Tracker charge identification and measurement of the proton flux in cosmic rays with the DAMPE experiment

Thesis

Reference

Tracker charge identification and measurement of the proton flux in cosmic rays with the DAMPE experiment

VITILLO, Stefania

Abstract

Many detectors on the ground, on balloons and in space already made a lot of efforts to improve cosmic-ray measurements, and several others are currently continuing them. The DAMPE detector is designed to pursue this task. The DAMPE Silicon Tungsten tracKer (STK) was assembled after testing individually all its components. The signals of the read-out chips of the silicon ladders were calibrated with an analysis based on ground and orbit data. A charge-loss correction of the tracker response was performed on-ground and on-orbit. We performed an analysis on 30 months of data from DAMPE, dedicated to calculate precisely the proton flux. The proton flux measured with this analysis allowed to improve the current knowledge of the energy dependence of the proton spectrum, which is the key element in understanding the origin, propagation and acceleration of cosmic rays in the Universe.

VITILLO, Stefania. Tracker charge identification and measurement of the proton flux in cosmic rays with the DAMPE experiment. Thèse de doctorat : Univ. Genève, 2018, no. Sc.

5290

DOI : 10.13097/archive-ouverte/unige:113361 URN : urn:nbn:ch:unige-1133614

Available at:

http://archive-ouverte.unige.ch/unige:113361

Disclaimer: layout of this document may differ from the published version.

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D´epartement de Physique Nucl´eaire et Corpusculaire

Professeur Xin Wu

Tracker Charge Identification and Measurement of the Proton Flux in Cosmic Rays with the

DAMPE Experiment

TH` ESE

pr´esent´ee `a la Facult´e des Sciences de l’Universit´e de Gen`eve pour obtenir le grade de Docteur `es Sciences, mention Physique

par

Stefania Vitillo

de

Samedan, Suisse

Th`ese n^◦ 5290

GEN`EVE

Atelier d’impression ReproMail

La d´ecouverte des rayons cosmiques est r´ecente compar´ee `a d’autres types de physique.

Notre compr´ehension des m´ecanismes qui d´ecrivent l’acc´el´eration des rayons cosmiques et leur origine est relativement nouvelle. Par cons´equent ce domaine de recherche est profond´ement int´eressant et extrˆemement stimulant. De nombreux d´etecteurs au sol, sur ballons et dans l’espace ont d´ej`a fait beaucoup d’efforts pour am´eliorer les mesures des rayons cosmiques, et plusieurs d’entre eux les poursuivent actuellement. Le d´etecteur DAMPE est l’un d’eux, con¸cu pour d´etecter des rayons cosmiques `a des ´energies de centaines de TeV.

Lors de la construction du d´etecteur `a traces de DAMPE (Silicon Tungsten TracKer, STK), seuls les meilleurs composants ont ´et´e choisis, en commen¸cant par la s´election des plaques de tungst`ene et la mesure de la plan´eit´e des plateaux, en ´evaluant aussi les effets des cycles thermiques sur ceux-ci. Tous les d´etecteurs en silicium ont ´et´e test´es apr`es la production et caract´eris´es individuellement, de sorte qu’une s´election finale a pu ˆetre faite pour choisir les meilleurs ´echantillons. Cette s´election a ´et´e ensuite valid´ee par des distributions r´esumant l’alignement et l’´epaisseur des d´etecteurs en silicium.

Les signaux des puces de lecture des d´edecteurs en silicium ont ´et´e ´etalonn´es `a l’aide d’une analyse bas´ee sur des donn´ees au sol et en orbite. Nous avons calibr´e, puis surveill´e le gain des puces `a intervalles r´eguliers en ´etudiant les donn´ees en orbite. A partir de ces observations, le d´etecteur `a traces STK a ´et´e recalibr´e pour corriger un ph´enom`ene de perte de charge.

Nous avons effectu´e une analyse bas´ee sur 30 mois de donn´ees de DAMPE (jan- vier 2016-juin 2018), d´edi´ee au calcul pr´ecis du flux de protons. Cette ´etude fait appel

`

a des donn´ees simul´ees par ordinateur (Monte-Carlo, MC), utilisant plusieurs mod`eles physiques. Une comparaison syst´ematique entre les donn´ees et les MC en utilisant toutes les distributions ´etudi´ees pour les protons a permis de s´electionner le mod`ele qui corre- spond le mieux aux donn´ees. Nous avons estim´e les incertitudes syst´ematiques de tous les crit`eres de s´election appliqu´es aux donn´ees, en comparant l’efficacit´e entre les donn´ees et les MC pour divers sous-d´etecteurs. Les contaminations par les ´electrons et le noyaux d’h´elium ont ´et´e ´etudi´ees et prises en compte dans la mesure finale. L’´etude sur les erreurs syst´ematiques a ´et´e compl´et´ee par l’estimation des incertitudes li´ees aux MC. Le

flux a ensuite ´et´e obtenu par une m´ethode it´erative diteunfolding, v´erifi´ee par recoupe- ment en injectant un spectre connu. Le flux de protons mesur´e avec cette analyse r´ev`ele une baisse de l’indice spectral au-dessus de 10 TeV. Ce r´esultat permet d’am´eliorer les connaissances actuelles sur la d´ependance ´energ´etique du spectre des protons, ´el´ement cl´e pour comprendre l’origine, la propagation et l’acc´el´eration des rayons cosmiques dans l’Univers.

L’examen du flux d’autres esp`eces de noyaux au-dessus de 10 TeV aidera `a com- prendre si ce changement de r´egime observ´e est d´ependant de la rigidit´e, ou s’il n’est visible que pour les protons. Les futures missions spatiales, comme HERD, pr´evoient de contribuer `a la mesure du flux des rayons cosmiques jusqu’`a des ´energies de 1 PeV.

2

The valuable help of a lot of people needs to be mentioned to underline the im- portance that each one had in the development of this work. I want to start with Professor Xin Wu, which was not only the director of this thesis, as he was responsible of all the steps necessary for this project, but also because he was present during the whole doctoral work to shed light on every doubt that I had, regardless of its consis- tency. He did not leave one email unanswered, or even forgotten it. This is impressive and deserves my deepest gratitude.

I would like to thank the members of the jury for accepting to evaluate this work.

It was only after someone coming from outside my group and my field appreciated this work that I truly realized its value. Thanks to Professor Ivan De Mitri and to Professor Tobias Golling.

I started the PhD with an exceptional situation, counting on the guidance of four expert Postdocs: Dr. Valentina Gallo, Dr. Philippe Azzarello, Dr. Andrii Tykhonov and Dr. Ruslan Asfandiyarov. The number of times that they helped me and clarified my doubts on a daily basis is countless, my profound thankfulness is not enough to express my gratitude towards all of you. In particular, Valentina worked with me in developing every part of this thesis. Even during her maternity leave, she did not stop to give me her valuable opinions on various subjects. Grazie davvero Vale! Thanks to Dr. Stephan Zimmer, David Droz and Maria Munoz, which joined the Geneva DAMPE group later and brought a lot of new discussions in the group, not only about physics. I want to thank the DAMPE Collaboration: each member, in one way or another, gave its con- tribution to this work. In particular, the discussions with Professor Paolo Bernardini, Dr. Antonio Surdo and Dr. Nicola Mazziotta where very fruitful in developing this work, thanks a lot.

A part of my PhD was also dedicated to the Alpha Magnetic Spectrometer detector (AMS-02) on the International Space Station and for that I worked under the supervision of Professor Martin Pohl. Thanks to him, I had the opportunity to know more a bigger collaboration, with respect to the DAMPE one, and I worked with Dr. Pierre Saouter, which showed me patiently the main parts of the knowledge acquired during his PhD in the AMS Geneva group. The opinion exchanges with Dr. Marion Habiby, Dr. Yang

Li and Dr. Mercedes Paniccia contributed to my general view of the experiment, thanks to all of you. I also had several discussions with Dr. Alberto Oliva, following Pierre’s suggestions, that helped me in developing the first steps of the thesis for DAMPE. Thank you Pierre.

This is the part dedicated to friends and family but some of the people mentioned above became very good friends during these years, and I think this made me day after day more enthusiastic of the work. Thank you for this to Valentina, Andrii, Ruslan and David. During my PhD, I met several friends that I will never forget and they also contributed unconsciously to this work, giving tips in other forms, less scientific in some cases, but very powerful. The time spent together was always so short but nevertheless it was used always in the best possible way. Thanks Veronica, Bogdana, Ksenia, Anatoly, Andrea, Marta, Leila and Misha.

During these years in Geneva I was strongly supported by Alberto, which gave his contribution, even remotely, in almost all the steps of my research. He spent entire evenings to discuss with me about my work, giving good advices even if he is working on a completely different subject. Grazie davvero.

Studying in Pisa gave me the opportunity to follow this path crossing several Profes- sors: Sandra Leone, Simona Rolli, Franco Cervelli and Alessandro Baldini. Thank you all. Many friends from the bachelor and master period continued with their PhD studies in Switzerland, and meeting them at CERN was always a pleasure. In particular, we shared our experiences and difficulties in our work accompanied by a good pizza and limoncello at the “leccesi”. Thank you Adele and Federica.

Who really supported all my choices during this period, even being not at all physics experts, are my parents Carlo and Caterina, my brother Roberto and my sister-in-law Rachell. Without such a beautiful family (and my mother’s lasagnas) this journey would have been impossible. Thank you. Now the family is getting bigger and Elena, Fabrizio, Gabriella e Carmelo became in these years very important to me. With you all, a lot of holidays changed their meaning to me, helping in having a break from the PhD work.

Thanks to all of you.

4

Introduction 9

1 Cosmic Rays in the Universe 11

1.1 Birth of particle physics through cosmic rays . . . 12

1.2 Cosmic-ray origin and propagation . . . 13

1.2.1 Possible sources of high energy particles . . . 13

1.2.2 Second order Fermi acceleration mechanism and diffusion model . 16 1.2.3 First order Fermi acceleration and diffusive acceleration . . . 19

1.3 Experimental Observations . . . 21

1.3.1 Confinement of cosmic-rays . . . 24

1.4 Cosmic-ray detection on ground through Extensive Air Showers (EAS) . . 25

1.5 Dark matter search . . . 27

1.5.1 Evidence of Dark Matter at galactic and galaxy cluster scales . . 27

1.5.2 Search of Dark Matter with cosmic rays . . . 29

1.6 Latest results on the proton flux measurement . . . 30

2 Dark Matter Particle Explorer 33 2.1 Space detection of cosmic rays . . . 35

2.2 The DAMPE experiment . . . 38

2.2.1 The DAMPE detector . . . 38

2.2.2 The Plastic Scintillation Detector (PSD) . . . 40

2.2.3 The Silicon-Tungsten Tracker (STK) . . . 41

2.2.4 The Bismuth Germanium Oxide imaging calorimeter (BGO) . . . 45

2.2.5 The Neutron Detector (NUD) . . . 49

2.2.6 Data acquisition and Trigger logic . . . 51

3 Silicon-Tungsten Tracker (STK) 55 3.1 Metrology of the STK . . . 55

3.1.1 The tungsten plates . . . 55

3.1.2 The trays . . . 57

CONTENTS

3.1.3 The silicon ladders . . . 60

3.1.4 Trays with ladders . . . 64

3.2 Calibration of the STK on-ground and on-orbit . . . 66

3.2.1 Particle track reconstruction . . . 67

3.2.2 Charge Measurement . . . 72

3.2.3 VA equalization on-ground . . . 73

3.2.4 Charge-loss correction on-ground . . . 76

3.2.5 VA equalization on-orbit . . . 77

3.2.6 Charge-loss correction on-orbit . . . 79

4 Measurement of the Proton Flux 87 4.1 Introduction to the flux measurement . . . 87

4.2 Data sample and live time calculation . . . 87

4.3 Candidate proton sample selection . . . 89

4.3.1 Monte Carlo (MC) simulation . . . 91

4.3.2 Preselection . . . 92

4.3.3 BGO-STK match . . . 94

4.3.4 STK-PSD match . . . 95

4.3.5 Trigger and Charge selection . . . 95

4.3.6 Correction in the PSD for protons and helium nuclei . . . 102

4.3.7 Electron background removal . . . 105

4.3.8 Helium background estimation . . . 109

4.4 Efficiencies and associated systematics . . . 111

4.4.1 Track selection . . . 112

4.4.2 STK cluster charge selection . . . 116

4.4.3 High Energy Trigger (HET) . . . 118

4.4.4 Charge reconstruction in PSD . . . 118

4.4.5 Systematic uncertainty related to the smear . . . 122

4.5 Monte Carlo Unfolding . . . 123

4.5.1 MC study . . . 125

4.5.2 Bayesian Unfolding . . . 128

4.5.3 Statistical error calculation . . . 131

4.5.4 Systematics related to the unfolding . . . 132

4.6 Interaction study . . . 133

4.6.1 Selecting different samples in DAMPE . . . 133

4.6.2 Cross-check with a parallel proton flux analysis . . . 136

4.7 Results . . . 137

Conclusions and outlooks 143 A Metrology of the STK 145 A.1 The tungsten plates . . . 145

A.2 The trays . . . 149

A.2.1 Distance Insert-Tray . . . 149 6

A.3 Planarity of the trays . . . 149

A.4 The silicon ladders . . . 149

A.5 Trays with ladders . . . 154

A.5.1 Distance between facing points analysis . . . 154

B Analysis 161 B.1 Charge smear for proton and helium MC QGSP . . . 161

B.2 Charge smear for helium MC FTFP . . . 161

B.3 Charge smear calculation for the MIP sample . . . 168

B.4 Efficiencies . . . 170

B.4.1 Energy cut in BGO . . . 170

Bibliography 177

CONTENTS

8

Cosmology comes from the Greek word “kosmos”, meaning harmony or order and the messengers of this order are the particles that we can detect directly (with space telescopes and satellites described in section 2.1) or indirectly (see air shower telescopes in section 1.4): hadrons, electrons, photons and neutrinos. The observation of these particles from cosmic rays created a bridge between the Universe and particle physics, leading to the birth of astroparticle physics. This field is quite new, since cosmic rays were discovered by Victor Hess in 1911 (Nobel prize in 1936) through measurements on balloons up to 5 km altitude [1]. We distinguish primary from secondary cosmic rays:

primaries are made for almost 90% of protons, 10% of helium and 1% of neutrons and heavier nuclei, such as oxygen and carbon. Only less than 1% [2] of the total amount are electrons and photons and they are produced by various types of sources (for example supernova remnants, pulsars or blazars). Primary cosmic rays, accelerated by the source, can be affected by various interactions in the interstellar medium (ISM), hence producing secondary cosmic radiation through a hadronic mechanism followed by a leptonic one, as:

p + target→p(n) +π⁺+π⁻+π⁰

π⁺ →µ⁺ν_µ ,π⁰ →γγ µ⁺→e⁺+ν_e+ ¯ν_µ

(1)

or through a purely leptonic mechanism:

e^±+ B→e^±+γ_sync (2)

e^±+γ_CMB→e^±+γ. (3)

where B is the magnetic field in the ISM (∼3 µG) and CMB is the cosmic microwave background made of photons with very low energy (6.626 ·10⁻⁴ eV). Therefore, the energy dependence of primary cosmic rays is the key element in understanding the origin, the acceleration and the propagation through the galaxy of cosmic rays. Moreover, cosmic rays can be also produced through the annihilation of Dark Matter particles

CONTENTS

(section 1.5), thus measuring any unexpected excess in the energy spectrum can give hints of the existence of Dark Matter particles.

In this thesis, we will focus on the proton component in cosmic rays measured with the DArk Matter Particle Explorer (DAMPE), a general purpose high-energy cosmic and gamma-ray detector, launched into a sun-synchronous orbit on December 17 2015, currently orbiting at an altitude of 500 km and taking data smoothly since then.

The thesis has the following structure:

Chapter 1gives an overview of the history of cosmic rays, with a derivation of the ac- celeration mechanism that they undergo. Some recent measurements in the cosmic-ray physics field are shown and an overview of the searches for Dark Matter with cosmic rays is given to complete the general picture.

Chapter 2introduces the high-altitude and space detection of cosmic rays through var- ious experiments, focusing on the characteristics of the DAMPE experiment, including a description of its data acquisition and of its trigger logic system.

Chapter 3 focuses on the construction and the metrology of the Silicon Tungsten tracKer (STK) of DAMPE, at the D´epartment de physique nucl´eaire et corpuscolaire (DPNC) of the University of Geneva. The on-ground and on-orbit performance of the flight model (FM) of STK are shown before and after the integration with the experi- ment.

Chapter 4describes in detail the various analysis steps that were applied to evaluate a preliminary measurement of the proton energy spectrum with the DAMPE experiment, including a detailed study performed to take into account of the systematic uncertanties.

10

Chapter 1

Cosmic Rays in the Universe

Already in 1785 Coulomb knew that there had to be a reason to explain why charged electroscopes, even insulated, could discharge. Almost 100 years later, with the discovery of radioactivity and the studies on radium by Marie and Pierre Curie, it was concluded that the discharge of electroscopes happens in the presence of radioactive material. With improved experiments with electroscopes (Wilson, Elster and Geitel), at the beginning of 1900 it was assumed that the radiation was of terrestrial origin but without conclusive proof. Wilson (Nobel prize for the invention of the cloud chamber in 1927) tried to verify the hypothesis that the radiation was of extraterrestrial origin in particular by performing experiments with electroscopes in tunnels to see a reduction of the radiation, but without success. So this idea was dropped for many years. In 1909 Theodor Wulf wanted to see the variation in ionization in the atmosphere at the ground level and on top of the Eiffel tower (300 m). If the radiation was of terrestrial origin, he was expecting a significant drop at higher altitude. He observed a decrease but it was not enough to confirm the terrestrial origin. Though Wulf’s data was not totally conclusive, this hypothesis remained the most accepted in the scientific community. The Italian physicist Domenico Pacini, measuring the ionization under the sea level in the Gulf of Genoa and in the Lake of Bracciano, challenged the assumption of the terrestrial origin of the radiation. In fact he observed a 20% reduction in ionization at three meters under the sea with respect to the ground level. He concluded that this was due to extraterrestrial radiation that in a medium was absorbed partially, like the water. So the key to solve this puzzle was to use a very convincing altitude dependent experiment:

a balloon.

The Austrian physicist Victor Hess confirmed finally the extraterrestrial origin of the radiation with a series of balloon flights between 1911 and 1912. He flew up to 5200 m and clearly observed a radiation rate first passing through a minimum and then increasing considerably with altitude above 1000 m [3]. To be sure that it was not correlated to the sun influence, he performed flights during the day and the night, without observing any difference. The results of Hess would later be confirmed by Kolh¨orster at a higher altitude (he reached 9200 m). The results of both physicists are

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

shown in Fig. 1.1. Hess called this radiation “H¨ohenstrahlung”, but with the suggestions

Figure 1.1: Ion pairs per cm³ and second as a function of the altitude for the measurements of Hess (left) and Kolh¨orster (right). Picture taken from [2].

of Glockel, Wulf and the influence of Millikan, the general recognized term was “cosmic rays”. Hess was awarded with the Nobel prize only in 1936, long time after the strong evidence of cosmic rays was achieved, testifying how difficult it was to accept this reality for the scientific community at the time. The years of the war 1914-1918 and the years immediately after were poor in additional experiments. In 1926 Millikan and Cameron performed some absorption experiments in water that led to believe that cosmic rays were almost exclusively γ rays. It was the Dutch physicist Clay who observed that the ionization increased with the geomagnetic altitude, proving that the cosmic radiation was made mostly by charged particles. In 1928 the Geiger-M¨uller counter tube was used in the experiments confirming this observation. In 1933 it was observed that more cosmic rays were coming from West than East at the equator, meaning that they carry positive electric charge (see the magnetic field lines scheme in Fig. 1.2). Cosmic rays were established to come from astronomical sources and the next steps were to investigate the nature of these particles and the possible interactions they undergo. The era of particle physics started with an accelerator (the Universe) available for free.

1.1 Birth of particle physics through cosmic rays

Relativity and quantum mechanics together allowed Dirac to predict the existence of a new fermion with charge opposite to that of the electron: the positron. The search of antimatter in cosmic rays began when Anderson in 1933 [5] discovered the positron with a cloud chamber. For this he shared the Nobel prize with Hess in 1936. The electron and positron pair production from a photon was predicted also by Dirac, which was observed

12

Figure 1.2: Scheme of the magnetic field lines of the earth. Picture taken from [4].

by Blackett [6] (Nobel prize in physics in 1948) and by Occhialini.

These were the years when the idea of “trigger” was developed too: Bothe and Kolh¨orster used two Geiger counters in combination with a cloud chamber so that when the counters gave a signal in coincidence, it was detecting a cosmic ray and a picture could be taken so that the “event” could be studied “offline”. Bothe shared the Nobel prize in physics in 1954 for the development of the coincidence technique.

But where exactly are these particles coming from? And how are they accelerated before reaching the Earth?

1.2 Cosmic-ray origin and propagation

1.2.1 Possible sources of high energy particles

Thanks to radio and γ-ray observations, we know that supernova remnants (SNR), distinguished in shell-like and Crab-like remnants, are possible sources of high energy particles originating within the galaxy whereas cosmic rays coming from outside the Galaxy could be produced by Active Galactic Nuclei (AGN). We will give a brief overview of these astrophysical objects.

Shell-like supernova remnant

A spectacular image of a shell-like supernova, the intensively studied Cassiopeia, is shown in Fig. 1.3. X-ray photons are the result of bremsstrahlung of very hot gas associated to the interstellar medium that encounters the supernova wave blast (the blue outer ring in Fig. 1.3). Some of the elements inside the SNR are clearly visible:

silicon (red), sulfur (yellow), calcium (green) and iron (purple). They produce X-rays making possible the creation of their location maps. The radio emission is associated to the synchrotron radiation of electrons accelerated by the shock wave and it is so intense

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

Figure 1.3: X-ray image of the supernova remnant Cassiopeia. Picture taken from [4].

that the relativistic particles have to originate inside the supernova. Theγ-ray spectrum coming from shell-like SNRs, indicates that they are sources of cosmic-rays up to and above 100 TeV, given the coincidence of the γ-ray image with those from X-ray and radio wavelengths [7].

Crab-like supernova remnant

Five supernovae were observed in our galaxy in the past millennium. After their explosion they became the brightest objects in the sky: pulsars. Pulsars are spinning neutron stars with enormously strong magnetic fields. While stars typically have radii of 10⁶ km, during a supernova explosion they shrink under a gravitational collapse to a size of just about 20 km. This process leads to densities of 6·10¹³ g/cm³, where electrons and protons are close enough to produce neutrons through the weak process:

e⁻+ p→n +ν_e.

In neutron stars, neutron decay will be prevented by the Pauli principle, because all the quantum states that can be reached by the electron and the proton are already filled. One of these five supernova remnants is the Crab Nebula, a young pulsar, that was observed already from the original supernova explosion in 1054 by the astronomers of that time and that is shown in Fig. 1.4 with todays techniques. The bright central X-ray source is the young pulsar which has a pulse period of 33.2 ms and is the energy source for the nebula. Jets of material are ejected perpendicular to the disc of the pulsar, possibly producing cosmic rays. The other four are very similar to the Crab and are close to it.

Active Galactic Nuclei (AGN)

At the core of a galaxy there is in general a supermassive black hole, and in 1%

of the cases this black hole is active as it emits radio waves and is surrounded by an 14

Figure 1.4: X-ray image of the supernova remnant Crab. Picture taken from [4].

accretion disk. In this case one speaks of an active galactic nucleus and it ejects high energy particles perpendicularly with respect to the disk. A scheme is shown in Fig. 1.5.

Following the so-called₅₇₈ unified model, there are various type of AGN with the same basic10 Messengers from the High-Energy Universe

Fig. 10.36 Schematic diagram for the emission by an AGN. In the “unified model” of AGN, all share a common structure and only appear different to observers because of the angle at which they are viewed. Fromhttp://www.astro-photography.net, adapted

respect to the line of sight. In blazars, emission is modified by relativistic effects due to the Lorentz boost.

Blazars. Observationally, blazars are divided into two main subclasses depending on their spectral properties.

• FSRQs. They show broad emission lines in their optical spectrum.

• BL Lacertae objects (BL Lacs). They have no strong, broad lines in their optical spectrum. BL Lacs are moreover classified according to the energies of the peaks of their SED; they are called accordingly low-energy peaked BL Lacs (LBLs), intermediate-energy peaked BL Lacs (IBL) and high-energy peaked BL Lacs (HBL). Typically FSRQs have a synchrotron peak at lower energies than LBLs.

Blazar population studies at radio to X-ray frequencies indicate a redshift distribution for BL Lacs that seems to peak atz∼0.3, with only few sources beyondz∼0.8, while the FSRQ population is characterized by a rather broad maximum between z∼0.6–1.5.

Non-AGN Extra Galactic Gamma Ray Sources. At TeV energies, the extragalactic γray sky is completely dominated by blazars. At present, more than 50 objects have been discovered and are listed in the online TeV Catalog. The two most massive close by starburst galaxies NGC 253 and M82 are the only non-AGN sources detected at TeV energies. Only 3 radio galaxies have been detected at TeV energies (Centaurus

Figure 1.5: Scheme of an AGN in the various parts, seen from several sides from the Earth.

Picture taken from [2].

structure but depending on the jets emitting direction the name of the AGN is different.

If the observer sees only the jet emission of the AGN we speak of Blazars. As soon as one looks at the AGN less perpendicularly, the toroidal structure is visible and we speak of Quasars. Parallel to the AGN jets, the black hole is hidden and one essentially observes

15

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

the jets and the associated radio emission. In this case we speak of radio Galaxies. There is an additional division into Seyfert 1 and 2 Galaxies that are connected to AGN of type I and II: type I AGN has little or no obscuration from the central source of radiation, while in type II AGN the line of sight to the central source is completely obscured. For more details see [8].

1.2.2 Second order Fermi acceleration mechanism and diffusion model In 1933 Zwicky and Baade speculated that big explosions in massive stars produce cosmic rays but only in 1949 Fermi finalized a model that could explain this assump- tion. Variable magnetic fields in astronomical sources, generating variable electric fields, accelerate charged particles produced by particle ejection. After production they un- dergo stochastic collisions with the interstellar medium (ISM) and accelerations which can be explained by the second order Fermi mechanism. We will report the calculation following [9]. In the original picture, particles are reflected by “magnetic mirrors” (ir- regularities in the galactic magnetic field) that for simplicity are assumed to be walls (see Fig. 1.6) with a certain velocity. We define (m, v) and (M, V) the mass and the P1: JZP Trim: 246mm×189mm Top: 10.193 mm Gutter: 18.98 mm

CUUK1326-17 CUUK1326-Longair 978 0 521 75618 1 August 13, 2010 1:7

564 The acceleration of high energy particles

(a) (b)

Fig. 17.1 Illustrating the collision between a particle of massmand a cloud of massM: (a) a head-on collision; (b) a following collision. The probabilities of head-on and following collisions are proportional to the relative velocities of approach of the particle and the cloud, namely,v+Vcosθfor (a) andv−Vcosθfor (b). Sincev ≈c, the probabilities are proportional to 1+(V/c) cosθwhere 0<θ <π.

17.3 Fermi acceleration – original version

The Fermi mechanism was first proposed in 1949 as a stochastic means by which particles colliding with clouds in the interstellar medium could be accelerated to high energies (Fermi, 1949). We first consider Fermi’s original version of the theory, the problems it encounters and how it can be reincarnated in a modern guise. The analysis contains a number of features which are important for particle acceleration in general. In Sect.17.4, the modern version of first-order Fermi acceleration is described.

In Fermi’s original picture, charged particles are reflected from ‘magnetic mirrors’ as- sociated with irregularities in the Galactic magnetic field. The mirrors are assumed to move randomly with typical velocity V and Fermi showed that the particles gain en- ergy stochastically in these reflections. If the particles remain within the acceleration region for some characteristic time τ_esc, a power-law distribution of particle energies is obtained.

Let us repeat Fermi’s calculation in which the collision between the particle and the mirror takes place such that the angle between the initial direction of the particle and the normal to the surface of the mirror isθ (Fig. 17.1a). We carry out a relativistic analysis of the change in energy of the particle in a single collision.

The mirror is taken to be infinitely massive and so its velocity is unchanged in the collision. The centre of momentum frame of reference is therefore that of the cloud moving at velocity V. The energy of the particle in this frame is

E^′ =γ_V(E+V pcosθ), where γ_V =

!

1− V² c²

"−1/2

. (17.9)

Thex-component of the relativistic three-momentum in the centre of momentum frame is p_x^′ = p^′cosθ^′ =γ_V

!

pcosθ + V E c²

"

. (17.10)

Figure 1.6: A particle of mass m and velocity v collides with a mirror of mass M and velocity V in a head-on collision in a) and a following collision in b). Picture taken from [9].

velocity for the particle and the mirror respectively, andθthe angle between the particle and the normal respect to the mirror. We are interested in the change in energy of the particle after the collision, assuming that the wall has infinite mass so that its velocity is unchanged after the collision. In the frame of the mirror the energy of the particle is:

E⁰ =γ(E + Vp cosθ) (1.1) whereγ=

1−^V_c²²₋1/2

. The x component of the momentum is:

p⁰_x=γ(p_xcosθ+VE

c² ). (1.2)

In the collision the energy is conserved and the x component of the momentum reversed (p⁰_x → −p⁰_x). The energy E⁰⁰ after the collision transforming back to the particle frame

16

will be:

E⁰⁰= E =γ(E⁰−Vp⁰_xcosθ) =γ(E⁰−V(−p_x) cosθ) =γ(E⁰+ Vp_xcosθ) (1.3) Remembering that ^p_E^x = ^mvγ_mc^cos2γ^θ = ^{v cos}_c2 ^θ and substituting Eq. 1.1 and 1.2 in Eq. 1.3 we obtain:

E⁰⁰ =γ²E

"

1 +2Vv cosθ c² +

V c

2#

(1.4) with

∆E = E⁰⁰−E = E

"

2Vv cosθ c² + 2

V c

2#

(1.5) expanding until the second order in V/c. To average the angle we take into account that the probability of a collision at angleθis≈γ_V(1 + V/c) cosθ, the particle is relativistic (v≈c), the scattering angle belongs to a uniform distribution between [0,+π], and that the variation in angle can be approximate with sinθdθ. The considerations mentioned above lead to:

*∆E E

+

= 2V

c

R

−1x[1 + (V/c)x]dx

R

−1[1 + (V/c)x]dx + 2

V c

2

= 8 3

V c

2

. (1.6)

If the mean distance between two collisions is L, then the time that elapses between them will be L/(c cosφ) where φ is the angle between the particle and the magnetic field. Averaging over all φ the mean time between two collisions is 2L/c. The average rate in increase of energy becomes:

dE dt = 4

3 V²

cL

E =αE, (1.7)

with α = ⁴₃

V² cL

. We recall some notions of the diffusion model of cosmic rays that is explained in detail in [9]. Particles in a volume dV, with parameters of energy E, space x and time t, are subjected in their travel by losses and gain in energy that can be explained in general by:

−dE

dt = b(E). (1.8)

with b(E) a function of the energy. If b(E) is positive, the particles lose energy. We are interested in the number of particles that enter the volume dV at an energy E per unit of time, i.e. the fluxφof the particles at that energy:

N(E)dE

dt =φ_E=−b(E)N(E). (1.9)

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

But the rate of particles in [E, E+dE] and in [x, x+dx] depends on the flux of particles in space, in energy, and from a possible injection source Q:

dN

dt (E,x,t)dEdx =[φ_x(E,x,t)−φ_x+dx(E,x + dx,t)]dE + [φ_E(E,x,t)−φ_E+dE(E + dE,x,t)]dx + Q(E,x,t)dEdx.

(1.10)

Simplifying the notation and using a Taylor expansion:

dN

dt =−∂φ_x

∂x −∂φ_E

∂E + Q (1.11)

φ_x is the flux of particles at point x through the energy interval dE, so by definition φ_x=−D^∂N_∂x, where D is the diffusion coefficient. Generalizing to three dimensions and using Eq. 1.9:

dN

dt = D∇²(N)−∂φ_E

∂E + Q = D∇²(N) + ∂

∂E[b(E)N(E)] + Q. (1.12) Eq. 1.12 can be completed by adding terms describing gains and losses due to spallation (interaction of the cosmic rays with the interstellar medium). In case of the propagation of cosmic rays of type Niwith a spallation lifetimeτ_i, if Nj(with j>i) particles contribute with a probability P_ji through spallation to N_i, with spallation lifetime τ_j we will have:

dN_i

dt = D∇²(N_i) + ∂

∂E[b(E)N_i(E)] + Q−N_i τ_i +X

j>i

P_ji

τ_j N_j. (1.13) Using Eq. 1.7 and 1.13 in the absence of diffusion, in a stationary condition, without an injection term, and Eq. 1.8 we have:

− ∂

∂E[αE N(E)]−N(E)

τ_esc = 0 (1.14)

withτ_escthe escaping time from the galaxy. Differentiating and rearranging the equation we obtain:

dN(E) dE =−

1 + 1 ατ_esc

N(E)

E ⇒N(E) = costant×E^{−[1+(ατesc)−1]}. (1.15) The Fermi acceleration mechanism results in a power-law energy spectrum with a spec- tral index [1 + (ατ_esc)⁻¹] . However there were problems in many parts:

• In his paper in 1949, Fermi assumed that the main acceleration of cosmic rays came from collisions with clouds, but the velocity of the interstellar medium is small compared to the speed of light (V/c≤10⁻⁴), resulting in a slow energy gain of the particles.

18

• Energy loss by ionization complicates this picture since it can be high if the particle has low energy. This acceleration mechanism is more effective if the particles are either injected into the acceleration region with energies greater than that corresponding to the maximum energy loss rate or otherwise the initial acceleration process must be sufficiently rapid to overcome the ionization energy losses.

• The calculation does not take into account the statistical nature of the acceleration process and also the average increase in energy.

• The theory does not predict the value of the spectral index.

For these reasons the second order acceleration model was modified by Fermi itself resulting in a first order acceleration.

1.2.3 First order Fermi acceleration and diffusive acceleration

The description follows [9]. We defineβand P, so that E =βE₀is the average energy of the particle after a collision and P is the probability that the particle remains in the accelerating region after one collision. Then after k collisions, there will be N = N₀P^k particles with energies E = E₀β^k. Taking the ratio of the two relations we have:

ln(N/N0)

ln(E/E₀) = ln P lnβ ⇒

N N₀

= E

E₀ ^{ln P}_lnβ

. (1.16)

So in this reformulation we obtain again a power-law energy spectrum:

N(E)dE = constant·E^{[−1+(ln P/lnβ)]}dE (1.17) It means that ln P/lnβ= (ατ_esc)⁻¹ according to Eq. 1.15. But we saw thatαis second order in (V/c) in the second order Fermi acceleration. If we suppose in Eq. 1.5 that there are only head-on collisions, we have that ∆E/E∝2V/c, that is first order in V/c.

This is referred asfirst-order Fermi acceleration.

The diffusive shock acceleration mechanism is a first-order Fermi acceleration in the presence of shock waves. It was discovered in the late 1970s and since then it is the generally accepted theory of acceleration of cosmic-rays. The material ejected by shock waves can reach a velocity of 10⁴km/s while the ISM is very slow compared to that (10km/s). We recall the shock wave theory to understand better what happens to a particle hitting on it. A shock wave traveling at speed U can be thought as a wall that separates two zones with different densities: ρ₁ and ρ₂ (a in Fig. 1.7). It is convenient to make the derivation in the reference frame where the shock is at rest and it sees the particle flow. The continuity equation imposes that the mass has to be conserved at the passage of the shock:

ρ₁v₁ =ρ₁U =ρ₂v₂ (1.18)

With simple fluid dynamic (full derivation in [9] in pages 315-318), we know thatρ₂/ρ₁ = (γ+ 1)/(γ−1), where γ is the ratio of specific heat capacities of the gas which for a

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

P1: JZP Trim: 246mm×189mm Top: 10.193 mm Gutter: 18.98 mm

CUUK1326-17 CUUK1326-Longair 978 0 521 75618 1 August 13, 2010 1:7

570 The acceleration of high energy particles

(a)

(c)

(b)

(d)

Fig. 17.3 The dynamics of high energy particles in the vicinity of a strong shock wave. (a) A strong shock wave propagating at a supersonic velocityUthrough stationary interstellar gas with densityρ₁, pressurep₁and temperatureT₁. The density, pressure and temperature behind the shock areρ2,p2andT2, respectively. The relations between the variables on either side of the shock front are given by the relations (11.72)–(11.74). (b) Theflow of interstellar gas in the vicinity of the shock front in the reference frame in which the shock front is at rest. In this frame of reference, the ratio of the upstream to the downstream velocity isv1/v2=(γ+1)/(γ−1). For a fully ionised plasma,γ=5/3 and the ratio of these velocities isv₁/v₂=4 as shown in thefigure. (c) Theflow of gas as observed in the frame of reference in which the upstream gas is stationary and the velocity distribution of the high energy particles is isotropic. (d) The flow of gas as observed in the frame of reference in which the downstream gas is stationary and the velocity distribution of high energy particles is isotropic.

than the sound and Alfv´en speeds of the interstellar medium, which are at most about 10 km s⁻¹. A strong shock wave travels at a highly supersonic velocityU≫cs, wherecsis the sound speed in the ambient medium (Fig. 17.3a), the Mach numberMbeingU/cs≫1.

It is often convenient to transform into the frame of reference in which the shock front is at rest and then the upstream gas flows into the shock front at velocityv₁=Uand leaves the shock with a downstream velocityv2(Fig. 17.3b). The equation of continuity requires mass to be conserved through the shock and so

ρ₁v₁=ρ₁U=ρ₂v₂. (17.31)

In the case of a strong shock,ρ2/ρ1=(γ+1)/(γ−1) whereγis the ratio of specific heat capacities of the gas (Sect. 11.3.1). Takingγ=5/3 for a monatomic or fully ionised gas, ρ₂/ρ₁=4 and sov₂=(1/4)v₁(Fig. 17.3b).

Now consider high energy particles ahead of the shock. Scattering ensures that the particle distribution is isotropic in the frame of reference in which the gas is at rest. It is instructive to draw diagrams illustrating the situation so far as typical high energy particles upstream and downstream of the shock are concerned. The shock advances through the medium at velocityUbut the gas behind the shock travels at a velocity (3/4)Urelative to the upstream gas (Fig. 17.3c). When a high energy particle crosses the shock front, it obtains

Figure 1.7: a) Scheme of a shock wave traveling at velocity U between two different materials with different pressure p, densityρ and temperature T. b) Velocity of the two materials ”sep- arated” by the shock. c) Velocity of the shock seen by a particle hitting from upstream and d) from downstream. Picture taken from [9].

monoatomic gas is 5/3 leading toρ₂/ρ₁= 4 and v₂ = 1/4v₁ (scheme b in Fig. 1.7). Now consider a particle hitting at the shock wave from upstream: the shock propagates at velocity U, but the total velocity that the particle will see is the relative velocity between the two media: ∆U = U− ¹₄U = ³₄U (scheme c in Fig. 1.7). If a particle reaches the shock wave from downstream again the velocity seen is ³₄U (scheme d in Fig. 1.7). In both cases the particle is subject to the same behavior and, unlike the original Fermi acceleration mechanism, the collisions are all head-on and the gain in energy is the same, regardless from the incoming direction with respect to the shock. We recall the Lorentz transformation in Eq. 1.1 with V = ³₄U, V c so that γ ≈ 1. Particles on the other hand are relativistic. So Eq. 1.1 will be in this case:

E⁰ = E + p_xV⇒∆E = pV cosθ= E

cV cosθ⇒ ∆E E = V

c cosθ (1.19) The probability that a particle hits the shock wave between [θ,θ+ dθ] is proportional to sinθdθ and the rate at which they appear in front of the shock depends on the x component of their velocity c cosθ. Imposing that for normalization the probability p(θ) = sinθcosθdθ is 1 gives to compute:

*∆E E

+

= V c

Z π/2 0

2 cos²θsinθdθ= 2 3

V

c. (1.20)

The fraction of energy that the particle gains each time that he crosses the shock is always (2/3)(V/c) and in one roundtrip it is:

*∆E E

+

= 4 3

V

c. (1.21)

20

Therefore we have:

β= E

E₀ = 1 + 4 3

V c ⇒ln

1 +4

3 V

c

≈+4 3

V

c. (1.22)

The probability to escape the acceleration zone P_esc using classical kinetic theory with Fig. 1.7 is ^U_c = ^4V_3c, so

P = 1−P_esc ⇒ln P = ln(1−P_esc) = ln

1−4V 3c

≈ −4V

3c (1.23)

and Eq. 1.17 becomes:

N(E)dE∝E^{[−1+(ln P/lnβ)]}dE∝E⁻²dE. (1.24) This provides an excellent physical justification why a power-law with a unique spectral index should be expected from cosmic rays. The fact that we observe a spectral index of

∼2.7 in cosmic rays instead of a 2 comes form the influence of the magnetic field inside the source and many types of possibles shocks (parallel or perpendicular to the magnetic field). A steeper observed spectrum is correlated with the fact that the ratio v₁/v₂ = 4 in the basic diffusive model becomes lower than 4 because of the effects mentioned above.

1.3 Experimental Observations

The observed differential flux Φ of cosmic rays in an energy interval [E, E+dE] is defined as follows:

Φ(E,E + dE) = N(E,E + dE)

∆T×A×dE (1.25)

where N(E,E + dE) is the number of cosmic rays between E and E + dE, ∆T is the observation time, A is the geometrical acceptance and dE is the energy bin. The observed energy spectrum integrated over all types of cosmic rays is shown in Fig. 1.8. The differential spectrum spans over many orders of magnitude in energy, from less than 1 GeV to 10²⁰ eV. The flux φ is approximated between 10 GeV and 10¹⁵ eV by φ ∝ E^−2.7, where the exponent 2.7 is the spectral index and for energies above 10¹⁶ eV until

∼10¹⁹ eV it is ∼3.1. The steepening of the flux is called the“knee”. After 5·10¹⁹ eV the evolution in energy of the spectrum is not so clear from the experiments. The highest energy cosmic rays have such large Lorentz factors that photons of the cosmic microwave background radiation (CMB) have very high energies in the rest frame of the cosmic ray and the photo-pion and photo-pair production can take place, which degrade the energy of the cosmic ray. This energy threshold is known as GZK cut-off (from the names Greisen, Zatsepin and Kuzmin). The existence of the cut-off depends upon the value ofγ of the cosmic rays. If the highest energy cosmic rays are dominated by iron nuclei rather than protons, the photo-pion production process would not be responsible for the cut-off.

One interpretation of the break in the cosmic-ray spectrum at 10¹⁵ eV is that it

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

Energy (eV) 109 10¹⁰10¹¹10¹²10¹³10¹⁴10¹⁵10¹⁶10¹⁷10¹⁸10¹⁹10²⁰

-1 sr GeV sec)2Flux (m

10-28

10-25

10-22

10-19

10-16

10-13

10-10

10-7

10-4

10-1

102

104

-sec) (1 particle/m2

Knee -year) (1 particle/m2

Ankle -year) (1 particle/km2

-century) (1 particle/km2

FNAL Tevatron (2 TeV)CERN LHC (14 TeV)

LEAP - satellite Proton - satellite Yakustk - ground array Haverah Park - ground array Akeno - ground array AGASA - ground array Fly’s Eye - air fluorescence HiRes1 mono - air fluorescence HiRes2 mono - air fluorescence HiRes Stereo - air fluorescence Auger - hybrid

Cosmic Ray Spectra of Various Experiments

28. Cosmic rays 15

[eV]

E

1013 10¹⁴ 10¹⁵ 10¹⁶ 10¹⁷ 10¹⁸ 10¹⁹ 10²⁰ ]-1 sr-1 s-2 m1.6 [GeVF(E)2.6E

1 10 102

103

104

Grigorov JACEE MGU Tien-Shan Tibet07 Akeno CASA-MIA HEGRA Fly’s Eye Kascade Kascade Grande IceTop-73 HiRes 1 HiRes 2 Telescope Array Auger

Knee

2nd Knee

Ankle

Figure 28.8:The all-particle spectrum as a function ofE(energy-per-nucleus) from air shower measurements [90–105].

and confinement in the galaxy [109] also need to be considered. The Kascade-Grande experiment [100] has reported observation of a second steepening of the spectrum near 8×10¹⁶eV, with evidence that this structure is accompanied a transition to heavy primaries.

Concerning the ankle, one possibility is that it is the result of a higher energy population of particles overtaking a lower energy population, for example an extragalactic flux beginning to dominate over the galactic flux (e.g. Ref. 106). Another possibility is that the dip structure in the region of the ankle is due topγ→e⁺+e⁻energy losses of extragalactic protons on the 2.7 K cosmic microwave radiation (CMB) [111]. This dip structure has been cited as a robust signature of both the protonic and extragalactic nature of the highest energy cosmic rays [110]. If this interpretation is correct, then the galactic cosmic rays do not contribute significantly to the flux above 10¹⁸eV, consistent with the maximum expected range of acceleration by supernova remnants.

The energy-dependence of the composition from the knee through the ankle is useful

February 8, 2016 19:55

Figure 1.8: Left: Flux of cosmic rays measured by various experiments shown together [10].

The energy scale of CERN and Tevatron are also marked. The green dashed line represents an energy spectrum E⁻³. Right: zoom of the cosmic-ray flux at higher energies observed on ground and multiplied by E^2.6[11]. φ(E)·E^2.6should be more independent of the energy of the particle and it can show additional features in the spectrum.

represents the energy at which cosmic rays can escape from the galaxy. It is expected that the cosmic rays with greater energies would display significant anisotropy if they originated from within the galaxy. The diffusive acceleration model of cosmic rays can explain the observation of cosmic rays until 10¹⁶−10¹⁷eV. In fact from the first Maxwell equation, the electric and magnetic fied in order of magnitude are:

E∼B·U (1.26)

where U is the velocity of the shock. The maximum acceleration energy of a particle of charge Ze, subject to the force F of this electric field will be then:

E_max= Z

Fdx = Z

Ze Edx = Z

Ze BU dx = ZeBUL (1.27) where L is the accelerator size. For a young supernova the acceleration time is t≈10³ years, B∼ 10⁻¹⁰T and U ∼10⁴km/s. For a nucleon at the speed of light, E_max ≈ 10¹⁶ eV.

Nuclei like carbon and oxygen are accelerated even to higher energies. In fact the so- calledknee in Fig. 1.8 appears almost at 10¹⁵−10¹⁶ eV and it is higher for nuclei than

22

protons (the integrated spectrum is dominated by protons). Observed energies of 10²⁰ eV can be reached by protons only if in Eq. 1.27 the accelerator shock has a velocity U∼c. Such velocities can be found in pulsars, active galactic nuclei, γ-ray bursts but not supernova remnants in our galaxy. But if the accelerated particles are iron nuclei, they can reach this energies with sources in our galaxy.

The cosmic-ray spectra for different nuclear species are summarized in Fig. 1.9. The 2 28. Cosmic rays

whereE is the energy-per-nucleon (including rest mass energy) and α (≡γ+ 1) = 2.7 is the differential spectral index of the cosmic-ray flux and γ is the integral spectral index. About 79% of the primary nucleons are free protons and about 70% of the rest are nucleons bound in helium nuclei. The fractions of the primary nuclei are nearly constant over this energy range (possibly with small but interesting variations). Fractions of both primary and secondary incident nuclei are listed in Table 28.1. Figure 28.1 shows the major components for energies greater than 2 GeV/nucleon. A useful compendium of experimental data for cosmic-ray nuclei and electrons is described in [1].

Figure 28.1: Fluxes of nuclei of the primary cosmic radiation in particles per energy-per-nucleus are plotted vs energy-per-nucleus using data from Refs. [2–13].

The figure was created by P. Boyle and D. Muller.

The composition and energy spectra of nuclei are typically interpreted in the context of propagation models, in which the sources of the primary cosmic radiation are located within the Galaxy [14]. The ratio of secondary to primary nuclei is observed to decrease with increasing energy, a fact interpreted to mean that the lifetime of cosmic rays in the galaxy decreases with energy. Measurements of radioactive “clock” isotopes in the low energy cosmic radiation are consistent with a lifetime in the galaxy of about 15 Myr [15].

February 8, 2016 19:55

Figure 1.9: Cosmic-ray fluxes from hydrogen until iron measured by various experiments. Pic- ture taken from [11].

chemical abundance integrated over the energy is shown in Fig. 1.10 in the solar sys- tem and in the galaxy. The most abundant cosmic rays are hydrogen (∼ 90%) and heavier nuclei (mainly helium). Immediately one can see in Fig. 1.10 the difference in the lithium, beryllium and boron abundances in the two environment, as well as in the sub-iron elements. This is due to the spallation of the most abundant cosmic nuclei, such as carbon, oxygen and iron, with the interstellar medium in the galaxy. One detail of the data is particularly important, the ratio of the unstable isotope ¹⁰Be to stable

9Be, which is discussed in the next section following [9].

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

100 T.K. Gaisser, T. Stanev / Nuclear Physics A 777 (2006) 98–110

spectrum above 10¹⁸eV that may be related to a transition from particles of galactic origin to those accelerated in extra-galactic sources. The question of whether there is a transition to cosmic rays of extra-galactic origin, and if so where it occurs, is of considerable interest.

Finally, the question of whether the spectrum extends beyond 10²⁰eV is currently the fore- most problem in high-energy particle astrophysics because of the difficulty of accounting for the absence of energy loss by protons in the microwave background radiation if the spectrum is not suppressed above this energy.

In what follows we discuss the three energy regions in order. A common theme is use of the primary composition as a clue to the nature of the sources of the particles.

2. Galactic cosmic raysE <10¹⁴eV

A classic problem in nuclear astrophysics is the determination of the cosmic-ray source abundances [5,6]. This requires a model of the galaxy, including the spatial distribution of cosmic-ray sources; density, composition and ionization state of the interstellar medium;

and the strength and topology of the magnetic field. Important recent investigations of cosmic-ray propagation from two different viewpoints may be found in Refs. [7,8]. Here we give only the main points in a simplified form. The starting point is a determination of the abundances of different nuclei near the solar system (but outside the heliosphere).

Fig. 2 shows the elemental abundances in the cosmic radiation. The overabundance by several orders of magnitude of secondary elements such as lithium, beryllium and boron

Fig. 2. Comparison of Solar system [9] and cosmic-ray elemental abundances. Nuclear abundances are from [10];

protons and helium are from [11,12].

Figure 1.10: Comparison between the chemical abundances measured near the solar system (but outside of the heliosphere) in black, and in the solar system in green. Picture taken from [12].

1.3.1 Confinement of cosmic-rays

We define the production rate through spallation of nucleus i from a nucleus j with higher atomic mass, with probability P_ji in a timeτ_j:

C_i=X

j>i

P_ij

τ_jN_j. (1.28)

The transfer equation for nucleus i will be (nothing else than a balance equation):

− N_i

τ_esc(i) + C_i− N_i

τ_spall(i) = 0⇒N_i= C_i

1

τesc(i)+ _τ ¹

spall(i)

(1.29) where τ_spal is the spallation time for nucleus i. For a radioactive nucleus j there is an additional term that takes into account its decay:

− N_j

τ_esc(j)+ C_j− N_j

τ_spall(j)− N_j

τ_r(j) = 0⇒N_j = C_j

1

τesc(j) +_τ ¹

spall(j)+_τ¹

r(j)

(1.30) If we assume for the beryllium isotopesτ_spall τ_esc:

N(¹⁰Be) N(⁷Be) =

1 τesc(⁷Be) 1

τesc(¹⁰Be)+_τ ¹

r(¹⁰Be)

C(¹⁰Be)

C(⁷Be) . (1.31)

24

In 1983, the ratio 10Be+^107BeBe+⁹Be = 0.28 was measured and reported by J. Simpson [14].

Inserting this value in Eq. 1.31 givesτ_esc≈2·10⁷ years. This is an example of how the measurements of cosmic rays help in understanding the Universe.

1.4 Cosmic-ray detection on ground through Extensive Air Showers (EAS)

In 1934 the Italian physicist Bruno Rossi was investigating the problem of why two Geiger counters placed at a distance could give coincidence signals. In 1937 the French Pierre Auger, not aware of Rossi’s study, performed more in detail the same observation and he concluded that this was due to extensive air showers (EAS) originated from a primary cosmic ray, which interacted on top of the atmosphere with its nuclei. A single cosmic ray impinging with the atmosphere produces a cascade in the air and detectors very far from each other could give coincidence signals produced by the charged component of the shower (Auger tested it with a distance of 300 m). The initial growth of the cascade is exponential until the typical energy per particle is degraded to about 1 GeV in the case of pion production. The greater the energy of the primary particle is, the wider will be the extension of the shower. The components of this extensive air shower produced by energetic particles are hadronic and electromagnetic particles: the atmosphere acts as a calorimeter with more than 20 km depth. A scheme of a shower originated by a charged particle and a figure of an EAS are shown in Fig. 1.11. The

Figure 1.11: Left: scheme of the components of an air shower generated by a charged cosmic ray. Picture taken from [2] Right: a picture that should give an idea of the size of an EAS on Earth.

components of the shower arrive to the surface of the Earth in “packages” and the