• No results found

Gamma-ray astronomy

N/A
N/A
Protected

Academic year: 2021

Share "Gamma-ray astronomy"

Copied!
58
0
0

Loading.... (view fulltext now)

Full text

(1)

Pointing calibration for Medium Size Telescopes in the Cherenkov Telescope Array

Birger Vaksdal vaksdal@kth.se Master Thesis

Supervisor (Humboldt): Dr. Ullrich Schwanke Supervisor (KTH): Prof. Felix Ryde Examiner (KTH): Prof. Bengt Lund-Jensen

TRITA-FYS 2016:71 ISSN 0280-316X

ISRN KTH/FYS/–16:71-SE Stockholm, Sweden

November, 2016

(2)

Abstract

The Cherenkov Telescope Array is a new observatory under construction by a large international collaboration. It will be built at two locations, La Palma in Spain and Paranal in Chile. The observatory will be constructed of sev- eral telescopes of three different sizes: Small, Medium and Large. As a part of the development, a prototype for the Medium Size Telescopes has been constructed in the Adlershof Science Park in Berlin, Germany.

In this thesis, a model for pointing calibration of this telescope prototype has been developed and improved. An initial approach was to use a four pa- rameter model, which during the work has been extended to include a fifth parameter. This parameter takes into account effects from different struc- tural loads on the telescope depending on the elevation, and decreases the error in the pointing with slightly above 40%.

(3)

Sammanfattning

Cherenkov Telescope Array ¨ar ett nytt observatorium som ¨ar under utveck- ling av en stor internationell forskargrupp. Det kommer byggas p˚a tv˚a platser, La Palma i Spanien och Paranal i Chile. Observatoriet kommer best˚a av flera teleskop i tre olika storlekar: sm˚a, medelstora och stora. Som ett led i utvecklingen har en prototyp f¨or de medelstora teleskopen konstruer- ats i Adlershof Science Park i utkanten av Berlin, Tyskland.

I detta arbete har en modell f¨or riktningskalibrering av teleskopprototypen utvecklats och f¨orb¨attrats. Den ursprungliga inriktningen var att anv¨anda en modell med fyra parametrar, denna har under arbetets g˚ang ut¨okats till att inkludera en femte parameter. Denna parameter tar h¨ansyn till effekter fr˚an varierande belastning p˚a strukturen beroende p˚a vilken h¨ojd teleskopet riktas mot, och minskar riktningsfelet med strax ¨over 40%.

(4)

Contents

1 Introduction 3

1.1 Outline . . . . 3

1.2 Author’s contribution . . . . 4

2 Gamma-ray astronomy 5 2.1 In general . . . . 5

2.1.1 Extraterrestrial radiation of different types . . . . 5

2.1.2 Gamma-ray sources . . . . 6

2.1.3 Extensive air showers . . . . 8

2.1.4 Imaging Atmospheric Cherenkov Telescopes (IACT) . . 9

2.2 Current telescope arrays for gamma-ray astronomy . . . . 10

2.2.1 H.E.S.S. . . . 10

2.2.2 MAGIC . . . . 10

2.2.3 VERITAS . . . . 10

3 Cherenkov Telescope Array (CTA) 12 3.1 Telescope types . . . . 12

3.1.1 Large Size Telescope (LST) . . . . 12

3.1.2 Medium Size Telescope (MST) . . . . 12

3.1.3 Small Size Telescope (SST) . . . . 13

3.2 Locations . . . . 13

3.2.1 Southern site, Paranal . . . . 13

3.2.2 Northern site, La Palma . . . . 14

3.3 Development . . . . 14

3.3.1 Prototype for the Medium Size Telescope . . . . 14

4 Pointing model 16 4.1 Background . . . . 16

(5)

4.2 Creating a pointing model . . . . 18

4.2.1 Rotations . . . . 19

4.2.2 Difference in elevation, ∆el . . . . 21

4.2.3 Difference in azimuth angle, ∆az . . . . 23

4.2.4 Combining elevation and azimuth . . . . 25

5 Pointing calibration 27 5.1 Measurements . . . . 27

5.2 Four-parameter model . . . . 28

5.2.1 Analysis using Root . . . . 28

5.3 Five-parameter model . . . . 29

6 Results 30 6.1 Initial situation . . . . 31

6.2 Four-parameter model . . . . 32

6.3 Five-parameter model . . . . 33

6.4 Parameter values . . . . 35

7 Conclusions 36 7.1 Conclusions of the thesis work . . . . 36

7.2 Future work . . . . 38

List of figures 39

Bibliography 41

A Root code for TMinuit minimization 44

(6)

Chapter 1 Introduction

The Cherenkov Telescope Array (CTA) is a new telescope array being devel- oped by a large group of institutes worldwide. It will be using a technology called Imaging Atmospheric Cherenkov Telescopes (IACT), to get new results in gamma-ray astronomy.

CTA will consist of several types of telescopes: Large Size Telescope (LST) with a diameter of 23 meters, Medium Size Telescope (MST) with a diameter of 12 meters and Small Size Telescope (SST) with a diameter of 6 meters. These will be built at two locations: at La Palma, Spain, and at Paranal, Chile. Both these locations are established telescope sites with the needed infrastructure already existing.

For observations with the telescopes there is a need to have a good under- standing about where the telescope is pointing, and several models are being tested for this by multiple research groups. One model being developed at Humboldt Universit¨at zu Berlin for the Medium Size Telescopes is described here, being the main part of the thesis work.

1.1 Outline

The thesis will begin with an introduction to gamma ray astronomy in chap- ter 2. This is followed by a presentation of the Cherenkov Telescope Array, its Medium Size Telescope and the prototype for this in chapter 3. The pointing model for the prototype is explained in chapter 4, with the pointing calibration performed described in chapter 5. The results of this is presented in chapter 6, and the thesis is finally concluded in chapter 7.

(7)

1.2 Author’s contribution

Creating a model for the pointing of the MST prototype. The work per- formed included analysis, calculations, programming in Root and evaluation of results.

The work for this thesis has been performed at Humboldt Universit¨at zu Berlin, at Campus Adlershof in Berlin, Germany.

The work at Humboldt also included technical work with the MST pro- totype. The main part of this has been the installation of about 30 new mirrors during March and April 2016, to continue the development of the prototype.

(8)

Chapter 2

Gamma-ray astronomy

2.1 In general

2.1.1 Extraterrestrial radiation of different types

The study of gamma rays traces its origins to the discovery of cosmic rays by Victor Hess in 1912. Using a balloon to reach higher altitudes, he mea- sured the radiation at different altitudes and found that it increased with increasing altitude [1]. From this, he concluded that the increased radiation has its origins outside of the atmosphere. This discovery was rewarded with the Nobel Prize in Physics in 1936 [2].

The extraterrestrial radiation is composed of several parts, all contribut- ing to our understanding of the Universe. In some cases, this gives an oppor- tunity to get a clearer picture of an astronomical object by combining data from several types of detectors. In other cases, new objects are discovered when parts of the Universe regarded as ”dark” by previous detectors are monitored by another type of detector.

(9)

Charged particles

These are mainly protons, but heavier nuclei and electrons are also detected.

There are several telescopes studying this, e.g. Pierre Auger Observatory in Argentina [3].

Neutrinos

Neutrinos have no charge, a very low mass and interact only through weal interaction. This means that they travel far without being disturbed, but on the other hand are hard to detect since they rarely interact with the detectors. The largest current neutrino telescope is IceCube, with a volume of approximately 1 km3 located in the Antarctic ice at the South Pole [4].

Photons

Electromagnetic radiation has vastly different properties at different energies, ranging from low energy radio waves to high energy gamma rays. For the Cherenkov Telescope Array described in this thesis, the main focus is gamma rays in the energy range from 100 GeV to 100 TeV [5].

2.1.2 Gamma-ray sources

Very high energy (VHE) gamma rays (in the energy span around GeV to TeV), could not have been produced by thermal emission from hot stars and other objects. The energy of thermal radiation depends on the temperature of the emitting body, and except for Big Bang there has been nothing in the known Universe hot enough to emit gamma rays of such high energies.

Several types of sources for gamma rays have been discovered, with a great range in both size and distance to the Earth (see below). Of these, more than 130 emit gamma rays exceeding 1 TeV [6].

Pulsar wind nebulae

A pulsar is a rapidly rotating neutron star, that is emitting radiation at regular, short intervals [7]. The pulsar has a strong magnetic field, which can accelerate charged particles around it to relativistic speeds.

Some pulsars are surrounded by a cloud-like structure of gas called neb- ula, often being large in size but with low density. When the charged particles

(10)

accelerated by the pulsar interact with the nebula, the particles are deceler- ated and large amounts of radiation is emitted as photons of various energies [8].

One example of this is the Crab Nebula, a remnant of a supernova that was recorded in 1054. The Crab Nebula has been observed in many energy ranges throughout the years and was discovered in gamma rays in 1989, using the 10 m telescope of the Whipple Observatory [9].

Active galactic nuclei (AGN)

Active galactic nuclei are galaxies with supermassive black holes in the centre.

These have a very high luminosity in some (or all) parts of the electromag- netic spectrum, ranging all the way from radio waves to gamma rays [10].

One motivation for studying AGNs is to get a better understanding of the processes that leads to the high energy output, e.g. accreation of matter onto the supermassive black hole.

A large part of the radiation from an AGN may be emitted in two fairly narrow cones, called jets, directed in opposite directions. There are several types of jets depending on the type of host galaxy, and there will be a need for much more observations on various wavelengths to get a clearer picture of the mechanisms involved in the creation of these.

Gamma-ray bursts (GRB)

Gamma-ray bursts are some of the most powerful events known to occur in the Universe, and by far the most luminous sources of electromagnetic radiation. There are several suggestions for the origins of GRBs. Some ideas explain it as one of the results of a large collapsing star [11], while other suggest merging of two neutron stars [12].

GRBs can occur in any direction in the sky, and they also usually have very short duration - from less than a second to a couple of minutes. This means that telescopes used to register gamma-ray bursts are required to have the ability to reach a new target in the sky quickly, before the event is over.

(11)

2.1.3 Extensive air showers

When a very high energy gamma ray hits the atmosphere, it will interact with molecules in the atmosphere and create a cascade of charged particles.

The start for this cascade is pair-production, where a newly created electron- positron pair receives the energy of the gamma ray.

The initial electron-positron pair has a very high energy and will emit photons through Bremsstrahlung while travelling through the atmosphere.

These photons will in turn create a new pair which will emit Bremsstrahlung and so on (see Figure 2.1, left). The particles in the cascade that have high enough energy, will travel faster through the atmosphere than the speed of light in air. This will generate flashes of Cherenkov radiation, which is emit- ted in the visible (mostly blue) and ultraviolet part of the electromagnetic spectrum.

Charged particles hitting the atmosphere will also create air showers (see Figure 2.1, right). Photons created in these showers will behave similar to gamma rays considering pair-production and the following effects, but the Cherenkov radiation from these showers will have different appearance when detected at ground level (see section 2.1.4).

Figure 2.1: Air shower of gamma-ray (left) and hadronic (right) origin. Image credit: [13]

(12)

2.1.4 Imaging Atmospheric Cherenkov Telescopes (IACT)

Imaging Atmospheric Cherenkov Telescopes work by collecting the Cherenkov light from air showers. The light from a Cherenkov flash is reflected by the mirror of a telescope to a camera, consisting of an array of photomultiplier tubes (PMTs), which records the image of the air shower. An IACT is often constructed as an array of several telescopes placed at some distance from each other, covering a much larger area on the ground than an individual telescope would be able to do.

The Earth is receiving large amounts of charged hadronic particles and, as mentioned in section 2.1.3, these are also creating air showers and the associated Cherenkov light. The main part of the Cherenkov light arriving at the telescopes is actually of hadronic origin, but the characteristics differ between these and showers of photonic origin making it possible to sort out the interesting events. The electromagnetic shower is detected as an elliptical cone, while the hadronic shower has a more irregular shape (see Figure 2.2).

Figure 2.2: Detection of Cherenkov light from gamma-ray (left) and hadronic origin (right). Image credit: [14]

(13)

2.2 Current telescope arrays for gamma-ray astronomy

There are several telescope arrays already in operation for detecting very high energy (VHE) gamma rays. Some of the more important are presented here.

2.2.1 H.E.S.S.

High Energy Stereoscopic System (H.E.S.S.), located in Khomas Highlands, Namibia. Five telescopes, four with a diameter of 12 meters and one larger with a size corresponding to a diameter of 28 meters. The four smaller telescopes went operational in 2003, with the fifth larger telescope running since 2012 [15].

In 2005 the first 14 sources discovered by H.E.S.S. emitting gamma rays above 1 TeV were presented, doubling the total amount of such sources [6].

Currently there have been 79 sources above 1 TeV discovered by H.E.S.S., more than half of the total confirmed TeV sources.

2.2.2 MAGIC

Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescope, located at La Palma, Spain. Two telescopes, both with a diameter of 17 meters.

MAGIC started operations with one telescope in 2004, with the second added in 2009 [16].

One of the goals with MAGIC is to cover lower gamma-ray energies than other ground-based gamma-ray telescopes. The energy threshold for MAGIC is estimated to be around 50 GeV [17], which creates an overlap with mea- surements from satellite-based instruments. In the other end of the spectrum, MAGIC also has great performance in the TeV region and has the second largest contribution of confirmed detection of TeV sources [6].

2.2.3 VERITAS

Very Energetic Radiation Imaging Telescope Array System (VERITAS), lo- cated in Arizona, USA. Four telescopes, all with a diameter of 12 meters.

VERITAS started operations with one telescope in 2004, with three more

(14)

The VERITAS telescopes are an improved version of the Whipple tele- scope that made the first gamma ray observation of the Crab Nebula, located at the same observatory site [19]. Initially there were plans to build seven telescopes, but only four were constructed.

One of the focus areas is the study of Active Galactic Nuclei (AGN), and VERITAS has built up a catalog of more than 20 detected AGN of which 10 are in the TeV region [20].

(15)

Chapter 3

Cherenkov Telescope Array (CTA)

The Cherenkov Telescope Array (CTA) is the next step for VHE gamma-ray astronomy. It will be constructed as a large number of telescopes of three sizes, located at two different telescope sites [5].

3.1 Telescope types

3.1.1 Large Size Telescope (LST)

An LST will have a diameter of 23 meter. A small number will be built, three or four at each of the two telescope sites.

These telescopes will be needed in the lower part of the energy range covered by CTA, up to around 100 GeV. A lower energy of the initial gamma ray gives a smaller air shower (see subsection 2.1.3). This means that a single larger mirror is needed to capture the air shower, it will be too small to be registered by two telescopes placed a certain distance from each other but too large to be correctly registered by one smaller telescope.

3.1.2 Medium Size Telescope (MST)

An MST will have a diameter of 12 meter. Several will be built, around 15 at the northern site and around 25 at the southern site.

(16)

These telescopes will perform work in the main energy range of CTA, around 100 GeV to 10 TeV. Here it will be a trade-off between the size of the individual telescopes to cover as much area as possible for each individual telescope location, and having a larger number of telescopes to cover a larger area at the telescope site.

3.1.3 Small Size Telescope (SST)

An SST will have a diameter of 6 meter. At the southern site, there will be a larger number of these, possibly up to 50 (while no SSTs will be built at the northern site).

These telescopes will mainly contribute to the CTA results for higher energies, above 10 TeV. Here the main objective is to cover a large area on the ground to correctly register the air showers from gamma rays with these high energies. The size of the individual telescopes is not considered as important in this case, so to reduce the cost these are of a much smaller size.

3.2 Locations

The telescopes for CTA will be built on two locations, one in the southern hemisphere and one in the northern hemisphere. Both locations are already established as centres for astronomy, with several telescopes and the support- ing infrastructure needed.

3.2.1 Southern site, Paranal

This telescope site will be located in the same region as the existing telescopes of the European South Observatory at Paranal, Chile [21]. This will be the larger of the two sites, with large, medium and small telescopes. One of the reasons for this is that the location in the southern hemisphere gives better opportunity to perform direct observations of the Galactic centre. Several layouts have been suggested for this site, generally with three or four large telescopes in a central location. Around this up to 25 medium size telescopes will be located either in circles with even spacing between the telescopes, or as several smaller clusters of 2-4 telescopes each. The same principles will be used for the small telescopes, but there will be up to 50 of these.

(17)

3.2.2 Northern site, La Palma

This telescope site will be located at the Roque de los Muchachos Observatory at La Palma, Spain [22]. This observatory consists of 12 telescopes run by different institutes and collaborations from several countries. According to current plans, the MAGIC telescopes (see section 2.2) will be shut down to be replaced with this part of CTA. The reason for this is both economy (they receive funding from the same sources) and location (CTA will be built in the same part of the observatory site where MAGIC is residing today).

There will be three or four large telescopes at the centre of this telescope site, with up to 15 medium size telescopes around these. At the northern site there will, according to the current plans, not be any of the small telescopes.

3.3 Development

Development for the three telescope types, as well as for many other aspects of CTA, is being carried out at many universities and institutes all over the world. In total, over 200 institutes in 32 countries are involved.

3.3.1 Prototype for the Medium Size Telescope

For the Medium Size Telescope, one stage in the development has been the construction of a prototype telescope to test some features. This includes e.g. mirror alignment and pointing. The prototype is located in the science park at Adlershof in southern Berlin, Germany, in the same area as the Humboldt-Universit¨at zu Berlin where the work for this thesis was carried out.

The prototype is a full-size prototype, however without a functional main telescope camera. The camera is under development by groups at other institutes and is therefore replaced with a dummy of the same weight, to correctly show how the structure will be affected by the camera when it is mounted (see Figure 3.1).

The prototype is constructed with a 9 meter high tower, at the top of the tower the mirror dish is mounted. The dish is 12 meters in diameter, with the camera dummy mounted in the focal plane 16 meters from the dish.

The dish prototype is designed to have 84 hexagonal mirrors, each with a diameter of 1.2 meter. After installing 30 new mirrors and removing some

(18)

old mirrors in April 2016, the prototype has 76 mirrors with some mirrors in the centre of the dish not yet installed.

Figure 3.1: MST prototype in Adlershof (Berlin, Germany), with dish, tower (red, almost covered by dish) and camera dummy (red octagonal structure).

(19)

Chapter 4

Pointing model

4.1 Background

When observing the sky, it is of great interest to make sure that the tele- scope is pointing towards the intended location on the sky as accurately as possible. For this purpose, the MST prototype has several cameras mounted for testing of different pointing concepts.

For one of these concepts, two cameras called LidCCD and SkyCCD are used, see Figure 4.1.

The LidCCD is used to track the movement of the main telescope camera, with several pointing LEDs used as reference points. This gives information about e.g. deformation due to structural loads, and where the main telescope camera is located relative to the telescope dish.

The SkyCCD is used to track the movement of the whole telescope struc- ture, to see where on the sky the telescope is pointing. The pointing model for the SkyCCD involves the difference between the actual pointing recorded through the SkyCCD and the intended pointing recorded by the drive system for the telescope (see section 4.2 ). This pointing model has been the main work for this thesis.

(20)

Figure 4.1: Two camera pointing concept. Image credit: C. van Eldik.

The SkyCCD is mounted in the 12 o’clock position, see Figure 4.2. It is pointing (roughly) parallel to the optical axis of the telescope, with small deviations that will be included in a pointing model.

(21)

Figure 4.2: The blue arrow shows position and direction of the SkyCCD.

4.2 Creating a pointing model

Here we create a model for the movement of the telescope.

First, we construct a way to represent rotations of the telescope - in the East-West direction, in the North-South direction and combined rotations.

We continue with constructing a model for small differences between the assumed and actual position of the telescope, both in elevation angle and in azimuth angle.

Calculations using this model are found in Chapter 5, while the code used for this is found in Appendix A.

(22)

4.2.1 Rotations

First, we need to find matrix representations of rotations around x-axis, y- axis and a combined rotation. Here, we will use the following definitions:

ϕx: Tilt of the (vertical) z-axis to the East (see Figure 4.3) ϕy: Tilt of the (vertical) z-axis to the South (see Figure 4.4)

East West

zenith telescope

axis ϕx

Figure 4.3: ϕx, tilt of the (vertical) z-axis to the East.

South North

zenith telescope

axis ϕy

Figure 4.4: ϕy, tilt of the (vertical) z-axis to the South.

(23)

Rotation around x-axis

x0 y0 z0

=

1 0 0

0 1 −ϕx

0 +ϕx 1

x y z

=

x y − ϕxz ϕxy + z

(4.1)

Rotation around y-axis

x0 y0 z0

=

1 0 −ϕy

0 1 0

y 0 1

x y z

=

x − ϕyz y ϕyx + z

(4.2)

Rotation around x+y-axes

x00 y00 z00

=

1 0 0

0 1 −ϕx x 0 1

1 0 −ϕy

0 1 0

y 0 1

x y z

=

1 0 0

0 1 −ϕx x 0 1

x − ϕyz y ϕyx + z

=

x − ϕyz y − ϕxyx + z)

ϕxy + ϕyxz

=

 small deviations, ϕx· ϕy ≈ 0



x − ϕyz y − ϕxz ϕxy + ϕyxz

(4.3)

Definitions

For the derivations in the next sections, we will use the following definitions:

x = sin(θ)cos(ϕ), y = sin(θ)sin(ϕ), z = cos(θ) (4.4) with θ being zenith angle and ϕ being horizontal angle (see Figure 4.5).

(24)

x

y z

telescope θ axis

ϕ

Figure 4.5: Zenith angle θ and horizontal angle ϕ.

4.2.2 Difference in elevation, ∆el

We start with defining the zenith angle from the rotation of the x+y-axes:

cos(θT el) = z00 = ϕxsin(θ)sin(ϕ) + ϕysin(θ)cos(ϕ) + cos(θ) (4.5)

We can also define the resulting angle as a deviation from the initial angle:

⇒ cos(θT el) = cos(θ + ∆θ) ≈ cos(θ) − sin(θ)∆θ (4.6)

Combining Eq. (4.5) and Eq. (4.6), we get:

⇒ cos(θ) − sin(θ)∆θ = ϕxsin(θ)sin(ϕ) + ϕysin(θ)cos(ϕ) + cos(θ) (4.7)

⇒ −∆θ = ϕxsin(ϕ) + ϕycos(ϕ) (4.8)

(25)

z/zenith

horizontal plane telescope

axis θ

el

Figure 4.6: Zenith angle θ and elevation angle el.

We have two different ways to define the altitude angle:

θ = zenith angle (from the vertical z-axis) and el = elevation angle (from the horizon), see Figure 4.6.

el = 90− θ (4.9)

sin(el) = cos(θ), cos(el) = sin(θ) (4.10)

∆θ = −∆el (from Eq. (4.9)) (4.11)

(26)

4.2.3 Difference in azimuth angle, ∆az

We start with defining the horizontal angle from the rotation of the x+y-axes:

tan(ϕT el) = y00

x00 = y − ϕxz

x − ϕyz = f (ϕx, ϕy) ≈

≈ f (0, 0) + ∂f

∂ϕx(0, 0)ϕx+ ∂f

∂ϕy(0, 0)ϕy y x z

xϕx+ y · z x2 ϕy =

= sin(θ)sin(ϕ)

sin(θ)cos(ϕ) cos(θ)

sin(θ)cos(ϕ)ϕx+sin(θ)sin(ϕ)cos(θ) sin2(θ)cos2(θ) ϕy =

= sin(ϕ)

cos(ϕ) cos(θ)

sin(θ)cos(ϕ)ϕx+ sin(ϕ)cos(θ) sin(θ)cos2(θ)ϕy =

= tan(ϕ) − cot(θ)cos(ϕ)

cos2(ϕ) · ϕx+ cot(θ)sin(ϕ)

cos2(ϕ) ϕy (4.12)

We can also define the resulting angle as a deviation from the initial angle:

tan(ϕT el) = tan(ϕ + ∆ϕ) = tan(ϕ) + ∂tan(ϕ)

∂ϕ · ∆ϕ =

= tan(ϕ) + 1

cos2(ϕ) · ∆ϕ (4.13)

Combining Eq. (4.12) and Eq. (4.13), we get:

tan(ϕ) + ∆ϕ

cos2(ϕ) = tan(ϕ) −cot(θ)cos(ϕ)

cos2(ϕ) · ϕx+cot(θ)sin(ϕ)

cos2(ϕ) ϕy (4.14)

∆ϕ

cot(θ) = −ϕxcos(ϕ) + ϕysin(ϕ) (4.15)

(27)

ϕ = 0 ϕ = 90

ϕ = 180

ϕ = 270

az = 0 az = −90

az = ±180

az = +90

Figure 4.7: Horizontal angle ϕ and azimuth angle az.

We also have two different ways to define the horizontal (azimuthal) angle, with different ranges for the angle (see Figure 4.7).

ϕ = 0, · · · , 360, az = −180, · · · , +180 (4.16) We get the following relations between ϕ and az:

sin(ϕ) = −sin(az), cos(ϕ) = +cos(az) (4.17)

∆ϕ = −∆az (4.18)

(28)

4.2.4 Combining elevation and azimuth

Here we apply the different definitions of the two types of horizontal angles and the two types of altitude angles.

We start with the elevation angle:

∆el = ϕxsin(ϕ) + ϕycos(ϕ) = −ϕxsin(az) + ϕycos(az) (4.19) We also assume that there is a constant offset for the elevation angle, between the SkyCCD and the drive system. This can have several origins, but will be taken care of by one constant in this model. For the elevation we now have:

∆el = const − ϕxsin(az) + ϕycos(az) (4.20) We continue with the azimuth angle. From the definitions above we have:

cot(θ) = cos(θ)

sin(θ) = sin(el)

cos(el) = tan(el) (4.21) Our previous expression:

∆ϕ

cot(θ) = −ϕxcos(ϕ) + ϕysin(ϕ) (4.22) becomes:

∆az

tan(el) = ϕxcos(az) + ϕysin(az) (4.23) Also for the azimuth angle we assume that there will be a constant offset between the camera and the drive system, resulting in:

∆az

tan(el) = const + ϕxcos(az) + ϕysin(az) (4.24) Our pointing model now becomes:

∆el = c1− p1sin(az) + p2cos(az) (4.25)

∆az

tan(el) = c2+ p1cos(az) + p2sin(az) (4.26)

(29)

Here, c1 is a constant offset in elevation angle between the SkyCCD and the drive system, while c2 is a constant offset in azimuth angle (see Fig- ure 4.8).

p1 is the tilt of the z-axis to the East in the East-West plane, while p2 is the tilt of the z-axis to the South in the North-South plane (see Figure 4.9).

horizon zenith

c1 SkyCCD

drive system

North

East c2

drive system

SkyCCD

Figure 4.8: The parameters c1 and c2 in the initial pointing model.

East West

zenith telescope

axis p1

South North

zenith telescope

axis p2

Figure 4.9: The parameters p1 and p2 in the initial pointing model.

(30)

Chapter 5

Pointing calibration

5.1 Measurements

Measurements with the MST prototype telescope were made in June 2015 by a team from Humboldt Universit¨at zu Berlin and Deutsches Elektronen- Synchrotron (DESY). Here, the telescope was pointed to 71 different stars, being the brightest visible stars from the Hipparcos catalogue with elevation of at least 20 degrees viewed from the prototype site (not to risk having any building or tree blocking the line of sight). For each star, two images were taken with 20 seconds of exposure per image (only one image per star is used in the current calculations).

These images were processed with the astrometric calibration software provided by Astrometry.net [23], to get the coordinates of the centre of the image. The coordinates obtained from astrometry.net are given in Right ascension (Ra) and declination (dec). These were converted to coordinates in azimuth (az) and elevation (el), to be comparable with the coordinates from the drive system. The coordinates for the drive system and for the centre of the image from each star were stored as the output from the measurement campaign, to be used for data analysis.

(31)

5.2 Four-parameter model

From Chapter 4.2, we have a model for the deviations in elevation and in azimuth:

∆el = c1 − p1 · sin(az) + p2 · cos(az) (5.1)

∆az

tan(el) = c2 + p1 · cos(az) + p2 · sin(az) (5.2)

From the measurements described in Chapter 5.1, we have the coordinates for the drive system (elD and azD) and the camera (elC and azC).

We create a ”predicted” position (el’ and az’), using

el0 = elC+ ∆el (5.3)

az0 = azC+ ∆az (5.4)

With optimal choice of parameters, this predicted position should be as close as possible to the position obtained from the drive system.

Close is here defined as minimal angular distance:

cos(ψ) = cos(el0− elD) − cos(el0) · cos(elD) · (1 − cos(az0− azD)

(5.5) where ψ is the angular distance.

5.2.1 Analysis using Root

The angular distance is minimized over all 71 data points using the analysis framework Root [24], with the package TMinuit. This gives the optimal values for the four parameters (c1, c2, p1, p2) used in this model.

See Appendix A for the Root code used for the minimization.

(32)

5.3 Five-parameter model

During the work, a trend has been noted in the data. For ∆el there is a dependence in elevation, where we have decreasing deviation with increasing elevation.

A new model was created with the el-dependence for ∆el included:

∆el = c1 − p1 · sin(az) + p2 · cos(az) + p3 · 45− el

(5.6)

∆az

tan(el) = c2 + p1 · cos(az) + p2 · sin(az) (5.7)

This model gives consistently less deviation for ∆el, see section 6.3.

(33)

Chapter 6 Results

For all calculations and plots in this chapter, the Root code found in Ap- pendix A has been used.

The model presented in section 5.2 was used initially, with the following parameters:

• c1 - constant offset in elevation.

• c2 - constant offset in azimuth.

• p1 - tilt of the vertical z-axis to the East.

• p2 - tilt of the vertical z-axis to the East.

The constant offsets c1 and c2 are assumed to be made up by two parts:

from the camera being only approximately aligned with the optical axis of the telescope, and from errors when performing the original calibration of the drive system of the telescope.

(34)

6.1 Initial situation

In Figure 6.1 we have the initial situation, before applying any model.

A constant deviation in elevation angle of slightly more than one degree can be seen, as well as approximately 0.2 degrees deviation in azimuth angle.

We also note a deviation in both angles that seem to be periodic in azimuth (upper left, upper right).

Figure 6.1: Initial situation, without model.

(35)

6.2 Four-parameter model

In Figure 6.2 we see the results after applying the first model, with four parameters.

For the deviation in elevation, there remains a linear trend depending on elevation (∆El vs El, lower left). This is taken care of in section 6.3.

Figure 6.2: Results with four-parameter model.

For the parameter values obtained using this model, see section 6.4.

(36)

6.3 Five-parameter model

Additional parameter

To account for the deviation in elevation seen in Figure 6.2, a fifth parameter has been included in the model (see section 5.3).

This parameter p3 is representing the different bending of the structure for different elevation angles. With the telescope pointing upwards, at an elevation of 90, the load is uniform for all parts of the disc. When the tele- scope is pointing horizontally, there are different loads for different parts of the telescope which will give a slight deformation, see Figure 6.3.

Figure 6.3: Bending of the structure for different elevation angles.

(37)

Applying the new model

In Figure 6.4, we see the results after including a fifth parameter to the model.

This gives a clear decrease of the deviation in elevation. The total deviation, expressed as the ”Min Chi square” value from the TMinuit optimization, decreases from 56.55 to 31.37 or with almost 45%.

For the azimuth angle (upper right, lower right) we still have larger devia- tions, and most of the remaining total deviation is due to the azimuth angle.

Dealing with this should be the focus for future work with the pointing model for the MST.

Figure 6.4: Results with five-parameter model.

For the parameter values obtained using this model, see section 6.4.

(38)

6.4 Parameter values

Four-parameter model

c1 = 1.12 ± 3.89 · 10−3 ◦ c2 = −1.73 · 10−1± 4.87 · 10−3 ◦

p1 = 1.31 · 10−1± 4.03 · 10−3 ◦ p2 = 5.43 · 10−2± 4.18 · 10−3 ◦

Five-parameter model

c1 = 1.13 ± 3.89 · 10−3 ◦ c2 = −1.73 · 10−1± 4.87 · 10−3 ◦

p1 = 1.29 · 10−1± 4.03 · 10−3 ◦ p2 = 5.63 · 10−2± 4.18 · 10−3 ◦ p3 = 1.18 · 10−3± 2.35 · 10−4 ◦

The values c1 and c2 are in line with the estimates in section 6.1, for the constant offsets in elevation and in azimuth.

p1, p2 and p3 are small enough to be within the expected range for a steel structure such as the MST, however large enough to give a measurable contribution.

(39)

Chapter 7 Conclusions

7.1 Conclusions of the thesis work

A model has been developed for the behaviour of the SkyCCD and the tele- scope prototype. Based on the the current set of measurements, the model will be used for the pointing calibration of the prototype.

The model can also be used for pointing calibration of other telescopes, using similar measurements and performing the same calculations with data from these telescopes to get new parameter values.

Model

For future work, the five-parameter model presented in section 5.3 and sec- tion 6.3 will be used.

The model gives deviation between the actual pointing for the reference camera (C) and the intended pointing from the drive system (D):

∆el = elD− elC = c1 − p1 · sin(azC) + p2 · cos(azC) + p3 · 45− elC (7.1)

∆az

tan(el) = azD− azC

tan(elC) = c2 + p1 · cos(azC) + p2 · sin(azC) (7.2) with el being elevation angle and az being azimuth angle.

(40)

Improvement with added parameter

Comparing the results obtained in section 6.2 and section 6.3, we get that including the fifth parameter decreases the pointing error with slightly above 40%. The deviations in elevation using the four-parameter model is al- most eliminated by the fifth parameter, included to account for these devia- tions. The majority of the remaining error comes from deviations in azimuth, mainly for lower telescope elevations.

This improved pointing gives better accuracy both for targeting a known source to gather more data, and to determine the exact location when dis- covering a new source to figure out its possible celestial environment.

Parameter values

The parameter values for the current setup of the telescope prototype can be found in section 6.4. For another similar telescope, a new measurement campaign will have to be performed. The output from this should be eleva- tion and azimuth coordinates from both drive system and ”correct” pointing (e.g. the camera solution used for the MST prototype). With this, the Root code available in Appendix A can be used to get the parameter values for the new telescope.

(41)

7.2 Future work

Improved model

There is still more work needed to improve the model for the SkyCCD. An important part will be to decrease the deviations in azimuth, with most of these deviations being for lower telescope elevations.

One step for improving the model is to get more data. There has been a data taking campaign during March and April 2016, which will give good possibilities to improve the model when that data is analysed later on.

Combine with LidCCD

The model for the SkyCCD also needs to be combined with a model for the LidCCD, to get a complete model for the bending of the telescope.

Single-CCD

There is also a model under development using only one camera placed in the centre of the telescope dish. This concept is called ”Single-CCD” [25] and will use a camera with a field of view wide enough to cover both the sky and the main telescope camera. The results from this model will be compared with the results from the SkyCCD/LidCCD model to find an optimal solution for the prototype of the Medium Size Telescopes, and later also the operational telescopes.

(42)

Acknowledgements

I would like to thank my supervisor at Humboldt Universit¨at zu Berlin, Dr.

Ullrich Schwanke, for the opportunity to work in the group for experimental elementary particle physics (Experimentelle Elementarteilchenphysik II) at Humboldt Universit¨at zu Berlin and for many valuable discussions through- out the work.

I would also like to thank Dr. Louise Oakes, both for valuable support with concepts regarding the thesis and discussions about several topics.

I would also like to thank my supervisor at KTH, Prof. Felix Ryde, for support with administrative matters among other things.

Finally, I would like to thank family and friends for all support through- out my studies.

The work for this thesis has used data from measurements performed with the Medium Size Telescope prototype in Adlershof Science Park, Berlin, Germany. This was provided by a team from Humboldt Universit¨at zu Berlin and Deutsches Elektronen-Synchrotron (DESY).

(43)

List of Figures

2.1 Air shower of gamma-ray (left) and hadronic (right) origin.

Image credit: [13] . . . . 8

2.2 Detection of Cherenkov light from gamma-ray (left) and hadronic origin (right). Image credit: [14] . . . . 9

3.1 MST prototype in Adlershof (Berlin, Germany), with dish, tower (red, almost covered by dish) and camera dummy (red octagonal structure). . . . 15

4.1 Two camera pointing concept. Image credit: C. van Eldik. . . 17

4.2 The blue arrow shows position and direction of the SkyCCD. . 18

4.3 ϕx, tilt of the (vertical) z-axis to the East. . . . 19

4.4 ϕy, tilt of the (vertical) z-axis to the South. . . . . 19

4.5 Zenith angle θ and horizontal angle ϕ. . . . . 21

4.6 Zenith angle θ and elevation angle el. . . . 22

4.7 Horizontal angle ϕ and azimuth angle az. . . . 24

4.8 The parameters c1 and c2 in the initial pointing model. . . . . 26

4.9 The parameters p1 and p2 in the initial pointing model. . . . . 26

6.1 Initial situation, without model. . . . 31

6.2 Results with four-parameter model. . . . 32

6.3 Bending of the structure for different elevation angles. . . . 33

6.4 Results with five-parameter model. . . . 34

(44)

Bibliography

[1] V. Hess, ” ¨Uber Beobachtungen der durchdringenden Strahlung bei sieben Freiballonfahrten”, Physik. Zeitschr. XIII (1912) pp 1084-1091

Available at https://www.mpi-hd.mpg.de/hfm/HESS/public/HessArticle.pdf [2] Nobel Media AB, ”The Nobel Prize in Physics 1936” [webpage] [Jan

16th, 2017]

Available at http://www.nobelprize.org/nobel prizes/physics/laureates/1936/index.html [3] https://www.auger.org/

[4] https://icecube.wisc.edu/

[5] CTA Consortium, ”Design Concepts for the Cherenkov Telescope Ar- ray”, arXiv:1008.3703v3 [astro-ph.IM]

[6] http://tevcat.uchicago.edu/

[7] D. Perkins, ”Particle Astrophysics”, 2nd ed., Oxford, UK: Oxford Uni- versity Press, 2009

[8] B. Gaensler, P. Slane, ”The Evolution and Structure of Pulsar Wind Nebulae” Annual Review of Astronomy and Astrophysics 44 (1) (2006), pp. 17-47

[9] T. Weekes et al., ”Observation of TeV gamma rays from the Crab Nebula using the Atmospheric Cherenkov Imaging Technique”, Astro- physical Journal 342 (1) (1989), pp. 379-395

[10] H. Krawczynski, E. Treister, ”Active Galactic Nuclei – the Physics of Individual Sources and the Cosmic History of Formation and Evolu- tion” Frontiers of Physics 8 (6) (2013) pp.609-629

(45)

[11] J. Sollerman et al., ”Supernova 2006aj and the associated X-Ray Flash 060218”, Astronomy and Astrophysics, 454 (2) (2006), pp. 503-509 [12] D. Eichler et al., ”Nucleosynthesis, neutrino bursts and γ-rays from

coalescing neutron stars”, Nature 340 (1989), pp. 126-128

[13] D. H¨afner, ”Development of a new analog Sum-trigger for the MAGIC experiment with a continuosly adjustable analog delay line and au- tomatic calibration” [Diplomarbeit], Munich, Germany: Ludwig- Maximilians-Universit¨at (2010)

[14] H. Dickinson, ”Very High Energy Gamma-Rays from Binary Systems”

[PhD Thesis], Durham, United Kingdom: Durham University (2010) Available at http://etheses.dur.ac.uk/290/

[15] http://www.mpi-hd.mpg.de/hfm/HESS [16] http://magic.mppmu.mpg.de

[17] J. Aleksic et al., ”The major upgrade of the MAGIC telescopes, Part II: The achieved physics performance using the Crab Nebula observa- tions”, Astroparticle Physics 72 (2016), pp. 76-94

[18] http://veritas.sao.arizona.edu

[19] T. Weekes et al., ”VERITAS: the Very Energetic Radiation Imaging Telescope Array System”, Astroparticle Physics. 17 (2) (2002), pp.

221-264

[20] N. Galante ”Status And Highlights Of VERITAS”, 5th International Meeting on High Energy Gamma-Ray Astronomy. AIP Conference Pro- ceedings 1505 (2012), pp. 202-208

[21] European South Observatory, ”About ESO” [webpage] [June 16th, 2016]

Available at http://www.eso.org/public/about-eso/

[22] Instituto de Astrof´ısica de Canarias - IAC, ”Observatorio del Roque de los Muchachos” [webpage] [June 16th, 2016]

Available at http://www.iac.es/eno.php?op1=2&lang=en

(46)

[23] D. Lang et al., ”Astrometry.net: Blind astrometric calibration of arbi- trary astronomical images”, The Astronomical Journal 139 (2010), pp.

1782-1800

Software package available at http://www.astrometry.net/

[24] The ROOT Team, ”About ROOT” [webpage] [May 31st, 2016]

Available at https://root.cern.ch/about-root

[25] D. Tiziani, ”Investigations towards a Single-CCD Pointing-Solution for the Medium-Sized Telescopes of the Cherenkov Telescope Array”

[Master Thesis], Erlangen-N¨urnberg, Germany: Friedrich-Alexander- Universit¨at (2015)

Available at http://www.ecap.physik.uni-erlangen.de/publications/

pub/2015 Tiziani Master.pdf

(47)

Appendix A

Root code for TMinuit minimization

This code assumes input in the form of a .root-file with azimuth and elevation for drive system and camera. If the data is given in any other form, just rewrite the part ”Read pointing data” to match the actual input data format.

// Pointing calibration for the MST prototype // Include external files

#include <TROOT.h>

#include <TMinuit.h>

#include <TNtuple.h>

#include <TMath.h>

#include <TFile.h>

#include <TGraph.h>

#include <TCanvas.h>

#include <TAxis.h>

#include <TGraphErrors.h>

#include <TMultiGraph.h>

// Two versions:

// 1: Version comparing actual and predicted position for the drive system.

// 2: As version 1, but with el-dependence for the deviation in el.

Int_t version_ID = 1; // Control which version of the code to use

References

Related documents

- Two gamma-ray shields (a Movable Gamma-Ray Shield, MGRS, and a Fixed Gamma-Ray Shield, FGRS, Fig. 2) for minimizing the flux of parasitic gamma radiation reaching the detector..

10-11-14 Gamma-Ray detection in Space 2/29..

 How can gamma-rays be studied using radio detection techniques..  Discuss backgrounds to gamma-ray identification,

• Low angular resolution is sufficient to identify if incident radiation is polarized or not, but a very high resolution is needed to determine the polarization angle. •

QED  strong magnetic fields  refractive index n  1  frequency-dependent decoupling of photon polarization states  frequency-dependent polarization phase lags 

● At higher energies, the cross section for scattering in low-Z materials is too small, and high-Z materials are used for both scattering and absorption... Polarized

● Energetic collisions: particle jet sources (microquasars, active galactic nuclei), in vicinity of accreting compact objects (Black Holes, neutron stars),.. cosmic ray collisions

 The outriggers determined more efficiently the core of the shower, which not only improves the angular resolution, it also allows for the determination of the shower energy