Università Degli Studi di Siena The Cosmic Ray Electron ... - Infn [PDF]

Università Degli Studi di Siena Facoltà di Scienze Matematiche Fisiche e Naturali

Tesi di Dottorato in Fisica Sperimentale PhD Thesis in Experimental Physics

The Cosmic Ray Electron Spectrum measured by the Fermi LAT

Candidato: Melissa Pesce Rollins

Relatore: Prof. R. Bellazzini

XXII CICLO

CONTENTS Acknowledgements 5 Introduction 7 1 The Large Area Telescope 11 1.1 Brief history of Space based gamma-ray missions 11 1.2 The Large Area Telescope 14 1.2.1 The Tracker 16 1.2.2 The Calorimeter 18 1.2.3 The Anti-Coincidence Detector 19 1.2.4 The Trigger System 20 1.3 The Fermi LAT performance 21 1.3.1 LAT event analysis 22 1.4 The Instrument Response Functions (IRFs) 23 1.4.1 The Effective Area 24 1.4.2 The Field Of View (FOV) 25 1.4.3 The Point Spread Function (PSF) 26 1.4.4 On-orbit response of the LAT 26 2 Launch and Commissioning 29 2.1 On-orbit environment 29 2.2 South Atlantic Anomaly (SAA) polygon 33 2.3 Instrument Science Operations Center (ISOC) 33 2.4 Detector calibration 36 2.5 First light 37 3 The first year of science with the Fermi LAT 41 3.1 Active Galactic Nuclei (AGN) and Blazars 41 3.2 Gamma Ray Bursts 44 3.3 Pulsars 46 3.4 Galactic Diffuse Gamma-ray Emission 50 3.5 Extragalactic Diffuse Gamma-ray Emission 51 3.6 Cosmic Rays 53 4 Geomagnetic and Solar environment 55 4.1 The Earth’s magnetosphere 55 4.1.1 The dipole field 56 4.1.2 Geomagnetic coordinate system - the L-shell parameter 4.1.3 Cutoff rigidity 59 4.2 Magnetically trapped radiation 60 4.2.1 Radiation belt electrons 64 4.2.2 Radiation belt protons 69 4.2.3 The South Atlantic Anomaly (SAA) 69 4.3 The cosmic ray albedo 71

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4.4 The Heliosphere 76 5 Cosmic Ray Electrons 79 5.1 The spectrum of Cosmic Rays 79 5.2 Energy Losses 82 5.3 Origins 85 5.3.1 Supernova Remnants (SNR) 86 5.3.2 Pulsars 88 5.3.3 Dark Matter 90 6 Analysis 93 6.1 Instrument simulation 93 6.1.1 On-orbit environment simulation 94 6.1.2 International Geomagnetic Reference Field (IGRF) 96 6.1.3 Electron simulation 97 6.2 Selection criteria 98 6.3 The CRE Instrument Response Functions 110 6.3.1 The effective geometry factor 110 6.3.2 Energy reconstruction 111 6.3.3 Energy resolution 113 6.4 Sources of background 113 6.5 Estimation of systematic uncertainties 123 6.6 Galactic Cosmic-Ray electron spectrum 129 6.6.1 Estimate of the uncertainty on the absolute energy scale 6.6.2 Positron fraction 138 6.6.3 The GCRE spectrum and its interpretation 142 6.7 Albedo electron spectrum 148 Conclusions 155 Acronyms 159 Bibliography 161

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ACKNOWLEDGEMENTS

Throughout the duration of my PhD studies I have been blessed to have the continuous love and support from my best friend and husband, Luca Baldini to whom I am indebted. I am particularly thankful for the constant encourangement and love from my family which have always stood beside me. I would like to thank my friends and colleagues Luca Latronico, Carmelo Sgrò, Johan Bregeon, Sara Marcatili, Gloria Spandre, Nicola Omodei, Giovanna Senatore, Massimiliano Razzano, Alessandro Brez, Dario Grasso, Michael Kuss, Marco Massai, Franco Angelini, Anders Borgland, Maria Elena Monzani, Eric Charles, Philippe Bruel, Simona Murgia, Luigi Tibaldo, Riccardo Rando, Troy Porter, Eric Grove, and Bill Atwood for making these last three years full of excitement and adventure. I would like to thank my advisor Prof. Ronaldo Bellazzini for his guidance and support for both my master and PhD thesis. I would also like to express my gratitude to Prof. Jonathan Ormes, my thesis refeere, for sharing his endless knowledge with me. Finally I would like to thank Mr. Frank Wolf for having taught me how much fun physics can be.

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INTRODUCTION

Cosmic rays (CR), high energy charged particles originating from outer space, were discovered in 1912 by Victor Hess [54]. The existence of radiation not originating from the Earth’s crust had also been reported by D. Pacini in 1912 [55]. He performed a series of experiments to measure how the rate of ionizing radiation differed between the surface of the Earth and under water. He found that the rate decreases when measuring from three meters of water and concluded that there must be a source of radiation in the atmosphere which does not originate from the Earth’s surface. However, it was not until the measurements were performed on balloon flights by Hess that it became possible to confirm with certainty that this radiation was not Terrestrial. Ever since their discovery the scientific community has made great efforts to understand their composition and origin. This almost century long quest has lead to many important discoveries not only in the CR community but also in the field of high energy particle physics. In fact, the muon was detected for the first time in 1936 by Carl D. Anderson [56] and the charged pion in 1947 by Cecil Powell, César Lattes, and Giuseppe Occhialini [57]. These discoveries were made possible with the aid of photographic emulsions plates placed in sites located at high altitude mountains where they were impacted by secondary products of primary CR with the Earth’s atmosphere. In 1941 with balloon flights near the top of the atmosphere carrying nuclear emulsion plates, Swann was able to confirm that the primary CRs where composed of mostly protons [58]. While Freier, Lofgren, Ney and Opperheimer in 1948 where the first to detect evidence for heavy nuclei in the primary CRs [59]. However, it was not until 1961 that the first observations of primary CR electrons were performed almost simultaneously by James A. Earl [53], Peter Meyer and Rochus Vogt [60]. Although they make up only roughly 1% of the total composition of the Galactic CRs, these particles provide valuable information regarding some of the fundamental questions in CR physics. Due to their small masses, cosmic ray electrons suffer significant radiative energy losses during propagation. For energies above a few GeV these energy losses are dominated by synchrotron radiation and inverse Compton scattering, with the rate of energy loss increasing with the square of the electron energy. As a consequence it can be excluded that the cosmic ray electrons measured at Earth are of extragalactic origin, thus distinguishing them from the other cosmic ray species. The study of the cosmic ray electron spectrum is also important to constrain theoretical models of production and propagation of CRs in the Galaxy. Prior to 2008, the CR electron energy spectrum was measured by balloon born detectors and one single space mission, AMS01. These experiments found that the electron intensity decreases more rapidly with energy than that of the CR protons, both of which are well described by a simple power law with spectral index of ∼ 3.3 and 2.7 respectively for energies greater than 10 − 20 GeV. Particular excitement came about when the Advance Thin Ionization Calorimeter (ATIC) detected an anomalous feature in

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the CR electron spectrum around 500 GeV [94] which lead to theoretical interpretations involving dark matter and new physics. The vast majority of the measurements made however exhibited sizable statistical errors and little to no information regarding the systematic uncertainties. These conditions made it therefore very difficult to make any solid constraints on the proposed theories. A new measurement of the CR electron spectrum with large statistics over a wide energy range was clearly needed to better investigate the shape and spectral index of the spectrum. The Fermi Space Telescope (Fermi), launched on the 11th of June 2008, is an international space mission designed to explore the gamma ray sky in the range from 10 keV to more than 300 GeV. The main instrument on board Fermi, the Large Area Telescope (LAT), is a pair conversion telescope designed to operate in the energy range from ∼ 20 MeV up to ∼ 300 GeV and consists of three subsystems: a silicon strip tracker-converter, a CsI imaging calorimeter and an anti-coincidence detector. Compared with its predecessor, the Energetic Gamma Ray Experiment Telescope (EGRET) [5], which flew on board the Compton Gamma Ray Observatory (CGRO), it has superior area, angular resolution, field of view and dead time that together provide a factor of 30 advance in sensitivity and capability of studying celestial sources. Fermi also has a secondary instrument, the Gamma-Ray Burst Monitor (GBM), designed to study Gamma Ray Bursts (GRB) and transient phenomena. It is composed of 12 NaI and 2 BGO scintillation detectors that cover an energy range from about 10 keV up to the LAT energies. The detectors are positioned on the spacecraft and oriented as to provide approximately uniform coverage of the unocculted sky. When a burst occurs, the GBM can compute its location on board allowing the autonomous re-pointing of the Fermi observatory to place the burst within the LAT field of view. The Fermi LAT relies on the pair production interaction to detect gamma rays and therefore it is by design also an electron detector and has proven to be an exceptional one. After only six months of operations the Fermi LAT collected enough statistics to provide the first systematics limited measurement of the CR electron plus positron1 spectrum from 20 GeV to 1 TeV [100]. From this measurement it was found that the spectrum is well described by a power law with spectral index of ∼ 3.04; no ATIC like feature was detected. The next logical step in the framework of the LAT data set is to extend the spectrum down to the lowest possible energies given the local magnetic field. The main topic of this thesis is on the work necessary to realise this measurement. In particular I took a leading role in developing an energy dependent event selection in the interval 100 MeV < E < 100 GeV, capable of picking out electrons from the 50 − 1000 times more abundant CR proton flux. The residual contamination was always kept below 20% over the entire energy range of my analysis. For energies below 20 GeV the analysis is particularly difficult due to the presence of the Earth’s magnetic field which causes the charged particles fluxes to vary drastically throughout the Fermi orbit. The population of electrons below a few GeV are not only of Galactic origin but also secondary products from the interaction of the Galactic CRs with the Earth’s atmosphere also known as the albedo. Having developed a reliable selection 1 The LAT does not distinguish electron from positrons. I will use the term electrons to refer to the sum of the two components.

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criteria for the electrons over such a wide energy range I have also analysed the albedo intensity with particular interest in updating the on-orbit background Monte Carlo (MC) simulation. The update of this simulation can help to improve our understanding of the geographic and geomagnetic variations in the charged particle environment over the Fermi orbit. Having the most accurate MC simulation also aids in the background rejection for both the electron as well as the photon analysis. Even though the Fermi observatory does not have a magnet on-board, I was able to measure the positron fraction thanks to the presence of the Earth’s magnetic field. When the incoming CR flux reaches the Earth’s atmosphere the positively charged particles are deflected towards the west while the negatively charged ones towards the east due to the polarity of the geomagnetic field. This is the well known east-west asymmetry [83] and its effect is clearly visible for energies in the rigidity cutoff region of the CR electron spectra. For Fermi’s nearly circular orbit this translates into the energy window of roughly 5 − 17 GeV. Using my electron selection I was able to measure the positron fraction in this energy range. During the period of my PhD studies I not only carried out the work on the CR electron spectrum but also actively participated in the commissioning phase of the Fermi LAT immediately following the launch of the observatory. My main role was that of the duty scientist whose responsibilities consists of monitoring the quality of the LAT data both at the single subsystem level as well as at the overall detector level. I was also required to identify and document problems in real time monitoring and housekeeping of the detector and being capable of identifying any problems at the data processing level. Another activity which I worked on after the launch of Fermi was that of monitoring the position and size of the South Atlantic Anomaly (SAA). The SAA can be defined by a 12 sided polygon and prior to launch a conservative definition of the SAA boundary was used based on models of the Earth’s radiation belts and data from other spacecraft. Due to the extreme conditions inside the SAA region, the LAT does not take science data while passing through the SAA. However, LAT housekeeping is recorded and transmitted to the ground during these transits. Special tracker and anti-coincidence counters (Low Rate Science Counters, LRS) sample the rate of fast trigger signals to determine position-dependent rate of the LAT along its orbit and are active during the SAA passages. My task was to use the data from these counters to redefine the boundary of this region and as a consequence increase the observational time of the detector. Thanks to this work the loss in observational time went from roughly 17% to ∼ 13% [17]. Clearly the role of the duty scientist is not only important during the commissioning phase of the observatory but is necessary throughout the entire mission. For this very reason I continue to work as duty scientist. In this thesis the work that I have carried out for the duration of my PhD studies is presented. Starting with an overview of the Fermi mission as a whole in chapter 1 where I describe the detectors which make up the observatory and the instrument response functions of the LAT. After which I discuss the main activities and results from the launch and commissioning phase known as the Launch and Early Orbit (LEO) in chapter 2. The numerous discoveries in high energy astrophysics made by Fermi in the first year of operations are briefly presented in chapter 3. Given the deciding role which the Earth’s magnetic field plays in the CR electron analysis both for the Galactic

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component as well as the albedo one, I have included a review of the geomagnetic and solar environment in chapter 4. Followed by an introduction in chapter 5 to the Galactic CRs with particular attention to the energy losses and proposed origins of the CR electrons. Finally in chapter 6 I present the analysis behind the CR electron spectrum including the instrument response functions for the electrons, development of the event selection and spectrum reconstruction. I also discuss the analysis approach used to measure the positron fraction in this chapter. Other important aspects of the analysis such as the identification and removal of background and estimation of the systematic uncertainties are also presented in this chapter, together with some possible theoretical interpretations of the resulting spectrum. Finally, I discuss my ongoing work on the update of the on-orbit background simulation with the Fermi LAT albedo electrons in section 6.7.

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1 THE LARGE AREA TELESCOPE

In this chapter a brief overview of the past gamma-ray experiments will be presented with the goal of highlighting the main discoveries made and the mysteries left to be solved. Most of these unanswered questions were caused by technological limitations of the detectors. In fact by reviewing the past experiments the need for a new high energy gamma-ray observatory becomes clearly evident and thus a description of the Fermi Large Area Telescope is presented. In the last two sections of this chapter the LAT performance and an introduction to the Instrument Response Functions are discussed. 1.1

brief history of space based gamma-ray missions

The primary interaction of photons for energies greater than a few MeV is the pair production effect. The basic schema of a pair conversion telescope is illustrated in figure 1 and briefly described in the following. As the incident radiation passes through

Figure 1: Basic principle of a pair conversion telescope.

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the instrument it will first encounter an anticoincidence shield, which is sensitive to charged particles. Second, the radiation will pass through thin layers of conversion foils (made of high Z material) and thus converting the photon into an electron positron pair. Once the conversion has occurred, the trajectories can be revealed and measured via particle tracking detectors and their energy measured by a calorimeter. The gamma-ray detector on board the third Orbiting Solar Observatory (OSO 3) was launched on the 8th of March 1967 into a nearly circular orbit of mean altitude 550 km and inclined at 33◦ with respect to the equatorial plane. OSO 3 operated continuously for 16 months, during which it performed a complete sky survey and recorded 621 photons above 50 MeV and illustrated how the distribution of gamma-rays is highly anisotropic with a noticeable concentration around the galactic center and extended regions along the galactic plane [1].

Figure 2: Conceptual structure of the high energy gamma ray detector flown onboard the OSO-III mission [1].

The satellite contained an MIT gamma-ray instrument whose body consisted of a multilayer CsI and plastic scintillator detector, coupled with an energy detector containing several layers of Nal in alternating layers of tungsten. The whole of the detector was enclosed by plastic scintillator detectors for anticoincidence. The photon direction was loosely determined by the solid angle defined by the geometry of the telescope. The next satellite mission for the exploration of the gamma-ray sky was NASA’s Small Astronomy Satellite (SAS 2) launched on the 19th of November 1972. The instrument consisted of a 32 level wire spark chamber interleaved with tungsten conversion foils

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1.1 brief history of space based gamma-ray missions

with an energy range of 20 MeV to 1GeV [4]. The energy information was derived by the multiple scattering, measured by means of the tracking planes, and the anti-coincidence system was provided by a set of plastic scintillator tiles and directional Cherenkov detectors placed below the spark chamber.

Figure 3: Schematic view of the gamma ray detector onboard the SAS-II satellite [4].

The missions’ scientific goals were to provide a full sky coverage within one year of operation, with early emphasis placed on the galactic plane. Due to a failure of the low voltage power supply, the data collection unfortunately stopped on June 1973. Nonetheless, SAS-II provided the first detailed information about the gamma ray sky and showed that the galactic plane radiation is strongly correlated with the galactic structural features and revealed for the first time a high energy (> 35 MeV) component of the diffuse celestial background [4] also discovering the pulsar Geminga. The ESA COS-B mission was launched on the 9th of August 1975 and outlasted it’s original two year lifetime reaching a full six years and eight months. The detector was sensitive to photons in the energy range spanning from 30 MeV to several GeV over a field of view of almost 2 sr [2]. During COS-Bs’ lifetime it made detailed observations of gamma-ray pulsars such as the Geminga pulsar, along with binary systems. The mission was also able to view nearly 50 per cent of the celestial sphere, and thus providing a gamma-ray map of the galaxy [3]. The detector consisted of a magnetic core wire matrix spark chamber whose triggering was provided by a three element scintillation counter and a 4.7 radiation lengths calorimeter. The whole of the telescope was surrounded by a plastic scintillator guard counter, serving as an anti-coincidence detector [2]. NASA’s Compton Gamma ray Observatory (CGRO) experiment, that was launched in 1991, carried amongst others, the Energetic Gamma Ray Experiment Telescope (EGRET). Like its predecessors, EGRET made use of the spark chamber system to detect gamma-rays by the electron positron pair production process. The directional

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Figure 4: Structure of the gamma ray telescope onboard the COS-B mission [2].

telescope consisted of an upper spark chamber containing 28 closely spaced spark chamber modules interleaved with twenty seven 0.02 radiation length plates. The lower spark chamber, was surrounded by two time of flight scintillator planes, widely spaced and did not have any radiation plates. The whole of the telescope was covered with an anti-coincidence scintillation dome. The initial direction of the incoming photon was determined from the upper spark chamber data. The lower spark chamber assembly, between the two time-of-flight scintillator planes, allowed the electron trajectories to be followed, provided further information on the division of energy between the electrons, permitted seeing the separation of the two electrons for very high energy gamma rays, and indicated the entry points of the electrons into the NaI monolithic calorimeter. The resolution was degraded to about 25% above several GeV due to incomplete absorption in the NaI calorimeter, and at energies below about 100 MeV where ionization losses in the spark chamber plates accounted for an appreciable portion of the total energy [5]. EGRET produced the first full sky survey in the energy range between 30 MeV and 10 GeV. The energetic sources detected were 271, of which only 100 have detectable counterparts at other wavelengths such as Active Galactic Nuclei (AGN) and pulsars. Thus leaving 171 objects emitting in the gamma-ray sky whose origins were completely unknown [6]. 1.2

the large area telescope

The Large Area Telescope (LAT) is the main instrument onboard Fermi. It is a gamma ray telescope based on the pair production effect. The LAT is modular in its structure, consisting of a 4 × 4 array of identical towers. Each tower consists of a tracker,

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Figure 5: The pair production telescope EGRET. An anti-coincidence detector (ACD) shield encapsulates the spark chambers preventing triggers from charged particles. The directional telescope consists of two levels of a four×four scintillator array with selected elements of each array in a time of flight coincidence. The initial direction of the electron pair is usually determined from the upper spark chamber data, whereas the lower spark chamber (that is between two time of flight scintillator planes) allows the electron trajectories to be followed. The energy of the gamma ray is determined in large part from the measurements made in the square monolithic calorimeter located below the time of flight plane [5].

calorimeter and data acquisition module. The Tracker (TKR) includes 18 xy layers of high resolution silicon strip detectors. The Calorimeter (CAL) contains eight layers of 12 CsI bars in a hodoscopic arrangement, for a total thickness of 8.6 radiation lengths. The LAT is enclosed in an Anti Coincidence Detector (ACD) composed of 89 plastic scintillator tiles. Therefore, the detection of a gamma ray with the LAT is confirmed if the following signature is observed: no signal in the anticoincidence shield, more than one track starting from the same location, and lastly an electromagnetic shower in the calorimeter. If this signature is detected for at least three xy layers in a row, the readout of the tower is initiated, and defines the main trigger primitive (the so called three in a row). However, a high signal in the calorimeter can also trigger the system by itself.

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Figure 6: Map of the source locations for the third EGRET catalog, shown in galactic coordinates [6].

More details on the LAT’s subdetectors trigger system and background rejection are presented in the following sections. 1.2.1

The Tracker

The Fermi tracker (TKR) consists of 16 towers each one with 37 cm × 37 cm active cross area. Each tower has 19 trays. The trays are composed of silicon strip detectors (SSD) which are glued edge to edge and wire bonded in groups of four, in order to help minimize the number of readout channels. The groups of four SSDs form a substructure which is called a ladder. Each tray is made up of four ladders. When designing the TKR, there are two conflicting requirements that one must face. The objective is to convert a passing gamma ray and detect the paths of the resulting electron positron pair. Therefore, in order to convert the photon, it must interact with a high Z material of a given thickness. Yet to trace the resulting paths, the thickness of the material which the particle passes through, must be as thin as possible. To resolve this dilemma, tungsten conversion foils of two different thicknesses are used. More precisely, out of the 19 trays which constitute a TKR tower,the first 12 contain 3% radiation length conversion foils, the next four 4 trays have the thickest, 18% radiation conversion foils, and the last 3 trays (the closest to the calorimeter) have no conversion foil at all. The last three trays do not have any conversion foils due to the fact that if a photon has passed through the

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Figure 7: Single module of the LAT TKR tower during the assembly. The tray structure and the front end electronic boards are clearly visible.

TKR and has not yet converted by the time it has reached the last three trays, it would no longer be able to trigger a three in a row. Therefore tungsten foils in the last three trays would only increase multiple scattering. The tray is structured in the following way: the main body consists of a carbon honeycomb structure, on each face is a kapton foil with a printed bias circuit, above this circuit are the four sets of ladders which are placed in parallel to each other. The conversion foils are placed on the bottom face of the tray, between the carbon structure and the bias plane. Each tray is rotated 90◦ with respect to the previous one so that each tungsten foil is followed by an xy detection plane. All the trays are mechanically identical, except for the top and bottom tray, which have SSDs only on one side. This is because the top and bottom trays contain the support mechanisms to anchor the TKR to the rest of the LAT. A side view of a single TKR module is shown in figure 7 while the structural layout of a tower is illustrated in figure 8. The readout electronics are mounted to the side of the tray, in order to minimize the gap between trays and maintain the specification distance of 2mm ±0.1 mm.

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Figure 8: Layout of a tower and its components

Communication between the readout electronics for each tray is provided by two flex cables per tower side. The data are digitized and zero-suppressed by the TKR readout electronics. The data for each detection plane contains the identifiers of the hit strips and the Time Over Threshold (TOT) of the layer logical OR. The TKR as a whole contains 9216 silicon sensors (over 83 m2 of covered surface) for a total number of electronics channels approaching one million [12]. 1.2.2

The Calorimeter

The calorimeter subsystem is also modular, consisting of 16 calorimeters for the full LAT, one per tracker tower. Each calorimeter module contains 96 crystals of size 2.3 x 3.0 x 31 cm, and they are readout by PIN photo diodes [13]. The crystals are individually wrapped for optical isolation, and are arranged horizontally in 8 layers of 12 crystals each. Alternating layers are rotated 90◦ with respect to each other in order to supply information for both the x and y axis. Each CsI crystal provides three spatial coordinates for the energy deposited in it. Two coordinates are from the physical location of the crystal in the array and the third coordinate is along the length of the bar. The indicated size is comparable to the CsI radiation length (1.86 cm) and the Moliere radius (3.8 cm) for electromagnetic showers. A schematic drawing of the Fermi LAT calorimeter is shown in figure 9 The principle function of the calorimeter is to measure the energy of the shower resulting from the pair conversion of the incident gamma rays in the tracker,

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Figure 9: Schematic view of the Fermi imaging calorimeter.

and to assist with the cosmic-ray background rejection. The positioning of the PIN photo diodes provides redundancy but it also allows to measure the light asymmetry from within the crystals. From the measure of this light asymmetry, the position of the electromagnetic shower along the CsI crystal (longitudinal position) can be determined.

1.2.3

The Anti-Coincidence Detector

The Anti-Coincidence Detector (ACD) has the fundamental task of discriminating incident charged cosmic rays from gamma rays that pass through the LAT. The charged particle background flux outnumbers the gamma ray flux by more than a five orders of magnitude at the same energy. There are several novelties in the Fermi ACD with respect to the past missions, for example a segmented scintillator tiles as opposed to a uniform block and the instrument does not depend on consumables. The lack of consumables has the advantage of avoiding instrument deterioration with time. The segmented ACD choice resides in the reduction of the accidental coincidences or self veto which can cause false signals. These events are caused when the electromagnetic shower produced by a gamma ray interacts within the ACD simulating the passage of a cosmic ray. The most common case is that of the backsplash effect. In the LAT the self veto effect is reduced by using the information gathered by the ACD to determine the direction from which the particle originated and the specific tile which the particle passed through. In doing this, the ACD system is used as a second level trigger as opposed the primary trigger. The reduction of the accidental coincidences facilitates the background rejection (especially at high energies) and therefore increases the sensibility of the instrument as a whole. The ACD for the LAT is shown in figure 10. There are 25 of plastic scintillator tiles on the top face of the LAT and 16 on each of the four lateral faces for a total surface of 8.6 m2 [14]. Each tile is read by means of two Wavelength-Shifting Fibers (WSFs) connected to Photo-Multiplier Tubes (PMTs). To ensure maximum coverage, the ACD tiles overlap

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Figure 10: Picture of the Anti Coincidence Detector in the assembly phase.

in one direction and 8 scintillating fiber ribbons seal the gaps in the other direction. The overall efficiency of the ACD is > 0.9997 [17]. 1.2.4 The Trigger System Two of the main design improvements of the LAT are a flexible trigger logic and onboard event filtering. The LAT trigger is organized in two levels. The first one is a hardware trigger which is based on special combinations of signals at the level of a single tower, namely the three in a row already mentioned previously. There are also two different calorimeter based trigger primitives with adjustable thresholds (nominally set at 100 MeV and 1 GeV of energy deposition per crystal log). The ACD also adds two other trigger signals, a veto and a CNO. The latter has a threshold of several MIPs and is used to identify cosmic ions with Z> 2 for on orbit calorimeter calibration purposes. In addition there are three other trigger sources: the Periodic trigger used to sample detector noise and pedestals, the Solicited trigger for special software trigger requests and the External trigger for ground testing. An electronic module (the GEM [15]) combines these signals in a 600 ns coincidence window and then "decides" whether the event is read out or not. The typical readout time per event is about 26 µs thus allowing the instrument to trigger on almost every particle that crosses the LAT. This is a revolution with respect to the previous generation of pair conversion telescopes, where due to the relatively large instrumental dead time it was necessary to apply harsh photon selections at the level of the hardware trigger. The LAT trigger rate is of the order of few kHz but due to telemetry bandwidth limitations an onboard event selection is applied and roughly half of the events are actually written on spaces craft memory. This is accomplished by several software configurable onboard filters. The rate of events down linked to Earth is of the order of few hundred Hz, still mostly charged particles (i. e. protons, electrons,

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GCR metals). The refined analysis, both for the photon (cfr.[98]) and CR electron science is performed on the ground. For more details about the on-orbit rates, see [69]. The second level, in the triggering logic, is a software trigger. Multiple filters in series are applied to each event and each filter is optimized to select a different classes of events (for example gamma rays or heavy ions). Within each filter events are accepted or rejected based on a sequence of tests, each one with tunable parameters. In the routine data taking configuration the onboard filter instance providing the main data source for photon science (the gamma filter) is configured to pass all the events depositing more than 20 GeV in the calorimeter. There is also another filter, the Diagnostic filter (dgn filter) which provides an unbiased sample of all trigger types, prescaled by a factor of 250. 1.3

the fermi lat performance

The design of the LAT was optimized using Monte Carlo simulations. However, extensive beam tests have been performed at SLAC, CERN and GSI heavy ion accelerator laboratories in order to verify the overall design of the instrument. Furthermore, hardware prototypes as well as the flight instrument itself (prior to launch) have been tested using cosmic rays on ground. The most extensive beam test was performed at the CERN accelerator in 2006. The CERN beams were chosen because they cover almost the entire energy range of the LAT for on-orbit operations as well as provide large fluxes of hadrons to verify the modeling of background interactions within the LAT. Due to schedule limitations it was not possible to perform the beam test on the full LAT, therefore a Calibration Unit (CU) consisting of two complete trackers and 3 calorimeter modules was assembled. The CU was equipped with several ACD scintillator tiles to measure the backsplash response from the calorimeter at high energies. The overall agreement between data and Monte Carlo simulations of the CU and beam test data are excellent, including the overall tracker performance and the PSF, the backsplash into the ACD, and the modeling of hadronic interactions. The largest discrepancies involve the energy calibration in the calorimeter which was found to be low ∼ 7%. A more detailed description of the beam test results, comparing the CU to the Monte Carlo simulations can be found in [99]

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Parameter Energy range Effective area at normal incidence1 Energy resolution (equivalent Gaussian 1σ): 100 MeV – 1 GeV (on axis) 1 GeV – 10 GeV (on axis) 10 GeV – 300 GeV (on axis) > 10 GeV (> 60◦ incidence) Single photon angular resolution (space angle) on axis, 68% containment radius: > 10 GeV 1 GeV 100 MeV on-axis, 95% containment radius Field of View (FoV) Timing accuracy Event readout time (dead time) GRB location accuracy on-board2 GRB notification time to spacecraft3 Point source location1 Point source sensitivity(> 100 MeV)4

Value or Range 20 MeV - 300 GeV 9, 500 cm2 9%–15% 8%–9% 8.5%–18% ≤ 6%

≤ 0.15◦ 0.6◦ 3.5◦ < 1.7× on-axis value 2.4 sr < 10µsec 26.5µsec 0 < 10 < 5 sec 0 < 0.5 3 × 10−9 ph cm−2 s−1

Table 1: Summary of the LAT instrument parameters and estimated performance [98]

1.3.1

LAT event analysis

All events which are down linked to Earth from the LAT undergo a full event reconstruction and data analysis. This stage includes the calculation of several different estimates for the direction and energy of the reconstructed event. The next stage is called the event analysis, where the best determination of the event energy and incoming direction are chosen using automated classification algorithms. For both the values a corresponding probability is calculated that expresses the degree of confidence that the chosen values do not lie far from the core of the corresponding distribution. In order to improve the on-orbit filtering a background rejection stage is also applied making use of information coming from all three of the detector subsystems. Therefore, as a result of the on-ground reconstruction analysis it is possible to determine the energy and direction for each 1 Maximum (as function of energy) effective area at normal incidence. Includes inefficiencies necessary to achieve required background rejection. Effective area peak is typically in the 1 to 10 GeV range 2 For burst (< 20 sec duration) with > 100 photon above 1 GeV. This corresponds to a burst of ∼ 5 cm−2 s−1 peak rate in the 50 − 300 keV band assuming a spectrum of broken power law at 200 keV from photon index of −0.9 to −2.0. Such burst are estimated to occur in the LAT FoV ∼ 10 times per year. 3 Time relative to detection of GRB. 4 For a steady source after 1 year sky survey, assuming a high-latitude diffuse flux of 1.5 × 10−5 cm−2 s−1 sr−1 (> 100MeV) and a photon spectral index of −2.1, with no spectral cut-off.

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1.4 the instrument response functions (irfs)

event with corresponding confidence levels as well as the probability that the event is indeed a photon. At this point, the data goes through a series of finer cuts to select data sets, of varying purity, of photons called event classes. These classes are defined, Diffuse, Source and Transient based on selection cuts that provide various levels of enhanced spatial and energy resolution. Depending on the particular needs a given analysis requires, one chooses a specific event class that satisfies them. However, harder selection cuts also bring the obvious trade off between efficiency, purity and resolution. 1.4

the instrument response functions (irfs)

The Instrument Response Functions (IRFs) provide a description of the instrument in terms of the transformation probability from the true physical quantities (i.e. energy and direction) to the corresponding measured quantities, taking into account the effects of the detector. It is important to note that the IRFs not only depend on the instrument itself, but also on the reconstruction algorithms as well as the background rejection. The response of the instrument can be expressed as: R( E0 , Ω0 | E, Ω)

(1.1)

where E0 and Ω0 are the measured photon energy and direction and E and Ω are the true quantities. Using the relation for probability composition: P( ab) = P( a|b) P(b)

(1.2)

the expression (1.1) can be rewritten as: R( E0 , Ω0 | E, Ω) = R E ( E0 |Ω0 , E, Ω) RΩ (Ω0 | E0 , E, Ω)

(1.3)

Under the reasonable assumptions that the measured energy does not depend on the measured direction (but only on the true energy and direction) and vice-versa, the equation simplifies: R( E0 , Ω0 | E, Ω) = R E ( E0 | E, Ω) RΩ (Ω0 | E, Ω)

(1.4)

so that we can define two new functions, only depending on the true physical quantities E and Ω: the Energy Response (∆E) ∆E( E0 | E, Ω) = R E ( E0 | E, Ω)

(1.5)

and the Point Spread Function (PSF) PSF (Ω0 | E, Ω) = RΩ (Ω0 | E, Ω)

(1.6)

With the knowledge of the IRFs together with the effective area it is possible to evaluate the detector response to a source with a known flux, F ( E, Ω, t): dNs 0 0 ( E , Ω , t) = dt Z Z E

Ω

Ae f f ( E, Ω)∆E( E0 | E, Ω) PSF (Ω0 | E, Ω) F ( E, Ω, t)dEdΩ (1.7)

In the following section the IRFs will be described in more detail.

23

the large area telescope

1.4.1

The Effective Area

The Effective Area can be written as: Ae f f ( E, Ω) = A geo ( E, Ω) Pconv ( E, Ω)ε det ( E, Ω)ε rec ( E, Ω)

(1.8)

where A geo ( E, Ω) and Pconv ( E, Ω) are the total geometrical area and the conversion probability (as a function of the photon energy and direction), respectively; ε det ( E, Ω) and ε rec ( E, Ω) in turn represent the detection efficiency of the instrument and the efficiency of the reconstruction algorithms and of the cuts necessary for background rejection. Once the effective area is known it is possible to determine the rate at which the instrument will detect a signal: dNs = dt

Z Z E

Ω

Ae f f ( E, Ω) F ( E, Ω)dEdΩ

(1.9)

where F ( E, Ω) is the source flux.

Figure 11: Effective area versus energy at normal incidence for three event classes. The Diffuse class is represented by the dashed line, the Source class by the solid line and the Transient class by the dotted line. The tightest selection cuts are applied for the Diffuse therefore justifying the smallest effective area of the three classes [18].

As already mentioned in the previous sections, the LAT tracker has 12 layers of 3% radiation length tungsten converters (called Front), followed by 4 layers of 18% radiation length tungsten converters (called Back). These sections have intrinsically different PSF due to multiple scattering, and the performance plots are presented for both these sections. In figure 11 the effective area for normally incident photons as a function of energy for the three event classes; Diffuse, Source and Transient averaged over all azimuth angles is shown, while in figure 12 the effective area separated for the front, back and total for the Fermi LAT is shown for the Diffuse class.

24

1.4 the instrument response functions (irfs)

Figure 12: The plot on the left is the effective area for normal incidence photons (defined here as cos(θ ) > 0.975); while the one on the right is for 10 GeV photons as a function of incidence angle [98].

1.4.2

The Field Of View (FOV)

The field of view is defined as the integral of the effective area over the solid angle divided by the peak effective area: R Ae f f (Ω)dΩ FOV = Ω (1.10) A peak and basically represents the portion of the sky that the detector can observe at the same time.From the geometrical point of view, the FOV mainly depends on the the aspect ratio of the instrument (i.e. the ratio between the thickness h and the width w). In the case of a detector with a planar geometry, the ideal case would be one with essentially no thickness. The effective area for such a detector would decrease as the cosine of the angle away from the normal: Ae f f (θ, φ) = A peak cos(θ )

(1.11)

and would be sensitive over 2π sr (or π sr considering only the portion of the sky not occulted by the Earth): R π/2 R 2π A peak cos(θ ) sin(θ )dθdφ 0 FOV = 0 =π (1.12) A peak The approach to the ideal case occurs as the ratio of the minimum tracker thickness to its width is minimized; in general the maximum angular acceptance is: w θmax = arctan (1.13) h and it can be easily shown that the fraction of the sky coverage of the real detector, compared to the ideal case, can be approximately written as:    π h F = 1 − cos − arctan (1.14) 2 w

25

the large area telescope

A design with a low aspect ratio is therefore highly desirable in terms of field of view and in the limit h 0.975); while the one on the right is for 10 GeV photons as a function of incidence angle [98].

incoming photon direction for the Fermi LAT is shown for both the front as well as the back sections. While in figure 14, the ratio of the PSF at 95% containment to that at 68% containment for the Fermi LAT is shown. 1.4.4

On-orbit response of the LAT

Immediately after launch an on-orbit calibration of the Fermi LAT was performed and is described in great detail in [17]. While examining down linked events it became clear that some unexpected interactions between background and gamma ray events

26

1.4 the instrument response functions (irfs)

Figure 14: The ratio of the PSF at 95% containment to that at 68% containment for the Fermi LAT. This ratio is a useful indicator of the magnitude of the tails of the distribution. The plots are defined in the same way as in figure 13 [98].

occurred. These interactions (called ghost events) happened due to the time evolution of the energy deposition in the detector, the timing of the electronics and of the trigger system together with the details of the reconstruction analysis. This was not observed in the MC simulation because each event is generated independently and interactions between subsequent events is not possible. Several examples of such ghost events where observed in real data. Such an event may occur, for example, if a photon strikes the LAT while the energy released by a background particle is still being collected from the detector subsystems. Figure 16 illustrates such an event as seen by the event display. Thus, when a photon event triggers the LAT, the signal of the photon as well as that of the background event are down linked to Earth together. When these ghost events are processed through the event reconstruction analysis routines (that have been trained on data samples unaffected by ghost hits) perfectly good photon events can be rejected. This in turn can lead to degradation of the LAT performance. To correctly resolve this issue the necessary procedure is to redesign the reconstruction analysis routines to correctly treat the events with these artifacts. This is currently being performed within the Fermi collaboration, however this task requires a fair amount of time. For the time being, the effect of ghost hits has been included in the MC used for the IRFs generation [18]. Thus, the the ghost-affected events are not recovered in the event reconstruction and analysis, but the performance degradation is accounted for in the IRFs. Using this approach, the estimated IRFs are once again a faithful description of the LAT performance in the space environment.

27

the large area telescope

Figure 15: Energy resolution (the 68% containment of the reconstructed incoming photon energy) for the front, back and total selection. The plot on the left is for normal incident photons (defined as cos θ > 0.9); the one on the right is for 10 GeV photons as a function of incidence angle [98].

Figure 16: Example of a ghost event in the Fermi LAT. A candidate photon event is seen on the right side of the detector while a ghost track, resulting from accidental time coincidence of a background event, is clearly visible in the upper left side of the detector. Candidate reconstructed tracks, as well as active volumes in the tracker and cal are shown for both events. [18]

28

2 LAUNCH AND COMMISSIONING

The Fermi observatory was successfully launched on a Delta II launcher from Cape Canaveral, Florida on June 11 2008. The first two months after the launch consisted of the commissioning phase, called the Launch and Early Orbit (L&EO). This phase is of fundamental importance for the instrument checkout and the study of the space environment. During this period several on-orbit calibrations are performed, for example the absolute timing, energy and direction measurements for individual events as well as fluxes and positions of gamma-ray sources. In this chapter some of the highlights of the commissioning phase will be briefly discussed. 2.1

on-orbit environment

The Fermi observatory is in a nearly circular orbit at 565 km altitude and 25.6◦ inclination with respect to the Earth’s equatorial plane. The satellite completes one full period in 96 minutes, also known as a run. A run starts when the satellite exits the region called the South Atlantic Anomaly (SAA) and ends when entering this region. For reasons which will be discussed in section 2.2, the detector does not take any data while passing through this region. Therefore it is a convenient point to define the boundaries of a run. There are however, orbits in which the satellite does not pass through the SAA and in these cases the start of the run is defined as the crossing of the equator by the satellite. In the top panel of figure 18 is an example of a run in which the satellite passes through the SAA and in the bottom panel is an example of a run without the SAA passage. The position of the SAA is shown by the blue polygon and the equator is represented by the dashed line. The x axis of this figure is the longitude and the y axis is the latitude of the Earth. The rate of charged particle background is dependent on the orbital position of the satellite. As an example, figure 19 illustrates the variations of the LAT event rate over a 2 day period. Most of the variations are due to the Earth’s magnetic field. This dependency is confirmed by the correlation between the rate of triggers with the McIlwain L parameter,shown in the bottom most plot of the figure. The rate of events triggering the LAT before any on board filter is applied varies from ∼ 1.5 kHz to ∼ 4 kHz (top panel of figure 19). The amount of telemetry bandwidth available for the down link of data to the ground is limited to 1.2 Mbs. Given this limitation some filtering of the data is necessary in order to reduce its volume. The on-board filter is designed to keep all possible gamma-rays and fill the rest of the allocated bandwidth

29

launch and commissioning

Figure 17: The launch of the Fermi observatory on June 11 2008 from Cape Canaveral Air Force Station in Florida. The observatory was launched with a Delta II launcher.

with background events giving priority to those that may be useful for calibration or diagnostics purposes. The rate of events passing the filters is shown in the second plot in figure 19, this rate is reduced by a factor of 5 with respect to the initial rate.

30

2.1 on-orbit environment

Figure 18: Top panel: Example of a run with a passage through the SAA, the start and stop of the run are labeled in black at the exit and entry into the SAA. Bottom panel: Example of a run without an SAA passage. The start and stop of the run are when the satellite crosses the equator from the southern to the northern hemisphere and are shown by the black points in the figure. The SAA is defined by the blue polygon. The SAA POCA is defined as the Point Of Closest Approach to the SAA and is labeled in red in the bottom panel. The orbital path is shown by the black curve with the gray points indicating 10 minute intervals. The x axis is the longitude and the y axis is the latitude of the Earth.

31

launch and commissioning

Figure 19: LAT rates in two days time span. From top to bottom: rate of triggers, rate of events sent to ground and rate of good gamma-rays (after full background rejection). The bottom plot is the calculated McIlwain’s L parameter that is correlated with the number of charged particles trapped in the Earth’s magnetic filed.

32

2.2 south atlantic anomaly (saa) polygon

2.2

south atlantic anomaly (saa) polygon

Fermi’s orbit intersects the South Atlantic Anomaly (SAA), a region of the Earth’s radiation belt which features geomagnetically trapped protons with energies up to hundreds of MeV and electrons with energies up to tens of MeV (for more detailed description of the SAA refer to chapter 4). The extreme conditions within this region impose constraints on the LAT operations. In fact the TKR electronics saturate due to the increase in the charge deposited per live time which would lead to large dead time fractions. The continuous flux of particles generates high currents in the ACD photomultiplier tubes (PMT) which leads to slow deterioration. Due to these reasons, the triggering, recording and transmission of science data are stopped and the bias voltages of the PMT’s are lowered from 900V to ∼ 400V during the SAA passages [17]. However, LAT housekeeping is recorded and transmitted to the ground during these transits as well as special TKR and ACD counters (Low Rate Science Counters, LRS). These counters can sample the rate of fast trigger signals to determine position-dependent rate of the LAT along its orbit. The position and size of the SAA can be defined by a 12 sided polygon. Prior to launch a conservative definition of this polygon, or SAA boundary, was determined based on models of the Earth’s radiation belts and data from other spacecraft. The inner radiation belts was modeled using trapped radiation models: Ap-8 [19] and PSB97 [20] in conjunction with the correct version of the International Geomagnetic Reference Field (IGRF-10) [87]. The polygon was calculated from these models based on the contour in latitude and longitude, where for E > 20 MeV trapped proton flux reached 1 cm−2 s−1 . For regions where the two models predictions disagreed, the larger flux was chosen. At this point, the smallest convex polygon circumscribing this contour was selected and padded by a 4◦ margin. This conservative definition for the SAA polygon was chosen with the intention to update the boundary based on particle rate measurements made with the LAT LRS in orbit. Figure 20 shows the average rate of the TKR LRS counters obtained during 14.85 days of nominal operations versus geographic latitude and longitude. Superimposed are the pre-launch SAA boundary (blue) used during the initial phase of the mission, and the refined polygon (magenta). The updated polygon reduced the loss in observational time from about 17% to roughly 13% of the total on-orbit time [17]. Given that the SAA moves at a rate of a few tenths of a degree per year and its size and particle fluxes vary with the solar cycle, annual cross checks will be performed. 2.3

instrument science operations center (isoc)

Operations support and science data processing for the LAT are provided by the LAT Instrument Science Support Center (ISOC). Some of the main objectives of the ISOC are the monitoring of the instrument’s health and safety, receiving, processing and archiving data, maintaining and optimizing the software that produces LAT science data products. The data taken by the LAT is down linked to the ground through the Tracking and Data Relay Satellite System (TDRSS) network to the White Sands Complex.

33

launch and commissioning

Figure 20: Average rate of the TKR Low Rate Science (LRS) counters obtained during the 14.85 days of LAT nominal science operations versus latitude and longitude. Superimposed are the polygon originally loaded on the spacecraft before the launch (blue) and the new improved polygon (magenta) derived from the measurements of the counters.

From White Sands the data is sent to the Mission Operations Center (MOC), which is responsible for sending the commands to the spacecraft, analyzing telemetry and providing overall support for the LAT operations. The overall schema of the data flow from the satellite to the ISOC is shown in figure 21. Shortly after the MOC receives the data, it is sent to the ISOC where it is processed via a pipelined infrastructure. The ISOC receives and processes the raw data (also called Level 0 data) and real time housekeeping data. After which, the ISOC is responsible for delivering the data in FT1 format (Level 1) plus the spacecraft’s pointing and livetime history in the standard FT2 format (this data is called the Level 2), as well as specialized instrument analysis tools. It takes on average 6 − 8 hours from the moment the event is readout from the detector, sent to ground, processed and ready to be analyzed. The average rate of events that pass the on-board filters is 400 Hz, which translates into roughly 4.5 million events to process every 3 hours by the ISOC L1 data processing. All events are digitized and reconstructed at this rate of data taking 24 hours a day 7 days a week. Prior to launch a huge amount effort was made to implement a set of web-based tools capable of monitoring the quality of the LAT data both at the single-subsystem level as well as at the overall detector level. This translates into the continuous monitoring of over a hundred thousand quantities. During the L&EO over 60 different configurations were loaded to the spacecraft for the purpose of on-orbit calibrations of all the subsystems of the detector and an overall monitoring of the health of the instrument after launch and while in orbit. The knowledge gained throughout the L&EO period allowed the Fermi Collaboration to implement an automated alarm system which checks over the

34

2.3 instrument science operations center (isoc)

Figure 21: Schema of data flow from the Fermi satellite all the way the LAT Instrument Science Support Center (LISOC). It takes on average 6 − 8 hours from the moment an event is readout from the detector, down linked to ground, processed and ready to be analysed.

data and catches problems without the need of human intervention. However, for the duration of the L&EO period and for the rest of the Fermi mission there are several fundamental quantities that are inspected every day by duty scientists to ensure that the overall quality of the data is good and that the instrument is working properly. In figure 22 is a screen shot of the Data Processing page. From this page it is possible to have access to all the information regarding the data including the processing status, delivery id, and configuration intent. The status of the automated alarms can also be viewed from this page.

35

launch and commissioning

Figure 22: The Fermi LAT Data Processing page. From this page it is possible to have access to all the information regarding the status of the data processing, delivery id, configuration intent, and any possible alarm that many have gone off. This page has also the links to all the quantities regarding the condition of the detector (all subsystems as well as the spacecraft), the event reconstruction (direction of arrival, energy deposited in the calorimeter, etc.) and navigation information (latitude, longitude, geomagnetic position, etc).

2.4

detector calibration

The initial configuration used on the LAT after turn on was based on a best estimate of the environment and understanding of the instrument based on simulations and the data taken during construction, integration and test phases. The first two months of the commissioning phase were spent (amongst other activities) running an exhaustive sequence of calibration runs taken in many different conditions in order to asses the performance of the instrument and fine tune its settings (for example timing, thresholds and trigger configuration). All the calibration constants to be used in the offline analysis (such as alignment constants) have been re-generated using on-orbit data. The peak of the minimum ionizing particles and the peaks of the most abundant heavy ions were measured to calibrate the energy response of the calorimeter crystals and showed excellent stability [21]. An example of such a measurement can be seen in figure 23 where the carbon peak position is stable to within 0.5% (for the whole calorimeter) after two months of operations. In figure 24 the energy deposited in all the calorimeter crystals from heavy nuclei collected during four days of on-orbit operations

36

2.5 first light

Figure 23: Position of the carbon peak for two months of on-orbit data. Notice how the peak position is stable to within 0.5% over the full time period [17].

is illustrated. The count rate in the charge peaks is similar to that of the primary galactic cosmic-ray abundance, modified by the loss of particles through interactions above the calorimeter and by the decreasing efficiency of the on-board heavy-ion filter for higher Z nuclei [17]. The three brightest sources in the LAT energy range are pulsars and during the L&EO they were used for several instrument calibration and optimization purposes. For example, by observing the Vela pulsar (also known as PSR J0835 − 4510) together with very precise information from radio wavelengths it was possible to check the pointing accuracy, angular resolution and timing capabilities of the LAT. No major problems were encountered throughout the instrument commissioning activities. No evidence of any reduction of the tracker hit efficiency (well above 99% on average) or increase of the overall noise level (less than 10−6 occupancy) with respect to the values measured on ground was observed. 2.5

first light

The commissioning phase was not only dedicated to the calibration of the instrument. Several other activities were performed during this period, for example the testing of the different observation modes (sky survey and pointing), demonstrating that the autonomous re-point capability in response to transients as well as validating the background rejection performance.

37

launch and commissioning

Figure 24: Energy deposited in all crystals from heavy nuclei collected during four days of on-orbit operations. Path length corrections are applied [17]

One of the most striking results which Fermi provided during this phase is the first gamma-ray sky map, shown in figure 25. The Galactic plane is clearly visible as well as the strongest point sources such as the Vela, Crab and Geminga pulsars. The statistics of this roughly four day Fermi sky map are comparable with those of the first EGRET one year sky survey. The sky map was measured while the instrument was in sky-survey mode, which provides a nearly uniform exposure every two orbits (as is shown in figure 26). Some of the highlights of the science performed in the first year of operations will be discussed in the following chapter.

38

2.5 first light

Figure 25: First light Fermi sky map. This is a photon-density map generated from 94 hours of mission elapsed time (which corresponds to an actual data taking time of roughly 74 hours). The Galactic plane is clearly visible as well as the strongest point sources such as the Vela, Crab and Geminga pulsars. The statistics are comparable with those of the first EGRET one year sky survey.

Figure 26: LAT source sensitivity for exposures on various timescales. In standard sky-survey mode, the LAT covers a nearly uniform exposure every two orbits, with every region viewed for ∼ 20 minutes every 3 hours [98].

39

3 T H E F I R S T Y E A R O F S C I E N C E W I T H T H E F E R M I L AT

High energy gamma-ray radiation serves as a probe into nature’s most violent astrophysical environments; for example particle acceleration in the vicinity of black holes, neutron stars, and supernovae remnants and possible signatures of dark matter decay or annihilation. This is true thanks to the fact that once the gamma-rays are emitted their propagation is largely unaffected by intergalactic magnetic fields, unlike the charged cosmic rays. The primary source of opacity for these unique probes is the conversion off of extragalactic background light (EBL) via γ + γ → e+ + e− production. However, this process can provide useful information regarding the density of the EBL between the high energy gamma-ray source and the observer, which is related to the rate of star formation over time. Prior to the launch of the Fermi mission, the high energy gamma-ray sky had been studied with only a few ground breaking missions that started in the mid 1960’s. Missions such as the SAS-2, COS-B and EGRET made remarkable observations ranging from the resolution of the Vela and Crab pulsar leading to the the first gamma-ray catalog of point sources to a complete survey of the high energy gamma ray sky. Yet, out of the 271 sources observed by EGRET [6], 60% were left unidentified (with no visible counterpart at other wavelengths). The Fermi mission was conceived to address important outstanding questions in high-energy astrophysics, many of which were raised but not answered by the first pioneering satellite missions. Some of the science objectives include to determine the nature of the unidentified EGRET sources, understand the mechanisms of particle acceleration occurring in astrophysical sources (i.e. pulsars, SNR), study the high energy behavior of Gamma Ray Bursts (GRBs) and transients, and resolve the galactic and extragalactic diffuse emission. Launched on June 11th 2008, the Fermi observatory has lived up to its expectations. The discoveries made in just the first year of operations have helped answer many of the open questions in high energy astrophysics, and is the main topic of this chapter. 3.1

active galactic nuclei (agn) and blazars

Blazars are a type of Active Galactic Nuclei (AGN) in which the emission is dominated by non-thermal radiation generated in a relativistic jet flowing out from the region near a central black hole. The angle between the line of sight and the axis of the jet is thought to be typically a few degrees or less resulting in detectable high energy emission. This idea was reinforced by the detection of short term variability of gamma-ray emission

41

the first year of science with the fermi lat

Figure 27: Photon spectral index distributions for the bright Fermi LAT blazars. Top panel: all sources in the LAT Bright AGN Sample (LBAS), middle panel: Flat Spectrum Radio Quasars (FSRQs), and bottom panel: BL Lacertae (BL Lac). The distributions are rather distinct with very little overlap between the FSRQs and the BL Lacs [10].

from the blazar 3C279 by EGRET on a scale of days [7]. The rapid variability required a compact emitting region, and such a region should be opaque to gamma-rays due to the high energy gamma-ray interacting with the lower energy photons producing an electron plus positron pair. However, if most of the photons are moving in the same direction, as in the case of a jet then such a region would no longer be opaque [8]. Multiwavelength campaigns gave the ultimate confirmation when observing correlated variability of gamma-ray flares with flares seen at other wavelengths, the first example being that of PKS 1406 − 076 where an optical flare was seen nearly simultaneous with a gamma one [9]. These detections provide valuable information regarding how such jets are formed, how they are collimated, and how they carry energy. Most blazars are observationally classified as Flat Spectrum Radio Quasars (FSRQs) or BL Lacertae (BL Lac) objects. The later of the two are in turn often classified as low energy peaked BL Lac objects (LBLs) and high energy peaked BL Lac objects (HBLs). Typically the term blazar includes AGN that are radio loud, with a flat radio spectrum, and exhibit polarization in the optical and/or radio as well as significant variability. After the first three months of sky survey operation, the LAT revealed 132 bright sources at | b |> 10◦ with significance greater than 10σ, this sample is known as the LAT

42

3.1 active galactic nuclei (agn) and blazars

Figure 28: νFν distribution of the summed LAT observations of 3C454.3 for the time period between August 3 - September 2 2008. The model, fitted over the 200 MeV to 300 GeV range, is a broken power law with photon indexes Γlow = 2.27 ± 0.03, Γhigh = 3.5 ± 0.3 and a break in energy Ebr = 2.4 ± 0.3 GeV with an apparent isotropic energy greater than 100 MeV of 4.6 × 1048 erg cm−2 s−1 . The error bars are statistical only [11].

Bright AGN Sample (LBAS) [10]. High confidence associations with known AGNs have been made for 106 of these sources. In particular this sample contains two radio galaxies (Centaurus A and NGC 1275), 104 blazars consisting of 58 FSRQs, 42 BL Lac objects, and 4 blazars with unknown classification. Only 33 of these sources were previously detected with EGRET. The analysis of the gamma-ray properties of the sources in the LBAS show that the average GeV spectra OH BL Lac objects are significantly harder than the spectra of FSRQs. The corresponding distributions of the spectral index of the BL Lacs and FSRQs is shown in figure 27. These distributions reveal a distinct separation between the two types of sources with almost no overlap. This is the first time that a distinction between the two populations appears so clearly. While a simple power law provides a good description of the SED for many blazar sources over the energy range covered by the LAT, there have also been detections where this was no longer the case. The blazar 3C454.3 observed by the LAT between the 7th of July and the 6th of October 2008, indicated a strong and highly variable gamma-ray emission. The spectrum (shown in figure 28)of this source was not consistent with a simple power law, but instead shows a spectral break at E ∼ 2 GeV and is well described by a broken power law with photon indexes of ∼ 2.3 for low energies and ∼ 3.5 for

43

the first year of science with the fermi lat

high energies. This is the first direct observation of a break in the spectrum of a high luminosity blazar above 100 MeV. 3.2

gamma ray bursts

Gamma Ray Bursts (GRBs) were first reported in 1973 based on the observations performed in 1969-71 by the Vela U.S military satellites that were monitoring for nuclear explosions possibly performed on behalf of the Russian military. These satellites observed transient flashes of radiation in the gamma-ray energy range that did not come from the Earth’s direction. Gamma Ray bursts are one of the brightest sources of gamma ray photons in the observable universe. Bursts can last from milliseconds to nearly an hour, although a typical burst lasts a few seconds. These burst cause external shocks due to the interaction between the ejecta and the circumstellar environment which give rise to afterglows in the X-ray and lower energy bands that are detected for hours up to months following the initial blast. The Burst and Transient Experiment (BATSE) onboard the Compton Gamma Ray Observatory (CGRO) measured about 3000 bursts and found that they are distributed isotropically in the sky, leading to the conclusion that these objects are of extragalactic origin [6]. However there is still much debate regarding the physical details, namely the primary energy source, emission mechanisms and energy transport of the GRBs. Fermi LAT GRBs Burst GRB 080825C GRB 080916C GRB 081024B GRB 081215A GRB090217 GRB 090323 GRB 090328 GRB 090510 GRB 090626 GRB 090902B

Characteristic long duration; weak long duration; intense; very extended emission;z = 4.36 short duration; weak; temporally extended emission long duration; 86◦ to the LAT boresight long duration;featureless light curve long duration; temporally extended emission; ARR; z = 3.6 short duration; temporally extended emission; ARR; z = 0.74 short duration; intense temporally extended emission; ARR; z = 0.903 long duration;temporally extended emission long duration;intense; ARR; temporally extended emission; z = 1.82

Table 2: Fermi LAT detected gamma-ray bursts in the time period between August 2008 and September 2009. Each of these bursts was also detected by the Fermi GBM. Half of these burst have an associated redshift and four of these bursts caused an autonomous re-point request (ARR) to be initiated. In the first year of data taking, the Fermi LAT together with the GBM have observed 10 GRB’s of various topologies (listed in table 2). While the GBM has observed more than 250. Two particularly interesting GRB light curves are illustrated in figures 29 and 30 corresponding to GRB 080916C and GRB 090902B respectively. The observations of the long-duration GRB 080916C detected photons from 8keV to ≈ 13.2GeV with

44

3.2 gamma ray bursts

Figure 29: Light curves for GRB 080916C observed by the GBM and the LAT, from lowest to highest energies. The inset panels give a view of the first 15s from the trigger time. In all cases, the bin width is 0.5s; the per-second counting rate is reported on the right for convenience [27].

a redshift from GROND of z = 4.24. The fluence for this GRB is ≈ 2.4 × 10−4 ergs cm−2 leading to the largest reported apparent isotropic gamma-ray energy release, ε iso ∼ = 8.3 × 1054 ergs. From simple γγ absorption arguments, the redshift and Fermi data provide the most stringent lower limits to date on the GRB outflow Lorentz factor, Γmin ∼ = 870 [27]. GRB 090902B was one of the brightest burst detected by both the instruments onboard the Fermi satellite measuring a 33.4 GeV photon, the highest energy yet detected from a GRB. This photon arrived 82 seconds after the GBM triggered and ∼ 50 seconds after the prompt phase emission had ended in the GBM band. The redshift associated to

45

the first year of science with the fermi lat

Figure 30: GBM and LAT light curves for the gamma-ray emission of GRB 090902B. The data from the GBM NaI detectors were divided into soft (8 − 14.3keV) and hard (14.3 − 260 keV) bands in order to reveal any obvious similarities between the light curve at the lowest energies and that of the LAT data. The vertical lines indicate the boundaries of the intervals used for the time-resolved spectral analysis. [28].

this GRB is z = 1.822 from this measurement it has been possible to place significant constraints on some models of the Extragalactic Background Light [28]. 3.3

pulsars

The first astronomical sources detected at gamma ray energies were pulsars. These rotating, magnetized neutron stars remain some of the best laboratories for studying

46

3.3 pulsars

extreme physical conditions of gravitational and magnetic fields as well as efficient acceleration of particles to very high energies. Pulsar studies are now done across the entire electromagnetic spectrum. Every band contributes to the understanding of these fascinating objects, but the gamma ray band is uniquely important for the discovery of the basic workings of the pulsar phenomena. Prior to Fermi’s launch only seven

Figure 31: Pulsar sky map in Galactic coordinates. Gamma-ray selected pulsars are represented by the blue squares, millisecond gamma-ray pulsars by the red triangles, while all other radio loud gamma-ray pulsars are shown by the green circles. The black dots are pulsars for which gamma-ray pulsation searches were conducted using rotational ephemerides and the gray dots are the known pulsars which were not searched via pulsations [32].

gamma-ray pulsars were known, five of which were discovered by EGRET [6]. After the first six months of data taking, the Fermi LAT has observed 46 high confidence gamma-ray pulsars (the distribution of these pulsars in galactic coordinates is shown in figure 31). These include the six EGRET pulsars, 24 previously known radio pulsars whose pulsed gamma-ray emission was discovered with the aid of the radio timing ephemerides. Eight of these radio pulsars were found to be millisecond pulsars. Sixteen previously unknown pulsars were discovered by searching for pulsed signals at the positions of bright gamma-ray sources seen with the LAT, or at positions of objects suspected to be neutron stars based on observations at other wavelengths [32]. The limiting flux for pulse detecting is non-uniform over the sky due to the different background levels, especially near the Galactic plane. The pulsed energy spectra can be described by a power law with an exponential cutoff, with cutoff energies ranging from ∼ 1 GeV to 5 GeV. The pulse shapes show substantial diversity, but roughly 75% of the gamma-ray pulse profiles have two peaks, separated by ≥ 0.2 of rotational phase. For most of the pulsars, the gamma-ray emission appears to come mainly from the outer

47

the first year of science with the fermi lat

Figure 32: The Fermi LAT gamma-ray source, the central PWN X-ray source, and the corresponding EGRET source superimposed on a 1420 MHz map of CTA 1. The small red circle represents the 95% error region for the LAT source, the large blue circle is the corresponding EGRET source 3EGJ0010 + 7309, and the central PWN source RX J00070 + 7302 is represented by the cross [34].

magnetosphere, thus favoring the outer gap model. However, the polar cap emission remains plausible for a remaining few [32]. Spatial associations imply that many of these pulsars power pulsar wind nebulae. Thanks to the large amount of gamma-ray pulsars discovered in the first year, it is possible to observe that the gamma-ray-selected young pulsars are born at a rate comparable to that of their radio-selected cousins and that the birthrate of all young gamma-ray-detected pulsars is a substantial fraction of the expected Galactic supernova rate. One of the first Fermi LAT discoveries was that of the radio quiet pulsar located near the center of the compact synchrotron nebula inside the supernova remnant CTA 1 (shown in figure 32). This gamma-ray pulsar coincides with the previously known gamma-ray source 3EGJ0010 + 7309 and therefore identifying the neutron star powering the PWN and the gamma-ray source. It has a period if 316.86 ms, a period derivative of 3.614 × 10−13 s s−1 with a characteristic age of 104 years (which is comparable to

48

3.3 pulsars

that estimated for the SNR) [34]. This detection lead to the indication that many of the yet-unidentified low latitude Galactic gamma-ray sources could also be pulsars.

Figure 33: The evolution of the Vela gamma-ray pulse profile over three decades of energy. Each pulse profile is binned to 0.01 of pulsar phase, and dashed lines show the phases of the two main peaks, P1 and P2, determined from the broad band light curve. A third peak is also seen, labeled P3 and it shows a shift in phase with energy. In the bottom left panel the 8 − 16 keV pulse profile of Harding et al. (2002) is shown, along with the radio pulse profile (in red). While in the bottom right panel, the 4.1 − 6.5 eV HST/STIS NUV pulse profile of Romani et al. (2005) is shown for comparison. [33].

The Vela pulsar is the brightest and most persistent source in the GeV sky and was one of the first objects to be observed by the Fermi LAT. It is a young (characteristic age, τc = P/2 P˙ = 11 kyr) neutron star embedded in a flat spectrum radio synchrotron nebula and is surrounded by a bright X-ray wind nebula. After only ∼ 75 days of observations the Fermi LAT measured some 32, 400 pulsed photons at E ≥ 0.03 GeV revealing new features including pulse structure as fine as 0.3 ms and a distinct third peak which shifts in phase with energy (as can be seen in figure 33). The spectra of 0.05 the Vela pulsar suggest averaged power law index of Γ = 1.51+ −0.04 with an exponential cut-off at Ec = 2.9 ± 0.1 GeV, illustrated in figure 34 [33].

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the first year of science with the fermi lat

Figure 34: The pulsed-averaged Vela spectral energy distribution (E2 dNγ /dE. Both statistical (capped) and systematic (uncapped) errors are shown as measured by the Fermi LAT (blue circles). EGRET data points (green diamonds, Kanbach et al. 1994) are shown for comparison. The curve is the best-fit power law with a simple exponential cut-off. [33].

3.4

galactic diffuse gamma-ray emission

Diffuse Galactic gamma-ray emission (DGE) is produced by interactions of cosmic rays (CRs), mainly protons and electrons, with the interstellar gas (via π0 production and Bremsstrahlung) and radiation field (via inverse Compton scattering). It is direct probe of CR fluxes from a distant location, and may contain signatures of physics beyond the Standard Model, such as dark matter annihilation or decay. EGRET on the Compton Gamma-Ray Observatory (CGRO) reported an excess diffuse emission for E> 1 GeV [35] relative to that expected from the DGE models consistent with the directly measured CR nucleon and electron spectra [36]. This measurement led to the proposal that the emission was the long-awaited signature of dark matter annihilation [37]. However, more conventional interpretations included variations of CR spectra in the Galaxy, contributions by unresolved point sources [38], and instrumental effects [39]. The Fermi LAT is an over an order of magnitude more sensitive than its predecessor, EGRET, with a more stable response due to the lack of consumables. Thanks to these improvements the LAT data permit more detailed studies of the DGE than have been possible ever before. The Fermi LAT has measured the diffuse gamma-ray emission for energies 100 MeV to 10 GeV and Galactic latitudes 10◦ ≤| b |≤ 20◦ , as can be seen in figure 35, and found that this region of the sky is well reproduced by the diffuse Galactic gamma-ray emission model that is consistent with the local CR spectra and inconsistent

50

3.5 extragalactic diffuse gamma-ray emission

Figure 35: Left panel: Diffuse emission intensity averaged over all Galactic longitudes for latitude range 10◦ ≤| b |≤ 20◦ . The red points correspond to LAT measurements, blue crosses to EGRET. Blue and red bands are the systematic uncertainties for EGRET and LAT, respectively. Right panel: LAT data with model, source, and UIB components for the same sky region as in the figure in the left panel. Model (lines): π0 -decay, red; Bremsstrahlung, magenta; IC, green. Shaded/hatched; total (model + UIB + source), black/hatched [40].

with the EGRET GeV excess. The LAT measured spectrum is significantly softer than the EGRET measurement with an integrated intensity JLAT (≥ GeV ) = 2.35 ± 0.01 × 10−6 cm−2 s−1 sr −1 compared to the EGRET integrated intensity JEGRET (≥ 1GeV ) = 3.16 ± 0.05 × 10−6 cm−2 s−1 sr −1 where the errors are statistical only [40]. The LAT spectrum is consistent with a model for diffuse emission that reproduces the local cosmic-ray spectrum and, for this region, does not require an additional component. 3.5

extragalactic diffuse gamma-ray emission

An apparently isotropic, presumably extragalactic, component of the diffuse gammaray flux was discovered by the SAS-2 [4] satellite and later confirmed by EGRET in the energy range 30 MeV - 10 GeV [22]. The extragalactic diffuse emission (EGB) is generally considered to be the sum of contributions from unresolved point sources and truly diffuse emission processes. Such processes include possible signatures of large scale structure formation, emission produced by the interaction of ultra-high-energy cosmic-rays with relic photons, as well as annihilation of cosmological dark matter. The Galactic inverse Compton (IC) emission (discussed in [25] and references therein) could also be attributed to the EGB if, for example, in the case of an extremely large electron halo, it appears quasi-isotropic.

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the first year of science with the fermi lat

Figure 36: Spectral energy distribution of the extragalactic diffuse emission between 1 keV and 100 GeV measured by various experiments including the Fermi LAT (filled black circles) [30]. The spectrum measured by Fermi is considerable softer than the one found by EGRET.

The EGB measured by EGRET is well described by a power law with index γ = 2.1 ± 0.3 over EGRET energies and is consistent with the average index for blazars that EGRET detected. This observation supports the hypothesis that the isotropic flux comes from unresolved AGN sources [22]. The LAT is over an order of magnitude more sensitive to point sources than EGRET, combined with the LAT’s sky-survey observational strategy it is possible to identify and subtract the contributions from the diffuse galactic emission, the background from misclassified CRs and from the unresolved sources. The extraction of these three components is the biggest challenge in the measurement of the EGB. Within the first year of operation, the Fermi LAT was able to measure the intensity of the EGB between 200 MeV and 100 GeV and found that the spectrum for the isotropic component is well reproduced by a power law with a spectral index of γ = 2.41 ± 0.05 and a total integral flux of F100 = (1.03 ± 0.17) · 10−5 cm−2 s−1 . This spectral index is considerably softer than the one reported by EGRET and it also does not show any spectral features at a few GeV (which was indicated by a re-analysis of the EGRET data in 2004). The spectral energy distribution of the EGB between 1 keV and 100 GeV is shown in figure 36, the LAT measurement is represented by the solid black circles. The difference in integral flux between the EGRET measurement and that of the LAT can be attributed to the fact that the LAT has resolved part of the EGRET EGB into point sources. In fact the obtained value of integral flux from the LAT corresponds to 71% of the EGRET EGB, which extrapolating the LAT logN-logS distribution in [26] to F100 = 1 · 10−9 cm−2 s−1 yields that resolved points sources in the LAT account for 8.5 31.4+ −7.4 % of the EGRET EGB [30].

52

3.6 cosmic rays

Figure 37: The Fermi LAT cosmic ray electron plus positron spectrum from 20 GeV to 1 TeV [100]. The gray band represents the systematic errors. The two headed arrow in the top right corner gives the size and direction of the rigid shift of the spectrum implied by the present uncertainty on the LAT absolute energy scale. The measurements made by several other experiments together with the conventional diffusive model are also shown.

3.6

cosmic rays

The exciting scientific results from only the first year of operations of the Fermi observatory serve as evidence of its extraordinary capabilities as a gamma-ray detector. However, the LAT has also the potential of being a cosmic-ray detector as well. This ability was recognized from the very first stages of the LAT design [41]. The main concept relies on the fact that electromagnetic cascades are akin to both electron/positron and photon interactions in matter and thus the detection of cosmic-ray electrons and positrons1 is possible with the LAT. After only 6 months of data taking, the Fermi LAT collected enough statistics (more than 4 million) to be able to measure the first systematics-limited cosmic-ray electron spectrum from 20 GeV to 1 TeV [100] shown in figure 37. The Fermi LAT as well as the HESS electron spectrum do not confirm the presence of the prominent feature detected by the ATIC experiment around 500 GeV. The spectrum measured by Fermi is much harder than the predictions from the conventional model and can be explained by assuming a harder spectrum at the source. 1 Referred to as electrons throughout this work due to the fact that the Fermi LAT does not distinguish the charge sign.

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the first year of science with the fermi lat

The significant flattening of the LAT data for energies greater than 70 GeV could also indicate the presence of one or more local sources of high energy cosmic ray electrons. The main proposed sources for the electrons are presented in chapter 5.3. Given the energy range in which the Fermi LAT operates, it is possible to extend the measurement of the cosmic-ray electron spectrum down to ∼ 100 MeV. However, the population of electrons over this wide range of energy is composed of galactic and albedo electrons. The albedo electrons are those resulting from the interaction of the galactic cosmic rays with the Earth’s atmosphere. Given the Fermi orbit it is possible to extend the measurement of the galactic cosmic ray electron spectrum down to ∼ 7 GeV, the details of this analysis are presented in chapter 6.6. While a study of the albedo population including the work to update the electron component of the on-orbit environment Monte Carlo simulation used by the Fermi Collaboration can be found in chapter 6.7. There is also on-going work to measure the cosmic-ray protons which however will not be discussed in this work.

54

4 GEOMAGNETIC AND SOLAR ENVIRONMENT

4.1

the earth’s magnetosphere

The Earths’ magnetosphere is the region of space containing magnetic fields of terrestrial origin. The Earth’s magnetic field (about 6 × 10−5 Tesla at the surface near the poles [70]) is induced and constantly maintained by the convection of liquid iron in the outer core. It is strongly influenced by the solar wind, a plasma of electrons and ions moving radially outward from the sun that impinge on the Earth’s field at velocities of 300 - 500 km s−1 . This moving plasma compresses the field on the sunward side, flows around the magnetic barrier, and distends the field lines into a tail extending several million kilometers down-wind from the Earth. The magnetosphere depicted in

Figure 38: An idealized illustration of the Earth’s magnetic configuration and plasma regions. Figure taken from [70]. figure 38 is not in a steady state but depends on the solar activity. In fact the overall size of the magnetosphere varies with solar velocity and density. The radiation belts are located well inside the magnetosphere and are regions where energetic ions and

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geomagnetic and solar environment

electrons experience magnetic trapping. The details of these belts will be described in more detail in section 4.2 of this chapter. In order to better understand the geomagnetic environment it is important to first discuss the Earth’s magnetic field as is done in the following subsection. 4.1.1

The dipole field

The general form to represent the geomagnetic core field is given by [70]: ∞

ψ=

n

1 m P (cos θ )(Cnm sin mφ + Dnm cos mφ) n +1 n r n =1 m =0

∑ ∑

Where the Legendre functions have the Schmidt normalization:   (n − m)!(2 − δ0,m ) 1/2 m Pn,m Pn = (n + m)!

(4.1)

(4.2)

Where Pn,m are the normal Legendre functions and δ0,m is unity for m = 0 and zero otherwise. The variable r is the distance measured from the center of the dipole and θ is the polar angle or co-latitude and φ is the longitude. Although in geomagnetism it is customary to write (4.1) as [70]  ∞  R E n +1 n ψ = RE ∑ (4.3) ∑ ( gnm cos mφ + hmn sin mφ) Pnm (cos θ ) r m =0 n =1 where the constant factor R E is included to give gnm and hm n the dimensions of a magnetic −( n + 1 ) field. Because of the r dependence of ψ the importance of the higher order terms decreases rapidly with the distance from the Earth. Thus, much of the trapped radiation theory is developed based on the dominant n = 1 or dipole term. Due to the fact that many important features of the Earth’s radiation belts can be described with a dipole field, in the following pages some useful relations for the dipole field will be derived . The dipole potential can be obtained from (4.3) by taking n = 1, m = 0 and is expressed as:  2 RE ψ = RE g10 cos θ (4.4) r Where r is the distance measured from the center of the dipole and θ is the polar angle or co-latitude. In spherical polar coordinates the components of B are [70]:  3  3 RE RE ∂ψ 0 =2 g1 cos θ = −2B0 cos θ (4.5) Br = − ∂r r r  3  3 1 ∂ψ RE RE 0 Bθ = − = g1 sin θ = − B0 sin θ (4.6) r ∂θ r r Where B0 is the mean value of the field on the equator at the Earth’s surface (B0 = 3.12x10−5 T). The dipole field is symmetric about its axis so that Bφ = 0 everywhere. The intensity of the dipole field at any point in space is:  3 q q RE 2 2 B = Br + Bθ = B0 (1 + 3 cos2 θ ) (4.7) r

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4.1 the earth’s magnetosphere

Figure 39: The Earth’s magnetic field can be approximated as dipole magnet tilted about 11.5 degrees from its rotational axis. Therefore magnetic north differs from geographic north.

As can be seen by (4.7) the field intensity falls as r −3 with the distance above the Earth and so at constant r the intensity increases as one moves towards the poles. In fact for a given value of r the field strength is twice as high over the poles as it is over the equator. Although it is important to remember that the Earth’s field is not a pure dipole located at the center of the Earth and so the contours of constant B on the Earth’s surface are not lines of constant latitude. There are distortions introduced by the fact that the magnetic axis is not aligned with the spin axis of the Earth and the center of the magnetic dipole is not at the center of the Earth (as illustrated in figure 39). 4.1.2 Geomagnetic coordinate system - the L-shell parameter Due to the fact the geomagnetic field is irregular any attempt to tabulate the trapped radiation fluxes as a function of position becomes a very difficult task. Such a tabulation increases in difficulty when trying to use geographical coordinates because they would require a three dimensional grid to completely describe the flux values in space. Furthermore, a spacial coordinate system based on geographical coordinates does not lead to insight into the relationships of fluxes at different locations not to mention the loss of the simplicity that the dipole formulas provide. What is needed is a coordinate system based on trapped particle motion which will have identical values for the coordinates of magnetically equivalent positions. In the case of a charged particle in magnetic field, the canonical momentum P is P = mv + qA = p + qA

(4.8)

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geomagnetic and solar environment

Figure 40: Illustration of the trajectories of trapped electrons and protons. The magnetic mirroring, gradient and curvature drifts in the geomagnetic field are also shown.

where A is the vector potential of the magnetic field. Three periodicities are readily apparent when considering the motion of charged particles in the geomagnetic field. Namely, the rapid gyration about the field lines, the north-south oscillation between magnetic mirroring points and the slow longitudinal drift about the Earth, as shown in figure 40. By calculating the action integral associated with each of these periodicities it is possible to obtain the three adiabatic invariants of the motion of these charged particles. These adiabatic invariants naturally lead to the needed geomagnetic coordinate system briefly discussed above. The first adiabatic invariant [70] J1 =

p2⊥ 2m0 B

(4.9)

is also known as the scalar value of the magnetic field. All particles mirroring at a given B will mirror at the same value of B throughout their longitudinal drift [70], thus making J1 a useful coordinate. The related function I of the second adiabatic invariant [70] s  Z s0 m B(s) I= 1− ds (4.10) Bm sm could be used as the second coordinate, since two positions in space with the same B and I values are magnetically equivalent from the standpoint of a trapped particle. Particles mirroring at a given value of B, I will drift around the Earth, mirroring at identical values of B and I in both hemispheres. There are unfortunately some drawbacks to these coordinates; it is not immediately apparent from the values of B and I at several positions whether they lie near the same magnetic drift shell, the quantity I does not vary linearly with any familiar variable and last but certainly not least it is not an easy coordinate to interpret. To bypass these difficulties McIlwain [71] devised a new coordinate system based on the simplicity of the dipole formulas. He recognized the convenience in a dipole field of the parameter, R0 , the distance from the dipole center

58

4.1 the earth’s magnetosphere

to the equatorial crossing of minimum B value of the field line. R0 in fact defines a field line as well as a drift shell therefore during its bounce and drift motion the particle remains on field lines having the same R0 . Furthermore, if the B and I values of a location are known, the equatorial crossing point of the field line passing through that point can be determined thus leading to the following relation R0 = f ( ID , BD , M D )

(4.11)

where f denotes a function of the dipole magnetic field value BD , the integral invariant function ID and the magnetic moment of the central dipole MD . From 4.11 it is possible to define a new variable, L, in terms of B and I calculated from the true, distorted geomagnetic field but at the same time using the same functional relationship relating the equatorial crossing distance to B and I for a dipole field. Thus, LR E = f ( I, B, ME )

(4.12)

where ME is the value of the dipole term for the Earth’s field. Similarly to R0 , LR E is roughly equal to the distance from the center of the Earth’s tilted, off-center, equivalent dipole to the equatorial crossing of the field line. Therefore the variable L can be used as the second spatial coordinate where together with B defines the coordinate system needed to describe the motion of the trapped particles. In fact positions around the world having the same B and L will, by definition, have the same L values. The final step in establishing this new and convenient coordinate system is to redefine the familiar polar coordinates (r, λ) in terms of the B and L values: r = L cos2 λ   B0 3r 1/2 B = 4− r3 L

(4.13) (4.14)

with r given in units of Earth radii. 4.1.3

Cutoff rigidity

Geomagnetic cutoff rigidities are a quantitative measure of the shielding provided by the earth’s magnetic field. Charged particles transversing the magnetosphere experience a vector force that results in a curved path. The general expression for this motion, expressed in three dimensional r, θ, φ coordinates, results in three differential equations with six unknowns: dvr dt dvθ dt dvφ dt

= = =

v2φ v2θ e (vθ Bφ − vφ Bθ ) + + mc r r v2φ e vr v θ (vφ Br − vr Bφ ) − + mc r rtanθ vr v φ vθ vφ e (vr Bθ − vθ Br ) − − mc r rtanθ

(4.15) (4.16) (4.17)

where m is the mass of the particle, B is the magnetic field and c is the speed of light. With these equations is it possible to calculate the cutoff rigidities for any position in

59

geomagnetic and solar environment

the magnetosphere. This is most often done for specific applications such as cosmic ray latitude surveys. On the other hand, for space applications it is only necessary to have a set of reference cutoff rigidities for specific orbits. Nonetheless, due to the fact that the fundamental problem has no solution in closed form, millions of special case solutions are required to obtain a world-wide set of geomagnetic cutoff rigidities. To bypass this issue it is common to use the vertical cutoff rigidity and approximations are used to extrapolate to other directions or nearby locations. Stormer found that a special case solution exists in dipolar field geometry which describes the geomagnetic cutoff rigidity: Rc = [ Mcos4 λ]/r2 [1 + (1 − sine sinξ cos3 λ)1/2 ]2 (4.18) Where Rc is the geomagnetic cutoff rigidity (in MV), M is the magnitude of the dipole moment in G cm3 , λ is the latitude from the magnetic equator, e is the angle from the zenith direction (where the zenith direction is a radial from the position of the dipole center), ξ 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 [88]. When calculating the vertical geomagnetic cutoff rigidity the denominator of equation 4.18 simplifies to a value of 4 and it reduces to: RCV =

M · cos4 λ/r2 4

(4.19)

The value for the dipole moment, M can be obtained by multiplying the g10 term (in units of G) of the International Geomagnetic Reference Field (IGRF) by the cube of the average radius of the earth (in cm). In fact for the IGRF 2000 magnetic field model, the magnitude of the dipole moment has a value of ∼ 58 thus allowing to simplify even further equation 4.20 to RCV = 14.5 cos4 λ/r2 (4.20) Recalling from section 4.1.2 the variable McIlwain L coordinate can be expressed in terms of the geomagnetic latitude, λ L=

cos2 λ r

(4.21)

therefore it is possible to express the vertical geomagnetic cutoff in terms of the McIlwain L coordinate [88] RCV = 14.5/L2 (4.22) The constant value of 14.5 in the above equations has been normalized for the IGRF 2000 magnetic field [87]. It is, however, important to note that due to the non-dipole terms in the geomagnetic field, the value of this constant can range from ∼ 14 to ∼ 16 depending upon the geographical position. Figures 41 and 42 illustrate the vertical rigidity and geomagnetic latitude maps for the Fermi orbit. 4.2

magnetically trapped radiation

Charged particles moving in the Earth’s magnetic field will travel in spiral paths around the geomagnetic field lines. Their trajectories are helical and are due to the fact that

60

4.2 magnetically trapped radiation

Figure 41: Map of the vertical geomagnetic cutoff for the Fermi orbit, namely altitude of 565 km and inclination of 25.6◦ . The map is obtained using the 10th generation IGRF code [87].

61

geomagnetic and solar environment

Figure 42: Map of the invariant lambda for the Fermi orbit, namely altitude of 565 km and inclination of 25.6◦ . The map is obtained using the 10th generation IGRF code. The dark blue line corresponding to λ = 0 represents the geomagnetic equator.

62

4.2 magnetically trapped radiation

Figure 43: Illustration of the concept of a pitch angle,α. From the figure it is possible to see that due to conservation of magnetic moment the pitch angle increases as the particle moves down the magnetic field line towards a more intense field(figure taken from [70]).

their motion is both parallel and perpendicular to the magnetic field. Thus exerting a force on the perpendicular component of their velocity that causes them to move around the field lines as well as along them. Now as these charged particles move in the geomagnetic field some become trapped and others are absorbed in the Earth’s atmosphere, at this point an obvious question arises: What factor determines whether a charged particle will become trapped or lost? To answer this question one needs to consider the angle between the direction of the magnetic field and a particle’s spiral trajectory, known as the pitch angle tan α =

v⊥ vk

(4.23)

As particles spiraling around the field lines move closer to the Earth, the strength of the magnetic field increases, which causes the parallel component of the particle’s velocity to decrease (with a corresponding increase in the perpendicular velocity component). As the parallel component goes to zero, the pitch angle increases to 90◦ (see figure 43). If this occurs at an altitude where the atmosphere is sufficiently thin (∼ 100 km) that the probability that the particle interacts with an atmospheric neutral or ion is low, they reverse direction and travel back up the field lines. The point in which the pitch angle goes to 90◦ is known as the mirror point. The particles that are reflected back and forth along geomagnetic field lines between mirror points are considered to be magnetically trapped. If, on the other hand the mirror point happens to be at an altitude where the atmosphere is dense enough for the charged particle to collide with an atmospheric particle, the particle will soon be absorbed by the atmosphere instead of being continuously reflected by the magnetic mirror force. Particles lost in this way must have pitch angles (in the equatorial plane, where the field is weakest) that fall

63

geomagnetic and solar environment

within a solid angle known as the atmospheric loss cone. The size of the loss cone varies with the radial distance of the field line from the Earth: the greater the distance, the smaller the angle of the loss cone. If a charged particle has a pitch angle greater than the loss cone angle but moves along a field line with a mirror point at low altitudes, it will continue to bounce between mirror points until an interaction with a plasma wave reduces the pitch angle to a value within the loss cone. The magnetically trapped particles make up the Earth’s radiation belt, also known as the Van Allen radiation belt, whose existence was confirmed by the Explorer 1 and Explorer 3 missions in early 1958 by Dr James Van Allen [72] and his research group at the University of Iowa. The trapped radiation associated with these belts was first mapped by the Sputnik 3, Explorer 4 Pioneer 3 and Luna 1 missions. The belt is essentially a torus of energetic charged particles around the Earth held in place by the Earth’s magnetic field. It is split into two distinct belts: an inner belt that resides from an altitude of 0.1 − 1.5R⊕ and an outer belt that extends from an altitude of about 3R⊕ to roughly 10R⊕ [84]. The inner belt consists of mostly energetic protons with energies exceeding 100 MeV and electrons in the range of hundreds of keV. The higher end of the proton population is generally thought to be a product of the decay of albedo neutrons which are themselves a result of cosmic ray collisions in the upper atmosphere. The outer belt consists mostly of electrons in the energy range 0.1 − 10 MeV. These particles are injected from the geomagnetic tail following geomagnetic storms.

4.2.1

Radiation belt electrons

The trapped electrons have energies extending up to several MeV (somewhat lower than those for the proton population that extend up E ≥ 50 MeV). As for the protons, the maximum flux of the trapped electrons occurs on the equatorial plane. As can be seen from the integral, omnidirectional flux plots shown in figures 44, 45, 46 the slot region is much more pronounced (compared to the proton fluxes) especially for higher energies. There is also a rapid decrease in flux with increasing energy. Electron fluxes are also susceptible to time variations, particularly in the outer radiation belt region. These time variations are dominated by magnetic activity. Major magnetic storms have been observed to produce changes throughout the trapping region. Some of these changes can cause only temporary variations in the trapped population but in some cases can lead to a movement of particles across L shells. Nonetheless the mechanism by which magnetic storms affect the radiation belts are not fully understood. The time behavior of 1MeV electrons at various L values is illustrated in figure 47. Also in this figure (bottom panel) is the correlation between the magnetic index, Dst , which is an index of the magnetic storms and the electron flux. What is immediately evident from this panel is how a change in the outer regions of the magnetic field results in a decrease in Dst leading to an increase in the trapped electron flux.

64

4.2 magnetically trapped radiation

Figure 44: Integral, omnidirectional electron flux greater than 40keV [70].

65

geomagnetic and solar environment

Figure 45: Integral, omnidirectional electron flux greater than 1MeV [70].

66

4.2 magnetically trapped radiation

Figure 46: Integral, omnidirectional electron flux greater than 5MeV [70].

67

geomagnetic and solar environment

Figure 47: Effect of the solar activity on electrons with energies greater than ∼ 1 MeV. In the lower panel the magnetic storm index Dst and the planetary magnetic activity index K p are shown. From this lower panel it is possible to clearly see the correlation between the magnetic activity and the trapped electron flux variations [70].

68

4.2 magnetically trapped radiation

Figure 48: Integral, omnidirectional proton flux greater than 100keV [70].

4.2.2

Radiation belt protons

Protons are found throughout the region of the magnetosphere where the geomagnetic field will sustain trapping. The maximum flux occurs on the equatorial plane at about L = 3.1 and in fact the maximum flux along any L value will be found at the equator. As can be seen in figures 48, 49, 50 the intensity contours become more closely spaced below L = 1.5, where the Earth’s atmosphere becomes dense enough to remove the energetic protons. Another interesting feature that can be observed is that the flux maximum moves closer to the Earth as the energy threshold increases. High energy protons, on the other hand, are those components of the radiation belts that are least affected by the geomagnetic activity. This is largely due to the fact that they reside in the inner radiation belt where the fractional changes in B are smallest. In figure 51 is an example of the impact of a magnetic storm on the integral omnidirectional flux of protons above ∼ 30 MeV. From this figure it can be observed how the greatest impact occurs at larger L values while the flux at L= 1.9 is unaffected. This plot refers to a magnetic storm that occurred on the 23 of September, 1963. 4.2.3

The South Atlantic Anomaly (SAA)

As mentioned in section 4.2 the geomagnetic field hosts what are called the Van Allen radiation belts, which are two separate tori of plasma around the the Earth. This plasma

69

geomagnetic and solar environment

Figure 49: Integral, omnidirectional proton flux greater than 10MeV [70].

Figure 50: Integral, omnidirectional proton flux greater than 50MeV [70].

70

4.3 the cosmic ray albedo

Figure 51: Sudden changes in the high energy proton fluxes caused by a major magnetic storm that occurred on the 23rd of September of 1963. The affect is much stronger for the protons located at the outer L shells [70].

is separated into two distinct belts, with energetic electrons forming the outer belt and a combination of protons and electrons creating the inner belt. The Van Allen radiation belts are symmetric with the Earth’s magnetic axis, which is tilted with respect to the Earth’s rotational axis by an angle of 11 degrees. Additionally, the magnetic axis is offset from the rotational axis by 450 kilometers. Because of the tilt and offset, the inner Van Allen belt is closest to the Earth’s surface over the south Atlantic ocean, and farthest from the Earth’s surface over the north Pacific ocean, as can be seen in figure 53. This region is called the South Atlantic Anomaly (SAA) due to the fact that the radiation intensity is greater within this region than elsewhere. The shape of the SAA changes over time while its size varies with altitude. The shape and particle density of the SAA varies on a diurnal basis, with greatest particle density corresponding roughly to local noon. At an altitude of approximately 500 km, the SAA spans from -50◦ to 0◦ geographic latitude and from -90◦ to +40◦ longitude. Figure 52 shows a map pf the particle intensity collected by South Atlantic Anomaly Detector onboard ROSAT. The highest intensity portion of the SAA drifts to the west at a speed of about 0.3 degrees per year [86]. 4.3

the cosmic ray albedo

Albedo particles are secondary particles produced by cosmic rays interacting with the Earth’s atmosphere. These particles are generally scattered upward but when these

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Figure 52: Map of the particle intensity illustrating the high concentration over the south Atlantic. The data were collected by the South Atlantic Anomaly Detector (SAAD) aboard ROSAT at an altitude of 500 km [85].

Figure 53: Illustration of the Van Allen radiation belts. In the figure it can be seen that the belts are symmetric with the magnetic rotational axis (which is tilted roughly 11◦ with respect to the rotational axis). The magnetic axis is offset from the rotational axis by 450 kilometers and combined effect of the tilt and offset cause the inner radiation belt to be closest to the Earth’s surface over the south Atlantic (figure taken from [84]).

particles lack sufficient energy to leave the Earth’s magnetic field they then re-enter the atmosphere in the opposite hemisphere following a similar magnetic latitude. These particle are called re-entrant albedo particles. There are a number of striking properties associated with the fluxes of these secondary particles: 1. The ratio e+ /e− is of the order of ∼ 4, to be compared with the ratio value of ∼ 0.1 from the primary flux [73].

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Figure 54: Geographical origin of electrons (a) and positrons (b) for the long lived secondary particles. The longitudinal as well as the charge dependence is clearly seen in these maps. [74]

2. The calculated flight time between the estimated origin and absorption points has a broad distribution extending from ∼ 10−2 to 10s. This time is much shorter than the typical confinement time of particles in the radiation belts, however the higher end of this range is also much longer than the Earth’s radius (R⊕ /c ' 0.021s) [73]. 3. The population of albedo particles come in two classes: short (flight time ≤ 0.3s) and long lived (flight time ≥ 0.3s) particles. Long lived particle account for ∼ 70% of the total secondary population [73]. 4. The origin and sink regions for the long lived particles appear to have a strong dependence on longitude as well as the particle’s charge [73]. As can be seen in figure 54 the long lived positively charged particles originate different longitude sub-intervals than due the negatively changed ones. While the absorption regions are inversed depending on the charge sign of the long lived particle. For the short lived particles the positions of the estimated origin and absorption points do not exhibit the interesting patterns seen for the long lived particles. Another striking difference between the short and long lived particle populations is that the e+ /e− ratio for the short lived particles is roughly half that of the long lived ones. In order to fully understand the reason why there is such a large e+ /e− ratio for the

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Figure 55: Geographic origin of electrons (a) and positrons (b) for the so called short lived secondary particles. It can be seen that these particles do not indicate any longitudinal dependence [74].

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4.3 the cosmic ray albedo

Figure 56: The Earth’s equatorial plane with the projections of the trajectories of four particles with rigidities: R A = 30 GV,R a = 5 GV, R B = 80 GV and Rb = −4.5 GV. The diamonds indicate the final (starting) point of the trajectories for the particles A and B (a and b). The dotted line indicates the altitude of the space shuttle orbit [74].

albedo population (both long and short lived) it is necessary to study some examples of trajectories of secondary particles via Monte Carlo simulations. Figure 56 illustrates a map o f the Earth’s geographical equator plane with the calculated trajectories of four charged particles. Particles A and B are both primary protons with momentum of 30 GV and 80 GV respectively. They interact with the atmosphere where the small diamonds are located and each produce a secondary particle, a and b with momentum of 5 GV and −4.5 GV respectively. Particle A arrives at the Earth’s equator plane on an almost horizontal east going trajectory and its secondary particle is also on an east going trajectory, while particle B is on a west going (still horizontal) trajectory and produces a negatively charged west going particle. From figure 56 it is possible to draw several conclusions [74] regarding the e+ /e− ratio • If a particle is east going it can be injected into the albedo flux only if it is positively charged. • Albedo particles are most easily produced with initial zenith angle ∼ 90◦ (approximately horizontally).

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• The rate of the east going primary particles is larger than the rate of west going ones. This last point can be explained when considering that a positively charged primary particle can reach the Earth’s equator from a horizontal west going direction only if it has a gyro radius larger than R⊕ (which corresponds to a rigidity of p/Z ≥ 60 GV), while the rigidity cutoff for an east going particle is much lower (p/Z ≥ 11 GV). Given that the production of electron and positrons in hadronic showers is approximately equal it is clear that the injection of the albedo positrons (mostly produced in the showers of nearly horizontal east going primary particles) is larger than the albedo electrons (mostly produced in the showers of less numerous west going primary particles) thus giving rise to the larger e+ /e− ratio. The longitude distribution of the points of origin for the long lived albedo particles can be seen in figure 54. The reason behind this interesting longitude dependence can be explained by noting that the axis of the geomagnetic field is not only titled with respect to the Earth’s rotational axis but also offset (namely that the center of the magnetic field does not coincide with the Earth’s geographical center). Thus while an albedo particle is oscillating along the field lines between symmetric mirror points it is accompanied by a longitudinal drift motion. The altitude of the guiding center of this motion has a minimum (i.e. where the particle has the highest probability of being absorbed by the atmosphere) at the mirror points that have a constant distance from the center of the magnetic field. Now due to the fact that the geomagnetic field is offset, the distance to its center varies as the particle goes through its longitudinal drift. Keeping in mind that positively charged particles drift westward (towards decreasing longitude) and negatively charged particles drift eastward (towards increasing longitude) it becomes clear why the source and sink positions of the albedo particles have such a longitude dependence. 4.4

the heliosphere

Solar activity not only has a strong impact on the geomagnetic field but also impacts the Galactic Cosmic Ray (GCR) flux entering our solar system. This effect is known as the solar modulation of the GCRs. The Heliosphere can be thought of as a threedimensional volume around the Sun that is filled by the solar wind and its embedded magnetic field. The solar wind is a hot plasma that expands in all directions from the solar corona with speeds ranging from slightly below 300 up to more than 1000 km/s [90] with nominal values of 300 − 500 km/s. It consists of particles, ionized atoms from the solar corona and magnetic fields. When this supersonic wind encounters the interstellar medium it undergoes a transition to subsonic speed, called the termination shock. Once subsonic, the solar wind may be affected by the ambient flow of the interstellar medium. Pressures cause the wind to form a comet-like tail behind the Sun. In the heliosheath region the solar wind is compressed and made turbulent by its interaction with the interstellar medium. Where the heliosphere meets the interstellar medium, is called the heliopause (see figure 57 for an illustration of the heliosphere and termination shock). The disturbances introduced by the interaction of the solar

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4.4 the heliosphere

Figure 57: Illustration of the heliosphere and termination shock. Voyager 1 traveled roughly 94 AU before leaving the heliosphere [47] therefore providing the first measurement of its size.

wind with the interstellar medium are not the only source of turbulence. The solar wind itself is not a quiet flow of gas, in fact continuous fluctuations of the magnetic field are produced by turbulent motions of the gas at the Sun and move outward. There are eruptions in the solar corona, coronal mass ejections (CME) and solar flares that can cause discontinuities in the magnetic field as well as shock waves. As the sun rotates, its magnetic field is also transported by the solar wind and gets warped into a spiral. As the GCRs move through the interstellar medium their intensities are greatly reduced when they propagate through the heliosphere. Furthermore, it has been found that there is a strong anti correlation between the variations in the GCR intensity and the sun spot number, as can be seen in figure 58. This process is highly energy and spatially dependent making it difficult to predict the true GCR intensities when measuring from the Earth. Nonetheless, the effect of this reduction can be neglected for energies greater than several tens of GeV.

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Figure 58: Correlation between the cosmic ray intensity variation and the sun spot number. From this plot it is possible to see the clear anti correlation between the solar activity and the GCR intensity [90].

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5 C O S M I C R AY E L E C T R O N S

Discovered in 1912 by Victor Hess, cosmic rays (CR) are energetic particles originating from outer space. They can be broadly divided into two categories, primary and secondary. The primary component are those particles that originate from extrasolar astrophysical sources, while the secondary cosmic rays are those which arise from the interaction of the primaries with the Interstellar Medium (ISM). The sun also emits low energy cosmic rays associated with solar flares. The overall composition of the primary cosmic rays consists of ∼ 90% protons, ∼ 9% helium nuclei (alpha particles) and about ∼ 1% are electrons [83]. The question of the origin of CRs remains only partially answered, with widely accepted theoretical expectations but incomplete observational confirmation. Theoretical models and indirect observations support the idea that CR are produced in the Galaxy by Supernovae Remnants (SNR), however there are also theories that support pulsars and dark matter scenarios. The main mechanism which is believed to be at the base of the CR production is via shock acceleration, happening when the expanding Supernovae collides with the ISM. In this chapter a brief overview of CR’s, with particular emphasis on the electron1 component, will be discussed. Starting with an examination of the spectrum of CR electrons in comparison with the nucleonic CR’s. In section 5.2 the main energy loss mechanisms for cosmic ray electrons are presented followed by an analysis of the possible origins of the CR electrons in section 5.3. Finally some possible interpretations for the Fermi LAT measurement of the CR electron spectrum will be proposed in section 6.6.3. 5.1

the spectrum of cosmic rays

Over the past ∼ 40 years there have been several experiments designed to measure the electron/positron and proton/antiproton components of cosmic rays between 1 GeV and several tens of TeV. The experimental techniques and detectors used vary from imaging calorimeters, magnetic spectrometers coupled with EM calorimeters, transition radiation detectors (TRD) or Cherenkov detectors. Each of these techniques has its advantages and its disadvantages, for example the imaging calorimeters, such as the Fermi LAT calorimeter together with all the experiments in red in figure 60, cannot distinguish the charge sign of the transversing particle but they typically have large acceptances and energy reach. Magnetic spectrometers (all those experiments 1 Throughout this work the term electrons will be used to refer to the sum of electrons and positrons due to the fact that the Fermi-LAT does not distinguish the charge of the particle.

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in blue in figure 60) on the other hand can distinguish the charge sign and when coupled with a TRD and calorimeter have excellent particle identification abilities. Yet, the acceptance and energy reach are limited by the dimensions and bending power of the magnet. Independently of the detector that one chooses to use, the exposure determines the number of counts collected which is of fundamental importance for the final measurement of the cosmic ray spectra. Equation 5.1 gives the relation between the total number of counts and the exposure factor of the instrument. NE≥E0 =

Z inf dN ( E) E0

dE

E f dE

(5.1)

Where E f is the exposure factor given by the product of the geometric factor and the total observing time, N ( E) is the total number of counts collected with energy E. Figure 59 illustrates the livetime vs geometric factor for the past, present and future ground, balloon and space cosmic ray experiments while figure 60 separates these experiments by the techniques used. What can be gathered from these two plots is that in general the magnetic spectrometers tend to have smaller geometric factors when compared to the imaging calorimeters, and that in order to have long livetimes it is necessary to bring the instrument into space. The striking message that both these plots convey is that the Fermi LAT for both the le and the he selections is one of the leading instruments both in terms of livetime and geometric factor for the present and past experiments. The le selection is smaller than CALET (scheduled for 2013) and CALET-Polar (scheduled for 2011) due to the dgn filter 250 onboard prescale factor. Due to the fact that the CRs consist of charged particles, their arrival directions do not provide any information regarding their sources of origin. However, when energetic atoms pass through even small amounts of matter they are quickly stripped of their electrons and thus studying the composition of the CRs it is possible to gather clues about the average sources. As mentioned in the introduction of this chapter the CRs are primarily made up of hydrogen and helium nuclei with a small percentage of electrons and heavy nuclei. The heavier nuclei provide most of the information about the origin of the GCRs through their elemental and isotopic composition. Radioactive CR nuclei produced by nuclear interactions during CR propagation through the galaxy can be used to study the mean interstellar gas density in the propagation volume and the time scales associated with the propagation process. Measurements of the composition of nucleonic CRs have been performed with great accuracy in the MeV to TeV range thanks to experiments such as Cosmic Ray Isotope Spectrometer (CRIS) [45], Balloon-borne Experiment with Superconducting Spectrometer (BESS) [46] as well as the Advance Thin Ionization Calorimeter (ATIC) [50], Cosmic Ray Energetics and Mass (CREAM) [52], and Transition Radiation Array for Cosmic Energetic Radiation (TRACER) [51]. The main difference between nucleonic CRs and CR electrons are the energy loss mechanisms which cause the electrons to suffer higher energy losses while passing through matter, radiation fields and magnetic fields than the nucleonic of the hadronic CRs (further discussion regarding the energy losses will be presented in section 5.2). These energy losses cause a considerably steeper energy spectrum and limit the possible sources of the CR electrons to those of galactic origin. The proton and electron CR flux from 1 GeV to several tens of TeV measured by ground, balloon and space based

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5.1 the spectrum of cosmic rays

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Figure 59: Livetime vs geometric factor for ground, balloon and space based experiments. The exposure factor determines the amount of statistics gathered and what is immediately clear from this plot is that the space based missions feature longer livetimes with respect to the balloon experiments. The livetime for the Fermi LAT is based on the full five year mission duration.

experiments is shown in figure 61. Both the electron plus positron as well as the −Γ with spectral index of proton spectra are well described by a power law dN dE ∝ E Γe± = 3.08 and Γ proton = 2.73 . Measuring the ratio of secondaries to primaries can lead to clues on the production mechanisms these particles and can be an important tool to discriminate between them. However, this measurement can be a rather difficult task when considering the fact that once the charge sign of the particle has been identified, the antiparticle competes with the particle of the same sign. For example when measuring the antiproton to proton ratio the antiprotons must be distinguished from a ∼ 20 times higher flux of negative electrons. While the positron to electron ratio is substantially more difficult when considering that the flux of the positrons must compete with the nearly 1000 times higher flux of protons. This is graphically illustrated in figure 62. While the antiproton to proton ratios have been found to be consistent with the predictions from purely diffusive propagation models, an anomalous rise was found in the positron fraction (which was already hinted by previous measurements but with smaller statistical significance) above 10 GeV by the PAMELA experiment, shown in figure 63. The rise in the positron fraction triggered much enthusiasm in the astrophysics community with over 200 papers published within the first year of the measurement. Several different interpretations were proposed ranging from astrophysical (pulsars for

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cosmic ray electrons

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)

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Figure 60: Livetime vs geometric factor for the different detector techniques. Again, the space based missions have longer livetimes with respect to the balloon experiments yet what is clear from this plot is that the imaging calorimeters feature larger geometric factors when compared to the spectrometers. The livetime for the Fermi LAT is based on the full five year mission duration.

example) to exotic sources (like dark matter scenarios) [42, 65, 68] to name a few. The dark matter interpretations typically require large, and somewhat artificial, annihilation rates while in the case of pulsars, the energetic requirements are reasonable but an efficiency factor needs to be introduced by hand and the mechanisms for the escape of the electron plus positron pairs from the pulsar environment are not well known. The debate regarding the interpretation of this anomalous rise is still open and new measurements are needed to provide additional clues on its origin. 5.2

energy losses

Cosmic ray electrons are distinct from all other cosmic ray particles by the absence of hadronic interactions and by significant electromagnetic energy losses during propagation through the galaxy. These energy losses cause a comparatively steeper energy spectrum with respect to the nucleonic cosmic rays and limit the distance to the possible sources of the locally measured energetic cosmic ray electrons. The energy losses of cosmic ray electrons can be expressed in the following form:

−

82

dE = A1 ln E + A2 E + A3 E2 dt

(5.2)

5.2 energy losses

Figure 61: Measured flux of cosmic ray protons (antiprotons), electrons plus positrons (positrons) from ground, balloon and space based experiments. Electrons are less than 1% of the protons at 10 GeV (with a steeper spectral index) while the positron and antiproton fluxes were deduced using information on the electron or proton fluxes with the respective ratios measured by the PAMELA experiment. All the data points are taken from the Cosmic Ray Database [44].

where the first term describes the ionization losses, the second term bremsstrahlung and adiabatic losses and the last term inverse Compton scattering and synchrotron radiation. Ionization losses are relevant for energies below a few MeV, while for energies above several 10’s of MeV the energy loss due to bremsstrahlung becomes comparable to or greater than ionization losses. At energies above a few GeV, the energy losses due to synchrotron radiation in the galactic magnetic fields and inverse Compton scattering off photons are the dominant processes. Given the orbit of the Fermi satellite, it is only possible to measure the GCR electrons for energies greater than a few GeV and therefore the energy loss mechanisms of most interest for this work are synchrotron and inverse Compton. These processes have an energy loss rate whose magnitude increases with the square of the electron energy:  dE h B2 i  = −kE2 , with k = C w ph + dt 8π

(5.3)

The constant C is equal to 10−16 if the energy densities of the photons and magnetic fields, w ph and h B2 i/8π, respectively, are measured in eV cm−3 , and dE/dt in GeV

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Figure 62: The flux ratio for antiprotons to electrons (dashed blue line), electron plus positrons to protons (solid red line) and positrons to protons (dashed red line). The fluxes are taken from the Cosmic Ray Database [44]. From this figure it is evident that the most difficult secondary to primary measurement to make is that of the positron to proton ratio.

s−1 [104]. As a consequence of equation 5.3, an electron starting with energy E0 decreases with time as: E(t) = E0 /(1 + kE0 t) (5.4) and the time it takes for an electron starting with energy E0  E to reach an energy of E, the so called radiative lifetime is given by: τ ( E) = 1/kE

(5.5)

This lifetime is too short to permit electrons to travel intergalactic distances through the cosmic microwave background and thus excludes with certainty an extragalactic contribution [104]. This is one of the first important clues in the search for the origin of the GCR electrons. The transport equation describes the diffusion, energy losses and possible energy gain which the CRs go through while moving through the interstellar medium [80]. It is given by:

→ ∂Ne ( E, t, − r) ∂ → − D ( E)∇2 Ne − (b( E) Ne ) = Q( E, t, − r) (5.6) ∂t ∂E → where Ne ( E, t, − r ) is the number density of the e− + e+ per unit energy, D ( E) is the → diffusion coefficient, b( E) is the rate of energy loss and Q( E, t, − r ) is the source term.

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Figure 63: Left panel: antiproton to proton ration measured by the PAMELA experiment [67] together with several proposed models for secondary production. The points are in fairly good agreement with the predictions. Right panel: The positron to electron plus positron ration measured by the PAMELA experiment together with a model for secondary production from Moskalenko and Strong. The data points show s clear rise as a function of energy above ∼ 10 GeV in contrast with the predictions of the model.

The diffusion coefficient is assumed to have a power law energy dependence, D ( E) = D0 ( E/E0 )δ . As mentioned above, for e− + e+ with energies greater than a few GeV only synchrotron and Inverse Compton energy losses are relevant therefore it is reasonable to take b( E) = b0 E2 . However, to solve the transport equation (5.6) it is necessary to → know the energy spectrum of the source term, Q( E, t, − r ) as well as the index, δ for the diffusion coefficient [80]. There are three main categories of galactic sources that have been considered to be at the origin of the GRCs and they will be discussed in the following sections.

5.3

origins

Even though CRs were discovered in 1912, the discovery of the CR electrons was made much later in 1961 simultaneously by P. Meyer and R. Vogt [60] and J. Earl [53]. Figure 64 shows a candidate electron event passing through the cloud chamber flown over Minneapolis, Minnesoda (geomagnetic latitude 55◦ corresponding to a cutoff energy of 0.7 GeV) by J. Earl in 1960. Electrons and gamma-rays were identified by the characteristic EM shower which they produced in the lead plates of the cloud chamber. The selection criteria required that the axis of the accepted showers had to pass through the illuminated areas of both the top and the bottom of the cloud chamber to ensure that the axis passed through all five of the lead plates. Therefore an event transversing through the entire thickness of the lead plates would almost certainly reveal its nature,

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be it electromagnetic or hadronic. In the figure the candidate electron event appears as a single minimum ionizing track which lies on the axis of the shower. Cosmic ray electrons are produced mainly in two process: "primary" production in astrophysical sources, believed to be Supernova Remnants (SNR) or pulsars, and "secondary" production by interactions of hadronic cosmic rays with the interstellar matter. Supernova explosions are generally accepted as the most likely source of the majority of cosmic rays. The mechanism thought to be responsible for the acceleration of the CR’s is diffusive shock acceleration. Radio observations and evidence of nonthermal X-ray emission from SNRs indicate that high-energy electrons are accelerated in SNR [92]. Such observations have shown that electrons with energies up to ∼ 100 TeV exist in the shock fronts of supernova remnants as well as in Pulsar Wind Nebulae (PWN), which makes them good candidates for electron accelerators. Dark matter scenarios have also been explored as a possible source of the cosmic ray electrons. In the following sections these three possibilities will be discussed in further detail. 5.3.1

Supernova Remnants (SNR)

In a supernova explosion the outer shell of the exploding star is ejected and expands supersonically as a shock front. As this shock front moves away from the core of the star it sweeps up the ISM until the mass of the stellar injection reaches roughly the swept up mass. At this point the wave begins to slow down due to radiative losses (known as the Sedov-Taylor phase [62]). This phase can be traced via X-ray emission originating from the shock waves and the hot shocked gas. The next stage in the SNR evolution is the cooling of the shell forming a thin (< 1 pc) and dense (1 − 100 million atoms per cubic meter) shell which surrounds the hot (few million K) interior. During this phase the ionized hydrogen and oxygen atoms recombine and this can be observed in the optical wavelengths. This radiative cooling becomes the dominant energy loss mechanism and cools the SNR for about 105 yrs until it merges with the surrounding ISM. The first two phases of the SNR evolution are thought to be responsible for the particle acceleration via the mechanism known as diffusive shock acceleration or first order Fermi acceleration. The diffusive shock acceleration is the acceleration that charged particles undergo when reflected by a magnetic scattering. SNR shock waves are thought to have moving magnetic inhomogeneities both preceding and following them. Therefore if a charged particle moving through a shock wave encounters these magnetic field variations it can be reflected back through the shock at an increased velocity. If a similar process occurs to the transversing particle it can bounce back and again gain energy. The resulting spectrum of these particles undergoing multiple reflections turns out to be a power law: dN (e) ∝ e− p de

(5.7)

where the spectral index p ≈ 2 [64], which is close to the expected value from the shape of the cosmic ray spectrum if taking into account energy dependent diffusion [63]. This acceleration mechanism is termed first order because the energy gain per shock

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5.3 origins

Figure 64: Cloud chamber picture of a shower produced by a CR electron. The incident electron is visible in the top section of the cloud chamber and its entrance point is indicated by an arrow. The cloud chamber consisted of five lead plates of 1.1 radiation lengths and the effective geometry factor of the instrument was 33.5 ± 1.5 cm2 sr [53].

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Figure 65: Left panel: Positron fraction as a function of energy. The data points correspond to the PAMELA measurement and the lines represent different values for the maximum energy of the accelerated particles (as well as the secondaries) at the SNR. The dashed line represents the standard contribution to the positron fraction from secondary diffusive pairs. The right panel shows the fluxes of the e− + e+ multiplied by the energy cubed for an Emax = 100 TeV (same as the solid line in the left panel). The dashed lines are the fluxes of positrons (upper curve) and electrons (lower curve) from interactions from interactions of the CRs in the Galaxy. The dash-dotted lines are the fluxes of positrons (upper curve) and electrons (lower curve) from the production sources and the thick solid line is the total flux [42]. The data points are the high energy Fermi LAT measurements. crossing is proportional to the velocity of the shock. In this mechanism regular matter is accelerated, which in the case of electrons are the negative electrons. Theories however also predict that not only the negative electrons get accelerated by the SNRs but also the secondaries can be accelerated. In [42] it is proposed that given that the CRs accelerated at the shock produce secondary e− + e+ inside the source through hadronic interactions and that this process occurs in the same spatial region around the shock in which the CRs are being accelerated. It is unavoidable that these secondaries take part in the same acceleration process. Therefore, SNRs could potentially account for both the positron excess seen by the PAMELA experiment as well as the relatively flat electron plus positron spectrum measured by the Fermi LAT at high energies. Some proposed fits are shown in figure 65 However, if this mechanism is responsible for the acceleration of the positrons then it should also accelerate other secondary particles such as antiprotons. The antiproton to proton ratio measured by the PAMELA experiment does not show any anomalous rise therefore causing some complications for this theory. 5.3.2

Pulsars

Another possible source of cosmic ray electrons are pulsars. Pulsars are rapidly rotating neutron stars that form after supernova explosions of stars with 1.44M and 5M . These objects have extremely high magnetic fields (∼ 1010 − 1013 G) and as the pulsar rotates

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these magnetic fields induce strong electric fields that can in turn accelerate particles [61]. As the pulsar rotates, its surrounding magnetosphere of charged particles co-rotates with it. This co-rotation is limited however by particle inertia and cannot persist beyond what is called the light cylinder, the surface where the velocity of these particle reaches the speed of light. The magnetic field lines that lie within the light cylinder

Figure 66: Schematic drawing of the geometry of a pulsar with angular velocity ω and magnetic field B and α is the angle between ω and B. The emission regions described by the polar cap and outer gap models are marked. This figure is taken from [93].

are closed and those crossing it are open. Since particles gyrate along the magnetic field lines, they can escape the pulsar magnetosphere only along open field lines. In the pre-Fermi era, two different models were proposed to explain the electrostatic acceleration in pulsar magnetosphere: Polar cap model and the outer gap model. In the polar cap model the acceleration occurs in the charge depleted zone near the polar cap of the pulsar. In the outer gap model acceleration occurs in vacuum gaps that form in the outer magnetosphere. The regions of the two models are shown in the schematic drawing of the pulsar in figure 66. The gamma ray profiles of the Fermi LAT detected pulsars have found that the outer gap models generally provide good fits to the observed profiles [32] therefore favoring this model. In the outer gap model, the electrons accelerated in the outer magnetosphere interact through synchrotron radiation or inverse Compton scattering and consequently new e− + e+ pairs are produced via γγ interaction. Therefore a cascade is initiated which forms a Pulsar Wind Nebula (PWN) which expands in the ambient medium. Where this PWN meets the expanding shell of

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the SNR a termination shock is formed. At this termination shock, shock acceleration can occur which in turn can re-accelerate electrons plus positrons (acceleration due to shock acceleration mechanism was already discussed in section 5.3.1). In contrast to the shock acceleration in SNRs, in pulsars, both negative electrons and positrons can be accelerated. In fact, in light of the PAMELA positron fraction measurement pulsars have been proposed as a possible source of positrons to explain such an excess. In [65] it was proposed that the high energy CR electron flux can be a sum of an almost homogeneous and isotropic GCR electron component produced by Galactic SNRs (the standard CR propagation model) and a local contribution from a few pulsars. This was done by summing the analytically computed electron and positron spectrum from observed nearby pulsars to the GCR electron component computed with the numerical CR propagation code GALPROP [82]. The main parameters needed for a given GALPROP model are the CR primary injection spectra, the spatial distribution of the CR sources, the size of the propagation region, the spatial and momentum diffusion coefficients and their dependence on the particle rigidity. In the case of [65] the electron injection power law index was taken to be 2.54, the index of the power law dependence of the diffusion coefficient, D was taken to be 0.33 and the CR nuclei injection index was taken to be equal to 2.42. While the source term was taken as:

→ Q( E, t, − r ) = Q0



E 1GeV

−Γ

→ e−E/Ecut δ(t − t0 ) δ(− r)

(5.8)

where the spectral index, Γ, was taken to be equal to 1.7, Ecut = 1100 GeV and δ(t − t0 ) = 6 × 104 yrs with an efficiency as a function of pulsar age and luminosity, ηe± = 40% [65]. → The δ(t − t0 ) δ(− r ) term is typical for a burst-like source where the t0 is the injection time (i.e. the instant in which the particles are released from the source into the ISM), → r is the distance to the source. As source can be considered burst-like when t0  t and − where t is the time it takes for the electrons to propagate through the ISM and reach the observer. It was found that both the PAMELA and Fermi data could be fit in the simple case of two nearby pulsars, in particular Monogem and Geminga as is shown in figure 67. However, with the new low energy GCR electron data which shows a steeper slope in the measured flux from ∼ 7 GeV to 20 GeV, this model is no longer a good fit and a new explanation is needed. 5.3.3

Dark Matter

The annihilation of dark matter particles has been proposed as another potential source of Galactic cosmic ray electrons. Weakly interacting particles suggested by Super Symmetry (like neutralinos) or theories of extra dimensions (such as Kaluza-Klein) can annihilate via the production of e± pairs or gamma-rays [94]. The direct production of e± pairs by Kaluza-Klein particles yields a spectrum of a delta function at the particle’s mass, which is broadened to lower energies due to propagation effects. The bump measured by the ATIC instrument has been interpreted as a possible signature of Kaluza-Klein dark matter particle with a mass of 620 GeV [94]. In figure 68 the ATIC bump is shown together with the propagated electrons from the annihilation

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Figure 67: Left panel: The positron fraction measured by PAMELA, HEAT, AMS01 and CAPRICE with the fit in the scenario in which local pulsars contribute to the positron flux. Right panel: electron plus positron flux multiplied by the energy cubed in a case in which only observed pulsars from the ATNF catalogue [66] with distance d < 1 kpc plus large scale Galactic component give a significant contribution. The contribution of the two pulsars is shown as the dot dashed lines while the GCR electron computed with GALPROP is as the black dotted line. The solar modular was taken into account using the force field approximation assuming a potential, Φ = 550 MV [65]. of a Kaluza-Klein particle (dotted line in the figure), the GALPROP general electron spectrum resulting from sources across the galaxy (dashed line in the figure) and the solid line represents the resulting fit to these components. This result caused a great deal of excitement in the scientific community. However, the measurements of the electron spectrum by the Fermi LAT [100] as well as the HESS telescope [48] do not confirm the presence of the bump in the energy region 300 − 700 GeV. Interpretation of these new results are left to the dedicated chapter in this work.

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Figure 68: The electron + positron spectrum measured by the ATIC experiment assuming an annihilation signature of Kaluza-Klein dark matter. The dotted line represents the propagated electrons from the annihilation of the dark matter particle, the dashed line represents the GALPROP general electron spectrum resulting from sources across the galaxy and the solid line represents the resulting fit. All error bars are one standard deviation [94].

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6 A N A LY S I S

As previously mentioned in the introduction chapter, the main topic of this thesis is the analysis behind the CR electron spectrum. This chapter is dedicated to the detailed description of the work carried out throughout the duration of my PhD studies. In particular, in section 6.1 I give an overview of the Monte Carlo simulation of the instrument, on-orbit background environment and the International Geomagnetic Reference Field model. All of these simulations are very important for the development and verification of the selection criteria. The event selection developed for the CR electrons can be found in section 6.2 followed by the resulting figures of merit such as the effective geometry factor and energy resolution, in section 6.3. In section 6.4 the potential sources of background are identified and the description of how they are removed from the event sample is presented together with an estimation of the systematic uncertainties tied to the selection in section 6.5. The method for reconstructing the Galactic CR electron spectrum and some possible theoretical interpretations are discussed in sections 6.6 and 6.6.3, respectively. In section 6.6.2 I present the measurement of the positron fraction using the geomagnetic field to separate the charge sign of the electrons from the positrons in the energy range 5 − 17 GeV. Finally in section 6.7 I describe the ongoing work on the update of the electron component of the on-orbit background Monte Carlo simulation. 6.1

instrument simulation

The Fermi LAT collaboration uses a very detailed Monte Carlo (MC) simulation to study the instrument performance and the response to celestial sources. The software code uses a precise description of the LAT geometry that includes the position and the material of all the detector elements, both active and passive (in figure 69 is an example of the full LAT detector integrated into the spacecraft as represented by our simulation software). The simulation is based on the GEANT4 [102] toolkit, widely used in high-energy physics experiments, to model particle propagation and interaction through the instrument (energy loss, multiple scattering, etc.) as well as the energy deposition in the active detector elements. A digitization algorithm takes care of converting this information into raw detector quantities that can be processed, by the reconstruction algorithms, in the same way as the real data. The digitization algorithm has the capability of including detector “defects” like sensors misalignment, real gain and noise level, non linearities etc. In this way the reconstruction algorithm can use the

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Figure 69: Simulation of the LAT geometry. Each subsystem is described in detail and used to calculate the response of the instrument to passing radiation. From this figure it is possible to distinguish the single TKR tower (yellow) and CAL (blue) modules, the individual ACD tiles (red) that surround the LAT, the batteries (cyan rectangles bottom center of figure), the radiator panels (orange squares) as well as the solar panels (green). actual calibration constants and the MC can provide a very accurate representation of the instrument response. The MC simulation has been extensively used for the design of the instrument and optimization of the event reconstruction and background rejection analysis. The Instrument Response Functions (IRF) for the electron analysis (just like the gamma-ray analysis) are evaluated using the MC simulation. However, no Monte Carlo simulation is perfect therefore both the physical processes and the geometry implementation have to be validated by comparing the simulation results with real data. The LAT MC simulation has been verified on ground with cosmic rays and with a series of beam tests on a Calibration Unit (CU) at CERN PS and SPS and at the GSI heavy ion accelerator laboratories [99]. 6.1.1

On-orbit environment simulation

The on-orbit particle environment is of fundamental importance when developing selection criteria to separate electrons from hadrons. This highly detailed model has been intensively used to develop all the γ-ray background rejection algorithms, both on-orbit and off-line. The model includes cosmic rays and earth albedo γ-rays starting from 10 MeV up to some TeV and is valid outside the South Atlantic Anomaly (SAA). Due to the extreme conditions in the SAA region the regular data taking is switched off and therefore it is not necessary to have the simulations inside this region. The

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particle fluxes for the background model are chosen to fit experimental data of several past experiments, further details can be found in table 3 as well as in [98]. In addition to the primary component of the cosmic radiation, the model includes the secondary particles produced by the interaction of the cosmic rays with the atmosphere and the Earth’s magnetic field taking into account the geomagnetic cutoff as well as the east-west asymmetries introduced by the geomagnetic field. This model provides a realistic simulation of the background particles which trigger the LAT while on-orbit. Figure 70 shows the flux of the background sources in the model. While in figure 71 is an illustration of how the cosmic-ray electron + positron spectrum is simulated in the background model as a function of both energy and geomagnetic latitude. The cutoff rigidity is clearly evident in the spectra and its dependence on geomagnetic position is also clear from this plot. Since the background model describes a realistic

Figure 70: This figure shows the orbit averaged E*Flux of all background sources in the model. Total (Black solid triangles), primary protons (light green solid triangles), He+heavies (lavender solid squares), primary electrons (red solid squares), albedo protons (blue solid squares), albedo positrons (light blue solid circles), albedo electrons (green solid squares), and albedo gammas (yellow solid triangles). Taken from [103].

on-orbit environment, it can be used to estimate the residual contamination, which is a useful figure of merit for the quality of the analysis. The production of this MC

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sample was one of the most important and time consuming activities for the electron analysis. Due to the required high rejection power, about 103 − 104 simulated events are needed to obtain one event that leaks through the selection and can be used for residual background evaluation. The power law spectrum of primary protons (the main source

Figure 71: This figure shows the galactic cosmic ray (GCR) spectra of the electrons and positrons in the model. Points are grouped in 0.1 radians geomagnetic latitude bins. Taken from [103]. of background) varies as E−2.7 makes it even harder to populate the high energy region of the spectrum. To evaluate the residual background used in the electron spectrum measurement, about 400 CPUs for 80 days of computing time were used. 6.1.2

International Geomagnetic Reference Field (IGRF)

The geomagnetic environment plays a very important role when it comes to the measurement of the cosmic ray particle fluxes. As already mentioned in chapter 4 the shielding provided by the Earth’s magnetic field is stronger in the equatorial region and smaller near the poles. This translates into large particle flux variations dependent on the orbital position of the detector. Due to these effects, the background model relies on the International Geomagnetic Reference Field (IGRF) [87] to estimate the expected rate

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> local geomagnetic cutoff Galactic Cosmic Rays protons + antiprotons electrons positrons He Z > 2 nuclei Splash Albedo protons + antiprotons electrons positrons Re-entrant Albedo protons + antiprotons electrons positrons Earth albedo γ-rays Neutrons

150 MeV to geomagnetic cutoff

10 MeV - 150 MeV

AMS AMS AMS

Nina Mariya Mariya

AMS AMS AMS AMS HEAO-3

Nina Mariya Mariya 10 MeV - 100 GeV, EGRET 10 MeV - 1 TeV, various sources

Table 3: Data sources for the LAT background model. Sources: AMS: Auguilar et al. (2002); Nina: Bidoli et al. (2002); Mariya: Voronov et al. (1991), Milkhailov et al. (2002); EGRET: Petry (2005); HEAO-3: Engelmann et al. (1990); neutrons; Selesnik et al. (2007). Taken from [98].

of cosmic ray particles for the Fermi orbit. The IGRF is a mathematical description of the Earth’s magnetic field (at five year intervals) and incorporates data from permanent observatories and from land, airborne, marine and satellite surveys. Production of the IGRF is an international collaborative effort relying on co-operation between magnetic field modellers and institutes and agencies responsible for collecting and publishing geomagnetic field data. 6.1.3

Electron simulation

Together with the background model, an electron simulation was used to study the LAT response to electrons and used to calculate the geometry factor which will be described in section 6.3. This model does not include all the details of the LAT on-orbit, but provides an isotropic flux in the LAT reference frame. The energy distribution in this model is a power law with index −1, so that we can accumulate high statistics in the whole energy range in a relatively short simulation time.1 1 Notice that a E−1 spectrum produces energy bins with equal number of events in case of logarithmic binning which is a common choice in high energy astrophysics

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6.2

selection criteria

The LAT is sensitive to electrons over more than five orders of magnitude in energy (∼ 100 MeV – ∼ 1 TeV). Across this huge energy range both the typical event topology and the relative fractions of signal and background in the cosmic-ray flux impinging on the detector undergo variations. For these reasons it’s not trivial to develop a single, unitary analysis strategy providing the necessary electron detection efficiency and the hadron rejection power across the whole energy range. In fact, two independent electron selections have been elaborated, one tuned for relatively low energies and the other for high energies respectively (which will be referred to as le and he in the rest of this work). The split point, in energy, between these two analyses can be naturally placed at 20 GeV for at least two reasons. The first one is that the on-board filtering accepts all events with energy equal to or greater than 20 GeV (whereas we only have a prescaled unbiased sample when below 20 GeV). The other one is that below ≈ 20 GeV, the shielding effect of the geomagnetic field (which depends on the geomagnetic latitude and, hence, on the position of the spacecraft across its orbit) becomes important. In fact the he selection has been mostly developed exploiting the data source provided by the gamma filter for the purpose of measuring the primary cosmic-ray electrons, whereas the le selection was also designed to measure the secondaries, using the dgn filter data source. It must be stressed, however, that these divisions are artificial and there’s a significant overlap in energy between the two selections. This can be used as an independent cross check for both of the analyses. This work is concentrated on the le analysis. The event selection developed for the electrons, just like for the photons [98], relies on the LAT capability to discriminate EM and hadronic showers based on the different topologies of these events measured in the three sub-detectors of the LAT. The distribution of the variables and the relative fractions of electrons and hadrons depend on energy and therefore when establishing the selection criteria it is imperative to analyze these distributions in several energy intervals. For any single variable, the signal and the background distributions at the very end of the selection chain (in other words after all the other variables have been applied) convey the additional rejection power provided by the single variable in question. In fact a quantity that might look promising at an early stage may reveal itself entirely useless for the event selection after all the other cuts have been applied. Therefore the final selection used to separate the electrons from the hadrons are not to be considered as a set of cuts to be applied in series, since the order in which they are applied does not change in any way the final result. One of the first requirements of the event selection is to have a reliable reconstructed event. This is important because most of the higher level event topology variables depend upon the direction of the reconstructed track within each of the subsystems of the LAT. To satisfy this requirement it is necessary to start with only those events that have at least one reconstructed track in the TKR and have deposited more than 5 MeV in the CAL. It is also important to make sure that the photons from the Earth’s limb are excluded from the sample of events being analyzed. This can be done by applying a simple cut on the reconstructed angle with respect to local zenith less than 105◦ . To better understand this cut it is necessary to consider the simple geometry illustrated in

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Figure 72: Simple cartoon of how the reconstructed angle with respect the local zenith, θ, is calculated. RE is the Earth’s radius, h is the thickness of the Earth’s atmosphere, H is altitude in which Fermi is orbiting (i.e 565 km). The dashed line represents the Earths’ atmosphere and the dark gray rectangle represents the Fermi observatory. figure 72, where RE is the Earth’s radius, H is the altitude of the Fermi satellite (565 km), θ is the angle between the reconstructed direction of the event and the local zenith, and h is the assumed thickness of the atmosphere. The value of θ is calculated as:   RE ◦ −1 θ = 90 + cos = 113.3◦ (6.1) RE + H Thus, the Earth’s limb is at ∼ 113◦ from Fermi’s field of view. If the Earth’s atmosphere is taken to be of thickness ∼ 50 km then θ = 112.2◦ . However, it is important to take into account the point spread function when calculating this angle, thus using a value of 7◦ for the photon PSF95% at 100 MeV [18] gives a final value for θ = 112◦ − 7◦ = 105◦ . In figure 73 the distribution for θ is shown for the candidate electrons events (before and after the selection cuts) and that for the photons selected from the source class. For the latter of the two, a prominent peak is evident for θ > 105◦ which is due to the photons originating from the interaction of GCR’s with the Earth’s limb. The peak is not as large for the candidate electrons because the charged particles get deflected by the geomagnetic field and therefore do not travel directly towards the LAT after transversing the atmosphere. The cut value for θ is represented by the vertical dashed line in both of the plots in figure 73. The ACD plays an important role in the event selection because it separates a charged particle from a neutral one. In fact in the photon analysis the ACD is used in conjunction

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Figure 73: Distribution of the reconstructed angle with respect to local zenith per event for the flight data. The left panel shown the data before the le electron selection cuts (in black) and after the cuts (in red). The events before the selection cuts have been normalized to those after the selection. The right panel shows the distribution for the source class photon candidate events after the first 88 hours of first light data. The large peak for zenith angle greater than 105◦ is due to the photons originating from the Earth’s limb. The cut on zenith theta serves to remove the remaining events that originate from the direction of the Earth’s limb.

with the found tracks in order to determine whether an event is a charged particle or a neutral. This approach is used to remove the vast majority of the background that enters within the Field Of View (FOV) in the photon analysis [98] and is used in the electron analysis to remove the neutral events by taking the events that fail this veto. The total energy released in the ACD (in MeV) per event as well as the average energy per tile are two distributions that help separate electromagnetic events from hadronic ones. For example figure 74 shows the total ACD energy per event in four different energy ranges for electrons (in red), hadrons (in blue), the sum of the two components from the Monte Carlo simulation (in gray) and the flight data (in black) after all the selection cuts have been applied excluding the low energy classification tree variable. The cut on this variable is energy dependent and the value used for each energy bin is represented by the position of the vertical dashed line. This particular distribution is helpful in separating the two populations of events for energies smaller than a several tens of GeV. For example in figure 75 a candidate electron and hadron event of ∼ 1 GeV reconstructed energy are shown (with the aid of the LAT event display) and one of the discriminating quantities is the total energy released in the ACD. The candidate electron event has 2.5 MeV in the ACD while the hadron event has 10.5 MeV. From the Bethe-Block equation which describes the mean rate of energy loss for a particle passing through matter, the energy loss of a particle is proportional to the square of the charge of the incident particle

−

100

dE ∝ z2 dx

(6.2)

6.2 selection criteria

Figure 74: The distribution of the total ACD energy per event towards the end of the event selection. The cut on this variable is energy dependent and increases with energy as can be seen by the figures. Top two panels corresponds to the energy windows of 500 MeV to 1 GeV (left panel) and from 1 - 5 GeV (right panel) in measured energy and the bottom two panels correspond to the energy window of 5 to 10 GeV (left panel) and 10 50 GeV (right panel). Hadrons are in blue, electrons + positrons in red, sum of hadrons and electrons + positrons from the Monte Carlo simulations in gray, and data in black.

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and therefore considering for example an alpha particle (which has z = 2), the expected energy released on average on axis is ∼ 8 MeV when transversing the ACD. If however, the event passes through the LAT at an angle, the energy released varies with angle as 1/ cos θ 2 where θ is the angle between the z axis of the ACD and the arrival direction of the event. Thus an alpha particle arriving at an angle of 60◦ will deposit on average 16 MeV in the ACD. For energies in the hundreds of GeV segmentation of the ACD tiles provides information about the topology of the the backsplash from the calorimeter and the average energy per tile conveys more valuable information. Figure 76 gives an example of a 1 TeV electron and hadron candidate as seen in the LAT event display. The number of ACD tiles hit for the supposed hadron event are significantly more numerous than for the electron event again proving to be a relevant variable for the selection criteria.

(a) A candidate ∼ 1 GeV electron:

(b) A candidate ∼ 1 GeV hadron:

- Measured energy: 1.07 GeV

- Measured energy: 1.05 GeV

- Calorimeter raw energy: 737 MeV

- Calorimeter raw energy: 772 MeV

- Transverse shower size: 21.5 mm

- Transverse shower size: 49.3 mm

- Energy released in the ACD: 2.5 MeV

- Energy released in the ACD: 10.5 MeV

Figure 75: An electron candidate (left panel) and a hadron candidate (right panel) with reconstructed energy around 1 GeV. The gray crosses represent the clusters in the tracker, while the dark grey squares on the bottom represent the energy released in the calorimeter crystals. The electron candidate features a smaller transverse size in the calorimeter and a higher energy release in the ACD tile pointed by the best track. The difference in the shower transverse size between electromagnetic and hadronic events in the CAL provides very good discrimination power throughout the entire energy range in question. The distribution of this quantity for the two populations has a small dependency on energy as is shown in figures 77 and 78. These figures depict the shower transverse size in mm after the ACD and high energy classification tree variable have been applied. The most striking difference can be found in the energy 2 for the top tiles of the ACD, while for the side tiles the energy released varies as 1/ sin θ.

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(a) A candidate ∼ 1 TeV electron:

(b) A candidate ∼ 1 TeV hadron:

- Measured energy: 834 GeV

- Measured energy: 1 TeV

- Calorimeter raw energy: 475 GeV

- Calorimeter raw energy: 823 GeV

- Good energy reconstruction probability: 0.728

- Good energy reconstruction probability: 0.146

- Transverse shower size: 23.2 mm

- Transverse shower size: 34.4 mm

- TKR extra clusters in the main tracks: 43/29

- TKR extra clusters in the main tracks: 1/6

- Number of ACD hit tiles: 41

- Number of ACD hit tiles: 65

- Average energy per ACD tile: 2.5 MeV

- Average energy per ACD tile: 10.2 MeV

Figure 76: An electron candidate (left panel) and a hadron candidate (right panel), with reconstructed energy around 1 TeV, passing the he selection cuts. The gray crosses represent the clusters in the tracker, while the dark grey squares on the bottom represent the energy released in the calorimeter crystals. The comparison between the two events illustrate some of the topological differences which are exploited in the event selection: the electron candidate features a smaller shower transverse size in the calorimeter, a higher fractional number of extra-clusters around the main track in the tracker and a smaller number of ACD tiles hit (in conjunction with a smaller average energy release per tile). bins ranging from 500 MeV to 5 GeV where a peak centered around ∼ 8 mm is present. This is a typical signature of a non interacting proton transversing the calorimeter. As already stated in chapter 1 the LAT calorimeter is composed of cesium iodide crystals, these crystals have radiation length of 8.39 g/cm2 (or 1.85 cm) and a MIP deposits on average in cesium iodide 1.243 MeV/g cm2 [107]. Therefore, a MIP will deposit a minimum of 8.39 g/cm2 · 1.243 MeV/g cm2 = 10.43 MeV per radiation length in the LAT calorimeter. To check whether the peak around 8 mm is indeed due to MIPs transversing the CAL it is necessary to take the ratio between the total raw energy measured in the CAL and the total radiation length transversed by the event in the CAL. This ratio is shown in figure 79, the right panel shows the distribution of the events accepted by the electron selection while the left panel shows the events rejected by the le analysis. The difference between the two distributions is striking yet the peak in the left panel is not at 10.42 MeV but shifted by about 10% to a value of ∼ 11.5 MeV.

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Figure 77: Shower transverse size for hadrons (blue), electrons + positrons (red), sum of hadrons and electrons + positrons from the Monte Carlo simulations (gray), and data (black) in the middle of the event selection. The top two energy windows correspond to reconstructed energy from 500 MeV to 1 GeV (left panel) and from 1 GeV to 5 GeV (right panel). The bottom two panels correspond to reconstructed energy from 5 GeV to 20 GeV (left panel) and from 20 GeV to 50 GeV (right panel). This increase in energy deposit can be explained by considering that the population of events with transverse shower size smaller than 15 mm (one of the cut values for the shower size in the le analysis) most likely consists of MIP protons (i.e 3 GeV is the energy at which a proton is at minimum on the Bethe-Block curve) but also of higher energy protons. For example a proton of 15 GeV (which is approximately the value in which the orbital averaged geomagnetic cutoff peaks) deposits roughly 10% more energy3 in CsI than a 3 GeV proton and thus giving the 11.5 MeV peak seen in the figure. Overall the transverse size of the hadronic shower is much larger than the EM one, as can be expected by the difference in cascade mechanisms. Given the fact that the LAT was not intended to be a hadronic detector, the hadronic shower is generally not fully contained in the CAL. As a consequence, the reconstructed energy of a hadronic event is often underestimated. Therefore the proton population in a given energy window can also include protons of much higher true energy and this effect can cause noticeable differences in certain distributions. The distance between the projected track from the TKR and the energy centroid in the CAL evaluated at the z axis of the centroid, called CalTrackDoca is a valuable quantity in the selection criteria for energies below ∼ 500 MeV as is shown in the two panels of figure 80 after all the 3 This value is estimated using the Bethe-Bloch formula for protons.

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Figure 78: Shower transverse size for hadrons (blue), electrons + positrons (red), sum of hadrons and electrons + positrons from the Monte Carlo simulations (gray), and data (black) after all the other selection cuts have been applied.

Figure 79: Distribution of the raw energy measured in the calorimeter normalized by the total radiation lengths in the calorimeter crystals, integrated along the event axis for the events passing the ACD and high energy classification tree variable. Left panel are all those events having shower transverse size less than 15 mm and reconstructed energy less than 1 GeV. These are the events which correspond to the peak around 8 mm in figure 77 top two panels. The peak at ∼ 11 indicates that these are MIPs having deposited 100 MeV in the CAL (with 8.6X0). The right panel shows the distribution of the events in with reconstructed energy between 500 MeV and 1 GeV and having a transverse shower size between 15 − 40 mm, for comparison. The scales are different in the two figures.

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Figure 80: CalTrackDoca is defined as the distance between the projected track and the energy centroid evaluated at the z of the centroid in the calorimeter. To facilitate the optimizations of the separation of hadrons and electrons as a function of energy, this variable was multiplied by the log of the measured energy. The cut is energy dependent and is relevant only for energies below ∼ 1 GeV. Left panel shows the distribution of this variable in the energy window of 100 - 200 MeV and the right panel from 200 - 500 MeV in measured energy. Hadrons (blue), electrons + positrons (red), sum of hadrons and electrons + positrons from the Monte Carlo simulations (gray), and data (black) at the end of the event selection.

Figure 81: Distribution of CalTrackDoca · logarithm of the true Monte Carlo energy for the same energy bins as in figure 80. When using the true energy the distribution for this variable is very different from the one in measured energy due to the underestimated energy measurement of the non-interacting protons. Hadrons (blue), electrons + positrons (red), sum of hadrons and electrons + positrons from the Monte Carlo simulations (gray), and data (black) at the end of the event selection.

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selection cuts have been applied. This is a perfect example of how the underestimation of the reconstructed hadron energy can be helpful in the separation of particle types. Figure 81 illustrates the CalTrackDoca distribution in the same energy intervals but using the true MC energy instead of the reconstructed energy, this plot demonstrates that the distribution for the reconstructed energy is effected by the underestimation of the hadron energy. The cut on this variable is a function of energy and does not remove any events for energies higher than a few GeV where there is no separation power remaining. After a careful analysis in each subdetector of the LAT, the remaining necessary hadron rejection power is achieved using a classification tree (CT) analysis. A Classification Tree (CT) is a fairly popular machine learning technique aimed to associate any given point (event) of a multidimensional space to one of several possible categories (typically signal or background), based on the coordinates of the point itself.Classification trees are widely used in high-energy physics and astronomy (see [105, 106] for an exhaustive review). Compared with different types of multivariate analysis approaches, they have the advantages of being statistically robust against outliers and noisy or redundant attributes. Moreover, given the relatively simple partitioning scheme of the phase space, they effectively provide interpretable models rather than black-box models such as other popular machine learning techniques (Artificial Neural Networks or, to less extent, Support Vector Machine). To be sure that any topological variable poorly reproduced by our detector simulation was not used in the training process, the top-level variables in input to the classification trees were carefully selected based on an extensive comparison between Monte Carlo and flight data. It is also worth mentioning that each single variable reflects the topological event properties that are known to provide some discrimination power, based on the underlying physics of the interaction in the detector. For the he analysis, two different classifiers (based on the event topology in the TKR and in the CAL, respectively) are trained on a Monte Carlo sample of events. The two continuous probability values ptkr and pcal provided by the classifiers are then combined in a single, energy-dependent electron probability that can in turn be used to achieve different levels of rejection power as a function of energy. For the le selection on the other hand the classification tree analysis combines all the relevant quantities in a single electron probability. Similarly to the he classification tree variable, the cut on the le CT variable is energy dependent and optimized in the energy range of ∼ 5 − 15 GeV (where the geomagnetic cutoff causes the largest hadron contamination). Given the fact that there is a fairly large energy overlap between the he and the le analysis, both the combined he CT variable and the le one can provide powerful rejection power for the le selection. In figure 82 the distribution of the le CT variable is shown in four energy windows after all the other selection cuts have been applied. The he combined probability is shown in figure 83 for the same energy windows as for the le one. The care that was taken in choosing the input variables for the CT is naturally reflected in the excellent agreement between data and Monte Carlo. An output variable from the classifiers can be tested the way any other selection variable is tested,as is evident in both figures 82 and 83.

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Figure 82: The distribution of the classification tree variable grown for the DGN sample of events after all the other selection cuts have been applied. Top two panels correspond to the energy windows of 100 - 200 MeV (left panel) and from 200 - 500 MeV (right panel) in measured energy and the bottom two panels correspond to 500 MeV to 5 GeV (left panel) and 5 - 20 GeV (right panel). Hadrons are in blue, electrons + positrons in red, sum of hadrons and electrons + positrons from the Monte Carlo simulations in gray, and data in black.

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Figure 83: The distribution of the product of the two he classification tree variables based on the topology of the event in the TKR and in the CAL, after all the other le selection cuts have been applied. Top left panel shows the distribution in the energy window 200 − 500 MeV while top right panel shows 500 MeV to 5 GeV, bottom left panel is 5 − 20 GeV and bottom right panel shows the 20 − 50 GeV. The cut value is represented by the vertical dashed line and hadrons are in blue, electrons + positrons in red, sum of hadrons and electrons + positrons from the Monte Carlo simulations in gray, and data in black.

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6.3

the cre instrument response functions

As already discussed in chapter 1.4 the IRFs describe the instrument in terms of the transformation probability from the true physical quantities (such as energy and direction) to the corresponding measured quantities. The response of the detector can be described in terms of the energy resolution, point spread function and the effective area. However for the CREs, it is reasonable to assume that the incoming flux is isotropic and so the effective area can be substituted with the effective geometry factor (which is a function of energy only). Therefore once the selection criteria have been optimized the two main figures of merit in the analysis are the effective geometry factor integrated over the detector and the energy resolution. Both of these quantities will be described in this section.

6.3.1

The effective geometry factor

The effective geometry factor is calculated using a MC simulation of only electrons. Due to the fact that most celestial sources have a power law spectrum, the natural choice is to use logarithmic binning for the energy scale. Thus the MC simulation used for the purpose of studying the geometry factor is produced according to a 1/E spectrum and an isotropic distribution around the instrument. In this way, each energy bin contains the same number of generated events. The effective geometry factor is then calculated in the following way: G ( E) = 2πsr · 6m

2



Npass (E) Noriginal (E)

 (6.3)

Where Npass ( E) is the number of events passing the selection cuts and Noriginal ( E) is the original number of events generated. While the 2πsr · 6m2 term comes from the area and angle over which the events have been generated in the simulation. The effective geometry factor is calculated as a function of true MC energy. The events that are not sent to the ground due to the various conditions of the on-board filters (for example the 250 prescale factor of the diagnostic filter) are part of the selection cuts and are taken into account in the Npass part of the calculation. The total number of events simulated, N, is a number whose value is based upon the specific analysis needs and can be written as: N = N0

Z Emax Emin

E−1 dE

(6.4)

which gives the following solution for the normalization constant:

N0 =

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N log( EEmax ) min

(6.5)

6.3 the cre instrument response functions

When calculating the geometric factor what we are interested in (as stated above) is the number of events, given the E−1 simulated spectrum, that fall in each energy bin, or in other words: Nisim = N0

= N

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log( EEi+i 1 ) log( EEmax ) min

(6.6) (6.7)

where Nisim are the number of simulated events in each ith bin and the interval between Ei and Ei+1 defines the bin width. The above solution holds when using logarithmic binning. If one is interested in using fixed bin width and binning in log (energy), the following solution is needed: Nisim = N

(log( Ei+1 ) − log( Ei )) (log( Emax ) − log( Emin ))

(6.8)

where again Nisim is the number of simulated events in each ith bin and the interval between Ei and Ei+1 defines the bin width. At this point we are now able to correctly calculate equation 6.3 for each bin by:   N(pass,i) 2 Gi = 2πsr · 6m (6.9) Nsim i where Gi is the geometric factor in the ith bin and N(pass,i) are the number of events that pass the selection cuts in the ith bin. In figure 84 the geometric factor for both the le and he selection are shown. The le geometric factor has been multiplied by the DGN prescale factor of 250 for graphical clarity as well as to give an idea of the relative electron efficiencies of the two selections. In the overlap region for the two selections the le geometric factor is larger than that for the he one however this higher efficiency is achieved at the expense of a larger residual hadron contamination. The drop off seen for the he geometric factor for energies lower than ∼ 40 GeV can be explained by the threshold of the high-pass condition of the gamma filter. Essentially this feature reflects the fact that events that deposit less than 20 GeV in the calorimeter can feature a reconstructed energy greater than 20 GeV after the shower leakage corrections have been applied. 6.3.2

Energy reconstruction

The energy reconstruction for the electron analysis is performed using exactly the same algorithm as the standard photon analysis. For EM cascades of several hundreds of GeV a significant fraction of the energy leaks from the back of the calorimeter. The shower imaging capability is therefore crucial in fitting the longitudinal shower profile in order to correct for the energy leakage and estimate the incoming energy with good accuracy. A detailed study, based on extensive Monte Carlo simulation, of this reconstruction has been performed to characterize its performance and to prove that it is adequate for events up to the TeV range.

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Figure 84: Geometric factor for the le and he electron selections. The geometric factor for the le analysis is multiplied by the dgn filter prescale factor (250) for graphical clarity and in order to give an idea of the relative electron efficiencies of the two selections (in reality it is 250 times smaller). In fact the le analysis provides a larger geometric factor between ∼ 40 GeV and 100 GeV which comes at the expense of a larger residual contamination; an effort to merge the two into a unique, optimal selection is ongoing. The drop of the he acceptance for events with reconstructed energy below ∼ 40 GeV is due to the threshold of the high-pass condition of the gamma filter (it reflects the fact that events depositing less than 20 GeV in the calorimeter can feature a reconstructed energy greater than 20 GeV after the shower leakage correction). The full event reconstruction sequence is a complex iterative process (details can be found in [98]). The energy reconstruction algorithm is completed only after TKR tracks are identified and fitted. The best track found provides the direction of the incoming particle and is used as a reference axis for the development of the EM shower. Three different algorithms are applied to estimate the energy correction necessary to account for leakage out the sides and back of the calorimeter and through the internal gaps between the calorimeter modules. (i) A parametric correction, which is based on the barycenter of the shower, covers the entire phase space of the LAT and provides the basic reconstruction method. (ii) A maximum likelihood fit, which is based on the correlations of the overall total energy deposited with the number of hits in the tracker and with the energy seen in the last layer. This method offers a very good energy resolution, but is designed to work only up to 300 GeV. (iii) A fit to the shower profile, which takes into account the longitudinal and transverse development of the shower, is a very effective method for events of several hundreds of GeV and can take into account CAL crystal saturation. The final energy estimate is done, event by event, selecting the best energy method using a CT technique. The CTs are trained with a MC simulation in order to select the

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method that is closest to the true (MC) energy. A second CT analysis estimates the probability of having good energy reconstruction and provides a “knob” to remove poorly reconstructed events at the expense of the effective area. The energy dispersion is evaluated with a MC simulation using a pure isotropic electron flux with a power law with spectral index Γ = −1. For each event the reconstructed energy is divided by the true energy. The resulting distribution peaks at 1 and is asymmetric with a larger tail at low values (figure 90). A first check on this distribution is done evaluating the most probable value by fitting the peak with a log-normal function and verifying that it does not differ significantly from 1 in the whole energy range. This ensures an unbiased response throughout the energy range in question. Figures 85 - 89 illustrate the energy dispersion distributions for energies between 100 MeV and 1 TeV. 6.3.3

Energy resolution

The energy resolution is defined, based on the energy dispersion distribution, as the half width of the smallest energy window containing 68% of the events4 . The 95% containment also provides useful information regarding the low energy tail. The energy resolution, calculated in several bins of true energy, (figure 90 for the le analysis) is less than 20% from 100 MeV and improves to less than 10% from 1 GeV all the way up to 100 GeV where the le analysis is limited by the statistics. For the he analysis (figure 91) the energy resolution is better than 5% at 20 GeV and gets worse with increasing energy, but it is still better than 15% at 1 TeV. Thanks to the wide field of view and the total thickness of the TKR and CAL detectors, candidate electrons for the he analysis traverse, on average, 12.5 radiation lengths while for the le analysis the total radiation lengths transversed on average by the candidate electrons is ∼ 11 radiation lengths. To validate our energy resolution evaluation we used beam test electron data collected with the Calibration Unit (CU) at the CERN SPS and PS [99]. For each beam configuration we produced a simulation that matches the beam conditions (like beam spot and incoming direction). The comparison of the 68% containment measured with electron data and the MC simulation shows an excellent agreement in the phase space covered with the beam test: from 0◦ to 60◦ , from 5 to 280 GeV. The excellent agreement between the beam energy and the reconstructed energy after the leakage correction has been applied is evident in figures 92 and 93. These figures compare the raw energy deposit and the reconstructed energy distributions for several electron beams impacting the LAT CU during the 2006 beam test campaign [99]. 6.4

sources of background

One of the most critical aspects of the spectrum reconstruction is the estimation and subsequent subtraction of the background contamination. This step of the analysis relies on the on-orbit environment simulation already described in detail in section 6.1.1 of this chapter. The procedure for removing these events from the selected data is 4 Corresponding to 2σ in case of a Gaussian distribution.

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MC Energy = 0.10--0.60 GeV = 0.24 GeV

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Figure 85: Energy dispersion distribution for electrons between 0.10 and 3.59 GeV, after the full set of le selection cuts has been applied. These plots are produced using a Monte Carlo sample of electrons with an isotropic angular distribution and a power law energy distribution with spectral index Γ = −1. They are used to determine the 68% and 95% energy resolution values, defined as the half width of the smallest energy window containing the 68% and 95% of the events, respectively (figure 90).

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6000 MC Energy = 1.47--8.80 GeV = 3.59 GeV

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Figure 86: Energy dispersion distribution for electrons between 1.47 and 21.54 GeV, after the full set of le selection cuts has been applied.

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MC Energy = 14.25--49.24 GeV = 26.49 GeV +15.3%

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Figure 87: Energy dispersion distribution for electrons between 14.25 and 316.23 GeV, after the full set of le selection cuts has been applied.

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Figure 88: Energy dispersion distribution for electrons between 128 and 333 GeV, after the full set of he selection cuts has been applied.

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Figure 89: Energy dispersion distribution for electrons between 333 GeV and 1 TeV, after the full set of he selection cuts has been applied.

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6.4 sources of background

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Figure 90: Energy resolution for electrons passing the le selection. The half width of the smallest energy windows containing the 68% and the 95% of the energy dispersion distribution are represented by the solid and dashed lines, respectively.

LAT 95% (HE selection) LAT 68% (HE selection) Beam test data 68% (0°) Beam test MC 68% (0 °) Beam test data 68% (60 °) Beam test MC 68% (60 °)

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Figure 91: Energy resolution for electrons passing the he selection; the half width of the smallest energy windows containing the 68% and the 95% of the energy dispersion distribution are represented by the solid and dashed lines, respectively. The blue and red points correspond to the points obtained from the beam test data (for 0◦ and 60◦ incidence angle and energy up to 282 GeV), along with the corresponding Monte Carlo simulations (specifically tuned for each single beam and detector configuration). The excellent agreement between the beam test data points and the Monte Carlo gives us solid ground for relying in our estimation of the energy resolution up to ∼ 1 TeV.

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Figure 92: Plots of the raw energy (blue) deposited in the calorimeter and the reconstructed energy (red) for beam energies 5, 10, 20 GeV for impact angles of 0◦ (top panel), 30◦ (middle panel) and 60◦ (bottom panel). The nominal beam energy is represented by the vertical dashed line. From these plots it is clear that the leakage correction is more pronounced at small angles and for larger energies. 120

6.4 sources of background

Figure 93: Plots of the raw energy (blue) deposited in the calorimeter and the reconstructed energy (red) for beam energies 50, 100, 282 GeV for impact angles of 0◦ (top panel), 30◦ (middle panel) and 60◦ (bottom panel). The nominal beam energy is represented by the vertical dashed line. From these plots it is clear that the leakage correction is more pronounced at small angles and for larger energies. 121

analysis

split into two separate methods; one for the primary particles (i.e above the geomagnetic cutoff) and one for the secondary particles (i.e at and below the geomagnetic cutoff). For the primaries the background is removed by subtracting the background rate of events from the count rate. The background rate is defined as the rate at which hadron events pass the selection cuts, as a function of energy, divided by the livetime of the MC simulation. The advantage of this method is that it only depends on the hadron model in the MC simulation. The uncertainty in the overall estimation of the background to simply the uncertainty in the hadron flux, which is fairly well known [77, 78]. In the case of the secondary particles the situation is slightly more complicated for several reasons. he proton flux at and below the geomagnetic cutoff is not as well known as that at higher energies, the fluxes below cutoff have strong dependencies with geomagnetic latitude and the effects on the actual shape of the spectrum are not well understood. There is also an uncertainty in the absolute energy scale which can have the effect of systematically shifting the count rate in energy. Now for energies larger than ∼ 20 GeV the overall impact of this uncertainty on the background subtraction is essentially constant in energy. However in the geomagnetic cutoff region where the shape of the count rate changes with energy the impact of this uncertainty can cause large variations in the residual background estimation. The final impact on the background subtraction is better visualized by considering the residual hadron contamination, BackgroundRate( E) Contaminationresidual ( E) = (6.10) CountRate( E) Figure 94 shows the residual contamination calculated using the count rate from the data (in black) and using the count rate from the MC simulation (in red). From this figure it is clear that there are some differences between the model of the CREs in the MC simulation and the data. The largest differences are concentrated in the energy region below 10 GeV while for larger energies the two quantities seem to differ only by a normalization constant. One possible way to verify that this difference is not due to a simple shift in energy, is to plot the count rate from the MC simulation of the events passing the le cuts (shown in red in top panel of figure 95), the same count rate with a rigid shift in energy of 20% (shown in black) together with the background rate. With these count rates it is possible to calculate the residual contamination shown in the bottom panel of figure 95. There are several differences between the two contamination curves (black: simple shift in energy, red: no shift in energy, both cases are based solely on MC) but when concentrating on the behavior below 10 GeV the black curve has a peak which is larger and at lower energies compared to the red curve in the same energy region. This trend is also seen in the residual contamination curves shown in figure 94 hinting at a possible explanation. However the dissimilarity at high energies seen in figure 95 which is not at all present in the contamination calculated using the data confirm that it is not just a simple shift in energy which is causing the differences. It is because of these uncertainties that for the electrons at and below the geomagnetic cutoff the background contamination is subtracted with a different method than for the GCREs. To avoid these differences the contamination is evaluated as the ratio of the hadrons that pass the event selection over all the particles that pass the selection cuts (i.e e− + e+ plus hadrons) based completely on the on-orbit Monte Carlo simulation.

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Figure 94: Difference between contamination calculated as the ratio of hadrons over all species that pass the electron selection (in red) and the contamination calculated as the ratio of background rate over count rate (black). In the top panel is a comparison between the orbital average contamination calculated using only Monte Carlo information and the contamination using the background rate and the flight data counts. The contamination is removed from the sample by multiplying the count rate by the purity as a function of energy, where the purity of the sample of events is taken simply as 1 − contamination. A second source of background that has been evaluated is composed of the celestial γrays (not included in the on-orbit environment model). This contamination is expected to be very low since the event selection requires some signal in the ACD subsystem. In fact, the geometry factor for photons, determined with electron selection cuts, is less than 8% of that for electrons at 1 TeV. The ratio between photon and electron fluxes is negligible throughout the entire energy region in question. The photon flux is found by taking an average of the all-sky intensity measured by Fermi. The overall gamma contamination in the final electron sample is always less than 0.2% and is neglected (figure 96). 6.5

estimation of systematic uncertainties

Given the large exposure factor of the LAT, the statistical errors associated with the electron spectrum are essentially negligible. Therefore, the estimation of the systematic uncertainties is a crucial aspect of the data analysis. The main contribution to the systematic uncertainties originate from the fact that the Monte Carlo simulation does not perfectly reproduce the topological variables used for the event selection. This in turn leads to an imperfect knowledge of the effective geometry factor as a function of energy. Consequently it is of fundamental importance to have a simulation of the detector which is as complete as possible and to verify its accuracy by means of

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Figure 95: Top panel: Counts/bin/MeV passing the electron selection (red), hadrons (blue) and the same counts with a shift in energy (black) all from the Monte Carlo simulation. Bottom panel: The contamination based on the counts with a simple shift in energy (shown in black) compared to the one without any shift (in red). Below ∼ 10 GeV the black curve has a larger peak which is shifted towards lower energies compared to the red curve. This trend is similar to the effect seen below 10 GeV in figure 94. However for energies greater than 10 GeV the contamination based on the counts shifted in energy does not resemble the one based on the data. From this simple exercise (based completely on the MC simulation) it is possible to conclude that the deviations found between the two curves in figure 94 cannot be explained only by a simple shift in energy.

cross-checks with real data. To first order, the relative uncertainty in the geometry factor at any given energy translates into an equal relative uncertainty in the measured flux value at that energy. However, any uncertainty on the response of the detector

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6.5 estimation of systematic uncertainties

Figure 96: Estimated gamma contamination (as a function of energy) in the data sample used for the cosmic-ray electron spectrum, using the Fermi all-sky gamma intensity. The values are negligible over the vast majority of the energy range of interest and reach a maximum value of the order of 0.2% around 1 TeV (not subtracted from the event sample). to background events can also potentially affect the flux measurement through the subtraction of the hadron contamination. This effect is accounted for by weighing the contamination of the sample by the uncertainty prior to the subtraction and therefore is relatively easier to keep under control, provided the contamination is reasonably low. It is important to stress that these two effects are not independent since to lower the contamination requires applying more stringent selection cuts, which in turn can induce larger systematic uncertainties on the response functions. The optimal selection is a trade off between the two. In the left panel of figure 97 the distribution of the total ACD energy for energies between 5 and 30 GeV is shown for both the electron (red) and hadron (blue) populations after all the other selection cuts have been applied. The vertical line represents the chosen cut value for the le event selection. The red dashed line is the integral function of the electron distribution, normalized to unity. It therefore represents the electron efficiency, relative to the events passing all the other cuts, when an additional cut on the total ACD energy is applied. The change in the efficiency, as the cut value is moved, translates directly into an equal change of the effective geometry factor in the energy bin under study. The blue dashed line represents the residual hadron contamination as a function of the cut value, based on the electron and hadron histograms in the figure. These two integral curves are the basic ingredients used in the preliminary phase of the analysis to assess the optimal cuts values. The right panel of figure 97 shows the comparison between flight data and the MC simulation for the same quantity. The MC distribution is shown as the sum of the electron and hadron components. Again, the distribution is shown after all the other cuts of the selection have been applied. Any differences found for the two distributions can give rise to systematic uncertainties in

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Figure 97: Monte Carlo simulation distribution of the total ACD energy per event for electrons (red histogram) and hadrons (blue histogram) in the energy bin between 5 and 30 GeV (left panel). All the other cuts of the event selection have been applied. The red and blue dashed lines represent the electron efficiency and the residual hadron contamination, respectively, for any given cut value on this variable. The vertical dashed line corresponds to the optimal cut value adopted for this analysis. Right panel shows the distribution of the total ACD energy per event for the data (in black) and the Monte Carlo simulation (in gray) for the same energy bin. The gray histogram is the sum of the electron and hadron histograms of that figure.

the effective geometry factor and in turn to the measured flux. In order to estimate the amount of uncertainty introduced by each variable in the event selection it is first necessary to perform a scan on several cut values around the optimal one for a given variable (while keeping the other selection cuts fixed). Having done this, it is possible to quantify the changes in the flux level induced by the changes in the cut value. This procedure, illustrated in figure 98, is sensitive to differential discrepancies around the cut values in the detector response to both signal and background and maps them to the actual measured spectrum. There are several important points to note from this figure. First of all the cut value in red corresponds to the actual value used for the event selection. The points to the right of this cut value correspond to high values of the geometry factor. The fact that they are all close to each other implies that the these cut values have an efficiency close to 1 (i.e do not remove any electrons). While the points to the left of the optimal value all correspond to smaller geometry factors, and thus smaller cut efficiency. The slope of the fit of the scatter plot with a first order polynomial is directly related to the agreement between data and the MC simulation for a particular selection variable in a given energy bin. Of course the slope by itself is not sufficient to estimate the magnitude of the systematic effects connected with the variable because the overall effect also depends on the cut value chosen. What can be done is to evaluate the fit function at the position of the optimal geometry factor and at the position of the largest geometry factor (i.e in correspondence to the last point on the right of the optimal value). The flux variation induced by the cut on the variable in question can be found by taking the difference between these two points (denoted as ∆sys in figure 98). Another important piece of information that can be taken from this figure is that the geometry factor evaluated with the left most cut is roughly half the size of the geometry factor evaluated with the right most cut. While the flux value

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Figure 98: Dependence of the measured flux on the cut value for the same energy bin and variable shown in figure 97. On the x-axis the effective geometry factor for each cut in the scan is reported. Each data point is labeled with the corresponding cut value (the one used for the chosen event selection is shown in red). For this particular case a tighter cut (i.e. data points on the left, corresponding to smaller geometry factors) translates into a systematically higher flux level. These cuts provide a lever arm for the linear fit but are unreasonable for the actual selection as can be seen from figure 97 where cutting at a value of ∼ 6 MeV would remove roughly half of the electron population while not having a significant impact of the reduction of the contamination.

changes at most by 10% between these two cuts. This is an indication of the very good data MC agreement, confirmed by the right panel of figure 97 for the ACD variable. Therefore, the basic idea is that by making a cut harsher on any of the variables used for the event selection causes the effective geometry factor to decrease and the residual hadron contamination to decrease as well (or vice versa). If the agreement between data and MC simulation were perfect the measured flux level would not depend on the cut value. Unfortunately, there are some differences between data and the MC simulation and thus the scatter plot of the measured flux (for each energy bin) versus the geometry factor for different cuts values is not constant (as shown in figure 98 for the total ACD energy). Throughout this study it was found that a straight line provides a reasonable description of the dependence of the flux as a function of the geometry factor in all the cases encountered. This analysis was performed separately for each selection variable in each energy bin covering the entire energy range in question. The positive (negative) contributions, corresponding to the variables for which the slope of the fit is positive (negative), are added in quadrature separately to provide an asymmetric error estimate. It is important to stress here that the contributions (both negative and positive) which the selection variables are found to have on the spectrum are an estimate of the effect

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(EGF-Ghost / EGF-NoGhost) ratio

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Figure 99: The ratio of the effective geometry factor calculated using the MC with the ghost events to the standard effective geometry factor (i.e. using the MC without the ghost events). From this ratio it is possible to estimate the effect which the ghost events have on the effective geometry factor. This effect translates directly into the systematic uncertainty on the measured electron flux.

of the systematic uncertainties. They are not errors in the statistical sense. Therefore the choice to add in quadrature the positive contributions, and separately the negative contributions was found to be a reasonable prescription for the estimate of the effect due to the systematic errors. The effect of ghost events has shown a strong dependence on the orbital position of the detector, with an increasing trend for larger McIlwain L. This effect was discussed in chapter 1.4.4 for the photon analysis, however there is reason to believe that the ghost events can also be problematic for the electron analysis. Therefore, it is important to study how these events can impact the measurement of the flux of the primary electrons while the LAT is in high McIlwain L regions of the orbit. To perform this study a special Monte Carlo simulation was made including the ghost events. From this simulation it was possible to estimate the amount of uncertainty introduced in the calculation of the effective geometry factor due to these events. From figure 99 is the ratio of the effective geometry factor calculated using the MC with the ghost events to the standard effective geometry factor (i.e. using the MC without the ghost events). From this study it was found that, similarly to the photon analysis, the overall effect due to the ghost events is a function of energy and ranges from ∼ 15% at 6 GeV to ∼ 5% at 100 GeV. For the time being this study was performed only for the GCRE measurement and still needs to be completed for the electrons with energies below the local geomagnetic cutoff.

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Another source of systematic uncertainties derives from the imperfect knowledge of the absolute background flux, which is dominated by the absolute proton flux. Incorporating this into the analysis is relatively easy for the primary spectrum, where the proton flux is well measured. The estimated uncertainty of the absolute proton flux (above geomagnetic cutoff) is ∼ 10%, therefore to obtain the amount of uncertainty introduced by the residual background this value is multiplied by the contamination remaining in the sample of events passing the electron selection. This number is then added in quadrature with the other sources of systematic uncertainties. However, around and below the geomagnetic cutoff, where the relative abundance of electrons and positrons is a complicated function of energy and the overall proton flux is strongly dependent on the geomagnetic latitude and not trivial to model as already discussed. Given these factors, the study of the systematic uncertainties for the secondary CREs is still work a in progress. 6.6

galactic cosmic-ray electron spectrum

The sample of events passing the gamma filter are the main source of GCR electrons given that these are all those events with raw energy > 20 GeV. For these energies the effects of the Earth’s magnetic field on the incoming GCR electron flux are negligible. Therefore it is possible to reconstruct the spectrum for energies > 20 GeV using simply this sample. However, in order to extend the energy range of the measured spectrum (down to lower energies) it is necessary to use the events sampled by the dgn filter. Unfortunately this extension down to energies of roughly 6 GeV is not a straightforward task and requires to acknowledge the fact that the rigidity cutoff varies as a function of orbital position. Consequently the spectrum must be measured in various bins of geomagnetic position. The rigidity cutoff range for the Fermi orbit spans from roughly 6 to 15 GeV, and thus essentially fixes the lowest energy that Fermi can measure the GCR electron spectrum. As already mentioned in chapter 4, the shielding effect of the Earth’s magnetic field is a function of orbital position. In particular, the rigidity cutoff decreases with increasing values of McIlwain L. Therefore to lower the energy threshold of the GCREs measured by Fermi, it is necessary to sample all those events collected when the detector was located at large values of McIlwain L. Figure 100 illustrates the distribution of McIlwain L and the corresponding vertical rigidities for the Fermi orbit, based on the IGRF model [87]. It important to stress here that the vertical cutoff rigidity distribution shown in figure 100 is simply an illustration and we do not depend on this model in any way for this analysis. Each McIlwain L bin has an associated rigidity cutoff value. It is possible to measure this value by considering that the shape of the primary spectrum around the geomagnetic rigidity cutoff can be parametrized as5 : f c ( E) '

1 1 + ( E/Ec )−6

(6.11)

5 This equation comes from the background simulation code used by the Fermi collaboration and is an eyeball fitting function to represent the AMS01 proton data.

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Therefore the full spectrum can be fitted with a function of the form: c p E − Γp dN = c s E − Γs + dE 1 + ( E/Ec )−6

(6.12)

Where the subscript s stands for secondary and represents the albedo population of electrons while the subscript p stands for primary and represents the primary component of the spectra. Γ are the spectral indexes. The value of Ec , obtained by the fit is an estimation of the rigidity cutoff. The fit for each of the McIlwain L bins is shown in figures 101 and 102.

Figure 100: Map of McIlwain L values for the Fermi orbit. Overlaid in contours are the corresponding values for vertical rigidity cutoff. These values were calculated using the 10th generation IGRF model. It is important to note that the model is not valid inside the South Atlantic Anomaly (SAA) region, illustrated by the dark gray polygon in this figure. Due to the complexity of particle orbits in the Earth’s magnetosphere, the geomagnetic cut-off is not sharp but rather a smooth transition and therefore it is necessary to include a multiplicative factor, X, to the value of Ec obtained by the fit. This factor serves as a sort of padding, and its value is driven by the need to balance between two requirements, namely to measure the lowest possible Galactic CRE energy while at the same time making sure that the measured flux value is not affected by the shielding due to the Earth’s magnetic field. The value of X which satisfies these requirements was chosen by performing a scan on several values of X around unity. Having done this, it is possible to quantify the changes in the flux level induced by the value of X used to extend the spectrum. An example of such a scan is shown in figure 103 for five values of X. The importance of the padding value used for the spectrum extension is better visualized by fixing an energy and considering the profile of the spectra in the scan. An example of such a profile can be found in figure 104, which depicts the profile of the flux multiplied by the energy cubed for several different values of X for measured energy of 8.38 GeV.

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Figure 101: Measured electron flux in several McIlwain L bins. Top plot corresponds to the 1.0 1.42 L>1.28 L>1.14 L>1.00→

LE selection HE selection(Abdo, et al., 2009)

102 10

102

103

Energy (GeV)

Figure 105: Illustration of the reconstruction technique used to measure the the primary cosmic-ray electron spectrum down the lowest accessible energy for the Fermi orbit. The GCRE flux is multiplied by the energy cubed. The blue squares are obtained via the le analysis and the red triangles are from the he analysis. The solid lines depict the systematic uncertainties and the vertical dashed lines show from which McIlwain L region of the orbit the flux was measured.

6.6.1

Estimate of the uncertainty on the absolute energy scale

From the 2006 beam test campaign the uncertainty on the absolute energy scale was estimated to be +5% to −10%. To perform an in flight validation of this energy offset it is necessary to find an astronomical source with a spectral feature whose energy position is well known. Having found such a source, the energy scale can be tested by comparing the position of the spectral feature measured by the LAT with the known position. The ratio of these two measurements provides an estimate for the offset in the energy scale of the detector. A potential candidate of such a feature is the rigidity cutoff in the electron spectrum. In fact, by using the equation 6.12 to fit the spectrum it is possible to obtain the value for the rigidity cutoff, as has already been discussed in the previous section. The reference value for the rigidity cutoff is found by performing the same procedure on the electron spectrum in the MC. Comparing the rigidity cutoff

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Energy (GeV) 6.8–7.3 7.3–7.8 7.8–8.4 8.4–9.0 9.0–9.7 9.7–10.6 10.6–11.5 11.5–12.4 12.4–13.5 13.5–14.6 14.6–15.8 15.8–17.2 17.2–18.6 18.6–20.2 20.2–21.9 21.9–23.8 23.8–25.8 25.8–28.0 28.0–30.4 30.4–32.9 32.9–35.7 35.7–38.8 38.8–43.1 43.1–48.0 48.0–53.7 53.7–60.4 60.4–68.2 68.2–77.4

Counts 109 532 1425 2777 3885 5648 5300 4409 6742 5880 9857 8527 7189 6102 9361 7883 6639 5674 4781 4234 3411 2899 2948 2325 1955 1527 1172 901

Residual contamination 0.11 0.07 0.09 0.11 0.08 0.09 0.10 0.08 0.08 0.07 0.08 0.09 0.07 0.10 0.10 0.10 0.10 0.12 0.10 0.11 0.13 0.13 0.14 0.16 0.17 0.14 0.15 0.18

E 3 · JE (GeV2 s−1 m−2 sr−1 ) 27 188 ± 26+ −14 27 189 ± 11+ −13 24 180 ± 6.8+ −12 +23 172 ± 5.2−12 23 182 ± 4.5+ −12 +22 175 ± 3.8−11 21 174 ± 3.9+ −11 +20 171 ± 4.0−10 18 163 ± 3.3+ −9 +19 171 ± 3.5−9 17 160 ± 2.9+ −9 16 162 ± 3.1+ −9 +15 161 ± 3.1−8 15 158 ± 3.5+ −8 +14 156 ± 3.0−8 14 157 ± 3.2+ −7 +13 159 ± 3.4−7 12 155 ± 3.6+ −8 12 156 ± 3.7+ −7 +12 165 ± 4.2−7 11 155 ± 4.5+ −7 +10 153 ± 4.8−7 9.4 149.9 ± 4.7+ −6.1 +8.7 143.1 ± 5.2−6.9 8.5 147.8 ± 5.9+ −8.4 7.0 145.7 ± 6.0+ −7.2 +7.1 140.8 ± 6.8−6.9 8.0 135.4 ± 8.0+ −5.8

McIlwain L> 1.72 1.67 1.6 1.56 1.51 1.46 1.42 1.42 1.28 1.28 1.14 1.14 1.14 1.14 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Table 4: Energy bin width, number of counts, residual hadron contamination, E3 · JE as well as the McIlwain L interval from which the data was collected for the GCRE spectrum shown in figure 105. The statistical errors for the E3 · JE are followed by the positive and negative systematic errors, shown in superscript and subscript respectively.

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E c (GeV)

analysis

20 Data Mc

15

14.9/L2

10

5

1.1

1.2

1.3

1.4

1.5

1.6

McIlwain L Figure 106: Rigidity cutoff values from data (black points) and MC (red points) for five different McIlwain L intervals. The value for the rigidity cutoff was obtained by fitting the spectrum with equation 6.12 for both the data and the MC. The red curve is the value of the rigidity cutoff calculated via 14.9/L2 , using the average value of McIlwain L for each interval.

position in energy between data and the MC provides an opportunity to validate the +5% to −10% uncertainty on the absolute energy scale. In figure 106 the rigidity cutoff values obtained by fitting the data (black points) and the MC (red points) electron spectrum versus the McIlwain L interval are shown. The red line in this figure is the expected rigidity cutoff value given the relation Ec = 14.9/L2 from [88]. This relation holds only for the vertical rigidity cutoff and is intended to serve as a visual guide in the figure. In fact, the above relation is not used in anyway for this analysis. The ratio of data to MC rigidity values as a function of McIlwain L is shown in figure 107. The values of the ratio shown in figure 107 are reported in table 5. The weighted mean is obtained by fitting the points in figure 107 with a constant, represented by the dot-dashed line. From this exercise the rigidity cutoff value measured by the LAT is 6.63 ± 0.44% higher than the MC. There are, however, some caveats to this approach. For example, in the on-orbit MC simulation the value of the rigidity cutoff is not zenith dependent. In other words, electrons arriving from all angles are treated as if they were arriving from the zenith. This approximation can change the value of the rigidity cutoff with respect to the zenith averaged one. Therefore the comparison between the rigidity cutoff from the data and the MC (which does not include the zenith dependence of the incoming electron flux) can introduce a bias. In order to estimate the amount of bias, it would be necessary to

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DataE c / McE c Ratio

6.6 galactic cosmic-ray electron spectrum

1.4 1.2 1 0.8 Mean = 6.63 ± 0.44 %

0.6 1.1

1.2

1.3

1.4

1.5

1.6

McIlwain L Figure 107: Data to MC ratio of the rigidity cutoff values shown in figure 106. The dot dashed line is a fit with a constant. The fit parameter is equivalent to the weighted mean of the points. Its value is 6.63 ± 0.44%, as reported in the figure.

make use of numerical methods to trace particle trajectories in the Earth’s magnetic field [89]. Using this simulation provides a more accurate representation of the shape of the spectrum and consequently a value for the rigidity cutoff closer to the zenith averaged one. It is important to stress that the value obtained from this exercise is not the uncertainty on the absolute energy scale for the LAT. However, this work shows that in principle the rigidity cutoff in the electron spectrum can be used for this purpose after the above caveats have been addressed.

McIlwain L interval 1.00 - 1.14 1.14 - 1.28 1.28 - 1.42 1.42 - 1.56 1.56 - 1.7

(Data Ec ) / (Mc Ec ) Ratio 1.07 ± 0.04 1.01 ± 0.02 1.10 ± 0.04 1.15 ± 0.04 1.14 ± 0.04

Ratio - 1 (%) 7.28 ± 3.68 1.34 ± 2.12 9.88 ± 3.84 14.82 ± 3.94 14.05 ± 4.41

Table 5: The ratio between data Ec and MC Ec for each McIlwain L interval shown in figure 107.

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Figure 108: The variable Earth azimuth gives the reconstructed angle from which the event originated. By selecting the two quadrants in the following intervals FT1EarthAzimuth >= 65 and FT1EarthAzimuth = 245 and FT1EarthAzimuth 20 GeV there are several interesting aspects of the measurements reported in figure 112. For example, the energy region between 20 − 80 GeV where the two Fermi CRE analyses overlap, provides an excellent cross check for the two independent event selections. The agreement was tested using a minimum χ2 fit using only the statistical errors. The two spectra are well described by a power law and statistically consistent even without taking into consideration the systematic uncertainties. In particular the le spectral index is 3.088 ± 0.023 in this region, while the he spectral index is 3.095 ± 0.001. The ATIC points are consistent with the Fermi he data up to roughly 200 GeV. However, above this energy ATIC reports a prominent spectral feature which is not

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E 3⋅ J(E) (m-2 s-1 sr -1 GeV 2)

6.6 galactic cosmic-ray electron spectrum

∆E/E = -15%

+15%

∆E/E = -10% +5%

102 AMS (Aguillar et al., 2002) HEAT (Du Vernois et al., 2001) Fermi low-energy Fermi high-energy ATIC (Chang et al., 2008) H.E.S.S. (Aharonian et al., 2009) H.E.S.S. (Aharonian et al., 2008)

10 1

10

102

103

Energy (GeV)

Figure 112: The GCRE energy spectrum multiplied by E3 from 1 GeV to 5 TeV. The Fermi points (from 7 GeV to 1 TeV) are shown in blue for the le analysis and in red for the he analysis. The systematic uncertainties for both the Fermi analyses are represented by the solid lines (again blue for the le analysis and red for the he ). The double arrow in the upper left hand corner illustrates the estimated uncertainty on the absolute energy scale for the Fermi points for both the analyses. The 2008 HESS points [48] are represented by the gray diamonds, while the 2009 ones [49] are the gray squares. The HESS systematic errors are shown by the gray solid lines while the uncertainty on the absolute energy scale is shown by the gray double arrow. AMS [75] points are the black circles, the HEAT [104] are the gray triangles and ATIC [94] are the black stars.

present in the Fermi CRE spectrum. The HESS telescope measured the CRE spectrum from 340 GeV to 4.5 TeV and provided information regarding both the systematic errors and the absolute energy scale (shown in gray in figure 112). In [49] the HESS collaboration report that the deviation between their data and ATIC in the energy range between 340 − 650 GeV is minimal at the 20% confidence level7 when applying a +10% shift in energy of the HESS points. However, they also claim that even though such a shift is within the uncertainty of their energy scale, it would cause an overshoot of the HESS data when compared to balloon experiments (including ATIC) above 800 GeV [49]. The Fermi data from 340 GeV to 1 TeV are consistent within the systematic errors with the HESS measurement in the same energy range. Around 70 − 100 GeV the Fermi spectrum suggests some spectral hardening. A simple test to investigate the significance of this potential feature is to perform a minimum χ2 7 assuming Gaussian errors for the systematic uncertainty which dominate the HESS measurement.

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fit with statistical and systematic errors added in quadrature. Given that the systematic errors dominate, this approach is equivalent to considering only the systematic errors in the fit. The systematic errors are to some extent bin to bin correlated and therefore the χ2 statistics does not apply. Therefore, if the resulting χ2 from the fit of the full spectrum is statistically consistent with a power law then it is not possible to make any claim on the significance of a potential feature with the current systematic errors. This is indeed the case, as shown by the residuals from the fit in figure 113. From the fit, the spectral index is Γ = 3.077 ± 0.008 (χ2 = 16.65 with 40 degrees of freedom).

Residuals (Data-Func)/Func

graphTotalError_7_1000: 200*x^(-3.077 ± 0.008) (7 GeV - 1000 GeV)

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5

10

102

3

10 Energy (GeV)

Figure 113: Residuals from the minimum χ2 fit of the Fermi GCRE spectrum from 7 to 1 TeV. The error bars have been calculated as the sum in quadrature of the statistical and systematic errors. The spectral index obtained from the fit is 3.077 ± 0.008.

The pre-Fermi diffusive model [79] is shown in figure 114 as the blue dashed line, together with the GCR electron spectrum multiplied by the energy cubed measured by several experiments including Fermi. The diffusive model uses a diffusion coefficient, δ = 0.33 with a source injection spectrum index Γ = 2.54 for energies greater than 4 GeV. When comparing the data with this model it is clear that some reconsideration may be required to better describe the measurements. One possible choice is to take the source injection spectrum index to be Γ ≈ 2.5 above ∼ 4 GeV (maintaining the diffusion coefficient spectral index δ = 0.33 and an Alfvén velocity of 30 km/s) to fit the high energy part of the Fermi-LAT data and a cutoff at ∼ 2 TeV to agree with the HESS data [48]. This situation provides a reasonable fit for energies greater than ∼ 100 GeV of the spectrum, however the low energy data is not well reproduced with this single power law injection spectrum index. To obtain an agreement with the Fermi-LAT data at low energy requires a separate injection spectra, namely α ∼ 1.5 − 2.0 below ∼ 4 GeV and a modulation parameter in the range Φ = 400 − 500 MV. An example of such a calculation using the GALPROP model [79] is shown in figure 115. Another possible

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E 3⋅ J(E) (m-2 s-1 sr -1 GeV 2)

6.6 galactic cosmic-ray electron spectrum

∆E/E = -15%

+15%

∆E/E = -10% +5%

102 AMS (Aguillar et al., 2002) HEAT (Du Vernois et al., 2001) Fermi low-energy Fermi (high-energy) ATIC (Chang et al., 2008) H.E.S.S. (Aharonian et al., 2009) H.E.S.S. (Aharonian et al., 2008) Pre-Fermi diffusive model

10 1

10

102

103

Energy (GeV)

Figure 114: The GCRE energy spectrum multiplied by E3 from 1 GeV to 5 TeV. The Fermi points (from 7 GeV to 1 TeV) are shown in blue for the le analysis and in red for the he analysis, same as in figure 112. The dashed blue line shows the purely diffusive model based on pre-Fermi data [79] normalized to fit the Fermi data at 100 GeV. In this model the diffusion coefficient is taken to be 0.33 and the source injection spectrum is taken to have an index of 2.54 for energies greater than 4 GeV.

scenario is that proposed by [109]. In this work the energy dependence of the diffusion coefficient, δ is taken to have a value of 0.46 with Alfvén velocity v A = 15 km/s8 . With this new diffusion setup a smoother break in the injection spectrum is required, namely Γ = 2.0 for E < 4 GeV and Γ = 2.43 for E > 4 GeV, to fit the data. The resulting fit to the electron spectrum is similar to that shown in figure 115. It is important to note that the force-field treatment of the solar modulation9 , used in the GALPROP model [79] is very approximate and does not take into account the configuration of the heliospheric magnetic field and drift effects. These effects can lead to the charge-sign dependencies of the solar modulation. A more complete analysis of the low-energy data would require the use of more realistic models for heliospheric propagation that include anisotropic diffusion and drift effects. This type of treatment is still work in progress. Some problems arise when interpreting the GCR electron spectrum in terms of the conventional models when considering the anomalous rise in the positron fraction measurement made by the PAMELA experiment (figure 111). Their data show that for energies below ∼ 10 GeV the positron fraction is about 5% and in agreement with 8 This choice is closer to the Kraichnan type spectrum (δ = 0.5), as opposed to the Kolmogorov value of 0.33 used in the previous example 9 In the force-field approximation [81], the solar modulation is described by the parameter, Φ which depends on the solar wind speed and the diffusion coefficient.

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the predictions from diffusive models. However for energies greater than 10 GeV, they report a rise which reaches values larger than 10% for E = 100 GeV, in contrast with the predictions. Such a behavior has been interpreted as an indication of pulsar or dark matter contributions to the cosmic-ray electron spectrum [65].

Figure 115: The e− + e+ spectrum computed with GALPROP compared with Fermi-LAT and other experimental data. Red points are from Fermi, the points below 20 GeV are from the le analysis while those for E> 20 GeV are from the he analysis. This model (represented by the blue dashed line) adopts an injection spectral index Γ = 2.5 for E > 4 GeV and Γ = 1.6 for E < 4 GeV and a steepening Γ = 4 above 2 TeV. The blue dotted line on the other hand shows the positron spectrum only. The solar modulation was treated using the force-field approximation with Φ = 450 MV. The continuous blue line shows the modulated spectrum. The red lines represent the secondary positron spectrum before (dashed) and after (solid) modulation while the orange lines represent the secondary electron spectrum, again before (dashed) and after (solid) modulation. The modulation was calculated using the formalism from [79]. In order for the Fermi LAT data to agree with both the electron + positron spectrum above 1 TeV reported by HESS [48] and the positron fraction reported by PAMELA [97], a contribution from additional source(s) may become necessary. Such scenarios have been discussed in many recent papers ([65] and references therein). For example, a combination of a steeper injection spectrum for primary electrons and an additional leptonic component at high energies. This condition provides a better fit to the Fermi LAT spectrum over the entire energy range and is shown in figure 116).

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6.6 galactic cosmic-ray electron spectrum

Figure 116: The e− + e+ spectrum (solid line) computed with the conventional GALPROP model [65] but with a different injection spectrum, namely an injection index Γ = 1.6/2.7 below/above 4 GeV (dotted line). An additional component with an injection index Γ = 1.5 and exponential cut-off is shown by the dashed line. Fermi-LAT data points are represented by the red filled circles, the points below 20 GeV are from the le analysis while those for E> 20 GeV are from the he analysis.

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6.7

albedo electron spectrum

In the on-orbit background model used by the Fermi Collaboration the albedo positrons and electrons are modeled separately. Because these particles are affected by the local magnetic field they must be simulated as a function of geomagnetic position. The albedo population is described by two components, re-entrant and splash, both of which represent the particles that are produced largely by incident protons interacting with the Earth’s atmosphere at large angles. The re-entrant component corresponds to the splash particles that have propagated back to the top of the atmosphere by spiraling along the magnetic field lines from the conjugate magnetic field location in the opposite hemisphere. In the current model both the re-entrant and splash populations of electrons an positrons are simulated as a function of latitude with both components taken to be equal and isotropic. No local zenith and azimuthal angular dependencies were considered and no east-west effects have been simulated. After one year of operations it is possible to use the data collected by Fermi to help update our model of the electron and positron albedo as well as the GCRE components. Though Fermi cannot distinguish the charges of the two particles, it is possible to combine our data with those from other experiments such as PAMELA and AMS (that have a magnet on-board) to maximize the amount of information from these measurements. An update of the on-orbit simulation can help to improve our understanding of the geographic (and geomagnetic) variations in the charged particle environment over the Fermi orbit. Having the most accurate MC simulation also aids in the background rejection for both the electron and photon analysis. Given that the electron albedo model does not include any variations in azimuth or zenith, the first natural step in the process of updating the model is to study how the candidate electrons (below the geomagnetic cutoff) vary as a function of these quantities. Comparing the existing model with the new data binned in geomagnetic latitude in a good place to start. In figures 117 - 120 the orbital averaged CRE flux binned in 0.1 geomagnetic latitude,λ, intervals is shown together with the flux from the MC simulation as well as three months of PAMELA data from mid 2006 [110]. For λ < 0.4 the measured flux from Fermi is always smaller than the flux from the MC simulation, however for λ > 0.4 the two fluxes intercept at around 1 GeV and the flux measured from the data shows an increasing trend when compared to the simulation. PAMELA is in an elliptical orbit and its altitude varies from 350 and 610 km„ whereas Fermi is at essentially constant altitude of 565 km. Differences in orbital altitude, the different solid angle of the observations, time variations of the flux and/or systematic errors in the measurements could be the cause of the differences between the Fermi and PAMELA fluxes. Nevertheless, for the λ intervals less than 0.5 the fluxes measured by Fermi and by PAMELA are in reasonable agreement and the position of the geomagnetic cutoff are in agreement throughout the λ intervals. The geomagnetic latitudes at which PAMELA and Fermi spends their time are shown in 121. The Earth’s magnetic field is greatest near the geomagnetic equator and it is reasonable to expect that as a consequence the albedo population would have a larger concentration in this region where it is more difficult for these particles to escape. This effect can be seen by mapping the count rate of events which pass the le selection

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6.7 albedo electron spectrum

Figure 117: Orbital averaged geomagnetic latitude, λ, binned spectra, data (black) monte carlo (red) and PAMELA (blue). The latitude interval corresponds to 0.0 < λ < 0.1 for the left panel and 0.1 < λ < 0.2 for the right panel.

Figure 118: Orbital averaged geomagnetic latitude, λ, binned spectra, data (black) monte carlo (red) and PAMELA (blue). The latitude interval corresponds to 0.2 < λ < 0.3 for the left panel and 0.3 < λ < 0.4 for the right panel.

Figure 119: Orbital averaged geomagnetic latitude, λ, binned spectra, data (black) monte carlo (red) and PAMELA (blue). The latitude interval corresponds to 0.4 < λ < 0.5 for the left panel and 0.5 < λ < 0.6 for the right panel.

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Figure 120: Orbital averaged geomagnetic latitude, λ, binned spectra, data (black) monte carlo (red) and PAMELA (blue). The latitude interval corresponds to 0.6 < λ < 0.7.

Figure 121: Fraction of time Fermi and PAMELA spend in each geomagnetic latitude interval. PAMELA is in an elliptical orbit at an altitude between 350 and 610 Km which explains the differences in the time spent in each lambda interval with respect to Fermi.

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6.7 albedo electron spectrum

Figure 122: Distribution of the candidate electrons passing the le selection with measured energy 300 < E < 800 MeV mapped over the globe. These are count rates and not actual fluxes. There is a clear concentration of the counts in the geomagnetic equator region. The contour lines represent the values of λ calculated using the 10th IGRF simulation. The dark region in the southern hemisphere represents the South Atlantic Anomaly (SAA) where the LAT does not take any data. criteria and have reconstructed energies less than ∼ 800 MeV, is shown in figure 122. From this map it is immediately clear that the greatest count rate comes from the geomagnetic equator region, i.e. for values of λ < 0.2. The contour lines shown on the map represent the values for λ from the 10th IGRF simulation. The next set of measurements important for the background model update are the electrons fluxes binned in azimuth, i.e. north, south, east and west. These fluxes are shown in figures 123 and 124 where the data is in black and the MC simulation is in red. The fluxes from the data are on average smaller than the simulation and for the east and west bins the fluxes intercept around 1 GeV similarly to what was seen for the latitude bins. In the north and south bins on the other hand, the shape of the spectra from the data is harder for energies < 500 MeV with a gradual softening with increasing energy. The spectral index from the MC simulation, for those same bins does not show any evident energy dependence. With the aid of the measurements from experiments which have the capability of separating the charges of the electrons and positrons, it would be possible to estimate the flux of the albedo positrons and electrons separately for the Fermi orbit. The last set of plots that are necessary for the background model update are the CRE fluxes binned in local zenith intervals. The correct measurement of these fluxes is complicated by the fact that the LAT operates in survey mode and therefore the angle between the reconstructed arrival direction of the event and the local zenith is continuously changing throughout the orbit. Thus it is necessary to calculate the effective area as a function of energy and angle and also to have an exposure map for each zenith bin. This analysis is still work in progress.

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Figure 123: Orbital averaged azimuth binned spectra. Right panel illustrates the electron spectra from the north and the left panel shows the electron spectra from the south. The Monte Carlo simulation is in red while the data is in black.

Figure 124: Orbital averaged azimuth binned spectra. Right panel illustrates the electron spectra from the east and the left panel shows the electron spectra from the west. The Monte Carlo simulation is in red while the data is in black.

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6.7 albedo electron spectrum

The systematic uncertainties for energies below the local geomagnetic cutoff have not yet been studied; therefore only the statistical errors are shown in the figures. However, given the results from the study of the systematic uncertainties due to the ghost events for the GCRE spectrum, it is realistic to expect the effect to be at least of the same order (i.e. ∼ 15%) if not greater.

153

CONCLUSIONS

The Fermi observatory was successfully launched on the 11th of June 2008 and began its first year sky survey on August 11. During this first year of operations, the Fermi Large Area Telescope (LAT) observed a large number of sources; including active galaxies, pulsars, gamma ray burst (GRB), and supernova remnants. A few of the major highlights from this sky survey are the detection of 40 new high confidence pulsars, bringing the total number of known gamma ray pulsars from 6 to 46 in just the first six months of operations. These include 16 discovered in blind searches and 8 millisecond pulsars [32]. In just the first three months, the Fermi LAT detected 132 bright sources at |b| > 10◦ with significance greater than 10σ [26]. From these observations it was found that the average GeV spectra of BL Lacertae (BL Lacs) objects are significantly harder than the spectra of Flat Spectrum Radio Quasars (FSRQ). The photon power law index distribution is roughly symmetric and centered at γ = 2.25, similar to what was observed by EGRET [112]. However, Fermi was able to confirm for the first time the existence of two spectrally distinct populations of blazars [26]. It has been an exciting year for GRB physics as well. The observed rate of GRBs with the Fermi LAT is about one per month. High energy emission has been observed from 10 GRBs in the first year of operations. The Fermi GBM detected all of these bursts at lower energies and six of them triggered follow up observations within 24 hours with the Swift satellite [111]. For half of these bursts if was possible to obtain their redshifts based on optical follow up observations. The large range of photon energies, distances and timescales of some of these bursts allow an experimental check of the assumption that all photons travel at the same speed in vacuum. For example, with the short burst GRB090510 with a redshift of 0.9, a ∼ 31 GeV photon was detected 0.829 seconds after the burst trigger. This burst made it possible to place the most stringent constraint on the quantum gravity mass, MQG >∼ 1.2MPl (where MPl is the Planck mass) assuming a linear dispersion relation [29]. The Fermi LAT has also made new important measurements of the Galactic and extragalactic diffuse emission. In fact one of the questions left unanswered by EGRET was the origin of the so-called GeV Excess in the spectrum of the galactic diffuse emission [35]. Based on the data from the first year of observations, the Fermi LAT’s measurement is softer above one GeV and is consistent with a model of diffuse emission that reproduces the local cosmic ray spectrum and does not require (at least for this part of the energy spectrum) any additional component [40]. The measurement of the extragalactic background spectrum from 200 Mev to 100 GeV by the Fermi LAT [30] was found to be a featureless power law and significantly softer that what had been previously reported by EGRET [22]. A possible reason for the discrepancy might be an overestimation of the flux in the EGRET analysis for energies greater than 1 GeV as already indicated by the galactic diffuse measurement at intermediate latitudes. The exiting new results provided by Fermi’s first year in orbit also include the precise

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measurement of the spectrum of cosmic ray (CR) electrons plus positrons10 from 20 GeV to 1 TeV [100]. In fact given its large acceptance for electrons, exceeding 2 m2 sr at 300 GeV, the LAT collected enough events after only the first six months of data taking to be able to provide this first systematics limited spectrum [100]. Prior to 2008, the high energy electron spectrum had been measured by several balloon borne experiments and one single space based mission (AMS01). The measured fluxes differed by factors of 2 to 3 with large statistical errors and little to no information regarding the systematic uncertainties. However, 2008 was a very exiting year for CR electron and positron physics with two unexpected detections. The ATIC experiment reported a prominent spectral feature at ∼ 500 GeV in the total electron spectrum [94] which lead to numerous publications on its theoretical implications [95]. Another interesting measurement was made by the PAMELA satellite, in particular the CR positron fraction from a few GeV to 100 GeV [97]. They in fact report a rise in the positron fraction above ∼ 10 GeV that increases with increasing energy reaching values larger than 10% around 100 GeV, in contrast with the predictions from the conventional CR diffusive model [36]. This model is based on the assumption that electrons originate from a uniform distribution of sources mainly associated with supernova remnants (SNR) and pulsars. Positrons are assumed to be produced as secondaries resulting from the interaction of CR protons with the interstellar medium and are predicted to be a small fraction (∼ 5%) of the total flux of electrons and positrons. Radio observations and evidence of non thermal X-ray emission from SNRs indicate that electrons with energies up to ∼ 100 TeV exist in shock fronts of SNR and in Pulsar Wind Nebulae (PWN) [92]. The method thought to be responsible for the acceleration of CR’s is diffusive shock acceleration [64] (or first order Fermi acceleration). This method describes the acceleration that charged particles undergo when reflected by magnetic inhomogeneities. SNR shock fronts are thought to have moving magnetic inhomogeneities both preceding and following them. Therefore if a charged particle moving through a shock wave encounters these magnetic field variations it can be reflected back through the shock at an increased velocity. If a similar process occurs to the transversing particle it can bounce back and again gain energy. The resulting spectrum is predicted to be a power law: dN (e) ∝ e− p de

(6.15)

where the spectral index p ≈ 2 [64], which is close to the expected value from the shape of the cosmic ray spectrum if taking into account energy dependent diffusion [63]. This model predicts a featureless spectrum from 10 GeV up to hundreds of GeV. While for larger energies, the stochastic nature of electron sources in space and time together with the increasing synchrotron and inverse Compton energy losses, the most likely thing to vary is the intensity. The spectral shape may also vary with position. Nearby sources will also start to contribute significantly to the observed local flux inducing deviations from a simple power law spectrum [104]. The CR electron spectrum reported by Fermi from 7 GeV to 1 TeV can be described, within the systematic errors, by a power 10 The LAT does not distinguish electron from positrons. I will use the term electrons to refer to the sum of the two components.

156

6.7 albedo electron spectrum

law with spectral index ≈ 3.077 ± 0.0008. The Fermi LAT electron spectrum is much harder than what is predicted by the pre-Fermi diffusive CR model [36]. No ATIC like feature is seen either by the Fermi LAT or in the results reported by the H.E.S.S collaboration [48]. The H.E.S.S electron spectrum steepens significantly above 600 GeV in agreement, within the systematic errors, with the Fermi detection. In the context of this intriguing moment for CR physics I have contributed to extending the Galactic CR electron spectrum measured by the Fermi LAT down to the lowest energies possible given the local magnetic field. To perform this task I developed a energy dependent selection criteria capable of picking out electrons from the 50 − 1000 times more abundant CR proton flux while at same time maintaining the residual contamination below 20% over the energy range of 100 MeV to 100 GeV. Given the large on-orbit trigger rates and the limited bandwidth available, during the routine science data taking configuration the main on board filter is such that all events with Edeposit > 20 GeV are transmitted to the ground. This is the main source of electrons for energies greater then 20 GeV that was used to measure the spectrum in [100]. However, for energies below this threshold it is necessary to make use of the Diagnostic filter (dgn filter) which provides an unbiased sample of all the events that trigger the LAT prescaled 1 : 250. The main source of data for my work comes from the dgn filter. In order to be able to extend the CR electron spectrum I took advantage of the Earth’s magnetic field and the fact that the rigidity cutoff varies as a function of orbital position. Therefore, by sampling all those events collected in different regions of geomagnetic coordinate, McIlwain L, I have been able to reconstruct the spectrum down to ∼ 7 GeV. This extension is very important to help make constraints on propagation models. The event selection for my analysis was developed independently of the one used to measure the electron spectrum from 20 GeV to 1 TeV (which I refer to as the he analysis). After the first year of data taking the Fermi LAT has collected enough statistics to measure the electron spectrum from 100 MeV to 100 GeV even with the 1 : 250 dgn filter prescale. Given that the event selection which I developed was done independently of the he analysis, the overlap region in energy between the two selections serves as a good cross check. In fact, the two spectra are well described by a power law and statistically consistent even without taking into consideration the systematic uncertainties. The le spectral index, obtained from a minimum χ2 fit, is 3.088 ± 0.023 in this energy overlap region, while the he spectral index is 3.095 ± 0.001. The Earth’s magnetic field effects the flux of the incoming CR charged particles and in particular introduces an asymmetry between the flux from the east direction and that from the west (known as the famous east-west asymmetry). The presence of this magnetic field essentially separates the positrons from the negatrons in the energy regions corresponding to the rigidity cutoff [83]. Inspired by the article [108], I used the east-west asymmetry (clearly detected in the Fermi LAT electron spectrum) to measure the positron fraction. I was able to perform this measurement only in the energy region between 5 and ∼ 17 GeV due to Fermi’s nearly circular orbit. However, the results for the positron fraction in this energy region are in agreement, within the statistical errors, with those made by other experiments. For energies below a few GeV, the electrons that we measure belong to the albedo population. These events originate from the interaction of the Galactic CR protons

157

analysis

with the Earth’s atmosphere. Using the event selection that I developed I performed an analysis of the intensity of these albedo electrons as a function of geomagnetic latitude, azimuth and energy with the goal of characterizing this radiation quasi trapped in the Earth’s magnetic field. In addition, this study also provides valuable information for updating the on-orbit environment Monte Carlo simulation. The update of this simulation is important to help improve our understanding of the geographic and geomagnetic variations in the charged particle environment over the Fermi orbit. Having the most accurate MC simulation also aids in the background rejection for both the electron as well as the photon analysis. Given that this model includes information on all the different particles present in the on-orbit environment, the complete update requires the work of a large group of people and is still ongoing. Clearly all of the results from this first year of Fermi LAT observations would not have been possible if the quality of the data and the overall health of the instrument while in orbit were not continuously monitored. The average rate of events that pass the on-board filters is 400 Hz, which translates into roughly 4.5 million events to process every 3 hours by the Instrument Science Operations Center (ISOC) data processing. All events are digitized and reconstructed at this rate of data taking 24 hours a day 7 days a week. Given the complexity of the detectors on the Fermi observatory over a hundred thousand quantities are necessary to correctly monitor every subsystem. Prior to launch a huge amount effort was made by the Fermi Collaboration to implement a set of webbased tools capable of monitoring these quantities. Part of these tools were developed to perform automatic monitoring however human intervention is still necessary in order to provide the best results. Starting from the launch and commissioning phase (also known as the Launch and Early Orbit or LEO) I actively participate in this work as a duty scientist. Some of my responsibilities are to monitor the quality of the LAT data both at the single subsystem level as well as at the overall detector level, identifying and documenting problems in real time monitoring and housekeeping of the detector and being capable of identifying any problems at the data processing level. During the LEO I also worked on the monitoring of the position and size of the South Atlantic Anomaly (SAA). The SAA can be defined by a 12 sided polygon and prior to launch a conservative definition of the SAA boundary was used based on models of the Earth’s radiation belts and data from other spacecraft. Due to the extreme conditions inside the SAA region, the triggering, recording and transmission of science data are stopped during the SAA passages [17]. However, LAT housekeeping is recorded and transmitted to the ground during these transits and special tracker and anti-coincidence counters (Low Rate Science Counters, LRS) are also active. These counters can sample the rate of fast trigger signals to determine position-dependent rate of the LAT along its orbit. My task was to redefine the boundary of this region using the information from the LRS counters. Once the new SAA definition was uploaded to the spacecraft the loss in observational time went from about 17% to roughly 13% of the total on-orbit time [17]. This thesis describes the work, summarized in the above paragraphs, which I performed during the three years of my PhD studies.

158

LIST OF ACRONYMS

ACD : AGN : ARR : BATSE : CAL : CERN : CGRO : CR : CT : DGE : DGN : EBL : EGRET : FOV : FSRQ : GAMMA : GBM : GCR : GLEAM : GRB : GSI : HESS : IC : IGRF : IRF : ISOC : LAT : LBAS : L1T : LEO : MC : MIP : PAMELA : PMT : PSF : PWN : SAA :

Anti Coincidence Detector Active Galactic Nuclei Automated Re-point Request Burst and Transient Experiment Calorimeter Conseil Européen pour la Recherche Nucléaire (European Organization for Nuclear Research) Compton Gamma Ray Observatory Cosmic Ray Classification Tree Diffuse Galactic gamma ray Emission Diagnostic filter Extragalactic Background Light Energetic Gamma Ray Experiment Telescope Field Of View Flat Spectrum Radio Quasars Gamma filter Gamma Ray Burst Monitor Galactic Cosmic Ray GLAST LAT Event Analysis Machine Gamma Ray Burst Gesellschaft für Schwerionenforschung High Energy Stereoscopic System Inverse Compton International Geomagnetic Reference Field Instrument Response Function Instrument Science Operations Center Large Area Telescope LAT Bright AGN Sample Level 1 Trigger Launch and Early Operations Monte Carlo Minimum Ionizing Particle Payload for Antimatter Matter Exploration and Light nuclei Astrophysics Photomultiplier tube Point Spread Function Pulsar Wind Nebula South Atlantic Anomaly

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analysis

SNR : SPS : TOF : TKR :

160

Supernova Remnant Super Proton Synchrotron Time Of Flight Tracker

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