A new unfolding method for the MAGIC telescope [Elektronische Ressource] / by Valentin Curtef

Sujets

• Astronomie

Informations

• Publié par: technischen_universitat_dortmund
• Publié le: 01 janvier 2008
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 7 Mo

Extrait

A new unfolding method for the
MAGIC telescope
Thesis submitted for the Degree of Doctor of Physics at the
University of Dortmund
by
Valentin Curtef
Supervised by
Prof. Dr. Dr. Wolfgang RhodeAnd we complain that we exhaust ourselves too fast
when, on the contrary, we should wonder how new the world
appears to us, just because, for a moment, we have forgotten it.
(A. Camus)Contents
Introduction 1
1 The MAGIC Telescope 3
1.1 Photons as messengers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
ˇ1.2 Cerenkov light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Extended air shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Electromagnetic shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Hadronic shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.3 Differences between γ- and hadron induced showers . . . . . . . . . . . . . . 9
1.4 The Magic Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.2 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.3 Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.4 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.3 Image cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5.4 Hillas parameters and γ/hadron separation . . . . . . . . . . . . . . . . . . . 15
2 Unfolding with regularization 19
2.1 Why unfolding? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Statement of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 The two unfolding methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Direct estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Probability estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Unfolding with regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Direct method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Probability method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Active Galactic Nuclei 31
3.1 The large scale structure of AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 The small scale structure of AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Stellar dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Gas dynamics from water maser . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.3 Gas dynamics of nuclear dust/gas disk . . . . . . . . . . . . . . . . . . . . . . 35
3.2.4 The blue bump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Classification of AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 The mechanism of AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
iii3.4.1 The SMBH and the accretion disc . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.2 The jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 The origin of γ rays in AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.1 Fermi acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.2 Synchrotron radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.3 Inverse Compton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 Superluminal motion and Doppler boosting . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.1 Superluminal motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.2 Doppler boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 The main unfolding program 47
4.1 Variables used for unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Optimization of the unfolding program . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.1 Optimization without Background . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2 Optimization with Background . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.3 The unfolding factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Test of the optimized unfolding method . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 Test on Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Test on Crab Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5 The spectrum of AGN at very high energies 63
5.1 Mrk421 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Mrk501 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 PKS 2155 304 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 The spectral energy distribution and γ-ray absorbtion 79
6.1 Leptonic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.1.1 SSC model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.1.2 EC models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.1.3 The modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2 Hadronic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.3 Absorbtion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3.1 Observation and modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3.2 The re absorbed spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3.3 How small is the observable universe at very high energies? . . . . . . . . . . 90
7 Conclusion 93
Appendix 94
A Trajectory of charged particles 95
B Apparent speeds for jet components 97
Acknowledgements 99
List of Figures 99
Bibliography 105Introduction
As Kepler developed his heliocentric system, he assumed that the planets travel around the sun
on circular orbits. Confronting this hypothesis with measured data for the orbit of the planet Mars,
an inconstancy occurred as one point was too far out from the theoretical orbit. Despite the epicycle
concept used in unanimity at that time, Kepler relied entirely on the experimental data and rejected
the hypothesis of a circular orbit for a new one, that of an elliptical orbit (K¨ ostler, 1995). It was
the first time in physics that an experiment had a crucial relevance, being a corner stone for modern
science.
The importance of scientific experiments lies in the fact that direct information is obtained from
phenomena being observed. In the field of Astronomy this information is predominantly in the form
of photons, messengers of the electromagnetic force, reasoning why the major part of the observed
universe is of electromagnetic nature. For high energy photons, the Earth’s atmosphere acts like a
shield and balloons or satellites are needed to observe them. The extreme case, of very high energy
photons demands a large collection area, which makes direct measurements difficult even by means
of balloons and satellites. The only chance to observe very high energy photons is indirectly, i.e. by
their interaction with the Earth’s atmosphere. From such an interaction electrons and positrons are
ˇcreated, which travel faster than the speed of light in the atmosphere and produce Cerenkov light
observable with the MAGIC telescope. Indirect observation of very high energy photons losses part
of the photon information (energy) in the atmospheric interaction. In order to recover the energy of
the initial photons, one needs to reconstruct it from the measurements, meaning to unfold. Thus,
unfolding is the normal step back to the direct information which enables physicists to understand
reality.
The unfolding method has a long history being already applied by Gauß (1794) for the orbit
reconstruction of planetoids from few data points. It has also difficulties, i.e. suffers from oscillations
induced by rare measured events which have a small weight and thus, a large error for the unfolded
solution. To overcome such problems, a regularization is needed, which means to cut out the
oscillating parts of the solution.
The present thesis describes an unfolding method whose principle is to determine the probability
that a certain set of events has a certain range of energy. Measured data include different character-
istics of the interaction of very high energy photons with the atmosphere. Only those characteristics
which correlate with the energy of the initial photon known from Monte Carlo simulatio