FACOLTÀ DI SCIENZE MATEMATICHE FISICHE E NATURALI Corso di
Laurea magistrale in fisica
Association of high energy photons to known sources with
the AMS-02 experiment
Tesi di laurea magistrale Master thesis
Candidato: Stefania Vitillo
Relatore:
1 High Energy Gamma Rays 3
1.1 γ rays and Charged Background . . . 3
1.2 Production Processes . . . 4
1.3 γ ray Interactions . . . 5
1.4 The Gamma Sky . . . 6
1.4.1 Diffused γ emission . . . 6
1.5 Cosmic γ ray Sources . . . 7
1.6 γ ray Detectors . . . 8
1.6.1 Earth based detectors . . . 8
1.6.2 Space based detectors . . . 9
2 The AMS-02 experiment 11 2.1 The Detector . . . 12
2.2 AMS-02 main components . . . 14
2.2.1 Transition Radiation Detector (TRD) . . . 14
2.2.2 Time Of Flight (TOF) . . . 15
2.2.3 Permanent Magnet (PM) . . . 17
2.2.4 Silicon Tracker (TRK) . . . 17
2.2.5 Anti-Coincidence Counters (ACC) . . . 18
2.2.6 Ring Imaging Čerencov Counter (RICH) . . . 19
2.3 Charge particle detection . . . 20
2.3.1 Charged particle Trigger . . . 20
3 Electromagneric Calorimeter 21 3.1 ECAL design . . . 22
3.1.1 Front end electronics . . . 24
3.1.2 ECAL Standalone Trigger . . . 24
3.2.3 Angular resolution . . . 30
4 Angular resolution 33 4.1 Importance of the direction . . . 33
4.1.1 Center Of Gravity method (COG) . . . 34
4.1.2 Cell Ratio (CR) method . . . 34
4.1.3 Lateral Fit method . . . 34
4.2 Event selection . . . 35
4.2.1 Angular resolution . . . 36
4.3 Point Spread Function . . . 37
5 Candidate Photon Selection 41 5.0.1 Event Preselction . . . 41
5.0.2 Boosted Decision Tree Training . . . 42
5.1 Photons Converted before ECAL . . . 45
5.2 Last Selection . . . 46
5.3 AMS Photon Acceptance . . . 46
5.4 Purity of the Photon Selection . . . 48
6 Study of Sources of High Energy γ rays 49 6.1 AMS-02 Source Sensitivity . . . 49
6.1.1 Exposure Time Maps . . . 50
6.1.2 Exposure Maps . . . 51
6.2 Detectable sources . . . 51
6.3 Photon - Source Association . . . 56
6.3.1 Distribution of expected γ from isotropic background in galactic coordinates . . . 60
6.3.2 Distribution of expected γ from diffused galactic background in galactic coordinates . . . 62
6.3.3 Expected distance of photons from sources . . . 64
6.4 Fit of the Data with Monte Carlo templates . . . 64
High energy γ rays can be produced through acceleration of charged particles by galac-tic astrophysical objects like Supernova Remnants or Pulsars, or by extragalacgalac-tic sources (Active Galactic Nuclei and Blazars). Because photons are neutral particles, they are not deflected by galactic magnetic fields and their incoming direction points back directly to the source. Chapter 1 gives details on the production processes and detection methods used for γ rays.
The Alpha Magnetic Spectrometer (AMS-02), a general purpose experimental appa-ratus installed on the International Space Station on May 16th 2011, has the capability to detect high energy γ rays because of its electromagnetic calorimeter (ECAL), which is able to trigger and identify γ rays. ECAL has an excellent energy resolution (about 1.4% at 1 TeV). At present, no other γ ray detector operating in Space has a better energy resolution for γ rays in the TeV region. Furthermore, from test beam studies, ECAL is expected to have a good angular resolution, a crucial feature to associate γ rays to known sources. Chapter 2 and Chapter 3 give details on the AMS-02 experiment and its electromagnetic calorimeter.
Assuming the angular resolution is the same for electrons and photons (both develop similar electromagnetic showers in the calorimeter), electrons were used to estimate the angular resolution because they can be traced by means of the AMS-02 silicon tracker. In fact, the electron direction was obtained by applying three different algorithms to the electromagnetic shower shape in ECAL, then comparing the results with the direction reconstructed by the silicon tracker. The best agreement was found using an algorithm that provides an angular resolution of about 0.5◦at 1 TeV. This algorithm was chosen to
analyze γ rays. Chapter 4 is dedicated to the study of the angular resolution of ECAL for high energy γ rays.
Chapter 5 shows how photons were identified using a Boost Decision Tree, which enhanced the separation between photons and background.
The angular error associated to each γ is transferred into galactic coordinates to obtain its Point Spread Function (PSF), which depends on the energy and on the
im-be detected by AMS-02, owing to the AMS-02 acceptance (geometric acceptance plus efficiency) and to its exposure time. Sources expected to be detectable by ECAL were taken into account in this thesis. For each selected γ, with its PSF, the distance from the nearest source (in number of σ) was used to associate γ rays detected by ECAL to Fermi’s sources. To estimate the amount of fake associations due to diffused photons, a Monte Carlo simulation was developed to generate random events distributed according to the expected diffused photon flux. In Chapter 6, a description of all the steps fol-lowed in the association between the candidate γ rays to known sources is reported.
This thesis shows that, thanks to the extraordinary capability of ECAL to reconstruct the incoming direction, AMS-02 can identify sources, among the known ones, emitting γ rays from 30 GeV to TeV energies.
High Energy Gamma Rays
"Let there be light." The Bible; Genesis 1:3
Gamma radiation represents the most energetic part of the electromagnetic spectrum (see Fig. 1.1). Therefore it provides information about the most energetic processes and phenomena in the Universe. The relative penetration power of γ rays derives from the absence of atomic interactions. In a layer of material a γ ray will however eventually collide with an individual atomic nucleus or electron. The γ ray arrival direction gets lost in repetitive interactions, the energy being redistributed among secondary particles and photons. With ∼ 27 radiation lengths (X0) and a characteristic thickness of 20 km,
the Earth’s atmosphere is a thick shield! Gamma ray detectors must therefore operate at high altitudes, above 40 km, to allow a direct measurement. An overview on the space-based observations one can be found in [1].
1.1
γ rays and Charged Background
In Fig. 1.2 the fluxes for protons, electrons and positrons as measured by AMS-02 ([2] and [3]), with the photons flux as measured by Fermi LAT in [5] are compared: γ rays are only a very small fraction of the total cosmic rays composition, whose flux is dominated by protons (p/γ ∼ 105) and by electrons (e/γ ∼ 103). Their energy spectra above 10
GeV is well described by power laws of the form: dN
dE = E
−η (1.1)
The energy spectrum of photons is less steep (ηγ ∼ 2.5) than the electron one (ηe∼ 3),
Figure 1.1: The electromagnetic spectrum, from radio to γ ray wavelenghts.
Figure 1.2: Fluxes for protons, electrons and photons compared.
1.2
Production Processes
• Sinchrotron radiation. A high energy cosmic ray electron in a typical interstellar magnetic field would radiate synchrotron photons at
Eγ ' 0.05 Ee TeV 2 · B (3µG)(eV) (1.2)
where Ee is the electron energy and B the interstellar magnetic field [4]. Both
higher magnetic field strength or very energetic e±shift this radiation up in energy
and into the γ ray regime.
• Inverse Compton Scattering. Up-scattering of photons of lower energy through collisions with energetic electrons is called Inverse Compton process. If photons of lower energy collide with energetic electrons, these photons may gain energy in the collisions, thus being promoted in energy. The typical energy of Inverse Compton scattered photons rises rapidly with energy:
Eγ' 1.3 Ee TeV 2 · Eph 2 × 10−4(eV) (GeV) (1.3)
where Ee is the energy of the electron and Ephis the energy of the thermal photon
involved in the process [4].
• Bremsstrahlung. Charged particle acceleration through electric fields of nuclei results in bremsstrahlung emission in the γ ray regime. In the Universe, cosmic rays electrons interact with the interstellar gas and emit Bremsstrahlung γ rays. • γ rays from nuclear transition. Whenever some energetic interaction, like
energetic collisions of cosmic rays, brings disorder into the state of a nucleus, a γ ray line emission from nuclear de-excitation is expected.
• Pion Decay. Pions are created during strong interaction events such as collisions of cosmic ray protons with ambient gas nuclei. Neutral pions π0 decay rapidly into
two photons, with an energy distribution peaking at mπ/2, half the rest mass of
the pion. In the laboratory frame the energy of the photons could reach the GeV band.
• Annihilation of pairs of particle and antiparticle also produces γ rays.
1.3
γ ray Interactions
The possible interaction processes involving a γ ray vary with the energy of the γ: • Photoelectric absorption. Atomic electrons are removed from their nuclei, thus
reducing the energy of the γ ray photon by the electron’s binding energy. This is the dominant process at energies below 100 keV.
• Compton scattering. Electrons are hit by the γ ray photons, and gain a fraction of the photon’s kinetic energy in this collision. This is the dominant interaction process in the 0.1 MeV to a few MeV regime.
• Pair creation. In the presence of an electric field (usually of the atomic nucleus), the γ ray energy may be converted into a particle-antiparticle pair, electron and positron. This interaction process cannot occur below a threshold of 1.022 MeV, and the cross section increases with energy so that it dominates over Compton scattering above several MeV.
1.4
The Gamma Sky
γ ray emission is a phenomenon of the most compact and energetic objects in the Uni-verse. In the Milky Way these are especially pulsars, accreting binaries (systems in which a neutron star or a black hole accretes matter from its normal stellar companion) and supernova remnants. Supernovae and their remnants are probably the sources of the bulk of cosmic rays in the Galaxy, which produce intense, though spatially diffuse emission of γ radiation. In extragalactic space, active galactic nuclei and blazars are the most common γ ray emitting objects. The γ ray all sky map is shown in Fig. 1.3.
Figure 1.3: The γ ray all sky map. The concentration of the emission along the Galactic Plane is the most striking aspect of the map. The plane stands out clearly against the rest of the sky, indicating that most of the measured γ ray fluxes come from regions or objects inside the Galaxy [5].
1.4.1 Diffused γ emission
At GeV energies the γ ray sky is dominated by galactic diffuse emission [6], originated by interactions of cosmic rays in the interstellar medium that represents more than 90% of the total luminosity of our galaxy (see Fig. 1.4).
Figure 1.4: The sky map view of the galactic diffuse emission [5].
1.5
Cosmic γ ray Sources
According to the characteristic production processes, the following different types of cos-mic γ ray sources may be identified:
-Galactic Sources
Supernovae Remnants (SNR). A supernova remnant is the structure resulting from the explosion of a supernova. The supernova remnant is bounded by an expanding shock wave, causing the acceleration mechanism for cosmic rays. Cosmic ray particles are not only produced in the sources but also accelerated to high energies in or near the source. Fig. 1.5 shows the energy spectrum of cosmic ray protons.
Pulsars. Pulsars are spinning magnetized neutron stars, that are remnants of su-pernova explosions. While stars typically have radii of 106 km, they shrink under a
gravitational collapse to a size of just about 20 km. This process leads to densities of 6 · 1013g/cm3and electrons and protons are so close to produce neutron through the weak process:
e−+ p → n + νe.
In neutron star, neutron decay will be prevented by the Pauli principle, because all the quantum states that can be reached by the electron and the proton are already filled. Pulsars have enormously strong magnetic fields, which are believed to be responsible for acceleration of cosmic ray protons and nuclei.
A detailed description on galactic sources can be found in [7]. -Extra Galactic Sources
Active Galactic Nuclei (AGN) and Blazars. Active galactic nuclei are the most energetic, luminous and persistent objects in the Universe and therefore they can be used to discover distant objects. The basic structure of AGN consist in cold material
Figure 1.5: The primary cosmic ray spectrum showing the power law E−2.7 dependence at energies below the ’knee’, steeping to E−3.0at energies above it.
that forms an accretion disk around massive black holes. In the course of absorption, the accretion material will undergo violent oscillations and will be ionized as a plasma (see Fig. 1.6): consequently charged particles may be accelerated to very high energies, and in interacting with the magnetic fields generated by the plasma currents, can radiate either at infrared, optical, and X-ray frequencies.
In some cases these charged particles can punch through the minor axis of the ac-cretion disc, giving rise to two narrow jets of particles travelling in opposite directions. AGN’s emitting γ rays is in the TeV energy region, are called blazars. Blazars are de-picted as AGN sources where a relativistic jet is pointing to the observer, so resulting very important for γ ray astronomy.
γ ray bursts. They are quicker sources typically lasting from 10 milliseconds to 10 seconds. γ ray bursts are quite common (around one or two per day), and result to be distributed almost isotropically over the sky [9].
1.6
γ ray Detectors
1.6.1 Earth based detectorsTo detect a γ ray, it must interact with matter. γ rays interacting at high altitude pro-duce electron-positron pairs with a subsequent development of electromagnetic showers. Earth-bound γ ray detectors use the electromagnetic showers to identify γ’s: however
Figure 1.6: Schematic representation of our understanding of the AGN phenomenon and its main components [8].
only γ rays with energy larger than 100 GeV produce detectable showers and earth based detectors make use of the atmosphere as calorimeter. For further details see [10].
1.6.2 Space based detectors
To avoid the interaction with the atmosphere, detectors must be mounted on a satellite platform, or on a balloon. Explorer 11 (1961) was the first γ ray detector installed on a satellite and the instrument aboard was able to detect γ rays above 50 MeV. In the years 1963 to 1970, Vela satellites were the first to detect γ ray bursts. Cos-B was the first ESA satellite dedicated to the detection of γ rays. CGRO (Compton Gamma Ray Observatory) was a giant of 17 tons, making it the largest astrophysical base of its time. The telescopes mounted on it, like EGRET (Energetic Gamma Ray Telescope), studied photon energies ranging from 20 keV to more than 30 GeV. CGRO’s successful career lasted until 2000 and showed that our Universe is a violent and rapidly changing place: the EGRET γ ray telescope detected 271 sources (60 are blazar but many of them remained unidentified). The Fermi Gamma-Ray Space Telescope, launched on June 2008, is detecting a lot of sources having high-confidence associations with known blazars. The Alpha Magnetic Spectrometer, (AMS-02), is a particle spectrometer installed on the International Space Station. Since May 2011, also is detecting γ ray’s.
AMS-02 compared with EGRET and Fermi
In the study of γ rays AMS-02 is highly competitive with EGRET and Fermi because this spectrometer is able to provide significant measurements of γ ray fluxes also above 100 GeV, up to a few TeV. Up to now only Cherenkov telescopes on Earth have reached TeV energies, although with viewing angles of only a few degrees. As a further important plus the ECAL (Electromagnetic CALorimeter) provides a better energy resolution than ever so far.
The AMS-02 experiment
The Alpha Magnetic Spectrometer (AMS-02) is a multipurpose astroparticle physics de-tector installed on the International Space Station (ISS) on May 19th 2011 during the STS-134 NASA Endeavour Shuttle mission. 02 is the improved version of the AMS-01 space spectrometer, which flew for 10 days on the Shuttle Discovery (NASA mission STS-91) in June 1998 for measure the cosmic rays spectrum.
AMS physical goals are:
• Indirect Dark Matter search. Pairs of photons, electron-positron or proton-antiproton, could be originated from dark matter annihilation. So measuring the fluxes of these particles might allow the dark matter detection.
• Antimatter search. The detection of anti-nuclei in cosmic radiation, like a nu-cleus of anti-He, is a direct proof of the existence of anti-matter domains in the Universe, since the probability to produce He by spallation of primary cosmic rays on the interstellar medium is extremely low [14]. So the detection of a single anti-helium or anti-carbon would be a smoking gun for the presence of large amounts of antimatter in the Universe and for the existence of anti-stars and anti-galaxies. The BESS-Polar experiment measured an upper limit on the flux ratio of anti-He to He of 10−7 in the rigidity range 1-14 GV [15] extended up to 140 GV by the
AMS-01 experiment with an upper limit of 1.1 × 10−6 [16].
• Cosmic ray physic. AMS-02 could provide precise measurements of B/C and
10Be/9Beratios and thus obtain more information in understanding cosmic rays in
the galaxy.
• γ ray physics: they are ideal tools to study astrophysical sources. Being neutral particles, they are not deflected by intergalactic magnetic fields and point back direct to their sources.
2.1
The Detector
AMS-02 (see Fig. 2.1) has been designed taking advantages from the experience on high energy particle physics experiments but unlike these ones, AMS-02 is a space-borne experiment. This imposed several strict constraints to the detector about the weight (≤ 7 tons), the power consumption (≤ 2 kW) and the resistance to mechanical and thermal stresses. Furthermore, the experimental apparatus was required to be largely redundant because it has to work in space for 10 years without any external intervention.
The AMS core is composed by a Permanent Magnet (PM) generating a field of about ' 0.15 T within a cylindrical shaped volume (diameter and height ' 1 m). Seven planes of silicon detectors inside this volume (inner Tracker) and two planes outside the field volume (outer Tracker) allow to reconstruct the tracks of charged particles (TRK). At both ends of the magnet two segmented scintillator planes (TOF) are placed and measure the Time Of Flight of charged particles. The AntiCoincidence scintillator Counter (ACC)is a barrel of scintillation counters surrounding the inner Tracker and providing a veto signal to the trigger produced by side particles. In AMS-02 three other sub detectors contribute to particle detection: the Ring Imaging Čherenkov (RICH), located below the magnet and measuring the particle velocity and charge; the Transition Radiation Detector (TRD), placed on top of AMS, and ensuring e/p separation and the Electromagnetic CALorimeter (ECAL), the bottom subdetector, allowing an accurate discrimination between γ, e+, e− and hadrons and the energy measurement.
Fig. 2.2 shows an exploded view of the AMS-02 detector and Fig. 2.3 show the charged particles path.
Figure 2.2: AMS-02 exploded view.
Figure 2.3: Example of particle crossing AMS-02.
In the following sections each AMS-02 main components is briefly reviewed. A de-tailed description of ECAL is given in the next chapter.
2.2
AMS-02 main components
2.2.1 Transition Radiation Detector (TRD)
Transition radiation (TR), is emitted in those cases when charged particles traverse the boundary between media with different dielectric properties. At each interface the emission probability for an X-ray photon is on the order of α = 1/137. So the number of transition radiation X-ray produced can be increased if the charged particle traverses a large number of boundaries. The interesting feature of transition radiation is that the energy radiated through photons increases with the Lorentz factor γ = E/m. For electrons and positrons the TR is maximal for momentum > 5 GeV/c, while protons start to emits TR photons from momentum ≈ 300 GeV/c. Because of this different behaviour of electrons and protons, such a radiation is useful to distinguish e from p.
AMS-02 TRD consist of 328 module, arranged into 20 layers [17]. Layers are organized in an octagonal conical structure and the top and the bottom four layers are oriented parallel to the magnetic field while the middle 12 layers run perpendicular to offer 3D tracking. Each module contains:
• a 20 mm thick radiator, made of polypropylene/polyethylene fiber fleece corre-sponding to 0.06 g/cm3. A large number of radiating interfaces is needed to increase
the probability of production of X-rays.
• 16 straw tubes of a diameter of 6mm and filled with a Xe − CO2 gas mixture: gas
detectors reveal transition radiation.
The structure of one module is shown in Fig. 2.4.
Figure 2.4: Principle of operation of TRD.
Using a likelihood selection to combine the measurements in the 20 layers, it is possible to obtain an electron/proton rejection of 102 for protons up to 250 GeV, with a 90%
Figure 2.5: The AMS-02 TRD after completion of the construction [17].
Figure 2.6: Likelihood method applied to electrons and protons.
2.2.2 Time Of Flight (TOF)
The Time Of Flight (TOF) of AMS-02 consist of four planes with respectively 8, 8, 10 and 8 plastic scintillators: two planes are located above the permanent magnet and two planes below. The TOF detector provides the fast trigger to the experiment and ensures the measurement of velocity and charge of the crossing particles. To save weight and thanks to the low magnetic field, the scintillator PMTs work without shielding. In fact the magnetic field worsens the TOF performances less than 10 % [18]. Each TOF counter is a 1 cm thick scintillator paddle (1.2 m2 area of each plane) coupled at both ends with
PMTs. The PMTs are arranged so that the angles between them and the magnetic field is compatible with a larger PMT response. In Fig.s 2.7 and 2.8 the top views of the upper time of flight and the lower time of flight detectors are shown. A schematic view is represented in Fig. 2.9. The efficiency of each counter is greater than 99%.
Thanks to its excellent time resolution (see Fig. 2.10), TOF is able to distinguish downgoing particles from upgoing ones at a level of 10−9. Furthermore, TOF provides a
Figure 2.7: Assembled paddle on the upper
TOF. Figure 2.8:TOF. Assembled paddles on the lower
Figure 2.9: Design of the AMS-02 upper and lower TOF.
light allows nuclei absolute charge determination up to Z ∼15.
2.2.3 Permanent Magnet (PM)
In the AMS-02 spectrometer the Permanent Magnet (PM) consists of over 6400 Nd-Fe-B blocks (with dimensions 5 × 5 × 2.5 cm3) that produce a bending field inside a cylindrical
volume ∼ 1 m in diameter and 1 m in height. The field of the magnet is 1.5 kG strong, approximatively uniform in one direction (X) (assigning the Z direction to the detector axis, so the Y is the bending axis), with a bending power of BL2 = 0.15 Tm (Fig. 2.12).
The external residual field is ≈ 3 G at a distance of 2 m, so ensuring negligible dipole moment and avoiding any interference with electronics.
Figure 2.11: The AMS-02 Permanent magnet. Figure 2.12: Magnetic field orientation and in-tensity.
2.2.4 Silicon Tracker (TRK)
The AMS-02 Tracker is made of 2264, 41 × 72 × 0.3 mm3 silicon microstrip sensors, with
an overall active area of ≈ 6.7 m2. From 7 until 15 sensors, are assembled in ladders,
whose variable length allows an excellent matching with the magnet geometry. The total number of ladders is 192. The ladders are distributed in 9 layers (one is shown Fig. 2.13): 7 are placed inside the magnetic field (inner tracker), one on top of TRD and the last on top of ECAL. The tracker planes are supported by carbon fiber structure, which can have excursions up to 30 µm due to changes in thermal conditions: so during data taking realignment of the planes is necessary. This is done by a Laser Alignment System (TAS) composed by 20 laser beams allowing an accuracy of order of 5 µm. The TAS range covers only the 7 inner tracker layers.
The TRK is able to measure the particle path with a precision of order of 10 µm in the bending direction Y and 30 µm in the X one [19]. The trajectory of a charged particle that travels in a uniform magnetic filed B is an helix with radius:
r = R
Figure 2.13: Tracker plane 2 view.
where R = pc
Ze is the Rigidity of the particle and ϑ the angle between the momentum (p)
of the particle and the magnetic field. The AMS-02 magnetic field is well known point for point, so the reconstruction of the full path can be used to measure the particle rigidity. The relative uncertainty on R depends on the spatial resolution σs, on the level arm l of
the inner Tracker and the level arm L of the full tracker ∆R
R = Rσs
BlL. (2.2)
The rigidity value that matches an uncertainty of 100%, is called Maximum Detectable Rigidity (MDR). For the inner tracker MDR is ≈ 200 GeV, while for the full tracker MDR ≈ 2 TeV.
2.2.5 Anti-Coincidence Counters (ACC)
The Anti-Coincidence Counters (ACC) consist of 16 scintillator paddles (220 × 830 × 8mm3) surrounding the inner Tracker with cylindrical symmetry. Wavelength shifting fibers, 1 mm in diameter collect the light coming from the scintillating paddles. The signals from ACC are used to provide a veto to the trigger so to eliminate particles that enters the tracker from the side or particles generated in secondary interactions inside the detector. The ACC planes have very high efficiency, better than 99.99%.
2.2.6 Ring Imaging Čerencov Counter (RICH)
A charged particle, traversing a medium with refractive index n(ω) at a velocity v exceed-ing the velocity of light in that medium (c
n), emits a particular electromagnetic radiation,
called Čerenkov radiation. Čerenkov radiation is emitted because the charged particle polarises atoms that coherently emit radiation at a characteristic angle ϑc determined
from the relation:
cos ϑc=
1
βn(ω) (2.3)
Eq. (2.3) provides a velocity measurement.
Also the charge of the incoming particle can be estimated by measuring the number of photons (Nγ) in a frequency range dω produced in a material:
d2N
dω dx = αZ
2sinϑ
c. (2.4)
To measure charge and velocity of cosmic ions, AMS-02 is equipped with a Ring Imaging Cherenkov detector (RICH). RICH (see Fig. 2.14) consists of a layer of radiator material, a conical mirror and an array of 680 PMTs that cover the entire lower base with the exception of a 64 × 64 cm2 central square hole to let particles reach unaffected ECAL.
It has a truncated conical shape with 60 cm upper radius, 67 cm lower radius and a height of 47 cm. The radiator is a primary component of this sub-detector since the
Figure 2.14: A design of the AMS-02 RICH. The radiator layer is placed upon the conical mirror. On the bottom is localized the PMT matrix to detect the photons.
velocity resolution depends strongly on its properties. It was chosen a 3 cm thick radiator consisting in blocks of silica Aerogels with a refractive index between 1.03 - 1.05 that surrounds a central block of sodium fluoride (NaF with nN aF = 1.335). Fig. 2.15 shows
RICH section and reconstruction technique and an example of Čerenkov light detect trough reflection method.
A good velocity resolutions allows to derive the mass of the crossing particle: ∆m m 2 = γ4 ∆β β 2 + ∆p p 2 (2.5)
Figure 2.15: Left: RICH structure and detection procedure. Right: Example of a Čerenkov ring generated thanks the help of the mirror.
where p is the particle momentum measured by the TRK. From Eq. 2.5 it is clear that the total uncertainty on the mass m is dominated by the β resolution that is ∆β
β ∼ 10
−3.
2.3
Charge particle detection
Being able to measure the absolute value of the charge |Z| (given by TRK, TOF and RICH), the sign of the charge (TRK), rigidity R (TRK), velocity β (TOF and RICH) and particles energy trough ECAL, AMS-02 can indirectly infer particles momentum and mass:
RZe
c = p = mγβc. (2.6)
2.3.1 Charged particle Trigger
For charged particles AMS-02 uses two-steps trigger:
1. Fast Trigger (FT) provided by the TOF detector, which is also used as time zero for the event;
2. A Level1 trigger (LVL1) provided by a combination of signals from TOF, ECAL (with an ACC veto).
Moreover, TOF use also the energy loss measurement to send to the trigger logic system a special flag for ions events disabling the ACC veto, so to avoid trigger inefficiency for highly charge particles (whose flux is low). The total LVL1 trigger rate ranges from 200 Hz to 2000 Hz, depending on the geomagnetic latitude.
Electromagneric Calorimeter
AMS-02 Electromagnetic Calorimeter (ECAL) is a fine grained lead scintillating fibers sampling calorimeter, measuring e± and γ energy from ∼ 2 GeV up to 2 TeV; ECAL
has a good energy resolution, and a high linearity. Its geometrical structure allows an accurate 3D imaging of the longitudinal and lateral profile of electromagnetic showers. It’s thickness corresponds to about ∼ 17 radiation lengths (X0) and ∼ 0.7 interaction
lenghts (λI) so that the 3D shower shape allows an accurate discrimination between
electromagnetic showers and hadronic cascades (see Fig. 3.1).
3.1
ECAL design
ECAL consist of a lead/scintillating fiber sandwich with an active area of 648 × 648 mm2 and a thickness of 166 mm. ECAL is subdivided in 9 SuperLayers (SLs) each
18.5 mm thick. Each superlayer is made of 11 grooved lead foils (1 mm thin) interleaved with scintillation fibers of 1 mm diameter, glued to the lead foils by epoxy. In SL’s the fibers run, alternatively, in orthogonal directions. So 5 SLs have fibers parallel to the Y axis and 4 SLs to the X axis (see Fig. 3.2 and 3.3).
Figure 3.2: Picture of the 9 ECAL SuperLayers.
Fibers of a SL are read out by 36 four anode Hamamatsu R7600-00-30 M4 photo-multipliers (PMTs) positioned on the two opposite ends to avoid dead areas (Fig. 3.4). Each anode reads an area of 9 × 9 mm2 defined as a cell, the smallest detected unit
corresponding to 35 fibers. Each SL is divided into two layers. Every layer has 72 cells for a total of 18 × 72 = 1296 cells and 36 × 9 (SLs) = 324 PMTs in the whole ECAL. This structure allows to sample the longitudinal profile in 18 independent measurements, 10 on the Y wiev and 8 on the X view (Fig. 3.5 and 3.6).
Figure 3.3: ECAL "pancake" geometry.
Figure 3.4: Picture of a super layer with the PMT positioning.
The scintillating fibers are coupled to PMTs (Fig. 3.7) through plexiglass light guides having a truncated pyramidal shape (Fig. 3.8). The PMTs are surrounded by a 1 mm thick soft iron square parallelepiped acting as a magnetic shield.
0 1 2 3 4 5 cell # 0 10 20 30 40 50 60 70 layer # 0 2 4 6 8 10 12 14 16 xz and yz view xz and yz view
Figure 3.5: View of the shower development in the xz and yz planes.
#Layer 0 2 4 6 8 10 12 14 16 18 E [GeV] 0 1 2 3 4 5 6 7 Longitudinal view Longitudinal view
Figure 3.6: View of the longitudinal profile of the shower produced by a 69 GeV MC generated photon.
Figure 3.7: Comparison in height between a
3.1.1 Front end electronics
The PMTs result to have an excellent linearity in the energy range from ≈ 7 MeV/cell (corresponding to MIP particles) up to ≈ 60 GeV/cell (corresponding to the highest energy that can be deposited in a cell by a 1 TeV particle). The anode signals are separated into two by voltage dividers: one of these two signals is amplified by a factor 33 (high gain) so to be able to measure MIP; the other one (low gain) is used to measure high energies (see Fig. 3.9).
Figure 3.9: Plot of the high ad low gain of the two anode signals [20].
In order to have a redundant signal in case of anode breakdowns, besides the 8 anode signals, the last dynode of each PMT is read. The 9 channels (2 × 4 anodes + 1 dynode) from 9 PMTs are sent to the ECAL intemediate board (EIB) and then to the data reduction board (EDR). This board receives the digitalized dynode signals and compares to a programmable threshold obtaining trigger bits. These bits are used by the ECAL TRigger board (ETRG) that produces the fast and Level1 ECAL standalone trigger.
3.1.2 ECAL Standalone Trigger
AMS-02 calorimeter has a key role in γ ray identification since the material in front ECAL corresponds to ∼ 0.5 X0, so a large fraction of incident photons do not convert
before reaching the calorimeter. Non-converting γ’s are identified by a dedicated ECAL Standalone Trigger. Searching a compromise between a high energy deposit in a single channel (for a better signal/noise ratio) and a good shower image reconstruction (for a good angular information), ECAL trigger is built up using 1 PMT as elementary granularity. This choise has also the advantage to allow the use of dynode signals, which are not amplified and very fast. ECAL trigger develops in two steps:
• a Fast Trigger available every 180 ns that provides the number of PMTs above threshold (∼ 100 MeV) in the 6 central superlayers (3 in the x view and 3 in the y view), how it is shown in Fig. 3.10;
• a Level 1 trigger (response of less than 1 µs) given by a fast reconstruction of the particle direction with the center of gravity method.
Figure 3.10: ECAL SLs involved in trigger logic (red).
Fast Trigger. The Fast Trigger is designed for a fast separation of photons from the large background of protons. It is obtained by imposing a threshold on each PMT of the 6 relevant SLs. The first SL is excluded because most part of the photons not convert or convert too late there. The last two SLs are not taken into account due to the large fluctuations in the final part of electromagnetic showers. The thresholds are chosen to ensure the 90 % efficiency at 2 GeV (see Tab 3.11). The trigger logic requires at least
Figure 3.11: Fast trigger efficiency (in %) for photons.
2 out of 3 SLs in each view with at least 1 PMT above threshold so to preserve the trigger in case of PMT failures and to maintain a high efficiency also on lately converting photons.
Level 1 Trigger. The Level 1 Trigger applies a selection criterion on the incoming particle direction. In fact, only if particles have an angle lower than 20◦ with respect to
the detector central axis, its trajectory crosses tracker planes and ECAL (see Fig. 6.3). To evaluate the particle path, the average position of PMTs above threshold, using the center of gravity method, is calculated (Fig. 3.13). The efficiency of Level 1 Trigger is shown in Tab. 3.14.
3.2
Performances
3.2.1 Electromagnetic showers
In describing particle showers it is useful to introduce the parameters: t = x
Figure 3.12: Maximum photon angle intersecting both tracker and ECAL: an angle of 20◦ corresponds to a distance of ∼1.5 PMTs between the impact point in the two farer SLs.
Figure 3.13: Example of centers of gravity: the average position of PMTs above threshold in a SL.
where X0 (in cm) is the radiation length of the calorimeter and x is the shower depth
(in cm): in this way the shower depth is measured in radiation length unit. The mean longitudinal profile of the energy deposition in an electromagnetic shower is described by the Rossi function [21]:
dE dt = E0b
(bt)a−1e−bt
Γ(a) (3.2)
where Γ is the gamma function, a is the shape parameter and b the scaling parameter related to the calorimeter material and nature of the electromagnetic particle [22]. The maximum is given by tmax= a − 1 b ≈ ln E Ec (3.3) where Ec is the critical energy of the medium, for which is widely used the
parametriza-tion Ec= 610 MeV/(Z + 1.24)and for lead is ∼ 8 MeV.
Fitting the longitudinal shape according to Eq. (3.2), it is possible to obtain the radiation length X0 (in layer units) from a linear fit from Eq. (3.3) (see Fig. 3.15).
Figure 3.15: Determination of radiation length in layer units at test beam [20].
As expected by construction, one radiation length is very close to the dimensions of one layer (the mean layer thickness: 0.925 cm):
Therefore ECAL, being made by 18 layers, has a thickness of ≈ 17 X0 ensuring ∼
75% containment of an e.m. shower produced by an electron with 1 TeV energy. The transverse development is described by the Moliere radius
RM = X0
21 MeV Ec
. (3.5)
A cylinder of radius RM contains, independently by the energy of the incident particle,
90% of the shower energy, while at 3 RM the containment arrives at 99%. In ECAL RM
is 2 cm, twice the length of a cell side.
3.2.2 Energy reconstruction and resolution
The AMS-02 detector was tested in 2010 using primary and secondary beams at the Super Proton Synchrotron (SPS) at CERN. The response of the detector was tested either with electron and positron beams between 8 GeV and 400 GeV. A Be target was also used to produce pion beams.
At test beam, as a first step, ECAL was equalized, i.e. the HV of all PMTs were adjusted in order to get the same response for the same energy deposit in the calorimeter. This equalization was done using MIP particles (specifically, protons). After equalization the ECAL response to electrons and positrons was studied. Because the read out of each cell have an efficiency that is ∼ 90% at the edge and ∼ 100% at the center of the cell, the reconstruction of the energy deposition varies with the impact point of the particles with respect to the cell. To correct this effect the impact correction S1/S3 was introduced. S1 is defined as the highest energy deposited in a cell of a layer. S3 the sum of S1 plus the two neighbour cells energy on the same layer. The ratio S1/S3 changes accordingly to the impact position. From test beam data the relation between this ratio and the impact of the particle was derived so allowing a correction to the measured energy (see Fig.3.16). Another correction is needed due to rear leakage, i.e. to recover the fraction of the shower energy not deposited in the calorimeter. Rear energy leakage is negligible at low energies, but it becomes important when energy increases. At test beam the effective energy (Ereal) was parametrized as a quadratic function of the energy of the last two
layers (El2l): Ereal Erec = α + βEl2l Erec + γ El2l Erec 2 (3.6) where (Erec) is the reconstructed energy, α, β and γ are evaluated at the test beam,
where the real energy of the particle (Ereal) is known.
These two corrections (S1/S3 and leakage) allow to obtain the expected energy recon-struction (see Fig. 3.17):
In Fig. 3.18 the energy resolution σ(E)/E is plotted as a function of the energy: this resolution is well parametrized as
σ(E) E =
(10.4 ± 0.2)%
Figure 3.16: Left: behaviour of the variable S1/S3 and the energy deposited in one view by 100 GeV electrons. Right: energy deposited as a function of the impact point before (black histogram) and after (red dots) impact correction [20].
Figure 3.17: Energy deposited before (black) the S1/S3 correction and the rear leakage correc-tion and after (blue) for a 100 GeV electron.
AMS-02 has an angular acceptance of ≈ 20◦: but the energy resolution resulted to change
negligibly with angle.
3.2.3 Angular resolution
The calorimeter angular resolution ∆θ68 is defined as the angular width around the
incidence beam direction containing 68% of the reconstructed angles. At 0◦, the angular
resolution results to be:
∆θ68=
(7.36 ± 0.08)◦
pE[GeV] ⊕ (0.28 ± 0.02)
◦ (3.8)
This resolution improves as the particle inclination increases, because of the larger energy deposition and the smaller leakage (see Fig. 3.19). The angular resolution is essential for the γ ray study and therefore is analyzed in detail in the next chapter.
Angular resolution
4.1
Importance of the direction
The capability to associate gamma rays detected by AMS-02 to known celestial sources depends on the uncertainty in the photon direction reconstruction. To study this un-certainty, the angular resolution evaluated for electrons is assumed to be the same for photons.
AMS-02 can reconstruct the path of a charged particle using not only the silicon tracker but also the electromagnetic calorimeter. To reconstruct the particle trajectory with ECAL, the point to be associated at the particle track can be derived by different meth-ods when these points are found (and in the following it will be shown how). How to check the reliability of the track obtained from a fit of these points?
Let’s assume to have a generic vector r with components rx, ry and rz (see Fig. 4.1),
then the angles θx and θy are obtained by:
tan θx = rx rz , tan θy = ry rz . (4.1)
This two angles are measured directly by the fit in the x and in the y view. The angular uncertainty is assumed to be the angular difference between the axis measured by ECAL and the one measured by the tracker. Different methods to reconstruct the crossing points on each ECAL layer will provide different tracks and therefore different fits. Three are the methods taken into account:
• the Center Of Gravity method (COG); • the Cell Ratio method (CR);
Figure 4.1: Design of a generic vector in space. θxand θy are the angles between the projections of the vector on respectively the xz plane and yz plane and the the z axis.
4.1.1 Center Of Gravity method (COG)
The Center Of Gravity procedure consists in calculating the center of gravity in each layer of the shower using the energy weighted centers of the cells belonging to the shower:
xCOGl = P ixiEi P iEi (4.2) where xi is the position of the i-th cell belonging to the shower, Ei its deposited energy
in the i-th cell and xCOG
l is the center of gravity of the shower in layer l.
4.1.2 Cell Ratio (CR) method
For each layer, this method uses the ratio between the energy deposited on the left of the most energetic cell (EL) and the one deposited on the right (ER). The logarithm of
this ratio depends linearly on the impact position inside the most energetic cell (see Fig. 4.2). This means that when logEL
ER is zero, the particle impinged on the center of the
cell.
4.1.3 Lateral Fit method
The energy distribution in each layer is parameterized, for each energy and for each angle (from Monte Carlo) with the shape:
Figure 4.2: Logarithm of the energy deposited in the neighbour cells of the most energetic one as a function of the impact position in that cell (dimension of a cell: 0.9 cm).
f (r) = 2rR
2
(r2+ R2)2 (4.3)
with r = x in x layers, r = y in y layers and R is the width of the distribution. Minimizing the χ2 between the template given for a particular layer and energy of the particle, and
the distribution of the energy released in that layer, permits to know the mean x0 (y0)
on that layer.
For each method, after the determination of the "impinging point" in each layer, the particle direction is obtained by fitting the layer points with a straight line.
4.2
Event selection
To study the ECAL angular resolution, the sample of electrons collected by AMS-02 from May 2011 to November 2013 has been selected according to the following criteria:
• only one track in the silicon tracker; • only one shower in the calorimeter; • deposited energy ED > 1.5 GeV;
• e.m. shower inside an area of 63 × 63 cm2 in each calorimeter layer (the total area
• Rigidity R ≤ − 2;
• both tracker and calorimeter must be present; • atomic number 0.8 < |Z| < 1.2;
• hits in the transition radiation detector (TRD) must be associated to the direction given by the tracker;
• a cut on the likelihood L is applied to separate e/p, e/He and p/He: Le/p< 0.57,
Le/He < 0.8 and Lp/He< 1.
4.2.1 Angular resolution
θx and θy were computed either by means of the tracker and either in ECAL by means
of each method. The difference between these two quantities gives the resolution in θx
and θy. The resolution in θx and θy obtained, using for ECAL the center of gravity, the
cell ratio and the lateral fit algorithm, respectively, are plotted and compared in Fig. 4.3 and in Fig. 4.4. E [GeV] 10 102 103 ] ° [x θ ∆ 0 1 2 3 4 5 6 7 8 9 Center of Gravity (x) Cell Ratio (x) Lateral Fit (x) x θ Energy vs resolution in
Figure 4.3: Resolution in θxas a function of energy obtained with COG, CR and LF algorithms.
The angular resolution results to be more accurate when using the lateral fit algorithm and therefore this is chosen as the method for the reconstruction of the photon direction.
E [GeV] 10 102 103 ] ° [y θ ∆ 0 1 2 3 4 5 6 7
Center of Gravity (y) Cell Ratio (y) Lateral Fit (y)
y
θ
Energy vs resolution in
Figure 4.4: Resolution in θy as a function of energy obtained with COG, CR and LF algorithms.
4.3
Point Spread Function
Using the lateral fit method it was obtained the reconstruction of the axis with the calorimeter on the sample of ∼ 6 · 106 electrons that was selected. In energy, cos θ
x and
cos θy bins the plot of ∆θx and ∆θy was obtained (examples of it are shown in Fig. 4.5
and 4.6). The spot in the plot is the Point Spread Function in the detector. From the projections of the resolution in θx and θy, the resolution in one of these two angles was
obtained. The resulting distributions were fitted with a gaussian function (examples in Fig. 4.7 and 4.8) to get the spread in ∆θx and ∆θy.
] ° [ x θ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 ] ° [ y θ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 Resolution_ebin_2_costhetax_bin_9_costhetay_bin_9 Entries 15994 Mean x 0.005545 Mean y 0.03803 RMS x 0.8118 RMS y 0.749 0 50 100 150 200 250 300 350 400 Resolution_ebin_2_costhetax_bin_9_costhetay_bin_9 Entries 15994 Mean x 0.005545 Mean y 0.03803 RMS x 0.8118 RMS y 0.749 < 1.00 y θ < 1.00 - 0.99 < cos x θ Resolution - 31.7 < E < 126.2 - 0.99 < cos
Figure 4.5: Resolution in θxand θy for energy 31.7 GeV < E < 126.2 GeV and 0.99 < cos θx, cos θy< 1.00. ] ° [ x θ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 ] ° [y θ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 Resolution_ebin_3_costhetax_bin_9_costhetay_bin_9 Entries 787 Mean x -0.05502 Mean y 0.0273 RMS x 1.351 RMS y 1.075 0 5 10 15 20 25 30 35 40 45 Resolution_ebin_3_costhetax_bin_9_costhetay_bin_9 Entries 787 Mean x -0.05502 Mean y 0.0273 RMS x 1.351 RMS y 1.075 < 1.00 y θ < 1.00 - 0.99 < cos x θ Resolution - 126.2 < E < 502.4 - 0.99 < cos
Figure 4.6: Resolution in θx and θy for energy 126.2 GeV < E < 502.4 GeV and 0.99 < cos θx, cos θy< 1.00.
ProjectionX Entries 787 Mean -0.05995 RMS 1.363 / ndf 2 χ 133.9 / 52 Constant 143.3 ± 8.3 Mean 0.02685 ± 0.01471 Sigma 0.362 ± 0.015 ] ° [ x θ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 0 20 40 60 80 100 120 140 160 180 ProjectionX Entries 787 Mean -0.05995 RMS 1.363 / ndf 2 χ 133.9 / 52 Constant 143.3 ± 8.3 Mean 0.02685 ± 0.01471 Sigma 0.362 ± 0.015 < 1.00 y θ < 1.00 - 0.99 < cos x θ Resolution - 126.2 < E < 502.4 - 0.99 < cos
Figure 4.7: Gaussian fit of the resolution in θx for 126.2 GeV < E < 502.4 GeV and 0.99 < cos θx, cos θy < 1.00. ProjectionY Entries 787 Mean 0.01173 RMS 1.135 / ndf 2 χ 97.51 / 44 Constant 156.6 ± 8.4 Mean 0.08551 ± 0.01357 Sigma 0.3497 ± 0.0133 ] ° [ y θ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 0 20 40 60 80 100 120 140 160 180 ProjectionY Entries 787 Mean 0.01173 RMS 1.135 / ndf 2 χ 97.51 / 44 Constant 156.6 ± 8.4 Mean 0.08551 ± 0.01357 Sigma 0.3497 ± 0.0133 < 1.00 y θ < 1.00 - 0.99 < cos x θ Resolution - 126.2 < E < 502.4 - 0.99 < cos
Figure 4.8: Gaussian fit of the resolution in θyfor 126.2 GeV < E < 502.4 GeV and < 0.99 cos θx, cos θy< 1.00.
Candidate Photon Selection
Photons can be detected by AMS-02 in two ways: by conversion mode and by direct photon measurement. In the first method photons are reconstructed from the e+e− pair
created by the photon itself before reaching the first tracker plane inside the magnet; in the second mode photons interact directly inside ECAL. In this thesis the second mode is used, since the material in front of ECAL correspond to ∼ 0.5 X0 and only the 32% of
the photons interact before reaching the calorimeter1. When a photon reaches directly
ECAL, it leaves no hits in TRD, TOF, TRK and RICH.
5.0.1 Event Preselction
γ’s are searched in the flight data sample of AMS-02 from May 2011 to July 2013. Some preselection cuts are applied initially to remove part of the background events by requiring:
• an ECAL stand-alone trigger flag; • only one reconstructed shower; • no tracks in the TRK;
• the reconstructed shower axis must be far at least 1.8 cm from ECAL sides in the first and the last layers (the calorimeter fiducial volume);
• the reconstructed shower direction is crossing the upper TOF plane within 50 cm from the AMS-02 z axis.
5.0.2 Boosted Decision Tree Training
After preselection cuts, photon events are selected using a Boosted Decision Tree (BDT). The BDT technique is the extension of a simple cut based analysis into a multivariate analysis: rather than to reject right away events that fail a criterion, BDT checks if other criteria may help to classify these events correctly.
A Decision Tree (DT) is a binary tree classifier formed by a structure of cuts organized into nodes (see Fig. 5.1) to separate signal and background with more selections, not only one. Repeating this procedure, a forest of trees is built so that each tree explores a
Figure 5.1: Structure of a decision tree.
different set of input variables and cuts. The process of building new trees can be opti-mized by using a boosting algorithm: for each iteration, events are re-weighted according to their misclassification rate. In this way, the algorithm learns to take more care about events that have been misclassified in the previous iteration and the discrimination power increases.
In absence of any test beam with photons, the BDT algorithm has been trained and tested using the AMS-02 Monte Carlo. For the generation of the events, AMS-02 is simulated at the centre of a cube of 3.9 × 3.9 × 3.9 m3 (Fig. 5.2). The AMS-02
geomet-rical acceptance is a cone of angle aperture [-20◦, +20◦]. For training purpouse, the MC
generates samples of three different particles:
1. Photons, inside AMS-02 geometrical acceptance with a uniform spectrum in energy between 0.5 - 2000 GeV, and interacting directly with ECAL.
2. Electrons, with a uniform spectrum in energy between 0.5 - 2000 GeV, coming from all six the faces of the generation cube.
3. Protons, with a uniform spectrum in energy between 0.5 - 2000 GeV, coming from all six the faces of the generation cube.
A uniform spectrum energy was requested in order to avoid bias in the selection due to different statistical weights among different parts of the spectrum.
Each particle sample is divided into two equal parts, one is used for training and one is reserved for testing procedures.
A set of variables is used in the BDT to discriminate photons from electrons (BDTele)
and photons from protons (BDTpro):
• Fraction of the total energy. The energy deposited in each layer is different for photons, electrons and protons because they start the shower at different depths in the calorimeter.
• Slope of the shower width. The slope of the linear fit of the shower width of each layer should be positive for down going particles. This allows to discriminate between down going and up going particles.
• Fit with the Rossi function. A fit with the Rossi function (eq. 3.2) is performed on the longitudinal shower profile, reading ECAL layers either from the top to bottom either from the bottom to top, so discriminating between down going and up going particles. A cut is applied on the resulting χ2 in order to reject protons
that should have a different longitudinal shower shape.
• The χ2 from the comparison of the lateral profile with the expected mean profile
for each layer is calculated.
• Ratio S1/S3: i.e. the ratio between the cell with the highest energy (S1) and the sum of this and the two neighbour cells (S3). This ratio is expected to be different between protons and electrons.
• The angle between the particle direction as reconstructed with the centroid method and with a fit of the most energetic cell in each layer.
Also non converted photons can be accompanied by hits in the other detectors owing to noisy channels and backsplash particles generated by the e.m. showers. This contami-nation is much weaker in the upper sub detectors of AMS-02, because the magnetic field deflects low energy charged particles generated by backsplash. The following selection criteria are applied in order to take advantage of the rejection power of TOF, TRD and RICH:
• TOF Selection. The difference in time of the TOF clusters closest to the shower axis in the Lower and the Upper TOF planes discriminates between backsplash particles and down going particles. Furthermore, a cut on the energy deposited in the two planes of the Upper TOF is applied.
• TRD Selection. The distance between the reconstructed tracks in TRD and the direction reconstructed with the shower center of gravity in ECAL.
• RICH Selection. The number of hits in the RICH.
So the BDT with these variables was used to discriminate e from γ and p from γ. The ability of this tree to separate was stored in the variables BDTele and BDTpro. The
results from the BDT process are probed on the test sample (Fig. 5.3 and 5.4): a quite total separation is obtained either for electrons and for protons.
Figure 5.4: Distribution for BDTpro.
Putting together the quantity BDTele and BDTpro,
ρBDT =
q
(BDTele− 1)2+ (BDTpro− 1)2 (5.1)
the result variable (BDT radius) provides the discrimination of photons from both elec-trons and from protons.
5.1
Photons Converted before ECAL
In MC simulations converted photons are split into two separate population in the plane (BDTele, BDTpro). This is due to the different depth in AMS-02 where they convert.
Furthermore, looking at their BDT distribution, in different energy bins, the differences between photons converting in the near ECAL and not-converted photons result to de-crease with increasing energy, primarily because the aperture angle of the e+e− pair
becomes smaller (θ ∼ 1/E) at larger energies. As a consequence part of the converted photons can be recovered by the very same selection used for unconverted photons. As a consequence the converted photon are treated as a signal with lower efficiency and no longer as background.
5.2
Last Selection
The photon sample is selected by applying a single cut close to 0 on the ρBDT distribution.
To further reduce background, another selection based on TRD, ACC, TRK2 and TOF
is applied.
• Fiducial Cone Veto. A fiducial cone around the shower axis is defined as a function of energy and if hits are present inside this cone in two or more layers of TRD, TRK or upper TOF, the event is discarded.
• ACC Selection. A cut on the amount of hits in the ACC system is applied as a function of the reconstructed energy.
• ECAL Edges Selection. Events where more than one ECAL layer has the highest energy deposition at the border of the calorimeter, are rejected.
5.3
AMS Photon Acceptance
The AMS photon acceptance has been estimated by Monte Carlo, generating photons isotropically on a cube of 3.9 × 3.9 × 3.9 m3 and multiplying the generation acceptance
(Agen= 6π · 3.9 × 3.9 m2· sr) by the fraction of events passing the selection described.
The acceptance dependence on the photon incidence angle θ and energy E is shown in Fig. 5.5.
Generated Energy (GeV)
1 10 102 103 ) cos( -1 -0.98 -0.96 -0.94 -0.92 -0.9 0 10 20 30 40 50 60 70 80 ) bins Acceptance vs photon energy in cos(
cm2·sr
Figure 5.5: Acceptance dependence on the incident angle and energy.
The acceptance can be factorized as: A(E, cos θ) = A0(E)A1(cos θ). The dependance
on energy and angle is showed in Fig.s 5.6 and 5.7 respectively. The acceptance as
a function of energy is reasonably flat between 5 and 300 GeV; the effective area for normal photon incidence is of the order of 2500 cm2.
Figure 5.6: Acceptance as a function of energy.
) θ cos( -1 -0.98 -0.96 -0.94 -0.92 -0.9 ) 2 Effective Area (cm 0 500 1000 1500 2000 2500 ) at 100 GeV θ
Average effective vs cos(
5.4
Purity of the Photon Selection
Similarly to what has been done for the photons the selection acceptance for electron and protons has been obtained from Monte Carlo. To understand the level of background contamination the expected rates for photons, electrons and protons have been compared. The rates have been obtained multiplying the fluxes3 for the corresponding acceptances:
the result is shown in Fig. 5.8.
Figure 5.8: The expected rates after the BDT and final selection: black dots are converted + not converted photons, while blue dots are electrons. The red dot is the unique proton survived at the selection.
3The fluxes for electrons and protons have not been corrected for the geomagnetic cutoff so that the
electrons and protons rate refer to the worst condition (polar orbit). The minimum allowed rigidity that
Study of Sources of High Energy γ rays
After identification of the photon candidates in AMS-02 data sample in order to un-derstand the ECAL capability to identify high energy γ sources, a two step study is performed: first association between the candidate photons and known γ ray sources is reached, then the possibility to infer the presence of a source from the spatial correlation of two photons is analyzed.
First of all from the sources listed in the First Fermi LAT Catalog of Sources above 10 GeV [23], the number of expected photons from these sources in AMS is evaluated.
6.1
AMS-02 Source Sensitivity
The number of photons with energy E > Emin expected from a given source is given by:
Nγexp = Z
E>Emin
Φ(E) · Γ(E) · dE, (6.1) where Φ(E) is the differential flux of the source and Γ(E) is the AMS exposure to the source.
The differential flux of the source is taken from the Fermi Catalog and has the form Φ = Φ0
E E0
α
(6.2) where Φ0 is the differential flux at E0. E0 (pivot energy) is the energy at which the
error on differential flux is minimal and α the best fit power-law index (an example of a spectrum is shown in Fig. 6.1).
The exposure Γ(E) is given by: Γ(E) =X
i
Figure 6.1: Flux spectrum for blazar J0009.2+5032, galactic longitude l = 116.11◦, galactic latitude b = −11.772◦.
where θ is the angle with respect to AMS zenith, cos θi indicates the i-th bin in cos θ,
T(cos θi) is the time the source is seen in AMS under an angle θ in the cos θi bin and
A(E, cos θi) is the average AMS photon effective area in the cos θi bin for a given energy
E (see Fig. 5.7).
6.1.1 Exposure Time Maps
The exposure time corresponding to a given photon inclination, i.e. in given cos θi bin,
was calculated for each 1◦×1◦ angular pixel in the galactic coordinates following the AMS
orbit with steps of 10 seconds for the 27 months of analyzed data. Also the trigger Live Time has been taken into account in the calculation. Fig. 6.2 shows the time exposure map obtained for 9◦ < θ < 13◦.
s
6.1.2 Exposure Maps
An example of a exposure (Γ(E)) map used to determine the number of photons expected from a source is shown in Fig.6.3: it ranges from 0 to 4 · 109s · cm2: this corresponds to
a minimum detectable photon flux of the order of 10−10 cm−2·s−1.
]° galactic longitude l [ -150 -100 -50 0 50 100 150 ]° galactic latitude b [ -80 -60 -40 -20 0 20 40 60 80 500 1000 1500 2000 2500 3000 3500 4000 6 10 × Exposure map 100 GeV < E < 116 GeV cm2·s
Figure 6.3: Example of exposure map for 100 GeV < E < 116GeV.
6.2
Detectable sources
For each of the 514 sources of the Fermi high energy Catalog, the number of expected photons visible by AMS are calculated using the formula 6.1. Three different energy threshold: 27.7 GeV, 52.9 GeV and 101 GeV have been taken into account.
For Eγ > 27.7 GeV the study was restricted to |l| > 30◦ and |b| > 10◦ where the
diffused galactic background is lower.
The corresponding number of photons expected from each source is shown in Fig. 6.4, 6.5 and 6.6.
For each energy threshold a minimum number (above the red line) of expected photons is fixed to restrict this study to the most intense sources (shown in Fig.s 6.7, 6.8 and 6.9). The total number of expected photons is slightly reduced (as shown in Tab. 6.1) while the number of accidental association with diffuse photons to any source decreases a lot.
γ N 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 10 2 10
from sources (E>27 GeV)
γ
Expected
Figure 6.4: Number of photons with Eγ > 27.7 GeV expected to detect from sources. The red line represent the minimum required photons from the sources.
γ N 0 0.5 1 1.5 2 2.5 3 1 10 2 10
from sources (E>52 GeV)
γ
Expected
Figure 6.5: Number of photons with Eγ > 52.9 GeV expected to detect from sources. The red line represent the minimum required photons from the sources.
γ N 0 0.5 1 1.5 2 2.5 3 1 10 2 10
from sources (E>101 GeV)
γ
Expected
Figure 6.6: Number of photons with Eγ > 101 GeV expected to detect from sources. The red line represent the minimum required photons from the sources.
] ° galactic longitude l [ -150 -100 -50 0 50 100 150 ] ° galactic latitude b [ -80 -60 -40 -20 0 20 40 60 80 Intense_Sources Entries 29 Intense_Sources Entries 29 > 27 GeV γ Intense Sources E
Figure 6.7: The 29 most intense sources for Eγ > 27.7 GeV: only the 12 sources with |l| > 30◦ and |b| > 10◦) have been considered for the association.
] ° galactic longitude l [ -150 -100 -50 0 50 100 150 ] ° galactic latitude b [ -80 -60 -40 -20 0 20 40 60 80 Intense_Sources Entries 48 Intense_Sources Entries 48 > 52 GeV γ Intense Sources E
Figure 6.8: The 48 most intense sources for Eγ > 52.9 GeV.
] ° galactic longitude l [ -150 -100 -50 0 50 100 150 ] ° galactic latitude b [ -80 -60 -40 -20 0 20 40 60 80 Intense_Sources Entries 52 Intense_Sources Entries 52 > 101 GeV γ Intense Sources E
E > 27 GeV E > 52 GeV E > 101 GeV (|l| > 30◦, |b| > 10◦)
Nsources 351 514 514
Nγexp (tot) 41 ± 6 38 ± 6 18 ± 4
Nsources(Nγ > 0.54, 0.15, 0.07) 12 48 52
Nγexp (more intense sources) 13 ± 4 22 ± 5 11 ± 3
Table 6.1: Total number of sources, number of γ rays expected from the total number of sources, number of sources with a visible number of photons, number of γ rays expected from these sources.
6.3
Photon - Source Association
Photons coming from a given source appear spread out in the galactic coordinate plane according to the detector Point Spread Function (PSF). Using the angular resolution in xz and yz plane obtained in Chap. 4, it is possible to obtain the PSF for each candidate source in galactic coordinates: an example is shown in Fig. 6.10.
] ° galactic longitude [ 78 79 80 81 82 83 84 85 ] ° galactic latitude [ -2 -1 0 1 2 3 4 5 0 5 10 15 20 25 30 35 40 45 of E = 40 GeV γ
Point spread function for a
Figure 6.10: Point spread function for a candidate γ.
The PSF appears as a ellipsoid (see Fig 6.11) with semi axes given by the resolution in galactic longitude σl and galactic latitude σb.
Figure 6.11: Point Spread Functions for candidate photon with Eγ > 27.7 GeV.
with galactic latitude (Fig.s 6.12 and 6.13).
The distance in σ units of the photon from the source will be expressed as: Nσns= s lγ− ls σl(bs) 2 + bγ− bs σb(bs) 2 . (6.4) ] ° galactic latitude b [ -100 -50 0 50 100 ] ° l [ ∆ 0 2 4 6 8 10 12 14 16 18
Resolution in galactic longitude as a function of galactic latitude
Figure 6.12: Resolution in galactic longitude ∆l as a function of galactic latitude b.
] ° galactic latitude b [ -80 -60 -40 -20 0 20 40 60 80 ] ° b [ ∆ 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Resolution in galactic latitude as a function galactic latitude
Figure 6.13: Resolution in galactic latitude ∆b as a function of galactic latitude b.
The shortest distance in number of σ’s between the candidate photons and the de-tectable sources (using as reference positions for sources the ones from Fermi Catalog) is
shown in Fig.s 6.14, 6.15 and 6.16 for the photons in the three energy samples: the peak at zero corresponds to candidate associations while the tail is due to diffused background or photons coming from sources excluded by the intensity cut.
Distance Entries 220 Mean 10.44 RMS 7.215 Underflow 0 Overflow 188 σ N 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 Distance Entries 220 Mean 10.44 RMS 7.215 Underflow 0 Overflow 188 > 27.7 GeV) γ
of photon candidates from nearest source (E σ
Distance in number of
Figure 6.14: Shortest distance in number of σ’s in galactic coordinates from nearest source for candidate photons of Eγ> 27.7 GeV, for |l| > 30◦ and |b| > 10◦.
Before choosing the maximum distance permitted for association of a photon to a source, the expected distance from sources for the isotropic diffused background, galactic diffused background and photons coming from sources have been studied.
Distance Entries 210 Mean 8.637 RMS 5.753 Underflow 0 Overflow 80 σ N 0 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 Distance Entries 210 Mean 8.637 RMS 5.753 Underflow 0 Overflow 80 > 52.9 GeV) γ
of photon candidates from nearest source (E σ
Distance in number of
Figure 6.15: Shortest distance in number of σ’s in galactic coordinates from nearest source for candidate photons of Eγ > 52.9 GeV.
Distance Entries 74 Mean 6.891 RMS 5.441 Underflow 0 Overflow 27 σ N 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 Distance Entries 74 Mean 6.891 RMS 5.441 Underflow 0 Overflow 27 >101.0 GeV) γ
of photon candidates from nearest source (E σ
Distance in number of
Figure 6.16: Shortest distance in number of σ’s in galactic coordinates from nearest source for candidate photons of Eγ > 101.0 GeV.
