact parameter are miss-reconstructed to ones with small reconstructed impact parameter. From 160 m onwards the number of reconstructed events is smaller than the one of the true events. Thus there exist a redistribution in the number of reconstructed events, some are shifted to smaller impact parameters. The true impact parameter in the QGSJET-II Monte Carlo goes up to 600 m while the one for SYBILL finishes at about 550 m. This can be explained probably in the following way. As already mentioned the maximal true energy in the SYBILL Monte Carlo is 60 TeV, while in the QGSJET-II Monte Carlo it is 100 TeV. Furthermore the energy of an event depends on the impact parameter and the amplitude (see next section). For constant amplitude the energy increases with increasing impact parameter resulting in larger energies which come along with larger impact parameter. Thus the maximal impact parameter of the QGSJET-II Monte Carlo has to be larger than the one of the SYBILL Monte Carlo. 4.5 The Energy Reconstruction The energy reconstruction of the showers is done with a so called lookup, which is in principle a table. It is generated with the proton Monte Carlo data. Every Monte Carlo shower event has a true energy E true, an amplitude A in the camera of each triggered telescope and a true impact parameter d true for each triggered telescope (see the former section about the impact parameter). With both the 39

51 Chapter 4. Analysis Algorithm Figure 4.6: Resolution of the impact parameter (QGSJET-II) Figure 4.7: Resolution of the impact parameter (SYBILL) 40

52 4.5 The Energy Reconstruction Figure 4.8: Relative number of events against d true (black line) and of d reco (red line) (QGSJET-II) Figure 4.9: Relative number of events versus d true (black line) and of d reco (red line) (SYBILL) Figure 4.10: Ratio of the number of events N reco /N true against impact parameter (QGSJET-II) Figure 4.11: Ratio of the number of events N reco /N true versus impact parameter (SYBILL) 41

53 Chapter 4. Analysis Algorithm true impact parameter and the amplitude the average energy Ē in each bin (d i, A i ) of the lookup is calculated with the formula n i=1 Ē (d i, A i ) = E true (d i, A i ), n where n is the number of events in each bin (d i, A i ). Figure 4.12 shows a picture of the lookup using the QGSJET-II Monte Carlo and figure 4.13 of the SYBILL Monte Carlo. Figure 4.12: Plot of the lookup: One can see the energy value in TeV (in a colour scale) against the true impact parameter and the amplitude (QGSJET-II) Figure 4.13: Plot of the lookup: One can see the energy value in TeV (in a colour scale) versus the true impact parameter and the amplitude (SYBILL) For every real shower it is possible for example with the Hillas analysis to determine the amplitude A and the reconstructed impact parameter d reco. With these two parameters one gets the energy Ē of the bin (d i, A i ), which corresponds to the values of d reco and A. The energy reconstruction only works properly if the difference between the reconstructed impact parameter d reco and the true impact parameter d true is small. The energy bias and the energy resolution are determined in section Muon Correction As already mentioned, before the mirrors of the telescopes lose a little bit of their reflectivity (3% per year) due to their interaction with the environment especially with dust and sand. Due to this a so called muon correction is applied regularly to every single telescope. As already mentioned before muons create Cherenkov rings in the camera. From the diameter of these rings one can calculate the energy 42