A New Measurement of Low Energy Antiprotons in the Cosmic Radiation

PETTER HOFVERBERG

Doctoral Thesis Stockholm, Sweden 2008

Doctoral Thesis A New Measurement of Low Energy Antiprotons in the Cosmic Radiation

Petter Hofverberg

Particle and Astroparticle Physics, Department of Physics Royal Institute of Technology, SE-106 91 Stockholm, Sweden

Stockholm, Sweden 2008 Cover illustration: The launch of the Resurs DK1 satellite from Baikonour Cos- modrome, Kazakhstan. Photo by Prof. Mark Pearce.

Akademisk avhandling som med tillst˚and av Kungliga Tekniska Högskolan i Stock- holm framlägges till offentlig granskning för avläggande av teknologie doktorsex- amen fredagen den 28 november 2008 kl 13.00 i sal FB52, AlbaNova Universitets Centrum, Roslagstullsbacken 21, Stockholm. Avhandlingen försvaras p˚aengelska.

ISBN 978-91-7415-170-1 TRITA-FYS 2008:48 ISSN 0280-316X ISRN KTH/FYS/--08:48--SE

c Petter Hofverberg, November 2008 Printed by Universitetsservice US AB 2008 Abstract

New measurements of the antiproton flux and the antiproton-to-proton flux ratio at the top of the atmosphere between 80 MeV and 2.0 GeV are presented. The measurement was conducted from July 2006 to March 2008 with the PAMELA satellite experiment. This is a period of minimum solar activity and negative solar polarity and the PAMELA measurement is the first observation of antiprotons during this particular solar state. The PAMELA instrument comprises a permanent magnet spectrometer, a scintillator based time-of-flight system, an electromagnetic calorimeter and an anticoincidence shield. These detectors can identify antiprotons from a background of cosmic-ray electrons and locally produced pions. The PAMELA instrument is mounted on the Resurs DK1 satellite that was launched from the Baikonur Cosmodrome on June the 15th into a semi-polar orbit with an inclination of 70◦. During approximately 500 days of data collection 170 antiprotons were identified. The derived antiproton spectrum shows a steep increase up to 2 GeV as expected for pure secondary production of galactic antiprotons. The antiproton flux is over-estimated by most current models of secondary production compared to PAMELA results. There are no indications of the excess of antiprotons at low energy predicted by theories of primordial black hole evaporation. The antiproton-to-proton flux ratio is in agreement with drift models of solar modulation, which are also favoured by recent PAMELA measurements of the positron fraction.

iii iv Contents

Abstract iii

Contents v

Introduction 1

1 Cosmic rays 5 1.1 Thebirthandaccelerationofcosmicrays ...... 5 1.2 Propagationinourgalaxy ...... 9 1.2.1 Thepropagationequation ...... 9 1.2.2 Fittingmodelstodata...... 11 1.3 Cosmicraysintheheliosphere ...... 14 1.3.1 Solarmodulation...... 14 1.3.2 Geomagneticﬁeldeﬀect ...... 20 1.3.3 Radiationbelts ...... 21 1.4 Antiprotons in the cosmic radiation ...... 25

2 The PAMELA experiment 29 2.1 Missionoverview ...... 30 2.2 Scientificobjectives...... 31 2.3 Thedetector ...... 33 2.4 Themagneticspectrometer ...... 34 2.4.1 Themagnet...... 36 2.4.2 Thesilicontrackingsystem ...... 38 2.4.3 Trackeralignment ...... 39 2.5 Thetimeofflightsystem ...... 40 2.6 Thecalorimeter...... 43 2.7 Theanticounters ...... 45 2.7.1 Activity in the anticounters during flight ...... 47 2.7.2 The use of the anticounter subsystems in flight ...... 48 2.7.3 Monitoring of the anticounter detectors ...... 48 2.8 Theneutrondetector...... 52 2.9 Thedataacquisitionsystem...... 52

v vi Contents

3 Proton and antiproton selection 55 3.1 Introduction...... 55 3.2 Trackercriteria ...... 58 3.2.1 Basictrackerselection ...... 59 3.2.2 Additionaltrackerselection ...... 59 3.2.3 Trackerantiprotonselection ...... 60 3.3 ToFsystemcriteria...... 62 3.3.1 Multipleparticlerejection ...... 62 3.3.2 ToFantiprotonselection...... 63 3.4 Calorimetercriteria...... 65 3.4.1 Lepton and hadron interactions in the calorimeter . . . .. 65 3.5 Selectinggalacticparticles ...... 73 3.6 Anticountercriteria ...... 74 3.7 The selected antiproton and proton candidates ...... 75 3.8 Electroncontamination ...... 75 3.9 Pioncontamination...... 79 3.9.1 Simulation ...... 79 3.9.2 Validation of the pion simulation at low energy ...... 81 3.9.3 Validation of the pion simulation at high energy ...... 83 3.9.4 The simulated pion contamination in the antiproton sample 84 3.9.5 Estimation of the pion contamination in ﬂight ...... 84 3.9.6 The pion contamination in the antiproton sample ...... 88 3.10 Theﬁnalantiprotonandprotonsamples ...... 88

4 Selection efficiencies 91 4.1 Concerningerrors...... 91 4.2 Trackerefficiency...... 92 4.2.1 Selecting an experimental proton sample ...... 93 4.2.2 The efficiency of the basic trackerselection ...... 96 4.2.3 The efficiency of the additional tracker selection ...... 98 4.2.4 Thetotaltrackerefficiency ...... 98 4.2.5 Biasesinthetrackerefficiency ...... 99 4.3 ToFefficiency...... 102 4.3.1 Selectingaprotonsample ...... 103 4.3.2 The dE/dx selectionefficiency ...... 103 4.3.3 The number of hit paddles selection efficiency ...... 104 4.3.4 Themassselectionefficiency ...... 105 4.3.5 ThetotalToFefficiency ...... 105 4.4 Calorimeterefficiency ...... 106 4.4.1 Calorimeterprotonefficiency ...... 108 4.4.2 Calorimeter antiproton selection efficiency ...... 110 4.4.3 Validationofthecorrectionfactor ...... 111 4.5 Triggerefficiency ...... 112 4.6 Totalselectionefficiency ...... 112 Contents vii

5 The p/p¯ ratio and p¯ flux 115 5.1 Correctionfactors ...... 115 5.1.1 Thegeometricalfactor...... 116 5.1.2 Transmission through the geomagnetic field ...... 119 5.1.3 Livetimeoftheexperiment ...... 119 5.1.4 Hadronicinteractions ...... 120 5.1.5 Energylossintheinstrument ...... 122 5.2 The number of p and ¯pat the top of the atmosphere ...... 127 5.3 Theantiprotonflux...... 128 5.4 Theantiproton-to-protonfluxratio ...... 129 5.5 Antiprotonmeasurements ...... 129

6 Discussion and conclusions 141

Acknowledgements 161

List of ﬁgures 163

List of tables 167

Bibliography 169 viii Introduction

Outline of the thesis

This thesis describes a study of antiprotons in the cosmic radiation. To put this subject into context, an overview to the field of cosmic rays is given in the first chapter. Emphasis is here put on the knowledge that can be gained about our universe from the observation of antiprotons with an Earth-orbiting satellite. Chapter 2 introduces the satellite and the instrument that have been used for the detection of antiprotons. The use of each of the sub-detectors for the analysis is presented in detail. The performance of the anticounter detectors in flight are covered as these were built by the astroparticle physics group at KTH, Stockholm. The remaining chapters describe the physics analysis and the results. Chapter 3 introduces the selection procedures that have been developed to select antiprotons among the vast quantity of cosmic rays that have been detected by the instrument. An extensive analysis of the contamination of electrons and primarily pions in the selected antiproton sample is also included here. The selection procedures all have an efficiency which has to be taken into account when reconstructing the number of antiprotons traversing the instrument. These selection efficiencies are estimated in chapter 4. All pieces of the analysis is then put together in chapter 5: the number of detected antiprotons and protons are compensated for detection efficiencies, for biases in the selection and other physical and instrumental effects, and the antiproton flux and the antiproton proton flux ratio is derived. The results are then discussed in comparison with previous measurements and theoretical models. Chapter 6 gives a summary of antiproton measurements and restates the most important results of the thesis.

The authour’s contribution

My work at the Particle and Astroparticle Physics group at KTH began in July 2003 when I started my diploma work for SEASA [1] - a scintillator based detector array for extensive air-showers. This work ﬁnished in December the same year and shortly afterwards I started a PhD position in the same group. The ﬁrst year as a PhD student was mainly dedicated to the PAMELA experiment. The anticoincidence

1 2 Contents detectors, which were built by my group in Stockholm, were being finalized and I was responsible for the software of the Digital Signal Processor of the read-out board for the anticounters. This software controls the in-flight behaviour of the detectors, in particular the data-taking- and calibration- mode of the detectors. This code has now been running in orbit for more than two years without failing. A significant amount of time was also spent in the INFN Laboratories in Rome where the integration of the PAMELA experiment took place. My responsibilities at that time was to interface the AC detectors with the PAMELA CPU, and to fine-tune the performance of the detector. As the PAMELA detector was waiting for shipment to the launch site in Khaz- akstan, I devoted increasingly more time to the SEASA experiment. The small scale of the SEASA experiment has allowed me to be involved in practically all as- pects of it. I have been responsible for the software development for the embedded Linux computer that controls the GPS system, the electronics board and the data handling to the SEASA data server. I have worked on integrating and testing the GPS system. I have designed a data acquisition and databasing system based on ROOT, and coupled to that, a monitoring tool to check the performance of the detector stations. I have performed hands-on work to get the detector stations up and running. More over, I have been solely responsible for the data analysis. This work was presented in my Licentiate thesis, which was defended in May 2006. A short summary of this work has been included in appendix A. The PAMELA experiment was launched in June 2006, shortly after defending my licentiate thesis. I was present at the downlink center NTsOMZ in Moscow when the first downlink of data from the satellite was made. My first assignment was thus to do shift-work at NTsOMZ to monitor the performance of the experiment. As the representant of the Stockholm group, my main concern was the flight behaviour of the anticoincidence detector. I therefore wrote the software for monitoring the detector in flight, and procedures for long term evaluation of the anticounter calibration. Some of this work is presented in this thesis. After the first months of the PAMELA mission, I started working on a simulation for estimating the pion contamination of the low energy antiproton selection. This task required a substantial amount of time due to the scale of the simulation work. It formed a good basis for the physics analysis which started later - the low energy antiproton selection. This has formed the major work during the last year, and has been made in collaboration with collegues in Italy and Germany. In particular, I have spent six months in Florence, Italy, working with the group responsible for the magnetic spectrometer. A number of trips has also been done to Trieste, Italy. This close collaboration between the groups in the PAMELA collaboration has been invaluable for the analysis and the thesis. My work has resulted in a number of reports, publications and presentations. A selection of them is presented below. Contents 3

Publications

• P. Hofverberg et al ’The antiproton-to-proton flux ratio between 80 MeV and 2 GeV.’, Proc. 37th COSPAR, Montreal, Canada, 2008. Submitted to Adv. Space. Res., November 2008. • P. Hofverberg et al ’Measurements of low energy antiparticles with the PAMELA experiment’, Proc. European Cosmic Ray Symposium, Kosice, Portugal, August, 2008. • O. Adriani et al ’The first observation of an anomalous positron abundance in the cosmic radiation’, arXiv:0810.4995, submitted to Nature. • O. Adriani et al ’A new measurement of the antiproton-to-proton flux ratio up to 100 GeV in the cosmic radation’, arXiv:0810.4994,submitted to Phys. Rev. Lett. • P. Picozza et al ’PAMELA - A Payload for Antimatter Matter Explo- ration and Light-Nuclei Astrophysics’, Astroparticle Physics 27 (2007) 296. • P. Hofverberg and M. Pearce, ’Cosmic Ray Anisotropy Studies with the Stockholm Educational Air Shower Array’, Proc. European Cosmic Ray Conference, Lisbon, Portugal, September 2006. • P. Hofverberg et al., ’The Data Acquisition System of the Stockholm Educational Air shower Array’, IEEE Trans. Nucl. Sci., Vol. 52, No. 6 (2005). • P. Hofverberg et al., ’First Results from the Stockholm Educational Air Shower Array (SEASA)’, Proc. International Cosmic Ray Confer- ence, Pune, India, August 2005. • S. Orsi et al.,’Pre-flight Performance Studies of the Anticoincidence Systems of the PAMELA Satellite Experiment’, Proc. International Cosmic Ray Conference, Pune, India, August 2005.

Presentations

• Max Planck Institute, Heidelberg, Germany. April 29th, 2008. Invited semi- nar, ’First results from the PAMELA experiment’. • 21st European Cosmic Ray Symposium, Kosice, Slovakia. September 9-12, 2008. Contributed talk, ’Measurements of low energy antiparticles with the PAMELA experiment’. • 29th International Cosmic Ray Conference, Pune, India. August 3-10, 2006. Contributed talk, ’First results from the Stockholm Educational Air Shower Array (SEASA)’ 4 Contents

Posters

• IEEE-NSS Dresden, Germany. October 19-25, 2008. Contributed poster, ’In-Flight Performance of the PAMELA Anticoincidence System’. • COSPAR 2008, Montreal, Canada. July 13-20, 2008. Contributed poster, ’The antiproton-to-proton ﬂux ratio between 80 MeV and 2 GeV’. • ECRS Lisbon, Portugal. September 5-8, 2006. Contributed poster, ’Cos- mic Ray Anisotropy Studies with the Stockholm Educational Air Shower Array’. • IEEE Real Time Conference, Stockholm, Sweden. June 4-10, 2005. Con- tributed poster, ’The Data Acquisition System of the Stockholm Ed- ucational Air shower Array’. Chapter 1

Cosmic rays

Nature has provided us with a source of sub-atomic particles, some particles hav- ing energies greatly surpassing what can be achieved by man-made accelerators. Although these ‘cosmic rays‘ have been known for over ninety years many basic questions regarding their nature and origin remains to be answered. This chapter aims to give an overview of the life of a cosmic ray; from acceleration at the source and propagation through the interstellar medium, to arrival at the solar system and the journey to Earth. When applicable, the focus lies on antiparticles and in particular on antiprotons.

1.1 The birth and acceleration of cosmic rays

Stars are the factories of the universe, producing the heavy elements we see on earth through fusion of lighter elements. During these processes, gravitational pressure is counteracted by the radiation pressure from fusion processes, and the star is in equilibrium. When the fusion of one element ends, the gravitational pull has no counteracting pressure and the star contracts. As the temperature and pressure inside the core increases, the fusion of a heavier element starts, and the contraction temporarily stops. Heavier and heavier nuclei are then produced by the steadily increasing intensity of the fusion. This escalation culminates in the production of 56Ni, which decays to 56Fe. At this point fusion stops, as iron cannot produce more energy through this process. The only thing holding back the collapse of the core is the pressure from electron degeneracy. If the mass of the core is larger than the Chandrasekhar limit1, the core will continue collapsing, further increasing the pressure and temperature. At this point, the temperature will be large enough to allow photo-disintegration of iron into lighter elements and free neutrons. Free electrons will recombine with protons, producing neutrons and neutrinos. Even though these two processes tends to lower the pressure and temperature, the rapid collapse of the core makes the total pressure roughly constant. As the core falls

1about 1.4 solar masses.

5 6 Chapter 1. Cosmic rays towards its centre, the outer layers are still relatively undisturbed. When the core reaches a radius of about 50 km, the density reaches the nuclear density, and the collapse is suddenly halted by strong force interactions and degeneracy pressure of neutrons. The core bounces back and creates a shock-wave carrying approximately 1051 J of energy, heating and ejecting the outer layers of the star. This matter starts its expansion in space - the supernovae explosion. Depending of the mass of the supernova, a newly born neutron star, black hole or a gas of dust is left behind.

This is a violent way a star can end its life and throw out a large part of its bulk matter in the process, becoming a supernovae. The shock ahead of a supernova remnant (SNR) is believed to be the primary acceleration site for cosmic rays. Supernova remnants have high magnetic fields, are sufficiently large and live long enough to be able to carry the acceleration process to high energies. Calculations [2] show that an acceleration efficiency of only 1 % would be enough to explain the total energy of cosmic rays in the galactic disc. The acceleration mechanism is believed to be first order Fermi acceleration, where particles are reflected between upstream and downstream regions of the shock front, gaining energy at each passing proportional to the velocity of the plasma flow. A attractive feature of this theory is that it naturally produces a power law energy spectrum, as observed. Calculations predict [3] that cosmic rays could be accelerated up to 1014 eV at supernova remnants with this acceleration process, and could thus explain the cosmic ray energy spectrum up to the “knee” - the break in spectral index around this energy of the cosmic ray spectrum. Figure 1.1 shows the measured cosmic ray energy spectrum, ranging over 10 orders of magnitude in energy and over 30 in flux, making it a formidable task to fully understand. The spectrum is rather featureless but two “kinks” can be seen, at the knee slightly above 1014 eV and at the “ankle” at 1018 eV. These energies are thought to be the limit of one type of accelerator, possibly supernovae in the first case, and a beginning of another, creating these shapes in the spectrum. Before 1995, there were many theories describing acceleration at SNR, but little evidence. To prove that SNR are really the acceleration site of cosmic rays there must be a way of directly “see” high energy cosmic rays and associate them to the SNR. One way to do that is to look for the synchrotron radiation that is emitted by ions when accelerated in the magnetic fields of the SNR. The characteristic 13 2 frequency of radiated synchrotron photons is νc =1.61 × 10 × B × E [3], where B is the magnetic field in Gauss and E the particle energy in GeV. Assuming a magnetic field of 10 µG and a maximum cosmic ray energy of 1014 eV, the spectrum of the radiated photons should span from radio up to the X-ray domain. However, observed synchrotron radiation is almost exclusively from electrons as the synchrotron energy loss is inversely proportional to the particle mass squared, 2 2 7 making electrons loose mp/me = 10 times more energy than protons, and even more than heavier ions. Thus, to prove that also nuclei are being accelerated, additional evidence is needed. 1.1. The birth and acceleration of cosmic rays 7

Figure 1.1. The cosmic ray energy spectrum measured at the top of the atmosphere [4].

The ASCA satellite measured the X-ray spectrum from supernova SN1006 in 1995 [5], as presented in Figure 1.2. This was the first experiment that had sufficient angular resolution to be able to separate the core from the rims of the SNR. A thermal spectrum was seen from the core, dominated by emission lines characteristic of highly ionized elements. However, from the rims, whose surface brightness is an order of magnitude higher than in the central regions, a virtually featureless spectrum was noticed. By observations of the radio spectrum of SN1006 made by the Rosat High Resolution Imager, it was shown that there is a strong correlation between the X-ray and radio surface brightness from the rims [6]. A natural explanation is then that the excess rim emission is due to synchrotron emission for accelerated electrons within the shock region. The X-ray spectrum was shown to be flat up to 20 keV, which corresponds to electrons of energy > 200 TeV. As first order Fermi acceleration does not differentiate between electrons and ions, there are good reasons to believe that ions, or cosmic rays, are accelerated to the same energies at these sites. This is therefore a key piece of evidence of cosmic ray acceleration up 8 Chapter 1. Cosmic rays to the knee by SNR. An additional argument for cosmic ray acceleration from SNR recently came from the HESS air Cherenkov telescope which measured the gamma-ray component of SNR RX J1713.7-3946 [7] and found a shell structure very similar to what ASCA had seen but at gamma-ray energies. The data was tested for two scenarios: one where the gamma rays are produced by high energy electrons through inverse Compton scattering, and another where the gamma rays are due to neutral pion decay from proton-proton interactions. The data favoured the latter case, and another piece for understanding cosmic ray acceleration was found.

Figure 1.2. An X-ray picture of the supernova SN1006 observed by ASCA. The bright regions in the picture shows the locations of the expanding shock which are believed to be the site of acceleration of cosmic rays[5].

Recently, the Chandra experiment, with its superior angular resolution compared to ASCA, found that the outer shells in SN1006 are not homogeneous but consists of several thin X-ray filaments [8]. Their results suggest that the acceleration occur in more compact regions, with a larger efficiency than previously believed. The HESS and Chandra observations show that the field of acceleration of cosmic ray is developing fast, providing data with better precision, and in new energy regimes. In particular, the angular precision of ground based observation techniques, such as HESS, has improved significantly and are now getting close to space based experiments. The HESS experiment is currently upgrading the telescope array with a fifth telescope. This will lower the energy threshold of the array and increase the separation capabilities between the neutral pion decay- and inverse 1.2. Propagation in our galaxy 9

Compton scattering- scenario respectively. A direct proof for cosmic ray acceleration at SNR would be the detection of neutrinos created in charged pion decay. This could be achieved in the near future as large volume neutrino telescopes that are currently under construction start to operate [9] [10].

1.2 Propagation in our galaxy

A major part of the lifetime of a cosmic ray is spent propagating through interstellar space. Although thought of as an empty void, interstellar space is pervaded by gas and magnetic ﬁelds which act as targets for interactions. The simple observation that the observed composition of cosmic rays are diﬀerent from that of the solar proves the importance of propagation in the interstellar medium.

Practically all our knowledge about cosmic ray propagation comes from studies of the secondary component of cosmic rays - particles resulting from interactions of primary particles with the interstellar medium. Additional information about propagation also arises from studies of γ-rays and synchrotron radiation from electrons. These two latter issues will however not be treated here. A comprehensive review of the field can be found elsewhere [11]. It is useful to point out why secondary particles are a good probe of propagation: if the primary component of cosmic rays is measured, the secondary component can be calculated using models of propagation, cross-sections, and interstellar gas densities. A measurement of the secondary component then allows for a comparison of the derived results and the accuracy of the models can be checked and parameters fine-tuned. The chemical composition of cosmic rays is remarkably similar to that of the matter in the solar system, but with a few important exceptions: the light elements lithium, beryllium and boron, and also the elements just lighter than iron (referred to as sub-Fe elements), are over abundant in the cosmic rays, as illustrated in Figure 1.3. The explanation of this difference is that these particles are being created in spallation processes with heavier nuclei in the interstellar medium. When this first was seen, an important conclusion was that cosmic rays were of galactic origin, by the following argument: since the spallation cross sections are fairly well known, the amount of matter traversed by the primary particles to produce the observed amount of secondaries can be estimated. Calculations show [12] that this density of matter is between 5-10 g/cm2. As it would take approximately 1010 years for cosmic rays to propagate through this amount of matter in the intergalactic medium, cosmic rays then have to be of primarily galactic origin.

1.2.1 The propagation equation At present it is believed that the diﬀusion model with the possible inclusion of convection gives the best description of cosmic ray propagation. The propagation 10 Chapter 1. Cosmic rays

Figure 1.3. The chemical composition of matter in the solar system (blue) and in cosmic rays in the galaxy (red), using Si = 100 as reference. From [13]. equation for cosmic rays of a speciﬁc type can be written in the general form [11]

δφ(~r, p, t) = q(~r, p, t)+ ∇∗~ (D ∇~ φ − V~ φ) δt xx (1.1) δ 2 δ 1 δ p ~ ~ 1 1 + p Dpp 2 φ − pφ˙ − (∇∗ V )φ] − φ − δp δp p δp h 3 i τf τr

Where φ(~r, p, t) is the cosmic ray density with total momentum p at position ~r, q(~r, p, t) the source term, Dxx the diffusion coefficient, V~ the convection velocity, Dpp the diffusive reacceleration coefficient, τf the time scale for loss by fragmentation and τr the time scale for radioactive decay. A more thorough description of the propagation equation is given elsewhere [11]. From this equation it is clear that the transport of cosmic rays is determined by three processes:

• Diffusion The diffusion of cosmic rays results from particles scattering on galactic magnetic fields. Diffusion explains the highly isotropic distribution of cosmic rays seen on earth, and is also the reason why they are retained so well in the galaxy. 1.2. Propagation in our galaxy 11

• Convection While the diffusion process is considered the most important process for cosmic ray propagation, there could also be a significant contribution from convection. Galactic winds are seen in many galaxies and support this idea [14]. In our own galaxy there is evidence from X-ray images for winds in the galactic centre, but the claims that cosmic rays are being convected are disputed [15]. Convection does not only transport cosmic rays, but can cause adiabatic energy loss as the wind speed increases. A good probe of convection is the ratio between secondary and primary cosmic rays. A pure convective transport is energy independent. If the diffusion rate decreases with decreasing energy, convection will eventually take over and the ratio would flatten at low energies. This is indeed what is being observed (see for example Figure 1.4) but convection does not match data particularly well.

• Reacceleration In addition to diffusion, scattering on magnetic fields can cause a stochastic acceleration of cosmic rays. This phenomena is referred to as reacceleration. Reacceleration may explain the peaks in the ratios of secondary to primary cosmic rays about 1 GeV (see Figure 1.4), if this process becomes significant at these energies. However, reacceleration cannot serve as the main mechanism of acceleration in the galaxy, at least not in the energy range 1 − 100 GeV. In that case higher energy particles would spend a longer time in the galaxy which would increase the relative abundance of secondary cosmic rays as energy increases, contrary to observation (see Figure 1.4).

1.2.2 Fitting models to data As mentioned in Section 1.2.1, the most favoured model for cosmic ray propagation is at present the diﬀusion model. There are two formalisms that are widely used to describe this model, the leaky box model (LBM) and the weighted slab model (WSM). The LBM consists of a volume with an absorbing wall around it in which the particles freely propagate. At every step the particle can escape with a certain probability Pesc, regardless of position. The characteristics of the model are de- 2 termined by the escape length x = vρτesc, measured in g/cm , where τesc is the escape time, v the particle velocity and ρ the average gas density of the interstellar gas in the galaxy, including the halo. The escape time may be a function of particle momentum and charge, but the fundamental feature of this model is that τesc is independent of spatial coordinates. Therefore, the LBM cannot predict anisotropies which is otherwise a powerful tool in cross-checking models against data. The WSM was suggested to solve the problem of a system of coupled transport equations for all isotopes involved in the process of nuclear fragmentation. The technique consists of transporting the cosmic ray beam through a interstellar gas of a certain thickness (x). The solution is then integrated over all values of x weighted with a distribution function G(x) derived from an astrophysical propagation model. 12 Chapter 1. Cosmic rays

The standard realization of the WSM assumes small energy loss or gain, and the model therefore breaks down for small energies where this approximation is no longer valid. Both models predict an exponentially decreasing path length distribution, but diﬀer in how the mean path lengths vary as a function of energy. To tune the models a number of free parameters exists that can be constrained from measurements. The most common are:

• the ratio of (stable) secondary to primary cosmic ray ﬂuxes

• the ratio of (unstable) secondary to primary cosmic ray ﬂuxes

• the ﬂuxes of antiprotons and positrons

• cosmic ray anisotropy

• properties of diﬀusive galactic gamma-rays

The ﬁrst three will be dealt with in detail below. For further details regarding cosmic ray anisotropy and diﬀusive galactic gamma-rays, see [11].

Stable secondary/primary ratios The most quoted ratio is the Boron-Carbon (B/C) ratio as Boron is entirely secondary and measurements are more accurate than other ratios and are available up to about 100 GeV. A summary of B/C measurements is shown in Figure 1.4, together with four different models of propagation, all in the framework of the weighted-slab formalism [16]. The Standard Diffusion Model (SDM) (solid line) is a pure diffusion propagation model. This model introduces an ad-hoc break in the diffusion constant Dxx to account for the observed decrease in the B/C ratio at low energies. However, once introducing the break, the model is not only consistent with the B/C ratio, but also with other secondary/primary ratios. There are additional problems with this model as the diffusion coefficient must have a strong dependence on rigidity to account for the bend at high energies, and this produces anisotropies which have not been observed. The Wind Model introduces a galactic cosmic ray wind (convection) directed outward from the galactic plane. The decrease of the B/C ratio arises naturally in this model, as convection implies an energy independent escape from the galaxy, and at low energies where the diffusion rate decreases it starts to dominate. However, it does not reproduce the decrease accurately as seen in Figure 1.4. A promising model is the Minimal Reacceleration Model. It assumes no convective motion in the system, and as in the SDM diffusion occurs by scattering on random hydromagnetic waves. The difference with this model is that the waves are allowed to move randomly, producing a stochastic acceleration of cosmic rays. This modifies the spectrum of primaries and secondaries below 10 GeV/n and reproduces the data for the B/C ratio well. Also, this model has no problems accounting for small anisotropies of cosmic rays and is thus the favoured 1.2. Propagation in our galaxy 13

Figure 1.4. The measured ratio of fluxes of secondary boron to primary carbon nuclei[17]. model among the ones shown here. However, the model is not in good agreement with data from HEA03 on the sub-Fe/Fe ratio [18]. The difference between the models are small at the energies which have been observed so far, and it is difficult to exclude models at this stage. It is clear that measurements of secondary to primary ratios at higher energies are needed, as the models starts to diverge at that point. The PAMELA mission will provide data from 100 MeV to 250 GeV per nucleon and could therefore clarify the situation.

Unstable secondary/primary ratios

Unstable cosmic rays can be used as “clocks” to derive the age of cosmic rays at detection. The unstable secondary nuclei that have a lifetime large enough to make them useful as probes are 14C, 10Be, 26Al, 36Cl and 54Mn. 10Be has the longest lifetime, 3.9 × 106 years, and is the most frequently measured isotope. 10Be is produced in signiﬁcant quantities in the spallation of carbon and oxygen, together with the stable isotope 9Be. Knowing the cross-sections for these processes, the produced relative abundance of 10Be to 9Be can be calculated. Comparing this ratio with the measured ratio of the 9B/10B then gives the age of the cosmic rays. Combining this with the column density of matter, that can be deduced from the stable secondary-primary ratios as described above, the halo size can be derived. The measurement of unstable secondaries can therefore give information about the propagation region of cosmic rays. 14 Chapter 1. Cosmic rays

Antiprotons The flux of antiprotons, produced in inelastic collision of cosmic rays, is one additional variable which when used together with secondary to primary ratios can constrain propagation models. The reacceleration model, that successfully reproduced the secondary-to-primary ratios of nuclei, produces too few antiprotons. Models without reacceleration reproduce the antiproton flux, but not the low energy decrease of the secondary to primary ratios. To fit a model with both measurements, breaks in the diffusion coefficient and injection spectrum have to be introduced, which would suggest new phenomena in particle acceleration and propagation. Another solution could be that there is a local source of C that would eliminate the excess of B which appears when propagation parameters are fitted to thep ¯ data. This model can describe current data well, but at the cost of introducing more parameters. Accurate measurements of thep ¯ flux are hence fundamental for testing current propagation models.

1.3 Cosmic rays in the heliosphere

After propagating through interstellar space, cosmic rays encounter the solar system. This can be thought of as a bubble of plasma moving around in the local interstellar medium, fed by the constant outflow of particles and photons from the sun. Embedded in the flow is the heliospheric magnetic field which pose another obstacle for the cosmic rays entering the solar system. Traveling to the Earth, cosmic rays move upstream in the particle flow, and this significantly alters the flux and shape of the low energy cosmic ray spectrum. Upon arrival, the magnetic field of the Earth poses the final obstacle before reaching the top of the atmosphere.

1.3.1 Solar modulation There is an outflow of particles from the sun which is commonly called the solar wind. This was predicted in 1958 by E.N. Parker [19] as he wrote down the equations of hydrodynamics for a hot plasma in the gravitational field of the sun. The following year, the Soviet satellite Lunik II measured a flux of particles emanating from the sun. The solar wind is now known to be released radially from the sun, and traces out a spiral pattern as the sun undergoes one revolution every 26 days. Interacting with the interstellar medium, it creates a bubble of magnetized plasma which includes all the planets in our solar system. This is explained in detail in Figure 1.5. The solar wind affects the environment on and around the earth in a variety of ways. One striking effect important for the work in this thesis is the anti-correlation between solar activity and the intensity of cosmic rays at the top of the atmosphere. Solar activity is measured by the number of sun-spots observed on the surface of the sun, while the intensity of cosmic rays generally is measured by the neutron or muon 1.3. Cosmic rays in the heliosphere 15

Figure 1.5. The top figure shows the heliosphere - the bubble of magnetized plasma that is created by the outflow of matter from the surface of the sun. The heliosphere forces the local interstellar medium (LISM) to flow around it. At large radial distances the LISM pressure causes the solar wind speed to decrease to subsonic speeds and a heliospheric shock is created - the solar wind termination shock. At even larger radial distances a contact surface is created, called the heliopause,which separates the solar matter from the interstellar matter. As the solar wind is interrupted by the Earth’s geomagnetic field the magnetosphere is created, shown in the bottom figure. As in the case of the heliosphere, a termination shock is created when the solar wind is decelerated to sub-sonic speeds. The magnetopause is defined as the boundary where the Earth’s magnetic field is balanced by the pressure of the solar wind. Inside the magnetopause, shielded from the solar wind, there are several distinct regions, where the most important is the two radiation belts surrounding the Earth. From [20]. 16 Chapter 1. Cosmic rays counting rate at ground level which are secondary or tertiary products from cosmic ray interactions at the top of the atmosphere. Figure 1.6 shows measurements of the sun-spot number and neutron monitor intensity versus time [21] and a strong correlation is evident. The greater the solar activity, the more effective is the solar wind in preventing cosmic rays from reaching the earth. This phenomena is known as the Solar Modulation.

Figure 1.6. The top curve shows the cosmic ray ﬂux from the neutron monitor in Climax, Colorado [22]. The middle curve shows the annual mean variation in cosmic ray ﬂux as measured by ionization chambers. The bottom curve shows the relative sunspot number.

Solar modulation strongly suppresses the sub-GeV part of the interstellar particle spectrum (the typical energy loss is a few hundred MeV [23]). A large fraction of the low energy particles are prevented from reaching the inner parts of the heliosphere, and higher energy particles loose some of their energy, replacing the low energy particles to some extent. The effect of the modulation on one type of particle therefore depends on the form of its interstellar spectrum. For example, the antiproton spectrum is more stable under modulation than the proton spectrum since the antiproton spectrum is harder at low energies. The number of particles shifted down from higher energies is comparable to the number of low energy particles suppressed by the solar wind. This is important for the time evolution of the antiproton-proton ratio and will be explained in detail later. The standard procedure to account for solar modulation in experiments has been to use a three-dimensional spherically symmetric model of solar modulation first developed by Gleeson and Axford [24]. The model accounts for three processes: • cosmic ray diffusion through the heliospheric magnetic field (HMF) 1.3. Cosmic rays in the heliosphere 17

• convection by the outward motion of the solar wind

• the adiabatic cooling, or deceleration, of the “cosmic ray gas” in this ﬂow

The first two processes lead to a rigidity dependent decrease in particle flux while the third process leads to a decrease of the energy of the particles. A realisation of this model in practice is the extensively used “force field approximation” where the effect of the solar modulation is expressed by a single parameter φ, depending only on particle diffusion. Experimentally φ is determined by fitting the observed spectrum of one type of particle with the known interstellar spectrum. A particle with the interstellar energy EIS and flux ΦIS then reaches the Earth with reduced energy E and reduced flux Φ, where Z and m is the charge and mass of the particle respectively.

E = EIS − |Z|φ (1.2) (E2 − m2) Φ(E)= 2 2 × ΦIS(EIS) (1.3) (EIS − m )

However, particle drifts in the HMF have been pointed out [25] as an important effect as the modulation becomes charge-sign dependent: oppositely charged particles drifts in opposite directions along the HMF lines. As described above, particle fluxes at the top of the atmosphere experience a maximum at solar minimum and a minimum at solar maximum. Due to features of the drift, during positive solar polarity (most recently during 1990-2000) a plateau like maximum occurs for positive particles. On the contrary, a peak-like maximum occurs for negative particles. At negative solar polarity (as the current solar epoch, 2000-2010) the opposite occurs. This can be seen in Figure 1.7 (top). Consequently, as protons are more heavily modulated than antiprotons, for reasons explained above, the antiproton-proton ratio will modulate approximately as the proton component, The antiproton-proton ratio should therefore be roughly constant during the positive solar polarity, but experience a more dramatic evolution during the negative solar polarity. This is illustrated in Figure 1.7 (bottom). The BESS experiment has measured the antiproton-proton ratio from 1995 to 2005, and the result [26], which is seen in the lower part of Figure 1.8, agrees well with the main characteristics of the drift model, briefly described above: a plateau like shape during the positive phase of the Sun, followed by a sudden increase at the solar field reversal. The BESS data then favours the drift model by Bieber [27], where the ratio is decreasing until the solar minimum, rather than the model proposed by Moskalenko. If the model by Bieber is correct, an increase of the antiproton proton ratio should follow the solar minimum. The PAMELA mission has measured the antiproton proton ratio from June 2006 to March 2008, a period of solar minimum, and can shed further light on this issue. This is presented in this thesis. 18 Chapter 1. Cosmic rays

Figure 1.7. Top: The predicted dependence of antiproton and proton intensity at 1 AU dependence upon solar tilt angle (the angle between the rotational axis and the magnetic axis, which increases with solar activity). Bottom: The predicted dependence of antiproton-proton ratio at 1 AU upon solar tilt angle. From [27]. 1.3. Cosmic rays in the heliosphere 19

× 10 -5 6

5 Previous BESS (A>0) Previous BESS (A<0) 4 BESS Polar (A<0) 3 Moskalenko et al. Bieber et al. 2 Antiproton/Proton Ratio 1

R model Tilt angle 60 L model 40

0 1996 1998 2000 2002 2004 2006 Year

Figure 1.8. Top: The antiproton-proton ratio measured by BESS in sex flights from 1995 to 2005 [26]. The ratio is shown for the energy 0.7 GeV, at which the particle flux is strongly effected by the solar modulation. Two different drift models are shown, by Moskalenko [28], and Bieber [27]. The data favours the latter, especially in light of the latest data-point from BESS polar. Bottom: Time variation of heliospheric current sheet tilt angles for two different models [29][30]. 20 Chapter 1. Cosmic rays

1.3.2 Geomagnetic field effect The last obstacle for cosmic rays before being detected by an Earth orbiting satellite or a high altitude balloon is the geomagnetic field. Charged particles traversing the magnetic field experience a force that results in a curved path and low energy particles can thus be prevented from reaching the atmosphere. The geomagnetic cutoff is largest at the equator and diminishes closer to the poles. The range is between about 15 GV at the equator to 1 GV at around 60◦ latitude. Stoermer found an analytical solution to the equation of motion in an offset dipolar field [31], which is a reasonable simplification of the Earth’s magnetic field. He found the cutoff rigidity could be expressed as

4 M cos λB Rc = 2 3 1/2 2 (1.4) 2r [1 + (1 − cos λBsinθsinφB) ] where Rc is the geomagnetic cutoff rigidity (in MV/c), M is the magnitude of the dipole moment in G cm3, λ is the latitude from the magnetic equator, ǫ is the angle from the zenith direction, ζ is the azimuthal angle measured clockwise from the direction to the north magnetic pole and r is the distance from the dipole center in centimeters. The dependence on φB contains the so called east-west effect: that the cutoff is larger from directions easterly for positively charged particles for the same zenith angle compared to westerly directions2. The Stoermer equation is only a rough approximation. The main discrepancies between the model and reality is that an offset dipole is an approximation of the Earth’s magnetic field. Another important shortcoming of the model that tends to underestimate the cutoff is that the so called earth shadow is not accounted for in the Stoermer formula. The earth shadow arises from that trajectories that would go through the Earth are disallowed. This can be understood from Figure 1.9. High energy particles (low numbers in the figure) travel in relatively simply trajectories to the earth. As the rigidity of the particle decreases the trajectory becomes more complicated, even forming intermediate loops (high numbers in the figure). When these loops intersect the earth, the orbit is forbidden. However, the change from allowed to disallowed trajectories is not well defined in rigidity. After a band of disallowed trajectories at some rigidity level, trajectories can again be allowed. This structure of allowed and forbidden trajectories in the energy spectrum is called the cosmic ray penumbra. The penumbra is hence the region where the transmission of charged particles decreases from fully allowed to totally forbidden. This region can in some cases, far from the equator, be surprisingly large. The penumbra consists of both stable and unstable regions. The stable regions generally contains simple trajectories while the trajectories in the unstable regions often are very long and complex. This makes it difficult to obtain a single simple geomagnetic cutoff. This is usually solved by only selecting particles well above the penumbra.

2This eﬀect can used to measure properties in the cosmic rays, for example [32] measured the east west eﬀect for leptons to estimate the electron to positron ratio. 1.3. Cosmic rays in the heliosphere 21

Figure 1.9. Calculated trajectories for cosmic rays of diﬀerent energies arriving at the Earth [33]. The energy decrease with trajectory number.

A precise measurement of the geomagnetic cutoff can be obtained by the brute force method of tracing cosmic ray trajectories in a model of the Earth’s magnetosphere. If an antiproton back-traced from the Earth reaches a certain large distance (rfree) from the Earth it is assumed that the trajectory of a proton penetrating to the initial position from interplanetary space is allowed. Using this back-tracing method, [33] computed world grids of vertical cutoff energies at 450 km height for various conditions of magnetic activity. The two top pictures in Figure 1.10 shows two of these world grids, one when the magnetic activity is quiet and the other with a highly disturbed magnetic field. The plots show that the cutoff increases up to about 15 GV around the equator for either quiet or disturbed magnetic fields. However, the cutoffs close to the pole change more dramatically between the two cases. During magnetic active periods the cutoffs are significantly lower. The method of back-tracing is extremely CPU intensive and the Stoermer approximation is therefore still used in many applications. The Stormer equation can be further simplified when a vertical geomagnetic cutoff is desired. Equation 1.4 then becomes, if introducing the McIlwain parameter L [34]

2 Rc = 14.9/L (1.5)

1.3.3 Radiation belts Decelerated cosmic rays or particles resulting from interactions in the upper atmosphere can be trapped by in the earth’s magnetic ﬁeld and remain there (theoretically) indeﬁnite. These particles are generally referred to as trapped particles. The motion of these particles consists of three components (see Figure 1.11):

• gyration about magnetic ﬁeld lines

• movement up and down magnetic ﬁeld lines 22 Chapter 1. Cosmic rays

Figure 1.10. World maps of vertical geomagnetic cutoﬀs at 450 km for quiet (top) and disturbed (bottom) magnetic conditions, calculated with the back-tracing method. From [33]. 1.3. Cosmic rays in the heliosphere 23

• slow longitudinal drift around the Earth, westward for positive particle and eastward for electrons.

Trajectory of trapped particle

Mirror point

Drift of electrons Drift of protons Magnetic ﬁeld line

Figure 1.11. The motion around magnetic ﬁeld lines for so called trapped particles. Because of magnetic mirroring, these particles can remain trapped for up to several years (indeﬁnite theoretically), bouncing between the north and the south side of the equator. From [35].

The resulting trajectories lie on toroidal surfaces, called drift shells, centred on the Earth’s dipole centre. Two such radiation belts have been discovered: the inner and outer Van Allen radiation belts. While the inner belt consists of protons and electrons, the outer belt solely consists of electrons. The trapped proton component (above 10 MeV) can be seen in Figure 1.12 (top). Higher energy protons remain closer to the earth than lower energy protons and are distributed over a smaller region. Figure 1.12 (bottom) shows the trapped electron population. Contrary to the proton population, this is distributed over two zones of high intensity: below altitudes of one Earth radius and above two Earth radii. They are separated by a lower intensity region called the slot region. As for protons, high energy electrons are confined more to the inner belt, and low energy electrons to the outer belt. At high latitudes the outer electron belt reaches down to very low altitudes. The radiation belts affect the radiation environment for satellite experiments such as PAMELA which traverses them regularly. Figure 1.13 shows the rate of particles hitting the side plastic scintillator in PAMELA as a function of orbital position. A striking feature is the high flux of particles slightly below the centre of the map, east of Brazil. This is due to a depression in the magnetic field caused by the separation of the dipole centre from the Earth’s centre and the inclination of the magnetic axis with respect to the rotation axis. As the trapped particle distribution is tied to the magnetic field, the radiation environment experiences a large peak when the inner electron belt and the proton belt comes closer to the earth. This is called the South Atlantic Anomaly (SAA). Two bands of slightly increased fluxes can also be seen, around latitudes of ±60◦. These are the outer electron bands, 24 Chapter 1. Cosmic rays

Figure 1.12. The trapped proton (top) and electron (bottom) component in the radiation belts. From [36]. stretching down towards the Earth. These bands give rise to northern and southern lights (aurora). This phenomena occurs as electrons collide with atoms in the atmosphere which then deexcite and emit photons, visible as large bands of green and red colour at ground. Trapped particles can be hazardous to equipment as the ionising doses in these regions can be high. Other problems can for example be surface charging from low energy electrons or Single Event Upset (SEU) from high energy protons in the inner belts. 1.4. Antiprotons in the cosmic radiation 25

Latitude 60 10 5 40

20 10 4 0

-20

-40 10 3

-60

-80 10 2 -150 -100 -50 0 50 100 150 Longitude

Figure 1.13. Rate (Hz) of particles traversing the side anticounter scintillator in the PAMELA experiment as function of geographical latitude and longitude. From [37]

1.4 Antiprotons in the cosmic radiation

Cosmic ray antiprotons have attracted much attention since its discovery by Golden et al [38] in 1979. Much of the attraction comes from the idea that antiprotons could be a good probe for exotic physics. The fundamental question therefore concerns their origin, if all antiprotons can be accounted for by secondary production mechanisms alone, or if there is a primary component from for example the evaporation of primordial black holes or dark matter annihilations - the latter one of the most intriguing issues in physics today.

The secondary component of antiprotons is produced in interactions between high energy cosmic rays and the interstellar medium. The simplest production reaction is pp → pppp¯, with a energy threshold of 7 proton masses. The kinetic energy of an antiproton produced in inelastic collisions depends on the energy of the primary proton (Ep). It can be shown [23] that an antiproton is produced with a minimum kinetic energy of

mp (Ep¯)min ≈ (1.6) Ep − 6mp

The minimal antiproton kinetic energy therefore decreases with increasing proton energy. Since the galactic proton spectrum falls rapidly at high energy, the antiproton spectrum decreases at low energy. Similarly, the antiproton spectrum falls off at high energy, reflecting the decreasing primary proton spectra. The antiproton spectrum exhibits a maximum at around 2 GeV where the combined result of these 26 Chapter 1. Cosmic rays two effects is at a minimum. The existence of the peak at 2 GeV has been well es- tablished by a series of flights of the BESS experiment and is shown in Figure 1.14. Secondary production can thus be considered the major production mechanism of antiprotons in the cosmic radiation. There is still room for a primary component of cosmic ray antiprotons. Mea- surements at low energy are complicated by the steeply falling flux of particles and by the influence of solar modulation, which is significant below 1 GeV. Present measurements at low energy are all conducted with balloon-borne instruments which introduce a large uncertainty due to the residual atmospheric overburden and none of the experiments have managed to collect a significant statistics of antiprotons. The results at low energy are therefore not clear, and a primary contribution of antiprotons could be present. Primary antiprotons at low energy could arise from the evaporation of primordial black holes [48]. Hawking [49] first showed that black holes emit particles and evaporate by quantum effects. Although the evaporation rate is very small for massive black holes, primordial black holes (PBH), which may have formed in the early Universe, have a small enough mass to produce an observ- able signal of antiprotons. The antiproton spectrum from PBHs has been shown to increase with decreasing kinetic energy thus providing a distinct signature below 1 GeV. Searches for low energy cosmic ray antiprotons could constrain the density of PBHs, or more importantly, demonstrate their existence. The BESS experiment has measured the antiproton spectrum down to 0.1 GeV and the results at low energy are inconclusive. The BESS 1995+1997 flights measured a slight excess below 1 GeV, but subsequent flights failed to confirm the claims. The BESS 1995+1997 flights were however the only flights during a solar minimum, where a signal would be most evident. The PAMELA mission has performed the first measurement of the antiproton spectrum at a solar minimum since the 1995+1997 BESS flights and is thus well suited to confirm or dispute the results. This study is presented in this thesis. There could also be a signal in the high energy part of the antiproton spectrum from annihilation of dark matter particles. The position of acoustic peaks in the Cosmic Microwave Background (CMB) and the existence of large scale structure suggests that dark matter is non-relativistic and non-baryonic. The most popular candidate in literature is weakly interacting massive particles (WIMPs) such as the lightest superpartner in supersymmetric theories [50]. Such massive relic particles could have been produced early in the Universe and diluted during the inflationary era. These particles could leave a signal in the antiparticle cosmic ray spectra. The neutralino is the lightest superpartner in supersymmetric models of dark matter. This is a majorana particle and two particles can thus annihilate producing jets of secondary particles and among them antiprotons which can be observed in the cosmic radiation. This is illustrated in Figure 1.15. Another interesting candidate for dark matter is the lightest Kaluza-Klein particle in models with universal extra dimensions. Annihilations of Kaluza-Klein particles in the galactic halo may give a significant contribution to the antiproton flux above about 10 GeV [51]. 1.4. Antiprotons in the cosmic radiation 27

Figure 1.14. The experimentalp ¯-ﬂux before the PAMELA mission (BESS00 and BESS99 [26], AMS [39], CAPRICE98 [40], BESS95+97 [41], MASS91 [42], CAPRICE94 [43], IMAX92 [44]) along with models of purely secondary antiproton production [45] (solid lines [45], dashed lines [46]) and for purep ¯ production (dotted line: [47], assuming the annihilation of neutralinos of mass 964 GeV/c2). 28 Chapter 1. Cosmic rays

~χ q

Z, h, H, A

q ~χ

Figure 1.15. Production of antiprotons from neutralino annihilation [37].

The experimental data at high energies is currently poor. The results from CAPRICE98, which end at 50 GeV, suggest a slight increase than what is expected from a purely secondary production, although the statistics is low (see Figure 1.14). The PAMELA mission is currently measuring the antiproton flux with significantly better precision than previous measurements. PAMELA will be able to measure the antiproton flux over a larger energy range, and with an order of magnitude improvement in statistics at high energy, compared to all previous measurements. Chapter 2

The PAMELA experiment

The PAMELA experiment is the most recent endeavour of the Wizard Collaboration which has a long history in cosmic ray research. Starting almost 15 years ago around R. Golden, who first discovered antiprotons in the cosmic radiation [38], the group has successfully built and flown a number of balloon experiments (MASS89 [52], MASS91 [42], Tramp-Si 93 [53], CAPRICE94 [43] and CAPRICE98 [40]) with the common purpose of increasing our understanding of the cosmic radiation. The Wizard Collaboration has pioneered the use of detection techniques such as electromagnetic calorimeters, spectrometers with a superconducting magnet and ring imaging Cerenkov detectors in balloon flights. The PAMELA experiment is the second satellite experiment of the collaboration, after NINA [54], and the most advanced to date. The PAMELA collaboration consists of a number of European groups: The Royal Institute of Technology (Stockholm, Sweden), INFN and Physics Depart- ment of University of Rome (Italy), Moscow Engineering and Physics Institute (Russia), INFN and Physics Department of University of Florence (Italy), IFAC (Florence, Italy), INFN and Physics Department of University of Trieste (Italy), INFN and Physics Department of Naples (Italy), University of Siegen (Germany), INFN National Laboratory of Frascati (Italy), INFN and Physics Department of University of Bari (Italy), Ioffe Physical and Technical Institute (St Petersburg, Russia) and Lebedev Physical Institute (Moscow, Russia). The opportunity to fly on a Resurs DK1 satellite is given by the RIM (Russian- Italian Mission) collaboration, which since 1995 has allowed Italian cosmic-ray experiments on the Russian space station MIR (SilEye experiments [55], [56]). In this chapter, an overview of the PAMELA mission is presented, including a description of each sub-detector in the instrument.

29 30 Chapter 2. The PAMELA experiment

2.1 Mission overview

The PAMELA experiment is the main piece of scientiﬁc equipment on-board the Resurs DK1 satellite. The primary task of the satellite is to take high resolution images of the surface of the Earth. The satellite and rocket, a Soyuz FG, were built by TsSKB Progress (the Central Specialized Design Bureau - Progress) in Samara, Russia. When completed, the satellite was transported to Baikonour Cosmodrome1, where it was launched on the 15th of June 2006. The satellite has since been in orbit, and the expected lifetime is at least 3 years, limited by the drag from the residual atmosphere and the solar wind.

Figure 2.1. The launch of the Resurs DK1 satellite hosting PAMELA from the Baikonour Cosmodrome, Kazakhstan [57].

PAMELA is housed in a pressurized container ﬁlled with nitrogen kept at 1 atmosphere pressure and a temperature between 0◦C and 45◦C. The part of the container which is located above PAMELA, and thus blocks the acceptance, is made of aluminium and is 1.7 mm thick. The container is connected to the satellite body with a mechanical arm which can move the container from the parked position in which it is kept during launch to the position kept during data acquisition mode where the container points out to space (Figure 2.2). The satellite has a total weight of 6.7 tonnes and a height of 7.4 m. The PAMELA detector is 1.3 m tall and has a mass of 470 kg. The average power consumption of PAMELA is 355 W, which is provided by the solar panels or batteries

1Baikonour Cosmodrome is famous for launching the satellite that brought the first man in space - Jurij Gagarin on the 12th of April, 1961. 2.2. Scientific objectives 31 of the host satellite. Data are down-linked to the mass memory of the satellite during acquisition, and radio-linked down to earth when passing the ground center in Moscow, NTsOMZ. The satellite is travelling in a semi-polar orbit (70◦) at an altitude between 350 km and 600 km when passing the north and south pole respectively. The orbital period is about 90 minutes. The trajectory will thus go through regions with varying geomagnetic cutoff, which affects both the flux and spectra of the incident cosmic rays. The trajectory also pass the outer electron belt and the South Atlantic Anomaly (SAA).

2.2 Scientiﬁc objectives

The primary aim of PAMELA is the detection of antiparticles in the galactic cosmic radiation. PAMELA is extending the energy range of antiprotons and positrons compared to previous measurements, to both lower and higher energies. After three years of data taking, the statistics will surpass previous experiments by more than an order of magnitude, and with a better precision as no compensation for atmospheric overburden needs to be done. Additional goals include the search for anti-nuclei, in particular anti-Helium, and the measurement of light nuclei. The expected detection capabilities can be summarized as • the measurement of the antiproton spectra from 80 MeV to 190 GeV (current limits are 200 MeV to 40 GeV). • the measurement of the positron spectra from 50 MeV to 270 GeV (current limits are 70 MeV to 40 GeV) • the search for anti-nuclei with a sensitivity better than 10−7 in the anti-helium ratio, from 100 MeV/nucleon to 70 GeV/nucleon (current limit 6.8 × 10−7). • the measurement of the proton spectra from 80 MeV to 700 GeV. • the measurement of the electron spectra from 50 MeV to 400 GeV. • the measurement of the combined electron and positron spectra up to 2 TeV. • the measurement of nuclei up to Z = 6 from 100 MeV per nucleon to 250 GeV per nucleon. A plethora of diﬀerent physics topics can be addressed with these measurements. A hot topic is antiparticles produced from exotic sources such as primordial black holes [48] or the annihilation of super-symmetric [46] or Kaluza-Klein [51] dark matter. This could produce an excess of antiprotons or positrons compared to what is expected from purely secondary production [58][23][28]. The PAMELA mission occurs during a minimum in the solar activity cycle which is optimal to study solar modulation, and in particular drift eﬀects. Ear- lier data, from in particular the BESS mission, supports solar modulation models 32 Chapter 2. The PAMELA experiment

Figure 2.2. The Resurs DK1 satellite. The lower picture shows the different satellite components. The upper picture shows the position of the container housing PAMELA during launch and acquisition mode [57]. 2.3. The detector 33 with a component of charge dependent drifts included [26]. PAMELA is measuring the positron-electron and antiproton-proton ratio, which are both sensitive probes for charge dependent solar modulation. Previous measurements have all been conducted with high altitude balloons, during a short period of time. PAMELA is the first experiment that measures these parameters during an extended period of time. The results will therefore greatly aid the study of solar modulation, and in particular, being able to differentiate between current drift models in literature [58][27]. The measurement of different species of nuclei is a powerful way of constraining cosmic ray propagation models. PAMELA studies nuclei up to Z = 6, and therefore also one of the most common variables in models of cosmic ray propagation - the Boron to Carbon ratio. PAMELA data is therefore expected to further constrain current models of cosmic ray propagation. Another goal of PAMELA is to measure the antihelium/helium ratio with a sensitivity of the order of 10−7. This is a factor of 50 improvement to contemporary results. The ability to measure the combined electron and positron spectra up to 2 TeV will allow for the investigation of a possible local component of cosmic rays [59].

2.3 The detector

PAMELA consists of a number of sub-detectors each with a specific task. The core of the PAMELA instrument is the magnetic spectrometer which measures particle rigidity by means of the bending of a particle trajectory in a magnetic field, generated by a permanent magnet. A schematic drawing of PAMELA is shown in Figure 2.3. The 6 detecting planes of the spectrometer, surrounded by the magnet, are clearly visible in the centre. A ToF system is employed to provide a trigger for the experiment and is composed of three planes of scintillator, referred to as S1, S2 and S3 (from top to bottom in the figure). This system also provides albedo particle rejection, and a measurement of particle velocity at low energy. Both the ToF system and the spectrometer are used to measure ionization energy in the detecting layers. This can be used to differentiate between particles of different absolute charge, and at low energies, between hadrons and leptons. An electromagnetic calorimeter is located below the spectrometer. This device can separate hadrons and leptons by means of their interaction pattern when traversing the orthogonal layers of absorber and silicon detectors inside the detector. The spatial development of a shower is reconstructed by the layers of silicon detectors which are divided into strips in alternating directions for each plane. Below the calorimeter are mounted the tail-catcher (S4) and the neutron detector, which are both used to enhance the lepton-hadron separation capability of the calorimeter. The tail-catcher is composed of layers of scintillators read out by photomultipliers. Surrounding the magnet (CAS) and on top of it (CAT) are the first two sets of scintillators that form the anticoincidence detector. The third (CARD) surrounds the open cavity between S1 and S2. These detectors are used to discriminate against 34 Chapter 2. The PAMELA experiment events that do not enter the acceptance cleanly. This could for example happen if a particle enters the experiment through the magnet, interacts, and produces secondaries that give a trigger. The anticoincidence system is made of single sheets of plastic scintillators read out by redundant photomultipliers. This detector has been developed by the astroparticle group at KTH, Stockholm.

2.4 The magnetic spectrometer

In PAMELA, particle rigidity is determined using a magnetic spectrometer. This detector measures the magnetic deflection as a charged particle traverses a known magnetic field. The magnetic deflection η is defined as the inverse of the rigidity R, 1 q η = = (2.1) R p and is thus a combination of the particle charge (q) and momentum (p). The deflection of a particle traversing the spectrometer is derived by fitting the equation of motion of a charged particle in a magnetic field to the measured coordinates of the particle trajectory. The sign of the deflection corresponds to the sign of the electric charge of the particle, and the amount of deflection gives the rigidity, by equation 2.1. The tracker also provides a measurement of the absolute value of the charge since the ionization energy loss from particles traversing the sensitive areas of the detectors is proportional to the square of the charge. The coordinates of the particle track are measured with 6 planes of high- resolution silicon micro-strip sensors, and the magnetic field is provided by a permanent magnet with a cavity defining the acceptance of the experiment. The dimensions and geometry of the silicon detectors and the strength of the magnetic field defines two very important features of the experiment; the Maximum Detectable Rigidity (MDR) and the Geometrical Factor (G). The MDR is defined as the particle rigidity for which the uncertainty is 100 %, and therefore sets the upper limit of the rigidity reconstruction for the experiment. The Geometrical Factor is defined as the proportionality factor between the detector counting rate and the flux of particles. For straight particle tracks, G is simply the geometrical acceptance of the experiment, but for curved tracks, and thus low rigidities, the influence of the magnetic field has to be taken into account. The MDR and G are in conflict when trying to optimise the performance of the experiment. A longer cavity increases the MDR while reducing G, and a larger acceptance increases G, but reduces the MDR as it is more difficult to maintain a high magnetic field over a large area. A main objective in the PAMELA experiment is the extension of the antiproton and positron spectra to higher energies and a high MDR has therefore been favoured in designing the spectrometer. The MDR is set by the measurement error, which is comprised of two factors whose relative weight changes with momentum. At high momentum, the measurement error is mainly due to the finite spatial resolution in measuring the impact points on the detecting planes. This effect is negligible at low energies, where instead the measurement 2.4. The magnetic spectrometer 35

Figure 2.3. The PAMELA instrument [57]. 36 Chapter 2. The PAMELA experiment error is dictated by Coulomb scattering of the particle as it crosses the detecting planes. These two measurement errors, pres and pms, can be derived as ∆p σ res ∝ p (2.2) p B × L2 ∆p 1 ms ∝ (2.3) p β where L is the path length of track inside the tracker cavity, σ the position measurement error and p the momentum. These two equations shows that a long tracker cavity, with a strong magnetic field and high spatial resolution reduces the measurement error for high momentum, while a small amount of matter in the path of the particles is needed to keep the error low at low momenta. The spatial resolution of the PAMELA spectrometer has been investigated with test beams which show a resolution of (3.0 ± 0.1) µm and (11.5 ± 0.6) µm in the bending and non-bending view, respectively. The spatial resolution in the bending view is shown in Figure 2.4 (left). Figure 2.4 (right) shows the resulting deflection error versus rigidity obtained with proton test-beams. A MDR of 1 TeV can be inferred from this plot. While the upper rigidity limit for detecting cosmic ray particles such as protons, helium nuclei and heavier nuclei is directly connected with the MDR, the upper rigidity limit for the detection of their antiparticles is complicated by their low abundance in the cosmic radiation. As the rigidity increases, the tracks approach a straight line in the tracker. Due to the finite resolution of the spectrometer, a high rigidity particle can then be assigned an opposite charge due to statistical fluctuations of the reconstructed impact points in the tracker planes. As the sign of charge is the only variable used for differentiating antiprotons from protons, and since the number of protons is much larger than the number of antiprotons, this will cause a spillover of protons to antiprotons, as shown in Figure 2.5. This phenomena sets an upper rigidity limit in the antiproton study.

2.4.1 The magnet The magnetic field in PAMELA is generated by a permanent magnet made of a Nd-Fe-B alloy. The magnet is composed of 5 identical modules put on top of each other forming a tower 436 mm high. The detecting planes of the spectrometer are housed in 9 mm gaps between each module, and at the top and bottom of the magnet. Each module is made of prisms, glued together to form a module of dimensions 228 × 240 × 80 mm3, as shown in Figure 2.6. A picture of the entire configuration is shown in Figure 2.6. Not shown in the picture is the ferromagnetic screens that ensure the residual magnetic field outside spectrometer to be below the levels set for a safe working of the satellite and other parts of the experiment. The resultant magnetic field is almost uniform and points in the negative Y- direction. Charged cosmic ray particles traveling in the Z direction bend in the X-direction, which therefore is referred as the bending view. The magnetic field in the cavity has been measured prior to launch using a Hall probe. Using a precision 2.4. The magnetic spectrometer 37

450

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Figure 2.4. Top: The spatial resolution of the tracker in the bending view defined as the standard deviation of a Gaussian fit to the residuals of the true and reconstructed position of a particle traversing the silicon planes. The line shows a Gaussian fit. Bottom: the deflection error ∆R measured by the magnetic spectrometer as a function of rigidity (R) obtained with a proton test-beam. The dashed line corresponds to ∆R = R. The function which is fitted to the measured error is determined by the contributions from multiple scattering and spatial resolution, given by equations 2.2. The intersection of the two curves give the maximum detectable rigidity. From [60]. 38 Chapter 2. The PAMELA experiment

103

102 Entries 10

-0.1 -0.08 -0.06 -0.04 -0.02 0 deflection (GV-1 )

Figure 2.5. The deflection distribution for negatively- and positively- charged reconstructed events that did not produce an electromagnetic shower in the calorimeter [60]. Strict requirements are put on the quality of the reconstructed track. The white area shows the proton distribution which “spill-over” to the negative side and thereby sets an upper limit in the antiproton study. positioning system with a mechanical arm for the probe, the x,y and z components of the magnetic field could be measured in a three dimensional grid consisting of 67367 points, 5 mm apart in each direction. Some of the results are shown in Figure 2.7. An average magnetic field of 0.43 T was measured.

2.4.2 The silicon tracking system

The detecting units of the spectrometer consist of 6 planes of silicon sensors evenly placed within the magnetic cavity with a spacing of 89 mm. Each plane consists of 6 sensors with a surface area of 53.33 × 70.00 mm2 and is 300 µm thick. An aluminium frame holds the sensors together, as shown in Figure 2.8. The silicon sensors are divided into two sets of strips, perpendicular to each other. This allows the determination of the spatial information in both the x- and y-view of the impact point of an incident particle by looking at which strip collected the ionization charge of the passing particle. A total of 2035 strips are implanted on the x-view, with a pitch of 25.5 µm, and 1024 strips in the y-view, with a pitch of 66.5 µm. The 2.4. The magnetic spectrometer 39

Figure 2.6. Left a prototype of a magnet segment, surrounded by its aluminium frame. Right The permanent magnet, composed of 5 identical segments placed in a tower. The tower is mounted on the base plate which connects the PAMELA instrument with the rest of the satellite. The dimensions of the magnetic cavity are 436 × 132 × 162 mm3 which provides a distance of 445 mm between the ﬁrst and last tracker plane. From [57]. measured spatial resolution on ground, measured in test-beams, is 4 µm in the x-view, the bending view, and 15 µm in the y-view.

2.4.3 Tracker alignment The nominal positions of the 36 sensors of the tracking system is known from the mechanical design of the spectrometer. In this ideal picture, the strips in each sensor is parallel and aligned with the strips in the other sensors in the plane, and the six planes are parallel and aligned with respect to each other. In reality, displacements of the sensors are introduced during construction, shipment and, in particular, the launch. Corrections to the sensor positions are therefore needed. Since the coordinates of the impact points can be measured with an accuracy of a few micrometers, the miss-alignment has to be corrected for with a precision of that order of magnitude or better if systematic errors for high energy events are to be avoided. The alignment procedure consists of selecting particles with a known deflection and comparing the expected coordinates with the measured coordinates. From the residuals of the comparison, a χ2 can be calculated, and by then fitting the six alignment parameters (three translation coordinates and three rotation angles) that minimize the χ2, the alignment of the detector can be made. In flight, a sample of electrons is selected for the alignment procedure as the rigidity, and thus the deflection, can be measured independently using the calorimeter. The alignment precision is evaluated by dividing the flight data set in two equal parts and applying the alignment procedure to both. This produces two inde- 40 Chapter 2. The PAMELA experiment

0.6

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Figure 2.7. The measured main component (y) of the magnetic field along the cross section going through the center of the cavity. From [57]. pendent sets of alignment parameters. By then using these two sets of alignment parameters on the full data set, the systematic error due to alignment can be derived as the difference between the reconstructed deflection between the two data sets. The result is a maximum systematic error of 5 × 10−4 cGV −1. The inverse is 2000 GV/c which is two times greater than the MDR. Since the MDR depends linearly on the spatial resolution, the systematic error of the alignment is about 1.5 µm.

2.5 The time of ﬂight system

The PAMELA instrument is subject to a nearly isotropic flux of cosmic rays, but only the fraction of particles that traverse the geometrical acceptance is of interest. A trigger system ensures that the sub-detectors of PAMELA are read out only in the case of a down-going cosmic ray traversing the magnetic cavity. For this reason a Time-of-Flight (ToF) system consisting of 3 layers of scintillators is employed in PAMELA, shown in Figure 2.9. The three detecting layers, which are referred to as S1, S2 and S3, are placed on top of the experiment (S1), and above and below the spectrometer (S2 and S3 respectively). Their sensitive areas are 330×408 mm2 for S1, and 150 × 180 mm2 for S2 and S3, with a thickness of 7 mm for S1 and S3 and 5 mm for S2. Each plane is made up of two layers of BC-404 scintillator, each segmented into paddles. The first and second layer of S1, referred to as S11 and S12, consists of 8 and 6 paddles respectively, while S2 is segmented into 2 paddles, and 2.5. The time of flight system 41

Figure 2.8. One of the spectrometer planes, consisting of 6 sensors and their readout electronics, attached to an aluminium frame. From [57].

S2 into 3. The two ends of each paddle are connected to a light guide which is read out by a photomultiplier (Hamamatsu R5900U). The segmentation of one layer in a plane is perpendicular to the segmentation of the other layer. This allows for a determination of both the x and y coordinate of an incident cosmic ray crossing a plane. The main trigger conﬁguration of the experiment is the requirement of a signal in at least one of the layers in each plane. In the radiation belts and inside the South Atlantic Anomaly (SAA), the requirement on S1 is removed as this detector is saturated by low energy particles.

TRIGGERdefault = (S11 OR S12) AND (S21 OR S21) AND (S31 OR S32) (2.4)

TRIGGERSAA,rad = (S21 OR S21) AND (S31 OR S32) (2.5)

The in-flight trigger rate for the default trigger configuration is shown in Figure 2.10. As well as providing the main trigger for the experiment, the ToF system also measures the velocity and ionisation energy loss in the scintillator planes for incident particles. This two fold task is done by splitting the signal from the PMTs into two parts; one part connected to an analog-to-digital converter (ADC) which measures the amount of ionization in the scintillator, and the second to a time-to-digital converter (TDC), which provides a relative measurement of the time the particle crossed the detecting layer. The time measurement makes it possible to determine the direction of an incident particle from the order in which the scintillator planes were hit. This is of fundamental importance as a proton entering the experiment from below (so called albedo particles) would bend in the magnetic field in the same direction as a antiproton entering from above. An up-going proton is then impossible to distinguish 42 Chapter 2. The PAMELA experiment

Figure 2.9. The ToF system. The three detectors S1, S2 and S3 are seen from top to bottom. The distance between S1 and S3 is 77.3 cm. The dark gray segmented areas are the scintillator pads, where only the top layer is visible. The segmentation of the bottom layer is perpendicular to the upper layer. Each pad is connected to a light guide (light gray) with a photomultiplier at the end. From [57]. 2.6. The calorimeter 43

Figure 2.10. Trigger rate in flight, for the default trigger condition [57]. As a consequence of the geomagnetic field, the trigger rate is lowest around the equator and increase closer to the poles. The South Atlantic Anomaly (SAA) is clearly seen outside the east cost of south America. The PAMELA instrument performs the calibration at the equator, where the flux is at a minimum, which explains the drop in flux just around 0◦ latitude. from a down going antiproton, if the direction is unknown. Qualification tests have shown that he time resolution of an individual paddle is about 50 ps. The flight time between S1 and S3 of a 1 GeV proton is 3.7 ns, and albedo particles can thus be rejected with 60 standard deviations. By combining the timing information from the ToF system and the track length from the tracker system it is possible to calculate the velocity (normally scaled to the velocity of light and then referred to as beta - β) of a particle traversing the experiment. The combined time resolution of the ToF has been measured to be around 300 ps, and this gives an error in the velocity measurement as shown in Figure 2.11 below 1 GeV. A separation of positrons and protons, or electrons and antiprotons, up to approximately 1 GV/c is possible using the β-measurement. A fourth plane of plastic scintillator is included below the calorimeter. This detector, referred to as the tail catcher, detects the charged component of the shower leakage from high energy particles traversing the calorimeter. The detector has a sensitive area of 480 × 480 mm2, a thickness of 10 mm and is read out by 6 PMTs.

2.6 The calorimeter

After particle charge separation is performed in the spectrometer, the main background for the antiproton and positron studies are electrons and protons respec- 44 Chapter 2. The PAMELA experiment

β resolution

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Figure 2.11. Beta resolution below 1 GeV. The plot has been made selecting a proton sample with the tracker and calorimeter. Assuming a proton mass, the velocity could be calculated using the rigidity from the tracker, and compared with the velocity measured by the ToF system. tively. To achieve the necessary separation between leptons and hadrons an imaging electromagnetic calorimeter is employed in PAMELA. The calorimeter consists of 22 detecting planes, inserted in a 180 mm high aluminium frame. Each plane is made up of two layers of 3 × 3 silicon sensors interleaved with a 2.6 mm thick tungsten absorber. Each sensor is 380 µm thick, and has an area of 80 × 80 mm2, which results in a total detecting area for each plane of 240 × 240 mm2. The total mass of the calorimeter is about 110 kg, and the thickness corresponds to 16.3 radiation lengths (X0), and about 0.6 interaction lenghts (λl). Figure 2.12 shows the calorimeter with some of the detecting layers partially extracted. The spatial information is obtained by the implementation of 32 strips in each sensor, with a pitch of 2.4 mm. The silicon detectors are single-sided, contrary to the silicon detectors used in the spectrometer which are double-sided. Two layers are thus needed for a full spatial reconstruction of a particle shower. This is accomplished by one detecting plane, where the top silicon layer, above the tungsten absorber, is segmented in the Y-view and the bottom silicon layer in the X-view. The longitudinal and transverse segmentation, combined with the measurement of the particle energy loss in each silicon strip, allows for a high identification (or rejection) power of electromagnetic showers. This has been extensively studied using simulations and test-beams [61] and the calorimeter performance is found to be sufficient to reach the scientific goals of PAMELA, with a proton rejection of about 105 while keeping 90 % of the selected positrons. Simulations show that an electron rejection of about 105 is achieved, with a 90 % antiproton selection 2.7. The anticounters 45

Figure 2.12. The electromagnetic calorimeter. The device is approximately 20 cm tall and the active silicon layer is about 24×24 cm2. Some of the detecting planes are seen partially, or fully, inserted. The 9 sensors forming one plane are seen on the top plane. From [57]. efficiency. The calorimeter is also used to measure the energy of electron and positron showers. This allows for an independent reconstruction of the particle energy, and can thus be used to cross-calibrate the rigidity reconstruction of the tracker. The energy resolution of the calorimeter is 5.5 % up to several hundreds of GV, as shown in Figure 2.13. A self-trigger mode is implemented in the calorimeter software to extend the combined electron and positron energy range of PAMELA up to 2 TeV. A trigger signal is generated when a specific energy distribution is detected in predetermined planes within the lower half of the calorimeter. The geometrical factor provided by the calorimeter self-trigger is about 600 cm2sr, i.e about 30 times larger than the default PAMELA geometrical factor defined by the spectrometer. The simulated energy resolution is about 12 % up to 800 GeV as shown in Figure 2.13.

2.7 The anticounters

The purpose of the anticoincidence (AC) system is to discriminate against out of acceptance events and events containing multiple particles. The latter could happen when a particle interacts inside PAMELA and generates secondary particles, or when a primary particle interacts in the satellite payload and creates a shower of particles which traverse the experiment. The focus here will be on the use of the anticounters in ﬂight and only a brief introduction to the construction of the AC 46 Chapter 2. The PAMELA experiment

Figure 2.13. The energy resolution of the calorimeter [60]. The filled symbols are for normal operation (experimental data) and the open symbols are for self-trigger mode (simulations). system is provided. The reader is instead referred to [37] for a complete review of the AC system. The AC system consists of nine plastic scintillators; four of them (CAS) covering the sides of the magnet, four (CARD) surrounding the empty cavity between S1 and S2, and one (CAT) just on top of the magnet, with a rectangular hole corresponding to the acceptance of the experiment. The anticounters are illustrated in Figure 2.14, where the left picture shows the CARD anticounters during integration of the PAMELA experiment in Tor Vergata, Rome, and the right a schematic view of the CAS and CAT subsystems. For redundancy, each CAS and CARD detector is read by two photomultipliers, each connected to a different electronics board. The two electronic boards will be referred to as main or extra. In case of a failure of one of the boards or PMTs, the anticounters would still operate with an almost identical efficiency. The CAT detector is read out by 8 photomultipliers due to its irregular geometry. In a similar fashion as CAS and CARD, 4 of the PMTs are connected to main board, and 4 to 2.7. The anticounters 47 extra board. Plastic scintillators with a thickness of 8 mm are used for the anticoincidence shield. Their efficiency for detecting charged particles is measured to be 99.9 % [62]. A particle traversing an AC detector is registered as a hit if it deposits at least 0.5 MIP2 in the scintillator, which corresponds to ∼ 0.8 MeV [37]. The anticoincidence is thus a binary detector, only providing information if there was a particle traversing a scintillator or not. 50 cm

Figure 2.14. Left The anticounter detectors during integration in Tor Vergata, Rome. The CARD detectors have just been mounted between S1 and S2, the two uppermost ToF detectors. Beneath S2, the CAS detectors can be seen covering the tracker and magnet. Right A schematic view of the CAT (green) and CAS (purple) detectors. The CAT detector consists of a single piece of scintillator read out by 8 photomultipliers, while the CAS system is composed of 4 identical scintillators each covering one side of the tracker and read out by two photomultipliers.

2.7.1 Activity in the anticounters during flight The activity in the anticoincidence detectors depends strongly on particle species and energy. This is evident in the top plot in Figure 2.15 which shows the fraction of events passing basic tracker selection (see section 3.2.1) with anticounter activity, defined as the fraction of events with a signal in the anticounter, for the two subsystems CAS and (CAT+CARD). The activity is generally higher in CAS than (CAT+CARD) which is mostly due to the large number of particles back-scattered from the calorimeter. The activity in CAS increases with energy as the activity in the calorimeter increases. This effect is also seen for the (CAT+CARD) system, but is less pronounced due to the greater distance between the calorimeter and (CAT+CARD). The activity in the anticounters is larger for negatively charged particles such as electrons (the most abundant negatively charged particle) which

21 MIP equals the energy released by a minimum ionizing particle when traversing perpendic- ularly through the detector 48 Chapter 2. The PAMELA experiment interact in the first layers of the calorimeter, while protons (the most abundant positively charged particle) interact at an almost random position in the calorimeter, or not at all. The relationship between the amount of back-scattering and the activity in the anticounter detectors can more clearly be demonstrated by plotting the anticounter activity versus the number of strips hit in the calorimeter (nstrip) - a good estimator for the level of activity in the calorimeter. This is shown in the middle plot of Figure 2.15. The activity in the CAS system, which is close to the calorimeter, is seen to increase significantly with nstrip, while the (CAT+CARD) system is much less affected. The dip around 40 nstrip is due to non-interacting particles. A large peak in the anticounter activity is seen at low rigidities, for both positive and negative events. The interpretation is most likely that a large fraction of these events are secondary particles produced when primary particles hit the satellite payload and create showers of particles where at least one goes through the PAMELA acceptance and generates a trigger, while others traverse an anticounter detector. As the (CAT+CARD) system is more exposed to secondary particles from interactions above the instrument than CAS, the activity should increase more for these types of events. This is also what is seen in the top plot of Figure 2.15. Except for the very lowest energies, where particles start to bend into the magnet, activity is greater in (CAT+CARD) than CAS.

2.7.2 The use of the anticounter subsystems in flight The conclusions that can be drawn from the previous section are that the CAS and (CAT+CARD) subsystems are sensitive to different types of events. The CAS detectors surround a large amount of material, and are mounted directly above the calorimeter. There is therefore a large probability that a secondary particle, produced in interactions in the tracker or magnet, or back-scattered from the calorimeter, will traverse the CAS detector. The CARD and CAT detectors, on the other hand, are far from the dense material inside PAMELA but are instead more exposed to showers of particles coming from interactions in the roof of the pressure vessel, just above PAMELA, or in the satellite payload. The CAT and CARD detectors may therefore be used to discriminate against these latter events. The selection requirements placed on the anticounters for flight data are • For high energy events: No activity in (CAT+CARD). • For low energy events: No activity in (CAT+CARD), with the possible inclusion of CAS.

2.7.3 Monitoring of the anticounter detectors The AC detectors are exposed to vibrations during launch and to radiation and temperature variations in ﬂight. The AC detectors were built using robust materials to withstand the mechanical shocks during launch. Vibration tests have been 2.7. The anticounters 49

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Figure 2.15. The anticounter activity during flight. The sample of events used for the study is defined as all events passing basic tracker criteria (see chapter 3). Top The activity in CAS (black) and (CAT + CARD) (red). Negatively charged events are assigned a negative rigidity, and positively charged events a positive rigidity. Bottom the anticounter activity versus number of strips hit in the calorimeter. 50 Chapter 2. The PAMELA experiment conducted for the AC detector alone and for the combined PAMELA system [60]. The temperature around PAMELA in flight is controlled and has been kept within 10 degrees during the the mission. Temperature dependent effects are thus not expected to play a significant role. The particle flux in space has been simulated and the total ionising dose is expected to be around 10 Gy for a three year mission. This could potentially degrade the electronics and all components have therefore undergone radiation tests with a total does of at least 50 Gy. No degradation of the electronics was seen. Although a significant degradation of the AC detectors is unlikely, a monitoring system is needed. A LED based solution was chosen to accomplish this. The system provides a way to check the response of the detectors to a known input. During the calibration of the PAMELA instrument, LEDs, which are glued to the scintillators, are flashed for approximately 1 second while the discriminator levels are increased from zero to maximum (1 V) in 256 steps. At each step, the LEDs emit about 6500 short light pulses, whose shape and time-scale are similar to pulses generated by a minimum ionizing particle traversing the detector. The number of pulses seen by the PMTs are read out at each step, resulting in an integral spectra for each PMT. An example of such a spectra for the two PMTs of CAT4 are shown in Figure 2.16. A spectra taken on ground and in flight are shown for each detector for comparison. A degradation of a scintillator or a PMT would result in a shift of the integral curve to lower threshold values as a smaller amount of light is collected. This is indeed seen for the main CAT4 PMT, while the extra CAT4 PMT shows the opposite behaviour, with a shift to higher values, although smaller. The reason for this behaviour is unknown, but the impact to the performance of the detector is believed to be small judging from comparisons of the singles-rate of the PMT connected to the main and extra board respectively. The impact from one PMT degrading to the performance of the entire CAT detector is small as only one out of the 8 PMTs in the detector has to signal a traversing particle. As will be shown below, CAT4 is the detector experiencing the largest degradation of all anticounter detectors. As the shift of the falloff of the integral curve is used as a measure of the stability of the anticounters, it is more convenient to make a transformation to a differentiate spectra and use the position of the peak. The differential curve for one flight calibration for the CAT 4 detector is shown in bottom of Figure 2.16. A Gaussian curve is fitted to the distribution to extract the mean and standard deviation which are later used to study the performance over time. PAMELA is calibrated once every orbit, at the point of lowest cosmic-ray trigger activity, i.e the crossing of the equator at the ascending node. For every calibration, the differential spectra are made and the mean and standard deviation of each fit to the spectra are saved. A histogram of the fitted mean values is produced regularly. The time evolution of the anticounter performance is studied using these histograms. A plot of the time evolution of the anticounter performance for each PMT is shown in Figure 2.16. Each point in the plot is derived from the mean and RMS of a monthly histogram, where the mean is plotted as the value and the RMS 2.7. The anticounters 51

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Figure 2.16. Top Integral calibration curve for the CAT4 anticounter detector. The main detector is plotted on the left side, and the extra on the right side. For each detector, the integral curve for one calibration on ground (red line), and for one calibration performed late in the PAMELA flight time (black) is plotted. This particular detector shows the biggest discrepancy between flight and ground and the reason is not fully known. The stability of the anticounters over time is measured by the point in voltage where the drop of the integral curve is largest. This point corresponds to the peak of the differential spectra. The differential curve of the main and extra detector of CAT4 is shown in the lower figure. A Gaussian is fitted to the curve to determine the peak location and width, which are later used as measures of the anticounter performance. 52 Chapter 2. The PAMELA experiment as the error bars. The first point in each plot is derived with ground data, and the remaining points each corresponds to one month of flight data. As the plot shows, the anticounter system generally behaves stably. No significant changes occurred after launch. With a few exceptions, the detectors then act stably during the entire flight. Two of the detectors show non-negligible changes during the flight, CAT1 and CAT4. However, the impact to the performance of the entire CAT detector is small.

2.8 The neutron detector

The lower-most detector in the PAMELA payload is the neutron detector. The main purpose of this detector is to increase the lepton-hadron separation derived from the calorimeter by measuring the neutron component which is created in hadronic showers. The device consists of 36 gas proportional counters ﬁlled with 3He and surrounded by a polyethylene moderator and cadmium foil, as shown in Figure 2.18. The counters are arranged in two planes and have a total area of 600 × 550 mm2. The polyethylene moderator is used to slow down the neutrons and thereby increase the cross-section for interacting with the 3He in the proportional counters. In the nuclear reaction a proton and a 3H are produced, which can be detected with the proportional counters. The estimated proton rejection factor at 50 GV/c is about 10.

2.9 The data acquisition system

A schematic overview of the PAMELA data acquisition (DAQ) is shown in Fig- ure 2.19. The PSCU (PAMELA Storage and Control Unit) handles all communications, data acquisition, storage and downlink tasks. The PSCU consists of four sub-systems:

• a space qualiﬁed processor built around a CPU based on ERC-32 architecture (with no redundant back-up).

• two redundant 2 GByte mass memory modules .

• a PIF (PAMELA interface board), that performs three tasks: communications with the IDAQ (Intermediate DAQ) system, handling the interface with the mass memory, and providing the interface with the VRL (Very high-speed Radio Link) module of the satellite.

• a TMTC (Telemetry and Control) board that handles the housekeeping op- erations of PAMELA, such as alarm, temperature and voltage monitoring.

Data acquisition is performed via a 2 MByte/s interface. Upon reciept of a trigger, data from the sub-detectors are read sequentially and stored in the PSCU mass 2.9. The data acquisition system 53

Figure 2.17. The performance of the anticounter detectors during the time considered in this thesis. Each plot corresponds to a particular detector where main PMT is indicated by black and the extra PMT by red. The value and error bars of each point in a plot corresponds to the mean and RMS of the distribution of the fitted peak values of the differentiate spectra for all calibrations during a month. An exception is the first point, which is ground data. 54 Chapter 2. The PAMELA experiment

Figure 2.18. The neutron detector during assembly. The polyethylene moderator (in white) is seen, as are some of the proportional counters. memory. A few times a day, the data in the PSCU mass memory is transferred to the satellite on-board memory via a 12 MByte/s interface. The data is down-linked to ground 2-3 times a day and the total amount of data is approximately 15 MByte. Down-linked data are received by the ground station NTsOMZ in (Moscow) at a rate of about 150 Mbit/s. A ﬁrst check of the data quality and the status of the PAMELA instrument is done automatically by “quicklook” scripts which run automatically on down-linked data. Data are then transferred using GRID protocols from Moscow to the INFN facility at CNAF (Bologna, Italy) and ﬁnally distributed to local computer facilities for physics analysis.

Trigger CMD/IF CPU Timeofflight 1553B Resurs Anticoincidence PIF satellite IDAQ Spectrometer board PSCU DAQ/IF VRL bus Calorimeter Mem CPU S4 TMTC VRL Neutrondetector main spare alarms serial temperaturesensors voltagesensors contactclosures powersupply powersupply housekeeping system controlboards board main+spare main+spare serial main spare

Figure 2.19. The PAMELA data acquisition system [60]. Chapter 3

Proton and antiproton selection

This chapter describes the methods that have been developed to select a proton and antiproton sample from the data collected with the PAMELA experiment between June 15th 2006 and March 1st 2008, and an estimation of the contamination from wrongly selected antiprotons.

3.1 Introduction

Protons and antiprotons are identical particles but with opposite signs of electric charge. Charge separation is therefore a fundamental feature in an experiment measuring the proton and antiproton component individually. While the proton is the most abundant positively charged particle, antiprotons only constitute a small fraction (about 10−3) of the negatively charged part of the cosmic radiation. It is therefore rather straight-forward to select protons with a small contamination of other types of particles, but is more challenging to do the same for antiprotons. The situation can be clarified by studying Figure 3.1 which shows the particle abundances in the cosmic radiation as a function of velocity and rigidity. The figure shows the particle rigidity between 0.4 GV/c and 2.8 GV/c which is the rigidity region of interest in this thesis. Negatively charged particles are assigned a negative rigidity in the figure. The positive side of Figure 3.1 is dominated by protons and helium nuclei, with a small contribution of positrons, positive pions, helium-3, deuterium and heavier nuclei. The massive particles, predominately protons and helium nuclei, become non-relativistic at low rigidity while the light particles, pions and electrons, are relativistic in the entire energy range shown here. Massive and light particles can therefore be separated easily at low rigidity using velocity and ionization measurements. Pions are not a natural component in the cosmic radiation but are created in interactions of primary cosmic rays with the experiment or the satellite. The

55 56 Chapter 3. Proton and antiproton selection two major sources of background for the proton selection are however helium nuclei and positrons. Looking at Figure 3.1, it is evident that the major component among the negatively charged particles in the cosmic radiation are electrons. A small number of antiprotons can be observed below 1 GV/c, among electrons with a wrongly measured β. The number of antiprotons is about 0.1 % of the number of electrons. Clearly, a high electron rejection is needed to select a clean sample of antiprotons. The situation is also complicated by the presence of negative pions, which are indistinguishable from antiprotons above approximately 1 GV/c. The pion contamination is discussed in-depth in section 3.9

Figure 3.1. The velocity (β) shown as a function of rigidity for all particles in the ﬂight data sample passing basic tracker selection.

After single particle events have been selected in the ﬂight data (see section 3.2), the proton and antiproton selection has to provide a good rejection of: 1) multiply charged particles, 2) positrons and electrons and 3) pions. This is achieved by using all of the PAMELA sub-detectors. The selection can be summarized as

• Single particle selection. By using a combination of the tracker, ToF system and anticounters, a large fraction of events with additional particles in the acceptance can be rejected. This selection reduces the pion contamination signiﬁcantly as pions are created in interactions with the payload and are thus often accompanied by additional particles. 3.1. Introduction 57

• Track quality selection. A number of cuts are applied on the track reconstruction to ensure good charge sign separation and an accurate rigidity measurement.

• dE/dx measurements with the tracker and ToF system. The amount of ionization (dE/dx) in the tracker and ToF planes is used primarily to reject multiply charged particles, and secondly to reject electrons, pions and deuterium at low rigidity. Figure 3.2 shows the dE/dx distribution for all events in the ﬂight data sample passing the basic tracker selection.

• Velocity measurements with the ToF system. As was shown in Figure 3.1, velocity measurements can be used to separate particles of diﬀerent mass at low rigidity. This provides additional electron and pion rejection capabilities to the dE/dx selection.

• Calorimeter selection The calorimeter provides the main electron rejection power above 1 GV/c where the dE/dx and β rejection are poor.

Figure 3.2. The dE/dx versus rigidity for all particles in the ﬂight data sample passing basic tracker selection.

The focus of the selection is to minimize the contamination of electrons and pions. With the combination of the dE/dx, β and calorimeter selection, the electron contamination is eliminated. A residual pion contamination is however present 58 Chapter 3. Proton and antiproton selection above 1 GV/c. The contamination of pions will be described in the last section of this chapter. In the following sections, the proton and antiproton selection criteria are presented. Each section deals with the selection using one of the sub-detectors, starting with the tracker.

3.2 Tracker criteria

The tracker is used for three diﬀerent purposes in this analysis

1. Determining the particle sign of charge

2. Reconstructing the particle rigidity

3. Selecting protons and antiprotons using dE/dx measurements

The primary task of the tracker is to unambiguously determine the charge sign of the incident particle. Even a small fraction of particles with a wrongly reconstructed sign of charge would result in a large background of protons in the antiproton sample. This occurs at high energies as described in section 2.4, due to the combination of the finite spatial resolution of the spectrometer and the nearly straight particle tracks in the tracker. This is not an issue at low energy as the curvature of the tracks is large and a small miss measurement of the particle track cannot change the reconstructed sign of charge. However, a low energy particle can be assigned a wrong sign in two other ways: 1) the particle scatters and changes trajectory significantly so that it will be reconstructed with the wrong sign of charge, 2) the tracker algorithm associates a wrong track to a particle trajectory due to noise or energy deposits from multiple particles in the tracker cavity. The tracker selection has to be able to discard these types of events. The second task of the tracker is to provide a reliable rigidity reconstruction. This is achieved by requiring that the reconstructed track fulfills certain quality requirements. This can include for example the number of points used in the track reconstruction, or the difference between the reconstructed and the measured coordinates of the track. The requirements of track quality at low energy can be relaxed compared to what is done at high energy as the curvature of the particle tracks is larger. Small deviations in the particle trajectory do not change the reconstructed rigidity significantly. Thirdly, the tracker is used to identify protons and antiprotons by measuring the amount of ionization in the silicon planes. A set of tracker selection cuts have been developed to achieve a reliable measurement of each of the three items mentioned above. The cuts have been divided into three categories: Basic tracker cuts, Additional tracker cuts and Antiproton selection cuts. The first category deals with the selection of good quality tracks with a reliable rigidity measurement. The second category adds an extra rejection for 3.2. Tracker criteria 59 scattering and noisy events. The last selection is the antiproton and proton selection using dE/dx measurements. These three groups of selection cuts are explained in detail below.

3.2.1 Basic tracker selection The basic selection on the reconstructed track are: 1. A single track 2. Number of points in x-view ≥4 3. Number of points in y-view ≥3

1/4 4. χ2 > 0 and χ2 < 3.6+1.85 ∗ |deflection| Selection 1) rejects events with more than one track reconstructed by the tracker algorithm. This constitutes a very small fraction of the total number of events. The second and third cut puts a lower limit on the number of points used in the reconstruction of the particle track. This ensures a certain quality of the track. The number of required points is larger in the x-view than in the y-view as the rigidity reconstruction is performed from the bending in the x-view. The number of points required in the x-view also put a condition on the integrated particle length in the magnetic field. A comparison between the measured and reconstructed impact points in the tracker planes is made with the χ2 of the tracker algorithm (cut 4)). First, a χ2 greater than zero is required, which means that the tracker algorithm converged. The χ2 of the track reconstruction is a function of deflection (and thus rigidity) as it primarily depends on multiple scattering which is proportional to 1/(pβ). The upper limit on the χ2 is determined from a distribution of flight data and is chosen so that the efficiency of the selection is about 95 % and constant with rigidity.

3.2.2 Additional tracker selection Further cuts have to be implemented on the tracker data to obtain a clean antiproton sample. These are:

1. A consistent proton dE/dx in the tracker planes. This is realised by requiring an upper limit on the absolute diﬀerence between the maximum energy deposit in one of the 12 tracker planes and the median energy deposited, scaled to the median energy deposited. |dE/dx − dE/dx | τ = max median < 10. (3.1) dE/dxmedian

2. A total singlet1 energy below 100 MIP.

1a singlet is a measured energy deposit in the silicon layers not associated to a track. 60 Chapter 3. Proton and antiproton selection

3. A particle track contained in the PAMELA acceptance.

4. A hit in the ToF paddles along the reconstructed track.

5. An upper limit on the number of clusters in the tracker close to the reconstructed track.

Selection 1) is applied to reject events with a significant amount of energy deposited in the tracker planes. The cut is justified from flight data, and is chosen so that the efficiency is high (> 99 %) and the rejected events are clearly interactions judging from visual inspection with the PAMELA event-viewer2. This is done from the combined information from the distribution of the variable for a sample of protons, and the inspection of the events in the sample using the event-viewer. The second cut rejects events with a large degree of noise, or events with interactions not associated to the track. As for 1), the cut is justified from flight data, and the level is chosen so that the efficiency is close to 100 %. The third selection (3) defines the geometrical acceptance of the experiment. The particle track is required to be inside the acceptance during its entire passage from S1 to S3. Cut (4) requires that there is a hit in the paddles in (S11 OR S12) and (S21 OR S22) pointed by the reconstructed track, and thus provides a consistency check between the reconstructed track and the ToF system. The last cut (5) is an upper limit on the number of singlets with a proton like energy deposit close to the track. This cut rejects a large fraction of events where a spurious singlet not associated to the primary particle track has been included in the reconstruction of the track. These types of events are potentially dangerous as there is a probability that they are assigned a wrong sign of charge. An example of a event which is rejected by this selection is shown in Figure 3.3. The selection cut has been fine- tuned with flight data to have a high efficiency of selecting good tracks (> 95 %) while rejecting a large fraction of miss identified events - events with a wrongly reconstructed track due to spurious clusters. Applying these cuts results in a clean antiproton sample regarding tracker data. No miss identified proton event is present in the antiproton sample judging from visual inspection.

3.2.3 Tracker antiproton selection The tracker is not only used for the reconstruction of the sign of charge and rigidity, but can also measure the absolute value of the particle charge. By using the mean value of the 12 tracker dE/dx measurements a reliable charge identiﬁcation can be made. The dE/dx measurements can also separate protons from other singly charged particles below approximately 0.8 GV/c where protons deposit signiﬁcantly more energy in the silicon planes than electrons and pions which are relativistic

2The PAMELA event-viewer is a ROOT software package which allows a user to visualize the particle trajectory and interactions in the sub-detectors of PAMELA (see Figure 3.3 for an example). 3.2. Tracker criteria 61

Figure 3.3. A miss identified proton event. A wrong set of clusters is chosen for the track reconstruction and a proton is wrongly assigned a negative deflection. 62 Chapter 3. Proton and antiproton selection down to very low rigidities. The cut also removes multi-particle events and particles interacting in the tracker material. The dE/dx cut is based on the behaviour of a sample of protons recorded in orbit and selected with the ToF system and the calorimeter. A non-interacting particle is required in the calorimeter which removes any contaminating electrons. A dE/dx and β cut on the ToF system is then applied to unambiguously select protons. The distribution of the tracker dE/dx for this sample of particles is shown in Figure 3.4, and is used for developing the tracker cut. Emphasis is put on achieving a high electron rejection while keeping a high efficiency for selecting protons, and the cut is therefore made stricter on the lower side of the proton band where the proton and electron distributions merge. The black lines correspond to the selection cut as defined below, where r is the particle rigidity. The form of the cut is justified from flight data itself. The result of the selection when applied to data is shown in Figure 3.5. All particles passing the criteria are plotted as a function of β and rigidity. Comparing this figure with Figure 3.1, it is evident helium nuclei and low energy electrons, positrons, pions and deuterium are rejected by this selection.

1 1 f = Max − 0.25, − 0.05 (3.2) T OP r1.45 r0.8 1 1 f =2.0+Max , (3.3) BOTTOM r1.7 r0.8

3.3 ToF system criteria

The ToF system performs particle selection primarily through the measurement of particle velocity. Combined with the rigidity information from the tracker, this uniquely identiﬁes antiprotons below 1 GV/c as their mass can be reconstructed. The ToF is also useful for rejecting multiple particle events or interactions above the tracker. This can be done by dE/dx measurements and the hit distribution in the two top ToF scintillators. No cuts are put on the lower scintillator (S3) as particles interacting below the tracker system should be part of the particle sample. The ToF dE/dx also provides an additional tool for separating protons from electrons, pions and multiply charged particles.

3.3.1 Multiple particle rejection To reject multiple particles entering the acceptance simultaneously only one paddle may be hit in each ToF layer. At least one hit paddle is required in each plane. • Number of hit paddles: 1≤(S11+S12)≤2, 1≤(S21+S22)≤2, and SXY<=1 Naturally, this cut only removes events where particles traverse diﬀerent paddles. To reject events where multiple particles traverse the same paddle, a cut on the ToF dE/dx cut is applied. This is explained in section 3.3.2. 3.3. ToF system criteria 63

9 103 8 dE/dx [MIP] 7

6 102 5

3 10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 Rigidity [GV/c]

Figure 3.4. Tracker dE/dx for protons selected from ﬂight data using the calorimeter. Particles within the black lines are selected as proton candidates.

3.3.2 ToF antiproton selection

Two selections are applied on the ToF dE/dx to separate proton candidates from electrons, pions and multiply charged particles: on S1 (the sum of the energy deposits in S11 and S12) and S2 (the sum of the energy deposits in S21 and S22). These cuts are determined from the behaviour of a proton sample selected with the calorimeter and the tracker dE/dx. This is done similarly to the selection of a proton sample for the development of the tracker dE/dx, but the final proton selection is made with the tracker dE/dx instead of the ToF dE/dx. The ToF dE/dx of the selected sample is shown in the two top plots in Figure 3.6. As for the tracker dE/dx, emphasis is put on extending the proton-electron separation to higher rigidities. As mentioned above, the dE/dx selection also removes events where more than one particle traversed a paddle simultaneously. The two cuts are defined below. The exact form of the cuts are chosen to fit the shape of the dE/dx distribution of the flight proton sample. 64 Chapter 3. Proton and antiproton selection

Figure 3.5. Negatively and positively charged particles selected with the tracker dE/dx.

1 f =1.95+ (3.4) TOPS1 r1.1 1 f =2.0+ (3.5) TOPS2 r1.3 1 1 f =0.05+ Max , (3.6) BOTTOMS1 r0.9 r0.4 1 1 f =0.1+ Max , (3.7) BOTTOMS2 r1.0 r0.5 The final antiproton and proton selection is made using the ToF velocity measurement. As the mass of a particle is uniquely defined by the rigidity and velocity, a selection is made based on the theoretical function describing the mass for protons in rigidity-β space. The β-rigidity distribution of protons selected with the calorimeter and tracker and ToF dE/dx is plotted in the bottom part of Figure 3.6. The lower proton selection band, shown in equation 3.8 where mp is the proton mass, is chosen to be approximately 2.5 standard deviations below this line. The upper band is more strict to increase the separation between antiprotons and lighter particles - pions and electrons. The result of the selection when applied to flight data is seen in Figure 3.7. All particles passing the selection are plotted as a function of β and rigidity. Comparing this plot with the rigidity-velocity plot of all particles selected with the basic tracker selection (Figure 3.1) and tracker dE/dx 3.4. Calorimeter criteria 65 selection (Figure 3.5), it is clear that the ToF selection increases the separation between antiprotons and electrons.

2 2 mp + r 0.13 f = q − 0.07 − (3.8) T OP r r 2 2 mp + r 0.1 f = q +0.25+ (3.9) BOTTOM r r

3.4 Calorimeter criteria

The main purpose of the calorimeter is to reject electrons. As has been shown above, antiproton candidates are selected using dE/dx and β measurements (see Figure 3.6). The separation between antiprotons and electrons for both these cuts worsens with energy and the distributions start to overlap at about 1 GV/c. An additional cut is therefore needed to remove the remaining electrons. Figure 3.7 shows the β-rigidity plot for all particles passing the basic tracker selection, the tracker and ToF dE/dx selection and the ToF β selection. The electron band is clearly seen around β = 1 for negative rigidities, and, the much less abundant, low energy antiproton candidates can be seen diverging from the electron band at rigidities less than 1 GV/c. A clear separation between electrons and antiprotons is achieved below approximately 0.8 GV/c. For higher rigidities, the electron contamination increases rapidly. This is not caused by an increasing electron ﬂux but is due to the decreasing separation of the dE/dx and β selection. In total, 103254 negatively charged particles are selected with all cuts preceding the calorimeter selection. Assuming that all particles are electrons, the calorimeter has to provide an electron rejection power of almost 105 in the rigidity range 1.0 GV/c to 2.78 GV/c to achieve an electron contamination in the order of a few percent in the ﬁnal antiproton sample. The selection cuts that have been developed to separate antiprotons and electrons using the calorimeter are presented here.

3.4.1 Lepton and hadron interactions in the calorimeter A high energy electron or positron radiates a bremstrahlung photon after travelling through approximately 1 radiation length of matter. This corresponds to 2 planes in the PAMELA calorimeter and an electron will thus interact soon after entering the calorimeter. The bremstrahlung photon will then pair produce an electron-positron pair, which in turn radiates another bremstrahlung photon. This multiplication process continues until the energy of the particles in the shower has reached the critical energy EC below which they lose energy due to collision losses only. The result is a cascade of particles that increases exponentially until the maximum number of particles is reached, after which the cascade decays slowly. 66 Chapter 3. Proton and antiproton selection

9 103 8

7 dE/dx S1 [MIP]

6 102 5

3 10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 Rigidity [GV/c]

9 103 8

7 dE/dx S2 [MIP]

6 102 5

3 10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 Rigidity [GV/c] β 3 1.2 10

2 0.8 10

0.6

0.4 10

0.2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 Rigidity [GV/c]

Figure 3.6. Top and Middle: ToF dE/dx for S1 (top) and S2 (middle). Particles within the black lines are selected as proton candidates. Note the band at around 5 MIP that indicates a residual contamination of multiple particles. Contrary to S2, where multiple particle events can be rejected using the tracker and S1, there is no tracking device immediately below or above S1 and a small fraction of events where an additional particle traverse the detector therefore pass the proton selection. Bottom: ToF β versus rigidity for protons selected from ﬂight data using the calorimeter and the tracker and ToF dE/dx. Particles within the two black lines are selected as proton candidates. 3.4. Calorimeter criteria 67

Figure 3.7. Negatively and positively charged particles selected with the ToF dE/dx and β selection, in addition to all previous selections.

The lateral spread of an electromagnetic shower depends mostly on the sampling depth of the shower, and less on the primary energy. The spread is accounted for by multiple scattering, and is thus inversely proportional to energy. The shower can therefore be decomposed into a low energy part with a wide spread due to multiple scattering, and a collimated high energy part close to the shower axis. The development of an electromagnetic shower is a statistical process, and shower to shower fluctuations are small. This is in sharp contrast to the development of hadronic showers. Hadronic showers are the result of inelastic interactions of the primary particle. As the nuclear interaction length in tungsten is 9.6 cm, a large fraction of incident hadrons passing through the PAMELA calorimeter without interacting. As electromagnetic showers interact in the first planes in the calorimeter, this class of hadrons can be easily selected with a very small background of leptons. In hadronic interactions, about 50 % of the energy is carried away by secondary particles which have large transverse momentum. The shower of secondary particles can contain neutrons, protons, pions and nuclei fragments, with large fluctuations in multiplicity and energy. Hadronic showers are therefore characterised by a large lateral spread, with large fluctuations from shower to shower. Flight events for each of these three different types of particle interactions in the calorimeter are shown in Figure 3.8; electromagnetic showers, non-interacting hadrons and hadronic showers. The PAMELA event-viewer has been used to produce a graphical version of the events. A non-interacting proton is shown in the 68 Chapter 3. Proton and antiproton selection bottom picture where only a single track is seen in the calorimeter, produced by the ionization of the passing antiproton. This is dramatically different from the event shown in the middle plot in Figure 3.8 which shows an interacting antiproton. The figure shows a large shower in the calorimeter, where the individual secondaries can be seen as non-interacting tracks at large angles from the direction of the incoming particle. The top event is an electromagnetic shower with the particle interacting in the very first layers of the calorimeter, producing a collimated shower which is fully contained in the calorimeter. These differences between lepton and hadron showers are exploited to build variables for selecting antiprotons with a high electron rejection factor. The differences between leptonic and hadronic showers can be broken down in the following categories:

• longitudinal proﬁle

• lateral proﬁle

• topological development

• starting point

Many of these features are energy dependent, and this is reflected in the selection criteria. For high energies (> 1 GeV), the energy dependence can be shown to be logarithmic. Below 1 GeV, the energy dependence is more complex. To develop cuts based on the shower features mentioned above, the shower has to be parameterized. However, many of the features require that the location and direction of the shower axis in the calorimeter is determined. This can pose a problem at low energies as the amount of scattering is high and the showers can be very irregular. The performance of these kind of cuts are therefore expected to degrade at low energy. In cases where it is possible, cuts that do not require a reconstruction of the shower axis are therefore favoured. A series of cuts have been developed based on the features of the shower development discussed above. These are explained in the following sections. As it is not possible to extract an unbiased electron sample, or a statistically significant antiproton sample, from flight data, simulation has been used to develop the selection cuts.

Longitudinal development The longitudinal shower development of protons and electrons is very diﬀerent, as was explained above. Almost 55 % of the protons traverse the calorimeter without interacting. These non-interacting protons constitute a gold-plated class of events in the sense that they can be selected with a high eﬃciency and a negligible background of electrons 3. The variable that has been chosen for selecting this class of events is the number of hit strips in the calorimeter (nstrip). The calorimeter consists of

3A large fraction of pions are however non-interacting and are selected with this cut. 3.4. Calorimeter criteria 69

Figure 3.8. An interacting electron (top), interacting antiproton (middle) and a non-interacting antiproton (bottom) shown with the PAMELA event-viewer. Only the XZ view of the calorimeter is shown. The energy deposited in each strip is color coded where light blue corresponds to 0-2 MIP and dark blue to 2-10 MIP. 70 Chapter 3. Proton and antiproton selection

44 planes, where one plane is inactive, and a down-going non-interacting particle will then ideally hit 43 strips. In reality the distribution of nstrip peaks around 46 as inclined tracks sometimes activate two strips in one plane. The number of hit strips for electromagnetic showers scales as the number of particles in the shower and thus increases linearly with the energy of the primary particle. The simulated distribution of the variable nstrip is showed in Figure 3.9 for antiprotons and electrons. Non-interacting antiprotons are selected as all events passing criteria 1) and 2) deﬁned below. 1. 20 < nstrip < 47 2. At least two out of the last three planes has an energy deposit greater than zero Selection 1) is indicated in Figure 3.9 as two black dotted lines. Selection 2) rejects very inclined electron showers which by coincidence can have a value of nstrip in the interval deﬁned in 1).

Lateral development The lateral development of an electromagnetic shower scales with the Moli`ere radius (RM ), given by RM = 21.2052X0/EC , where EC is the critical energy. On average, 95% of the deposited energy lies inside 2 RM which corresponds to about 1.8 cm or 7.5 strips for the PAMELA calorimeter. For hadronic showers, 95 % of the total deposited energy for hadronic showers is contained within a radius of interaction length, which corresponds to almost 10 cm for the PAMELA calorimeter. To characterise the lateral spread and select antiprotons the quantity qout is introduced. It is deﬁned as the fraction of energy deposited outside a cylinder of radius 8 strips around the track. The distribution of this variable for antiprotons and electrons is shown in Figure 3.10. Particles passing criteria 1) and 2) below are selected as antiprotons.

1. qout > 0.41 − 0.015r 2. (qtot/r) < Max(1240.0 − 800.0r, 245.0)

Cut 1) is a lower limit of the variable qout. This cut is indicated in Figure 3.10 with a black dashed line. The second cut is an energy-momentum match. The energy deposited in the calorimeter divided by the particle rigidity has to be lower than a certain value chosen from the distribution of this variable for antiprotons. This cut is introduced to reject two types of events: a) events where the calibration failed. These events have generally a higher noise level which can fake a higher energy deposit outside the track. b) events with multiple particles in the calorimeter, which also fake a higher value of the variable qout. It has been shown that interacting antiprotons in general deposit a large fraction of energy outside the shower core. However, two types of interacting antiproton events can deposit a large fraction of energy close to the shower axis. These are, 3.4. Calorimeter criteria 71

Antiprotons Electrons

120 120 Nstrip Nstrip 600 600 100 100

500 500

80 80

400 400

60 60 300 300

40 40 200 200

20 20 100 100

0 0 0 0 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Rigidity [GV/c] Rigidity [GV/c]

Figure 3.9. The distribution of the variable nstrip for simulated antiprotons (left) and electrons (right). The horizontal band of non-interacting antiprotons is clearly seen in the left plot. The band goes down to about 1 GV/c where antiprotons start to annihilate in the calorimeter. The nstrip distribution for electrons instead increase linearly with rigidity. Notice that the number of electrons presented here is signiﬁcantly larger than what is recorded in ﬂight. The black dashed lines are the upper and lower limit of nstrip when selecting antiprotons.

1) events where an antiproton breaks up a nucleus in the detector material and the fragments deposit a large fraction of their energy in a single strip, 2) events where a low energy antiproton annihilates with a proton and deposits a large amount of energy within a few strips. A variable (qtr) has been developed to select these types of events. This is deﬁned as the fraction of energy deposited inside a cylinder of radius 4 strips. The distribution of this variable for antiprotons and electrons is shown in Figure 3.11. All particles passing the criteria below are selected as antiprotons. qtr > 0.983 (3.10)

Starting point of the shower Electromagnetic and hadronic showers have very diﬀerent interaction probabilities. This is evident from the radiation length, X0 =0.35 cm, which characterises the interaction probability for electrons, and the nuclear interaction length λ =9.59 cm. 72 Chapter 3. Proton and antiproton selection

Antiprotons Electrons

1 1 1400

Qout 160 Qout

0.9 0.9

140 1200 0.8 0.8

120 0.7 0.7 1000

0.6 100 0.6 800

0.5 0.5 80

0.4 600 0.4 60

0.3 0.3 400 40 0.2 0.2 200 20 0.1 0.1

0 0 0 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Rigidity [GV/c] Rigidity [GV/c]

Figure 3.10. A variable describing the lateral spread of showers. The variable qout is plotted for simulated antiprotons (left) and electrons (right). Particles above the dotted line are selected as antiprotons. Notice that the range of the qout distribution for antiprotons starts at 0.025 for better visibility and non-interacting antiprotons are thus cut out, since they produce a very low value of this variable.

This means that an electron will interact almost immediately in the calorimeter, while a proton has a roughly equal probability for interacting in any of the calorimeter planes. The variable noint has been developed to characterise this diﬀerence

2 9+log(r) noint = θij ∗ i (3.11) Xj=1 Xi=1 where θij = 1 if the i-th planes of the j-th view have a cluster along (less than 4 mm away) the track with a deposited energy typical of a proton (order of one MIP), otherwise θij = 0. The sum is made up to the rounded value of 9 + loge(r). This variable will increase as the depth of interaction increases. The distribution of this variable for antiprotons and electrons is shown in Figure 3.12. Particles passing the criteria 1) and 2) below are selected as antiprotons. Cut 1) is a lower limit of the variable noint. Cut 2) is applied to only select interacting particles.

1. noint > 81.2 − 14.0r 3.5. Selecting galactic particles 73

Antiprotons Electrons

1 1 Qtr Qtr 500 0.95 250 0.95

0.9 0.9 400 200

0.85 0.85

300 150 0.8 0.8

0.75 0.75 200 100

0.7 0.7

50 100 0.65 0.65

0.6 0 0.6 0 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Rigidity [GV/c] Rigidity [GV/c]

Figure 3.11. The distributions of the fraction of energy inside a cylinder of radius 4 strips for simulated antiprotons (left) and electrons (right). The dashed black line corresponds to the lower limit for selecting antiprotons.

2. nstrip > 50

3.5 Selecting galactic particles

As was described in section 1.3.2, low energy charged particles are deflected by the geomagnetic field of the earth. The geomagnetic field can trap decelerated cosmic rays or particles resulting from interactions in the atmosphere inside the field where they can remain up to several years. As this thesis concerns the measurement of galactic cosmic rays, it is important to separate this component from trapped particles inside the geomagnetic field. The rigidity that is required to penetrate the geomagnetic field at each point in the satellite trajectory is referred to as the cut-off. As mentioned in section 1.3.2, an approximation of the cut-off is the Stoermer Vertical Cut-off. This is used as a basis for the determination of the cut-off for PAMELA. The cut that is used to separate galactic particles from trapped particles is of the form

rigidity > cut-oﬀPAMELA = k ∗ SV C(lon, lat) (3.12) where SVC is the Stoermer Vertical Cut-Oﬀ which is a function of latitude and longitude and can be found in tables. The constant k has to be determined so that 74 Chapter 3. Proton and antiproton selection

Antiprotons Electrons

120 120 700

Noint Noint 2200

100 600 100 2000

1800 500 80 80 1600

1400 400 60 60 1200

300 1000

40 40 800 200 600

20 20 400 100 200

0 0 0 0 1.3 1.4 1.5 1.6 1.7 1.8 1.9 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Rigidity [GV/c] Rigidity [GV/c]

Figure 3.12. A variable for describing the starting point of the shower. The distribution for antiprotons (left) and electrons (right) is shown. The dashed black line is the selection cut for antiprotons.

all trapped particles are rejected. This can be done by first observing the proton flux measured in regions with a low cut-off (SVC < 50 MV/c) where all particles safely can be considered as galactic particles. This flux can then be compared to the flux measured when applying cut-off cuts of different levels (that is, different values of k). The lowest cut that reproduce the flux measured in regions with a cut-off (SVC < 50 MV/c) is then selected. Studies have shown that a value of k =1.2 fulfills this requirement [63].

3.6 Anticounter criteria

The anticounter detectors are used to reject multiple particle events. This is an important issue at low energy as a large fraction of the low-energy tracks in the spectrometer are accompanied by multiple particles. Referring to the discussion in 2.7, a requirement of no activity in either of the CARD or CAT detectors is applied. No cut is put on the CAS detector, as this could potentially reject events with back-scattered particles from interactions or annihilations in the calorimeter. 3.8. Electron contamination 75

3.7 The selected antiproton and proton candidates

Applying the tracker, ToF, calorimeter, anticounter and orbital cuts, 171 antiproton and 8452835 proton candidates are selected. Visual inspection of the antiproton events show that one event is clearly a miss identified secondary particle which entered the calorimeter from the side and passed one of the calorimeter selection cuts. This event is removed from the sample. The remaining sample is shown in Figure 3.14, where all particles before the ToF β selection are plotted as 1/β versus rigidity. The blue lines correspond to the β selection cuts. A small residual sample of electrons, pions and antiprotons (with a wrongly reconstructed β) is seen close to β = 1. The number of protons and antiprotons inside the β selection band is shown in Table 3.1. The spatial distribution of the selected protons and antiprotons, plotted as the latitude and longitude of the satellite when the event was collected, is shown in the top part of Figure 3.15. The proton and antiproton distributions match well, and no anisotropies are evident. The time of measurement for all selected events is shown in the bottom part in Figure 3.15. The figure shows that the events have been collected over the entire flight period, with the exception of a few occasions when the instrument was turned off. A decrease in efficiency of the instrument can be noted, as the number of particles is decreasing with time (see also section 3.2.1).

3.8 Electron contamination

Below 0.8 GV/c, electrons are rejected using dE/dx and β measurements and the remaining contamination is assumed to be zero. This is confirmed by a visual inspection of all selected events below 0.8 GV/c which are all annihilating in the calorimeter and are therefore known to be antiprotons with certainty. The main electron rejection power above 0.8 GV/c is provided by the calorimeter. The efficiency for selecting electrons using the calorimeter above this rigidity is estimated using simulations. An electron spectrum in the rigidity interval 0.3 to 10.0 GV/c with a uniform arrival distribution was simulated and all events where the primary particle traversed S3 were saved. The calorimeter electron efficiency is then calculated from this sample as the fraction of particles passing the calorimeter selection. The result is presented in Figure 3.16. An upper limit on the electron contamination in the selected antiproton sample can be estimated using the simulated electron efficiency and the distribution of selected events in flight before the calorimeter selection is applied. This sample of events, which has been selected using basic tracker criteria, dE/dx and β selections, contains a large fraction of electrons and a small fraction of antiprotons. Assuming all particles in the sample to be electrons, the electron contamination is calculated by convoluting the distribution of events with the calorimeter electron efficiency derived from simulation. This gives the upper limit on the number of electron events 76 Chapter 3. Proton and antiproton selection

Figure 3.13. An antiproton event of about 0.8 GV/c shown with the PAMELA event-viewer. The event can be selected unambiguously as an antiproton since: 1) a track with a negative curvature is seen in the bending-view of the tracker (left), 2) the energy deposited in the tracker and ToF planes are consistent with that of an (anti)proton, 3) the velocity measured with the ToF system is consistent with a particle with a mass of an (anti)proton, 4) the particle is annihilating in the calorimeter. 3.8. Electron contamination 77

Rigidity GV/c p p¯ 0.4 - 0.8 1165802 5 0.8 - 1.2 1367561 4 1.2 - 1.6 1724266 29 1.6 - 2.0 1619140 41 2.0 - 2.4 1415407 40 2.4 - 2.78 1160659 52

Table 3.1. The number of proton and antiproton candidates selected with the tracker, ToF and calorimeter.

Figure 3.14. All selected protons and antiprotons before the ToF β selection. The blue lines are the primary β selection based on the error of the β measurement for protons. Antiprotons passing the β selection are plotted as ﬁlled dots. 78 Chapter 3. Proton and antiproton selection

p, p Spatial Distribution

Latitude 60

-20

-40

-60

-80

-150 -100 -50 0 50 100 150 Longitude

p, p Time Distribution

104

103

102

-1 10 06-07 06-10 06-12 07-04 07-07 07-10 08-01 Date

Figure 3.15. Top The spatial distribution of protons (coloured distribution) and antiprotons (black dots). All events are selected close to the poles due to the requirement of a particle rigidity greater than 1.2 × cut-off. The spatial distribution of the antiproton sample is consistent with the proton distribution.Bottom The time distribution of the selected antiprotons (red) and protons (black). Except for a few periods of down-time, the collection has been fairly constant. A short increase in flux can be noticed in December 2006. This was due to a big solar flare which occurred on December 13th. The flux of protons increased with 3 orders of magnitude during a few minutes. 3.9. Pion contamination 79 in each bin of the selected antiproton sample. The result is given in Table 3.2. The electron contamination is included in the antiproton flux and ratio as a systematic error.

3.9 Pion contamination

No experiment has ever detected a negatively charged hadron besides antiprotons in the cosmic radiation. There is therefore no contamination expected from cosmic ray hadrons in the antiproton sample. There is a small but non-negligible probability that a cosmic-ray interact with the material above PAMELA and produces secondary particles. Virtually any type of particle can be created in such inelastic collisions but the production cross-section decreases significantly for heavier particles. The lightest family of hadrons, and thus the most abundantly created in these interactions, are pions. A pion traversing the acceptance of PAMELA is easily mistaken for an antiproton as the two particles interact in a similar fashion. There are two different possibilities for separating (and rejecting) pions from antiprotons: 1) by dE/dx and β measurements. This is possible below approximately 1 GV/c where antiprotons are slower than pions and deposit a larger amount of ionization energy in the Tracker and ToF planes. 2) to identify signatures from multiple particles inside the experiment which are created in the inelastic collision together with the pion. This leaves single high energy pions which cannot be separated from antiprotons and present an irreducible background. One such event is illustrated in Figure 3.17. The amount of pion contamination in the antiproton sample has to be understood and if necessary subtracted. This is done using both simulations and flight data in the following way:

• Simulations are performed to understand the shape of the pion energy spectrum.

• Flight data are used to derive the pion contamination at low energy where pions and antiprotons can be separated using dE/dx and β measurements. The results from ﬂight data are then used to validate the simulation method, and scale the results from the simulation if necessary.

3.9.1 Simulation The amount of pions created in inelastic collisions with protons has been simulated. Clearly, this requires a large simulated statistics of protons as interactions producing pions are rare. To reduce the amount of processing time, it was decided to use a two step method. In the first step, only the top part of PAMELA is simulated: the S1 detector and the dome covering the instrument. An incident proton flux is simulated on this setup, and events fulfilling the following three criteria are saved for later processing: 1) an inelastic collision has occured, producing at least one negative pion, 2) at least one interaction in S1 and 3) a negative pion has crossed 80 Chapter 3. Proton and antiproton selection

×10-3 0.18

0.16

Efficiency 0.14

0.12

0.1

0.08

0.06

0.04

0.02

0 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Rigidity [GV/c]

Figure 3.16. The probability (eﬃciency) of selecting an electron with the calorimeter antiproton selection.

Rigidity GV/c N(e−) 0.4 - 0.8 0 +0.02 0.8 - 1.2 0.15−0.02 +0.23 1.2 - 1.6 0.52−0.11 +0.43 1.6 - 2.0 0.67−0.18 2.0 - 2.4 0.0+0.20 +0.39 2.4 - 2.78 0.18−0.05

Table 3.2. An upper limit on the number of electrons in the antiproton sample. 3.9. Pion contamination 81

Figure 3.17. An illustration of a proton interacting with the dome above the PAMELA instrument producing a shower of secondary particles. A single negatively charged pion is traversing the acceptance of the experiment. This type of events is impossible to distinguish from an antiproton event if none of the other particles produced in the shower hits the instrument and if the energy of the pion is higher than the energy of a MIP antiproton. the spectrometer cavity. Events passing 1), 2) and 3) are saved and used as input to a standard GPAMELA simulation where the events are processed further. The simulation in the first step is done using the FLUKA package [64]. This simulation tool has been widely used for simulating nuclear interactions, and is known to produce accurate results. The simulation work has been made by A. Bruno, and is presented in detail elsewhere [65]. The proton spectrum measured by PAMELA was used as the primary spectrum in the simulations. A statistics of protons corresponding to the flight time of the data set used in this thesis was then simulated. The results are compensated for live-time of the experiment, and for the influence of the geomagnetic field. The rigidity distribution for pions surviving the basic tracker criteria are presented in Figure 3.18. This spectrum of pions is used to estimate the pion contamination in the antiproton sample.

3.9.2 Validation of the pion simulation at low energy Negative pions can be selected unambiguously in ﬂight in a rigidity window between 0.3 GV/c and 1.0 GV/c. This is accomplished using the calorimeter and ToF system 82 Chapter 3. Proton and antiproton selection

103

Number of Pions 102

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 3.18. The derived pion spectrum from simulations passing the basic tracker criteria. to reject the electrons and antiprotons respectively. The lower limit in rigidity is set by the need of a suﬃciently large shower size in the calorimeter to allow for the separation between pions and electrons. The upper limit of the pion selection is set by the ToF β separation between pions and antiprotons. The pion selection can be summarized in the following steps

1. Requiring a single particle traversing the experiment.

2. A signature of a non-interacting particle in the calorimeter.

3. A relativistic particle measured by the ToF system.

A serie of cuts (1) is applied on anticounters, tracker and ToF system to achieve a clean sample of single particle events. The second cut selects hadrons and rejects electrons with a high efficiency. Cut 3) is then applied to reject antiprotons which are considerable slower than pions below 1 GV/c. The selection is applied on flight data, and on the set of simulated data which has been described earlier. The result is shown in Figure 3.19. The agreement between flight data and simulation is very good, and there is no need to normalise the level of pion contamination in simulation to what is seen in flight data. 3.9. Pion contamination 83

50 Flight Simulation Selected Pions 40

0.4 0.5 0.6 0.7 0.8 0.9 1 Rigidity [GV/c]

Figure 3.19. Selected ﬂight (black) and simulated (red) negative pions.

3.9.3 Validation of the pion simulation at high energy As described above, it is impossible to separate negative pions and antiprotons above 1-2 GV/c on an event-by-event basis. However, pions and antiprotons have a different sensitivity to selection cuts which can be exploited to understand the pion contamination. For example, a large fraction of pion events have a hit in the CAT or CARD anticounters as these events are the result of an inelastic collision above the PAMELA instrument which creates a shower of particles. Antiprotons are primary particles (only a negligible amount of antiprotons are produced in interactions in the experiment) and are thus unlikely to produce a hit in one of the top anticounters. Requiring a cut on the CAT and CARD anticounters will thus reduce the pion signal considerably, but leave a large fraction of antiprotons. Thus, if a sample of selected antiproton candidates is reduced significantly by a cut on CARD or CAT, there is probably a dominant fraction of pions in the sample. This effect is shown in Figure 3.20. It shows the evolution of the (flight) antiproton distribution above 1.5 GV/c when applying a series of selection cuts (shown by simulations not to decrease the antiproton signal dramatically). Each line corresponds to the number of selected events when adding an additional selection cut. The basic cuts which are used to select the sample is a dE/dx selection on S1 to select charge one particles, and a requirement of a non-interacting particle in the calorimeter. Figure 3.20 shows that the selection cuts have a strong impact on the distribution at low energy, while the distribution remains roughly constant above 5 GV. 84 Chapter 3. Proton and antiproton selection

This suggests that the majority of the events below 5 GV/c are not antiprotons but pions, which matches what is expected from simulations of the pion contamination. All events in Figure 3.20 are negative hadrons. If we assume that all events remaining after the CAS cut are antiprotons, two other hypotheses can be investigated:

1. That a majority of the particles in the sample in Figure 3.20 remaining after the CAS cut are antiprotons and the rest pions.

2. That the pion simulation produces satisfactory results.

These hypotheses can be tested by observing how the pion rigidity distributions in flight and simulation are affected when applying the selection cuts described earlier. The flight pion rigidity distribution is defined as the number of events after the basic cuts are applied subtracted by the number of events surviving the CAS cut, which are assumed to be antiprotons, (see top part of Figure 3.20). If 1) and 2) holds, a similar fraction of events should be rejected when applying each cut. The result of this approach is plotted in Figure 3.20 (bottom). The agreement is reasonably good and supports the use of the simulation to estimate the pion contamination.

3.9.4 The simulated pion contamination in the antiproton sample The estimated number of pions in the selected antiproton sample is derived by applying the antiproton flight selection to the distribution of simulated pions shown in Figure 3.18. The number of surviving pions versus rigidity is plotted in Figure 3.21. The figure shows that there is a pion contamination above 1.2 GV/c. As the antiproton spectrum increases rapidly in this rigidity region, the pion contamination can be considered significant between 1.2 GV/c and 2.0 GV/c, and small at higher and lower rigidities.

3.9.5 Estimation of the pion contamination in flight The selected sample of flight antiproton candidates contains antiprotons and a number of pions which depends on rigidity. Antiprotons are significantly heavier than pions and thus have a lower velocity assuming an identical rigidity. The ToF system can therefore be used to separate pions and antiprotons at low energy. Complete separation is only achieved below approximately 1.0 GV/c. However, the β can be used to estimate the magnitude of an antiproton and pion contribution in a selected distribution of particles on a statistical basis also at higher rigidities. This can be seen in Figure 3.22 which shows the β distributions of the selected proton and antiproton candidates in three different rigidity intervals: 0.8−1.2 GV/c (bottom), 1.2 − 1.6 GV/c (middle) and 1.6 − 2.0 GV/c (top). At all three intervals, a pion component and an antiproton component is clearly noticeably, although the separation between the two components decreases with increasing rigidity. The pion 3.9. Pion contamination 85

AntiProton Candidates vs Pion Cuts

103 Events

102

Basic Cuts (7193) +Trk (4647) 10 +ToF (1199) +PionCut (1065) +CARD+CAT (792) +CAS (745)

2 3 4 5 6 7 8 9 10 Rigidity [GV/c]

Pion Cut Efficiencies

102

Efficiency [%] 10

1 Trk Flight ToF Flight PionCut Flight CARD+CAT Flight Trk Sim ToF Sim 10-1 PionCut Sim CARD+CAT Sim

10-2 2 3 4 5 6 7 8 9 10 Rigidity [GV/c]

Figure 3.20. Top Selected antiproton candidates above 1.5 GV/c for diﬀerent selection cuts. Bottom The fraction of remaining pions after the application of certain selection cuts. The results are shown for ﬂight data (solid lines) and simulations (dashed lines). 86 Chapter 3. Proton and antiproton selection

Pion Contamination 18

Pions 16

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 3.21. The simulated pion contamination remaining after the antiproton selection cuts have been applied component is in good agreement with the simulated pion contamination which is shown in blue color. A method has been developed to estimate the pion and antiproton components in ﬂight using the measured β distribution. This method is applied in two equal width rigidity bins from 1.2 GV/c to 2 GV/c, and the result is used to subtract the pion contamination from the sample of antiproton candidates. The upper limit in rigidity of this method is set by the resolution of the ToF β measurement. At higher rigidities, simulations are used to estimate the contamination instead. The method is explained below. A β distribution (A) containing an antiproton (B) and a pion (C) component is generated for each rigidity interval (1.2 − 1.6 GV/c and 1.6 − 2.0 GV/c). The total number of events NA = NB +NC is selected as the number of antiproton candidates in the rigidity interval in question. The β distribution of the antiproton component is generated by a random sampling from the corresponding proton distribution. As there is no pure sample of pions, the pion β has to be sampled from a proton β distribution. The proton sample is chosen with a rigidity interval making the β distribution comparable to a β distribution of pions with rigidities in the interval in question. A straight-forward calculation shows that the pion β distribution in the intervals 1.2 − 1.6 GV/c and 1.6 − 2.0 GV/c compares to proton β distributions in the intervals 8.0 − 10.7 GV/c and 10.7 − 13.4 GV/c.

While the total number of generated events is kept ﬁxed (NA), the number of antiprotons NB is varied from 0 to NA. The number of pions NC is then naturally varied from NA to 0 as NC = NA − NB. For each generated β distribution A, containing NB events with an antiproton β, and NC events with a pion β, a 3.9. Pion contamination 87

0.8-1.2 GV/c

103

102

-1 10-1.5 -1 -0.5 0 0.5 1 1.5 Beta [v/c] 1.2-1.6 GV/c

103

102

-1 10-1.5 -1 -0.5 0 0.5 1 1.5 Beta [v/c] 1.6-2.0 GV/c

103

102

-1 10-1.5 -1 -0.5 0 0.5 1 1.5 Beta [v/c]

Figure 3.22. The β distribution of the selected proton and antiproton candidates in three rigidity intervals. The proton distributions are shown in black, antiproton candidate distributions in red, and simulated pion distribution in blue. A Gaussian is fitted to each of the proton and antiproton distributions to guide the eye. The standard deviation and mean from the fit of the proton distributions are used in the fit of the antiproton distributions as fixed parameters. 88 Chapter 3. Proton and antiproton selection

Kolmogorov-Smirnoff test is performed to check the compatibility with the sample of antiproton candidates in that rigidity interval. The set of parameters NB and NC that gives the highest probability from the Kolmogorov-Smirnoff test is selected as the number of antiprotons and pions in the corresponding rigidity interval. The result is shown in Table 3.3. The estimated number of pions using simulations is stated in the last column, and the agreement with the flight estimation is excellent.

Rigidity GV/c p¯ π− Sim. π− 1.2 - 1.6 23 6 6 1.6 - 2.0 29 11 12

Table 3.3. The estimated number of pions and antiprotons in the rigidity intervals 1.2 to 1.6 GV/c and 1.6 to 2.0 GV/c. The last column shows the estimated number of pions derived from simulations.

3.9.6 The pion contamination in the antiproton sample The estimated number of pions in each bin of the selected antiproton sample are shown in Table 3.4. The contamination is estimated directly from flight data between 0.4 GV/c and 2.0 GV/c, and using simulations between 2.0 GV/c and 2.78 GV/c. The use of simulations for estimating the pion contamination above 2.0 GV/c is justified by three different methods:

1. By a direct comparison of the simulated and ﬂight pion spectra between 0.3 GV/c and 1.0 GV/c.

2. By requiring that the simulated and ﬂight pion component scales identically with selection cuts above 1.5 GV/c

3. By estimating the pion component in ﬂight data between 1.2 and 2.0 GV/c using statistical methods and comparing with the number of pions surviving the selection cuts in simulations.

In all three methods, the agreement between ﬂight data and simulation is good. The use of simulation is therefore well motivated. The pion contamination in Table 3.4 is subtracted from the antiproton sample.

3.10 The ﬁnal antiproton and proton samples

The selected number of antiprotons is compensated for the contamination of pions and electrons. As the pion contamination is thoroughly investigated and understood, and results from simulation and ﬂight are in good agreement, this contamination is subtracted from the antiproton sample in each bin. The estimation of the electron contamination is done purely with simulations and the uncertainties are therefore large. The electron contamination is therefore 3.10. The ﬁnal antiproton and proton samples 89

Rigidity GV/c π− 0.4 - 0.8 0 0.8 - 1.2 0 +4.5 1.2 - 1.6 6.0−2.8 +5.8 1.6 - 2.0 12.0−4.2 +4.0 2.0 - 2.4 3.9−2.9 +3.5 2.4 - 2.78 2.0−2.1

Table 3.4. The pion contamination in flight data. The numbers are given with 90 % Poisson upper and lower limits. An error of 10 % is added on top of the Poisson errors to the last two bins, which are estimated from simulations. This represents the uncertainty in the simulation method, and is estimated considering the difference between the derived pion contamination using the flight and simulation method respectively, which is shown in Table 3.3. not subtracted from the antiproton sample, but is included as an additional systematic error. A visual inspection of the selected events shows no clear electrons, which supports the level of contamination seen in simulation. A summary of the number of antiproton and proton candidates, and the estimated pion and electron contamination is shown in Table 3.5.

Rigidity GV/c p¯ π− e− p 0.4 - 0.8 50 0 1165802 +0.02 0.8 - 1.2 40 0.14−0.02 1367561 +4.5 +0.24 1.2 - 1.6 29 6.0−2.8 0.52−0.11 1724266 +5.8 +0.43 1.6 - 2.0 41 12.0−4.2 0.67−0.18 1619140 +4.0 +0.20 2.0 - 2.4 40 3.0−2.9 0 1415407 +3.5 +0.39 2.4 - 2.78 52 2.0−2.1 0.18−0.05 1160659

Table 3.5. The number of detected antiproton- and proton- candidates and the estimated numbers of residual electrons and pions in the antiproton sample. The number of antiproton candidates is shown in column 2. Column 3 and 4 shows the estimated pion and electron contamination. Column 5 shows the number of selected protons. 90 Chapter 4

Selection eﬃciencies

The efficiencies of the proton and antiproton selections discussed in chapter 3 are presented in this chapter. These can be studied in several different ways: using simulations, test-beam data or flight-data. In each case, a sample of protons or antiprotons is selected, and the surviving fraction of events when applying a cut is used as a measure of the efficiency of the cut. In all cases possible, the efficiencies will be estimated using flight data as this minimizes uncertainties if an un-biased sample of particles can be selected. By using a sample from all flight data, the detector performance over time is naturally included in the estimated efficiency which is otherwise difficult to achieve using simulations. The drawback of using flight data is that independent detectors have to be used to select the sample of particles and determine their rigidity. This can give rise to biased samples of particles if the response of different detectors are correlated. Simulations are therefore used to cross-check the results. As it is impossible to select an unbiased, statistically significant antiproton sample, all efficiencies are derived from a proton sample. It is assumed that the proton and antiproton efficiencies are identical, which is a good approximation for all detectors except the calorimeter, where instead simulation is used for the efficiency estimation. This difference is due to differing cross section for inelastic interactions for protons and antiprotons. The proton and antiproton efficiencies of the Tracker, ToF and Calorimeter selection are presented below.

4.1 Concerning errors

The technique for calculating the efficiency of the selection cuts applied here makes use of two identically binned histograms. Histogram A is filled with all events in the data sample while histogram B is filled with the sub-sample of events satisfying the selection criteria (i.e, all events “passing the cut”). The estimate of the true efficiency of the cut is ki/Ni, where ki is the number of events passing the cut

91 92 Chapter 4. Selection eﬃciencies

(= number of events in bin i in histogram B), and Ni the number of events in bin i in histogram A. The statistical uncertainty of the estimation is frequently calculated using binomial errors. Applying a cut to a sample of data can be seen as a binomial process, with probability of ”success” (i.e true eﬃciency) ǫ. The error on the expected number of events passing the cut = ǫN is σ = ǫ(1 − ǫ)N. ′ ′ Since the true eﬃciency ǫ is unknown, the estimate ǫ = k/N is used.p Inserting ǫ and dividing with N, the error is

∆ǫ = (1/N) k(1 − k/N) (4.1) p In the limiting cases k = 0 and k = 1 this method gives an unreasonable error of zero. A better method, which removes this problem, has been proposed by [66], and is used here. It is based on the binomial distribution, but uses Bayes’ theorem to overcome the problems introduced when applying the estimated eﬃciency ǫ′ as the true eﬃciency, and exhibits reasonable behaviour even in limiting cases.

4.2 Tracker eﬃciency

The tracker efficiency is defined as the total efficiency of the basic cuts, defined in section 3.2. These can be summarized as the efficiency for the tracker to reconstruct a good quality track from a single particle traversing the tracker cavity. The total tracker efficiency is defined as the efficiency of the basic and additional tracker cuts. The tracker efficiency depends on four phenomena.

1. The amount of deposited energy in the silicon planes

2. The curvature of the track.

3. The amount of multiple scattering.

4. Time

The energy released in a medium by a through-moving particle depends on the particle velocity as dE/dx ∼ β−2. A particle with a relatively low velocity traversing the tracker will thus deposit a larger amount of energy in the silicon planes than a particle with a higher velocity. This will affect the tracker efficiency in the following way. The position of a particle hitting a silicon plane is determined by a weighted average technique of the positions of the clusters created in the plane by the passing particle. A cluster is defined as one or more strips in the sensitive planes of the spectrometer with a signal 7 standard deviations from the intrinsic noise of the channel. The number of created clusters naturally depends on the amount of deposited energy in the plane. As the multiplicity of clusters increases, the probability that the tracking algorithm will find a unique track decreases, and therefore also the tracker efficiency. The tracker efficiency, due to this effect only, is therefore expected to be constant for relativistic particles (above approximately 4.2. Tracker efficiency 93

2 GV/c for protons) and proportional to β. The amount of deposited energy also increases with incident particle charge (dE/dx ∼ z2), and the tracker efficiency thus decreases for multiply charged particles. The efficiency is also expected to decrease with the amount of track curvature (2), as the track reconstruction algorithm primarily is developed for high energies, with nearly straight tracks. Finally, the tracker efficiency is affected by the amount of multiple scattering (3) as the particle deviates from the theoretical trajectory. Multiple scattering depends on the particle charge, momenta and β, as θ ∼ z/(pβ), where θ is the scattering angle. This effect thus increase at low energies and for multiply charged particles. To summarize: the tracker efficiency is expected to be constant for same charge particles at high energies (relativistic, straight tracks), and drop at low rigidity (∼ 1 GV/c) due to increased deposited energy, track curvature and multiple scattering. The tracker efficiency for PAMELA also depends on time, since the performance of the Viking VA1 chips, responsible for the readout of the tracker, degrades with a roughly constant rate. This creates dead areas in the tracker where the position of a passing particle cannot be detected. As the number of reconstructed positions in the particle trajectory is reduced, the probability of reconstructing a track decreases, and also the quality of the track. This results in a decrease of the tracker efficiency over time. However, the performance in general is not affected. The following section presents the selection of an experimental proton sample for the derivation of the total tracker efficiency.

4.2.1 Selecting an experimental proton sample A series of strict cuts are applied to raw ﬂight data to achieve a clean sample of protons which can be used for the measurement of the tracker eﬃciency. Firstly, events with multiple particles in the acceptance must be rejected. Secondly, charge one particles are separated from particles with multiple charge using dE/dx measurements with the ToF system. Finally, using the calorimeter, a clean sample of protons can be selected from the remaining charge one sample which still contains a small fraction of deutrons, electrons and pions. All these cuts are described in detail below. In neither of the selections mentioned above, the tracker system can be used as that would bias the proton sample and a substitute method has to be devised. Most importantly, the rigidity reconstruction, which normally is made by measuring the track curvature in the tracker, is instead performed by the ToF system. As the rigidity is a function of the particle mass (m) and velocity (β) only,

βm rigidity = (4.2) 1 − β2 p it can be reconstructed measuring the velocity and assuming a proton mass. The rigidity derived with the ToF system in this manner is henceforth referred to as the ToF rigidity. A problem with this method is that β normally is evaluated using both the ToF and the tracking system: The ToF system measures the time difference 94 Chapter 4. Selection efficiencies for a particle traversing the scintillators S1, S2 and S3, while the tracking system evaluates the flight path-length between them and the combination of these two measurements gives the velocity of the particle. As the tracker information cannot be used in this study, a straight line approximation of the particle trajectory is made. The uncertainties introduced with this approximation have been evaluated with simulations and are negligible in the rigidity region of interest.

The resolution of the ToF rigidity is limited by the time resolution of the ToF system, and therefore degrades with energy. The resolution of the ToF rigidity, defined as the relative difference to the rigidity measured with the tracker system, is plotted in Figure 4.1. An rapid increase is evident above 1.0 GV/c, and the method is therefore only used up to 1.7 GV/c. The derived tracker efficiency using this method is therefore extrapolated from 1.7 GV/c to 2.8 GV/c. This is valid as the efficiency is expected to be constant above about 1 GV/c.

0.22 tracker 0.2 )/R ToF

-R 0.18

tracker 0.16 (R

0.14

0.12

0.1

0.08

0.06 0.4 0.6 0.8 1 1.2 1.4 1.6 ToF-Rigidity [GV/c]

Figure 4.1. The ToF rigidity resolution. The resolution worsens for high rigidities as β approaches unity, and a small difference in the measured times produce a large relative difference in the reconstructed β. A small decrease is also seen at low rigidities as the straight track approximation becomes worse. 4.2. Tracker efficiency 95

Single particle selection Some events in the proton sample contain multiple particles traversing the acceptance simultaneously. These are mostly due to showers of secondary particles from interactions in the experiment itself, or in the satellite payload. As the spectra of secondary production falls steeply with energy, the number of multi-particle events increases rapidly for lower energies. To reject as many of these events as possible a strict single particle selection is made:

1. No signal in CAT or CARD. This removes the majority of the shower events. 2. The number of hit paddles in S11, S12, S21 and S22 must be exactly one. This removes events where 2 or more particles traverse diﬀerent paddles.

3. An upper limit on the dE/dx signal in S11, S12, S21 and S22. This removes most of the events where 2 or more particles have traversed the same paddle.

4. A positive value of β in order to remove albedo particles

Charge one particle selection A charge one selection is made by requiring a proton-like energy deposit in the ToF scintillators. This can be seen in Figure 4.2, where the proton selection band is indicated by the black lines. As the deposited energy scales as the charge squared, multiple charged particles are rejected with this cut. Below 0.8 GV/c protons are no longer MIP particles, and are thus separated from lighter charge one particles such as electrons and pions with the dE/dx cut. Above this energy further rejection has to be applied to achieve a clean proton sample, as will be described below. Note that the rigidity in Figure 4.2 is ToF rigidity, which assumes a proton mass. Contaminating particles with a mass diﬀerent from protons will therefore have a wrongly assigned rigidity. These can instead be rejected using the calorimeter.

Proton selection The charge one selection leaves a sample with predominately protons, but there is still contamination from mostly electrons and deutrons and also pions. Electrons and pions are MIP particles down to very low rigidity, and the dE/dx selection should normally discard these particles up to about 0.8 GV/c. However, as the ToF rigidity is determined from the β assuming a proton mass, the electron and pion ToF rigidities will be over-estimated as they are relativistic particles down to very low rigidity. There will therefore be a contamination of low rigidity electrons and pions above a ToF rigidity of approximately 0.7 GV/c, where the dE/dx selection is no longer capable of separating protons from lighter particles. To reject these particles only non-interacting particles are selected above 0.7 GV/c. The electron contamination is then close to zero. Pions are more diﬃcult to reject as they are hadrons, similarly to protons. The peak of the pion rigidity distribution is around 0.3 GV/c and falls steeply for lower rigidities, and is negligible below 0.1 GV/c. 96 Chapter 4. Selection eﬃciencies

20 103 18

14 ToF dE/dx [MIP] 102 12

6 10

0 0.4 0.6 0.8 1 1.2 1.4 1.6 1 ToF Rigidity [GV/c]

Figure 4.2. The dE/dx in the ToF system. The proton and helium band are clearly visible. The proton band also includes deutrons, and above approximately 1 GV/c other charged one particles as electrons and pions.

The pion contamination in ToF Rigidity then starts at 0.7 GV/c, increases up to 2.0 GV/c, and then falls oﬀ. To reject pions, the track reconstructed in the calorimeter is back-propagated through the PAMELA acceptance and required to be inside the cavity at all points along the track. The contaminating pions are low rigidity particles with a highly curved track, and therefore enter the calorimeter with an inclined track. A part of these events are therefore rejected using this method. There is still a small fraction of deutrons in the proton sample. As a deuteron is approximately twice as massive as a proton, a proton and a deuteron of the same rigidity will have diﬀerent velocity. Therefore, these two types of particle can be separated using the ToF β measurement. A crude measurement showed that the deuteron proton ratio is about 1 to 2 % depending on rigidity.

4.2.2 The efficiency of the basic tracker selection A flight sample of protons (sample A) selected according to the methods described above is used for the derivation of the basic tracker efficiency. The efficiency is defined as the fraction of events (B) in the sample A passing the basic tracker cuts. To see the time evolution of the tracker efficiency four sub-samples are selected from sample A: from July 2006, January 2007, July 2007 and January 2008. The efficiencies for these periods are plotted in Figure 4.3. The figure shows that both 4.2. Tracker efficiency 97 the level and the structure of the efficiency changes over time. For the July 2006 sample, which is directly after launch, the tracker performance is close to ideal. The efficiency increases as the rigidity increases reaching a plateau above 1 GV/c. As the number of malfunctioning VA1 chips increases the efficiency falls. The rigidity dependence also changes slightly. Figure 4.3 also shows the simulated tracker efficiency for two different tracker configurations: a configuration with malfunctioning VA1 chips as in flight during July 2006 and a configuration as in flight during January 2008. The configuration of malfunctioning VA1 chips in flight is changing within each month, but when gen- erating the simulated data for July 2006 and January 2008 only the most frequently occuring configuration is used. Naturally, there is a discrepancy between flight and simulated tracker efficiency. However, the levels and trends are similar.

0.9 2006-07 0.8 Sim. 2006-07 Efficiency

0.7 2007-01 0.6

0.5 2007-07 0.4

0.3

0.2 2008-01 Sim. 2008-01 0.1

0 0.4 0.6 0.8 1 1.2 1.4 1.6 ToF Rigidity [GV/c]

Figure 4.3. Tracker efficiency for flight and simulated data at 4 different times in the PAMELA flight.

A more thorough approach has been used to derive the average simulated tracker efficiency during the PAMELA flight from launch to March 2008. Unique configurations of malfunctioning VA1 chips are identified in experimental data, and by looping over all data the frequency of each configuration can be derived as the number of triggers with that particular tracker VA1 configuration. From the distribution of VA1 configurations, simulated data can be generated by weighting the number of simulated events with each tracker configuration according to its frequency. The resultant tracker efficiency using this simulated data sample is shown in the lower plot of Figure 4.4, together with the average total experimental tracker efficiency. There is a discrepancy between flight and simulation of a few percent 98 Chapter 4. Selection efficiencies which is natural since the VA1 chips are flagged in data by hand, as either malfunctioning or working, but in reality there is a region in time where the performance of the chips is degrading and this is not taken into account in the simulation.

0.9

0.8 Efficiency

0.7

0.6

0.5

0.4 Flight

0.3 Simulation

0.2

0.1

0 0.4 0.6 0.8 1 1.2 1.4 1.6 Rigidity [GV/c]

Figure 4.4. Flight and simulated eﬃciency of the basic tracker cuts. A diﬀerence between simulations and experimental results is evident. This is caused by the crude simulation of the degradation of the tracker over time.

4.2.3 The efficiency of the additional tracker selection The efficiency of the additional tracker cuts (see Section 3.2.2) is calculated from the sample of events passing the basic tracker cuts. Using data from the entire flight period, the efficiency shown in Figure 4.5 is achieved.

4.2.4 The total tracker efficiency By multiplying the basic and the additional tracker efficiencies, the total efficiency is derived. While the efficiency of the additional tracker cuts can be evaluated up to 2.8 GV/c, the range of the basic tracker cuts is limited to 1.7 GV/c due to the time resolution of the ToF system which is used for the rigidity reconstruction. However, as discussed above, the basic tracker efficiency reaches a plateau above 1 GV/c, allowing the efficiency to be extrapolated up to 2.8 GV/c. Back-scattering from the calorimeter could in principle cause a decrease in the tracker efficiency at high rigidities. This effect is however negligible, as will be shown in the next section. 4.2. Tracker efficiency 99

The total tracker efficiency is shown in Figure 4.6. The efficiency is low, and is due to the decreasing number of functioning VA1 chips. It should be stressed that at low energies, this affects only the efficiency of the tracker and not the performance in general. This results in a reduced statistics of antiprotons.

4.2.5 Biases in the tracker efficiency The tracker efficiency has been evaluated using flight protons. Below 0.7 GV/c, a sample of interacting and non-interacting protons is used, while only non-interacting protons are selected above 0.7 GV/c. The calculated efficiency is then applied also to antiprotons, assuming the efficiency for the two particle species to be identical. These two assumptions, 1) that antiprotons and protons have a identical tracker efficiency, and 2) that non-interacting protons constitute an unbiased proton sample when estimating the tracker efficiency, are not completely true and corrections have to be applied to the estimated efficiency to compensate for this. In particular, two effects have to be compensated for 1. Antiproton/proton bias due to dead areas in the tracker 2. particles back-scattered from the calorimeter Correction 1) has to be introduced as positively and negatively charged particles bend in opposite directions while traversing the tracker cavity as a consequence of the magnetic field. In case of a spatially homogeneous tracker efficiency all arrival directions are equally favoured and the total antiproton and proton efficiencies are identical. However, if dead areas with an inhomogeneous spatial distribution are introduced in the tracker, as is the case in PAMELA, certain arrival directions and curvatures can be favoured and a charge sign dependent efficiency can result. This effect is expected to be negligible at high energy where particle tracks are close to a straight line and the difference between tracks with positive and negative curvature is small. However, at lower energies, the track curvature increases and the charge-sign effect should increase accordingly. The second correction (2) concerns particles back-scattered from the calorimeter. This effect can decrease the tracker efficiency in the following three ways: • By producing an upward-going secondary particle that is recognised by the tracker algorithm as a second track. The event is then rejected as only events with a single track are accepted. • By producing clusters in the tracker planes which reduce the probability for the tracker algorithm to find the correct track. • By producing clusters close to the particle track. The event is then rejected by the additional tracker selection (Section 3.2.2). Since only non-interacting protons are selected for the efficiency sample above 0.7 GV/c, the efficiency will be overestimated. Correction 2) is applied to compensate for this. 100 Chapter 4. Selection efficiencies

0.9

0.8 Efficiency

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 4.5. Eﬃciency of the additional tracker cuts evaluated using ﬂight data.

2.5 Efficiency

1.5

0.5

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 4.6. The total tracker efficiency, defined as the combined efficiency of the basic and additional tracker selection. 4.2. Tracker efficiency 101

The corrections 1) and 2) are estimated using simulations. A sample of protons and antiprotons are simulated with a uniform arrival distribution and a flat rigidity spectrum between 0.3 GV/c and 3.0 GV/c. As explained in the previous section, the flight distribution of malfunctioning Viking VA1 chips is introduced in the simulations to mimic the degradation of the tracker efficiency over time. A charge dependent efficiency would result in a shift in the arrival distribution of reconstructed events. Furthermore, the shift should occur at opposite directions for oppositely charged particles. This is indeed what is seen in the simulated data and is shown in Figure 4.7.

S12 impact position

0.018

0.016

0.014

0.012

0.01

0.008 Protons

0.006 Antiprotons

0.004

0.002

0 -20 -15 -10 -5 0 5 10 15 20 [cm]

Figure 4.7. S12 impact distribution in the bending view for simulated protons and antiprotons between 0.3 GV/c and 2.8 GV/c.

As it is difficult to derive corrections 1) and 2) individually, they are computed together in the following manner. A sample of protons traversing the tracker cavity is selected which contain non-interacting protons above 0.7 GV/c, and both non- interacting and interacting protons below 0.7 GV/c. Non-interacting particles are selected as in Section 3.4.1. The tracker efficiency for this sample, ǫpnonint, is then calculated. This corresponds to the tracker efficiency derived in flight. A second sample containing all (anti)protons traversing the tracker cavity are selected, and the efficiency (ǫpall¯ ) ǫpall is calculated. The correction factor to the (anti)proton tracker efficiency is then calculated as (Cp¯ = ǫpall¯ /ǫpnonint) Cp = ǫpall/ǫpnonint. The correction factors for protons and antiprotons are presented in Figure 4.8. The proton correction for back-scattering from the calorimeter is negligible compared to other corrections and will be omitted in the derivation of the proton and antiproton flux. The antiproton correction factor for the charge bias of the tracker 102 Chapter 4. Selection efficiencies efficiency is in the order of a few percent, and increasing at low energy as expected, although the shape of the correction factor is irregular. The irregular shape is probably the result of the large number of different tracker configurations, where each give a different contribution to the tracker efficiency. This correction factor is applied to the antiproton tracker efficiency.

1.5

1.4

p Backscattering 1.3

p Trk Charge Bias+ Backscattering 1.2

Correction Factor 1.1

0.9

0.8

0.7

0.6

0.5 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 4.8. Tracker efficiency correction factors for protons (black) and antiprotons (red). The proton efficiency is corrected for particles back-scattered from the calorimeter. The antiproton efficiency is also corrected for the tracker charge bias.

4.3 ToF eﬃciency

The ToF efficiency is defined as the sum of the cut efficiencies below, which are explained in detail in section 3.3.

1. A proton-like dE/dx in S1 and S2. 2. 1 or 2 paddles hit in each of S1 and S2. 3. A proton-like mass.

The efficiency of the first two cuts depends mainly on the scintillation light collection efficiency while the efficiency of the third cut depends on the time resolution of the ToF system as the mass is reconstructed from the β measurement. To estimate the efficiency of these cuts, an unbiased sample of protons is selected from all flight data. This procedure is explained below. 4.3. ToF efficiency 103

4.3.1 Selecting a proton sample Selecting a pure proton sample for the derivation of the ToF efficiency is significantly easier than for the tracker efficiency as the track reconstruction by the tracker can be used without biasing the sample. All track-related variables are then available, and the rigidity can be measured with a good precision. A difficulty is instead to select a sample with a low contamination of shower particles. This is especially true for S1 - the top scintillator, since there is no independant detector directly below that can be used to reject multi-particle events. This is much less of a problem for S2 since the tracker can be used for this purpose. Requiring no singlets in the tracker removes practically all multi-particle events in S2. Achieving the same multi-particle rejection in S1 is impossible. However, as S1 and S2 are similar detectors, the results for S2 can be used in the derivation of the efficiency for S1. When doing this, simulation has first been used to prove a similar behaviour for the two detectors before results from S2 are extrapolated to S1. It is stressed that efficiencies are not taken directly from simulations. The proton samples are selected differently depending on which efficiency is being determined, for the natural reason that the detector in question can not be used in the selection of the proton sample. However, in common for all are

• a good quality track reconstructed by the tracker

• a tracker dE/dx passing the proton selection deﬁned in Section 3.2.2

• a non-interacting particle in the calorimeter

• no signal in CAT or CARD

• no singlets in the tracker

This selection alone provides a proton sample with a very low contamination. The remaining selection cuts are: 1) a dE/dx in S1 or S2 passing the proton selection defined in Section 3.3.2, 2) a reconstructed mass passing the proton selection defined in Section 3.3.2. The dE/dx selection is used for the study of the β efficiency, and the β selection for the study of the dE/dx efficiencies. For the derivation of the efficiency of the β-selection, a stricter upper limit on the dE/dx in the tracker is used to remove deutrons as the β selection, which normally rejects these particles, can not be used.

4.3.2 The dE/dx selection efficiency Using the proton sample selected above, the efficiency of the dE/dx selection is calculated as the fraction of protons inside a band, defined from flight data, in the dE/dx versus rigidity plot. The derived selection efficiency is presented in Figure 4.9. The efficiency of the S2 selection is high, and weakly dependent on rigidity due to the increased probability of delta ray production which results in a 104 Chapter 4. Selection efficiencies higher energy release in the scintillator. A fit is made to the flight efficiency with the function

f = A + B × rC (4.3)

where A, B and C are fitted parameters and r the rigidity. The following values are found: A=(1.00 ± 2.5 × 10−3), B=((−7.51 ± 2.5) × 10−3) and C=((5.74 ± 1.4) × 10−1). The fit parameters are correlated and the error of the fitted function has to be calculated using the error matrix V. The variance of the function f assuming the fitted variables xj = A, B, C to be correlated is then

T dfi V = A × V × A , where Aij = (4.4) dxj

The error matrix is generated by the MINUIT fit in ROOT. The errors to the fitted function are then simply calculated as the variance squared. The efficiency of S1 is slightly lower, and a large decrease can be seen at low rigidities. This is not a true decrease in efficiency, but rather a contamination of shower particles in the proton sample which increase at low rigidities due to geometrical reasons. A test was performed to check this theory: the efficiency of S11 was derived requiring a proton-like energy deposit in S12. In case the drop in efficiency in S1 is due to shower particles, the effect should be removed or at least significantly decrease for S11 when applying the cut on S12 as this should remove a large fraction of the shower particles. The result confirmed this and supports the theory of a contamination of shower particles. Simulations show that the efficiency for S1 and S2 behave similarly, and should be roughly constant at low rigidities. The efficiency for S1 can therefore be calculated from the results for S2. The fit parameters from S2 are used as starting parameters for the fit to S1, but the range is chosen from 1.2 GV/c where the contamination from shower particles is small. The result is then extrapolated down to 0.3 GV/c. The fitted values are: A=(4.6 ± 5.7 × 10−3), B=(−3.64 ± 5.7 × 10−3) and C=((9.8 ± 6.7) × 10−4).

4.3.3 The number of hit paddles selection eﬃciency

The efficiency for the selection of the number of hit paddles is obtained similarly as for the ToF dE/dx selection. As for the dE/dx selection, there is a contamination of shower particles for S1 at low rigidity. Simulation shows that the behaviour of the efficiency is similar for S1 and S2, and can be fitted with a constant value A across the entire rigidity range. For S1, the line is fitted above 1.2 GV/c where the contamination from shower particles is small. The efficiencies and the fits are shown in Figure 4.10. The results of the fits are A=(0.993 ± 1.1 × 10−4) for S1, and A=(0.998 ± 7.1 × 10−5) for S2. 4.3. ToF efficiency 105

1.1

1 Efficiency

0.9

S1 0.8 S2

0.7

0.6

0.5 0 1 2 3 4 5 Rigidity [GV/c]

Figure 4.9. The efficiency of the ToF dE/dx selection for S1 and S2. The decrease in efficiency for S1 due to contamination of multi-particle events is clearly seen. The solid red and black lines are the result of the fit to the data-points. The fit to S1 is done using the result from the fit of S2. Notice that the scale of the y-axis is different from the previous plots. The efficiency is calculated to 5 GV/c to increase the accuracy of the fit.

4.3.4 The mass selection eﬃciency

A proton sample is selected with the common selection described above. However, the mass selection can not be used which is the most eﬀective cut against deutrons. Instead, a more strict upper limit on the tracker dE/dx is used. Using this proton sample, an eﬃciency as in Figure 4.11 is achieved.

4.3.5 The total ToF eﬃciency

The total ToF efficiency is defined as the efficiency of the dE/dx, npaddles and mass selection. As the efficiency of each cut has been derived using an unbiased proton sample and are uncorrelated to each other, the efficiencies and their associated errors can be multiplied to achieve the total ToF efficiency. This is presented in Figure 4.12. 106 Chapter 4. Selection efficiencies

1.1

1.05 Efficiency 1

0.95

0.9 S1 S2 0.85

0.8

0.75

0.7 0 1 2 3 4 5 Rigidity [GV/c]

Figure 4.10. The efficiency of the ToF npaddles selection. A false reduction of efficiency for S1 is evident also here, though smaller than for the dE/dx selection. The red and black lines are the result of the fit to the data points where the result of the fit to S1 is done using the results from S2. Notice that the scale of y-axis is different to previous plots. The efficiency is calculated up to 5 GV/c to increase the efficiency of the fit.

As all ADC1 and TDC2 signals are read out by a common electronics board, a bias of the efficiency of each of the individual ToF cuts could be introduced as the proton samples used to derive the efficiencies of each of the cuts are selected using cuts on the other ToF variables. This effect is estimated by comparing the efficiency of the S2 dE/dx selection using two different methods for selecting the proton sample. Method 1) is the standard selection presented above, and method 2) is similar to method 1) but excluding all selections on the ToF system. Comparing the two methods, a difference of (0.2) % above 1 GV/c is found. This is added to the total ToF efficiency as a systematic error. The difference is greater below 1 GV/c, but is likely due to an increased contamination of shower particles as the β cut, which is an effective cut for multiple particles, is removed in this case.

4.4 Calorimeter eﬃciency

In contrast to the Tracker and ToF system, the calorimeter performs a destruc- tive measurement of a particle. The passage of a proton or an antiproton in the

1ADC: Analog to Digital Converter 2TDC: Time to Digital Converter 4.4. Calorimeter eﬃciency 107

0.9

0.8 Efficiency

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 4.11. The efficiency of the ToF β selection. calorimeter thus depends largely on the cross-section for hadronic interactions. The cross-section for pp andpp ¯ interactions versus kinetic energy is shown in Figure 4.13. Below 1 GeV, the inelastic cross-section (total minus elastic in the figure) for antiprotons increases dramatically as antiprotons annihilate with protons. For protons in the same energy range, the cross-section for elastic interactions dominates and is thus very different from antiprotons. The difference in hadronic cross-section for antiprotons and protons is lower at higher energies, but can not be assumed identical until approximately 100 GeV. The interactions of antiprotons and protons can therefore not be considered equal in the calorimeter, and the efficiency of the calorimeter selection for protons and antiprotons will have a non-negligible difference. The proton efficiency can still be estimated from a proton sample selected in flight, but the antiproton efficiency must be estimated using simulations. This introduces an error in the estimation of the antiproton efficiency, as a discrepancy between simulations and flight data is expected. This discrepancy is mainly due to three factors:

1. Incomplete models of hadronic interactions in the simulation

2. Problems with calibrations in ﬂight, which can result in areas in the calorimeter with a wrongly assigned energy deposit. This will negatively aﬀect the performance of the selection cuts, in particular nstrip and noint.

3. Multiple particles in the calorimeter. The eﬀect is similar to point 2). 108 Chapter 4. Selection eﬃciencies

0.9

0.8 Efficiency

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 4.12. The efficiency of the total ToF selection. This is defined as the efficiency of the multi-particle selection, dE/dx selection and β selection.

To take these issues into account also in the simulated antiproton efficiency, a scaling factor is applied. The scaling factor is calculated as the ratio between the proton efficiency estimated using flight data, and the proton efficiency estimated with simulations.

4.4.1 Calorimeter proton efficiency The calorimeter proton efficiency is estimated using both simulations and flight data. For the simulations, the GPAMELA program was used. A set of protons were generated with a random arrival direction and a rigidity between 0.3 GV/c and 3.0 GV/c. The subset of the data which passed the basic and additional tracker criteria was selected. From that sample, the efficiency was calculated as the fraction of particles passing the calorimeter selection (explained in Section 3.4). The resulting efficiency versus rigidity is plotted in Figure 4.14 (red markers). The efficiency is approximately 70 % above 1 GV/c and decreases at lower rigidities. The decrease can be explained by 1) the kinetic energy of the particle is not sufficient for creating a shower. The particle will therefore lose its remaining energy by ionization. Neither the qtr or the nstrip cut will therefore be effective. 2) the large amount of multiple scattering results in a poor reconstruction of the shower axis which affects the qout, noint and qtr cuts negatively. The calorimeter proton efficiency obtained using flight data is shown in Fig- ure 4.14 (black markers). The efficiency is calculated from a sample of protons 4.4. Calorimeter efficiency 109

10 2

total ⇓

Cross sectionCross (mb) p p

10 elastic

Plab GeV/c

10 -1 1 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8

√s GeV

1.9 2 10 10 2 10 3 10 4

10 2 ⇓ total

− Cross sectionCross (mb) p p

10 elastic

Plab GeV/c

10 -1 1 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8

Figure 4.13. Cross sections for pp (top) andpp ¯ (bottom) hadronic interactions. Taken from [67]. 110 Chapter 4. Selection efficiencies selected from the full flight period. The sample is selected requiring: 1) a track reconstructed from data fulfilling the basic and additional tracker criteria 2) a proton-like dE/dx in the Tracker and ToF-system, 3) a proton-like velocity measured with the ToF-system. This leaves a small (< 1 %) contamination of positrons above 1 GV/c. The efficiency is calculated as the fraction of particles in the sample passing the proton calorimeter selection. The result, as shown in Figure 4.14, is systematically lower than the simulated efficiency as expected. The ratio between the simulated efficiency and the efficiency derived in flight defines the correction factor, which is shown in blue in Figure 4.14.

0.9

0.8

0.7

0.6

0.5 Flight

0.4 Simulation

0.3 Correction Factor

0.2

0.1

0 1 1.5 2 2.5 3 Rigidity [GV/c]

Figure 4.14. The calorimeter proton efficiency estimated with simulation (red) and using flight data (black). The blue data points (top in figure) corresponds to the correction factor which is calculated as the ratio of the flight efficiency with the simulated efficiency.

4.4.2 Calorimeter antiproton selection eﬃciency

The antiproton efficiency is estimated using simulations similarly to the proton efficiency and the result is shown in black in Figure 4.15. Comparing the antiproton efficiency with the proton efficiency presented in Figure 4.14, a clear difference can be noted which reflects the hadronic cross-sections for protons and antiprotons, presented in Figure 4.13. This is most clearly seen at low energies, where the inelastic cross-section for antiproton becomes very large while the cross-section for protons is dominated by elastic collisions. 4.4. Calorimeter efficiency 111

The final antiproton efficiency is derived by multiplying the simulated antiproton efficiency with the correction factor. The result is shown in red in Figure 4.15.

0.9

0.8

0.7

0.6

0.5 Simulation 0.4

Scaled to Flight 0.3

0.2

0.1

0 1 1.5 2 2.5 3 Rigidity [GV/c]

Figure 4.15. The calorimeter antiproton eﬃciency estimated with simulation (black) and scaled with the ﬂight correction factor (red).

4.4.3 Validation of the correction factor The correction factor is applied to the antiproton efficiency to compensate for the different selection efficiencies that are present in flight and in simulation. The correction factor is derived from proton data, but the selection cuts have a different efficiency for antiprotons and protons, and the “noise” introduced in flight will therefore affect the antiproton and proton selection cuts differently. An uncertainty in the antiproton selection efficiency is therefore introduced by applying the correction factor. The magnitude of this uncertainty can be understood by studying the simulated, scaled simulated, and flight antiproton efficiency when removing a selection cut. The cut qtr is chosen as this cut has a strong effect on the correction factor at low energy. When removing the qtr selection cut, the number of selected antiprotons in flight decreases with 10.0 % below 1.5 GV/c, and 5.1 % above 1.5 GV/c. The same operation on simulated data rescaled with the correction factor gives a decrease of 9 % and 6 % respectively. Thus, the simulated efficiency corrected with the proton correction factor reproduces the behaviour of the flight antiproton sample well. To accommodate the differences that do exist, a conservative error of 5 % is added to the antiproton calorimeter efficiency. 112 Chapter 4. Selection efficiencies

4.5 Trigger eﬃciency

The trigger efficiency of the PAMELA instrument is calculated as the product of the trigger efficiency for each layer required in a particular trigger configuration. For example, for the trigger configuration (S11 AND S12) AND (S21 AND S22) AND (S21 AND S31), the efficiency is PS11 × PS12 × PS21 × PS22 × PS31 × PS32, where Pij is the trigger efficiency for the ToF layer ij. The trigger efficiency is calculated from a flight sample of protons selected from the entire flight period. Protons are selected requiring a non-interacting track in the calorimeter, a reconstructed track in the tracker passing the basic tracker criteria and a dE/dx in the tracker planes compatible with a proton. The trigger efficiency ǫji for each layer i in plane j is then calculated as Number of events with a signal in ij ǫ = (4.5) i Number of events with a signal in j!i where layer j!i is the layer coupled to layer ji (i.e layer S12 for layer S11). An independent calculation of the trigger efficiency [68], yields an efficiency greater than 0.997 with an error of the order 0.5 × 10−4. As this is completely negligible compared to other errors described in this section, the trigger efficiency will be omitted when calculating the total selection efficiency.

4.6 Total selection eﬃciency

The derived efficiencies for the ToF, tracker and calorimeter are uncorrelated and the total antiproton and proton selection efficiency can thus be calculated by multiplying the individual efficiencies and associated errors. The individual efficiencies are shown in the top plot of Figure 4.16, and the total efficiencies in the bottom plot in the same figure. The efficiency of the selection is dominated by the tracker and calorimeter selection at low energy, and the tracker selection at high energy. Further studies could be conducted to improve the calorimeter selection at low energy to achieve an increased efficiency. Unfortunately there is little room for improvement of the tracker efficiency as it is not a selection inefficiency, but an inefficiency of finding a track. Thus, making the tracker criteria less strict will not increase the tracker efficiency significantly. The errors on the selection cuts are with one exception less than one percent in each bin. The exception is the antiproton calorimeter selection, which is derived using simulations. A higher error is introduced to accommodate the inevitable differences that do exist between simulation and flight. The magnitude of the error is justified by flight data. The total selection efficiency, seen in the bottom part of Figure 4.16, is between 40 − 50 % below 0.8 GV/c where only the tracker and ToF selection is used to identify protons and antiprotons. The efficiency is identical for protons and antiprotons. The calorimeter selection is applied above 0.8 GV/c and the total 4.6. Total selection efficiency 113 selection efficiency decreases to about 25 %. A difference between the selection efficiencies for antiprotons and protons is introduced by the calorimeter selection. The selection efficiency of the anticounter cut is assumed to be 100 % and is therefore not introduced in the total efficiency. This is justifiable, as only single particle events going cleanly through the instrument should be considered in the derived proton and antiproton sample respectively. Also the trigger efficiency is assumed to be 100 %, as was mentioned previously. 114 Chapter 4. Selection efficiencies

0.9

Efficiency 0.8

0.7

0.6

0.5

0.4 Tracker ToF 0.3 Calorimeter p

0.2 Calorimeter p

0.1

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

0.9

0.8 Efficiency

0.7 Protons

0.6 Antiprotons

0.5

0.4

0.3

0.2

0.1

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 4.16. Top: The derived selection efficiencies for the tracker, ToF and calorimeter selection. The calorimeter efficiency is given separately for protons and antiprotons. Bottom: The total selection efficiency for protons and antiprotons. The efficiency below 0.8 GV/c is identical for protons and antiprotons and only the latter is seen in the figure. Chapter 5

The p/p¯ ratio and p¯ ﬂux

In this chapter, all steps necessary for deriving the antiproton flux and thep/p ¯ flux ratio at the top of the atmosphere will be presented. The antiproton and proton selection, which has been presented in Chapter 3, resulted in a number of detected antiprotons and protons between 0.4 GV/c and 2.8 GV/c and an estimation of the contamination of pions and electrons in the antiproton sample. The efficiency of the selection was investigated in Chapter 4. Combining these results, by subtracting the contamination and compensating the remaining number of particles for the selection efficiencies, the number of antiprotons and protons in the spectrometer can be derived. These numbers are then corrected for losses in the payload and known biases in the selection to derive the number of antiprotons and protons at the top of the atmosphere (TOA). These correction factors are presented in the next section. In the final sections, the antiproton flux and antiproton-to-proton flux ratio is presented and discussed in the context of earlier measurements and theoretical calculations of secondary and primary production of antiprotons.

5.1 Correction factors

A number of different phenomena change the energy spectrum of particles that is reconstructed by the experiment from the “real” spectrum impinging on the instrument. Some of these phenomena are due to the instrument and can be compensated for in the analysis of flight data. Others are consequences of the environment around the detector and must be treated using models, predictions and measurements. This is, for example, the shielding effect of the geomagnetic field or the adiabatic deceleration of cosmic rays in the outward flow of particles from the sun. In the reconstruction of the flux of antiprotons at the top of the atmosphere, the corrections listed below are performed. The corrections that are different for protons and antiprotons are labeled (p/p¯).

115 116 Chapter 5. The p/p¯ ratio and ¯p ﬂux

• Atmospheric corrections

1. Transmission through the geomagnetic ﬁeld

• Instrumental corrections

1. Selection eﬃciencies (p/p¯) 2. Tracker charge bias (p/p¯) 3. The geometrical factor 4. The live-time of the experiment 5. Interaction losses in the experiment (p/p¯) 6. Energy loss in the experiment

5.1.1 The geometrical factor The geometric acceptance of an experiment is deﬁned by the 4-dimensional integral

G(r)= dΩdS|cosθ|f(x, y, θ, φ, r) (5.1) ZS0,Ω where S0 is a reference plane within the instrument, orthogonal to the Z axis and located at height z = z0, Ω is the total solid angle, r the rigidity and f a weight function that is either 1 or 0 depending if the incident particle satisfies the acceptance requirements of the instrument. Note that the geometrical factor includes a dependence on the rigidity of the incident particle. This is necessary as the acceptance window varies with rigidity in presence of a magnetic field. Particles with a smaller rigidity are more deflected towards the walls of the magnetic cavity where they are lost before reaching the lower planes of the tracking system. Thus, the acceptance, and the geometrical factor, is expected to decrease at low rigidities. It can also be observed that the geometrical factor does not depend on particle species. The trajectory of a particle is uniquely defined by the initial rigidity r, the coordinates (x,y) at z = zo, the direction of incidence (θ, φ), and the magnetic field B(x,y,z). For the calculation of the geometrical factor, a set of particles are generated on the reference plane S0, each with the parameters (x, y, θ, φ, r). Each particle is then propagated through the instrument, using the same tracking routine employed in the reconstruction of flight data. This routine is based on the interpolation method of Runge-Kutta [69] for solving the equation of motion of a charged particle in an homogeneous magnetic field. The geometrical factor is then calculated with

• the reference plane S0 corresponding to the upper end of the magnetic cavity

• the angular domain of integration limited to the downward hemisphere, characterised by π/2 <θ<π. 5.1. Correction factors 117

• the weight function f equal to 1 or 0 depending whether the trajectory satisﬁes the acceptance requirements.

The acceptance requirements are:

• the trajectory must cross at least one of the layers in each plane of the ToF system. • the trajectory must traverse the magnetic cavity of the spectrometer without touching the walls of the cavity.

The result of this computation for negative particles between 0.01 GV/c and 500 GV/c is shown in Figure 5.1. A ﬁt to the data points are made with the function

− G(r)=(1/f α +1/Aα)( 1/α), where f = B + C × log(r/(GV/c)) (5.2) where r is the rigidity, and A, B, C and α are fitted parameters. The parameters resulting from the fit are: A=21.61, B=65.29, C=48.78 and α=3.65. The geometrical factor is almost constant for the rigidity range considered here (> 0.4 GV/c). The difference between the geometrical factor for positively and negatively charged particles is plotted in Figure 5.1 (bottom). Above 0.4 GV/c, this is of order of 10−4. The geometrical factor which has been derived for negatively charged particles will therefore be used also for positively charged particles, as the difference in geometrical factor is negligible compared to other uncertainties. Uncertainties on the estimated geometrical factor, as shown in Figure 5.1, are composed of two parts 1. The computational error 2. The geometric error The computational error has been estimated to be in the order of 0.2 % and symmetric [68]. The difference between the nominal geometry of the experiment (the geometry according to the geometric specifications of the instrument) and the real geometry introduces a geometric error in the geometrical factor. This uncertainty is estimated by comparing the calculated geometrical factor for two different models of the geometry of PAMELA: the nominal model, and a model where all mechanical tolerances are taken into account. For example, the uncertainty of the length of the magnet cavity is known to be 100 µm. A model with a longer cavity, and therefore a larger geometric factor, can then be constructed within the uncertainties of the nominal geometry. Similarly, a model with a smaller geometric factor is possible. Taking into account the mechanical tolerances of all pieces in the instrument according to two worst-case scenarios, an upper and a lower limit of the geometrical factor can be derived. The resulting errors are about 0.3 %, and are thus in the same order as the computational error. 118 Chapter 5. The p/p¯ ratio and ¯p flux

Geo. Factor [cm^2*Sr] 10

10-1 1 10 102 Rigidity [GV/c]

- 0.006 )/G + -G - 0.005 (G

0.004

0.003

0.002

0.001

-0.001 10-1 1 10 102 Rigidity [GV/c]

Figure 5.1. Top: The geometrical factor for negative particles. Bottom: The relative diﬀerence of the geometrical factor for negative (G−)and positive (G+) particles. 5.1. Correction factors 119

5.1.2 Transmission through the geomagnetic field As described in section 1.3.2, the geomagnetic field of the earth deflects charged particles and can prevent low energy particles from reaching PAMELA. The momentum needed for a galactic cosmic ray to reach the satellite has been approxi- mated by the Stoermer Vertical Cutoff (SVL), discussed in Section 3.5. This can be written as p ≥ 14.9Z × cos4λ[GV/c] (5.3) where Z is the charge of the cosmic ray and λ the geomagnetic latitude. As was discussed in Section 3.5, the rigidity of selected particles is required to be larger than 1.2×SVL, to unambiguously select galactic particles. As the trajectory of PAMELA is highly inclined, the geomagnetic cut-off will change significantly during the orbit, from less than 1 GV/c close to the poles, to approximately 15 GV/c at the equator. The fraction of an orbit for which a cosmic ray of given rigidity can reach the orbit from outer space will then be a continuously increasing function of rigidity, saturating at unity for particles above 15 GV/c. This geomagnetic transmission function can be derived directly from flight data. Assuming that the particle flux is isotropic, the loss of particle intensity can be compensated for by multiplying the measured flux with the inverse of the transmission function. The geomagnetic transmission function for the PAMELA orbit, generated from all flight data, is shown in Figure 5.2. This has been generated by integrating the time spent at each cut-off interval over the entire flight. The Stoermer vertical cutoff is derived from a map which contains the cutoff for each geomagnetic latitude and longitude and height above the Earth [34]. The geomagnetic transmission is calculated for a vertical cutoff. This is a simplification as the satellite occasionally “sweeps” back and forth when taking pictures of the surface of the Earth. This can result in a lower or higher effective geomagnetic cutoff, depending on the orientation of the satellite. The change due to this effect is estimated to be less than 10 % for inclinations below 10◦ [70]. This is within the conservative lower limit used for the geomagnetic cut-off.

5.1.3 Live time of the experiment

The live time Tl is deﬁned as the time the experiment is operational and ready for a new trigger. The opposite - the dead time, is then the time the instrument is switched oﬀ or is reading out and processing data. As most of the data volume is produced by the tracker, this sub-detector contributes to about 90 % of the total dead time of PAMELA. The live time is measured by a DAQ counter which increments with a known frequency when the IDAQ (Internal Data Acquisition) system has not asserted the busy line. The live time of the data used in this analysis is estimated to be

7 Tl =3.211 × 10 s (5.4) 120 Chapter 5. The p/p¯ ratio and ¯p ﬂux

0.8

0.6 Transmission fraction 0.4

0.2

0 0 2 4 6 8 10 12 14 16 Rigidity [GV/c]

Figure 5.2. The geomagnetic transmission function: the fraction of time spent at geomagnetic locations where a cosmic ray at a certain rigidity can penetrate from outer space to the orbit of PAMELA. Galactic cosmic rays of rigidity 2 GV/c can thus be detected in about 40 % of the time. The Stoermer Vertical Cut-Off times a factor of 1.2 has been used to calculate the cut-off at each position in the orbit. The use of this particular cut-off has been validated with flight data.

There is a systematic bias in the estimation of the live-time since when the trigger signal arrives at the trigger board, the count of the live-time and dead-time does not stop until the next clock cycle. The resulting error is rate dependent but has been estimated to be less than 0.8 % [63]. A conservative error of 1 % is therefore added to the live-time.

5.1.4 Hadronic interactions A particle entering the acceptance of PAMELA with a direction and momentum such that it would traverse the instrument cleanly should always be accounted for in the calculation of the particle flux. Even though the integrated amount of material a particle has to traverse within the instrument is small, there is a probability that a particle interacts inside the acceptance and does not reach S3. Interacting events are assumed to be rejected by the selection cuts that are applied on flight data. This loss is not accounted for in the selection efficiency due to the non- interacting requirement of the efficiency sample. This must be taken into account in the calculation of the proton and antiproton fluxes, and also for the antiproton- to-proton flux ratio as the cross-section for inelastic interactions are different for the two types of particle. 5.1. Correction factors 121

To estimate the loss of particles due to inelastic interactions two diﬀerent methods have been used

• Method A: A GPAMELA simulation of the fraction of particles lost above S3 due to inelastic interactions

• Method B: A theoretical calculation of the interaction probability for particles traversing the integrated amount of material above S3, assuming straight tracks

The results of both methods are used to deﬁne a correction factor, which is the rigidity dependent function that applied to the measured ﬂux of particles compensates for the loss of particles due to hadronic interactions in the instrument.

Method A For method A, the simulation tool GPAMELA has been used. A sample of particles with a uniform arrival direction and a momentum between 0.4 GV and 100 GV were simulated through the PAMELA acceptance. The starting point, direction and momentum were chosen in such a manner that the particle would traverse the acceptance cleanly if not interacting inside the acceptance. This sample is referred to as sample 1). The same sample of particles was simulated again but with hadronic interactions turned oﬀ (sample 2). The diﬀerence in the number of particles reaching S3 for sample 1) and sample 2) is then solely dependent on hadronic interactions. From this value, and the number of particles in the sample, the correction factor can be derived.

Method B Method B is an approximate theoretical method [71]. The thickness and inelastic interaction probabilities for all the materials above the calorimeter are summed, and the total interaction probability for a vertically through-going particle is derived. This is clearly a simpliﬁcation, but is a useful cross-check to method A. The characteristics of all materials above the calorimeter is shown in Table 5.1.

The results of the two methods are shown in Figure 5.3. The correction factors can be understood by studying the cross-section for (anti)proton inelastic collisions, given in Figure 4.13, section 4.4. The figure shows that the inelastic cross-sections for protons and antiprotons are similar within a few percent in the energy region above 10 GeV. Furthermore, the cross-sections decrease for energies up to about 100 GeV and then increase. This explains the high energy part of the derived correction factors in Figure 5.3, where the correction factors for protons and antiprotons both approach unity. At low energies, the cross-section for inelastic interactions for antiprotons increase dramatically as antiprotons annihilate. This is reflected by the large increase in the correction factor for antiprotons at low energy. However, as shown in Figure 5.3, also the correction factor for protons, derived with simulations, 122 Chapter 5. The p/p¯ ratio and ¯p flux

Name Atomic Density ∆Z Vertical depth Structure g/cm3 mm (g/cm2) Container Aluminium alloy Al 2.61 1.7 0.4437 Gas N2 0.00125 322.38 0.04027

S1+S2+S3 detectors Aluminium Al 2.7 0.99 0.267 PVC C8H8 0.105 27 0.0945 Mylar H4C5O2 4.17 0.069 0.018 Scintillator H11C10 3.096 21 2.166

Tracker Silicon Si 2.33 1.8 0.419 TOTAL 3.45

Table 5.1. The material above the calorimeter. increase below 1 GV/c. This is not what is expected considering the cross-sections for protons, or from the theoretical model presented in Figure 5.3. The reason for this increase at low energy is unknown. An error of 5 % is therefore added to the correction factors for hadronic interactions below 1 GV/c. Above 1 GV/c, an error of 2 % is applied. The matter located above the instrument corresponds to 0.44 g/cm2. This is significantly smaller than the atmospheric overburden for a high altitude balloon flight such as BESS (which had roughly 5.0 g/cm2 during the first polar flight [72]). Taking into account the characteristics of the materials in the dome and in the atmosphere, the correction for losses in the two cases are of the same order order of magnitude, between 5 and 15 % depending on energy (see Figure 5.3). However, the systematic error which is introduced by this overburden of material is much lower for PAMELA, as secondary production of antiprotons in the dome is negligible [65], but amounts to up to 30 % of the total detected antiprotons for balloon experiments.

5.1.5 Energy loss in the instrument As a particle traverses the experiment it gradually looses energy due to interactions with matter. The reconstructed rigidity is therefore lower than the rigidity at the top of the instrument1 (TOI). The exact amount of energy a particle looses depends on the amount of matter traversed. The integrated amount of matter above S3 is approximately 3.8 g/cm2 (see Table 5.1). A method to compensate for this energy loss therefore has to be devised. There exist a number of diﬀerent methods in literature, and a method proposed by D’Agostini is used here [73] to compensate

1The dome - the aluminium container located above the PAMELA instrument, is included in the instrument when referring to the TOI energy. 5.1. Correction factors 123

1.25

1.2 Proton (A) Antiproton (A) Proton (B) 1.15 Antiproton (B) Correction Factor p p, 1.1

1.05

1 10 102 Rigidity [GV/c]

Figure 5.3. The p,p ¯ correction factors for inelastic interactions. for the energy loss of protons. This method uses Bayes’ theorem to unfold the true from the reconstructed rigidity distribution. This method is not applicable to antiprotons due to the small statistics. Since the energy loss in the instrument is not measured2 and the number of antiprotons are small, there are no methods of compensating for this loss without introducing errors which are in the same order of magnitude as the errors between the energy at TOI and the reconstructed energy. Therefore, instead of compensating for the energy loss for antiprotons, a systematic error is introduced. This is explained later. The method by D’Agostini deals with binned data, and not with individual events. Following the syntax in [73], the TOI rigidity are referred to as causes Ci which each can produce several possible eﬀects Ei (reconstructed rigidity). If the initial probability of the ith cause is P0(Ci), the conditional probability of the j th eﬀect to have been produced by the ith cause is, using Bayes theorem

P (Ej |Ci)P0(Ci) P (Ci|Ej )= nC (5.5) l=1 P (Ej |Cl)P0(Cl) P 2The ionization loss in the ToF layers and tracker layers is measured and could be used to measure a part of the energy loss (the energy loss in the dome is still unknown), but due to the large number of malfunctioning VA1 chips this method is not used. 124 Chapter 5. The p/p¯ ratio and ¯p ﬂux

where nC is the number of causes. If nE is the number of effects and n(Ej ) the number of observed events for each effect j, then, omitting the efficiency, the best estimate of the true number of events is

nˆ(Ci)= n(Ej )P (Ci|Ej ) (5.6) Xj=1

The initial probabilities of the causes are unknown, but can be derived iteratively assuming a ﬂat spectrum initially. The probabilities P (Ej |Ci) are estimated with Monte Carlo methods. By using GPAMELA, a set of particles with an initial position above the container are traced through the instrument, and the rigidity at TOI compared with the rigidity in the spectrometer. By doing this for a spectrum of particles, the probabilities P (Ej |Ci), which henceforth is called the smearing matrix can be derived. An example of a proton smearing matrix between 0 and 2.8 GV/c can be seen in Figure 5.4. A proton spectrum measured by PAMELA has been used [63].

2.5

1.5 Reconstructed Rigidity [GV/c]

0.5 0.5 1 1.5 2 2.5 Simulated Rigidity [GV/c]

Figure 5.4. The proton smearing matrix. The matrix is constructed by a simulated proton spectrum of 50000 events sampled from the experimental proton spectrum measured by PAMELA.

To check the performance of the unfolding, two sets of simulated proton data are constructed with identical rigidity distribution at TOI. One set is used to generate 5.1. Correction factors 125 the smearing matrix which is then applied on the second set to unfold the reconstructed distribution. The result of such a test made with two sets of simulated protons according to a spectrum measured by PAMELA is shown in Figure 5.5. Variations between the true and unfolded spectra of up to 0.5 % are noticed when repeating this test with diﬀerent input spectra.

12000

10000 Input

Reconstructed 8000 Unfolded

6000

4000

2000

0 0.5 1 1.5 2 2.5 Rigidity [GV/c]

Figure 5.5. Performance of the unfolding for an input spectra of protons as measured by PAMELA.

As was mentioned above, a systematic error is added to the experimental antiproton spectrum to accommodate for the uncertainties that are introduced by energy loss in the instrument. To estimate these errors, the following method was applied. A large number of antiprotons were simulated traversing the experiment. The rigidity at TOI and in the spectrometer (REC) were saved for each event. From this series of events, a large number of TOI and REC spectra were assembled, each with 171 events (the number of selected antiprotons in flight). The events in the first TOI spectra corresponds to the events in the first REC spectra etc. The relative difference between the REC and TOI number of events in bin i for all spectra is a measure of the fluctuations in bin i due to energy loss in the instrument. The distribution of the relative difference for bin 4 (1.6 GV/c and 2.0 GV/c) is shown in Figure 5.6. The errors introduced by energy loss are clearly asymmetric and the RMS for the negatively and positively signed distribution is therefore used to define the upper and lower errors introduced by energy loss in the instrument. The upper and lower errors for all bins are shown in Table 5.2. 126 Chapter 5. The p/p¯ ratio and ¯p flux

Rigidity (GV/c) Error (Upper) Error (Lower) 0.4-0.8 0.0 0.160 0.8-1.2 0.028 0.034 1.2-1.6 0.023 0.022 1.6-2.0 0.015 0.021 2.0-2.4 0.018 0.019 2.4-2.78 0.017 0.017

Table 5.2. Upper and lower errors of the antiproton spectrum introduced by energy loss in the instrument.

200

180

160

140

120

100

0 -0.25 -0.2 -0.15 -0.1 -0.05 -0 0.05 0.1 0.15 0.2 0.25 (TOI-REC)/TOI

Figure 5.6. The distribution of the relative difference between the TOI spectra and REC spectra between 1.6 and 2.0 GV/c. The negatively and positively signed distributions are used to define the upper and lower errors in a bin due to energy loss of particles while traversing the instrument. Each distribution is indicated by a different color for clarity. 5.2. The number of p and p¯ at the top of the atmosphere 127

5.2 The number of p and ¯pat the top of the atmosphere

The raw numbers of selected proton- and antiproton- candidates were presented in Table 3.5, section 3.10. These numbers are now compensated for the following eﬀects to derive the number of selected particles at the top of the atmosphere:

1. the estimated pion contamination is subtracted from thep ¯ sample

2. the number of p andp ¯ are corrected for the selection eﬃciencies.

3. the number ofp ¯ is corrected for the eﬀect of tracker charge bias.

4. the number of p andp ¯ are corrected for hadronic interaction losses

5. the number of p andp ¯ are corrected for energy loss

6. the number of p andp ¯ are corrected for the transmission through the geomagnetic ﬁeld

The efficiencies3 of the items presented above all show a rigidity dependence. Correcting the number of protons or antiprotons with the efficiency in the center of each bin will therefore give a biased result. The mean efficiencyǫ ¯ for each bin is therefore used, which is calculated with a weighting technique using proton and antiproton fluxes J(r) in the following way

ǫ(r)J(r)dr ǫ¯ = (5.7) R J(r)dr R where r is the particle rigidity. A theoretical interstellar spectrum from [74] is used for antiprotons. This spectrum is modulated with a solar modulation parameter φ = 500 MV/c, adapted for a period of minimal solar activity. For protons, the flux under study is used. However, the flux depends on the efficiency so an iterative approach is adopted. A first estimate of the efficiencies ¯ǫ are obtained from the efficiency distribution ǫ(r) and the raw proton spectrum JP (r), where linear interpolation is used to obtain the value at any given rigidity. A new spectrum is obtained by applying the calculated efficienciesǫ ¯ to the raw spectrum. Again, a new spectrum and a new set of efficiencies can be obtained from this second spectrum. This iterative procedure is continued until the spectrum from one iteration to the next does not change more than 1 %. Applying this technique, the number of protons and antiprotons at TOA are calculated. The result is shown in Table 5.3.

3The term eﬃciency, which is normally used for selection cuts, is used also for correction factors. 128 Chapter 5. The p/p¯ ratio and ¯p ﬂux

Rigidity DETECTED TOA GV/c p¯ p p¯ p 0.4 - 0.8 1165802 5 14162616 66 0.8 - 1.2 1367561 4 21698489 69 1.2 - 1.6 1724266 23 21625684 343 1.6 - 2.0 1619140 29 17787433 339 2.0 - 2.4 1415407 37 13969076 375 2.4 - 2.78 1160659 50 10467072 455

Table 5.3. The number of antiprotons and protons: column 2,3) detected by the experiment, with the estimated contamination of pions subtracted, column 4,5) estimated at the top of the atmosphere. The errors have been omitted for clarity.

5.3 The antiproton ﬂux

The antiproton ﬂux at the top of the atmosphere is calculated as

1 TOA F (E)= × NP¯ (E) (5.8) Tlive × G × ∆E

where G is the geometrical factor, Tlive the live time, ∆E the width of the energy TOA bin, E the kinetic energy and Np¯ the number of antiprotons at the top of the atmosphere as given by Table 5.3. The resulting ﬂux is presented in Table 5.4 and in Figure 5.7. Data points are centered in each bin according to a technique developed by Laﬀerty and Wyatt [75]. Each value (x0) is determined as the abscissa value at which the measured spectrum is equal to the expectation value of the ”true” spectrum. This can be expressed as

1 x2 f(x0)= f(x)dx (5.9) x2 − x1 Zx1 where f(x) is a theoretical model of the antiproton spectrum [74]. This method does not have the same problems with non-linear spectra as when using the mean value or weighted average. The error-bars in the figure are the sum of the statistical and the systematic errors. Each component of the error is shown separately in Table 5.4. Statistical errors dominate over systematic errors over the entire energy range although of the same magnitude close to 2 GeV. The pion and electron contamination gives the largest contribution to the systematic error above 0.8 GV/c. The contamination of pions constitutes an irreducible background which can only be estimated and subtracted. The pion contamination has been estimated with a number of different methods, using both flight data and simulations. The agreement between the different methods are good, and it is therefore believed that the pion contamination has been estimated with a good accuracy. However, as the number of pions constitutes a large fraction of the signal in some bins, the associated Poisson errors which are added to the remaining events are considerable. 5.5. Antiproton measurements 129

The systematic error introduced from the contamination of electrons is zero below 0.8 GV/c and small at higher energies. This is explained in detail in section 3.8. The systematic errors of the selection efficiencies has been discussed in Chap- ter 3. The efficiencies of the tracker and ToF system are estimated with uncertainties below 1 % above 1 GV/c, and a few percent at lower rigidities. An uncertainty of 5 % is assigned to the antiproton calorimeter efficiency as this efficiency is estimated using simulations. As can be noticed in Table 5.4, the systematic errors are significantly smaller for the first energy bin as the selection of antiprotons can be achieved with a zero contamination of pions and electrons, thanks to the velocity measurements of the ToF system. Additionally, all selection efficiencies in this bin are derived using flight data and are thus completely independent of simulations. The third bin in the PAMELA antiproton flux is higher than what is naively expected considering the other data points in the spectrum. Excluding the scenario that this is indeed the correct flux, the increase could be due to: 1) a statistical fluctuation, 2) a remaining electron and pion contamination or 3) a wrongly estimated efficiency in this energy region. The contamination of pions and electrons are believed to be under control, as discussed earlier, and point 2) is therefore ex- cluded. Concerning 3), the calorimeter efficiency decreases in this energy region, and this was therefore investigated further. A modified set of calorimeter selection cuts (an identical selection as described in section 3.4 but excluding the qout cut) were developed which has a lower efficiency, but not the decrease around 0.7 GeV as the previous selection cuts. The antiproton spectrum that is produced by this selection is identical to the spectrum in Figure 5.7 within statistical fluctuations, and in particular, the flux between 0.59 GeV and 0.92 GeV does not change more than a few percent. It is therefore believed that the small increase in the antiproton flux seen in this energy interval is due to a statistical fluctuation.

5.4 The antiproton-to-proton ﬂux ratio

The antiproton-to-proton ﬂux ratio is calculated as

TOA TOA R(E)= NP¯ /NP (5.10)

TOA TOA where E is the kinetic energy and NP¯ and NP are the number of antiprotons and protons respectively at the top of the atmosphere as given by Table 5.3. The result is presented in Table 5.5 and in Figure 5.8. For a discussion concerning errors, see the previous section.

5.5 Antiproton measurements

The antiproton flux measured by PAMELA is shown in Figure 5.9 superimposed with results from previous BESS flights and models of secondary and primary antiproton production. The BESS flights were carried out in 1995, 1997, 1999, 2000 130 Chapter 5. The p/p¯ ratio and ¯p flux

Kinetic energy (GeV)p ¯ ﬂux range mean (m−2sr−1s−1GeV −1) +3.86+0.73 −3 0.08-0.30 0.19 4.52−2.32−0.19 × 10 +3.41+0.22 −3 0.30-0.59 0.44 3.42−1.93−0.27 × 10 +0.35+0.31 −2 0.59-0.92 0.75 1.50−0.35−0.21 × 10 +0.31+0.29 −2 0.92-1.27 1.09 1.38−0.31−0.22 × 10 +0.25+0.18 −2 1.27-1.64 1.45 1.47−0.25−0.14 × 10 +0.26+0.16 −2 1.64-2.00 1.81 1.82−0.26−0.13 × 10

Table 5.4. The antiproton ﬂux at the top of the atmosphere with statistical (ﬁrst) and systematic (second) errors. ) -1 GeV -1 s -1 sr -2

10-2 flux (m p

10-3

10-1 1 kinetic energy (GeV)

Figure 5.7. The antiproton ﬂux at the top of the atmosphere measured with the PAMELA instrument. Data are compensated for contamination of pions and electron, all known detector eﬃciencies and biases and for geomagnetic transmission. The data is collected during a solar minimum at a negative solar polarity. 5.5. Antiproton measurements 131

Kinetic energy (GeV)p/p ¯ ratio range mean +0.46+0.09 −5 0.08-0.30 0.19 0.54−0.28−0.03 × 10 +0.30+0.02 −5 0.30-0.59 0.44 0.30−0.17−0.03 × 10 +0.37+0.32 −5 0.59-0.92 0.75 1.56−0.37−0.22 × 10 +0.42+0.40 −5 0.92-1.27 1.09 1.89−0.42−0.30 × 10 +0.45+0.33 −5 1.27-1.64 1.45 2.64−0.45−0.26 × 10 +0.62+0.40 −5 1.64-2.00 1.81 4.30−0.62−0.32 × 10

Table 5.5. The antiproton-to-proton ﬂux ratio at the top of the atmosphere with statistical (ﬁrst) and systematic (second) errors.

10-4 /p p

10-5

10-6 10-1 1 kinetic energy (GeV)

Figure 5.8. The antiproton-to-proton flux ratio at the top of the atmosphere measured with the PAMELA instrument. Statistical and systematic errors are included. For further comments about the data, see the derivation of the antiproton flux. 132 Chapter 5. The p/p¯ ratio and ¯p flux and 2004 and have thus measured the antiproton flux during one half of a 22 year solar cycle. Since the energy spectrum at low energies is significantly affected by solar modulation, the results measured at different points in the solar cycle may vary significantly. The BESS 1995 and 1997 flights (here-after referred to as the BESS 95+97 flights) occured during a solar minimum, as the PAMELA flight, but with a positive solar polarity. The influence of the solar modulation on the antiproton and proton spectra are similar during both periods, and the PAMELA and BESS95+97 results are therefore comparable. The 1999 and 2000 flights were flown at solar maximum, before and after the solar field reversal respectively, while the 2004 flight occured roughly in between a solar maximum and minimum. The PAMELA and BESS results, shown in Figure 5.9, support the characteristic feature of secondary production with a peak in the antiproton flux at 2 GeV and a sharp decrease to lower energies. Antiprotons at low energy can therefore be considered to be mainly of secondary origin. However, the PAMELA results are systematically lower than the BESS 95+97 results. Three theoretical models [58] describing pure secondary production of antiprotons, but which differ in Galactic propagation, are shown in Figure 5.9: i) a diffusive reacceleration model (DR - solid line), ii) a plain diffusion model (PD - dashed line) and iii) a diffusion and convection model (DC - dotted line). All three models are modulated with a spherically symmetric modulation model with a modulation parameter of φ = 550 MV/c, corresponding to a solar minimum. The DR model reproduces the PAMELA data reasonably well. This model also reproduces the secondary to primary nuclei ratios, without introducing ad-hoc breaks in the diffusion coefficient and/or in the injection spectrum. However, this model produces a bump in proton and He spectra at about 2 GeV per nucleon which has not been seen. The DC model reproduces all present cosmic ray particle data well, including the antiproton flux from BESS 95+97, but at the cost of introducing breaks in the diffusion constant and the injection index. The predicted antiproton flux from this model is over-estimated compared to the new results from PAMELA, as seen in Figure 5.9. The PD model predicts an even higher antiproton flux, and do not reproduce the boron to carbon ratio below 1 GeV. The conclusion is that none of the models above can reproduce the combined PAMELA antiproton flux and other cosmic ray particle data. As was discussed in section 1.4, there might be a contribution of primary antiprotons at low energy. Two proposals of such sources are evaporation of primordial black holes [48] and annihilation of neutralino dark matter. These processes may have a peak below 1 GeV which would produce a flatter composite antiproton spectrum than what is expected from a purely secondary spectrum of antiprotons. A calculation of a primary contribution of antiprotons from the evaporation of primordial black holes with an explosion rate of 0.4 × 10−2 pc−3yr−1, modulated with a spherically symmetric modulation model with a modulation parameter of φ = 550 MV/c, is shown in Figure 5.9. A contribution from such a primary source of antiprotons would be most evident during a solar minimum. As was mentioned above, BESS 95+97 flights and PAMELA are flown at solar minimum which is the most favourable condition to detect a possible primary contribution to the an- 5.5. Antiproton measurements 133 tiproton spectrum. The result from BESS 95+97 shows a possible excess in the antiproton flux below 1 GeV. This excess has not been confirmed by subsequent BESS flights which were flown at or close to solar maximum. PAMELA has now made the first measurement of antiprotons at solar minimum since the BESS 95+97 flights. The collected statistics of PAMELA is lower than for the BESS flights, but the result is not complicated by the atmospheric overburden which plays a significant role below 1 GeV. The result, which is seen in Figure 5.9, is consistent with pure secondary production of antiprotons. The antiproton-to-proton flux ratio measured with the PAMELA instrument is plotted in Figure 5.10 together with BESS flights from 1995 to 2004. The PAMELA data is presented from 0.08 GeV, the lowest energyp ¯-p ratio measured to date, to 2 GeV. PAMELA results above 2.0 GeV are presented later. Superimposed on the data is the DC model modulated with a drift-model [58] for various solar tilt angles for negative and positive solar polarity. The model predicts an increasing antiproton-to-proton flux ratio for increasing solar activity (solar tilt angle) since protons modulate harder than antiprotons at low energy due to their different interstellar spectrum. The PAMELA data are in good agreement with the drift-model at 5◦ solar tilt angle but systematically lower than the model at 15◦ tilt angle which is the approximate tilt angle during the PAMELA mission [30]. The PAMELA data agrees well with results from BESS flights during similar solar activity (BESS 1995+1997 and BESS polar 2004). The drop in the PAMELA ratio at about 0.5 GeV would be insignificant if not confirmed by other flights. A similar reduction in thep ¯/p ratio is seen in the data from BESS 2000 and BESS-Polar 2004. The BESS 1999 flight, flown at a positive solar polarity, instead shows an increase at the same energy, and this feature could therefore be connected with drift-effects as spherically symmetric models of the solar modulation predict a similar behaviour in positive and negative states of the solar polarity contrary to drift models. The antiproton-to-proton flux ratio is a good probe for charge dependant solar modulation. The evolution of the ratio evaluated at 1 GeV versus solar tilt angle is shown in Figure 5.11 (top). Thep/p ¯ ratios are scaled with the local interstellar p/p¯ intensity (derived from [58] for negative solar polarity). The data are from PAMELA (red) and BESS (black). The evolution of the solar tilt angle during the PAMELA mission is seen in Figure 5.11 (bottom). As the average solar tilt angle did not change significantly during the PAMELA mission, and the antiproton statistics is limited, only a single value of thep/p ¯ ratio is shown. An average value of 15◦ was chosen. A theoretical prediction of thep/p ¯ ratio versus solar tilt angle at 1 AU is superimposed on the data [27]. The model ranges over one complete solar cycle, starting at the solar maximum in 1990 and ending at the maximum predicted to occur around 2010. From Figure 5.11 it is evident that the antiproton-to-proton flux ratio changed very moderately during the last decade. This is in agreement with spherically symmetric models of solar modulation. However, it is also compatible with drift models of solar modulation. In these models, positive particles (protons) drift 134 Chapter 5. The p/p¯ ratio and ¯p flux BESS 2000 BESS-Polar 2004 BESS 1999 Caprice98 BESS 95+97 PAMELA kinetic energy (GeV) 1 -1 10

-2 -3

GeV s sr (m flux p ) 10 10

-1 -1 -1 -2

Figure 5.9. The antiproton flux measured by PAMELA and BESS (BESS 95+97 [76], BESS 1999 and 2000 [26] and BESS-polar 2004 [72]). The solid line shows the prediction from a diffusive reacceleration (DR) model modulated with a spherically symmetric modulation model with a modulation parameter φ = 550 MV/c. The dotted line and dashed lines are a diffusion and convection (DC) and a plain diffusion (PD) model respectively. Both models are modulated as the DR model. The dotted-dashed line is a calculation of the antiproton spectrum from the evaporation of primordial black holes [77], modulated with a spherically symmetric model of 550 MV/c [78]. 5.5. Antiproton measurements 135 inward to the Sun through the polar regions at A > 04, and are thus relatively insensitive to changes in the heliospheric current sheet (HCS). The proton intensity therefore experiences a flat maximum during A > 0 states. Antiprotons drift in through the HCS at A > 0 and are thus sensitive to solar modulation. However, thep ¯/p ratio modulates roughly as protons since antiprotons are less affected by solar modulation than antiprotons as a consequence of their interstellar spectrum. The result is that thep/p ¯ ratio has a flat minimum during the solar minimum at A> 0 solar polarity. The data from the BESS flights during the last decrease thus supports both spherically symmetric models and drift models. Both spherically symmetric models and drift models predict an increase of the p/p¯ ratio at the solar field reversal that follows the solar maximum. For the spherically symmetric model, this is only due to the relatively harder modulation of protons than antiprotons mentioned above. Drift models predict a larger increase in thep/p ¯ ratio at the solar field reversal reflecting the charge sign dependence. The BESS 2000 experiment, flown shortly after the solar field reversal showed an increase, in agreement with drift models, as seen in Figure 5.11. Oppositely to the A > 0 epoch, protons drift inward to the sun through the HCS at A < 0 solar polarity. Thep/p ¯ ratio should therefore be sensitive to changes in the HCS which results in a peak-like intensity, which is seen in Figure 5.11. This behaviour of the p/p¯ ratio is very different from what is expected in spherically symmetric models where antiprotons and proton modulate identically during periods of positive and negative solar polarity. A validation of the peak-like behaviour of thep/p ¯ ratio in the A< 0 solar polarity would therefore be a stunning validation of the importance of drifts in solar modulation. The PAMELA measurement is flown shortly before, during, and after the solar minimum at A< 0. The statistics is unfortunately not sufficient to allow for a temporal study of thep/p ¯ ratio which would be useful to check this. The result from PAMELA agrees well with the model in Figure 5.11, but also with spherically symmetric models of solar modulation. The PAMELA instrument has primarily been designed to study high energy cosmic rays. The result for thep ¯-p ratio from 2 GeV up to 100 GeV [79] is shown in Figure 5.12. The antiproton selection requires i) a downward going particle, using the ToF-system, ii) a proton-like charged particle, using dE/dx measurements in S1, S2 and the tracker, iii) a negative deflection in the tracker and iv) no electromagnetic shower in the calorimeter. The selected numbers of antiprotons and protons were corrected for calorimeter selection efficiency and losses in the instrument. Error bars include statistical errors only. Contamination of electrons and pions are not subtracted from the number of selected events. Studies have shown that the electron contamination is negligible over the entire energy range and pion contamination is estimated to be less than 5 % (1 %) above 2 GV (5 GV) respectively [79]. Superimposed on the data are the results derived in this thesis. The data below and above 2 GeV are consistent and supports the method used in this thesis to derive the antiproton flux andp ¯/p ratio. Notice that statistical and systematic

4the sign of the solar polarity is denoted by A. 136 Chapter 5. The p/p¯ ratio and ¯p ﬂux BESS 1999 BESS 2000 BESS 1995-97 BESS-polar 2004 BESS 1993 PAMELA 1 kinetic energy (GeV) -1 10 -4 -5 -6

10 10 10 /p p

Figure 5.10. Thep/p ¯ ﬂux ratio between 80 MeV and 2 GeV measured with PAMELA, plotted together with the results from selected contemporary experiments (BESS95+97 [76], BESS1999+2000 [26] and BESS-Polar 2004 [72]). A theoretical calculation of thep ¯/p ratio for a pure secondary production of cosmic rays modulated with a drift model with solar polarity and tilt angle of (from top) (A< 0) 65◦, 45◦, 25◦, 15◦, 5◦ and solid line (A> 0) 10◦ [58]. 5.5. Antiproton measurements 137

8 /P

P A>0 A<0 7

6 BESS

5 PAMELA

1 | | | 0 90o 10o 90o 10o 90o 1990 2000 2010 ] °

18 Solar Tilt Angle [ 16

2006 2007 2008 2009 Year

Figure 5.11. Top: The evolution of thep/p ¯ ratio at 1 GeV versus the solar tilt angle. The approximate time (in years) at (90◦, A > 0), at the solar field reversal and at (90◦, A > 0) are indicated. Intensities are relative to a theoretical model of the interstellarp/p ¯ [58]. The range of the abscissa corresponds to an entire solar cycle starting at the solar maximum at 1990 and ending at the predicted solar maximum at 2010. Black dots are measurements from BESS [76][26][72], red dots are PAMELA data. The solid line shows a theoretical calculation from Bieber et al [27]. The shaded area corresponds to the time of the solar field reversal and regions left and right of this area are periods of positive and negative solar polarity respectively. Bottom: The evolution of the solar tilt angle at the time of the PAMELA mission computed using two potential field models applied to photospheric magnetic field observations from Wilcox Solar Observatory [30] (R-model). The average tilt angle has not changed significantly during the PAMELA mission and thep ¯/p ratio should therefore be approximately constant. An average tilt angle of 15◦ has been used in the top figure for the PAMELA data. 138 Chapter 5. The p/p¯ ratio and ¯p flux errors are included in the data below 2 GeV, while only statistical errors are shown above 2 GeV. An overlap of the data is present at 2 GeV. The result in Figure 5.12 is compared with theoretical calculations assuming pure secondary production of antiprotons during the propagation of cosmic rays in the galaxy. Previous measurements of thep ¯/p ratio are shown and the agreement with PAMELA data is excellent. PAMELA has identified approximately 1000 antiprotons to date, which at high energies is an improvement to existing statistics of an order of magnitude. The PAMELA instrument has measured antiprotons over the most extended energy range ever achieved, from 80 MeV, lower than all previous experiments, to above 100 MeV. The result is precise enough to put significant constraints on models of secondary production, solar modulation and contributions from exotic sources. PAMELA is continuously taking data and is expected to continue until December 2009. 5.5. Antiproton measurements 139 2 10 CAPRICE 1998 BESS 1999 CAPRICE 1994 IMAX 1992 BESS 2000 MASS 1991 BESS 1995-97 HEAT-pbar 2000 BESS-polar 2004 BESS 1993 PAMELA kinetic energy (GeV) 10 1 -1 10 -3 -4 -5 -6

10 10 10 10 /p p

Figure 5.12. The antiproton-to-proton flux ratio from 80 MV to 100 GeV measured with PAMELA. The dashed lines shows the upper and lower limits calculated by Donato et al [74] for a diffusion model. The dotted-dashed line shows the calculation by Ptuskin et al [80] for a plain diffusion model. These two curves were obtained using a spherically symmetric model of solar modulating with a modulation parameter φ = 500 MV/c, adopted for a period of solar minimum. The dotted line shows the calculation of a drift model at a solar tilt angle of 15◦, by Moskalenko et al [58]. Contemporary measurements are (IMAX [44], BESS1999 and 2000 [26], HEAT-pbar [81], CAPRICE98 [40], CAPRICE94 [43], BESS-polar 2004 [72], MASS91 [42] and BESS95+97 [76]) 140 Chapter 6

Discussion and conclusions

The low energy antiproton component of the cosmic radiation has been investigated in this thesis. This work adds to the knowledge that has been obtained during the last decades, starting with the discovery of the antiproton in the laboratory in 1955 [82]. The first successful measurement of antiprotons in the cosmic radiation was reported in 1979 by Golden et al [38]. A total of 25p ¯ were detected between 5 and 12 GeV. The same year, Bogomolev et al [83] reported a detection of 2 cosmic ray antiprotons between 2 and 6 GeV. For both experiments, this was an excess of antiprotons compared to what was expected from secondary production mechanisms. A number of new theoretical models and experiments were proposed to understand the issue better. Two years after the first detection, Buffington et al [84] measured a large flux of antiprotons with energies of a few hundred MeV. The magnitude of the flux was such that it could not be explained by any model of secondary production of antiprotons. Stimulated by the possibility of a primary source of antiprotons, new balloon flights were deployed which had a better particle identification than the experiment by Buffington, which identified antiprotons only from the topology of the annihilation products in the calorimeter. The PBAR [85] and LEAP [86] balloon experiments both failed to detect any antiprotons and the earlier results were questioned. A third generation of experiments were constructed to investigate cosmic ray antiprotons more accurately. The Wizard collaboration, formed around R. Golden, has played an important role in this endeavour. The MASS and CAPRICE balloon experiments, equipped with high resolution magnetic spectrometers, were a significant improvement on previous experiments and collected a higher statistics of antiprotons with significantly better precision in an energy range (for CAPRICE 98) between 4 and 50 GeV. The results of these measurements all favoured a pure secondary production of cosmic ray antiprotons and thus disputed the results of the earliest measurements of the antiproton spectrum. Although all experimental data at this time favoured secondary production, there was room for a primary component of antiprotons. Measurements were of poor quality at the very lowest energies and the energy region above 50 GeV was completely unexplored. Both

141 142 Chapter 6. Discussion and conclusions are regions of energy where contributions from primary sources may be seen. An- nihilation of dark matter particles could contribute to the high energy part of the spectrum while the low energy part could reveal an excess of antiprotons originat- ing from the evaporation of primordial black holes. Measurements at low energy are however complicated by the strong influence of solar modulation and have to be conducted over an extended period of time. The BESS balloon experiment was built to study the low energy part of the antiproton spectrum and has performed successive flights over one half of a solar cycle. Results from BESS mainly support pure secondary production of antiprotons, even though suggestions of a primary component have been seen [72]. The PAMELA space experiment was built by the Wizard collaboration with the aim of extending the measured antiproton spectrum to lower and (primarily) higher energies to widen our understanding of secondary production, propagation and solar modulation of antiprotons and to possibly reveal primary contributions to the antiproton spectrum. The work presented in this thesis has been made in the framework of the PAMELA collaboration. The focus is on antiprotons at low energy and continues the measurements conducted by previous experiments mentioned above but with the advantages of a space based experiment and with a high precision detector. The antiproton flux and antiproton-to-proton flux ratio between 80 MeV and 2.0 GeV has been presented and compared with contemporary measurements and theoretical predictions. The antiproton flux is in general agreement with theoretical calculations of a pure secondary production of antiprotons. The PAMELA data have been compared to three different models of secondary production i) a diffusive reacceleration model (DR), ii) a plain diffusion model (PD) and iii) a diffusion and convection (DC) model [58]. The DR model reproduces the PAMELA data well, while the PD and DC models overestimate the antiproton flux. However, none of models can reproduce the whole variety of cosmic ray particle data. The antiproton flux measured with PAMELA is in agreement with most other experimental results obtained by contemporary experiments. The most recent measurement of the antiproton flux during a solar minimum, BESS 1995+1997 [76], suggested an excess below 1 GeV. If correct, this could indicate a primary contribution of antiprotons from for example evaporation of primordial black holes [48]. Such an excess would be most significant during a period of solar minimum [77]. The PAMELA experiment is thus well suited to confirm or dispute the excess seen by BESS. The PAMELA results show no sign of such an excess. The statistics of antiprotons collected with PAMELA are however small below 1 GeV which makes it difficult to draw any definite conclusions about the origin of antiprotons at the very lowest energies. The second BESS-Polar flight, which flew for 30 days, from December the 22nd 2007 to January the 22nd 2008 in Antarctica, collected higher statistics at low energy and will shed further light on this issue when the results are published. The antiproton-to-proton flux ratio below 2 GeV measured by PAMELA shows good agreement with theoretical calculations of a pure secondary production of antiprotons and also with earlier measurements during similar periods of solar ac- 143 tivity. A small decrease is seen at 0.5 GeV which also is present in the results from the BESS 2000 and BESS-Polar 2004 flights, which were both conducted during periods of negative solar polarity. The BESS 1999 flight, which occured during a period of positive solar polarity, instead showed an increase at the same energy, and this feature may be connected with drifts in the heliosphere as spherically symmetric models of the solar modulation predict a similar behaviour in positive and negative states of the solar polarity whereas drift models do not. Thep/p ¯ ratio at 1 GeV was compared to previous measurements at the same energy and to theoretical calculations of the evolution of the ratio with solar activity. The new measurement by PAMELA agrees well with the prediction of drift models [27] but cannot rule out spherically symmetric models of solar modulation. A sharp increase of thep/p ¯ ratio after the present solar minimum would be a striking validation of drift models. Forthcoming data from PAMELA and other experiments, such as BESS-Polar, will help to clarify this issue. Measurements of the positron fraction at low energy with PAMELA [87] show an overabundance compared to spherically symmetric models, but are consistent with drift models. This is another piece of evidence supporting drift models rather then spherically symmetric models of solar modulation. The results of the positron fraction from PAMELA are highly interesting also at higher energies, where an increase is evident above 10 GeV, contrary to what is expected from pure secondary models of positron production. This result has been submitted to Nature for publication [87]. Thep ¯/p ratio from 2 GeV to 100 GeV, which is submitted for publication [79], was presented and compared to the ratio below 2 GeV obtained in this thesis. The data below and above 2 GeV are consistent and validate the methods that have been used in the work presented in this thesis. The obtained statistics of antiprotons at high energy are an order of magnitude better than all previous measurements and the results are consistent with pure secondary models of antiproton production and with results from previous experiments. This data will make it possible to put significant constraints on secondary models of antiproton production and propagation. The PAMELA experiment has presented a number of highly interesting results which will be used to develop and constrain models of dark matter, cosmic ray propagation and solar modulation. The statistics, energy range and quality of the data is unprecedented. PAMELA is continuously taking data and the results presented in this thesis should improve in the future. The PAMELA mission is scheduled to take data until December 2009. The primary difficulty when detecting antiprotons in the cosmic radiation is the inherently low fluxes. All measurements to date suffer from a low statistics, although the PAMELA mission has increased the number of detected antiprotons compared to all previous measurements by an order of magnitude at high energy. A natural continuation of the study of cosmic ray antiprotons is to use detectors with a significantly larger acceptance to make precision studies of cosmic rays, at low and high energy, possible. The AMS-02 experiment, comprising a spectrometer 144 Chapter 6. Discussion and conclusions with an acceptance of 0.5 m2sr and a MDR of 2.5 TV/c and scheduled to fly on the International Space Station (ISS), will increase the statistics of antiprotons by an order of magnitude and will explore higher energy regions than what has been possible to date. ISS is in low Earth orbit at a low geomagnetic latitude and the AMS experiment will therefore not be suited to study low energy antiprotons as the experiment only is exposed to regions with a high geomagnetic cutoff. Improved measurements of the low energy part of the antiproton spectrum are instead expected from balloon experiments. The BESS-polar experiment is currently flying long duration balloon flights which can last for up to 30 days at Antarctica. The first flight in 2004 was aborted after 9 days, but the second flight in December 2007 lasted for 30 days. The results from this flight and forthcoming flights with the BESS-polar instrument are highly anticipated. Ultra long duration balloon flights can also be a possibility within the near future. These types of balloons, that are still under development, are expected to fly at a higher altitude than present balloons and are intended to stay aloft for periods up to 100 days. This could give new opportunities to the study of low energy antiprotons. Today, either conventional balloons or satellites are used, each with their own benefits and drawbacks. A balloon flight spends all its time at a specific geomagnetic cutoff and can therefore have a large exposure to low energy particles when launched at the South or North pole. Satellites only spend a fraction of time close to the poles and thus have a small exposure for low energy particles. However, satellite experiments can be operational for years while balloon flights generally last tens of days which limits the collected statistics. Ultra-long duration balloon flights would change this. A large acceptance detector mounted on an ultra-long duration balloon flight at Antarc- tica would be the optimal method for detecting low energy antiprotons with high statistics as the instrument is located continuously at a small geomagnetic cutoff at a long period of time. The future for antiproton measurements is therefore bright, but challenging. 145

Figure 6.1. The Resurs DK1 satellite carrying the PAMELA experiment prior to launch. Baikonour Cosmodrome, Kazakhstan, June 2006. Courtesy Pr. Mark Pearce. 146 Summary of previous work

Here follows a summary of my work which is covered in detail elsewhere [88].

The SEASA experiment

The ’Stockholm Educational Air Shower Array’ (SEASA) [89] project has estab- lished seven detector stations in the Stockholm area, distributed according to Fig- ure 2. Each detector station consists of three scintillator detectors, separated by approximately 15 m, which are read out by large area photomultipliers placed directly on top of the scintillators. Cosmic ray activity at stations separated by ar- bitrary distances is correlated using timing signals from GPS navigation satellites. A low-cost and highly scalable data acquisition system has been produced using embedded Linux processors which communicate station data to a central server running a MySQL database.

Detecting and visualising air showers When a high energy cosmic ray interacts at the top of the earth’s atmosphere, a cascade of secondary particles is created and to a good approximation moves through the atmosphere as a thin disc. Depending on the energy of the primary particle, the radius of the disc at ground can range from tens of meters to kilometers for the highest energy particles. As the flux of the interesting highest energy cosmic rays is low, a large detecting area is desirable. One way to detect air showers is to place a grid of detectors on the ground to sample the shower. Air showers can be identified through ’simultaneous’ signals in detectors across the network. In the SEASA project, the “nodes” of such a detector grid will be placed in high schools in the Stockholm area. A station comprises of three plastic scintillator detectors with photomultiplier read out, a data acquisition system based on programmable logic array (PLA) and an embedded Linux processor, a high voltage supply and a GPS receiver system. Each detector consists of a single piece of plastic scintillator, approximately 1.5 cm x 30 cm x 100 cm, read out by a large diameter (76 mm) photomultiplier glued to the centre of the scintillator’s largest surface, as illustrated in Figure 3. Air showers are identified by coincidental signals from the three scintillator detectors

147 148 Chapter 6. Discussion and conclusions

Figure 2. The seven stations constituting the SEASA air shower array. Four stations are located at high schools and are labeled after the corresponding schools. The three stations at the AlbaNova area are shown in greater detail in the inset picture in the upper right corner.

(“triggers”). Air showers with a primary particle energy above 1014 − 1015 eV are detectable by a station depending on the separation of the scintillator detectors [1].

An important issue for the project is to visualize data interactively and in an interesting way to engage students in the project. Therefore, a ’live’ web-based viewer system has been developed. A server running a MySQL database under Linux constitutes the core of the system, where the information from the detector nodes is stored. Data from the server is sent in real-time to “viewer clients”, on-line java-applet clients displaying live information about the detector nodes, as well as some trigger statistics and housekeeping “on demand”. Hardware parameters, for example high voltage levels and coincidence window length, can also be set from the viewer.

In order to make the project accessible to as many schools as possible, care has been taken to minimise the system cost. This was achieved by simplifying the scintillator detector design (e.g. no light guides and a centralized high voltage system) and using a commercial embedded Linux system which can interface directly to a web browser, avoiding the need for expensive software licenses. A complete station costs approximately 2500 Euros, if material is purchased for 5 stations at a time. Signiﬁcant discounts are possible if (e.g.) the scintillator material can be ordered in bulk. 149

Figure 3. One of the detectors opened showing the plastic scintillator, wrapped in reﬂective material, and the photomultiplier glued on top.

Data acquisition system The design of the data acquisition system has been motivated by the need to produce a compact, configurable, scalable and low cost system. The system has four main components: an analogue front-end, a PLA, a GPS receiver and an embedded Linux processor, as shown in Figure 4. The analogue front-end follows the design used for the anti coincidence system of the PAMELA satellite experiment [90], which is based on off-the-shelf components. The photomultiplier (PMT) signals are integrated and the output sent to a comparator, with the reference voltage provided by an 8-bit DAC which is configured by the PLA. An Altera Cyclone EP1C6T144C6 Programmable Logic Array is the key digital component. It processes data arriving from the detectors (to identify coincidences, for example) and environmental sensors forming events which are sent to the Linux system. In the present design, a simple coincidence is formed between the discriminated PMT pulses, which are 100 ns long. The relative time between the leading edges of the discriminated pulses are also recorded, which allows a crude estimation of the local shower angle. The length of the comparator pulse is sampled at both edges of a 100 MHz clock which allows the energy deposited in the scintillator to be estimated with a ’time-over-threshold’ approach. A GPS receiver card (Motorola M12+) and antenna (Motorola Timing 2000) [91] are used to provide a time tag for each coincidence event. This information is used to allow coincidences observed at widely separated stations to be correlated. The basic time tag is provided by the time-of-day information (hh, mm, ss) from the 150 Chapter 6. Discussion and conclusions

Figure 4. The data acquisition system for a detector station. The three circuit boards contain: analogue front-end, PLA, GPS receiver and atmospheric pressure sensor (bottom left), Axis 82 developer board (bottom right) and programmable high voltage supply (top right). The empty region seen top left houses a display unit. The power consumption for the data acquisition board is less than 5 W.

GPS unit. The precision of the tag is increased by using a 100 MHz counter implemented in the PLA to measure the offset between the GPS Pulse Per Second (PPS) signal and the coincidence trigger. By using both falling and rising edges of the counter pulse, a timing resolution of 5 ns is achieved. This approach follows that pioneered by the Leeds group [92]. The GPS receiver also provides a so-called sawtooth correction which compensates for the granularity of the internal GPS clock used to produce the PPS signal. The PLA is controlled and read out through a RS232 link which connects to an embedded Linux system (Axis 82 developer board [93]). The Linux system provides cold start configuration of the GPS receiver through a second RS232 link, as well as configuring the PLA by an Altera Passive Serial Loader (APSL). This interface uses the General Purpose IO Pins (GPIO) on the ETRAX chip, and provides a very simple way to configure Altera FPGA chips.

Cosmic ray anisotropy studies

Four of the stations have been built by high school students and are located on the attics or roofs at their high schools. The separation between these stations are in the order of kilometers and the energy threshold to trigger multiple stations is therefore above 1018 eV. To be able to study lower energetic cosmic rays a more dense cluster of three detector stations has been deployed at the AlbaNova University Area (the 151

AlbaNova array). This cluster detects air showers with energies above 1016 eV and is being used to study the cosmic ray arrival distribution in this energy regime. To study the cosmic ray anisotropy the direction of the primary cosmic ray must be reconstructed. This can be done as the air shower front travels in essentially the same direction as the primary particle. Assuming a flat shower front, the direction can be determined by measuring the time difference between hit detector stations. By fitting the geometry of the detectors and the trigger times to the shower plane the incident angles of the shower can be reconstructed. With a fixed geometry the accuracy of the reconstruction ultimately depends on the trigger time resolution, set by the GPS system. The time resolution of the GPS systems is therefore investigated. The pointing accuracy, or angular resolution, of the AlbaNova array has been assessed by simulations and this is described. The dependence of the angular resolution on the timing accuracy is also investigated, as well as the trigger efficiency of the array. The final section describes the methods used to study cosmic ray anisotropies. Finally, the hypothesis of a uniform flux of cosmic rays are tested using data taken during approximately six months of operation of the AlbaNova array.

Time resolution of the system To test the performance of a GPS system, the oﬀset between the time-tags produced by the GPS system subject for measurement and a reference system, fed with a common trigger signal, is investigated. The output from the GPS card is a 1 Pulse Per Second (PPS) signal with an accuracy of ± 25 ns. The PPS can only be emitted on the rising edge of the GPS-cards internal 100 MHz oscillator, which introduces a built in uncertainty. The output from the GPS card also contains a negative sawtooth correction. This correction is a prediction of how early or late the next PPS signal will be due to the limitations of the internal 100 MHz oscillator. With the aid of this correction the PPS should be accurate to within 5 ns according to the developer of the GPS cards [91]. The principle of the test is as follows. For every trigger, a time stamp from each GPS card is retrieved. These time stamps should be identical in a perfect system. The time stamp is provided by the sawtooth corrected PPS and a 100 MHz oscillator implemented in the Programmable Logic Array (PLA) in the readout electronics. The information in the PPS signal gives the time within the second and the oscillator determines the trigger time relative to the PPS with a 5 ns resolution. A self calibrating system for the 100 MHz crystals were used to compensate for diﬀerences in the crystal frequencies and variations in the crystal frequency. To be self calibrating, the system counts the number of oscillations between PPS’s, and uses this value to calibrate the number of oscillations from the trigger to the PPS. All measurements in the test were done with a satellite mask angle of ten degrees to exclude unreliable time measurements from satellites close to the horizon. 152 Chapter 6. Discussion and conclusions

The result of the measurement for the AlbaNova E station is shown in Fig. 5. The oﬀset of -18.5 ns for the mean value changes sign when the GPS cards are exchanged, indicating a systematic error between these two. This eﬀect can be canceled by calibrating each card against a “standard card”, and then correcting the time stamps from each card accordingly. The standard deviation of 13.6 ns is the time resolution for this pair of GPS systems. The time resolution of a single GPS system is 9.6 ns considering the GPS systems equal and independent [88]. The time resolution for each of the seven GPS systems in the present array were measured to be less than 15 ns.

Figure 5. The diﬀerences between time stamps from AlbaNova E and AlbaNova W (the reference system) when fed with a common trigger signal.

In the test, the GPS cards mostly tracked the same satellites. It is inevitable that detector stations spread out over a larger area will have diﬀerent sets of satellites visible to them. A test was therefore conducted where the GPS cards were conﬁgured to use independent sets of satellites. The standard deviation then increased by approximately 50 %.

Simulation of the angular resolution The angular resolution of the sub-array at AlbaNova has been assessed with Monte Carlo simulations, using the simulation engine AIRES. Primary particles with ener- 153

16 dE −3.0 gies above 10 eV following the power-law dN ∼ E were generated and injected at the top of the atmosphere. The lower energy was chosen considering the energy threshold of the AlbaNova array, known to be slightly higher than this value from simulations (see section 6). The injection angle was sampled from a uniform distribution. A total of 2000 cosmic rays with the above properties were generated and the ground particles from each shower were repeatedly used to hit the ground at diﬀerent oﬀsets relative to the detector array. The impact coordinates of the shower core was set to follow a 9 × 9 grid with a node separation of 50 m and the origin placed in the centre of the detector array. The number of detected showers outside this area is negligible and can thus be disregarded. A detector is triggered if it is hit by an electron, muon or heavier charged particle. If a photon hits the detector it is triggered with a 1% probability. This value corresponds to the probability that a photon deposit at least 1 MeV in a 1 cm thick scintillator. To simulate imperfections in the GPS time tagging a time jitter σt sampled from a Gaussian with a standard deviation of 15 ns is added to the time of the hit. This value is based on the time resolution measurements presented in section 6.

The trigger efficiency The trigger efficiency of the air shower array has been determined from the simulations simply by dividing the number of detected showers with the number of incident cosmic rays for bins of energy. Fig. 6 shows the result of the simulation for the two different trigger criteria: 3/3 detectors hit or at least 2/3 detectors hit. The energy threshold is consequently around 1016.5 eV and the most probable energy slightly higher, ∼ 1017 eV. Thus, SEASA detects cosmic rays with energies below the knee with this setup. The trigger efficiency is slightly underestimated in this study as the simulation program does not propagate particles close to the core and a detector station is thus not triggered if an air shower strikes directly on top of it. The underestimation is believed to be around 5 % as the efficiency should saturate at 100 % for large energy showers (see Fig. 6).. The underestimation is believed to be equal for all energies.

The angular resolution of the AlbaNova array The angular resolution of the detector array is derived by comparing the shower direction reconstructed from the timing information of the hit detectors with the direction of the primary particle inputted in the simulation. The precision of the reconstruction is measured as the angular distance between the two shower directions, characterised by the parameters (θ1, φ1) and (θ2, φ2), where θ is the zenith angle and φ the azimuthal. The angular distance between two directions is then calculated as

−1 Ψ= cos (cosθ1cosθ2 + sinθ1sinθ2cos(φ1 − φ2)) (1) The angular resolution of the detector array is defined as the angular distance which contains 68% of the reconstructed angles. This is the most common way to 154 Chapter 6. Discussion and conclusions define the angular resolution and therefore makes it straight-forward to compare the result from SEASA to other air shower arrays. Some experiments use the 50% level as the angular resolution and this is therefore included in the results below. The distribution of the angular distance is plotted in Fig. 7 below for the 3/3 trigger criteria. Superimposed on the distribution is the integral of the histogram with the corresponding axis to the right in the plot. The vertical dotted line marks the 68% level of the integral and thus the angular resolution. The angular accuracy of the AlbaNova array is summarised in Table 1 for the two trigger criteria. The errors have been calculated by randomly regenerating the histogram of the angular distance a large number of times from the true distribution. The RMS of the derived distribution of the angular resolution is then used as the error for the true angular resolution. The angular accuracy, as shown in Table 1, is the same for both trigger modes, within statistical fluctuations. This is an important conclusion and makes it possible to increase the trigger rate by loosening the trigger criterion without compromising the angular accuracy of the array. The time resolution of 15 ns used in the simulations is only valid for the Al- baNova array, mainly due to two reasons: First, the relative time accuracy between two GPS setups decreases with separation distance because of differences in the

Figure 6. The trigger eﬃciency for the AlbaNova sub-array for two diﬀerent trigger criteria. 155

Figure 7. The histogram shows the angular distance between the reconstructed angle and the true angle of the primary particle for the 3/3 trigger criteria. The axis to the right in the plot corresponds to the integral of the angular distance, superimposed on the histogram. The dotted vertical line marks the 68 % level of the integral and is the definition of the accuracy of the angle reconstruction for the three station setup for SEASA. atmosphere along the satellite-antenna path lengths. Secondly, the set of visible GPS satellites can change when the separation between the antennas is large, which has a negative influence on the relative time resolution. The effect of the time resolution on the angular resolution has been investigated by varying the Gaussian time jitter σt, introduced in the last section, and the result is presented below in Fig. 8. The angular accuracy is seen to decrease approximately linearly with the time resolution.

Validation of the simulations To conﬁrm the validity of the simulations the diﬀerence between the reconstructed angles by the AlbaNova array and by each station in the array are derived for real and simulated data. These are compared below in Fig. 9 and the agreement is relatively good for AlbaNova W and E. The shift in the histograms between simulated and real data for the azimuthal distributions are likely caused by the crude measurement of the local coordinate system for the detectors in each station. 156 Chapter 6. Discussion and conclusions

Trigg. Crit. Resolution 68% Resolution 50% Ψ2/3 6.5± 0.3 4.5± 0.2 Ψ3/3 7.0± 0.3 4.5± 0.2

Table 1. The angular resolution of the detector array for two diﬀerent trigger criteria and levels. The 68% level is used for the deﬁnition of the angular resolution for SEASA.

Figure 8. The angular resolution as a function of the time resolution in the system. For the array at AlbaNova, a time resolution of 15 ns is used, but this is expected to increase with a larger array as described in the text.

The agreement is however poor for AlbaNova S. This is most likely due to the eﬀect of the roof and walls that surround this station. Simulations that takes this into account will be performed in the future. However, the results in Fig. 9 are a good indicator that the simulations are correct. The diﬀerence between the reconstructed angles are in fact slightly smaller for real data indicating that the performance of the array may be better than the simulations show.

Anisotropy searches This section presents a preliminary study of the methods that can be used by the SEASA experiment to search for small and large scale cosmic ray anisotropies. To date, the collected statistics are poor due to the short period of data taking, the small exposure and of the numerous tests that have been performed during the 157

Figure 9. A comparison between real data (filled) and simulations (dotted) of the difference between the reconstructed angles by the entire AlbaNova array (super angles) and reconstructed angles by single detector stations (station angles). The top row shows the difference in reconstructed zenith angle Θ for the three detector stations. The middle row shows the azimuthal angle φ and the bottom row the space angle difference Φ. The agreement between data and simulations are good except for the azimuthal distribution for AlbaNova S which most likely is caused by the fact that this station is located inside a building. Notice that the difference between super angles and station angles are somewhat smaller for real data than for the simulations. 158 Chapter 6. Discussion and conclusions initial phase of the project. SEASA aims to lower the energy threshold in the future, by adding more stations and loosening the trigger criteria, thereby increasing the rate of detected showers. More accurate studies of small and large scale anisotropies will then be feasible. The search for anisotropies relies heavily on the estimation of the number of cosmic rays expected from each direction in the sky assuming a uniform flux over the celestial sphere. Such a estimation is henceforth called a coverage map. An unbiased coverage map is crucial in order to separate true anisotropies from acceptance effects. This is relatively straight-forward for ultra high energy cosmic rays (E > 1018 eV) where the total acceptance almost exclusively depends on the geometrical acceptance of the experiment. The derivation of the coverage map is more complicated at lower energies as variations in the atmospheric conditions then influences the detector acceptance heavily. This is balanced somewhat by the large number of low energy events.

The coverage map The coverage map for a given data set is obtained by integrating the acceptance of the experiment over the data taking period. The acceptance generally depends on weather conditions and the direction in the sky, characterised by declination and right ascension. This corresponds to (θ(t),φ(t)) at UTC 1 t, in horizontal coordinates. Using the simplification that the acceptance is independent of azimuthal angle φ and weather conditions, the acceptance is a function of zenith angle θ only. The zenith angle distribution has been shown [94] to be almost unaffected by anisotropies, and this distribution is therefore used as a basis when calculating the acceptance. The function 1 P (θ)= Acos(θ)sin(θ) (2) θ−θ0 1+ exp ∆θ is fitted to the measured zenith angle distribution and converted to declination 1 acceptance through the formula a(θ) = sin(θ)∗P (θ) (solid angle effect). A coverage map, that only depends on declination, is then generated by integrating the acceptance over one sidereal day.

24h W (δ)= a(θ)dt (3) Z0 The resultant coverage map in galactic coordinates can be seen in Fig. 10

A ﬁrst measurement of the cosmic ray anisotropy The hypothesis that the ﬂux of cosmic rays is isotropic can be tested using data from the SEASA experiment. A simple approach is to derive the angular two point

1Coordinated Universal Time 159

Figure 10. The coverage map in galactic coordinates. correlation function w(Φ). In its angular form it is deﬁned by the expression

δP = N[1 + w(Φ)]δΩ (4) where δP is the probability to find a second object within an angular distance of Φ from the primary object within an area δΩ if the mean object density is N. The two point correlation function thus represents an “excess probability” above what is expected from an isotropic distribution. The measured sky-plot of cosmic rays is plotted in galactic coordinates in Fig. 11. The two-point correlation distribution is derived by calculating the distance between all possible pair of events for this data set. To compare this to the hypothesis that the arrival distribution is isotropic a second two-point correlation distribution is derived from a randomly generated isotropic distribution convoluted with the coverage map derived in the previous section. Possible deviations of the first distribution from the second then reveals anisotropies of the cosmic ray arrival distribution. Both correlation distributions mentioned above are plotted in Fig. 12. The probability that the observed flux is a random sampling from an isotropic flux is checked with a Kolmogorov test and it is found to be 82%. The hypothesis of an isotropic flux is therefore supported.

Conclusions

A measurement of the cosmic ray anisotropy has been made using the AlbaNova array which forms a sub array of the SEASA outreach project. The result favors a scenario with a uniform ﬂux of cosmic rays in the energy regime above 1016 eV, and therefore agree with previous measurements, for example KASCADE [95]. It is a crude measurement of the cosmic ray anisotropy but it shows that the array is stable and in particular that the GPS timing is reliable. 160 Chapter 6. Discussion and conclusions

Figure 11. A sky map in galactic coordinates showing the detected events.

Figure 12. The distributions of the two point distance for measured events and randomly generated isotropic events. Acknowledgements

I would first like to thank Prof. Mark Pearce for all his support during my PhD studies. His encouragement has pushed me to achieve more than I ever would have done otherwise. I’m also deeply thankful for him, very generously, giving me all the opportunities that I have got, making the best out of these years. Support from the Swedish National Space Board are acknowledged. Im also grateful for the generous scholarships from The Royal Swedish Academy of Sciences and The Knut and Alice Wallenberg Foundation. A big hug goes to all colleagues, present and past, at the astroparticle physics group at KTH. It has been great working there and I will miss you all in the future. A special thought goes to the people whom I spent my first years with at KTH: Jens, Janina, Sara, Tore, Hank and Pelle. Work has not been the same without you. Thanks also to my present room-mates Cecilia, Tomi and Juan. I have had the benefit to work in the international collaboration around the PAMELA experiment which has given me the opportunity to travel the world and meet wonderful people. First I would like to thank Prof. Oscar Adriani for giving me the possibility to visit his group in Florence during six months. I had a great time there, and i learnt alot from the thorough knowledge of physics in the group. I want to give a special thanks to Elena and Paolo who always took the time to help me with my analysis. Thanks also for all your efforts helping me out with practical things and for making me feel welcome in the group. Lorenzo made a big effort finding me apartment(s), even though it didn’t turn out for the best every time. Massimo was a great friend during my stay and I hope I will see you somewhere, sometime in the future. A number of (chaotic) journeys went to Moscow where I would have been more lost than usual if it wasn’t for Stas and Nikolaj. Getting by (surviving!) in Moscow isn’t easy, but you did your best to help me and I truly enjoyed the stays their in the end. A sincere thank you goes to Mirko Boezio who has given me great support during this last year. Thanks for giving me the opportunity to come to Trieste where I had a great time both in the office, producing most of what I have presented in this thesis, and outside the office, climbing mountains, eating delicious food and discussing Simpson’s and roman history. You should credit yourself for getting me addicted to Italy and in particular all sorts of Italian food and beverages!

161 162 Chapter 6. Discussion and conclusions

A very special thought goes to my close friends and family. I’m amazed you are still there even though I have been out of touch for long periods. You mean everything to me, and I will try to show that better in the future. My last thought goes to the person who actually had to endure my company during these last months of writing, which I cannot believe could be very pleasant at all times. Claudine, you are my everything, och jag ¨alskar dig ¨over allt. List of Figures

1.1 Thecosmicrayspectrum ...... 7 1.2 SN1006inX-rays...... 8 1.3 Thechemicalcomposition...... 10 1.4 Themeasuredboronthecarbonratio ...... 13 1.5 Themagnetosphereandheliosphere ...... 15 1.6 Neutron flux at ground and relative sunspot number ...... 16 1.7 Prediction of Antiproton-proton ratio over time ...... 18 1.8 Antiproton-protonratio ...... 19 1.9 Cosmicraytrajectories...... 21 1.10 Worldmapsofgeomagneticcutoffs ...... 22 1.11 Motionoftrappedparticles ...... 23 1.12 Trappedprotonsandelectrons ...... 24 1.13EventrateinCAS1...... 25 1.14 Recentexperimentalantiprotonflux ...... 27 1.15 Neutralinoannihilations ...... 28

2.1 ThelaunchofPAMELA...... 30 2.2 TheResursDK1satellite ...... 32 2.3 ThePAMELAinstrument ...... 35 2.4 Theerrorofthedeflectionreconstruction ...... 37 2.5 Thespilloverphenomena...... 38 2.6 Themagnet...... 39 2.7 Themagneticfield ...... 40 2.8 Aspectrometerplane...... 41 2.9 TheToFsystem ...... 42 2.10 PAMELAtriggerrateinflight ...... 43 2.11Betaresolution ...... 44 2.12 Theelectromagneticcalorimeter ...... 45 2.13 The energy resolutionof the calorimeter ...... 46 2.14 Theanticounterdetectors ...... 47 2.15 The anticounter activity during flight ...... 49 2.16 Integral and differentiate anticounter calibration curves ...... 51 2.17 The performance of the anticounter detectors over time ...... 53 2.18 Theneutrondetector...... 54

163 164 List of Figures

2.19 ThePAMELAdataacquisitionsystem...... 54

3.1 All-particle β versusrigidity...... 56 3.2 All-particle dE/dx versusrigidity...... 57 3.3 Amissidentifiedprotonevent...... 61 3.4 Tracker dE/dx selection ...... 63 3.5 Particles selected with the tracker dE/dx selection...... 64 3.6 ToF dE/dx and β selection ...... 66 3.7 Particles selected with the ToF selection...... 67 3.8 Event-views of three different calorimeter events ...... 69 3.9 The nstrip distribution for electrons and antiprotons ...... 71 3.10 Lateralcalorimetervariable ...... 72 3.11 The fraction of energy inside a cylinder of radius 4 strips...... 73 3.12 A calorimeter variable for describing the starting point of the shower. 74 3.13Anantiprotonevent ...... 76 3.14 Theselectedprotonsandantiprotons...... 77 3.15 The spatial and time distribution of protons and antiprotons. . . . 78 3.16 Thecalorimeterelectronefficiency...... 80 3.17 Anexampleofapionevent ...... 81 3.18 The pion distribution derived with simulations...... 82 3.19Lowenergypions...... 83 3.20 Antiproton candidates versus selection cuts...... 85 3.21 Thesimulatedpioncontamination ...... 86 3.22 The β distributions of the selected proton and antiproton candidates 87

4.1 TheToFrigidityresolution ...... 94 4.2 The dE/dx intheToFsystem...... 96 4.3 Trackerefficiencyovertime...... 97 4.4 Flight and simulated efficiency of the basic tracker cuts...... 98 4.5 Flight and simulated efficiency of the additional tracker cuts. . . . 100 4.6 Totaltrackerefficiency...... 100 4.7 S12impactdistribution ...... 101 4.8 Trackerefficiencycorrectionfactors ...... 102 4.9 The efficiency of the ToF dE/dx selection ...... 105 4.10 The efficiency of the ToF npaddles selection ...... 106 4.11 The efficiency of the ToF β selection ...... 107 4.12 TheefficiencyofthetotalToFselection ...... 108 4.13 Cross-sections for hadronic interactions ...... 109 4.14 Thecalorimeterprotonefficiency ...... 110 4.15 The calorimeterantiprotonefficiency ...... 111 4.16 Thetotalselectionefficiency...... 114

5.1 Thegeometricalfactor ...... 118 5.2 The geomagnetictransmissionfunction...... 120 5.3 The p,pbar correction factors for inelastic interactions...... 123 List of Figures 165

5.4 Theprotonsmearingmatrix...... 124 5.5 Unfoldingperformance...... 125 5.6 Antiprotonenergylosserror...... 126 5.7 The antiproton flux measured with the PAMELA instrument . .. 130 5.8 The antiproton-to-proton flux ratio measured with the PAMELA instrument ...... 131 5.9 The antiproton flux measured by a number of experiments . . ... 134 5.10 Thep/p ¯ flux ratio from all contemporary measurements...... 136 5.11 The time evolution of thep/pratio ¯ ...... 137 5.12 The PAMELAp ¯ − pratio, entireenergyrange ...... 139

6.1 TheResursDK1satellitebeforelaunch ...... 145 2 TheSEASAarray ...... 148 3 ASEASAdetectors...... 149 4 Thedataacquisition...... 150 5 Timediﬀerence ...... 152 6 Triggereﬃciency ...... 154 7 Angularresolution ...... 155 8 Angularresolutionvstimeresolution...... 156 9 Validationofthesimulation ...... 157 10 Thecoveragemapingalacticcoordinates...... 159 11 SEASAskymap ...... 160 12 Twopointcorrelationfunction ...... 160 166 List of Tables

3.1 The number of selected proton and antiproton candidates ..... 77 3.2 Electroncontamination ...... 80 3.3 Antiproton and pions between 1.2 to 2.0 GV/c ...... 88 3.4 The pion contamination in ﬂight data ...... 89 3.5 The number of antiproton and proton candidates ...... 89

5.1 Thematerialabovethecalorimeter ...... 122 5.2 Energylosserrors...... 126 5.3 The number of protons and antiprotons at TOI...... 128 5.4 The antiproton ﬂux measured with the PAMELA instrument . .. 130 5.5 The antiproton-to-proton ﬂux ratio measured with the PAMELA instrument ...... 131

1 TheangularresolutionofSEASA...... 156

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