Cosmic-ray electrons and positrons with the Fermi Large Area Telescope

UNIVERSITÀ DI PISA

F

S

Anno Accademico 2016/2017

Tesi di Dottorato

Cosmic-ray electrons and positrons with

the Fermi Large Area Telescope

Relatore Candidato

Contents

1 Introduction 1

1.0.1 About this work . . . 4

2 Cosmic-ray electrons and positrons 5 2.1 Introduction . . . 5

2.1.1 Basic observables in CR science . . . 6

2.1.2 Origin and propagation of cosmic rays . . . 11

2.2 Electrons and positrons . . . 13

2.2.1 Sources of CREs . . . 16

3 The Large Area Telescope 19 3.1 The tracker . . . 22

3.2 The electromagnetic calorimeter . . . 24

3.3 The anti-coincidence detector . . . 26

3.4 Triggers and filters . . . 26

3.5 Event reconstruction . . . 30

3.6 Instrument Response Functions . . . 34

3.7 Energy measurement . . . 35

4 Analysis 41 4.0.1 Basic formalism . . . 42

4.1 Event selection . . . 42

4.1.1 On-board filters . . . 43

4.1.2 Fiducial and quality cuts . . . 43

4.1.3 Removal of Z >1 particles . . . 45 4.1.4 Proton removal . . . 46 4.1.5 LE orbital selection . . . 54 4.2 Geomagnetic correction . . . 60 4.3 Systematics . . . 62 4.3.1 Selection cut . . . 63

4.3.2 Residual background contamination . . . 64 iii

4.3.3 IVC corrections . . . 64

4.3.4 Geomagnetic correction . . . 65

4.3.5 Energy measurement . . . 65

4.4 Fitting the spectrum . . . 68

4.4.1 Detector Response Matrix . . . 69

4.4.2 Treatment of systematic uncertainties . . . 71

4.5 Results and discussion . . . 73

5 Conclusions 81 Appendices 83 A Energy measurment uncertainty 85 A.1 Absolute energy scale uncertainty . . . 85

A.2 Energy reconstruction uncertainty . . . 88

B Tables 91

Bibliography 105

Chapter 1

Introduction

Cosmic rays (CR) are high energy charged particles of celestial origin, whose existence has been known since the beginning of the XX century. After more than one hundred years of scientific studies, we know that those first observations were actually measuring secondary CRs, produced by the interaction of primary particles with the atmosphere. Primary CRs of several different species have been observed, including both particles and antiparticles: protons, antiprotons, electrons, positrons, helium nuclei and other heavy ions up to atomic numbers Z>60.

Although accounting for less than 1% of the total composition of the Galactic CRs, cosmic-ray electrons and positrons (CRE) provide valuable information regarding some of the fundamental questions in CR physics. In fact, due to their small masses, they suffer significant radiative energy losses during propagation by synchrotron radiation on galactic magnetic fields and by inverse Compton (IC) scattering on the interstellar radiation field, so that above a few hundred GeV the majority of the CREs observed on Earth must be produced by sources closer than a few hundred pc [1]. Thus, high-energy CREs provide unique information about candidate lo-cal accelerators and may possibly reveal signatures of new physics. Fur-thermore, they can be used to constrain theoretical models of propagation of CRs in the nearby galactic space.

Recent direct measurements of the CRE spectrum have been reported by space-based experiments, such as PAMELA [2] and AMS-02 [3], below 1 TeV. An indirect measurement of the spectrum up to 5 TeV has been performed by the ground-based telescope H.E.S.S. [4], which observed a cut-off in the spectrum at∼ 2 TeV [5].

The observation, announced by PAMELA in 2008 [6], of an anoma-lous increase of the fraction of positrons on the total CRE intensity above 10 GeV, generated widespread interest among the scientific community.

Figure 1.1. A view of the Fermi spacecraft before the launch, showing both the LAT and the GBM.

Such interest followed mainly from the possible interpretation of such re-sult, which was later confirmed by AMS-02 [7], in terms of Dark Matter annihilation.

The experimental observations of CRs (and of CREs in particular) is a field experiencing a rapid evolution. Recently, both the CALET and DAMPE experiments, launched in 2015, have released their first measure-ment of the CRE spectrum up to 3 and 4.6 TeV, respectively [8, 9]. Both are expected to update these results in the future. H.E.S.S. has also recently reported a preliminary extension of the spectrum up to 20 TeV [10] and further updates are expected from AMS-02 in the next few years.

In this work I will describe a measurement of the CRE spectrum be-tween 7 GeV and 2 TeV, for which I used the data collected by the Large Area Telescope (LAT), one of the two scientific instruments that are parts of the Fermi mission. It was the first measurement of the spectrum above 1 TeV performed directly in space. This research has been conducted over a period of three years, starting from 2014, as part of my Ph.D. at Univer-sità degli Studi di Pisa.

The Fermi spacecraft was launched by NASA on 2008, June 11. It fol-lows an orbit at 565 km of altitude, with an inclination angle of 26.5° and a period of∼96 minutes. There are two instruments on-board Fermi : the Large Area Telescope (LAT) and the Gamma Burst Monitor (GBM) (Fig-ure 1.1).

3 The LAT is a pair conversion telescope, capable of measuring γ rays in an energy range spacing from a few tens of MeV to a few hundreds of GeV. The GBM [11] complements the LAT in its observations of transient phe-nomena and is sensitive to X-rays and gamma rays with energies between 8 keV and 40 MeV.

The instrument of interest for this work is the LAT. In fact, thanks to its calorimetric capability, it can also act as a detector for electrons and positrons. A first measurement of the inclusive spectrum of CREs between 20 GeV and 1 TeV, based on the data taken in the first six months of mis-sion, was published by the LAT collaboration in 2009 [12], followed in 2010 by an update [13], using one year of data and extending the inferior energy limit to 7 GeV.

The LAT, though not equipped with an on-board magnet for charge separation, was also able to measure separately the positron spectrum up to 200 GeV, exploiting the magnetic field of the Earth and the so-called East-West effect, confirming a previous result reported by PAMELA.

In 2015 the Fermi-LAT collaboration released a completely revised event-level analysis framework, usually referred to as Pass 8, which has sig-nificantly improved the LAT efficiency, as well as its angular and ener-getic resolution (especially in the high-energy range), both for photons and CREs. The measurement described here is made using seven years of the new, Pass 8 processed, data.

I conducted this research as a member of the Fermi-LAT international collaboration, which I joined in 2013, working within the local Fermi-LAT group at the section of Pisa of the I.N.F.N. (Istituto Nazionale di Fisica Nu-cleare), under the supervision of Prof. Luca Baldini. This study has been object, in 2017, of a collaboration paper [14], of which I was one of the cor-responding authors.

The thesis is divided in three parts:

• In Chapter 2 I will briefly introduce the physics of cosmic rays, with a focus on electrons and positrons, and I will review the current sta-tus of both the experimental measurements and theoretical models, highlighting the most relevant open problems in the field

• In Chapter 3 I will describe the Large Area Telescope, with the aim of providing the reader all the information required to understand the details of the analysis

• Finally, in Chapter 4, I will describe the analysis of the data and dis-cuss the results found

1.0.1

About this work

As customary when participating to large collaborations, I have cooper-ated with a team of people during the course of this research. The number of people which have been involved directly into the analysis has varied through time from a minimum of three to a maximum of approximately ten people (including myself). Many others, inside the Fermi -LAT collab-oration, have contributed in a minor but significant way through sugges-tions, ideas, or by reviewing our work.

It is thus difficult to entirely disentangle my personal contribution from the work made by other people of the team; also it would be impossible to explain the former without the necessary context provided by the latter. In describing the work, I will focus on the parts which I carried on per-sonally, or in which I was involved in first person with a relevant role. As for the rest, I will report only what is essential for the reader in order to understand the analysis, and defer anything else either to an appendix, or to the aforementioned publication.

Chapter 2

Cosmic-ray electrons and

positrons

2.1

Introduction

Cosmic rays were discovered in 1912 by Victor Hess who, in a series of balloon flights, showed the existence of a kind of radiation whose intensity increases with altitudes [15], thus proving that it was not generated by any terrestrial source1.

Most CRs observed at Earth are not of direct celestial origin, but rather produced by the interactions of other particles with the atmosphere. It is customary to use the adjective primary for particles accelerated by celes-tial sources and secondary for those produced by decay, spallation or other interactions of primary particles during their propagation.

The typical particles observed at ground level are secondary muons2 produced by the decay of pions and kaons generated in CR-induced air showers; because of their long decay time (2.2 µs) muons can easily cross the entire atmosphere and even be detected underground.

Outside the atmosphere the situation is more heterogeneous and sev-eral different species of charged cosmic rays have been observed: p, p, e±,

αas well as nuclei of both light and heavy elements.

The all-particle spectrum of CRs is shown in Figure 2.1. It covers some impressive eleven decades in energy and is the result of a century of steady scientific effort. In the early days, this search has also lead to the discovery

1_{Roughly at the same time, Domenico Pacini independently came to similar}

conclu-sions by observing that the radiation level decreases when measuring it underwater [16].

2_{Actually, the particles with the highest flux at ground level are ν and ν. They are,}

however, far more difficult to detect.

of new particles: the positron in 1932 [17], the muon in 1937 [18] and the pion in 1947 [19, 20] were all observed for the first time in CRs.

Currently, the study of CRs exploits a variety of different experimen-tal techniques, which keep improving over time. At a fundamenexperimen-tal level, the vast majority of instruments fall into either one of two main cate-gories: ground-based experiments, which observe CR-induced showers in another medium (often the atmosphere), and balloons or space experi-ments, which attempt to observe CRs interacting directly inside the detec-tor. As a general rule, the former provide much wider collection area, thus being useful for the study of the far end of the energy spectrum (where the flux of particles can be as low as 1 yr−1km−2sr−1, or even less), while the latter provide better energetic and angular resolution, as well as bet-ter particle identification capability, but are essentially limited to the TeV region (or shortly above).

2.1.1

Basic observables in CR science

A complete review of CR-related observations and their theoretical inter-pretation is well outside the scope of this work. Here I will briefly consider the most relevant observables in CR science, summarizing the current sta-tus of their measurements, and introduce the basic of the current produc-tion and propagaproduc-tion models. I will do this initially for CRs in general, than I will focus the discussion on CREs in section 2.2.

Spectrum

Overall, the all-particle spectrum in Figure 2.1 is well approximated by a power-law with an index of roughly−2.7 up to an energy of∼3×1015eV, where the index steepens to nearly−3.1 (a feature which is often called the knee). A second spectral steepening has been observed at∼ 8×1016 [25] (the second knee), though the evidence for that is less compelling. A third feature is visible between 1018 and 1019 eV, where there is a hardening of the spectrum (the ankle). Particles in the region of the ankle and above are often referred to as Ultra High-Energy Cosmic Rays (UHECRs). If one as-sumes that the CRs below the ankle are of Galactic origin, while particles above the ankle originate outside the Galaxy, than the ankle can be nat-urally interpreted [26] as the result of the extragalactic sources having a harder injection spectrum compared to the Galactic ones (but see also [27] for a different explanation of this feature in terms of a purely extragalactic component and [28] for a discussion).

2.1. INTRODUCTION 7

Kinetic energy [GeV]

9 10 1010 1011101210131014 101510161017101810191020

]

sr

GeV

s

) [m

J(E

Figure 2.1. Compilation of CR spectra measurements, edited from [21] (courtesy of prof. Luca Baldini). The dashed line has been obtained by summing up the energy spectra of the most abundant CR species (p, He, C, O and Fe), measured by several different space-and balloon-borne experiments (references can be found in the original work). The high energy points are taken from the data published by the Tibet [22], Kascade [23] and Auger [24] collaborations.

1957 1967 1977 1987 1997 2007 2017 0 2000 4000 6000 8000 10000 N. of sun spots 120 130 140 150 160 170

Monthly average counts / hour

Figure 2.2. Red: number of sun spots per month of observations (source: WDC-SILSO, Royal Observatory of Belgium, Brussels [34]). Blue: monthly average of counts rate from the IGY NM Jungfraujoch (JUNG) neutron monitor, provided by the NMDB database [35]. (I acknowledge the NMDB database (www.nmdb.eu), founded under the European Union’s FP7 programme (contract no. 213007) for providing this data).

Above ∼ 5×1019 eV it has long been predicted [29, 30] that the Uni-verse would become opaque to CRs, due to protons reaching the threshold for resonant production of pions (through∆ decay) in inelastic interactions with the cosmic microwave background. Observation of a drop of the spectrum in that energy region, recently reported by some ground based experiments [31, 32, 33, 24] seem to confirm the existence of this so-called GZK cut-off (named after Greisen, Zatsepin and Kuzmin, who originally proposed it).

Below a few tens of GeV, the spectrum is influenced by the presence of the solar wind, an effect which is known as the solar modulation of CRs. The effect is twofold: first, CR intensity is greatly reduced when they propa-gate through the heliosphere, as apparent in Figure 2.1 from the change of shape of the spectrum around the GeV region; second, a temporal varia-tion of the intensity can be observed, in anti correlavaria-tion with the 11-year cycle of the solar activity. The anti correlation is visible when comparing, for example, the number of sun spots (which gives an estimate of the so-lar activity) with the rate of CRs observed at Earth by neutron monitors (Figure 2.2). I will discuss the modulation of electrons and positrons in 2.2.

2.1. INTRODUCTION 9 Chemical composition

The chemical composition of CRs provides valuable information about their origin and propagation. Data are now available for elements up to Z =60 (for example from ACE/CRIS [36] for elements up to Fe and from SuperTIGER [37] for heavier elements). Below the knee, roughly 90% of CRs are protons3with He nuclei accounting for the majority of the rest.

The relative abundances of the most common elements (C, O, Ne, Mg, Si, Fe, Ni) are remarkably similar to those observed in the solar system (Figure 2.3), which is somewhat expected if one generically assumes that the acceleration mechanisms get the particles to be accelerated from the Interstellar Medium (ISM).

The situation is different for the less abundant nuclei, which are found in significantly higher fraction in CRs. It is believed that these elements are produced by the interaction of primary particles during their prop-agation; thus, measuring their abundance ratio with respect to primary species (for example, the ratio of Boron to Carbon, recently measured with high precision by CREAM [39], PAMELA [40] and AMS-02 [41]) provides an estimate of the grammage of gas (integral of gas density along the path) encountered by CRs during their lifetime, which is an important input for CR propagation models.

It is to be noted that the spectra of individual species of charged cos-mic rays may not necessarily follow the trend of the all-particle spectrum shown in Figure 2.1. In fact, there are evidence of a hardening of the spec-trum of both protons and helium between 200 and 300 GeV reported by CREAM [42] and PAMELA [43] and confirmed by AMS-02 [44, 45]. The slopes for these two species are also slightly different, with the proton spectrum being softer.

In general, chemical composition is energy dependent. For example, there are evidence of a change in composition around the knee (see [46] for a review). The composition of UHECRs is still matter of debate and some tension exists between different experimental observations. A review of the topic can be found in [47].

Another striking characteristic of the cosmic-ray composition is the presence of antimatter particles, namely antiprotons and positrons. Those particles are believed to be mostly of secondary origin, though recently there has been evidence that at least a fraction of the positrons observed at

3_{The statement is true only when the relative abundances are measured as function of}

GeV/nucleon, as it is somewhat customary in this energy range. Using a different metric it can be said, for example, that the fraction of nucleons arriving as free protons is close to 79% [38].

Figure 2.3. Comparison of GCR solar minimum abundances (filled circles) with solar system elements abundances (open circles), normalized to silicon. Origi-nally published in [36] (see therein for references to the sources of the data).

Earth are, indeed, primary particles (see 2.2). At the current status, no such evidence exists for antiprotons. A recent high-precision measurement of the spectrum of antiprotons has been released by AMS-02 [48]; the ques-tion whether it is possible to explain it in terms of a purely secondary pro-duction is still open. Searches for antihelium in CRs have been performed, for example, in AMS-02 data, but no clear observation has been confirmed at the present time.

Anisotropies

The observed direction of arrival of CRs is mostly isotropic. This is due to their propagation in the ISM, where the directions of the particle momenta are randomized by the scattering on the turbulent Galactic magnetic field. However, a small anisotropy, of order of 10−3−10−4, has been detected in the energy range from 1010 to 1015 eV. This anisotropy was originally reported by underground muon experiments more than fifty years ago (a collection of such early measurements, as well as a general review of CR anisotropies below 1015 eV can be found in [49]) and has been stud-ied with increasing sensitivity by the current generation of ground based experiments [50, 51, 52]. The origin of such anisotropy is still matter of

2.1. INTRODUCTION 11 debate, but it is believed that it can either trace the spatial distribution of the acceleration sources, or be the consequence of an anisotropic diffusion, or else a combination of the two (again, see [49] and reference therein for a review).

The Larmor radius (eq: 2.2) of UHECRs is comparable or greater than the size of the Galactic disk; thus, if these particles were of Galactic origin, a certain degree of anisotropy towards the sources would be expected. The absence of such anisotropy has been traditionally interpreted as an argument for their extra-galactic origin. Recently, a large scale dipole anisotropy above 3×1018 eV has been observed by the Auger experi-ment [53]; since the excess region is located outside the Galactic plane, such result is considered a strong evidence in favour of the extra-galactic hypothesis.

2.1.2

Origin and propagation of cosmic rays

Most of the Galactic Cosmic Rays (GCRs) are believed to be produced through diffusive shock acceleration (DSA) in Supernova Remnants (SNRs), while the situation is less clear for UHECRs.

The idea that GCRs could be accelerated by supernovae, mainly based on energetic arguments, dates back to 1934 [54], while the concept of dif-fusive acceleration of particles by scattering on magnetic clouds was intro-duced by Fermi in 1949 [55]. DSA, an evolution of Fermi’s original idea, happens when particles repeatedly cross the front of a shock and, after each crossing, their direction is isotropized by means of scattering with magnetic plasma turbulence, statistically allowing them to cross the front once again [56, 57]. It can be shown, with simple kinematic arguments, (see for example [58]) that each cycle of scattering back and forth produces a net fractional momentum gain which is proportional to β ≡ |u2−u1|, where u2 and u1 are the velocities of the plasma respectively upstream and downstream the shock front. For this reason DSA is often also called first-order Fermi mechanism, to distinguish it from the original proposed mechanism, where the gain was only of second order in the scattering cen-tre velocity.

In a supernova explosion, the outer shell of the exploding star is ejected and expands supersonically as a shock front, creating the condition for DSA. A complete mathematical description of the process can be rather complicated, since it depends on the details of the environment around the shock, and I defer to [59] and reference therein for a review. Here I will only mention that, in the (extremely simplified) case of linear DSA, i.e. if

accelerated particles do not participate to the dynamic of the process, it can be shown that this mechanism produces an energy spectrum that is, for ultra-relativistic particles:

dN(E)

dE ∝ E

−α+2 _(2.1)

with α=4 in the limit of strong shocks. Traditionally, the natural arise of a power-law spectrum has been one of the arguments for considering DSA a good candidate acceleration mechanism for GCRs. Beside the theo-retical expectations, evidence that SNRs are indeed accelerating CRs come from observation of γ rays. In fact, protons accelerated by SNRs which happen to be located close to a molecular cloud, may interact with the gas producing γ-rays through neutral pions decay: π0 → γγ. The signature

of this process, a steep rise of the spectrum below 200 MeV, has been ob-served in the γ-ray spectrum of SNRs by AGILE [60] and Fermi [61].

Whether all hadronic GCRs (I will discuss electrons and positrons later in 2.2) are accelerated by SNRs is still an open question. It was suggested [62] that the knee structure could arise from the superposition of several different cut-off of different CR species. In the SNRs paradigm this result is naturally achieved because the acceleration process is rigidity depen-dent, so that the heaviest particles will be accelerated to higher energies than e.g. protons. However, accelerating proton to 3×1015 eV requires some mechanism for magnetic field amplification (possibly in non linear DSA regime). Again, I defer the reader to [59] for a thorough discussion of the problem.

The other piece of the puzzle necessary to explain CR observations is their propagation inside (and, for UHECRs, outside) the Galaxy. Again, the topic is too wide to be reasonably summarized in these pages. Since the object of this work are electrons and positrons, which are believed to be of purely Galactic origin, here I will only introduce a few basic concepts inherent to the propagation of GCRs. Further details, for the specific case of CREs will be discussed in section 2.2.

A useful quantity for describing the interaction of charged particles with magnetic fields is the Larmor radius (or gyroradius) rL, that is the ra-dius of the orbit of a charged particle moving in a uniform, perpendicular magnetic field. For a particle of momentum p and charge Ze moving in a magnetic field B, it is equal to:

rL = p

2.2. ELECTRONS AND POSITRONS 13 The typical values of rL for CRs below the knee, assuming B of the or-der of ∼ 5 µG, are much smaller than the size of the Galaxy disk. Thus, magnetic scattering on inhomogeneities of the Galactic magnetic field pro-duces a diffusive behaviour which resembles a random walk.

The basic predictions from the most sophisticated propagation models available, can be summarized using a much simpler (and non-physical) model, the so-called leaky-box model [63], in which the Galaxy is described as a cylinder of radius Rd ∼15 kpc and height h'300 pc. Above and be-low the two faces of the cylinder there is a magnetized halo, which extents for H ' 3−4 kpc. As said, CRs motion is diffusive, similar to a random walk: the escape time τ is thus equal to H2/D(E) where D(E) is the dif-fusion coefficient. If the difdif-fusion coefficient depends form energy in the form of D(E) ∝ Eδ _{and the spectrum produced by acceleration sources}

(e.g. SNRs) is of the form Ns(E)∝ E−γ, then the spectrum of primary CRs observed at Earth is given by ([58]):

N(E) ' Ns(E)RSN

2πR2_dH ∝ E

−γ−δ _(2.3)

where RSN is the rate of supernova explosion. Since the measured spec-trum of primaries has index ' −2.7 then we have δ = 0.7, assuming the above described simplified model of acceleration at SNRs. This value is actually larger of what is predicted by less naive derivations and of what can be inferred from the most updated experimental observations (e.g. of the B/C ratio), which both point to values of δ in the range 0.3−0.6 [41].

For purely secondary particles the spectrum becomes:

Nsec(E)∝ E−γ−2δ (2.4) thus, in this simplified scheme, the ratio between secondary CRs and their parent primaries is expected to decrease as E−δ_{. I will discuss in section 2.2}

the implication of this prediction in the light of the recent measurements of the positron spectrum.

2.2

Electrons and positrons

The first observations of CREs was made in 1961 simultaneously by P. Meyer and R. Vogt [64] and J. Earl [65]. The main difference with hadronic species lays in the energy loss mechanisms, which cause the electrons to suffer higher energy losses while propagating through the ISM and the

galactic magnetic fields. These two mechanism are inverse Compton scat-tering and synchrotron radiation emission, which both shows a similar behaviour in the ultra-relativistic limit:

dE dt =kE 2 _(2.5) with k= 4 3 σT c ωph me2 (2.6)

where meis the electron mass, σTis the Thompson cross-section, and ωphis the density of the interacting radiation field. The immediate consequences of equation 2.5 are:

• The observed energy spectrum of CREs is expected to be steeper than that of the hadronic species

• CREs of the highest energies cannot be of extra-galactic origin: in fact, they must be accelerated close to the Earth

More in detail, the transport equation for the case of CREs can be written, assuming stationary conditions and the simple case of homogeneous and isotropic diffusion, as [66, 67]: ∂Ne(E, t,−→r ) ∂t −D(E)∇ 2_N e− ∂ ∂E(b(E)Ne) = Q(E, t, −→ r ) (2.7) where Ne(E, t,−→r ) is the number density of CREs per unit energy, D(E) is the diffusion coefficient, b(E) is the rate of energy loss and the term Q(E, t,−→r ) represent the contribution of sources. Above ∼ 10 GeV radia-tive energy losses dominate, so that b(E) is essentially equal to the right side of equation 2.5. Thus, the expected radiative lifetime of a high-energy CRE is:

L(E) = 1

kE (2.8)

and the corresponding diffusion distance is: rdi f f(E) ∼

q

2L(E)D(E) (2.9)

At 1 TeV Lis of the order of ∼ 105yr and rdi f f is consequently≤ 1 kpc, much smaller than the Galaxy radius. For this reason, CREs represent a unique probe for production and propagation models in the nearby Galac-tic space.

2.2. ELECTRONS AND POSITRONS 15

E [GeV]

10

10

10

]

GeV

sr

s

Intensity [m

×

E

0

50

100

150

200

250

Figure 2.4. Differential intensity of CREs as a function of energy. The figure shows the most updated measurements available before the analysis presented in this work was published: AMS-02 [69] (blue points), H.E.S.S. low-energy [5] (white squares) and high-energy [70] (black-squares), previous Fermi low-energy (empty red triangles) and high-energy (full red triangles) analysis.

As in the general case of CRs, the basic observables for CREs are the spectrum, the chemical composition (which in this case reduces to the frac-tion of positrons on the total) and the presence of anisotropies.

Recent measurement of the CRE spectrum have been reported by space experiments such as PAMELA [68], and AMS-02 [69], as well as from ground experiments such as H.E.S.S. [5, 70] (Figure 2.4). As already men-tioned, the Fermi -LAT collaboration has also published a measurement of the spectrum [13] from 7 GeV to 1 TeV.

As expected, the observed spectrum is softer compared to the proton spectrum, with a difference of spectral indices δ'0.3−0.4. In particular, AMS-02 has found that the spectrum is well described by a power-law of

index -3.17 from 30.2 GeV to 1 TeV, slightly in tension with the previous Fermi measurement, which reported a spectral index of -3.11. Also, H.E.S.S has observed a cut-off of the spectrum at 2 TeV.

Positrons present in CRs were long believed to be secondary particles. This view was recently challenged by the observation by PAMELA of an anomalous rise of the positron fraction in CREs above 10 GeV [71], which followed from previous, although less significant hints ([72, 73]), and was later confirmed by Fermi [74] and AMS-02 [7] (see Figure 2.5). Such obser-vations seem to imply that at least a portion of the positrons observed at Earth must of be of primary origin.

There have been many attempts to explain this excess in terms of pri-mary production from either astrophysical sources ([75, 76]) or exotic sources (e.g. dark matter [77, 78, 79]), or even as a feature of the propagation. Cur-rently, its origin is still an open question in cosmic-rays science.

I will discuss CRE acceleration sources in the rest of this section; but first I will briefly cover the third observable inherent to CREs, that is their level of isotropy. Since, as already mentioned, high energy CREs originate close to the Earth, it is possible that their spectrum is dominated by one or a few nearby sources, in which case a certain degree of anisotropy could be expected. However, no such kind of anisotropy has been observed at the present status. The results of a search for anisotropies based on the data sample collected for this work has been published by the Fermi -LAT collaboration, excluding dipole anisotropies at∼ 10−3level [80]. This re-sult is starting to rule out some of the simplest models of emission from a single nearby source.

2.2.1

Sources of CREs

As with other ordinary matter particles, negative electrons are believed to be accelerated in SNRs (2.1.2). This has been confirmed by observations of non-thermal X-rays emission, showing that electrons of energies up to

∼ 100 TeV are indeed present at the outer edge of SNRs [81]. It has been suggested ([76]) that the positron excess can be explained entirely in terms of re-acceleration at SNRs as well.

In addition, both electrons and positrons can be accelerated by pul-sars [82, 83]. A pulsar is a rapidly rotating neutron star formed after the supernova phase of a star with mass between 1.44 and 5 solar masses. The extremely high magnetic fields that this object possess (∼ 1010 - 1013 G), drawn by their rotation, can induce strong electric fields that in turn

2.2. ELECTRONS AND POSITRONS 17

10

₁₀

E [GeV]

10

e

/(e

+

e

)

Figure 2.5. Ratio between the intensity of e+and the total intensity of e++e−as a function of energy. Data points correspond to the measurements reported by PAMELA [71] (black), AMS-02 [7](blue) and Fermi [74](red) respectively.

can extract and accelerate electrons from the star surface. A pulsar ro-tating with angular velocity Ω is surrounded up to a distance known as light radius rl =c/Ω by a comoving plasma configuration called ’magne-tosphere’ [84, 85]. The stripped electrons can initiate an electromagnetic cascade by interacting with the pulsar magnetic field and such cascades fill the magnetosphere with a relativistic magnetized wind. In some cir-cumstances, when the wind hits the expanding ejecta of the progenitor supernova, a termination shock forms in the impact, where electrons and positrons can be accelerated through DSA. Such objects are called Pulsar Wind Nebulae (PWN). Observations at various frequencies of synchrotron and Inverse Compton emission demonstrate that high energy leptons are indeed present in PWN [86]. though the exact fraction of accelerated pairs which are released in the ISM is currently unknown and the escape mech-anisms are not clearly understood. Since both negative and positive parti-cles are accelerated, it is possible to explain the positron excess in term of production at pulsar and PWN [87].

Another possible explanation is that e± pairs are produced by Dark Matter (DM) decay or annihilation, for example by WIMPs (weakly in-teracting massive particles) [88, 89]. There are two major problems asso-ciated with the DM scenario: first, it requires some kind of mechanism

Time [Year] 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Relative to Jul-Dec 2006 -/e +_e0.8 1 1.2 1.4 1.6 1.82 A<0 A>0

PAMELA 0.5 GeV - 1.0 GeV

Figure 2.6.Positron fraction measured by PAMELA over nearly 9 years, normal-ized to its value in 2006. The transition between positive and negative polarity is marked with a shaded area. Originally published in [90].

for boosting the cross-sections, compared to what is predicted by the sim-plest models, in order to produce a signal which stands significantly over the astrophysical background. This problem can be partially alleviated by assuming that the local flux is enhanced by the presence of some local clumps of DM. The second problem is the absence of a similar ’excess’ of antiprotons, which requires one to postulate that the candidate DM parti-cle is leptophilic.

Finally, I note here that CREs, like other charged species, are affected by solar modulation, an effect which will be marginally relevant for the present measurement, as I will discuss in section 4.5. The solar modulation is slightly different for electrons and positrons, because the solar magnetic field experiences a change of polarity with a periodicity of 22 years. The polarity of the solar magnetic field is usually expressed in terms of the projection of its dipole term on the solar rotation axis, A. During positive (A > 0) polarity cycles the modulation of negative charged particles is higher, while the opposite is true during negative polarity. Thus, below a few GeV, the fraction of antiprotons over protons, as well as of positrons over electrons (Figure 2.6), is not constant over time, as recently confirmed by PAMELA and AMS-02 [90].

Chapter 3

The Large Area Telescope

As anticipated in Chapter 1, the LAT is a space telescope capable of mea-suring γ rays and CREs across more than five decades of energy, from a few tens of MeV up to to TeV scale. It is composed of three main sub-systems:

• A silicon tracker (TKR) for measuring the direction of incident parti-cles

• A CsI(Tl) calorimeter (CAL) for energy measurement

• A segmented anti-coincidence detector (ACD) for charged cosmic-ray background rejection

Both the CAL and the TKR are divided in 16 modules (also referred to as towers) in a 4×4 scheme. A cutaway of the LAT, including all its subsys-tems, is shown in Figure 3.1.

The basic operating principle of the LAT is the following: a γ ray con-verts into a e++e− pair inside the TKR and initiates an electromagnetic shower. If the initial energy of the photon is sufficient (as it is almost al-ways the case above a few hundreds MeV), the shower propagates into the CAL, where it is absorbed. This is illustrated schematically in Figure 3.2.

For electrons and positrons the principle is similar, with the only differ-ences that a) being charged particles, they usually leave a detectable signal in the ACD and b) the electromagnetic cascade is initiated by bremsstrahlung emission, rather than by pair production.

Events with topologies different from the above described are possible and, in fact, routinely happen in the LAT; for example, particles with very large incidence angle respect to the zenith of the instrument may miss the

Figure 3.1. Schematic diagram of the Large Area Telescope. The dimensions of the telescope are 1.8×1.8×0.72 m3. The modular structure is clearly visible.

CAL or the TKR entirely (depending on their impact point); showers in-duced by low-energy photons (typically below∼100 MeV) may be com-pletely absorbed into the TKR or, conversely, the conversion into a pair may happen directly into the CAL. Though such alternate topologies are relevant for gamma-ray analyses, in the present work I will be interested primarily in CRE events which follow the basic scheme.

In the rest of this chapter I will give a brief description of the LAT. This is not meant to be a complete review of the instrument, but rather an intro-duction to the aspect of its functioning that are required to understand the work here presented. I will start by describing the three subsystems of the LAT as well as the basics of the instrument triggers and of the data filtering which happens on-board. Than I will move to the off-line reconstruction algorithms and the characterization of the instrument performances. Fur-ther information concerning the instrument can be found in [91].

Through this document I will often use a spherical coordinates system centred on the instrument, which I will refer to as the "LAT reference sys-tem" or "LAT reference frame". In this frame, shown in Figure 3.3, the plane at z=0 corresponds to the bottom of the TKR, with the z axis pass-ing through the centre of the ideal square defined by the instrument top surface.

21

Figure 3.2.Schematic representation of the basic functioning principle of the LAT.

+x +y +z v φ θ

Figure 3.3.The LAT coordinates system. The (0,0,0) point is located at the bottom of the TRK and above the CAL, in the ideal center of the 4×4 grid of towers. The used convention for the zenith (θ) and azimuth (φ) angles is also shown.

Figure 3.4.Side view of one of the 16 modules of the TRK.

3.1

The tracker

The tracker [92] is responsible for promoting the conversion of photons into e+e−pairs, measuring their incident direction and providing the pri-mary trigger for the instrument. It also contributes to the energy measure-ment at low energy (below a few hundred MeV).

A side view of a single TKR module is visible in Figure 3.4. Each of the 16 modules is 37.3 cm wide and 66 cm tall and is assembled from 19 individual trays supporting a total of 36 planes of silicon detectors. A tray is a carbon-composite panel with single-sided silicon strip detectors (SSDs) bonded on both sides (Figure 3.5), with the strips on top parallel to those on the bottom. The first and last trays of a tower have strips on the internal side only.

SSDs are made of 384 parallel strips spaced at 228 µm pitch over an area of 9.85×9.85 cm2, and a thickness of 400 µm. Sets of 4 SSDs are bonded to form "ladders". There are 4 ladders in each plane, for a total of 16 SSDs per plane (576 per tower).

Adjacent trays are mutually rotated of 90°, so that the detectors on the bottom of a tray combine with those on the top of the tray below to form an orthogonal x–y pair, with only 2 mm between them. In total there are 18

3.1. THE TRACKER 23

Figure 3.5. Exploded view of a mid tray, illustrating the integration of detectors and readout electronics multi-chip modules (MCM) on the sides.

tracking planes, each ensuring measurement of both x and y coordinates. In order to enhance the chance of a γ ray to convert in a pair, the first 16 x–y layers starting from the top are preceded by a converter foil of high-Z material (tungsten). The last two layers have no converter, because the trigger of the TKR, requiring hits in 3 adjacent x–y layers, would be in-sensitive to photons converting here (see section 3.4). The upper twelve planes of tungsten are each 2.7% of a radiation length (RL) in thickness (0.095 mm), while the final four are each 18% RL (0.72 mm). This choice is a compromise between two somewhat conflicting needs: reducing the effect of multiple scattering on the angular resolution, especially at low en-ergy, requires minimizing the material traversed by the photon from the conversion point to the first tracking layer; maximizing efficiency, in par-ticular for the relatively rare high-energy photons, which are less affected by multiple scattering, requires increasing it. Overall, approximately 63% of photons above 1 GeV are converted at normal incidence.

The TKR readout is binary, with a single threshold discriminator for each channel, and no pulse height information is collected at the strip level. The logical OR of all the discriminated strip signals on the same detector plane1 is used for trigger purpose and the system measures and records also the time-over-threshold (TOT) of this layer-OR signal, which provides charge deposition information that is useful for background re-jection.

The individual electronic chain connected to each SSD strip consists of a charge-sensitive preamplifier followed by a simple shaper with a peak-ing time of ∼ 1.5 µs (which is the relevant time interval for trigger pur-poses). The discriminated output remains high for∼10 µs for Minimum Ionizing Particles (MIPs) at the nominal∼1/4 MIP threshold setting. An

1_{More precisely the logical OR is taken separately for half of a plane. More details can}

Table 3.1.Summary of tracker characteristics and performance metrics.

Metric / Characteristic Measurement

Active area1 1.96 m2

Gamma-ray conversion probability1 63%

Active area fraction within a Tracker module1 95.5%

Overall Tracker active area fraction1 _89.4%

SSD strip spacing 0.228 mm

Power consumption per channel 180 µW

Tower-module mass 33.0 kg

Single-plane hit efficiency in active area >99.4%

Dead channel fraction 0.2%

Noisy channel fraction 0.06%

Noise occupancy <5·10−7

1_{At normal incidence}

important effect of this permanence will be discussed in section 3.5

Some of the relevant characteristics and performance metrics of the TKR are summarized in Table 3.1.

3.2

The electromagnetic calorimeter

The calorimeter [93] is the main instrument for measuring the energy of the incoming particles. It also provides an image of the shower develop-ment, which is used both for background rejection and, to some extent, for measuring the incident direction. As in the case of the TKR, there is also a CAL module for each of the 16 towers. However, differently from the TKR, which has a compact structure, there are 4 cm gaps between the CAL modules.

A single CAL module (Figure 3.6) is made of 96 CsI(Tl) crystals of size 2.7×2.0×32.6 cm3. The height of each crystal is designed to be slightly greater than one radiation length (X0 =1.86 cm in CsI), while its width is almost one Moliére radii (RM =3.6 cm). The crystals are optically isolated and arranged in 8 layers of 12, with a total vertical depth of 8.6 X02. The arrangement of the crystals is hodoscopic: crystals of two adjacent layers have mutually orthogonal directions in the x-y plane.

A single crystal is read out with four photo-diodes, two at each end: a large photo-diode, with 147 mm2 area, covering the energy range from

2_{Including the TKR the total instrument depth is 10.1 X}

3.2. THE ELECTROMAGNETIC CALORIMETER 25

Figure 3.6. Exploded view of one module of the CsI calorimeter, showing the hodoscopic 12×8 structure.

2 MeV to 1.6 GeV, and a small photo-diode, with 25 mm2 area, covering the energy range from 100 MeV to 70 GeV. Each photo-diode is connected to a charge-sensitive preamplifier, whose output is split to a fast shaping amplifier (∼ 0.5 µs peaking time) for trigger purposes and a slow shap-ing amplifier (∼3.5 µs peaking time) for spectroscopy. The signal coming from the slow shaper is split again into two track-and-hold stages with gain ×1 and ×8 respectively. Therefore four gain ranges are provided by each crystal end, of which the lowest non-saturated is dynamically se-lected during normal data-taking operation. A zero-suppression discrim-inator eliminates all single-crystal signals with an energy<2 MeV.

Each crystal effectively provides a position measurement in all the three spatial coordinates. Two of them derive directly from the position of the crystal in the hodoscope. The third is estimated from the asymmetry in light yield between the two ends of the crystal, from which is possible to determine the longitudinal position of the energy deposition with an accu-racy which varies from a few millimetres up to a fraction of millimetre, as described in [91] (see also [94] for more details about the on-orbit calibra-tion of the light asymmetry measurement). Hence, the CAL is effectively able to reconstruct a full 3-dimensional image of the shower development. Such imaging capability is fundamental for reducing the loss in energy resolution due to shower leakage, which for events above a few GeV is the dominant source of inaccuracy. It also plays a key role in distinguishing and rejecting hadronic showers and, for high energy events, can be used

to help the reconstruction algorithm in determining the right direction of track.

3.3

The anti-coincidence detector

The purpose of the ACD [95] is the rejection of background from charged particles. The key characteristics of the ACD are its high efficiency, greater then 0.9997 on average for a MIP, and its segmented nature.

In fact, as shown in Figure 3.7, instead of being a monolithic object, the ACD is segmented into several tiles of plastic scintillator: 25 of these tiles cover the top of the LAT, while other 64 cover the side faces (16 each). The reason behind this design choice was reducing the loss of effective area due to the so called "backsplash effect": isotropically distributed sec-ondary particles coming from electromagnetic showers in the CAL (mostly 100–1000 KeV photons) which produce false vetoes in the ACD via Comp-ton scattering. Segmentation allows to consider only ACD tiles nearby the photon candidate, effectively reducing the possibility of a self-veto.

The scintillation light from each tile is collected by wavelength shifting fibers (WLS) that are embedded in the scintillator and are coupled to two photomultiplier tubes (PMTs) for redundancy.

In order to keep the highest possible hermeticity, scintillator tiles are overlapped in one spatial direction, while the gaps in the other direction are covered by flexible scintillating fibers (ribbons) read out by a PMT at each end. These gaps, where the efficiency is inferior, account for <1% of the total area.

The tile threshold is at 0.45 MIP for onboard use in rejection of back-ground particle (see section 3.4). A zero-suppression theresold at∼100 keV is used to sparsify the signal. The output of each PMT is connected to a fast shaping amplifier (with ∼ 400 ns shaping time) for trigger purposes and two separate slow electronic chains (with ∼ 4 µs shaping time and different gains) to measure the signal amplitude.

To minimize the chance of light leaks due to penetrations of the light-proof wrapping by micro-meteoroids and space debris, the ACD is com-pletely surrounded by a low-mass micro-meteoroid shield (0.39 g cm−2).

3.4

Triggers and filters

The readout of the instrument is controlled by the hardware trigger. There are several different type of triggers that can initiate a readout of the LAT,

3.4. TRIGGERS AND FILTERS 27

Figure 3.7. ACD structure. Top - ACD tile shell assembly, with tile rows shown in different colors. Clear fiber cables are seen in the cutout. Ribbons and bottom row (long) tiles are not shown. Bottom - ACD base electronics assembly (yellow) with PMTs shown. The LAT grid is shown in gray below.

optimized for different purposes: collection of scientific data, instrument monitoring and calibration. Here I briefly describe the characteristics of the trigger system which are relevant for this work.

Each subsystem of the LAT provides one or more trigger primitives (or trigger requests), which are combined by the Central Trigger Unit (CTU) to form a certain number of trigger engines. These are compared to a table of allowed trigger conditions and, in case a condition is satisfied, the readout of the LAT starts. There are 8 different trigger primitives, listed below:

TKR: three consecutive tracker layers over threshold in the same tower (three-in-a-row)

CAL_LO: at least 100 MeV in a single crystal of the calorimeter

CAL_HI: at least 1 GeV in a single crystal of the calorimeter

VETO: the signal in any of the ACD tiles above the veto threshold. If a

TKR primitive is generated in coincidence within the same tower, a ROI (region of interest) primitive is issued

CNO: the signal in any of the ACD tiles above the CNO threshold (25 MIPs), indicating the passage of a heavy ion

PERIODIC: running continuously at 2 Hz during normal science

opera-tions

plus other two which are not used in flight. All the 82possible combina-tions of primitives collected within a coincidence window of 700 ns from the first one are mapped into one of the trigger engines (Table 3.2), which are optimized for different class of events. Some of the engines are pre-scaled, i.e. only an event out of N, with N a settable number, is actually allowed to trigger the read-out. This feature is useful to reduce the occu-pancy from those engines which are used for calibration purposes, and is not applied to engines designed for data-taking.

Each engine in the table (a part from the periodic trigger) is associated with a specific physical event. For example, engine 4 typically signal the passage of a heavy ion. Engine 7 is the most relevant for γ rays, requiring a trigger signal in the TKR without associated ROI vetoes. Engine 9 is intended to recover those events for which the veto in the ACD may be caused by backsplash from the CAL. Engine 6 ensures that almost every event presenting a high energy deposition in the CAL is accepted.

The read-out of the LAT is always global, even if the trigger requests are issued by a single module, and requires a minimum dead-time of

3.4. TRIGGERS AND FILTERS 29 Table 3.2. Definition of standard trigger engines in terms of primitives used (1: required, 0: excluded, x: either). Engine 0, 1, 2 and 8 are omitted, since they are not relevant for usual science operations.

Engine PERIODIC CAL_HI CAL_LO TKR ROI CNO Prescale

3 1 × × × × × 0 4 0 × 1 1 1 1 0 5 0 × × × × 1 250 6 0 1 × × × 0 0 7 0 0 1 × 0 0 0 9 0 0 1 1 1 0 0 10 0 0 0 1 1 0 50

26.5 µs (and possibily longer, depending on how the instrument is read). The trigger rate is of ∼ 2−4 kHz and the global fraction of dead-time is less than ∼ 10%. Such rate needs to be further reduced before being downlinked to the ground.

For this task the LAT is equipped with three on-board filters, running in parallel:

• HIPfilter, designed to select heavy ions, mainly for calibration pur-poses (average rate 10 Hz)

• DIAGNOSTICfilter, used to collect data from thePERIODICtrigger plus an unbiased sample of all the trigger, pre-scaled by a factor 250 (av-erage rate 20 Hz)

• aGAMMAfilter, designed to accept γ rays.

The GAMMAfilter is the one routinely used for the collection of scientific data. It is composed by a sequence of tests (performed in hierarchical or-der) that an event must undergo in order to get accepted for downlink. These tests are designed to exclude ill-formed events and to act as a first stage of background rejections against charged particles. They exclude, for example, events not presenting at least one rudimentary track in the TKR, or whose track points to an ACD tile with signal. The use of the ACD veto signal is disabled in case of an event for which the energy deposited in the CAL exceed a given threshold (adjustable, currently 20 GeV), in order to preserve the relatively rarer high-energy particles for ground analyis. A more detailed description of theGAMMAfilter can be found in [96].

For the purpose of this work, both events coming from the γ filter and from theDIAGNOSTICfilter will be employed, as described in Chapter 4.

3.5

Event reconstruction

Upon transmission to ground, raw data undergo a complex analysis from a series of specifically designed algorithms, deputed to attempt event-by-event a reconstruction of its full development in the detector. In the pro-cess, a few hundreds of variables (figures of merit) are produced, providing a high-level description of the topology of each event in all the subsystems. After that, a multivariate analysis is performed on these quantities to find the best possible estimates for the particle’s energy and incoming di-rection. Another set of high-level variables are also produced, quantifying the quality of the reconstruction and estimating the probability that the particle is indeed a celestial γ ray.

This stage of the work has been improved significantly since the begin-ning of the mission. The initial scheme of analysis was developed before the launch of the LAT and was called Pass 6. A first upgrade was released in 2011 under the name of Pass 7. Reconstruction in Pass 7 did not differ substantially from what was done in Pass 6, the main change being a small adjustment in how the energy of the photon was assigned.3

A much more radical change has been put in place for the subsequent iteration of the event-analysis scheme, Pass 8, which was released in 2015 and is the current publicly released framework, used for many of the on-going scientific analysis performed on LAT data. The reconstruction algo-rithms have been entirely rewritten, and the selection of events redefined. Pass 8 brought a significant improvement to the performances of the LAT with respect to all the metrics: efficiency of the selection(s), angular and energetic resolution, background rejection.

One of the reasons which drove the development of Pass 8 was the dis-covery, soon after the launch, of an unexpected source of noise, consisting of remnants of electronic signals which persist in the various subsystems for a few µs after the passage of a particle4. If a particle traverses the LAT a few µs before the instrument has entered in read out mode, it is possible that the signal it leaves in the various electronic channels is erroneously read out together with the event data [98]. The entity of this effect varies according to the trigger rate, which is mostly driven by the rate of charged CR. .

Such pile-up signals, usually referred to as “ghost events”, could

con-3_{In 2013 the Fermi collaboration has reprocessed all the data collected since the}

be-ginning of the mission using an updated set of calibration constants [97]. Unless other-wise specified, in this work I will always refer to this reprocessed dataset (often called “P7_REP”) when referring to Pass 7.

3.5. EVENT RECONSTRUCTION 31

(a)

Simulated 1.6 GeV gamma-ray

Overlaid pile-up activity

Calorimeter centroid Calorimeter axis

(b)

Figure 3.8. Effect of the CAL clustering stage on the event reconstruction. The picture shows the signal produced by a gamma ray crossing the detector in pres-ence of a ghost particle. Pass 7 reconstruction is on the left panel: a single particle in the LAT is assumed. The CAL axis (blue line on the bottom) is flipped by ghost activity far from the gamma ray. The effect of the clustering, introduced in Pass 8 is on the right panel: the gamma ray is isolated and the event correctly reconstructed.

fuse the reconstruction and lead to a degraded energy or direction mea-surement, or even to incorrectly reject a good γ-ray event as background. In fact, in Pass 6 and Pass 7, the energy in the CAL was always treated as a single deposit, with the result that the reconstructed shower centroid and axis were altered in presence of ghost activity.

In Pass 8 the reconstruction is able to identify and remove the vast ma-jority of ghost events, recovering the full instrument efficiency. This is pos-sible because a preliminary stage of clustering of the CAL crystal energies is performed, with the shower axis and centroid computed separately for each cluster found (Figure 3.8). In this way, the pile-up signal can be dis-tinguished from the one left by the triggering particle and appropriately discarded.

Describing in detail the reconstruction algorithms and how they were modified in the transition between Pass 7 and Pass 8 is beyond the scope of this thesis. Here I will only summarize the basic functionality, underlying the most relevant changes to each subsystem:

CAL

As already mentioned, in Pass 8 CAL energy deposits are organized in clusters using a Minimum Spanning Tree algorithm, with the shower axis and centroid computed separately for each cluster. Clusters are associated with candidate tracks from the TKR to select the cluster corresponding

to the actual incoming particle and remove ghost activity. After that, an estimate of the particle energy is attempted starting from the deposited energy. Since energy measurement is a critical aspect of this analysis, I will describe in some detail the algorithms used in section 3.7. Here I will only note that in Pass 8 the modelling of the shower profile has been extended to handle events of energies up to 3 TeV.

TKR

The Pass 7 tracker reconstruction code made us of a track-by-track com-binatoric pattern recognition algorithm to find and fit up to two tracks, representing the electron-positron pair. TKR hit clusters in adjacent lay-ers were merged into candidate tracks with a Kalman filtering technique ([99],[100]), using the CAL centroid and axis as seed.

A limitation of such approach was that it made the efficiency and qual-ity of the track-finding intrinsically dependent on the accuracy of the CAL reconstruction. In addition to that, the track-finding algorithm could be also confused by a too high number of hits, in particular in presence of:

• multiple hits produced by electrons and positrons interacting readily in the tracker

• backsplash particles moving upwards from the calorimeter, causing a large number of randomly hit strips in the lower planes of the tracker (particularly for high-energy events)

with the result of both a loss of events (whose reconstruction failed at all or which were mislabelled as background) and a degraded direction mea-surement.

The Pass 8 reconstruction addresses these issues by introducing a global approach to track-finding that tries to model the shower development with one or more tree-like structures. In this process tracker hits are linked together and the Tree structures are built by attaching links that share a common hit.

The head of the Tree represents the assumed gamma-ray conversion point. For each tree, the primary and secondary branches, defined as the two longest and straightest, represent the primary electron and positron trajectories (if unique) and sub-branches represent associated hits as the electron and positron radiate energy traversing the tracker. The Tree axis is evaluated and used to associate the tree to a particular cluster in the calorimeter, which allows an estimate of the energy associated with the tree.

3.5. EVENT RECONSTRUCTION 33 Once an estimate energy is available, up to two tracks are extracted from the hits along the primary and secondary branches and fitted with a Kalman Filter technique, which accounts for multiple scattering. Tests with Monte Carlo simulations and flight data show that the new tracker pattern recognition significantly reduces the fraction of mis-tracked events. At the end of the process, the primary track (when available) is used to estimate the direction of the γ-ray. If a vertex has been found, the contri-bution of the two tracks is combined in producing the estimate.

ACD

In Pass 8 the ACD phase of the energy reconstruction has been fully re-written. It starts, as before, by estimating the energy deposited in each of the tiles and ribbons. Subsequently, these energy depositions are associ-ated to incident particle directions: here a major improvement occurred, since in Pass 7 only tracks derived from the TKR were used, while now directional information derived from calorimeter clusters is propagated as well. This additional CAL information is particularly important for iden-tifying background events at high energies or large incident angles, which are more susceptible to tracking errors. In these cases, the CAL provides the more robust directional information.

For each track is calculated whether its projection intersects an ACD tile or ribbon with non-zero energy deposition; if not so, the distance of closest approach is computed between the track projection and the near-est such ACD element. Track-tile associations are used when considering whether the event should be identified as charged particle and rejected in later analysis stages. Previously, a simple energy scaling dependence was used to characterize the robustness of such associations. However, widely varying event topologies can lead to large differences in the qual-ity of directional reconstruction for events of the same energy. In Pass 8, ACD reconstruction utilizes also event-by-event directional uncertainties to capture this information and to provide better background rejection.

The last major improvement comes from utilizing the fast ACD signals, provided to the LAT hardware trigger, to remove out-of-time signals from the ACD and mitigate the impact of ghost signals in the slower ACD pulse-height measurements. This is especially important at low energies, where calorimeter backsplash is minimal and a small deposition of energy in the ACD can lead to the rejection of an event.

3.6

Instrument Response Functions

Here I will briefly introduce a few metrics required for the characterization of the LAT, which I will refer to as Instrument Response Functions (IRFs). These are specific parametrizations of the instrument performance, allow-ing to convert the raw counts registered by the detector into physically meaningful quantities such as fluxes and spectral indices. In general, the IRFs are not intrinsic to the detector: they depend on the reconstruction algorithms and they always subtend a specific event selection, so that a detector may very well have different response functions in the context of different analyses.

Though the IRFs routinely used for LAT analyses are primarily de-signed for application to γ-ray study, most of what I will say will apply directly to electrons and positrons as well and I will use the same metrics to describe the performance of the CRE selection which will be introduced in Chapter 4.

1. Effective Area, Ae f f(E, ˆv, s), is the product of the cross-sectional ge-ometrical collection area, γ-ray conversion probability, and the effi-ciency of a given event selection (denoted by s) for a γ ray (or an electron) with energy E and direction ˆv (in the LAT reference frame); 2. Point Spread Function (PSF), P(ˆv0; E, ˆv, s), is the probability density to reconstruct an incidence direction v0 for a γ ray (or an electron) with energy E and direction ˆv (in the LAT reference frame), given the event selection s;

3. Energy Dispersion, D(E0; E, ˆv, s), is the probability density to measure an event energy E0 for a γ ray (or an electron) with energy E and direction ˆv (in the LAT reference frame), given the event selection s. Another quantity which will be useful in the following is the Accep-tance,A(E), that is integral of the effective area over the solid angle:

A(E) =

Z

Ae f f(E, θ, φ)dΩ (3.1) The acceptance is essentially the ratio between the flux of events in the instrument and the observed count rate.

It is handy to synthesize the accuracy of the energy and direction mea-surement by quoting the half-width of the smallest window which enclose a certain fraction of events (usually 68% or 95%) in the PSF or in the En-ergy Dispersion. These widths are usually given in units of solid angle

3.7. ENERGY MEASUREMENT 35 for the PSF and as a fraction of the central value in the case of the energy dispersion and are referred to as angular and energetic resolution, respec-tively.

3.7

Energy measurement

Two different energy reconstruction algorithms are employed by LAT anal-yses: a Parametric Correction (PC) and a fit of the Shower Profile (SP).

The PC algorithm was found to give better results at low energy (roughly below a few GeV). It works as follows: initially, the overall energy is taken to be simply the sum of the crystal energies. Starting from this quantity, a series of corrections are made to account for the energy loss due to leakage out the sides and back of the CAL and through the internal gaps between CAL modules. The amount of energy deposited in the TKR is evaluated by treating the tungsten-silicon detector as a sampling calorimeter, where the number of hit silicon strips in a tracker layer provides the estimate of the energy deposition at that depth. This “tracker” energy is added to the corrected CAL energy and contributes with an important correction at low energies (reaching∼50% on average at 100 MeV).

For higher energies, where the fraction of energy released in the tracker is negligible and the energy loss is mostly due to the leakage of the shower out of the CAL, a full three-dimensional fit of the SP has proven to be more effective.

A dedicated multivariate analysis is performed to decide, event by event, which of these two algorithms is more likely to produce the best es-timate of the energy, which is then chosen as the energy of the photon (or electron). In a small number of cases, the energy is assigned as a weighted average of the estimate of the two algorithms. This happens mostly in the transition region where their performance are comparable (∼a few GeV), in order to avoid introducing spectral features with a sharp transition.

Given the energy range of interest for this analysis, in practice only the SP fit is used and I will describe it in the rest of this section, specifying that this is not in any way the result of my work. For further details the interested reader can refer to [101].

The SP fit is performed on a layer basis, that is the quantities actually used in the fit are the values eiof the energies deposited in the 8 layers. In order to compute the predicted values for the ei, a gamma function is used

to model the average longitudinal development of the shower [102]:  dE(t) dt  =P(E,α,β)(t) = E× (βt)α−1βe−βt Γ(α) (3.2)

where t is the longitudinal shower depth in units of radiation length, α the shape parameter and β the scaling parameter. The position of the maxi-mum of the profile is T= (α−1)β.

The actual parameters used in the fit are not directly α and β, but rather two quantities which have been found to be less correlated and more gaus-sian distributed:

S0=ln(α)cos θc+βsin θc (3.3) S1 = −ln(α)sin θc+βcos θc (3.4) with tan θc = 0.5. A GEANT4 simulation of photons interacting in a CsI(Tl) volume is used to parametrize the shower shape at different en-ergies and incidence angles. The mean (µi) and RMS (σi) of the two Si as functions of energy are extracted from the simulation. The RMS of the residuals of the fit are used to parametrize the estimated model uncer-tainties δe(E). Compared to Pass 7, all these parametrizations have been extended in Pass 8 to cover the energy range up to 3 TeV.

As dicussed in [103], equation 3.2 can be used to model the single showers as well. The predicted energy in the i-th layer is then:

ei =

Z ∞

0 fi(t)P(E,α,β)(t)dt (3.5) where the factor fi(t) is the fraction of energy deposited in the i-th layer by the shower slice comprised between t and t+dt. This factor accounts for the fact that, in the case of particles with non vertical incident direc-tions, their lateral development in a single slice along the shower axis may intersect different CAL layers, as illustrated in Figure 3.9.

The radial profile is modelled as the sum of a core part and a tail part [103]: f(t/T, r) = 1 dE(t) dE(t, r) dr = p 2rRC2 RC2+r2 + (1−p) 2rRT 2 RT2+r2 (3.6) where RC and RT are the medians of the core and tail part, respectively, measured in units of Moliere radii, and p is the relative weight of the two components. The values of RC, RT and p are, again, estimated from GEANT4simulations. They depends on the ratio t/T in a way which has been found to be nearly independent from energy.

3.7. ENERGY MEASUREMENT 37

Figure 3.9. One step of the development of an individual shower inside a calorimeter module. The arrow corresponds to the photon trajectory. The red disk represents a shower slice at a given shower depth for which the fraction of energy deposited in each layer is computed. Edited from [101].

In practice the fit is performed by moving along the shower trajectory in step of 1.85 mm (0.1X0) and computing the energy deposited in each crystal, using the radial and longitudinal profile. The full geometry of the LAT is taken into account, including the gap between the towers and the presence of passive materials (like the carbon structure). The predicted deposits in the single crystals are then summed up to form the predicted energy in the 8 layers ei, which are compared to the measured deposits ei. The free parameters of the fit are the energy and two shapes parameters, for a total of 5 degrees of freedom.

In order to better constraint the fit, a term is added to the χ2 which corresponds to the penalty applied to S0 and S1 for being far from their expected value. Since S0and S1are reasonably gaussian and uncorrelated, the term added is simply∑is2i, with si = (Si−µi(E))/σi(E). This addi-tional constraint is especially useful to avoid overestimating the energy when the shower is poorly contained in the CAL.

The shower fit χ2than becomes:

χ2(S0, S1, E) = 8

∑