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DIPLOMARBEIT

Investigations on gamma-hadron separation

for imaging Cherenkov telescopes exploiting

the time development of particle cascades

Heike Prokoph

Leipzig, den 16.07.2009

Universität LeipzigFakultät für Physik und Geowissenschaften

Diese Diplomarbeit wurde am Deutschen Elektron-Synchrotron (DESY) in Zeuthen in

enger Zusammenarbeit mit der Humboldt-Universität zu Berlin angefertigt.

Verantwortlicher Hochschullehrer: Prof. Dr. Th. Naumann

1. Gutachter: Prof. Dr. Th. Naumann

Fakultät für Physik und Geowissenschaften

Universität Leipzig

2. Gutachter: Prof. Dr. Th. Lohse

Institut für Physik

Humboldt-Universität zu Berlin

Abstract

Imaging Atmospheric Cherenkov Technique has proven an extremely successful ap-

proach to γ-ray astronomy in the TeV energy regime. While the results achieved

with current instruments, like H.E.S.S. and MAGIC, are already very impressive, the

detailed understanding of processes in cosmic particle accelerators as well as their

use for cosmological applications requires wider energy coverage, improved resolution,

and higher detection rates. These demands have triggered the initiative to build the

Cherenkov Telescope Array (CTA). The Design Phase for the optimization of the per-

formance of the array started in 2008. The major challenge of the Cherenkov Technique

is the presence of an overwhelming background of air showers initiated by cosmic ray

protons and nuclei. The primary discriminator between hadron and γ-ray initiated

showers is based on the spatial development of air showers.

In this thesis, the arrival time structure of Cherenkov images is used as an additional

discriminator against the hadronic background. It was shown in previous studies by

the MAGIC collaboration that the time profile of the image can reduce the background

in a single telescope essentially. For stereoscopic observations, as used in H.E.S.S. and

CTA, it has been suggested by the HEGRA collaboration to be of minor importance.

The background rejection potential of the time structure has been investigated in this

work using Monte Carlo simulations. The pixel arrival times in the image have been

used to define characteristic timing parameters which were investigated with respect

to their gamma-hadron separation potential. For both the time profile along the image

and the time spread an improvement of about 10 % in background rejection for a γ-ray

point source could be obtained compared to the common Hillas parameter analysis.

Using an additional direction cut (the θ2 cut), the improvement on gamma-hadron

separation remains, but due to the limited statistics it cannot be stated how large this

improvement is. For diffuse γ-ray emission no improvement on background rejection

could be obtained using the pixel timing information.

Zusammenfassung

Die abbildende atmosphärische Cherenkov Technik hat sich als sehr erfolgreiche Me-

thode in der Gammastrahlungsastronomie im TeV Energiebereich bewährt und die Re-

sultate, die mit gegenwärtigen Instrumenten, wie HESS und MAGIC, erzielt wurden,

sind sehr eindrucksvoll. Allerdings erfordert das detaillierte Verständnis von Prozessen

in kosmischen Teilchenbeschleunigern sowie der Gebrauch der Resultate für kosmologi-

sche Anwendungen eine breitere Energieabdeckung, verbesserte Auflösung und höhere

Detektionsraten. Dies hat die europäische Initiative ausgelöst, die Cherenkov Teleskop-

Anlage (CTA) zu errichten, die sich seit 2008 in der Planungsphase befindet.

Die größte Herausforderung der Cherenkov Technik ist die Unterdrückung des do-

minierenden Hintergrundes von Luftschauern, ausgelöst durch Protonen und Kerne

der kosmischen Strahlung. Die dabei hauptsächlich verwandte Methode basiert auf der

räumlichen Entwicklung der durch hadronische oder Gamma-Strahlung ausgelösten

Luftschauer, aber auch andere Methoden, wie die Analyse der zeitlichen Struktur, wel-

che in dieser Arbeit genutzt wird, sind möglich. Es wurde in vorhergehenden Studi-

en von der MAGIC Kollaboration gezeigt, dass durch die Analyse des Zeitprofils des

Cherenkov-Bildes der Hintergrund in einem einzelnen Teleskop wesentlich verringert

werden kann. Für stereoskopische Beobachtungen, wie in H.E.S.S. und CTA, konnte

mit bisherigen Teleskopesystemen wie HEGRA keine erhebliche Verbesserung erzielt

werden.

Die Methode der Untergrundunterdrückung mittels Pixel-Ankunftszeiten, ist detail-

liert in dieser Arbeit unter Verwendung von Monte Carlo Daten von HESS-II unter-

sucht worden. Die Pixel-Ankunftszeiten im Kamerabild sind verwendet worden, um

charakteristische Zeit-Parameter zu definieren, die in Bezug auf ihr Gamma-Hadron-

Unterscheidungspotential analysiert wurden. Sowohl mit dem Zeitprofil entlang dem

Bildes als auch der zeitlichen Aufweitung des Schauerbildes kann im Vergleich zu der

gebräuchlichen Hillas-Parameteranalyse eine Verbesserung von circa 10 % in der Unter-

grundunterdrückung für eine γ-Punktquelle erreicht werden. Unter Verwendung eines

iv Zusammenfassung

zusätzlichen Richtungsschnittes (dem θ2 Schnitt), bleibt die Verbesserung der Gamma-

Hadron-Trennung erhalten. Aufgrund der geringen Statistik und dem dadurch resul-

tierenden großen Fehler, kann aber keine Aussage darüber getroffen werden, wie groß

diese Verbesserung ist. Für diffuse γ-Strahlung konnte hingegen keine zusätzliche Unter-

grundunterdrückung unter Verwendung der Pixel-Zeit-Informationen erreicht werden.

Contents

Abstract i

Zusammenfassung iii

1 Introduction 1

2 Imaging Atmospheric Cherenkov Technique 5

2.1 Air showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Electromagnetic showers . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Hadronic showers . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.3 Differences between electromagnetic and hadronic showers . . . 9

2.2 Cherenkov emission of air showers . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Cherenkov effect . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Cherenkov emission of particle cascades . . . . . . . . . . . . . . 10

2.2.3 Time development of Cherenkov emission . . . . . . . . . . . . . 11

2.3 The Imaging Atmospheric Cherenkov Telescopes . . . . . . . . . . . . . 13

2.3.1 Shower imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2 Stereoscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.3 Gamma-hadron separation . . . . . . . . . . . . . . . . . . . . . 17

3 Using Timing Parameters for Cherenkov Systems 19

3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Definition of timing parameters . . . . . . . . . . . . . . . . . . . . . . 20

3.2.1 TimeGradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.2 TimeRMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Monte Carlo Samples 23

4.1 The H.E.S.S. Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.1.1 H.E.S.S. Phase I . . . . . . . . . . . . . . . . . . . . . . . . . . 24

vi Contents

4.1.2 H.E.S.S. Phase II . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 H.E.S.S. Analysis Chain . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Gamma-Hadron Separation Using Timing Information 31

5.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 TimeGradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 TimeRMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6 Summary and Outlook 51

List of Figures 53

List of Tables 55

Bibliography 57

Chapter 1

Introduction

Almost 100 years after the discovery of charged cosmic rays (CR) by V. Hess [1], their

origin is still unknown, mainly because charged particles are deflected by interstellar

and intergalactic magnetic fields, and therefore contain no directional information and

arrive nearly isotropically on Earth. In order to identify sources of CRs, one needs

to look at uncharged particles which point back to their origin, neutrinos and γ-rays.

The investigation of cosmic γ-rays lead to the development of a new field of research,

Gamma-Ray Astronomy.

Gamma-rays are the highest energy photons in the electromagnetic spectrum and

their detection presents unique challenges. Because the Earth’s atmosphere is opaque

to high-energy γ-rays, no direct detection is possible on Earth. Thus, only satellite- or

balloon-borne detectors are able to detect primary cosmic γ-rays directly. With these

instruments a picture of the γ-ray sky up to several tens of GeV was obtained [2].

The Large Area Telescope (LAT) on board of the Fermi Gamma-ray Space Telescope

[3] is designed to detect photons with energies up to 100 GeV. A picture of the sky

seen by Fermi is shown in Figure 1.1. Due to the small flux of γ-rays, which decreases

rapidly with increasing energy, instruments for the detection of very high-energy γ-rays

(above ≈ 10 GeV) require a large effective detection area. Thus, one uses ground-baseddetectors in the high-energy regime. When very high-energy γ-rays enter the Earth’s

atmosphere, they interact with the air constituents producing an extensive air shower.

The relativistic secondary particles of these air showers in turn emit so-called Cherenkov

light that can be detected by ground-based telescopes. This method is called Imaging

Atmospheric Cherenkov Technique. Since this technique uses the Earth’s atmosphere

as detector, the effective detection area is typically ∼ 1000 m2, compared to ∼ 1 m2 forsatellite-borne detectors.

Ground-based γ-ray astronomy effectively began in 1989, with the first detection

2 Chapter 1 Introduction

Figure 1.1: An all sky picture of the universe in GeV γ-rays, as it was seen by the FermiLAT after 95 hours of detection [3]. One can clearly see the Galactic planeand some of the brightest sources in the γ-ray regime.

of a TeV γ-ray source, the Crab Nebula, with the 10 m Cherenkov telescope of the

Whipple Observatory [4]. Since then, results from the latest generations of telescopes

have revealed different classes of objects emitting γ-rays in the TeV regime. Most of

the known sources have been discovered during the last few years with the H.E.S.S.

stereoscopic system of imaging atmospheric Cherenkov telescopes [5], the VERITAS

telescope system [6] and the MAGIC telescope [7]. The H.E.S.S. survey of the central

part of our galaxy has shown a large number of new sources that nicely line up with the

galactic plane (see Figure 1.2). Most sources have plausible associations with known

objects such as pulsar wind nebulae or supernova remnants that are also visible in other

wavelength bands [8]. However, a new class of ”dark sources” has also been discovered,

which have not yet been seen at other energy bands. These sources might be a clue to

solving the puzzle of the origin of the galactic cosmic rays.

The impressive physics achievement obtained with the current generation instru-

ments has triggered the initiative to build the Cherenkov Telescope Array [9]. It is

a future ground-based γ-ray observatory which will provide the greatest insight into

the non-thermal high-energy universe. CTA foresees a factor of 5− 10 improvement insensitivity in the energy domain of about 100 GeV to some 10 TeV. An extension of the

3

accessible energy range well below 100 GeV, to overlap with space-borne experiments,

and to above 100 TeV is foreseen. Also the angular resolution will be about three times

better than for the existing telescopes. The CTA observatory will consist of two arrays.

A southern hemisphere array, which covers the full energy range from some 10 GeV to

about 100 TeV for a deep investigation of galactic sources and of the central part of our

Galaxy (see Figure 1.2), but also for the observation of extragalactic objects. A north-

ern hemisphere array, consisting of the low energy instrumentation (from some 10 GeV

to about 1 TeV) complements the observatory and is dedicated mainly to northern

extragalactic objects.

Figure 1.2: Upper panel: Survey scan of the central part of our Galaxy with the H.E.S.S.telescopes. Lower panel: A simulation of the same part with the plannedCherenkov Telescope Array. With the improved sensitivity and the foreseenangular resolution a much deeper look into the universe is possible. Plotsfrom [10]

Since beginning of 2008, the CTA consortium has been performing a Design Study

for the optimization of the performance of the planned observatory. The determination

of the arrangement and characteristics of the CTA telescopes is a complex problem,

balancing cost against performance in different energy bands. It has to be taken into

account, that γ-ray observations are still limited by non-γ-ray backgrounds. Potential

background sources are the sun, the moon and stars but also light from man made

sources, e.g. from satellites, airplanes and city lights. However, the most troublesome

sources are the background of cosmic radiation. Charged cosmic radiation over the

4 Chapter 1 Introduction

range of interest is 103 − 104 times more numerous than a photon of a given energy,and produces superficially similar extensive air showers [11]. It is therefore necessary

to develop methods to separate the signal from the background. Most of these methods

are based on the spatial development of air showers, but also the time development

can be used to distinguish between them. This was already studied with HEGRA [12]

and MAGIC with slightly different results due to differences in their detection methods.

In this thesis the time development of the particle cascade is investigated with respect

to the future CTA experiment and is arranged as follows. In Chapter 2 the principle of

imaging atmospheric Cherenkov telescopes will be introduced and the gamma-hadron

separation methods based on the spatial development of the showers are explained.

The use of timing parameters is briefly discussed in Chapter 3. In Chapter 4 the

H.E.S.S. Phase II Monte Carlo samples used to study the performance of CTA using

timing parameters are presented and the standard analysis procedure used in the cur-

rent H.E.S.S. experiment is explained. This analysis is adapted for the CTA study,

performed in Chapter 5. In this chapter the different timing parameters are inves-

tigated with respect to their gamma-hadron separation potential and the results are

presented.

Chapter 2

Imaging Atmospheric Cherenkov Technique

The Imaging Atmospheric Cherenkov Technique is a very powerful method in γ-ray

astronomy to detect very high-energy γ-ray events. It uses the Cherenkov light, which

is emitted in extensive air showers (EASs), resulting from a highly energetic γ-ray (or

cosmic ray proton or nucleus) hitting the upper atmosphere.

In this chapter the physics of these air showers is explained and the emission of

Cherenkov light within air showers is presented. Afterward the detection principle of

Cherenkov telescopes is explained and the reconstruction of the shower and identifica-

tion methods of the primary particle are outlined.

2.1 Air showers

When a high-energy particle hits the upper atmosphere, it initiates a cascade of sec-

ondary particles by interacting with atomic nuclei of the air. Depending on the type of

the primary particle, the development of the shower differs. In case of a photon or an

electron the interactions are of electromagnetic type and the initiated shower is called

electromagnetic shower. In case of a primary hadron the shower develops in a complex

way as a combination of electromagnetic sub-showers and hadronic multi-particle pro-

duction while interactions via the strong and the weak force occur. This kind of shower

is called a hadronic shower [11].

2.1.1 Electromagnetic showers

Photons and electrons (positrons)1 initiate electromagnetic showers in the atmosphere.

The number of particles in the cascade at first multiplies, than reaches a maximum

1Electrons and positrons will be from now on called electrons throughout the thesis.

6 Chapter 2 Imaging Atmospheric Cherenkov Technique

and attenuates as more and more particles fall below the threshold of further particle

production [13].

The two dominant processes for production of secondary particles are:

• Pair Production: Photons with energies higher than twice the mass of an electroncan produce an electron-positron pair within the field of an atomic nucleus.

• Bremsstrahlung: Charged particles passing through matter are deflected by nu-clei, thus accelerated, which leads to the emission of photons.

For the extinction of the shower the following processes are of major importance:

• Ionisation: All charged particles lose energy when passing through matter. Theloss by ionisation and excitation is described by the Bethe-Bloch formula [14].

• Photo effect: Absorption of photons in the atomic shell.

In the Heitler model [15] an electromagnetic shower can be described as a chain of pair

production and bremsstrahlung processes which occur alternating, see Figure 2.1. It is

assumed that both radiation length for electrons and mean free path for γ-rays are equal

(given by X0)2 and that the energy of the primary particle E0 is, in each interaction,

divided equally between the two secondary particles. After each interaction length the

number of particles in the shower, Np, is doubled, leading to an exponential growth of

the number of particles with atmospheric depth x, while the energy of each particle Ep

decreases exponentially:

Np(x) = 2m with m = x

X0. (2.1)

Ep = E0 · 2−m . (2.2)

The process repeats until the energy of each individual particle has become so small

that neither pair production nor bremsstrahlung can take place. In the model of Heitler

this critical energy Ec is the energy where the energy loss by radiation decreases to the

2 Typically X0 denotes the radiation length, i.e. the path length after which the particle’s energyhas dropped to 1/e of its initial energy E0. For pair production, the corresponding atmosphericlength is called mean free path, which is in air approximately 9/7X0.

2.1 Air showers 7

same order of magnitude as the energy loss by ionisation. The maximum number of

particles, i.e. the shower maximum Nmax = E0/Ec, is therefore reached at

xmax = X0 ·ln (E0/Ec)

ln 2. (2.3)

After the maximum number of particles is achieved the particles are gradually absorbed

by ionisiation, while only a few low energy pairs are still created. Eventually the shower

dies out.

x = X0

x = 2X0

x = 3X0

x = 4X0

atmospheric depthenergy per particle

E0

E0/2

E0/4

E0/8

X0e+ e−

γ

Figure 2.1: Heitler model of an electromagnetic air shower initiated by a primarygamma ray.

This simplified cascade model shows some of the main properties of an electromag-

netic air shower:

• The number of particles in the shower increases exponentially up to the maximumof the shower.

• The maximum number of shower particles is proportional to the primary energyE0 of the incident particle.

• The atmospheric depth of the shower maximum is proportional to the logarithmof the primary energy of the primary particle.

These properties hold true for hadronic showers, even if there are some significant

differences in their development, which will be explained in the following.


2.1.2 Hadronic showers

A hadronic air shower consists of three components: a hadronic core, a muonic com-

ponent and electromagnetic sub-showers [11].

A cosmic ray nucleus hitting the atmosphere scatters inelastically on nuclei of air

molecules and thereby produces mesons like pions and kaons as well as nucleons and

hyperons. High-energy hadrons feed the electromagnetic part of the shower, primarily

by photons from the decay of neutral pions (π0 → γγ) and eta particles. Each highlyenergetic photon generates an electromagnetic sub-shower starting at its point of inter-

action. Nucleons and other highly energetic hadrons contribute further to the hadronic

component. Charged pions and kaons of lower energy decay to feed the muonic part

of the shower (π+ → µ+ + νµ and charge conjugate). In Figure 2.2 this is illustratedschematically.

primary hadron

N: high-energy nucleus

n,p: product nucleus

π0

γ

e+ e−

γ

e+e−

π−

νµµ−

νe νµ

e−

p

n npπ0

N

n p n

Nn

p

N

n

np

p

electromagnetic component muonic component hadronic component

Figure 2.2: Schematic model of an air shower generated by a hadron. Note that thelength of the arrows does not correspond to the lifetime of the particle.

2.2 Cherenkov emission of air showers 9

2.1.3 Differences between electromagnetic and hadronic showers

Although the development of hadronic showers is similar to that of electromagnetic

showers there are still some significant differences.

• In the strong hadronic interaction a large part of the energy goes into the gener-ation of new particles like muons and other secondary hadrons. At each interac-

tion, about one third of the energy goes to the electromagnetic component of the

shower. Since most hadrons undergo further interactions, most of the primary

energy finds its way into the electromagnetic component.

• The interaction length λI of hadrons is larger than for photons (λp ≈ 85 g/cm2

compared to λγ ≈ 35 g/cm2), and therefore hadrons penetrate deeper into theatmosphere.

• The lateral development of electromagnetic showers is determined by elastic mul-tiple Coulomb scattering. The mean scattering angle for high-energy photons is

very small, leading to a small lateral spread. The secondary particles participat-

ing in strong interaction of hadronic showers receive a high transverse momentum,

e.g. by inelastic scattering and decay processes, which leads to a much greater

lateral extension.

• Due to complex multi-particle processes in the development of hadronic showers,they are less regular and have larger fluctuations.

2.2 Cherenkov emission of air showers

Most of the particles in an air shower are highly relativistic. Therefore, they travel

faster than the speed of light in air and emit Cherenkov radiation. A short overview

about the emission of Cherenkov light in air showers will be given with special emphasis

on the time development of the shower. For further information see [16].

2.2.1 Cherenkov effect

As a charged particle travels through matter, it polarizes the medium it propagates

through. The polarized atoms emit electromagnetic waves. Normally these emitted


photons interfere destructively with each other and no radiation is detected. But if

the particles travel faster than the speed of light in the medium the photons interfere

constructively, which leads to a light emission cone according to Huygens principle (see

Figure 2.3(a))

The angle θ between the particle track and the emission direction depends on the

velocity v = βc of the particle and the velocity of light c′ = c/n in the medium (with

the refractive index n and the speed of light in vacuum c):

cos θ =c′

v=

1

βn. (2.4)

This equation is called the Cherenkov condition. It means that light emission can only

take place if β ≥ 1/n, which leads to a minimal energy of the particle

Emin =mc2√1− β2

=mc2√

1− n−2. (2.5)

2.2.2 Cherenkov emission of particle cascades

The threshold energy Emin (Eq. (2.5)) indicates that light particles, like electrons,

dominate the Cherenkov emission in air showers. Because the density of air, and hence

the refractive index (n = n(h)), are not constant within the atmosphere the threshold

energy and the Cherenkov angle depend on the atmospheric altitude h. With the

assumption of an isothermal atmosphere one can use the barometric formula [14] and

obtains

n(h) = 1 + η0 · e−h/h0 , η0 = 0.00029 , h0 = 7.1km. (2.6)

Together with Eq. (2.4) this leads to a height dependent Cherenkov emission angle

θ. The Cherenkov emission of a single particle at the height h results in a ring on

observation level H. The radius R is given by

tan θ =R

h−H. (2.7)

As one can see from Figure 2.3(b), the light emitted from particles at different heights

superimposes at the observation level. This results in an almost homogeneous distribu-

2.2 Cherenkov emission of air showers 11

βc · t

cn· t

θ

(a)

θ

(b)

Figure 2.3: (a) Emission of Cherenkov radiation along the particle track of a charged(fast moving) particle. (b) The height dependence of the Cherenkov angleleads to a ring structure of Cherenkov photons on ground.

tion of photons in a circle of about 80 m to 120 m (for electromagnetic showers) around

the shower core. In Figure 2.4 one can see this ring structure of an electromagnetic air

shower on ground level. Hadronic showers however result in more heterogeneous and

asymmetric structures reflecting the differences in the shower development described

in Section 2.1.

2.2.3 Time development of Cherenkov emission

In addition to the space-angular development one can investigate the time structure of

the emitted Cherenkov photons within air showers. According to [18], the Cherenkov

light time structure from air showers at the ground can be estimated in the following

way. The time delay of Cherenkov photons emitted at the height H with respect to the

particles moving in the shower core (the lateral development of the cascade is neglected)

is defined as

t(R) =

∫dl

v(l)− H

c(2.8)


Figure 2.4: Cherenkov light distribution on ground for a 300 GeV γ-ray shower (left)and a 1 TeV proton shower (right). The side length is 400 m. The picturesare taken from Monte Carlo simulations from [17].

where R is the distance from the shower core to the point of impact of the Cherenkov

photons on ground and v(l) is the speed of the Cherenkov light (see Figure 2.5).

R

H L

p0

ph

θ

Figure 2.5:

The function v(l) can be approximated by [18]

v(l) = v(h) = c/n(h) = c/(1 + (η0/ρ0) · ρ(h)) (2.9)

where ρ0 = 1.29 ·10−3 gr/cm3 is the atmospheric density at sealevel. By substituting this into Eq. (2.8), the equation can be

written as

t(R) =H

c(

1

cos θ− 1) + (η0/ρ0)

(p0 − ph)c · cos θ

(2.10)

where the first term determines the geometrical time delay and

the second term determines the height dependence of the speed of light in atmosphere.

For further details see [19].

Following this equation the light emitted from electrons deep in the atmosphere will

be detected earlier than the photons coming from the upper layers of the atmosphere

for small distances to the shower core (R ≤ 150m). The situation changes at largerdistances (see Figure 3.2 and the explanations in Section 3.2.1). Since the refractive

2.3 The Imaging Atmospheric Cherenkov Telescopes 13

index is so close to 1, the Cherenkov light almost keeps pace with the particles. There-

fore, most of the light from a γ-ray shower near the edge of the Cherenkov light pool

arrives within in a few nanoseconds [20].

2.3 The Imaging Atmospheric Cherenkov Telescopes

Cherenkov flashes from air showers can be detected on ground level by Imaging Atmo-

spheric Cherenkov Telescopes (IACTs). The idea of an IACT is to image the Cherenkov

light by reflecting and focusing it onto a fast and light sensitive camera [21]. In the

following section, the design of current IACTs will be introduced.

Telescope design

Currently two types of IACT mirror arrangements are realized, spherical and parabolic,

depending on the reflector’s frame on which spherical mirrors are positioned (see [22]

and the references therein).

A spherical reflector of the so-called Davies-Cotton design [23] can reproduce a dis-

tant point source as a small but constant spot size image over the whole field of view

(FoV) of the camera. This is also called good off-axis performance. A disadvantage of

a spherical reflector is its asynchronism, leading to a photon arrival time spread (for a

point source) of about 6 ns between photons striking the edge of the reflector and those

striking the center.

For a parabolic reflector spherical mirror facets are arranged on a parabolic surface.

In such constructions, the parabolic frame ensures the isochronous collection of light,

leading to a small photon arrival time spread over the whole camera, whereas the

spherical shape of the mirrors provides acceptable off-axis performances.

2.3.1 Shower imaging

Independent of the telescope design is the principle of shower imaging, which can be

seen in Figure 2.6. The Cherenkov light emitted from the air shower is reflected by

a mirror and mapped onto the camera, located in the focal plane of the telescope.

Due to the height dependence of the refractive index, light emitted in the upper part

of the shower has a smaller Cherenkov emission angle and is therefore displayed at


smaller distances from the camera center than light emitted at the shower end which is

emitted under a larger Cherenkov angle. This means that the angular position of the

light in the camera corresponds to the height of emission and is therefore reflecting the

extension of the shower in the atmosphere. Due to the typical dimensions of an γ-ray

air shower (longitudinal extension ∼ 10 km, transversal extension ∼ 500 m for an energyE ≈ 1 TeV) the obtained image in the camera has elliptical shape. This characteristicis used to parameterize the image and to reconstruct the shower properties.

Figure 2.6: Detection principle of an air shower with an IACT. The Cherenkov lightfrom the shower is mapped onto the camera in the focal plane of the tele-scope. The different emission angles within the air shower correspond todifferent positions in the camera in the focal plane [24].


Image parametrization

A standard method for image parametrization is based on the so-called Hillas pa-

rameters [25] which are calculated after proper calibration [26] and image cleaning

procedures. Hillas parametrized the image in the camera as an ellipse. This ellipse can

be characterized by parameters which can be written in terms of higher order moments

of the light distribution in the camera. They correspond to the position, the shape and

the orientation of the image. Some Hillas parameters are shown in Figure 2.7 and their

definitions are summarized in Table 2.1.

Using these parameters one can determine air shower properties such as energy (∼Size) and direction (∼ Delta) while others (Width, Length) allow to determinethe primary particle and can therefore be used for gamma-hadron separation.

y

x

Wid

th

Leng

th

Dist

δ

Figure 2.7: Geometrical definition of the Hillas parameters.

Size Total intensity of the shower image.Width The rms spread of light along the minor axis of the image;

a measure of the lateral development of the cascade.Length The rms spread of light along the major axis of the image;

a measure of the longitudinal development of the cascade.Delta The angle between the major axis and the x-axis of the camera.

Table 2.1: Shower image parameter definitions.


2.3.2 Stereoscopy

Using stereoscopy a shower is simultaneously detected by two or more telescopes. In

this technique, the telescopes are separated by a distance comparable with the radius

of the Cherenkov light pool (R ∼ 100 m). The detection principle is shown in Figure2.8. Assuming a vertical shower, the impact point of the shower corresponds to the

point of intersection of the straight lines on observation level (x, y)core, defined by the

major axes of the ellipse in each camera. For non-vertical showers, the direction of the

shower can be obtained by superimposing the two camera images into a single camera

plane coordinate system. The intersection point of the major axes corresponds to the

shower direction (θx, θy)shower. Although one pair of detected images is sufficient to

determine the shower parameters, the information from other images helps to improve

the accuracy of reconstruction.

Figure 2.8: Reconstruction of the direction of an air shower using stereoscopy. (Left :)The shower core of a vertical shower corresponds to the point of intersectionof the straight lines on observation level, defined by the major axes of theellipse in each camera. (Right :) By superimposing the two camera imagesinto a single camera coordinate system, the direction of the shower can bereconstructed.


Compared to single telescopes, a system of two or more Cherenkov telescopes has

several advantages: (i) an increased effective detection area and therefore an enhanced

sensitivity, (ii) an excellent suppression of local background like muons and night sky

background (NSB) and (iii) a precise reconstruction of the shower geometry [27, 28].

2.3.3 Gamma-hadron separation

The determination of the shower direction allows effective suppression of the cosmic

ray background for a γ-ray point source analysis, due to the uniform distribution of

the arrival direction of hadronic showers. Therefore, a cut on θ2, the square of the

angular difference between the reconstructed shower position and the source position,

can be applied. This is equivalent to placing the data into a round bin centered on the

source position. The value of this cut (shown in Table 4.1 for H.E.S.S. analyses) can

be adapted to the expected source size as extended sources need a larger θ2 cut than

point-like sources.

Another (additional) method to reject the much more numerous cosmic ray back-

ground events is to exploit the fact that images of a hadron-initiated EAS are on average

longer and wider than those initiated by γ-rays (with the equivalent energy). Cuts on

the width and length of shower images have long been used to perform background

rejection in VHE astronomy, but a fixed width (or length) cut has a poor acceptance

at high energy. To avoid this problem, cuts on a width (or length) parameter that

scales with energy are needed. These parameters are the mean-scaled-width (MSCW)

and length (MSCL), defined as

MSCW =1

Ntel

Ntel∑i=1

widthi − 〈widthi 〉σi

(2.11)

and similar for MSCL. These parameters are defined as the mean of the difference of

the parameter observed in the image with the parameter expected from γ-ray Monte

Carlo simulations for each telescope. The expectation values 〈width 〉 and σ are takenfrom lookup tables and are based on image intensity, impact parameter and zenith

angle Z of observations. For H.E.S.S. the distribution of the two parameters and the

applied cuts for gamma-hadron separation can be found in Section 4.3.

Chapter 3

Using Timing Parameters for Cherenkov

Systems

3.1 Motivation

With the rapid development in technology it is possible to built detectors with a high

bandwidth and a fast digitization and readout. This allows to sample the pulse of the

Cherenkov light within very short time slices in each camera pixel. From this sampling

pixel timing information can be derived in addition to the overall (integrated) intensity

within a camera pixel.

Some IACT experiments like HEGRA and MAGIC have investigated the use of those

additional information with respect to the improvement of shower reconstruction and

gamma-hadron separation. The results of the studies vary slightly, due to the different

detection techniques and sampling rates.

The HEGRA experiment was the first Cherenkov telescope array to provide good

shower reconstruction using stereoscopy. This also lead to a good background suppres-

sion on the basis of shape image parameters as described in Section 2.3.3. The analysis

presented in [29] made use of fast digitizers, which sampled the voltages signal at a

frequency of 120 MHz, enabling the investigation of the pulse shape and the time struc-

ture of Cherenkov images. It is pointed out, that there is no efficient gamma-hadron

separation possible based on timing information like the time spread of the image, due

to the strong correlation with the image shape parameters. Also improvements in the

reconstruction of the impact parameter can be achieved in case of a single telescope,

but they are of limited use in the stereoscopic approach.

20 Chapter 3 Using Timing Parameters for Cherenkov Systems

MAGIC is a system of two IACTs. MAGIC-I is a single-dish Cherenkov telescope

which is operating since 2007 with an ultra-fast FADC, which digitizes the signals with

2 GSamples/s. The construction of MAGIC-II was completed in early 2009. In [30]

the results of using timing characteristics is investigated for the analysis of single-dish

IACT data. The main conclusions of this study are (i) an improvement of background

suppression, due to the suppression of local muons and of isotropic background from

hadron-initiated showers, (ii) an improvement of shower reconstruction and energy es-

timation, mainly due to the better determination of the impact parameter with the use

of the longitudinal time profile and (iii) an enhancement of the efficiency and lowering

of the threshold of the image cleaning procedure. For MAGIC-II no investigation on

using timing information has been published yet.

For CTA with its planned 50 to 100 telescopes, it is important to figure out in how

far the use of pixel timing information will help to improve the performance of CTA

as an observatory (within a reasonable cost range). This can be done by investigating

the improvement of shower reconstruction (as it is shown by the MAGIC collaboration

for a single-dish analysis) or by developing gamma-hadron separation methods on the

basis of timing information. This thesis is focused on the latter approach.

3.2 Definition of timing parameters

In order to describe the timing characteristics of an air shower, some time-related

parameters are introduced. Those timing parameters characterize both the longitudinal

development and the spread (lateral development) of the shower.

3.2.1 TimeGradient

To describe the longitudinal time development of an air shower the time profile along

the major axis of the elliptical shower image is used. A typical event display of an

γ-ray air shower is shown in Figure 3.1, where the distribution of the intensities as well

as the arrival times are illustrated. One can see the elliptical shape of the image in

Figure 3.1(a) and a time development along the major axis in Figure 3.1(b). A simple

way to characterize the time profile is to project the pixel coordinates onto the major

axis of the image, reducing the problem to one dimension. The arrival time versus the

3.2 Definition of timing parameters 21

space coordinates along the major axis is fitted to a linear function t(x) = m · x + n.The slope of this linear fit is called TimeGradient. It measures how fast the arrival

times change along the major axis.

0

10

20

30

40

50

60

70

80

(a) Intensity distribution (in p.e.).0

2

4

6

8

10

12

(b) Arrival time distribution (in ns).

Figure 3.1: Event display of a 1 TeV γ-ray air shower at an impact distance of 400 m.(a) The intensity distribution is used to parametrize the ellipse and definethe major axis using Hillas parameters. (b) The distribution of the arrivaltimes shows a clear time development from the inner part of the camera tothe edge, leading to a positive TimeGradient.

From the description of the time delay at a certain distance from the shower core in

Section 2.2.3, it is obvious, that the TimeGradient strongly depends on the impact

parameter of the shower. Therefore, Figure 3.2 shows the propagation of Cherenkov

light into the telescopes for two different impact parameters. For a small impact param-

eter (left part of Figure 3.2), the light emitted at the shower tail will arrive before the

light which is emitted in the upper atmosphere. This leads to a negative TimeGradi-

ent. For large impact parameters (right part of Figure 3.2), the situation is reversed

and the light emitted at the shower head arrives first (due to the shorter path length).

The sign of the TimeGradient is positive. Due to these properties, the TimeGra-

dient helps to avoid the degeneracy between small, nearby showers and the large,

distant ones [30]. The use for gamma-hadron separation will be discussed in Section

5.2.

22 Chapter 3 Using Timing Parameters for Cherenkov Systems

Che

renk

ovlig

ht, v

=c/

n(h)

ImpactParameter

show

erpa

rtic

les,

v=c

head

tail

Figure 3.2: Propagation of Cherenkov light emitted at different stages of the showerdevelopment into two telescopes. While the emitted light travels with avelocity v = c/n(h), the shower front of an electromagnetic air shower movesnearly with the speed of light c. This leads to different time developmentsin the cameras for small (left part) and large (right part) impact parametersand hence to different TimeGradients.

3.2.2 TimeRMS

To describe the lateral development of the particle cascade, the spread of the arrival

times of the image is used. The TimeRMS is defined by

TimeRMS =

√∑ki=1 (ti − t)2

k(3.1)

which is the root-mean-square of the arrival time of all k pixels belonging to the image.

Due to the differences in the lateral development of EAS between γ-ray and hadron

initiated showers, this parameter is expected to be a good background discriminator.

This will be investigated in Section 5.3.

Chapter 4

Monte Carlo Samples

For the planned Cherenkov Telescope Array the Design Phase of the array started at

the beginning of 2008. Many different aspects of the array and the telescope design are

under investigation within different work packages. The objective of the work package

Monte Carlo is to provide an array design which optimizes the performance/cost of

the array whilst meeting the physics requirements. This requires the development of

software for array simulation and performance estimation followed by a study of in-

strument performance (spectral sensitivity, angular resolution, background rejection,

energy resolution) as a function of telescope parameters (dish size, FoV, pixel size,

trigger scheme, readout scheme) and array configuration. One of the defined subtasks

is to establish the usefulness of pixel timing information for the different array con-

figurations. Due to the different results from former studies (Section 3.1) this has to

be figured out carefully for the planned CTA with respect to the costs of the required

readout system.

In this chapter the Monte Carlo (MC) samples used for this CTA study are presented.

Since at the beginning of this thesis no CTA MC samples were available, H.E.S.S.

Phase II MCs are used. These simulations also provide pixel timing information and

can be used for an estimation of the improvement with pixel timing information while

using stereoscopy. In Section 4.1 the H.E.S.S. experiment is introduced and the MC

simulations are summarized in Section 4.2. Afterward the H.E.S.S. analysis chain is

described in more detail in Section 4.3.

4.1 The H.E.S.S. Experiment

The High Energy Stereoscopic System (H.E.S.S.) is a system of Imaging Atmospheric

Cherenkov Telescopes that investigates cosmic γ-rays in the 100 GeV to 100 TeV energy

24 Chapter 4 Monte Carlo Samples

range [5]. H.E.S.S. is situated in the Khomas Highland of Namibia at 1.8 km above

sea level. The full four-telescope system (H.E.S.S. Phase I) has been in operation since

December 2003. In order to decrease the energy threshold of the system (down to

20 GeV) and to improve the sensitivity and angular resolution over the current energy

range, a fifth, large mirror telescope is under construction on the H.E.S.S. site and will

be operational in 2010 (H.E.S.S. Phase II). With this update, there will exist at least

two different operational modes in H.E.S.S.: a hybrid mode, when at least one small

H.E.S.S.-I telescope and the large fifth telescope (CT5) have triggered and a single

mode, when CT5 is triggered alone.

Figure 4.1: Photo of the current four telescope H.E.S.S. Phase I array, with an artist’simpression of the Phase II 28 m Ø telescope in the center of the arraysuperimposed.

4.1.1 H.E.S.S. Phase I

The H.E.S.S. Phase I experiment consists of four IACTs (CT1 − CT4) arranged in asquare with 120 m side length, to provide multiple stereoscopic view of air showers. The

telescopes use the Davies-Cotton design and consist of an optical reflector of 107 m2

with a focal length of 15 m. The total field of view of H.E.S.S. is 5◦ with an angular

resolution of 0.1◦. The mirror focuses the Cherenkov light emitted by an air shower

onto a camera. The camera contains 960 photomultiplier tubes (PMTs), also called

pixels, and is divided into 38 overlapping sectors of each up to 64 pixels. The camera

trigger starts a readout process when any of these sectors contains p pixels with an

amplitude exceeding q photo electrons within a time window of 2 ns. The typical choice

4.1 The H.E.S.S. Experiment 25

is (p, q) = (3, 4) [31]. This trigger system, called sector trigger, allows to distinguish

between a shower event, which is expected to be more compact, and the night sky

background (NSB). The PMT signals, which are stored in an analogue memory [32]

while awaiting the trigger, are then read out, digitized, and integrated within a 16 ns

window. Once a camera triggers on a shower image, the signals are sent from the

camera’s on board data-acquisition system to the central trigger, which demands that

at least two telescopes have been triggered within a 80 ns period. In stereoscopic

operation, the stereo trigger rate is ∼ 300 Hz for current trigger conditions.

4.1.2 H.E.S.S. Phase II

In Phase II of the project [33], a large dish telescope CT5 with a 600 m2 mirror will be

installed at the center of the H.E.S.S. array. The dish is rectangular. 850 mirror facets

are assembled to approximate a parabolic shape, which minimizes the time dispersion

of photons forming the image. The camera is mounted at the focal plane, 37 m away

from the dish. The increased mirror area causes a higher night sky background in the

camera. In order to keep it to a similar level, the pixel aperture is four times smaller

than for H.E.S.S. Phase I. With a field of view reduced from 5◦ to 3.2◦, the camera

consists of 2048 pixels (pixel size = 0.07◦). The camera is divided into 96 sectors of 64

PMTs and uses a sector trigger comparable to the H.E.S.S.-I trigger.

When CT5 will be running in single mode, one expects a trigger rate up to 3 kHz.

The electronics for the H.E.S.S.-I cameras would not fit for the new camera. New

electronics have been designed. It is based on a new GHz sampling circuit, the Swift

Analogue Memory (SAM) [34]. The narrow pulse in the SAM will allow the use of a

smaller window and therefore integrate much less night sky background.

When the telescope is triggered, it records the pixel intensities as well as the time

of the maximum signal (T0) and the time over a defined threshold (ToT) for an inte-

gration window of 16 ns. The signal is read with a sampling frequency which can be

varied between 500 MHz and 3 GHz.

Since the fifth telescope of H.E.S.S. is still under construction, all studies performed in

this thesis are based on Monte Carlo simulations.


4.2 Monte Carlo simulations

Any simulation of an IACT consist of two parts: the simulation of the development

of the extensive air shower and emission of Cherenkov light by the shower particles as

one part and the detection of light and the recording of the signal by the detector as

the other part.

The first part is based on the CORSIKA program [35]. With this program one can

define different properties of the extensive air shower, like the type and the energy range

of the primary particle, the particle direction as well as the spectrum. Also specific

environment parameters, like the atmospheric composition, geomagnetic field strength

and the observation level of the detector, can be set as input for the program.

The second component of the simulation is termed sim telarray [36] and runs

directly after CORSIKA. sim telarray simulates in a very detailed way the telescope

response to the photon data. This includes PMT noise and the NSB in the camera.

Within this simulation program one can specify the entire detection process, e.g. the

reflector layout, the mirror reflectivity, the quantum efficiency of the PMT and the

trigger condition.

Monte Carlo data sets

The MC samples used have been generated for H.E.S.S. Phase II at a zenith angle of

20 ◦. For this analysis the reflectivity of the mirrors has been set to 100%. This is

not true for the existing H.E.S.S.-I telescopes, due to degradation processes like the

desert winds, but a better reflectivity is expected for CTA. In addition to this the

fast readout simulation for CT5 (with a 1 GHz sampling rate) was enabled to provide

timing information for every pixel.

The MC samples used to assess the hadron suppression potential of the presented

methods, consist of two different type of primary particles, γ-rays and protons. The

γ-rays are point sources at 0.0◦ offset (the source position is equal to the center of the

camera), while the protons are isotropically generated over the whole FoV and have no

preferred direction. To compare the separation power in more detail, a subset of diffuse

γ-rays has also been used. For photons as well as for protons the energy spectrum was

simulated according to a power law with E−2.

The γ-rays are re-weighted according to the Crab spectrum as the standard candle in

γ-ray astronomy. The spectrum used here was measured by the H.E.S.S. collaboration

4.3 H.E.S.S. Analysis Chain 27

[37]:

dN

dE= 3.45× 10−7

(E

TeV

)−2.631

s m2 TeV. (4.1)

The simulated energy range of the primary γ-rays is 0.05 to 10 TeV.

The cosmic ray protons are re-weighted according to the cosmic ray spectrum mea-

sured by the HEGRA collaboration [38]:

dN

dE= 0.11

(E

TeV

)−2.721

s sr m2 TeV. (4.2)

Since protons need a about three times higher energy to generate the same amount of

Cherenkov photons on observation level as γ-rays, the energy range of the protons is

0.01 to 50 TeV. At higher energies gamma-hadron separation is usually easier, because

more Cherenkov light will be emitted and the irregularities in hadronic showers will

appear stronger in the image.

4.3 H.E.S.S. Analysis Chain

In order to analyze the simulated data sets, the Standard Analysis of H.E.S.S. Phase I

is used [39]. It is used to reconstruct the direction and energy of the incident γ-rays,

rejecting the cosmic-ray background and determine the spectrum of the flux of the

detected sources.

First, an image cleaning is performed using a two-stage tail-cut procedure to remove

the NSB fluctuations from the shower image. The tail-cut cleaning requires a pixel to

have a signal greater than 5 (or 10) photo-electron equivalents (p.e.) and a neighboring

pixel to have a signal larger than 10 (or 5) p.e. Then the cleaned image is parame-

terized with the Hillas parameters defined in Section 2.3.1 which are the basis of the

Standard Analysis technique. Afterward quality cuts are applied to guarantee a good

reconstruction of the shower. The quality cuts are:

• A minimum required Size (minimum number of photoelectrons in the image) toavoid too small and faint images, which cannot be well parametrized.

• A cut on the local distance (distance from the image center of gravity to thecamera center) to avoid a truncation of the images at the edge of the camera.


• A telescope multiplicity (number of telescopes which has to be triggered byone shower) to guarantee a stereoscopic reconstruction.

Typical values used in H.E.S.S.-I analyses are a minimum local distance that is required

not to exceed 2 ◦, a minimum size of 80 p.e. and a minimum of two triggered telescopes.

After the pre-selection of the MC data sets, the properties of the shower are recon-

structed. The shower direction is obtained by using stereoscopy, introduced in Section

2.3.2. To estimate the energy of the primary γ-ray, the relation of the properties of the

recorded image in each camera and the particle’s energy has to be determined from

Monte Carlo simulations. Since the energy of the initial γ-ray is connected with the

Cherenkov light emission in the shower, the intensities (Size) of the shower images are

a good parameter for the energy estimation. But this connection is affected by further

observation parameters like the zenith angle Z and the impact parameter. Therefore,

for each telescope image, lookup tables for the energy are generated for various zenith

angles and contain the expectation value of the energy of the simulated γ-ray, 〈Etrue〉,depending on the Size and the impact parameter d. The reconstructed energy Ereco of

the γ-ray candidate is then calculated by averaging over the telescopes:

Ereco =1

Ntel

Ntel∑i=1

〈Etrue(Z, Size, d) 〉 . (4.3)

After the reconstruction, the scaled parameters MSCW and MSCL are calculated

and used for background rejection. The distributions of MSCW and MSCL for γ-rays

and protons with a zenith angle of Z = 20◦ can be seen in Figure 4.2. Due to the small

overlap of the distributions (especially for MSCW), a cut is applied on these shower

parameters to distinguish between photon and hadron initiated cascades. The typical

cut values for H.E.S.S.-I are −2.0 < MSCL < 2.0 and −2 < MSCW < 0.9.In addition to the cuts on the mean scaled parameters, a cut on θ2 can be applied

for a γ-ray point source. This is a very efficient background rejection method used in

stereoscopic Cherenkov systems.

To measure the separation power of the applied cut, the quality factor Q is intro-

duced, which is a quantity describing the gain in significance achieved by different

separation algorithms. It is defined by

Q =�γ√�h

(4.4)

4.3 H.E.S.S. Analysis Chain 29

]σMSCL [-2 0 2 4 6 8

no

rmal

ized

0

0.02

0.04

0.06

0.08

0.1

0.12 MC Gamma

MC Proton

]σMSCW [-2 0 2 4 6 8

no

rmal

ized

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 MC Gamma

MC Proton

Figure 4.2: Mean scaled length (left) and width (right) for Monte Carlo gamma andproton events. The images for γ-induced showers show normal distributionswhile those for hadron-induced shower are much longer and most notablywider.

with the efficiency for γ-rays (index γ) and hadrons (index h)

�γ/h =n

N(4.5)

where n is the number of events passing the cut and N is the number of all triggered

events (before cuts). The quality factor and the applied cuts for the H.E.S.S.-I Standard

Analysis are summarized in Table 4.1. Based on this analysis, the separation potential

of the timing parameters will be investigated in the next chapter.


MSCW Size θ2 No θ2 No θ2 All AllCuts max min max γ BG Q γ BG Q

[σ] [p.e.] [deg2] % % % %

Std 0.9 80 0.0125 49 2.4 3.2 35 9.4e-3 36Hard 0.7 200 0.01 15 0.23 3.2 13 7.5e-4 47Loose 1.2 40 0.04 84 9.2 2.8 68 0.11 21

Table 4.1: Different selection cuts applied to H.E.S.S.-I data, the percentage of γ-ray(Γ = 2.6, Z = 20◦) and background events (Z = 20◦) retained by those cuts,and the corresponding quality factors (Q) for the analysis with and withoutθ2 cut. Cut of MSCW > −2 and −2.0 < MSCL < 2.0 are applied in allcases [39].

Chapter 5

Gamma-Hadron Separation Using Timing

Information

In this chapter the differences between photon and hadron initiated extensive air show-

ers are investigated with respect to the time development of the cascades. Therefore,

the H.E.S.S. Standard Analysis described in Section 4.3 is applied to the Monte Carlo

data sets with some slight modifications which will be described in Section 5.1. To

investigate the influence of the timing parameters defined in Section ?? on gamma-

hadron separation, different cuts on the TimeGradient (Section 5.2) as well as on

the TimeRMS (Section 5.3) are analysed and discussed.

5.1 Analysis

In order to investigate the separation power of the timing parameters, a pre-selection

and a shower reconstruction of the MC data sets is done based on Hillas parameters.

First, a two-stage tail-cut image cleaning is applied to all five telescopes using the

standard values (5 and 10 p.e.) for the four small telescopes (CT1−CT4) and lowertail-cuts, namely 4 and 7 p.e., for CT5. Since the reconstruction mechanisms for the

H.E.S.S. Phase II MCs are not fully developed and optimized yet (due to different

telescope designs and the different energy threshold between the small telescopes and

CT5), the shower is reconstructed only with the four H.E.S.S.-I telescopes. Therefore,

the telescope multiplicity was set to at least three small telescopes. A minimum local

distance and a minimum size cut are applied on CT1−CT4 to remove incorrectlyreconstructed events. The cut values can be found in Table 5.1. In addition to the

multiplicity cut it is demanded that CT5 must have triggered. This is obvious since CT5

is the telescope which contains the timing information we are interested in. Although,

32 Chapter 5 Gamma-Hadron Separation Using Timing Information

a little improvement of the shower reconstruction is expected by adding CT5 to the

analysis, this was not taken into account here. To be able to use the full power of the

timing information no other cuts are applied on CT5. This can be done because the

shower is still reconstructed by using the stereoscopic approach of the small telescopes

and an image cleaning has been performed to reduce the night sky background and

electronic noise of the pixels.

tail-cuts size local dist. MSCL MSCW Reconstructiontelescope min/max min max [min,max] [min,max] (trigger)

[p.e.] [p.e.] [deg] [σ] [σ]

CT1−CT4 05/10 80 0.525 [-2 , 2] [-2 , 0.9] yes (≥ 3 tels)CT5 04/07 − − − − no (yes)

Table 5.1: Pre-selection cuts applied on the MC data sets. The reconstruction is donewith the H.E.S.S.-I telescopes, to which the standard cuts are applied. Thetelescope multiplicity was set to at least three telescopes with the additionalcondition that CT5 must have triggered.

After the reconstruction of the shower with CT1−CT4, the scaled parameters MSCWand MSCL are calculated and used for background rejection. The cut values used are

the standard cuts from Table 4.1 which have been optimized for a γ-ray point source

with a spectral index of −2.6 and a zenith angle of Z = 20◦. With these cuts one cancalculate the efficiencies for γ-ray and hadron selection of the used analysis.

As all MC data sets have been simulated with a E−2 spectrum, they have to be

weighted, according to their desired spectrum (see Section 4.2). The weights are defined

by

wi =E−2iE−Γi

(5.1)

where the spectral index Γ is 2.63 for γ-rays and 2.72 for protons. With these weights

Eq. (4.5) can be written as

�i =n

N=

∑nk=1wk∑Nk=1wk

(5.2)

where n is the number of events passing the cut and N is the number of triggered

5.1 Analysis 33

events. The error of the efficiencies [40] is taken as

σ(�i) =

√(1− n

N)∑n

k=1w2k∑N

k=1wk. (5.3)

With those equations, the efficiencies of the pre-selection cuts of Table 5.1 can be

calculated for the three different MC data sets. For a γ-ray point source at 0.0◦ offset

�γ = 0.2191±3.8 ·10−4, for diffuse γ-ray emission �γ = 0.1602±3.3 ·10−4 and for diffuseprotons �p = 0.0078 ± 1.3 · 10−4. The results for the γ/hadron efficiencies of the pre-selection cuts (summarized in Table 5.2) are comparable with the results from [39]. The

reduced efficiency for selecting events in this analysis compared to the standard cuts

results from the different telescope multiplicity. In the Standard Analysis of H.E.S.S.

the telescope multiplicity is set to at least two telescopes (which is equal with the

trigger condition used) while in the analysis presented here, it was requested that at

least three small telescope and CT5 must have triggered.

With the obtained efficiencies the quality factor Q (Eq. (4.4)) can be calculated for

the different MC samples. For a γ-ray point source it is Q = 2.475 ± 0.020 and fordiffuse γ-ray emission Q = 1.809± 0.014, see Table 5.2. These two quality factors areused as reference values to compare the investigated cuts on the timing parameters

with the standard cuts, used for stereoscopic Cherenkov systems.

In addition to the pre-selection cuts in Table 5.1 one can apply the θ2 cut for the

point source analysis. Using the cut value from the H.E.S.S.-I analysis, θ2 < 0.0125,

the resulting quality factor increases by a factor of ten due the isotropic distribution

of the proton arrival direction. The huge background suppression potential of this cut

(�p = 2.9 ·10−5±8.1 ·10−7) leads to a quality factor of Q = 31.47±0.44. The efficienciesand the quality factor are summarized in Table 5.2.

In the following sections the longitudinal as well as the lateral time development of

an EAS are investigated. Therefore, the pre-selection cuts are applied and the quality

factors from Table 5.2 are used as reference values. Due to the efficient background

rejection of the θ2 cut, the results of the analysis would be limited by the proton

statistics. Therefore, the following analyses on gamma-hadron separation are done

without the θ2 cut.


pre-selection pre-selection with θ2

nγ np Qpre nγ np Qθ

γ-ray point source 21.91 0.78 2.47± 0.02 17.06 2.9e-3 31.5± 0.4diffuse γ-ray emission 16.02 0.78 1.81± 0.01

Table 5.2: The percentage of the γ events, nγ, and the proton events, np, passing thepre-selection cuts (see Table 5.1) and the resulting quality factors Q for γ-raypoint sources and diffuse γ-ray emission.

5.2 TimeGradient

The longitudinal temporal development of an EAS can be described by the time profile

along the major axis of the camera image. As discussed in Section 3.2.1 the TimeGra-

dient, measuring how fast the arrival times change along the major axis, is strongly

correlated with the impact parameter of the shower. The correlation of the true im-

pact parameter dtrue with the TimeGradient is shown in Figure 5.1 for γ-ray events

from a point source at 0.0◦ offset. It can be seen, that for small impact parameters

(dtrue < 100 m) the TimeGradient is negative while it becomes positive for large

ones (dtrue > 200 m).

In this analysis, the impact parameter is reconstructed using the stereoscopic view of

the H.E.S.S.-I telescopes as described in Section 2.3.2. The TimeGradient for each

event is calculated as follows. First, the major axis of the image is defined and the

angle δ with the x-axis is calculated. δ is independent of the position of the ellipse in

the camera and has values between −π/2 and π/2. To decide on the true sign of theTimeGradient one has to determine head-tail information of the image. They are

obtained by using the position of the reconstructed source in the camera and expanding

the interval of δ to [0, 2π]. The major axis is then rotated by −δ and the arrival timesas a function of the x-coordinates can be fitted by a linear function. The slope of this

fit is the TimeGradient of the event. Filling all events in a histogram, one can see

the dependence of the TimeGradient on the reconstructed impact parameter. This

is shown in Figures 5.2 − 5.4 for a γ-ray point source at 0.0◦ offset, for diffuse γ-rayemission and for diffuse proton emission, respectively.

It can be seen that there are slight differences between the different MC data sets.

Figure 5.2 shows the correlation of the TimeGradient with the reconstructed impact

5.2 TimeGradient 35

ImpactParameter [m]0 50 100 150 200 250 300 350

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Figure 5.1: Color plot of the correlation of the TimeGradient with the true im-pact parameter for simulated γ-ray events at 0.0◦ offset after pre-selectioncuts. One can clearly see that the TimeGradient increases with increas-ing impact parameter. For small impact parameters (dtrue < 100 m) theTimeGradient is negative while it is positive for large ones. The colorpalette shows the number of entries.

parameter for a γ-ray source pointing directly to the center of the camera. Comparing

the upper panel of this figure with Figure 5.1 one can see the similar behavior. This

reflects the fact that for a γ-ray point source analysis the impact parameter can be very

well reconstructed by using stereoscopy. In the lower panel of Figure 5.2 one can see the

profile of the distribution where the error bars are the spread of the distribution (and not

the spread of the mean). For small impact parameters (dreco < 50 m) the mean of the

TimeGradient in each bin is negative, as expected from the temporal development.

With increasing distances to the detector (the mean of the) TimeGradient increases

nearly linearly. For distant showers (dreco ∼ 350 m) the mean of the TimeGradientfluctuates more due to the low statistics in these bins. The spread of the distribution



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Figure 5.2: Correlation of the TimeGradient with the reconstructed impact param-eter for γ-rays pointing to the center of the camera. (Upper panel :) Colorplot of the correlation, where the color palette shows the number of entries.(Lower panel :) Profile plot of the correlation where the error bars are thespread of the distribution.

5.2 TimeGradient 37


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Figure 5.3: Correlation of the TimeGradient with the reconstructed impact parame-ter for diffuse γ-ray emission. (Upper panel :) Color plot of the correlation,where the color palette shows the number of entries. (Lower panel :) Profileplot of the correlation where the error bars are the spread of the distribution.The distribution of the TimeGradient for constant impact parameter ismore spread than in Figure 5.2 reflected in larger error bars in the profileplot.


(reflected by the error bars) is very small in the range from 100 to 250 m and becomes

larger for distant showers due to the low statistics. For very nearby showers the error

bars are determined by the accuracy of the reconstruction of the impact parameter.

Comparing the γ-ray point source with the diffuse γ-ray emission (Figure 5.3) one

can see that the distribution for diffuse γ-rays is more spread. This results in larger

error bars over the whole range of impact parameters. In addition to the larger error

bars, one can see some events with a TimeGradient of zero in the upper panel of

Figure 5.3 at impact parameters smaller and larger than expected. This can have

different reasons. On the one hand, the image in CT5 can be very small (since no size

cut was applied) and all pixels in the image have the same arrival time. On the other

hand, the images can be truncated by the camera edge of CT5 (since no local distance

cut is applied) and cannot be very well parameterized. The latter one is more probable

due to the large field of view from which the diffuse γ-rays arrive.

For diffuse proton emission, the distribution of the TimeGradient versus the re-

constructed impact parameter is shown in Figure 5.4. Due to the pre-selection cuts on

MSCW and MSCL the proton statistics is very low and the correlation between the

TimeGradient and impact parameter is not as obvious as for γ-ray events. Never-

theless, it can be seen from the lower panel of Figure 5.4 that the TimeGradient

increases for increasing impact parameter, starting with negative values for nearby

showers.

In the following the TimeGradient and especially the correlation with the impact

parameter will be investigated in respect to gamma-hadron separation. Therefore, an

expectation value for the TimeGradient is determined using the MC truth of a γ-

ray point source. The TimeGradient in dependence of the true impact parameter is

approximated by a polynomial function of fifth order. The spread of the distribution

in dependence of the impact parameter is in the following treated as the error. It

is approximated by a polynomial function of second order, as shown in Figure 5.5.

Although the fits are not perfect, they approximate the TimeGradient dependence

on the impact parameter very well.

Based on the fit, a scaled TimeGradient is defined by

ScaledTimeGradient =TimeGradient − 〈TG〉

〈σ〉(5.4)

which is the difference of the TimeGradient from the expected one, 〈TG〉, divided

5.2 TimeGradient 39


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Figure 5.4: Correlation of the TimeGradient with the reconstructed impact param-eter for diffuse protons. (Upper panel :) Color plot of the correlation, wherethe color palette shows the number of entries. (Lower panel :) Profile plotof the correlation where the error bars are the spread of the distribution.


true ImpactParameter [m]0 50 100 150 200 250 300

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14 / ndf 2χ 386.7 / 154Prob 0p0 0.049± -1.253 p1 0.0022± -0.1117 p2 0.000035± 0.002068 p3 2.534e-07± -1.165e-05 p4 8.526e-10± 3.098e-08 p5 1.074e-12± -3.205e-11

/ ndf 2χ 386.7 / 154Prob 0p0 0.049± -1.253 p1 0.0022± -0.1117 p2 0.000035± 0.002068 p3 2.534e-07± -1.165e-05 p4 8.526e-10± 3.098e-08 p5 1.074e-12± -3.205e-11

/ ndf 2χ 1.611 / 158Prob 1p0 0.235± 3.857 p1 0.00338± -0.03328 p2 1.020e-05± 9.677e-05

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4.5 / ndf 2χ 1.611 / 158Prob 1p0 0.235± 3.857 p1 0.00338± -0.03328 p2 1.020e-05± 9.677e-05

Figure 5.5: (Left :) Fit of the TimeGradient in dependence of the true impact pa-rameter for γ-rays. The light blue shadow indicates the spread of the dis-tribution, the error of the mean is denoted by the small black error bars.(Right :) The spread is plotted as a function of the true impact parameterand is approximated by a fit function.

by the expected spread of the distribution, 〈σ〉. The distribution of the obtained scaledTimeGradient is shown in Figure 5.6. On the left side of the figure the distribution

of this variation is shown for γ-ray point source events at 0.0◦ offset superimposed

with diffuse proton background. The γ-ray events are normally distributed around

zero with an rms of about one, as expected. For proton events the distribution is

also normally distributed around zero, but slightly wider. Therefore, one can try to

use this variable to develop a cut for gamma-hadron separation. Comparing the scaled

TimeGradient for proton background events with diffuse γ-ray emission (right side of

Figure 5.6), the differences are not that evident. This encourages the assumption that

a cut on the TimeGradient results in an improvement on gamma-hadron separation

for γ-ray point source analyses, where the source is pointing to the center of the center

of the camera, rather than for diffuse γ-ray emission, where the source is isotropically

distributed over the whole field of view of the telescope.

By looking at the distribution of the scaled TimeGradient in Figure 5.6 it is

obvious that a set of cuts, namely a minimum and a maximum cut, have to be applied

and optimized. The upper cut is determined by applying a cut in the range of [−10, x],

5.2 TimeGradient 41

σ(TG - ) / -10 -5 0 5 10 150

0.001

0.002

0.003

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0.006γ point

diffuse p

σ(TG - ) / -10 -5 0 5 10 150

0.0005

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0.0015

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0.0025

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0.0035

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0.0045 γ diffuse diffuse p

Figure 5.6: Normalized distribution of the difference of the TimeGradient with theexpectation value received from γ-ray Monte Carlo simulations. (Left :) γ-ray emission pointing to the camera’s center is superimposed on a diffuseproton background. (Right :) The diffuse proton background is comparedto diffuse γ-rays.

where x is running from −10 to 15. For every cut value, the efficiencies for signal andbackground events are calculated and the quality factor Q determined. The cut xmax,

where Q has its maximum, is used as upper cut value on the parameter. Then the

lower cut is determined by applying a minimum cut in the range of [x, xmax], where x is

running from xmax to −10. The cut xmin, where Q has its maximum, is used as lowercut. With these optimized cuts (xmin, xmax) the maximum quality factor is calculated.

Comparing a γ-ray point source at 0.0◦ offset with diffuse proton emission, the best

cut values obtained with this algorithm are at xmin = −2.83 and xmax = 1.38. Byapplying these cuts, 91.0± 0.2 % of the γ-rays (signal) are kept, while 71.0± 1.3 % ofthe protons (background) survive the cut. This results in a maximum quality factor

of Q = 2.723 ± 0.027. Compared to the quality factor after the pre-selection cuts(Qpre = 2.474± 0.020), this is an improvement of 10.2± 1.1 % when applying this cuton the scaled TimeGradient in addition to the pre-selection cuts. The results are

summarized in Table 5.3.

Applying the same cut optimization algorithm to the diffuse γ-ray emission no further

improvement compared to the pre-selection cuts can be achieved due to the similar

behavior of the distribution of the scaled TimeGradient for diffuse γ-ray and proton


emission.

To draw a conclusion of how good the improvement of the cut on the scaled TimeGra-

dient is for stereoscopic systems like CTA, it has to be compared with the usually

used θ2 cut for point source analyses. Therefore, the θ2 cut is applied to the data sets

in addition to the pre-selection cuts, leading to a quality factor of Qθ = 31.47 ± 0.44(see Section 5.1). Comparing directly the improvement of 10 % in respect to the pre-

selection cuts to the improvement obtained for the θ2 cut, it is obviuos that the timing

cut is not very efficient for gamma-hadron separation. Nevertheless, one can use the

timing cut in addition to the θ2 cut. This can be done by applying the optimized cuts

on the scaled TimeGradient after the θ2 cut and calculate the signal and background

efficiencies. This analysis results in �γ = 0.9344±2.3 ·10−3 for a γ-ray point source and�p = 0.51±0.21 for diffuse protons. The large error on �p results from the limited statis-tics for protons after the direction cut. The quality factor is given by Q = 41.2± 8.6.This leads to an improvement of 31± 27 % compared to the gamma-hadron separationusing pre-selection cuts and θ2 cut without timing information. The results are sum-

marized in Table 5.3.

cut value nγ np Q improvement(min,max) % %

No θ2 cut (-2.83,1.38) 91.0 71.0 2.72 ± 0.03 + 10.2 ± 1.1 %

θ2 < 0.0125 (-2.83,1.38) 93.4 ∼ 51 41.2 ± 8.6 + 31 ± 27 %

Table 5.3: Calculated quality factors Q and their improvement compared to pre-selection cuts without θ2 cut (Qpre = 2.47 ± 0.02) and pre-selection cutswith a cut on θ2 < 0.0125 (Qθ = 31.5 ± 0.4) for the scaled TimeGradi-ent . The percentage of γ events, nγ, and proton events, np, represents theevents which pass the timing cut after the pre-selection (with or without θ2)is applied.

To sum up, adding the TimeGradient cut both to the pre-selection cuts and to

the pre-selection cuts including a θ2 cut, an improvement on gamma-hadron separation

can clearly be seen. Due to the limited proton statistics after the θ2 cut, it cannot be

stated how large the improvement is. Further studies have to be performed at higher

level analyses to make an precise prediction on the potential of the TimeGradient

as an additional gamma-hadron separation method.

5.3 TimeRMS 43

5.3 TimeRMS

The TimeRMS, defined in Section 3.2.2, is reflecting the lateral temporal spread of the

image. Therefore, it is expected that the differences in the lateral development between

photon and hadron initiated showers is also reflected in this variable. In Figure 5.7 the

distribution of the TimeRMS is shown for γ-ray point sources, diffuse γ-ray emission

and diffuse protons.

TimeRMS [ns]0 1 2 3 4 5

0

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diffuse p

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0.005γ diffuse

diffuse p

Figure 5.7: Normalized distributions of the TimeRMS. A γ-ray point source is super-imposed on a diffuse proton background (left). The diffuse proton back-ground is compared with diffuse γ-rays (right).

One can see that γ-rays at 0.0◦ offset have a very small time spread, whereas the

distribution of the TimeRMS for diffuse protons has enlarged tails. For diffuse γ-

ray emission no evident differences between the different primaries can be seen. This

encourages the assumption that a cut on the TimeRMS results in an improvement on

gamma-hadron separation for point sources rather than for diffuse emission and will

be investigated in the following.

To measure the separation power of the TimeRMS, the signal (γ-ray) and back-

ground (proton) efficiencies are calculated in dependence of the TimeRMS cut after

the pre-selection cuts have been applied. Different values for the TimeRMS cut in the

range of [0, x] are used, where x is running from 0 to 10 ns. The calculated efficiencies

can then be plotted as a function of the TimeRMS, as shown for a γ-ray point source

on the left side of Figure 5.8. It can be seen that signal and background events show


a similar behavior. For very small cut values (TimeRMS < 0.7 ns) the efficiencies

for signal and background are less than 50 %, which means that most of the events

do not survive the cut, while for larger cuts (TimeRMS > 2 ns) more than 90 % of

background and signal events pass the cut. For cut values in between one can see that

the efficiency curve for the γ-rays increases steaper than the one for protons. This

means, when applying a cut in this interval, more γ-ray than proton events are kept.

For very large cut values (TimeRMS > 5 ns) the efficiencies are nearly 100 % which

means, that nearly all events lie in the range of [0,5] and a cut on the TimeRMS is

inefficient for large TimeRMS.

With the signal and background efficiencies the quality factor Q is calculated as a

function of the cut on the TimeRMS, see right panel of Figure 5.8. One can see that for

small cut values the quality factor increases from zero up to a maximum with increasing

TimeRMS and than decreases slightly. For large cut values, where the efficiencies are

nearly 100 %, Q becomes equal to the quality factor after the pre-selection cuts of the

analysis, as expected.

TimeRMS [ns]0 1 2 3 4 5

effic

ienc

y

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TimeRMS [ns]0 2 4 6 8 10

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Figure 5.8: Signal and background efficiencies (left) and the resulting quality factorQ (right) as a function of the TimeRMS cut for γ-ray point sources afterpre-selection cuts.

The maximum of the quality factor for the γ-ray point source at 0.0◦ offset is at

a TimeRMS of 1.21 ns. Applying a cut at this value, one keeps 96.9 ± 0.21 % of theγ-ray events while rejecting 17.9 ± 1.5 % of the hadronic background. This leads to a

5.3 TimeRMS 45

quality factor of Q = 2.65± 0.02, which is an improvement of 6.9± 1.0 % compared tothe quality factor obtained with gamma-hadron separation using the pre-selection cuts

alone.

For diffuse γ-ray emission no evident improvement in gamma-hadron separation af-

ter the pre-selection cuts is expected due to the similar behavior of the distribution.

Applying the same analysis to the diffuse γ-ray emission one can see in Figure 5.9, that

the cut efficiencies for signal and background do not differ from each other. This is also

reflected in the quality factor as a function of the TimeRMS. For small TimeRMS val-

ues (TimeRMS< 1.5 ns) the quality factor Q steeply increases and than goes slightly

to the maximum which is equal to the quality factor obtained with gamma-hadron sep-

aration using the pre-selection cuts alone. This means, that for a diffuse γ-ray emission

no improvement is possible with an additional cut on the TimeRMS. These results are

summarized in Table 5.4.

TimeRMS [ns]0 1 2 3 4 5

effic

ienc

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gamma proton

TimeRMS [ns]0 2 4 6 8 10

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0

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1.

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