Thesis Outline
This introduction started with a quick discussion of TeV scale CR physics, especially the CR proton and electron spectra as observed on and in the vicinity of the earth.
The question of the origin and energy source of those particles has been presented as one of the driving forces of astroparticle physics research. Astronomy withγ-rays was introduced as a possible way for the investigation of this question and different detector principles sensitive to different energy regimes were quickly characterized and compared.
The detection and investigation of differentγ-ray sources within the Milky Way is a very interesting and active field of research. However, low energyγ-ray instruments such as the Fermi observatory not only detect isolatedγ-ray sources within the Milky Way but also a large scale ’diffuse γ-ray emission’ that is enhanced towards parts of the Milky Way disc. For the Fermi observatory, this diffuse emission is primarily a foreground for the detection of isolated sources. This foreground is by now not detected with TeV γ-rays to which Cherenkov telescopes are sensitive. Cherenkov telescopes have thus yet no foreground for the detection ofγ-ray sources but must deal with a large background due to TeV cosmic rays whose energy deposit in the earth atmosphere leads to detector signatures that are in part hardly distinguishable from the signature of a γ-ray. The physical source of the diffuseγ-ray foreground in case of the Fermi observatory and the CR background in case of ground based γ-ray observatories is, however, very similar.
In both cases CRs are the energy source - once (Fermi) in form of the interaction with galactic gas or radiation fields and once (ground based observatories) directly via the energy deposit in the earth atmosphere (Cherenkov telescopes) or the detector (Extensive Air Shower Arrays).
It will be pointed out later in this thesis that the detection of a large scale diffuse TeV γ-ray emission in the Milky Way is in fact technically difficult with established Cherenkov telescope data analysis methods. New and modified analysis methods will therefore be discussed.
Additionally, arguments that stem from very different observational results and support the existence of dark matter particles were discussed in the present chapter. Especially in the Milky Way, the dynamical properties of the material within the Milky Way hint towards the presence of dark matter in the Milky Way.
WIMP dark matter has been introduced as one plausible class of the yet undetected dark
1.4 Astroparticle Physics, the Milky Way and Dark Matter: Thesis Outline matter. Given a sufficient WIMP density in the Milky Way, the annihilation of WIMPs is under some assumptions expected to produce a diffuse γ-ray flux from the whole Milky Way galaxy. The development and comparison of methods to search for such an extended and weak diffuseγ-ray flux caused by annihilating dark matter particles in the Milky Way with Cherenkov telescopes is the main topic of this thesis. To conduct such a search, it is necessary to develop a detailed understanding of systematic effects that come with the usage of Cherenkov telescopes as γ-ray detectors. A technical introduction to the properties of the H.E.S.S. array is given in the next chapter to prepare a discussion of systematic effects. Additionally, a search for γ-rays produced by annihilating dark matter must distinguish putative signal γ-rays due to dark matter annihilations from a possible large scale TeV diffuse γ-ray emission in the Milky Way and from γ-rays generated in ordinary small scale astrophysical γ-ray sources. A general knowledge of the properties of the Milky Way as well as typical astrophysicalγ-ray sources as discussed in the present chapter is thus necessary.
2 The High Energy Stereoscopic System
The High Energy Stereoscopic System (H.E.S.S.) is an array of Imaging Atmospheric Cherenkov Telescopes (IACTs) operated since 2003 in the Khomas Highland in Namibia, about 100 km south-west of the Namibian capital Windhoek. This chapter provides a detailed discussion of the technical design and operation of the telescope array as well as a description of the standard data pipeline used in this thesis for the analysis of VHE γ-ray data out of recorded H.E.S.S. data. The chapter starts with a discussion of the physical foundations of the detection of γ-rays with Cherenkov telescopes. Of special importance are the Cherenkov effect as well as the development of γ-ray and cosmic ray shower in the atmosphere. The H.E.S.S. instrument itself is discussed in the subsequent section that covers the hardware setup of the array as well as the description of available atmospheric monitoring devices. The calibration of recorded data and the investigation of the data quality is described afterwards. Monte Carlo simulations of the instrumental response to γ-rays are important to prepare the final section which covers the data analysis chain that is used later in the thesis. Of special importance in the last section are the background suppression and event reconstruction methods as well as the description of the background subtraction.
2.1 Physical Foundations
2.1.1 Cherenkov Light
The 1958 Nobel prize in physics was awarded to P. A. Cherenkov, I. M. Franck and I.
Y. Tamm for the discovery and interpretation of the Cherenkov effect which is the name for the emission of electromagnetic radiation by an electric charge moving faster than the speed of light in a medium.
Following Ginzburg [1996], the assumption of a charge with energy E0 and velocity v leads by conservation of energy and momentum to the possibility of the emission of a photon with energy~ω under the angle1
cosθ= c nv
1 + ~ω
2E0(n2−1)
1The formula given here for the Cherenkov angle is derived in a purely kinematical argumentation but is in all practical cases equivalent to the usual formula cos(θ) =c/(nv) (see f.i. Jackson [1998]). The correction stems from the recoil of the charged particle after the photon emission and is always small for optical and UV emission because no charged particle with massmexist that is sufficiently small to have~ω∼1 eV =γmc2with boost factorγ.
relative to the moving direction of the charged particle. Here,nis the index of refraction in a given medium andcis the vacuum speed of light. No real emission angle is possible whenv < c/nandn≥1, i.e. usually when the charge is moving slower than the speed of light in the medium. However, ifv > c/n (andn >1) the emission of a real photon with frequencyω is possible under the Cherenkov angle given above. No physical preference for any frequency ω fulfilling the condition v > c/n(ω) exists and thus the number of photons emitted per frequency interval is constant, i.e. dN/dω= const. In terms of wavelength intervals this means withdω∼1/λ2dλfor the number of Cherenkov photons emitted per wavelength interval
dN dλ = k
λ2
which is also called ’Franck-Tamm’ formula. The proportional constant is
k= 2παZ2sin2(θ)L where α is the fine structure constant, L is the path length where the charged particle emits Cherenkov photons and Z is the mean number of electrons in the medium (see Eidelman et al. [2004]). The constant can be justified in a lengthy calculation (see Jackson [1998]) but is essentially the electromagnetic coupling (Z2α) and a factor (sin2(θ)) that suppresses Cherenkov photon emission for v < c/n. The emission of Cherenkov radiation outside of a small band in the optical and near UV is usually suppressed because thenn(ω)∼1.
2.1.2 Particle Shower
Electron, Positron andγ-ray Induced Air Showers
Electrons, positrons and γ-rays behave very similar in the earth atmosphere at high energies. In all cases, electromagnetic cascades are generated by alternating electron-positron creation and bremsstrahlungs radiation of hard photons.
Consider first a primaryγ-ray entering the earth atmosphere. The pair creation process is the dominant energy loss mechanism for the considered energy range (E >100 GeV in the laboratory frame or ∼ √
2mNE > 10 GeV in the center of mass frame where mN ∼1 GeV is the mass scale of an air molecule). On average, theγ-ray will therefore interact with the nucleus of an air molecule via the pair creation process after travel-ing one radiation length (XP ∼ 37 g/cm2 in air, Eidelman et al. [2004]). This leads typically to a first interaction in a height of ∼ 28 km above sea level (asl) for a γ-ray entering the earth atmosphere at zenith. The result of the pair creation process is in practice always an electron-positron pair as the generation of all other possible particles is phase space suppressed. Electrons and positrons are deflected in the electric field of air molecule nuclei and emit typically hard photons via bremsstrahlung. The emission of soft bremsstrahlung is in practice suppressed because the high energy electron or positron would have to pass an air nuclei at distances much larger than the molecular size scale where the nuclei charge is screened by the electrons (see f.i. Heitler [1954]).
The alternating cascade of pair creation with subsequent hard bremsstrahlung generates a cascade of ultra relativistic charged particles and stops when the particles reach the critical energy of ∼ 81 MeV after ∼ 10 cascade steps in a typical atmospheric height
2.1 Physical Foundations of ∼ 10 km asl. The production of particles in the bremsstrahlungs and pair creation cascade is always strongly forward directed in the laboratory frame due to the boost from the center of mass frame. However, the multiple Coulomb as well as Compton scattering lead to a finite lateral extension of a γ-ray air shower which is described by the Moliere theory. The typical radius of a 1 TeV γ-ray shower is RM ∼ 20 m in air (see Hillas [1996]). The outlined model of a γ-ray shower has first been described in Heitler [1954]. In practice, γ-ray showers are simulated with Monte Carlo software that is described later but does in principle implement the described effects.
If a primary electron or positron enters the earth atmosphere in contrast to a primary γ-ray the shower development is in general the same as described above but the first interaction is of course not a pair creation but a bremsstrahlungs process. The mean free path length for pair creation at high energies is slightly larger than the radiation length for bremsstrahlung (factor 9/7) which can be used to some extend to separate electron or positron air showers from γ-ray air showers based on the reconstruction of the first interaction height in the atmosphere (see H.E.S.S. Col. [2008]). In practice, electron and positron initiated shower constitute an irreducible background for the detection ofγ-ray initiated showers.
Hadronic Air Showers
The majority of cosmogenic particles hitting the earth atmosphere with GeV and higher energies are hadronic particles, i.e. protons and heavier nuclei. A proton or heavier nu-cleus entering the earth atmosphere is in general strongly interacting with nuclei of air molecules. The nuclear interaction length in air is ∼90 g/cm2 (Eidelman et al. [2004]), i.e. a factor of ∼ 3 larger than the radiation length for an incomingγ-ray. The strong interaction leads to secondary particles. Phase space considerations show that the light-est strongly interacting particles are preferred to be produced as secondary particles, i.e.
the dominant component of hadronic air shower are pions followed by kaons. To a good approximation, every nuclear interaction results in ∼2/3 of the energy to be deposited into charged and ∼1/3 into neutral pions on average. However, statistical fluctuations can be large. The produced secondary particles are typically unstable and can either decay or undergo another strong interaction with air nuclei, depending on the nuclear interaction length and the decay time. Of primary interest is the decay of neutral pions for which the decay time is very short (∼10−17s,cτ ∼25 nm see Eidelman et al. [2004]).
In contrast, charged pions have a much larger decay time (τ ∼ 10−8s, cτ ∼ 7.8 m see Eidelman et al. [2004]) for the dominant decay into muons and neutrinos. Charged pions with sufficiently large Lorentz boost factor are thus likely to interact again strongly and thus transfer again ∼1/3 of their energy into neutral pions. A large fraction (∼ 90%, see Engel et al. [2011]) of the energy of a primary hadron entering the earth atmosphere is thus deposited in electromagnetic subshowers.
Given the complexity of hadronic interactions, it appears very difficult to gain a quanti-tative understanding of the shower process in a simple model. Major differences between hadronic air and γ-ray showers are that
• the statistical fluctuations of a hadronic air shower are much larger than for a γ-ray shower. This leads to an in general less uniform and symmetric shower development (see also Longair [2011]).
• The transverse size of a hadronic air shower is typically larger than for a γ-ray shower of similar energy. The increased transverse size of a hadronic vs. a γ-ray shower is primarily connected to the few hard hadronic interactions with large transverse momentum in the final states that stand out of the larger number of soft interactions with low energy and high multiplicity final states (see also Engel et al. [2011]).
• The longitudinal size of a hadronic shower is also typically larger than for a γ-ray shower of similar energy. This is a result of the nuclear interaction length in air to be larger than the radiation length in air.
In practice, the instrumental response of a Cherenkov array to cosmic ray showers can be simulated with Monte Carlo methods (Bernlöhr [2008]). Alternatively it can be obtained by observing regions in the sky that do not containγ-ray sources resulting in only cosmic rays (mostly protons, iron and to a small fraction electrons and positrons) triggering the array.
2.1.3 Imaging of Particle Showers
The Cherenkov light emitted towards the spherical mirror of a H.E.S.S. I telescope by charged particles moving faster than the speed of light in the atmosphere is imaged onto the telescope camera if the emission is seen in the telescope field of view. Cherenkov light emitted within a telescope field of view at the same zenith (˜θ) and azimuth ( ˜φ) angle relative to the telescope pointing is in good approximation imaged on the same point of the telescope camera by the spherical telescope mirror. To develop a qualita-tive understanding of the image of particle shower in a H.E.S.S. camera consider first the simple case of a particle propagating straight and without energy loss through the atmosphere while emitting Cherenkov light2. Typically, the emitted Cherenkov photons do not hit theO(10 m) radius H.E.S.S. mirror for geometric reasons or are not imaged to the telescope camera due to the limited field of view (see fig. 2.1 left side). Emission that is imaged by the mirrors onto the camera is in general possible in up to two atmospheric regions differing for geometric reasons in height above the observation level (see fig. 2.1).
The Cherenkov emission angle depends on the atmospheric level because the index of refraction changes with height above the observation level. The range of the Cherenkov emission angle within one of the two possible regions in the atmosphere where Cherenkov photons are emitted that are imaged on a camera is typically≤0.2◦ which is comparable to the FoV of a single PMT (see Spengler [2009] for details). The H.E.S.S. camera image of the Cherenkov emission of a particle propagating without energy loss straight through the atmosphere is thus given by up to two clustered PMTs with Cherenkov photon signal
2This is in fact a model for the Cherenkov emission of heavy magnetic monopoles. See Spengler [2009]
for details of the model and the imaging process.
2.1 Physical Foundations
Figure 2.1: Left: Cherenkov photons emitted by a single charged particle moving straight through the atmosphere are imaged onto the camera when hitting the mirror within the field of view. Emission under different zenith angles translates to different imaging points on the radial camera axis. Right: Two Cherenkov photon emitting charged particles moving straight through the atmosphere at the same distance to a IACT but with a difference in azimuth angle. The azimuth angle between the two propagating particles translates into a width of the camera image in contrast to the radial length of the image due to the emission under different Cherenkov angles.
where each cluster has O(1) PMT. A line connecting the two PMT clusters triggered due to Cherenkov light intersects with the path of the Cherenkov light emitting particle in the plane of the camera. Thus, the direction of a Cherenkov emitting particle can be inferred from the connecting line between two triggered PMT clusters.
Figure 2.1 shows on the right side two Cherenkov light emitting particles propagating in the atmosphere without energy loss. The two particles propagate parallel and at the same distance to a telescope but with different azimuth angles relative to the telescope pointing. The azimuth angle difference between the two propagation directions trans-lates into an angle between the two connecting lines between the PMT clusters triggered by the Cherenkov emission of each particle.
The simple model for the imaging of Cherenkov photons emitted by a charged particle moving on a straight line through the atmosphere can be generalized to the more com-plicated imaging of the Cherenkov photons emitted in a particle shower. In this case, the Cherenkov photons that are emitted at different Cherenkov angles but from parti-cles seen at the same azimuth angle relative to the pointing axis are imaged on different points on the radial axis of the camera. The emission under different Cherenkov angles can occur due to varying particle energy or atmospheric emission height and the imag-ing on the radial camera axis leads to the finite length of an image in a camera. Thus, the image length of a particle shower in a Cherenkov camera reflects the longitudinal development of the shower. The lateral extension of a particle shower translates in turn into the width of a camera image (see also fig. 2.2).
As outlined above, the transverse size (Rγ ∼20 m for a 1 TeV primary) ofγ-ray showers is dominantly due to the multiple scattering of the shower particles. In contrast, the transverse size (RH∼70 m for a 1 TeV proton primary, see Hillas [1996]) of hadronic air showers is dominantly due to the transverse momentum of the neutral pions produced in hadronic interactions and typically larger than the transverse size ofγ-ray showers. This difference translates into an angular width difference of the camera image for hadronic andγ-ray initiated particle showers. Hadronic air showers seen at a distance ofD∼10 km have a typical image angular width of w ∼ 2RH/D ∼ 0.8◦ which compares to the typical angular width corresponding to a γ-ray shower of w ∼ 2Rγ/D ∼ 0.2◦. The width is used later as a very powerful tool for the separation of γ-ray events from the background due to hadronic events.
2.1.4 Night Sky Background
The photon intensity due to Cherenkov light emitting particle showers is very small compared to other photon sources even during the nights without moon- and sunlight in afield sites. In a typicalγ-ray shower, O(100 Photons/(m2TeV)) reach altitudes of ∼2 km asl in a radius of∼100 m around the primary particle (see f.i. Hillas [1996]). Thus, a 1 TeVγ-ray primary producesO(104) Cherenkov photons that are hitting a telescope mirror3 of ∼100 m2. With an average photon detection efficiency of ∼ 10% this leads
3This example calculation refers to the telescope mirrors of the H.E.S.S. phase one telescopes.
2.1 Physical Foundations
Figure 2.2: Shower images in IACT cameras with sufficient number of PMTs are ellip-tically shaped. The transverse development of an air shower translates into the width of an image in a Cherenkov camera. The longitudinal shower de-velopment is in turn characterized by the radial length of the shower image.
to a typical image amplitude in one H.E.S.S. camera of 1000 pe (photo electrons4) for a 1 TeV γ-ray shower and a dynamic range of ∼100 pe to ∼50000 pe for the typical energy range of H.E.S.S. (∼100 GeV to ∼50 TeV). The residual light in a dark night without moon- or sunlight is called night sky background (NSB). Important sources of NSB are (see Preu et al. [2002] and Mellinger [2009] for more information):
• Chemical processes in the upper atmosphere leading to air-glow which is f.i. the
• Chemical processes in the upper atmosphere leading to air-glow which is f.i. the