Studies of the influence of the geomagnetic field on the sensitivity of

gamma-ray observations

Maria Krause1

1Brandenburg University of Technology, 03046 Cottbus, Germany∗

(Dated: 3rd September 2010)

Cherenkov Telescope Array (CTA) is a ground-based observatory; high energy gamma

radiation is detected by the measurement of particle showers in the atmosphere. The site of

the instrument has an immediate influence on the sensitivity (weather, height above sea level,

etc.). Several possible sites for CTA are being considered at the moment including Namibia,

Argentina, Canary islands and Mexico. The geomagnetic field affects the development of

showers and distorts the images of the air shower in the telescope. The aim of this work

is to quantify the influence of the strength and the direction of the geomagnetic field at

the different possible locations on the sensitivity of CTA using Monte Carlo simulations of

particle showers.

I. INTRODUCTION

A. What is gamma-ray astronomy?

Gamma-ray astronomy is the study of photons with an energy from few MeV to > 108 TeV

and γ-astronomy above a few 1010 eV is called very high energy (VHE) γ-astronomy. The

main goal of gamma-ray astronomy is to explore the production and propagation of VHE

γ-rays in the universe. Typical sources are supernovae remnants, pulsars, active galactic

nuclei or binary systems such as microquasars. The research of very high energy gamma-ray

astronomy started about 20 years ago with the first observation of the Crab Nebula by the

Whipple observatory. In contrast to charged cosmic rays, only neutral particles can point

back to the location of their origin because charged particles will be deflected by the magnetic

field of the universe. Therefore, up to an energy of 1019 eV most information on the initial

direction is lost [1].

∗Electronic address: maria krause@gmx.net

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B. Cherenkov radiation

Cherenkov radiation is emitted when charged particles pass through matter with a velocity

v which is higher than the velocity of light in the dielectric medium, vc >

1n where c is the

velocity of light and n is the refractive index. The radiation occurs over a broad band. The

Cherenkov radiation is emitted at an angle (Cherenkov angle) which depends on the refractive

index and is radiated in the forward direction. During the flight of the particle through the

dielectric medium, it interacts electrically with the molecules in its vicinity. Hence, it disturbs

the neutrality of the molecules and because of the induced polarization, the molecules turns

on and off as the particle passes. That is the reason why the molecules radiate. If the particle

moves slow, the disarrangement is symmetrical around and along the particle trajectory.

Therefore there is no residual electric field and no measurable radiation [1]. The Cherenkov

equation shows the relation between the refractive index n and the angle Θ which can be

calculated with the relative values of v and n.

cosΘ =c

nv=

1

nβ(1)

Near to the threshold velocity cosΘ = 1 and therefore v/c = 1/n, there is a maximum

Cherenkov angle where v = c. The radiation will only occur if n > 1. This is the optical

region of the spectrum of almost all materials.

An energetic primary particle which develops in the atmosphere can initiate Extensive Air

Showers (EAS) (figure 1). These are cascades with an electromagnetic, a muonic, a hadronic

and a neutrino component. We want to consider the electromagnetic cascades produced by

a photon. The secondary particles in the EAS with a higher speed than the one of the light

in that specific medium (in our case: air) emit Cherenkov light which can detect by using a

very large Cherenkov telescope array. Hence, we get information about the original cosmic

ray. This method is called Imaging Atmospheric Cherenkov Technique (IACT).

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Figure 1: Production of Extensive Air Showers [2]

C. Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) will be a ground-based high energy gamma-ray

observatory which will study astrophysical sources at an energy range from 10 GeV to 100

TeV. Allowing a deeper investigation of galactic sources, the central part of the milky way and

the observation of extragalactic objects like pulsars and microquasars. Current instruments

of gamma-ray astronomy are Whipple, CANGOROO, H.E.S.S., MAGIC, MILAGRO and

VERITAS [3]. One of the design goals of CTA is to be 10 times more sensitive than the

current instruments.

The observatory will consist of 50 to 100 telescopes with diameters of 23 m, 12 m and about

7 m, with two sites one in both the northern and southern hemisphere. The aims of CTA are

to find the origin of cosmic rays and dark matter as well as to understand the physics beyond

the standard model. With the help of CTA, it will be possible to have a greater sensitivity

on gamma-ray sources, improved angular resolution with better observations and flexible and

robotic operations.

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Figure 2: Artist’s model of the Cherenkov Telescope Array [3]

At the moment the instrument is in the planning phase.”First light“ will probably be in

2014.

II. GEOMAGNETIC FIELD

Finding a good site for the Cherenkov Telescope Array is currently being researched. There

are a lot of facts which are very important to find the best location, including the geomagnetic

field. The geomagnetic field is different in various places of the Earth. The magnetic field

changes with both time and location and modifies the way it is varying. It is irregular and it

has to measured regularly in different places which can be done with satellites [4]. Figure 3

shows the intensity of the geomagnetic field on the world including the candidate sites. The

table below shows the possible locations for CTA with their latitudes, longitudes, elevations,

declinations, horizontal and vertical intensities.

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Figure 3: The Total Intensity - Main Field (in nT) measured by the National Geophysical DataCenter [4].

Site Latitude Longitude Elevation Declination Horizontal VerticalIntensity Intensity

[m] [µT] [µT]

ALMA 22◦59’56”S 67◦45’39”W 5000 - 4.7◦ 21.697 -7.991

H.E.S.S. 23◦16’18”S 16◦30’00”E 1800 -13.62◦ 12.190 -25.684

Salar de Pocitos 24◦26’40”S 67◦06’10”W 3650 -4.72◦ 21.266 8.860

(Argentina)

El Leoncito 31◦44’11”S 69◦16’ 9”W 2600 0.7◦ 20.179 -12.529

(Argentina)

La Silla 29◦15’00”S 70◦43’48”W 2400 0.7◦ 20.815 -11,336

(Chile)

Beaufort West 32◦28’48”S 22◦14’60”E 1750 -24.07◦ 11.023 -24.0650

(South Africa)

La Palma 28◦45’42”N 17◦53’26”E 2230 2.3◦ 31.635 26.749

VERITAS 31◦41’18”N 110◦53’00”W 1270 10.42◦ 24.915 40.299

San Pedro Martir 31◦02’00”N 115◦25’00”W 2800 11.30◦ 25.385 38.596

(Mexico)

Sierra Negra 18◦59’00”N 97◦18’00”W 4000 4.45◦ 27.768 29.868

(Mexico)

Hanle 32◦ 45’36”N 78◦57’36”E 4515 1.55◦ 31.853 38.604

(India)

Oman A 23◦6’00”N 57◦31’5”E 2000 1.08◦ 35.029 24.869

Table I: Site candidates for CTA

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The Figure 4 shows the absolute value of the geomagnetic field component∣∣∣ ~B⊥∣∣∣ normal to

the direction of the Extensive Air Showers versus azimuth and zenith angle for the H.E.S.S.

observatory and the site of San Pedro Martir. An azimuth angle of 0◦ means that the particle

comes from the north and flights into the south direction, 180◦ means the opposite [5]. Figure

4 uses the measured total intensity of the geomagnetic field which was obtained from the epoch

2005 International Geomagnetic Reference Field (IGRF) model of the National Geographic

Data Center [4]. We can see a big difference between the locations because the deviation

of particles depends on the Lorentz force ~F = q · ~v × ~B. This happens because San Pedro

Martir is in Mexico on the northern hemisphere and H.E.S.S. (The High Energy Stereoscopic

System) is in Namibia on the southern hemisphere. The total field is the intensity of the

entire magnetic field at the given location and is calculated by the horizontal and vertical

component.

For Mexico, the minimum influence of the geomagnetic field is expected to occur for EAS

which develop in the direction of the magnetic north at a zenith angle ZE = (90◦ − I) =

(90◦− 56, 07◦) = 33, 93◦ and an azimuth angle AZ = 0◦. At this point the angle between the

shower axis and the Earth’s magnetic field becomes smallest. The inclination I is the angle

between the magnetic field vector and the horizontal plane which is tangent to the Earth’s

surface at that point. Mexico has an inclination of 56, 07◦[4], thus the maximum influence is

expected for EAS developing perpendicular to the direction of the lines of the geomagnetic

field, for Mexico at ZE = 56, 07◦ and AZ = 180◦. For Namibia, the minimum influence of

the Earth’s magnetic field should occur at a zenith angle ZE = 25, 38◦ and AZ = 180◦, and

the maximum influence should be at ZE = 64, 22◦ and AZ = 0◦ which could not be seen on

the diagram.

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]°Azimuth Phi [0 50 100 150 200 250 300 350

]°Z

enith

The

ta [

0

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T]µ30'00''E- Magnetic Field [°16'18''S, 16°H.E.S.S. 23

]°Azimuth Phi [0 50 100 150 200 250 300 350

]°Z

enith

The

ta [

0

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T]µ25'00''W - Magnetic Field [°02'00''N, 115°San Pedro Martir (Mexiko) 31

Figure 4: The absolute value of the total field of the strength of the geomagnetic field to thedirection of the EAS versus azimuth angle (AZ) and zenith angle (ZE) for the H.E.S.S. observatoryin Namibia and the site candidate for CTA San Pedro Martir

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III. INFLUENCE OF THE GEOMAGNETIC FIELD ON THE MEASUREMENTS

The Earth’s magnetic field deflects the electrons and positrons in the EAS. Therefore

the observation of these particles depends on the longitude, latitude and azimuth angle. If

we want to find the best site for the Cherenkov Telescope Array, we need to consider the

sensitivity of the telescopes.

A. Lateral distribution and photon position of Cherenkov photons

To get an overview over the sensitivity of the sites, we simulated the lateral distribution

of the particle showers for each of the 12 sites and the special case B = 0. The lateral

distribution which is influenced by the Cherenkov angle and Coulomb scattering angle shows

the density of Cherenkov photons on the ground as a function of the impact parameters.

We simulated for various azimuth e.g. 0◦, 90◦, 180◦ and 270◦ and zenith angles at 20◦ and

40◦. The energy of the primary photon is 100 GeV. Because we want to measure only the

geomagnetic effects on the showers, the altitude of all sites is 2000 m. If we would simulate

on the specific heights, we would measure both the shower development and the geomagnetic

effects. Figure 5 shows the position of Cherenkov photons on the ground of the H.E.S.S.

and San Pedro Martir site for a zenith angle of 20◦ and 40◦. As we can see there are big

differences in the particle density between these two plots. All in all we have an amount of

Cherenkov photons of approximately 3 · 109 for a zenith angle of 20◦ and about 2 · 109 at 40◦.

Consequently, we have a particle density of nearly 5 to 6 Cherenkov photons per m2 at 20◦

and 2 photons per m2 for 40◦. For this result, just the Cherenkov photons in the light pool

of 120 m on the ground are important. For a typical gamma-ray shower, the radius of the

Cherenkov ring is approximately 120 m to 140 m.

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distance to shower core [m]10 210

]-2

par

ticl

e d

ensi

ty [

m

2

10 °=20θH.E.S.S., °=0ϕ°=90ϕ

°=180ϕ°=270ϕ

distance to shower core [m]10 210

]-2

par

ticl

e d

ensi

ty [

m

-110×9

1

2

°=40θH.E.S.S., °=0ϕ°=90ϕ

°=180ϕ°=270ϕ

distance to shower core [m]10 210

]-2

par

ticl

e d

ensi

ty [

m

2

10 °=20θSan Pedro Martir, °=0ϕ°=90ϕ

°=180ϕ°=270ϕ

distance to shower core [m]10 210

]-2

par

ticl

e d

ensi

ty [

m

-110×9

1

2

°=40θSan Pedro Martir, °=0ϕ°=90ϕ

°=180ϕ°=270ϕ

Figure 5: Lateral distribution of 250-700 nm Cherenkov light in simulations of 100 GeV gamma-rays for the site of H.E.S.S. and San Pedro Martir at 2000 m altitude. On the left-hand side areshown the diagrams for a zenith angle of 20◦ and on the right-hand side are the plots for 40◦.

Looking at the zenith angle, we can see that the effect of the geomagnetic field is very

small because the shift is about 8% for a zenith angle of 20◦ and about 12% for a zenith of

40◦. The particle density of Cherenkov photons on the ground of the two sites at the same

height has not a big difference. On the other hand the difference between the two locations

is much larger, if we would measure the particle density on the ground at different heights

such as 1800 m for H.E.S.S. and 3000 m for San Pedro Martir.

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x [m]-500 -400 -300 -200 -100 0 100 200 300 400 500

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]

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°Cherenkov photon positions 270

Figure 6: Cherenkov photon positions on the ground for the H.E.S.S. site for θ = 20◦.

x [m]-500 -400 -300 -200 -100 0 100 200 300 400 500

y [m

]

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°Cherenkov photon positions 270

Figure 7: Cherenkov photon positions on the ground for the H.E.S.S. site for θ = 40◦.

Figure 6 and 7 show the density of Cherenkov photons on the ground. There are consi-

derably less photons on the ground, if we observe electromagnetic showers at a zenith angle

of 40◦ and ellipses are more pronounced. The path length through the atmosphere is larger

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for bigger zenith angles, therefore more Cherenkov photons are scattered in the atmosphere.

B. Finding the energy threshold

The first experiment which had great successes was the Whipple telescope. It achieved

an energy threshold of approximately 350 GeV. The current generation of IACT has the aim

lowering the energy threshold to below 100 GeV. All new observatories such as H.E.S.S.,

VERITAS and CANGOROO-III are based on a stereoscopic approach or plan to adopt

stereoscopy (MAGIC). Therefore it is possible to image the electromagnetic showers si-

multaneously as there is more than one telescope for each observatory. An observatory with

only one telescope is not very precise because it is impossible to filter out the Cherenkov

photons from the background events such as muons or hadrons. It is important that the

triggering of Cherenkov telescopes uses very short time duration of a few nanoseconds of the

Cherenkov light signal from the EAS. Hence, the measurements are more precise and we can

get better results of the shower parameters, energy and the direction of the origin of cosmic

ray [6].

We simulated the energy threshold for an array of nine telescopes with a diameter of 23 m,

separated by 80 m. Because of the nine telescopes the rate of background events reduces

significantly during the short time window. As only events which are triggered in at least two

telescopes will be considered for the study. Figure 8 shows the measurements of the energy

spectra of the detected showers for zenith angles of 20◦ and 40◦. We can see that the energy

threshold which is the maximum of the curves of energy spectra is about 20 GeV (ZE=20◦)

for both sites and about 38 GeV (ZE=40◦) for H.E.S.S. and about 31 GeV (ZE=40◦) for San

Pedro Martir. The energy threshold for 40◦ has to be smaller as the photons travel further

through the atmosphere.

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Energy/TeV10

log-2.5 -2 -1.5 -1 -0.5

dN/d

E

-210

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310 , h=1800m°=20θH.E.S.S., Simulated energy spectrum

°=0ϕ°=90ϕ

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°=20θEnergy of primary particle

°=0ϕ°=90ϕ

°=180ϕ°=270ϕ

San Pedro Martir

Energy/TeV10

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dN/d

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-310

-210

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310 , h=3000m°=40θSan Pedro Martir, Simulated energy spectrum

°=0ϕ°=90ϕ

°=180ϕ°=270ϕ

Figure 8: Energy spectra of the detected showers for H.E.S.S. (1800 m) and San Pedro Martir(3000 m). The energy threshold is the maximum of each curve.

IV. CONCLUSION & OUTLOOK

The intensity of the geomagnetic field on the surface of the Earth fluctuates from about

20µT to about 70µT [4]. It is expected, that it is important, of benefit, to select a location

with a low absolute value of the Earth’s magnetic field, because the influence of this field has

its minimum their. But during our simulations we learnt that the geomagnetic effects has

not a big influence on the density of Cherenkov photons on the ground; but the number of

triggered particles are significant different.

The site altitude is also important because the number of photons on the ground depends on

the density the shower travels through the atmosphere. CTA should not be built at an height

above 4000 m as the amount of atmosphere above the detector decreases exponentially.

Acknowledgment

The author would like to thank my supervisor Gernot Maier for his help and willingness

to answer all my questions during my project. A big thanks goes to Stefan Schlenstedt for

allowing me to work in the astro-particle group. I want to thank Heike Prokoph, Gareth

13

Hughes and Christian Skole for their constructive critics, inspiring discussions and their

assistance to develop the source code.

[1] T. Weekes, Very High Energy Gamma-Ray Astronomy, Bristol, 2003.

[2] DESY Zeuthen - CTA group

http://www.desy.de/cta

[3] Cherenkov Telescope Array;

http://www.cta-observatory.org/

[4] National Geographic Data Center (NGDC);

http://www.ngdc.noaa.gov/geomag/

[5] S. C. Commichau et al., Monte Carlo Studies of Geomagnetic Field Effects on the Imaging Air

Cherenkov Technique for the MAGIC Telescope Site, Nucl. Inst. and Meth. A 595 (2008) 572-586.

[6] S. Funk et al., The Trigger System of the H.E.S.S. Telescope Array, Astroparticle Physics 22

(2004), 285-296.