Precision Measurement of the Boron to Carbon
Ratio in Cosmic Rays with AMS-02
by
Wei Sun
Bachelor of Science, University of Science and Technology of China
(2010)
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2015
c Massachusetts Institute of Technology 2015. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Physics
December 10th, 2014
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ulrich J. Becker
Professor of Physics
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Krishna Rajagopal
Chairman, Associate Department Head for Education
2
Precision Measurement of the Boron to Carbon Ratio in
Cosmic Rays with AMS-02
by
Wei Sun
Submitted to the Department of Physics
on December 10th, 2014, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
A precision measurement of the Boron to Carbon ratio in cosmic rays is carried out in
the range 1 GeV/n to 670 GeV/n using the first 30 months of flight data of AMS-02
located on the International Space Station. Above 20 GeV/n, it is the first accurate measurement. About 5 million clean Boron and Carbon nuclei are identified.
The experimental and analysis challenges in achieving a high precision measurement
are addressed. Boron is exclusively produced as a secondary particle by spallation
from primary elements like Carbon in collisions with interstellar medium. The unprecedented precision and energy range of this measurement deepen the knowledge
of cosmic ray propagation. Using this measurement, the diffusion coefficient in GalProp model is determined to be (6.05±0.05)×1028 cm2 /s, and the Alfven velocity is
(33.9±1.0) km/s. This makes the prediction of secondary anti-proton background in
dark matter search one order of magnitude more accurate.
Thesis Supervisor: Ulrich J. Becker
Title: Professor of Physics
3
4
Acknowledgments
I am very grateful to many people who helped me during my PhD.
Firstly, I would like to thank my advisor Prof. Ulrich Becker. I learned so much
from Prof. Becker, not only physics knowledge and technical skills, but also scientific
principle and life philosophy. I feel so lucky to have the opportunity to work on my
thesis with one of the best physicists.
I would like to thank Dr. Alberto Oliva and Dr. Andrei Kounine. I learned a lot
of particle physics and data analysis by working with them at CERN on the Boron
to Carbon ratio and the Transition Radiation Detector.
I want to thank Prof. Paolo Zuccon for discussions on the Silicon Tracker and
advices on scientific writings. Thank Prof. John Belcher for reading my thesis and
the discussions about plasma physics in our galaxy.
Thank Prof. Samuel Ting and the AMS Collaboration for building the AMS
detector and making the experiment a success. Thank Dr. Robert Irwin from MIT
Writing Department for helping me with the English writing. During the PhD, I
got supports from many of my friends, including Andrew Chen, Matthew Krafczyk,
Andrew Levin, Prof. Richard Milner, and so on.
I would also like to thank my future wife and children. Even though I do not
know who you are at this moment, the belief that I will meet you at some point in
the future and we will have a happy life together always encourages me during the
hard time of my PhD.
In the end, I would like to dedicate this thesis to my parents.
5
6
Contents
Introduction
23
1 Cosmic Ray Boron and Carbon
25
1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
1.2
Origin of Cosmic Ray Boron and Carbon . . . . . . . . . . . . . . . .
25
1.2.1
Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . .
26
1.2.2
Stellar Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . .
27
1.2.3
Spallation of Cosmic Rays in Galactic Propagation . . . . . .
30
1.3
Acceleration of Primary Cosmic Rays . . . . . . . . . . . . . . . . . .
31
1.4
Propagation of Cosmic Rays in Our Galaxy . . . . . . . . . . . . . .
33
1.4.1
Milky Way and Galactic Magnetic Field . . . . . . . . . . . .
34
1.4.2
Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
1.4.3
Leaky Box Model . . . . . . . . . . . . . . . . . . . . . . . . .
35
1.4.4
Diffusive Halo Model . . . . . . . . . . . . . . . . . . . . . . .
37
Propagation of Cosmic Rays in the Solar System . . . . . . . . . . . .
38
1.5.1
Solar Modulation . . . . . . . . . . . . . . . . . . . . . . . . .
38
1.5.2
Influence of the Geomagnetic Field . . . . . . . . . . . . . . .
39
The Boron to Carbon Ratio . . . . . . . . . . . . . . . . . . . . . . .
41
1.6.1
Why Boron to Carbon Ratio . . . . . . . . . . . . . . . . . . .
41
1.6.2
Previous Measurements of the Boron to Carbon Ratio . . . . .
42
1.6.3
The Physics Picture of the B/C Spectrum . . . . . . . . . . .
44
1.6.4
Constraints on Propagation Parameters . . . . . . . . . . . . .
45
1.6.5
Prediction of Anti-Proton Background in Exotic Physics Search 45
1.5
1.6
7
2 The Alpha Magnetic Spectrometer
2.1
51
The AMS-02 Detector . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.1.2
Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
2.1.3
Transition Radiation Detector (TRD) . . . . . . . . . . . . . .
55
2.1.4
Silicon Tracker . . . . . . . . . . . . . . . . . . . . . . . . . .
56
2.1.5
Time of Flight Counters (TOF) . . . . . . . . . . . . . . . . .
58
2.1.6
Ring Imaging Cherenkov Detector (RICH) . . . . . . . . . . .
59
2.1.7
Electromagnetic Calorimeter (ECAL) . . . . . . . . . . . . . .
60
2.1.8
Anti-Coincidence Counter (ACC) . . . . . . . . . . . . . . . .
61
Operation and Data Acquisition . . . . . . . . . . . . . . . . . . . . .
62
2.2.1
AMS-02 on the ISS . . . . . . . . . . . . . . . . . . . . . . . .
62
2.2.2
Data Flow in the Detector . . . . . . . . . . . . . . . . . . . .
63
2.2.3
Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
2.3
Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.4
Physics Goals of AMS-02 . . . . . . . . . . . . . . . . . . . . . . . . .
66
2.2
3 Event Reconstruction
69
3.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.2
Rigidity Determination . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.3
Velocity Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.4
Charge Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4 Charge Measurement by the TRD
79
4.1
Ionization and Delta Rays . . . . . . . . . . . . . . . . . . . . . . . .
79
4.2
Reconstruction Algorithm . . . . . . . . . . . . . . . . . . . . . . . .
83
4.3
TRD Track Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4.4
dE/dx and Delta Ray Probability Density Functions (PDFs) . . . . .
87
4.5
Performance of the Reconstruction . . . . . . . . . . . . . . . . . . .
90
4.6
Outlook: Future Improvements in TRD Charge Measurement . . . .
93
8
5 Data Analysis
95
5.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
5.2
Event Pre-Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
5.3
Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
5.4
Charge Selection by the Tracker . . . . . . . . . . . . . . . . . . . . . 105
5.5
Fragmentation Identification and Purity Estimation . . . . . . . . . . 107
5.6
Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.7
Exposure Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.8
Isotope Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.9
Reconstruction Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.10 Survival Probability of Boron and Carbon . . . . . . . . . . . . . . . 115
5.11 Top of Instrument Correction . . . . . . . . . . . . . . . . . . . . . . 122
5.12 Rigidity Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6 Results
131
6.1
The Energy Spectrum of the Boron to Carbon Ratio . . . . . . . . . 131
6.2
Result Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.3
Constraints on Cosmic Ray Propagation Model . . . . . . . . . . . . 138
6.4
Improvement of P̄ /P Background Prediction in Dark Matter Search . 140
6.5
Galactic Magnetic Field and Plasma Density . . . . . . . . . . . . . . 142
Conclusion
145
A Search for anti-Carbon
147
B Production Mechanism of Cosmic Ray Boron
149
C GalProp Parameters
151
9
10
List of Figures
1-1 Important reactions for the production of primordial Boron and Carbon isotopes in the Big Bang Nucleosynthesis [1]. The legends at upper
left and lower right parts of the plot indicate the reaction mechanisms.
For example, from the upper left legend we read that the reaction to
produce 2 H from 1 H is 1 H + n →2 H + γ. . . . . . . . . . . . . . . .
27
1-2 Relative abundances of stable light isotopes in the Big Bang nucleosynthesis as a function of the baryon to photon ratio η [1]. The relative
abundances of Boron and Carbon are less than 10−15 at η = 6.16×10−10
(measured by WMAP [2]). . . . . . . . . . . . . . . . . . . . . . . . .
28
1-3 The relative abundance of Boron in stars, A(B), as a function of
metallicity, [F e/H] [3]. A(B) = log(N (B)/N (H)) + 12. [F e/H] =
log(N (F e)/N (H)) − log(N (F e)/N (H))Solar . . . . . . . . . . . . . . .
29
1-4 Comparison of galactic cosmic ray abundances at solar minimum (red
filled circles) with solar system nuclei abundances (blue open circles)
[4]. In the solar system, Boron cannot be created from spallation of
Carbon (C + p → B + X). . . . . . . . . . . . . . . . . . . . . . . . .
31
1-5 Schematic view of the diffusion halo model [5]. . . . . . . . . . . . . .
37
1-6 Maximum geomagnetic cutoff rigidity for AMS-02. . . . . . . . . . . .
41
1-7 Previous measurements of the Boron to Carbon ratio in cosmic rays
from HEAO [6], CNR [7], ATIC [8], CREAM [9], TRACER [10], and
AMS-01 [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
42
0
1-8 The effects of diffusion coefficient Dxx
(upper plot) and Alfven velocity
VA (lower plot) on the Boron to Carbon ratio, simulated by GalProp
0
=
[12]. The black solid curves use the default GalProp parameters (Dxx
6.1 × 1028 cm2 /s, VA = 30km/s). . . . . . . . . . . . . . . . . . . . . .
46
1-9 Measurement of anti-proton to proton ratio [13] by PAMELA, BESS,
CAPRICE, and HEAT. The lines are model calculations using leaky
box model (dotted), diffusive re-acceleration model (dashed), and plain
diffusive model (solid), respectively. . . . . . . . . . . . . . . . . . . .
47
0
1-10 The effects of diffusion coefficient Dxx
(upper plot) and Alfven velocity
VA (lower plot) on the anti-proton to proton ratio, simulated by GalProp [12]. The black solid curves use the default GalProp parameters
0
(Dxx
= 6.1 × 1028 cm2 /s, VA = 30km/s). . . . . . . . . . . . . . . . .
49
2-1 Layout of the AMS-02 detector and functions of its subdetectors. . .
52
2-2 Configuration of the magnet blocks and the field lines. The arrows
forming a circle on the right figure show the magnetic field directions
inside each magnet block. . . . . . . . . . . . . . . . . . . . . . . . .
53
2-3 Magnetic field over the X-Z plane at Y = 0 (center, see Figure 2-2),
measured in 2010. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
2-4 Computer generated view of the TRD on top of the magnet vacuum
case (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
2-5 A TRD module, containing 16 proportional drift tubes. . . . . . . . .
55
2-6 Layout of nine layers of the Silicon Tracker in AMS-02. . . . . . . . .
57
2-7 Layout of the TOF: upper TOF (left) and lower TOF (right). The
lower TOF has a larger area so that more deflected particles by the
magnet will be accepted. . . . . . . . . . . . . . . . . . . . . . . . . .
58
2-8 Layout of the RICH. . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
2-9 Structure of the ECAL active part. . . . . . . . . . . . . . . . . . . .
61
2-10 The ACC after integration (left) and the arrangement of its components (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
62
2-11 The positron fraction measurement by AMS-02 with the first 18 months
of data, compared with the results from PAMELA and Fermi-LAT [14]. 66
3-1 Basic principles of different path integral fitting algorithms used in
AMS-02 reconstruction.
. . . . . . . . . . . . . . . . . . . . . . . . .
71
3-2 Schematic view of AMS-02 sub-detectors measuring charge along the
path of a particle (center) and the charge spectra (from flight data)
of each sub-detector for light cosmic ray elements (from Z=1 to Z=8):
(a) Tracker Layer 1; (b) TRD; (c) Inner Tracker; (d) TOF; (e) RICH;
(f) ECAL [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
3-3 Charge spectrum measured by the Tracker Layer 1 for events identified as Boron by the Inner Tracker and the TOF, the corresponding
template fits clearly show the charge changing fragmentation processes
(C→B, O→B, etc.) happening inside the TRD [15]. . . . . . . . . . .
76
4-1 Schematic view of ionization and delta rays in the TRD. The red line
indicates the track of the Carbon. The green circle indicates the tube
hit by the Carbon (defined as “dE/dx tube”). The blue circles indicate
the tubes hit by the delta rays generated from the ionization of the
Carbon in the TRD (defined as “delta ray tubes”). . . . . . . . . . .
80
4-2 Event display of a typical cosmic ray proton in the TRD with side view
(upper) and front view (lower). See text for the explanation of the red
bars and lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4-3 Event display of a typical cosmic ray Carbon in the TRD with side
view (upper) and front view (lower). The 2 hits in the top 4 layers in
the side view are noise. . . . . . . . . . . . . . . . . . . . . . . . . . .
83
4-4 Algorithm flowchart of the TRD charge reconstruction. . . . . . . . .
84
4-5 Probability density function of the distance between TRD track and
tube center for a fired tube. This analytical function is to make the
TRD track fitting easier. . . . . . . . . . . . . . . . . . . . . . . . . .
13
87
4-6 The TRD ADC spectrum of protons in the rigidity range 55 GV to
65 GV, and the corresponding parameterization with Equations 4.8
and 4.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
4-7 dE/dx Probability Density Functions of Helium (red), Lithium (green),
Beryllium (blue) and Boron (black), derived from flight data. Saturation of electronics happens around 3400 ADC, as indicated by the
orange line. The saturation influences charge measurement of Boron
and Carbon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
4-8 Delta ray amplitudes as functions of the Tracker charge. The amplitudes have already had pedestals subtracted. . . . . . . . . . . . . . .
90
4-9 Delta ray amplitudes as a function of rigidity for Z = 6 particles measured by the Tracker and the TOF. . . . . . . . . . . . . . . . . . . .
91
4-10 Charge distribution of cosmic ray nuclei, measured by the TRD alone.
91
4-11 Comparison between charge measured by the TRD and charge measured by the Inner Tracker. The TRD charge reconstruction only uses
dE/dx. See Figure 4-12 for comparison. . . . . . . . . . . . . . . . . .
92
4-12 Comparison between charge measured by the TRD and charge measured by the Inner Tracker. The TRD charge reconstruction uses both
dE/dx and delta rays. . . . . . . . . . . . . . . . . . . . . . . . . . .
92
5-1 Charge measurements along particle’s track in AMS-02. ∆Z is the
charge resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
5-2 Distributions of TOF-related selection cut variables for good (red,
solid) and bad (black, dashed) samples of Z = 6 events. Both samples
are normalized to 1 in the plots. The blue lines indicate the cuts. . . 100
5-3 Distributions of Tracker-related selection cut variables for good (red,
solid) and bad (black, dashed) samples of Z = 6 events. Both samples
are normalized to 1 in the plots. The blue lines indicate the cuts. . . 101
5-4 Beta spectrum of Z = 6 events before (black, dashed) and after (red,
solid) selection cuts on the TOF. . . . . . . . . . . . . . . . . . . . . 102
14
5-5 1/Rigidity distribution of Z = 6 events before (black, dashed) and
after (red, solid) selection cuts on the Tracker. . . . . . . . . . . . . . 102
5-6 Selection efficiency as a function of rigidity estimated by Method One
for Boron (red, solid) and Carbon (black, dashed). . . . . . . . . . . . 103
5-7 Selection efficiency ratio between Boron and Carbon as a function of
rigidity, estimated by Method One (red, solid) and Method Two (black,
dashed). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5-8 Tracker Layer 1 XY hit pickup efficiency ratio between Boron and
Carbon as a function of rigidity. . . . . . . . . . . . . . . . . . . . . . 104
5-9 Corrected Inner Tracker charge as a function of rigidity for particles
with Z = 1 to Z = 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5-10 Inner Tracker charge spectrum for particles with Z = 3 to Z = 8.
Gaussian fits are applied on each charge peak. The tail cannot be well
approximated by the Gaussian fits. The charge resolutions of Boron
and Carbon are approximately 0.1 charge unit. . . . . . . . . . . . . . 106
5-11 Inner Tracker charge spectrum for Boron (red, solid) and Carbon (black,
dashed) selected by the TOF, the TRD, and the Tracker Layer 1, and
corresponding charge ID cuts (blue line for Boron, green line for Carbon).107
5-12 Event display of an incoming Carbon fragmentation to Boron in Upper
TOF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5-13 Template fits on the Tracker Layer 1 charge spectra (black dots with
error bars) of Boron (a, b) and Carbon (c, d) identified by the Inner Tracker at two selected rigidity bins (4.1GV − 5.3GV , 139.2GV −
210.5GV ). The dashed lines are templates (the red dashed lines are
Carbon templates), the solid blue lines are the fitted results. The purple straight lines correspond to the cuts on Tracker Layer 1 charge to
suppress fragmentations. . . . . . . . . . . . . . . . . . . . . . . . . . 110
5-14 Trigger efficiency ratio between Boron and Carbon as a function of
rigidity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
15
5-15 Exposure time (normalized to the last bin) as a function of kinetic
energy per nucleon (logarithmic scale) for
10
B,
11
B, and
12
C. The
difference is due to the conversion from rigidity to Ek /A, see Equation
5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5-16 The Boron to Carbon ratio (statistical error only) as a function of
Ek /A, with Ek /A measured and calculated in different ways: (1) from
rigidity measured by the Tracker (Inner + Layer 1) with 11 B/(11 B +10
B) = 0.6 (red, dashed) and
11
B/(11 B +10 B) = 0.7 (blue, dotted); (2)
from velocity measured by the RICH (black, solid). . . . . . . . . . . 114
5-17 Tracker reconstruction efficiency, estimated from flight data. . . . . . 115
5-18 Cumulative material distribution of AMS-02 along Z coordinate at (X,
Y) = (5 cm, 5 cm). Particles enter AMS-02 at Z ≈ 170 cm. . . . . . 116
5-19 Survival probability (estimated from hadronic interaction models) at
(X, Y, Z) = (5cm, 5cm, −75cm) as a function of Ek /A for
inverse triangle),
11
B (blue, triangle) and
12
10
B (red,
C (green, dot) with an
inclination angle of 0◦ , The cross sections used in the calculation are
taken from Shen’s parameterization [16]. . . . . . . . . . . . . . . . . 117
5-20 Inner Tracker charge distribution for MC generated
12
C at 10.0GV −
12.6GV . The blue curve is a template fit aimed at getting the fraction
of survived Carbon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5-21 Survival probability ratio (estimated from MC simulation) as a function of MC generated rigidity for
and
12
10
B and
12
C (red, solid), and
11
B
C (black, dashed). . . . . . . . . . . . . . . . . . . . . . . . . . 119
5-22 Tracker Layer 1 charge spectrum for all particles (red, solid) and Z ≤ 2
particles (black, solid). The blue and green lines correspond to the cuts
to select Boron and Carbon samples, with non-negligible backgrounds
from Z ≤ 2 particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5-23 Inner Tracker charge distribution for the Carbon sample selected by
the Tracker Layer 1, as shown in Figure 5-22. The negative charge bin
represents the events without a Tracker track being reconstructed. . . 121
16
5-24 Survival probability ratio (estimated from flight data) between Boron
and Carbon as a function of rigidity (estimated from geomagnetic cutoff).122
5-25 Fraction of Carbon spallation into Boron when transversing the material above the Tracker Layer 1, estimated from MC. The blue line
indicates the average value. . . . . . . . . . . . . . . . . . . . . . . . 123
5-26 Rigidity resolution spectrum at R = 256 GV and corresponding parameterization using double Gaussian fit. This is from MC data. . . . 125
5-27 Relative rigidity resolution (defined as |RigL1 − RigL9|/RigL9) for
Helium and Carbon as a function of RigL9. This is from flight data.
We observe that Helium has a slightly better rigidity resolution than
Carbon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5-28 Rigidity resolution ratio between Carbon and Helium (the ratio between the two curves in Figure 5-27) as a function of RigL9. We take
the fluctuation of 8% as systematic error. . . . . . . . . . . . . . . . . 126
5-29 Resolution matrix for rigidity unfolding. . . . . . . . . . . . . . . . . 127
5-30 Boron and Carbon raw counts spectra (without any corrections, statistical error only) before (black, dashed) and after (red, solid) rigidity
unfolding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5-31 Raw Boron to Carbon ratio spectra (without any corrections, statistical
error only) before (black, dashed) and after (red, solid) rigidity unfolding.128
5-32 Estimation of systematic error due to unfolding: varying the width of
rigidity resolution function by 8%, as already mentioned before (see
Figure 5-28), and observe the influences on the unfolded result. . . . . 129
6-1 The Boron to Carbon ratio measured by AMS-02 with the first 30
months of flight data. Statistical errors are shown in red error bars,
and systematic errors are shown in blue error bars. The measured
results are listed in Table 6.1. . . . . . . . . . . . . . . . . . . . . . . 133
17
6-2 Comparison of the Boron to Carbon ratio measured by AMS-02 to
previous experiments [6] [7] [8] [9] [10], [11]. Statistical and systematic
errors are summed in quadrature (for comparison with literature). The
statistical and systematic errors for AMS-02 are listed in Table 6.1. . 134
6-3 The Boron to Carbon ratio spectrum in the energy range 20 - 670 GeV/n
can be described by a power law. The power law index is fitted to be
−0.302 ± 0.028.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6-4 Stability of the results against selection cuts: by varying the cuts in a
wide phase space and doing the analysis 500 times, the number of selected Borons is changed by ∼ 20%, but the B/C value is only changed
by a few per mil. Shown in the figure is an example for energy bin
8.4-10.2 GeV/n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6-5 Stability of the measurement over time: Comparison of the Boron to
Carbon ratio (raw counts, without unfolding) of 5 different periods (6
month for each period) in the first 30 months of data collection. . . . 136
6-6 Check of unfolding: Comparison between B/C measurement with the
L1 configuration with unfolding applied (Red) and that with the L9
configuration without unfolding applied (Blue). Errors are statistical
only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
p
6-7 Check of unfolding: The test variable (L1 − L9)/ σ12 + σ92 shows similar fluctuations in the low and high energy regions, demonstrating the
correctness of the unfolding for the L1 configuration. . . . . . . . . . 137
6-8 Relative errors as functions of energy: L1 configuration, statistical error only (Red); L1 configuration, systematic error only (Orange); L1
configuration, statistical error and systematic error summed quadratically (Blue); the L9 configuration, statistical error only (Black). . . . 138
18
6-9 χ2 of the GalProp fit (represented by color code) as a function of dif0
and Alfven velocity VA , showing the correlation
fusion coefficient Dxx
between these two parameters. The correlation can be approximated
0
0
with a linear function VA = 19.7Dxx
− 85.9 (Dxx
in units of 1028 cm2 /s,
VA in units of km/h), as indicated by the red line on the plot. See
Figure 6-9 for the zoomed-in version. . . . . . . . . . . . . . . . . . . 139
6-10 Zoom-in of Figure 6-9. . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6-11 Best χ2 fit of GalProp on the Boron to Carbon ratio measured by
AMS-02 (see also Figure 6-3). The fit is performed above 10 GeV/n
to avoid influences of solar modulation at low energy. . . . . . . . . . 141
6-12 Prediction of anti-proton background in anti-proton to proton ratio
for anti-protons produced from interactions between cosmic rays and
interstellar medium. The bands correspond to ±1σ variations. The red
0
solid band uses Dxx
constrained by AMS-02 B/C measurement, and
0
the blue textured band uses Dxx
constrained by B/C measurements of
AMS-01 [11], TRACER [10], and CREAM [9]. . . . . . . . . . . . . . 142
19
20
List of Tables
6.1
Energy spectrum of the Boron to Carbon ratio between 0.9 GeV/n and
669.7 GeV/n. The columns are: kinetic energy per nucleon, raw counts
of Boron, the Boron to Carbon ratio, statistical error, systematic error. 132
6.2
0
The fitted results of the diffusion coefficient Dxx
in the GalProp model,
with the Boron to Carbon ratio measured by AMS-02 and three recent
experiments (AMS-01 [11], TRACER [10], CREAM [9]). . . . . . . . 142
21
22
Introduction
Cosmic rays are unique tools to understand the universe and explore new physics.
Primary cosmic rays are produced in Big Bang and Stellar nucleosynthesis. Secondary
cosmic rays are of particular interest: they are almost absent in cosmic ray sources
and entirely produced in interactions between primary cosmic rays and interstellar
medium. Therefore, the ratio of secondary to primary cosmic ray nuclei measures the
net effect of the galactic propagation. This is critical for background calibration in
exotic physics searches with anti-proton and positron measurements.
Among various secondary to primary ratios, the measurement of the Boron to
Carbon ratio has the smallest error. The high abundances of cosmic ray Boron and
Carbon make the statistical error small. Most detector effects largely cancel between
Boron and Carbon thanks to the similarity of their charges and nuclear cross sections,
leading to a small systematic error.
The Alpha Magnetic Spectrometer (AMS-02) is a particle physics detector installed on the International Space Station with an acceptance of ∼ 0.45m2 sr. It is
designed to measure cosmic rays from about 1 GeV to about 1 TeV. It started taking
data on May 19, 2011 and could last for 10 to 20 years. It flies at an altitude between
330 km and 435 km. With its long duration and large acceptance, AMS-02 accumulates unprecedented statistics of cosmic ray events. During the first 30 months of data
collection, AMS-02 identified about 1.1 million Boron and 3.8 million Carbon nuclei
above 1 GeV/n (kinetic energy per nucleon), with about 2 thousand Boron and 17
thousand Carbon nuclei above 100 GeV/n.
This thesis describes the measurement of the Boron to Carbon ratio with AMS-02
in the range 1 GeV/n to 670 GeV/n. The experimental and analysis challenges in
23
achieving a high precision measurement are addressed, such as high resolution charge
identification (σZ ∼ 0.1 for Carbon) and control of nuclear interactions in the material
of AMS-02 (as primary Carbon produces secondary Boron inside AMS-02).
The outline of this thesis is listed in the following:
• Chapter 1 (Cosmic Ray Boron and Carbon) describes the origin, acceleration and propagation of cosmic ray Boron and Carbon, and discusses the
significance of the Boron to Carbon ratio measurement to exotic physics (such
as dark matter) search in cosmic rays.
• Chapter 2 (The Alpha Magnetic Spectrometer) describes the design and
performance of each subdetector. Data acquisition system and Monte Carlo
simulation procedures are also presented.
• Chapter 3 (Event Reconstruction) summarizes the reconstruction methods
of charge, rigidity and velocity.
• Chapter 4 (Charge Measurement by the TRD) presents my work on the
TRD (Transition Radiation Detector) charge reconstruction, including TRD
track fitting for ions, charge measurement with dE/dx, and an innovative
method of measuring charge with delta rays extending the charge measurement
range from 1<Z<6 to 1<Z<26.
• Chapter 5 (Data Analysis) describes the procedure of the data analysis,
with focus on efficiency differences between Boron and Carbon due to delta ray
production, nuclear interaction and isotope composition. Analysis of systematic
errors are stated.
• Chapter 6 (Results) presents the result of the Boron to Carbon ratio measurement, and shows corresponding improvement in the prediction of anti-proton
background.
24
Chapter 1
Cosmic Ray Boron and Carbon
1.1
Overview
Carbon nuclei (hereafter, “Carbons”) are primary particles produced in Stellar Nucleosynthesis and accelerated by supernova remnants, whereas Boron nuclei (hereafter,
“Borons”) are considered to be secondary particles from spallation of heavier elements
(Carbon, Nitrogen, Oxygen) in the interstellar medium. The abundance of cosmic
ray Boron reflects the amount of interstellar medium that primary cosmic rays traveled through when propagating in our galaxy. The diffusion of cosmic rays in our
galaxy, characterized by the escape time tesc , is caused by cosmic rays scattering in
the interstellar medium.
In this chapter we introduce the present knowledge of the origin, acceleration
and propagation of cosmic ray Boron and Carbon, and explain the importance of a
precision measurement of the Boron to Carbon ratio up to 670 GeV/n.
1.2
Origin of Cosmic Ray Boron and Carbon
The nuclei observed in the cosmic rays can have different origins: (1) Big Bang
Nucleosynthesis; (2) Stellar Nucleosynthesis; (3) Spallation of cosmic rays in galactic
propagation. In this section we review the origins of cosmic ray Boron and Carbon.
25
1.2.1
Big Bang Nucleosynthesis
Trace amounts of Boron and Carbon isotopes are produced in the Big Bang Nucleosynthesis [17].
In the first 100 seconds after the Big Bang, when the universe is very hot (T ≥
1010 K), any nucleus heavier than proton and neutron formed at this stage are immediately dissociated by high energy photons. For example, Deuterons produced from
the reaction p + n → d + γ are destroyed in the reaction d + γ → p + n. When the
temperature drops to T ≈ 109 K, Deuteron starts to accumulate and further reactions
proceed to produce heavier nuclei. This process lasts until ∼ 103 s after the Big Bang,
when almost all remaining free neutrons (with a half life of about 14.7 min [18]) have
decayed (n → p + e− + ν¯e ). The nuclei production during this period is Big Bang
nucleosynthesis, and the produced nuclei are called primordial nuclei.
Observations of cosmological clouds show that the abundances of primordial D
[19] and 3 He [20] relative to 1 H are on the order of 10−5 . The relative abundance
of primordial Li (O(10−10 ) [21]) is measured by observing metal-poor stars. Since
there are no stable nuclei with 5 or 8 nucleons, there is a bottleneck that prevents the
Big Bang nucleosynthesis from efficiently producing nuclei beyond 7 Li; therefore, the
relative abundances of primordial Boron and Carbon are expected to be much smaller
than 10−10 . Figure 1-1 shows the relevant reactions for the production of Boron and
Carbon isotopes [1]: (1) 10 B is mainly produced from 6 Li, 7 Be and 9 Be; (2) 11 B from
7
Li, 8 Li and
11
C; (3)
12
C mostly produced from
11
B and
12
B.
The Big Bang Nucleosynthesis model has only one free parameter, the baryon to
photon ratio (or the baryon density), η [17]. Figure 1-2 shows the relative abundances
of
10
B and
11
B as a function of η, along with 6 Li, 9 Be and CN O isotopes [1]. The
most recent measurement of η is from WMAP: η = 6.16 ± 0.15 × 10−10 [2]. For this
value of η, the expected relative abundances of primordial Boron and Carbon are less
than 10−15 .
26
Figure 1-1: Important reactions for the production of primordial Boron and Carbon
isotopes in the Big Bang Nucleosynthesis [1]. The legends at upper left and lower
right parts of the plot indicate the reaction mechanisms. For example, from the upper
left legend we read that the reaction to produce 2 H from 1 H is 1 H + n →2 H + γ.
1.2.2
Stellar Nucleosynthesis
Fusion reactions are responsible for creating stable heavy elements during stellar
evolution. Carbon is created through the 3α process [22] during the Helium burning
phase, when the temperature is about 108 K. The first step of the 3α process is:
α + α →8 Be .
27
(1.1)
Figure 1-2: Relative abundances of stable light isotopes in the Big Bang nucleosynthesis as a function of the baryon to photon ratio η [1]. The relative abundances of
Boron and Carbon are less than 10−15 at η = 6.16 × 10−10 (measured by WMAP [2]).
28
8
Be is not stable and breaks up into two α particles. The life time τ (8 Be) ≈ 3×10−16 s
is larger than the time scale of an α + α scattering at T ≈ 108 K, leading to a small
equilibrium of 8 Be concentration 8 Be/4 He ≈ 10−9 . The second step of the 3α process
is α-capture by the short-lived 8 Be:
8
Be + α →12 C ∗ →12 C + γ .
(1.2)
This reaction is greatly enhanced due to a resonance effect which arises because a
Carbon nucleus has an energy level close to the combined energy of the reacting 8 Be
and 4 He nuclei [23]. The abundance ratio of Carbon to Hydrogen in the solar system
is about 4 × 10−4 [24], which is comparable to the ratio in cosmic rays.
Figure 1-3: The relative abundance of Boron in stars, A(B), as a function of metallicity, [F e/H] [3]. A(B) = log(N (B)/N (H)) + 12. [F e/H] = log(N (F e)/N (H)) −
log(N (F e)/N (H))Solar .
Boron is a fragile element (binding energy is 6.93 MeV/n for 11 B) and is destroyed
29
by proton capture in deep layers of stars at T ≥ 6 × 106 [25]. Due to the sensitivity to
destruction by warm protons, any convection of surface layers to deep layers in stars
should result in a depletion of Boron. However, observations of Boron abundances as
a function of metallicity [3] (see Figure 1-3) show that Boron is accumulated along
the history of stellar evolution. The reason for the observed abundance evolution
is still a puzzle; however, from the plot we observe that even in very old stars, the
abundance ratio between Boron and Hydrogen is less than 10−9 , which is five order
of magnitude less than that in cosmic rays.
Another source of Boron production in stars is the ν-process in Type Ic supernovae
[26]: high energy neutrinos scatter on
12
C to produce
11
B. During the core collapse,
most of the released gravitational energy is carried away by neutrinos (the total
number of neutrinos is about 1058 for a star with mass about 10M ). In spite of the
vast amount of neutrinos, the abundance of Boron produced in the ν-process is only
B/H ≈ 10−7 [26], due to the small cross section of neutrino scattering (∼ 10−47 Eν m2
[18]).
1.2.3
Spallation of Cosmic Rays in Galactic Propagation
Cosmic ray Boron is produced from the spallation of cosmic ray nuclei in galactic
propagation. For example, the spallation of Carbon:
C +p→B+X .
(1.3)
Figure 1-4 shows a comparison between galactic cosmic ray abundances and nuclei
abundances in the solar system [4]. The relative elemental abundances in the solar
system are representative of galactic cosmic ray sources, so the 105 discrepancy in
Boron abundances shows that most Borons are of secondary origin. A small fraction
of cosmic ray Carbons also originate from spallation of heavier elements.
The main sources of Boron are high energy Carbon, Nitrogen and Oxygen colliding with the Interstellar Medium (see Appendix B for future discussions). The cross
section of the nuclear interaction between nuclei and the interstellar medium is al30
Figure 1-4: Comparison of galactic cosmic ray abundances at solar minimum (red
filled circles) with solar system nuclei abundances (blue open circles) [4]. In the solar
system, Boron cannot be created from spallation of Carbon (C + p → B + X).
most constant for particles with energy larger than 1 GeV/n. Therefore the amount
of secondary Boron produced from the spallation depends on the amount of interstellar medium that the primary particles passed through. Later in this chapter we
will present galactic cosmic ray propagation, including galactic structure, Interstellar
Medium, galactic magnetic field, and diffusion.
1.3
Acceleration of Primary Cosmic Rays
High energy (GeV/n or higher) primary cosmic ray nuclei (e.g., Carbon) are assumed
to be accelerated by the shock wave of supernova remnants [27]. This is supported
both by simple energy estimations and experimental observations:
• In our galaxy, the measured frequency of core collapse supernovae is 1.9 ±
31
1.1/century [28] and the typical kinetic energy released by one supernova explosion is about 1051 erg [29], so the estimated energy output rate is about
6 × 1041 erg/s. Given that the total cosmic ray input luminosity of the Milky
Way is about 7.9 × 1040 erg/s [30], supernova remnants are able to provide the
required energy as long as there exists an acceleration mechanism (e.g., Fermi
acceleration, as will be presented later) which can convert 10% of its output
energy into high energy cosmic rays.
• Observations of supernova remnant gamma rays, which are produced by either
accelerated electrons (synchrotron radiation or inverse Compton scattering) or
accelerated protons (nuclear interaction), would support the acceleration of cosmic ray by supernova remnants. Recent measurement by the Fermi LAT [31]
of characteristic pion decay (π 0 → γ + γ) in the supernova remnant gamma ray
spectra provides evidence that cosmic ray protons are accelerated in supernova
remnants.
Supernova remnants accelerate cosmic rays through the diffusive shock acceleration [32] [33] (the 1st order Fermi acceleration). After the supernova explosion, a
strong shock wave spreads out from the supernova and propagates through interstellar medium (in the form of plasma) at supersonic speed. The shock compresses the
plasma and a fraction of the kinetic energy of incoming upstream plasma is transferred to the internal degree of freedom of downstream plasma; thus, in the rest frame
of the shock, the particle’s velocity increases when passing through the shock front
from downstream to upstream, and vice versa. Due to the presence of magnetic inhomogeneities in both upstream and downstream, collisionless diffusion without energy
loss allows some of the particles to cross the shock front back and forth many times.
The energy gain per cycle is α = ∆(E)/E ∝ Vrel , where Vrel is the relative velocity
of particles in upstream and downstream medium.
The diffusive shock acceleration leads to a power law of cosmic ray energy spectrum
[34] [35]. Let the particle’s escape probability be Pesc ; then the number of particles
32
left after n collisions is:
N (E > En ) ∝
∞
X
(1 − Pesc )m =
m=n
(1 − Pesc )n
,
Pesc
(1.4)
where En is the energy of particles after n collisions, which is:
En = E0 × (1 +
∆(E) n
) = E0 × (1 + α)n .
E
(1.5)
Combining the above two equations to cancel n, we get:
N (E > En ) ∝ En−γ
⇒
with
N (E) ∝ E −γ−1 .
γ=−
ln(1 − Pesc )
ln(1 + α)
(1.6)
(1.7)
The expression of γ shows that the spectrum becomes steeper with a higher escape
probability Pesc and a lower energy gain α. Measurements show that the energy
spectra of cosmic ray fluxes follow the power law (N (E) ∝ E −2.7 for protons [18]).
1.4
Propagation of Cosmic Rays in Our Galaxy
The abundance of secondary cosmic ray Boron from 1 GeV/n to 670 GeV/n directly
depends on the propagation of heavier parent nuclei in our galaxy. Two observations
show that cosmic rays go through lengthy and complex propagations in the Milky
Way:
• In spite of strong anisotropy of cosmic ray sources (mainly distributed on the
galactic plane), the observed galactic cosmic rays in the solar system show a
high level of isotropy.
• The amount of secondary light elements (Li−Be−B) observed in cosmic rays is
about 25% of their parent particles (C −N −O) [18]. To obtain this abundance,
cosmic rays should go though ∼ 5g/cm2 . However, the average column density
across our galaxy is just about 10−3 g/cm2 [36]. Therefore, cosmic rays must be
33
confined in our galaxy and diffuse for a long time before reaching us.
In this section we review the galactic propagation of cosmic rays, with a focus on
diffusion and fragmentation of primary cosmic ray nuclei like Carbon.
1.4.1
Milky Way and Galactic Magnetic Field
The Milky Way [37] is a spiral galaxy with a diameter of ∼ 30kpc. Most of the
bright stars reside in a fairly flat disk (∼ 1kpc thick) surrounded by a bright central
bulge. The Sun is located on the lower arm of the disk and is about 8.5 kpc away
from the center. The entire disk is surrounded by a vast dimmer halo. The space
between the stellar systems in the Milky Way contains interstellar medium (ISM),
including ionized gas, molecular gas, dust, and cosmic rays, with an average density
of ∼ 1 nucleon/cm3 [38] [39].
The interstellar space is also filled with magnetic fields on the order of 10µG [40]
(measured via the Faraday rotation of linearly polarised radiation [41]). Recently,
Voyager 1 escaped from the solar system and entered the ISM. It directly measured
the galactic magnetic field to be about 4µG [42]. Galactic magnetic field has a high
level of inhomogeneity. The turbulence motion of the plasma in the ISM leads to the
turbulence motion of the magnetic field. The field lines are frozen in the ISM plasma
and move together with the plasma [43]. Recent observations [44] on the local ISM
show the turbulence wave number spectrum can be described by Kolmogorov model,
E(k) ∼ k −5/3 [45]. See Section 1.4.2 for cosmic ray diffusion in galactic magnetic
field.
1.4.2
Diffusion
Diffusion is a random walk normally caused by collisions. During the propagation,
cosmic rays follow the magnetic field lines with helical trajectories. They constantly
experience scatterings with interstellar medium and magnetic field irregularities, leading to diffusions in both spatial and momentum space. The collisionless scattering
with magnetic field irregularities is of resonant character, a particle with rigidity R
34
mainly interacts with magnetic irregularities with dimensions similar to the its Larmor radius [12]:
k∝
1
1
B
=
=
,
rg
R/B
R
(1.8)
where rg is the Larmor radius, and k is the wave number, which is inversely proportional to the dimension of magnetic irregularities. Using the measured galactic
magnetic field strength by Voyager 1 (4µG [42]):
R ≈ 10−12 rg (GV ) ,
(1.9)
where rg is in units of cm. The wavelength of the magnetic inhomogeneities is measured to be 107 cm to 1020 cm [46], corresponding to rigidity ranges from 10−5 GV to
108 GV. This covers cosmic ray spectra up to the “knee” region [47].
The diffusion process is usually described by the diffusion coefficient D in the
Fick’s Law [48]:
∂φ
= D∇2 φ ,
∂t
(1.10)
where t is time, and φ is the concentration per unit volume. The diffusion coefficient
D is inverse proportional to the escape time tesc (typically 108 years [49] for energy
range of GeV), which relates to the amount of material traversed by cosmic rays, λ,
by:
λ = ρx = ρctesc ,
(1.11)
where ρ is the ISM mass density, c is the speed of light, and λ is usually in units
of g/cm2 . Therefore the amount of Boron, proportional to the amount of material
traversed by primary particles like Carbon, directly reflects the diffusion process of
cosmic rays (see Section 1.6.3 for more details).
1.4.3
Leaky Box Model
The leaky box model [50] [51] is straightforward. The model assumes that the diffusion
process takes place so quickly that the distribution of cosmic rays in the Milky Way
is homogeneous. Cosmic ray freely propagates in the galaxy with a probability of
35
escaping (described by characteristic escape time τesc ) and a probability of having
inelastic nuclear interactions (fragmentation, decay, etc., defined by characteristic
interaction time τint ). The basic leaky box model equation [50] can be written as:
∂Ni
Ni
Ni
= Qi − i − i ,
∂t
τesc τint
(1.12)
where the index i means the constants and conditions of the equation are different
for different particle species, Ni are the number densities of particles, and Qi are
the cosmic ray sources, including primary sources like supernova shocks and second
sources like spallation from other isotopes. The leaky box model is justified in many
cases of flux measurements; however, it fails when involving synchrotron radiation
and inverse Compton scattering [52].
A similar model is the weighted slab model [50] [53]. Instead of using escape
time to characterize the propagation, it uses the path length. The model views the
propagation of cosmic rays as a convolution of two independent processes: one for the
nuclear physics, the “slab”, and one for the astrophysics, the “weight”, or the path
length distribution. In the framework of this model, the amount of material traversed
by a particle is expressed in grammage, x = ρ · l. Then the number density is:
Z
Ni =
+∞
Nis (x)Gi (x)dx ,
(1.13)
0
where Nis (x) are the number densities of particles after traveling through a slab of
matter with thickness x; and G(x), the path length distribution function, is the
probability that a particle has crossed x in matter. The cosmic ray sources are
implemented via the initial conditions of Nis (x): Nis (0, E) = Qi (E). The weighted
slab model is satisfactory in high energy region where the energy loss of particles can
be ignored; However, it needs significant modifications when energy change is not
trivial [53].
36
Figure 1-5: Schematic view of the diffusion halo model [5].
1.4.4
Diffusive Halo Model
The diffusive halo model [5] [12] [54] is the most detailed and effective model to date.
Its geometry description reflects the most essential features of the real system, and it
takes into account many important physics processes. A schematic view of the model
is shown in Figure 1-5. The cosmic ray sources are distributed in a relatively thin
disk with a radius of R ≈ 20kpc and a thickness of 2h ≈ 300pc. The diffusion of
cosmic rays can happen both in the source disk and in the halo around the disk. The
halo is of a cylinder shape, with a radius of R and a height of 2H ≈ 8kpc. It assumes
zero cosmic ray density for boundary conditions, since cosmic rays will escape to
intergalactic space once they reach the boundaries. A complete set of known stable
and radioactive isotopes, up to
64
N i, are incorporated in the model for calculations
of nuclear interactions. Electrons, positrons, and anti-protons are also included. The
physics processes are described by the transport equation (see below), which can be
solved numerically by software packages such as GALPROP [12] and DRAGON [55].
A parameter fit matches existing experimental measurements.
The transport equation for high energy charged cosmic rays propagating in our
37
galaxy can be written as [12]:
∂ 2
∂ ψ
p ~ ~
ψ ψ
∂ψ
∂
~
~
~
= q+∇·(D
[p Dpp ( 2 )]− [ṗψ− (∇·
V )ψ]− − , (1.14)
xx ∇ψ− V ψ)+
∂t
∂p
∂p p
∂p
3
τf τr
where:
• ψ = ψ(~r, p, t) is the cosmic ray density per unit of momentum p at position ~r
and time t.
• q = q(~r, p, t) is the cosmic ray source term, which includes primary sources and
contributions of fragmentation and decay from progenitor species.
~
~
• ∇·(D
xx ∇ψ) describes the diffusion in position space. Dxx is the spatial diffusion
tensor. Usually an isotropic diffusion process is assumed, in which case Dxx is
replaced by a scaler D.
~ · (V~ ψ) quantifies the density change due to convection. V~ is the convection
• −∇
velocity.
•
∂
∂ ψ
[p2 Dpp ∂p
( p2 )]
∂p
is the diffusion term in momentum space, which is the diffusive
re-acceleration (second order Fermi acceleration) by interstellar turbulence, the
strength is controlled by the coefficient Dpp .
∂
• − ∂p
(ṗψ) represents the density change due to energy gain or loss.
∂ p ~
• − ∂p
[ 3 (∇ · V~ )ψ] represents the density change due to convection.
• τf is the time scale for density loss by fragmentation.
• τr is the characteristic time for density loss by radioactive decay.
1.5
Propagation of Cosmic Rays in the Solar System
1.5.1
Solar Modulation
When entering the solar system, cosmic rays are influenced by the solar wind, which
consists of a stream of charged particles released from upper atmosphere of the Sun,
38
as well as interplanetary magnetic field resulted from the plasma formed by charged
particles. The velocity of ejected particles is between 350km/s and 700km/s [56].
The region of space in which the solar wind is dominant is called heliosphere. The
field polarity changes when going from northern to southern heliosphere. The surface
in between is called the heliospheric current sheet [57], which has a spiral shape due
to the angular difference between magnetic dipole axis and rotation axis of the Sun.
The solar activity varies with a period of 11 years (one solar cycle) [58],
Similar to galactic propagation, the charged particle undergoes convection, diffusion and energy changes while propagating in the helioshpere. This effect is called
solar modulation. Solar modulation can be described in a simplified way by the force
field approximation [59] on the Parker model [60]. In the model, the solar wind is
regarded as a radial field with a potential φ. The modulation on local interstellar
(LIS) energy spectrum JLIS (E) is expressed as:
E2 − M 2
J (E) =
JLIS (E + Zeφ) ,
(E + Zeφ)2 − M 2
(1.15)
where M is a particle’s mass, and Z is a particle’s absolute charge. The parameter φ
can be interpreted as the average energy loss per charge unit of cosmic rays traveling
through heliosphere to reach near Earth orbit. Its value ranges from ∼ 250M V to
∼ 1500M V depending on the strength of solar activities [61]. The solar modulation is
significant for particles with low rigidity (less than ∼ 20 GV); particles with rigidity
larger than 20 GV are less affected.
1.5.2
Influence of the Geomagnetic Field
Before reaching AMS-02 on the ISS at an altitude between 330km and 435km, cosmic
rays need to go through earth geomagnetic field [62]. It is approximately a tilted
(∼ 11◦ to the Earth rotation axis) and displaced dipole field (magnetic bottle) with
a strength of 25µT to 65µT at the Earth surface. The field is centered at the Earth
inner core but with an offset of about 300km; therefore, at a certain altitude from
the ground, the magnetic field line is distorted. The highest distortion is in the south
39
Atlantic ocean near the coast of Brazil, where the field strength is the weakest. This
allows charged cosmic rays to penetrate deeper, leading to stronger radiations. This
phenomenon is known as the South Atlantic Anomaly (SAA) [63].
Currently the widely used model for precision geomagnetic field calculation is the
IGRF model [64]. In this model, geomagnetic field is represented in terms of a scalar
potential:
B(r, θ, φ, t) = −∇V (r, θ, φ, t) .
(1.16)
The potential is expressed as a finite series of spherical harmonics:
N X
n
X
a
m
V (r, θ, φ, t) = a
( )n+1 [gnm (t)cos(mφ) + hm
n (t)sin(mφ)] × Pn (cos θ) , (1.17)
r
n=1 m=0
where a is the mean radius of the Earth, N is chosen to be 13 for the time after epoch
1995 in the latest IGRF model, and the coefficient gnm (t) (hm
n (t)) can be linearly
extrapolated from gnm (T0 ) (hm
n (T0 )) and the corresponding derivative provided in the
IGRF model by fitting to satellite data.
The curvature of a charged particle traveling in the geomagnetic field depends on
the local field strength and the particle’s rigidity. For a particle with very low rigidity,
the curvature might be so large that it is eventually bended back by geomagnetic
field; therefore, such low rigidity particles cannot be received by AMS-02 at all. This
phenomenon is called geomagnetic cutoff. The rigidity value below which no galactic
cosmic ray can penetrate the geomagnetic field to reach the detector is defined as
geomagnetic cutoff rigidity. Particles recorded by the detector with rigidity values
lower than the geomagnetic cutoff rigidity are secondary particles, which originate
from interactions between incoming galactic cosmic rays and the Earth atmosphere.
Since geomagnetic field changes very slowly, geomagnetic cutoff rigidity is only
determined by the location of the detector and the direction of the incoming particle.
The Stormer equation [65] [66] applies dipole approximation to evaluate geomagnetic
cutoff rigidity:
Rc =
M cos4 λ
p
,
r2 (1 + 1 − sin θ sin φ cos3 λ)2
40
(1.18)
where M is the dipole moment, θ and φ are the local zenith and azimuthal angle,
and λ is the latitude along the dipole. Figure 1-6 shows a map of the maximum local
geomagnetic cutoff rigidity for AMS-02 using the Stormer equation.
Figure 1-6: Maximum geomagnetic cutoff rigidity for AMS-02.
1.6
The Boron to Carbon Ratio
1.6.1
Why Boron to Carbon Ratio
As discussed in previous sections, measurements of the ratio between cosmic ray secondary and primary flux ratios are important for quantifying cosmic ray propagation
in our galaxy. Among the different secondary to primary flux ratios (e.g., Li/C, Be/C,
B/C, Sub-Fe/Fe), the Boron to Carbon ratio is the most interesting one because:
• Compared to the ratios of heavier elements (e.g., Sub-Fe/Fe), B/C has smaller
statistical errors due to their high abundances. It also has lower systematic
errors due to less nuclear interactions and delta ray productions in the detector.
• Compared to the ratios of other light elements (e.g., Li/C), B/C presents lower
systematic errors because Boron has similar properties as Carbon in charge and
41
mass; therefore, instrument efficiency effects due to delta ray productions and
nuclear interactions are greatly canceled in the ratio.
Boron-to-Carbon Ratio
1.6.2
Previous Measurements of the Boron to Carbon Ratio
0.4
0.3
0.2
0.1
HEAO (A&A 1990)
CRN (ApJ 1990)
ATIC-2 (ICRC 2007)
CREAM (Astropart. Phys. 2008)
AMS01 (ApJ 2009)
TRACER (ApJ 2011)
0.02
1
102
10
103
Kinetic Energy (GeV/n)
Figure 1-7: Previous measurements of the Boron to Carbon ratio in cosmic rays from
HEAO [6], CNR [7], ATIC [8], CREAM [9], TRACER [10], and AMS-01 [11].
The earliest measurements of cosmic ray nuclei fluxes date back to the 60s [67].
In the early days, most of the measurements were balloon-based experiments with
limited statistics and particle identification powers. Two satellite-based experiments
in the 1980s, HEAO [6] and CNR [7], performed measurements on B/C at about
0.5-50 GeV/n and 50-300 GeV/n, respectively. In the 2000s, three balloon-based
experiments ATIC [8], CREAM [9] and TRACER [10] extended the measurements
to higher energy. The test flight of AMS (AMS-01 [11]) in 1998 measured B/C up to
∼ 50 GeV/n. The results of the B/C measurements in the six experiments mentioned
above are presented in Figure 1-7. The energy range is far below the “knee” [47]. We
42
observe that all the previous measurements show large errors at Ek /A> 20 GeV/n.
• HEAO [6]: The detector is made of five Cherenkov counters with different
refractive indices, with four flash tube arrays to detect Cherenkov photons. The
three inner Cherenkov detectors are mostly used for velocity measurement; the
top and bottom ones are used for charge determination. The detector performed
measurements in the energy range from 0.6 GeV/n to 35 GeV/n.
• CRN [7]: The detector is a combination of two scintillators, two gas Cherenkov
counters, and a six-layer TRD. The charge is mainly determined by the scintillators, which also provides time of flight measurement. The gas Cherenkov
counters determine energy from 40 GeV/n to 150 GeV/n by measuring velocity.
The TRD is designed for energy measurement. For energies below 500 GeV/n,
the MWPC of the TRD measures energy by dE/dx which approximately rises
logarithmically with energy; for energies above 500 GeV/n, transition radiation
X-rays become significant, they are used for energy measurement. The detector
performed measurements in the energy range from 50 GeV/n to 1500 GeV/n.
• ATIC [8]: The detector measures a particle’s energy with a BGO calorimeter
following a 30cm Carbon target. On the top of the instrument is a silicon
detector for charge measurements and separation between incident particles
and backsplashes. Three layers of scintillators are used for time of flight, trigger
and charge measurement. The detector performed measurements in the energy
range from 10 GeV/n to 300 GeV/n.
• CREAM [9]: The calorimeter of the detector is designed to measure very high
energy; medium energy is determined by the TRD; low energy is measured by
a Cherenkov detector. A scintillating detector and a silicon detector are used
for charge measurement. The detector performed measurements in the energy
range from 10 GeV/n to 2000 GeV/n.
• TRACER [10]: The detector uses two pairs of scintillators and Cherenkov counters for charge measurement. In low energy region, a particle’s energy is determined by the velocity measurement from Cherenkov counters; in medium energy
43
region, a TRD determines a particle’s energy according to the relativistic rise in
dE/dx; in high energy region, a particle’s energy is measured by the TRD using
both dE/dx and transition radiations. The detector performed measurements
in the energy range from 1 GeV/n to 10000 GeV/n.
• AMS-01 [11]: The detector is a magnetic spectrometer with a magnetic field
of 0.14T. Silicon trackers inside the magnetic field measure rigidity and charge.
Scintillators at the top and the bottom of the detector measure time of flight
and charge. The detector performed measurements in the energy range from
0.35 GeV/n to 45 GeV/n.
1.6.3
The Physics Picture of the B/C Spectrum
From Figure 1-7 we observe that the Boron to Carbon ratio is measured to be slightly
over 0.3 at 1 GeV/n, and it decreases with energy to be less than 0.1 for energies
above 100 GeV/n. The decrease can be interpreted in three ways: in terms of diffusion
coefficient D, mean free path lm , and escape time tesc (effectively λ, the amount of
material traversed by primary cosmic rays), respectively.
In the Kolmogorov model [45] (validated by observations in [44], see Section 1.4.1),
the diffusion coefficient is parameterized as [36]
D ∼ R1/3 ,
(1.19)
where R is a particle’s rigidity. The physics interpretation of this relationship is
the following: as energy (rigidity) increases, the Larmor radius rg increases, and the
density of magnetic irregularities which provide resonant collisions at wave number
k ∼ 1/rg decreases (according to Kolmogorov spectrum). A particle with higher
energy experiences collisions less frequently, leading to an increasing diffusion coefficient.
Therefore, primary cosmic rays with higher energy diffuse through the galaxy
faster; they have a longer mean free path lm and a shorter escape time tesc . They
traverse less material in the ISM, leading to a lower probability of spallations into
44
secondary cosmic rays.
1.6.4
Constraints on Propagation Parameters
The Boron to Carbon ratio is very sensitive to the propagation parameters, especially
0
in the
those related to diffusion process: for example, the diffusion coefficient Dxx
Diffusive Halo Model (see Section 1.4.4) and the escape time tesc in the Leaky Box
Model (see Section 1.4.3).
To show the constraints, we use the Diffusive Halo Model (GalProp) as an example.
0
In Figure 1-8, we vary Dxx
and VA , and observe that the B/C spectrum is sensitive
0
to Dxx
over the whole energy range (1-1000 GeV/n), whereas it is only sensitive to
VA for energies below 10 GeV/n.
1.6.5
Prediction of Anti-Proton Background in Exotic Physics
Search
Measurements of cosmic ray anti-protons have particular physics interests, since antiprotons might have exotic primary sources such as annihilation of dark matter particles [68] and evaporation of black holes [69] [70]. Anti-protons can be produced as
a secondary particle as well from the interactions between cosmic rays and the ISM:
they have the same production mechanism as secondary Borons. Therefore, to search
for exotic sources of primary anti-protons, an accurate estimation of the secondary
anti-proton background is a must. This is also true for estimating secondary positron
background in the positron fraction measurement [71]. As illustrated in Section 1.6.1,
the measurement of the Boron to Carbon ratio provides the best predictions for the
productions of secondary cosmic rays.
Taking indirect dark matter search as an example: The positron fraction measurement [14] shows an excess starting from tens of GeV, suggesting the existence of
WIMP (Weakly Interacting Massive Particle, a dark matter candidate) with a mass
value of a few hundred GeV. However, this excess might have a pulsar origin [72] (pair
production of electron and positron). Anti-protons are abundantly produced through
45
B/C
D0xx = 5.5 × 1028 cm2/s
D0xx = 6.1 × 1028 cm2/s
D0xx = 6.5 × 1028 cm2/s
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
B/C
1
102
103
Kinetic Energy (GeV/n)
10
VA = 25 km/s
VA = 30 km/s
VA = 35 km/s
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
1
102
103
Kinetic Energy (GeV/n)
10
0
Figure 1-8: The effects of diffusion coefficient Dxx
(upper plot) and Alfven velocity VA
(lower plot) on the Boron to Carbon ratio, simulated by GalProp [12]. The black solid
0
curves use the default GalProp parameters (Dxx
= 6.1 × 1028 cm2 /s, VA = 30km/s).
hadronization in many dark matter models [73], which allow dark matter particles
to annihilate into quarks or gauge bosons. However, due to the large mass value,
46
Figure 1-9: Measurement of anti-proton to proton ratio [13] by PAMELA, BESS,
CAPRICE, and HEAT. The lines are model calculations using leaky box model (dotted), diffusive re-acceleration model (dashed), and plain diffusive model (solid), respectively.
anti-protons are not likely to be massively produced in pulsars. Therefore, searching for primary anti-protons at a few hundred GeV is important for determining if
the positron excess is due to dark matter or pulsar. To achieve that, an accurate
estimation of secondary anti-proton background up to a few hundred GeV is critical.
Similar to the Boron to Carbon ratio, the measurement of the anti-proton to proton ratio has much smaller systematic errors than that of the anti-proton flux because
lots of systematics cancel between anti-proton and proton. Previous measurements of
the anti-proton to proton ratio, up to 180 GeV, are summarized in Figure 1-9. AMS02, with higher maximum detectable rigidity (MDR) and more data, will extend the
measurement to higher energy with smaller errors [74].
As shown in Section 1.6.4, a precision measurement of the Boron to Carbon ratio
up to a few hundred GeV provides stringent constraint on cosmic ray propagation
47
models. To show the impact in predicting the secondary anti-proton background,
0
and the Alfven velocity VA
we do the same variations of the diffusion coefficient Dxx
in the model calculation for anti-protons. The result is plotted in Figure 1-10. We
observe that the background at a few hundred GeV greatly depends on the diffusion
coefficient, which the Boron to Carbon ratio is very sensitive to.
48
P/P
×10-3
0.15
0.1
D0xx = 5.5 × 1028 cm2/s
D0xx = 6.1 × 1028 cm2/s
D0xx = 6.5 × 1028 cm2/s
0.05
0
1
102
103
Kinetic Energy (GeV/n)
10
P/P
×10-3
0.15
0.1
VA = 25 km/s
VA = 30 km/s
VA = 35 km/s
0.05
0
1
102
103
Kinetic Energy (GeV/n)
10
0
Figure 1-10: The effects of diffusion coefficient Dxx
(upper plot) and Alfven velocity
VA (lower plot) on the anti-proton to proton ratio, simulated by GalProp [12]. The
0
black solid curves use the default GalProp parameters (Dxx
= 6.1 × 1028 cm2 /s, VA =
30km/s).
49
50
Chapter 2
The Alpha Magnetic Spectrometer
2.1
2.1.1
The AMS-02 Detector
Overview
The AMS-02 Detector [75] is a general purpose particle physics detector with a large
acceptance (∼ 0.45m2 sr). It is installed on the International Space Station (ISS),
and it might be operating for 10 to 20 years. It was delivered to the ISS on May
19, 2011 by the Space Shuttle Endeavor (mission STS-134). Since then, AMS-02 has
been collecting data at a stable rate of 1.4 × 109 events per month. The detector is
operated and monitored at the Payload Operation and Control Center (POCC) at
CERN.
To bring a large scale high energy physics detector from ground to space, there
exist many challenges. The detector must be able to resist the large acceleration
(∼ 3g) and vibration (∼ 150dB) during the launch. The weight limit (∼ 7.5t), size
limit (∼ 3m × 4m × 5m), power limit (∼ 2kW ) and bandwidth limit (∼ 10M bit/s)
for operation on the ISS put constraints on the detector design. All the electronics
are certified against radiation damage in space. The thermal system releases AMS-02
from influence of the extreme space thermal environment(−25◦ to +55◦ in vacuum).
Extensive beam test, thermal test, and electronics test have been taken. In order to
test the detector design in space, a prototype version of the detector, AMS-01, was
51
Figure 2-1: Layout of the AMS-02 detector and functions of its subdetectors.
built and flown onboard the Space Shuttle Discovery (mission STS-91) in 1998 [76].
In the 10-day mission, AMS-01 collected more than 108 events, and demonstrated the
concept of a large scale particle physics detector in space. Analysis of AMS-01 data
produced significant physics results [76], including cosmic ray anti-Helium search,
proton and Helium in near Earth orbit, and positron fraction measurement.
As shown in Figure 2-1, AMS-02 is made of multiple subdetectors to carry redundant measurements of cosmic rays. The core of the detector is a magnetic spectrometer with a permanent magnet and nine layers of Silicon Tracker. The Silicon Tracker
measures a particle’s rigidity and charge. The Time of Flight detector (TOF) provides
trigger for charged particles, and determines a particle’s velocity and charge. The
Transition Radiation Detector (TRD) and the Electromagnetic Calorimeter (ECAL),
separated by the magnet, are primarily designed for providing independent measurements to identify electrons and positrons from a large background of hadrons. The
ECAL also measures a particle’s energy and provides trigger for high energy photons.
52
The Ring Imaging Cherenkov Detector (RICH) is mainly designed for high resolution
velocity measurement. The Anti-Coincidence Counter (ACC) surrounds the Inner
Tracker to reject events with charged particles entering the detector from the sides.
AMS-02 is also equipped with a GPS module for precision time measurement, as well
as a pair of Star Trackers to locate the position of the detector.
2.1.2
Magnet
Figure 2-2: Configuration of the magnet blocks and the field lines. The arrows forming
a circle on the right figure show the magnetic field directions inside each magnet block.
AMS-02 is equipped with a permanent magnet [76] made of 6400 high grade
N d − F e − B blocks, with a total weight of almost 2 tons. The blocks are grouped
into 64 sectors, constituting a cylinder with a length of 800mm and an inner diameter
of 1115mm. This configuration, as depicted in Figure 2-2, provides a dipole field of
53
Figure 2-3: Magnetic field over the X-Z plane at Y = 0 (center, see Figure 2-2),
measured in 2010.
0.14T in the center of the magnet, with negligible field (less than 2 × 10−2 T ) outside
the magnet. This is required to eliminate the torque effect on the space shuttle and
the ISS. Two measurements of the magnetic field map using Hall probes were made in
1997 and 2010, respectively. The result shows that the field strength is stable within
1%. Figure 2-3 shows part of the measurement results in 2010 [75].
The reference frame of AMS-02 is based on the magnet. The center of the frame
is at the center of the magnet. The X axis is oriented along the direction of the
magnetic field lines. The Z axis is defined along the cylinder symmetry axis, with the
direction towards the top of the instrument. The Y axis is set so as to complete the
right handed Cartesian coordinate system. With this definition, the Y-Z plane is the
bending plane.
54
2.1.3
Transition Radiation Detector (TRD)
Figure 2-4: Computer generated view of the TRD on top of the magnet vacuum case
(blue).
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Figure 2-5: A TRD module, containing 16 proportional drift tubes.
The TRD [77] is mounted between the first layer of the Tracker and the first layer
of the TOF. It has an inverted octagonal pyramid shape, as shown in Figure 2-4. The
TRD consists of 20 layers of 20mm thick fleece radiators, with 20 layers of drift tubes
interleaved in between. There are in total 5248 drift tubes, with 6mm diameter and
0.8m to 2m length. They are grouped into 328 modules, each of which consists 16
55
tubes (see Figure 2-5). All drift tubes are filled with Xe and CO2 , and they work in
the proportional mode. To compensate the gas gain change due to gas diffusion across
tube walls, a daily high voltage adjustment is performed, and gas is refilled using a
gas supply system approximately once a month. The TRD gas system is equipped
with 49kg Xe and 5kg CO2 , allowing for a steady operation in space for 30 years if
no micrometeorite strikes.
The primary purpose of the TRD is to identify positrons from the proton background by transition radiation. The abundance ratio between proton and positron is
about 1000 at 10 GeV, and it increases with energy. At an electron efficiency of 90%,
the TRD proton rejection factor is shown to be better than 104 around 10 GeV and
drops to 102 around 600 GeV [78]. Besides, the TRD is able to measure the charge
of cosmic ray nuclei up to F e [79], see Chapter 4.
2.1.4
Silicon Tracker
The Tracker [80] [81] [82] is composed of 2264 double sided micro strip Silicon sensors
with a total active area of 6.4m2 . They are grouped in 192 ladders. The ladders are
arranged in 9 layers along the Z axis. As shown in Figure 2-6, Layer 1 is on top of
the TRD, Layer 2 to Layer 8 are placed inside the magnet bore, and Layer 9 covers
the top of the ECAL. This arrangement maximizes the maximum detectable rigidity
(MDR) by maximizing the lever arm.
The substrate of the sensor is a n-doped Silicon wafer with a high resistivity of
6kΩ/cm, inversely biased with an operating voltage of 80 V . It is operated at full
depletion mode. The electrons and holes, which are created through ionization by the
transversing charged particle, drift in the electric field. They are eventually collected
by the strips on the surfaces. On the junction side (Y side) of the sensor there are p+
strips, with implantation and readout pitches of 27.5µm and 110µm; On the ohmic
side (X side) there are n+ strips, with implantation and readout pitches of 104µm
and 208µm. The sensor has a dimension of 72.045 × 41.360 × 0.300mm3 . The 300µm
thickness makes the Tracker a very transparent detector, so that multiple scattering
is reduced.
56
Figure 2-6: Layout of nine layers of the Silicon Tracker in AMS-02.
Each ladder represents a mechanical and readout unit, it contains 7 to 15 sensors
depending on the ladder’s position. The p+ strips of different sensors are connected
together directly with micro bondings; the n+ strips are bonded through Upilex cables
which connects to the readout electronics. The ambiguity of the n+ strip positions
on the X side is removed during the track reconstruction with the help from the
TOF and the TRD. In total, each ladder has 1024 readout channels, with 640 for p+
strips, and 384 for n+ strips. Since December 1st, 2011, the X side of 6 ladders is
not operational due to power supply malfunctions, leading to ≈ 1.2% loss in readout
channels and ≈ 1% loss in Tracker reconstruction efficiency [80].
Different layers of the Tracker are aligned with cosmic rays. The Tracker Alignment System (TAS) confirms that the internal seven layers have a position accuracy of
a few microns. The relative positions of the two external layers have larger movements
due to the changing thermal environment. Dynamic alignment makes the position
accuracy of the external layers better than 10µm [83], leading to an MDR of 2T V for
single charged particles [84]. With flight data calibration, the charge resolution for
57
Carbon is about 0.1; this represents a misidentification probability lower than 10−6
with 99% selection efficiency [85].
2.1.5
Time of Flight Counters (TOF)
The TOF [86] consists of four layers of scintillation counters disposed in pairs above
(Upper TOF) and below (Lower TOF) the magnet. Each layer includes eight or ten
1cm thick polyvinyl toluene scintillators with either rectangular or trapezoidal shape.
The scintillation photons are collected by two or three photomultiplier tubes (PMTs)
through plexiglass light guides at each end of the counters. The configuration of
counters and PMTs is plotted in Figure 2-7. To overcome the non-negligible impact
of residual magnetic field on the PMTs that are very close to the magnet, a special
class of fine mesh PMT is chosen for its capability of working in high magnetic fields
while keeping good timing characteristics. All light guides are twisted and tilted
in order to minimize the angle between the axis of PMT and the direction of local
magnetic field.
Figure 2-7: Layout of the TOF: upper TOF (left) and lower TOF (right). The lower
TOF has a larger area so that more deflected particles by the magnet will be accepted.
The anode signals from PMTs on the same side of a counter are summed together
for trigger decisions, as well as time and charge measurements. The dynode signal of
58
each PMT, whose gain is very low, is read out independently for charge measurement
of particles with Z > 4. There are three thresholds for the anode signals: (1) The low
threshold (LT) signals are very fast and are used for time measurement; (2) The high
threshold (HT) signals provide trigger signals for charged particles; (3) The super
high threshold (SHT) signals are used for the Z > 1 trigger selection.
Analysis of the ISS data [87] [88] shows that the time resolution of the TOF is
160ps for Z = 1 particles and 48ps for Z = 6 particles. This corresponds to velocity
resolutions of 4% and 1.2%, respectively. Besides, the TOF is capable of measuring
the charge of cosmic rays up to Z = 30. The charge resolution is 0.16 for Z = 6
particles, and 0.4 for Z = 26 particles.
2.1.6
Ring Imaging Cherenkov Detector (RICH)
The RICH [89] is located between the Lower TOF and the 9th layer of the Tracker
(see Figure 2-1). It has a height of 605mm, a diameter of 1200mm at the top and
1340mm at the bottom. The main components of the RICH, as shown in Figure
2-8, are the Cherenkov radiators in the top, the external conical reflector, and the
light detection plane in the bottom. The radiator consists of 92 silica aerogel tiles
(AGL) with a refractive index n = 1.05, representing 90% of the radiator geometrical
acceptance, as well as 16 sodium fluoride crystals (NAF) with a refractive index
n = 1.33, covering the central square of 34 × 34cm2 . Due to the different refractive
index, the AGL is able to measure particles with β > 0.95, whereas the NAF provides
measurements for particles with β > 0.75. The reflector, a conical mirror, surrounds
the expansion volume so as to improve the detection efficiency by reducing the lateral
loss of Cherenkov photons. The detection plane is made of 680 multi-pixel PMTs,
with 10800 total readout channels. To avoid too much material in front of the ECAL,
PMTs are arranged in such a way that the detection plane has a central hole matching
the ECAL shape and dimensions. The detection efficiency, however, is not diminished
too much, because the photons produced in the NAF in the center have a large cone
size, and no sensor is needed in the center of the detection plane.
Flight data shows that the RICH has a relative velocity resolution of ∼ 10−3 for
59
Figure 2-8: Layout of the RICH.
single charged particles, and O(10−4 ) for heavy nuclei [90]. The RICH is also able to
measure charge up to F e; the resolutions are better than 0.5 for light elements [91].
2.1.7
Electromagnetic Calorimeter (ECAL)
The ECAL [92] is not used in the measurement of the Boron to Carbon ratio. It
is a three dimensional sampling electromagnetic calorimeter with about 17 radiation
lengths. The active part, with a volume of 64.8cm × 64.8cm × 16.65cm, is a sandwich
of lead and scintillating fibres (see Figure 2-9). The ECAL consists of 9 super layers.
Each layer has a height of 18.5mm and is composed of 10 interleaved layers of lead and
fibers. There are 4 super layers aligned along the direction of the magnetic field line
(X direction) and 5 super layers aligned perpendicularly (Y direction). Each super
layer is read out by 36 four-pixel PMTs. The active area covered by each pixel is
called a cell. The ECAL is subdivided into 1296 cells (324 PMTs) in total, leading to
a sampling of 72 measurements on each layer and 18 measurements of the longitudinal
shower profile. Two sets of gain values (33 times difference between each other) are
used to extend the dynamic ADC range to cover from the minimum ionizing particles
to 1 TeV electrons. The ECAL also acts as a trigger device: the last dynode signal
60
of each PMT of the 6 central super layers is used to generate a standalone ECAL
trigger for photons with energies larger than 2 GeV.
Figure 2-9: Structure of the ECAL active part.
With calibrations, the ECAL achieves an angular resolution of σ(θ)/θ ≈ 1◦ and
p
an energy resolution of σ(E)/E = (10.4 ± 0.2)%/ E(GeV ) ⊕ (1.4 ± 0.1)%, with
linearity better than 1% at least up to 300 GeV. The ECAL energy can be used to
identify electrons and positrons from protons by matching the measured energy with
a particle’s rigidity measured by the Silicon Tracker. A Boosted Decision Tree (BDT)
is constructed based on electromagnetic shower shapes to reject proton background.
According to flight data, the ECAL proton rejection factor is more than 104 from
2 GeV to 300 GeV, and better than 103 up to 1 TeV [93]. The ECAL can also
perform charge measurement up to Oxygen [94], even though it is not helpful in
practice due to its small acceptance and low charge resolution.
2.1.8
Anti-Coincidence Counter (ACC)
To identify undesired events with charged particles coming from the sides of the
detector and assure a clean track reconstruction, the Inner Tracker is surrounded
by 16 plastic scintillator panels, the ACC. The scintillation lights coming from both
ends of each panel are collected by wavelength shifter fibers, which are read out by
61
Figure 2-10: The ACC after integration (left) and the arrangement of its components
(right).
16 PMTs outside the magnet. Figure 2-10 shows how the components of ACC are
arranged [95]. The inefficiency of the ACC has been studied with atmospheric Muon
data, using the tracks reconstructed by the TRD and the Tracker. An upper limit of
1.3 × 10−4 is obtained at 95% confidence level [95]. Signals from the ACC are inserted
into the Level-1 trigger logic as a veto for necessary physics trigger settings.
2.2
2.2.1
Operation and Data Acquisition
AMS-02 on the ISS
AMS-02 is mounted on the Integrated Truss Structure on the ISS. It has a tilted angle
of 12◦ towards the center of the ISS to avoid solar panels in its field of view. The ISS
62
flies in near Earth orbit with a period of 92 minutes at an altitude between 330km
and 410km. The orbit has an inclination angle of 51.6◦ with respect to the Earth
equator. Since the orbit of the ISS is fixed and AMS-02 cannot rotate on the ISS,
particles from two regions of the sky cannot be detected by AMS-02, corresponding
to the south and north poles.
The data is transmitted to ground via two separate radio links: the S band for
critical housekeeping data (CHD) and the Ku band for science data and CHD. Because
the Ku band is not always available, an AMS laptop is maintained on the ISS for data
buffering. The data is received at the White Sands NASA Facility. Then it goes to
the NASA Marshall Space Flight Center, and is eventually transmitted to the POCC
at CERN for detector monitoring and physics data analysis.
2.2.2
Data Flow in the Detector
The analog data (over 200k channels in total) from each sub-detector’s front-end
electronics is digitized and compressed by 264 Digital Signal Processors (DSP). After
going through two levels of processors for reduction, the data is collected by the main
DAQ computer (JMDC), and sent to the ground.
About 1000 cosmic ray events are recorded by AMS-02 per second, leading to an
internal data rate of 1 GB/s. With the DAQ system’s filtering and compression, the
data rate to the ground is reduced to 300 kB/s.
2.2.3
Trigger
The trigger is a system of electronics that uses simple criteria to decide quickly if an
event should be recorded by the detector. The trigger is generated from signals of the
TOF, the ACC, and the ECAL [96] [97]. Three fast triggers are built: the FTC for
charged particles, the FTE for electromagnetic showers in the ECAL, and the FTZ
for particles with low velocity and high charge. The three triggers are combined with
an OR logic to produce the fast trigger signal (FT).
After the DAQ system is triggered by the FT, the signals are sent to a dedicated
63
processor (JLV1) to generate 14 trigger signals corresponding to different trigger
conditions. They are grouped into four categories:
• Normal charged particles (Z = 1). It requires signal coincidences in different
layers of the TOF.
• Particles with high charge (Z ≥ 2). It requires large energy deposition in the
TOF.
• Veto signal, which sets an upper limit of the number of fired ACC panels.
• Events with electromagnetic showers.
It requires energy deposition in the
ECAL.
Out of the 14 trigger signals, 7 physics triggers are built:
• High Charge (Z ≥ 2): This is the major trigger for Boron and Carbon, it
requires 4 out of 4 TOF layers passing super high threshold, and the number of
ACC hits less than 5.
• Normal Charge (Z = 1): 4 out of 4 TOF layers passing high threshold, and no
ACC hits.
• Unbiased Charge: 3 out of 4 TOF layers passing high threshold, pre-scaled by
a factor of 100 to reduce the trigger rate.
• Slow High Charge: Similar to the Normal High Charge, but with much longer
gate width (640ns). This is a special trigger for strangelet.
• Electron and Positron: 4 out of 4 TOF layers passing high threshold, and 2 out
of 2 ECAL projections passing threshold.
• Gamma: 2 out of 2 ECAL projections passing threshold, and the shower angle
is in the geometric acceptance.
• Unbiased ECAL: Existence of ECAL activities, pre-scaled by a factor of 1000
to reduce the trigger rate.
64
Among the 7 trigger settings, the two unbiased triggers are supposed to be ≈ 100%
efficient, so they can be used to evaluate trigger efficiencies in data analysis. Depending on its location, AMS-02 has a trigger rate varying from 200 Hz (near the Earth
magnetic equator) to 1500 Hz (near the SAA or at high Earth magnetic latitude that
the ISS can reach).
2.3
Monte Carlo Simulation
A Monte Carlo simulation (MC) is necessary for understanding and evaluating responses of the detector to cosmic rays. The MC provides:
• Study of nuclear fragmentation inside AMS-02.
• Study of rigidity resolution and energy loss, thus providing the response functions (resolution matrix) for rigidity unfolding.
• Estimation of geometrical acceptance.
• Evaluation of efficiencies of sub-detectors.
• Study of multiple scattering.
The MC for AMS-02 is based on the GEANT4 package [98]. The simulation of
hadronic interactions, which is important for measuring Boron and Carbon, is done
with two independent models. One is the default GEANT4 hadron model, another
is the dual parton model (DPMJET) [99] implemented in GEANT4 framework.
The simulation has four steps: (1) The technical drawings for mechanical assembly
are used to generate the geometry descriptions of AMS-02. (2) The GEANT4 package
is then applied to simulate the transport, energy loss and interactions of incoming
particles. (3) Simulation of electronics converts physical signals from GEANT4 into
digital signals which are equivalent to the signals from detectors in real experiments.
(4) In the end, AMS-02 offline reconstruction software processes the simulated digital
signals as it would do for the real data, producing root files which contain reconstructed values as well as raw information of the simulation.
65
Comparisons between data and MC have been made in many ways, including
cross sections of nuclear interactions, rigidity resolution, charge-sign confusion. A
good agreement down to percent level has been achieved.
2.4
Physics Goals of AMS-02
Figure 2-11: The positron fraction measurement by AMS-02 with the first 18 months
of data, compared with the results from PAMELA and Fermi-LAT [14].
AMS-02 has a great potential in the indirect detection of dark matter through
precision measurements of its possible annihilation products: positrons, anti-protons,
anti-Deuterons and photons. Among these measurements, the positron fraction is of
great interests today, since the unexpected rise of positron fraction after ∼ 10 GeV has
been observed by recent experiments, including PAMELA and FERMI. To understand
whether this rise has an astrophysics origin (e.g., nearby pulsar) or a particle physics
66
origin (e.g., WIMP dark matter), a high precision measurement towards TeV region
is needed. In 2013 AMS-02 published its first paper [14] on the positron fraction
measurement up to 350 GeV. It confirmed the rise and observed a new phenomena of
slope change (see Figure 2-11). The measurement will be extended to higher energy
with smaller errors as more data will be collected in the future. Hints of dark matter
out of positron fraction will be favored or vetoed by other AMS-02 measurements,
including positron flux, anti-proton fraction, and high energy photon flux.
One of the primary physics goals for AMS-02 is to search for primordial antimatter [100]. The Sakharov conditions [101] must be followed for a universe with
Baryon asymmetry:
• Baryon number violation.
• C-parity violation and CP-parity violation.
• Interactions outside thermal equilibrium.
However, neither Baryon number violation (e.g. proton decay) nor strong CP violation has been observed yet, allowing for a possibility of the existence of anti-matter
domains in our universe. Heavy anti-nuclei (Z > 1) are very unlikely to be produced in the collisions between cosmic rays and the ISM; therefore, any high energy
anti-Helium observed in space must have primordial origins and provides a strong
evidence for the existence of an anti-universe. To date no primordial anti-Helium has
been observed, the current lowest upper limit is obtained by the BESS experiment
[102] at ∼ 10−7 from 1.6 GV to 14 GV. With unprecedented large acceptance and
long duration of data taking, AMS-02 is able to improve the upper limit by more than
three orders of magnitude and extend the search range to ∼ 1 TeV [75]. If AMS-02
discovers primordial anti-Helium, the analysis can be extended to anti-Carbon search.
With its high resolutions of charge and mass measurements, AMS-02 is capable of
performing measurements of the fluxes and ratios of charged cosmic rays with charge
Z from 1 to 26, as well as isotopes of light elements. These results will provide key
inputs to the understanding of the origin, acceleration, and propagation of cosmic
rays. This is also very important for improving the background estimation for exotic
67
physics search.
68
Chapter 3
Event Reconstruction
3.1
Overview
Due to its large acceptance and long exposure time, AMS-02 measures cosmic rays
with very small statistical errors compared to previous space experiments. To achieve
comparable systematic errors, analysis work of detector calibration and event reconstruction is carried out with the first year’s flight data.
In this chapter we go through the reconstruction algorithms of rigidity, velocity
and charge. These variables are essential for cosmic ray Boron and Carbon measurements. Among them, the calibration and charge reconstruction of the TRD is my
contribution. They are of crucial importance for understanding nuclear fragmentations of Boron and Carbon nuclei, as well as proton-electron separation in dark matter
search with positron fraction and anti-proton fraction measurements.
3.2
Rigidity Determination
The first step of rigidity reconstruction is to associate Tracker clusters to the right
track (track finding) [84]. After calibration and alignment, we have a set of X and
Y side clusters with amplitudes and coordinates reconstructed from signals of the
Silicon strips in each cluster. The X and Y side clusters are matched with each other
according to their amplitudes to form 3D hits. The matching is easier for particles
69
with higher charge like Boron and Carbon thanks to the high signal to noise ratio.
While the Y coordinate is precisely known, the X coordinate is ambiguous, because
the X readout channels of adjacent sensors are connected with each other. To remove
this ambiguity, as well as noise from delta rays and fragmented particles, a track
finding algorithm is designed as:
• Perform track finding on Y side only from Layer 3 to 8: link a straight line
between one cluster on Layer 3 or 4 and another on Layer 7 or 8, and check
whether there exist clusters on Layer 5 or 6 near the line and compatible with
a curved track.
• Among the candidates on Y side, perform a similar search for 3D hits, accept
all the allowed combinations of X and Y sides compatible with the path integral
fitting with reasonable χ2 .
• Select the candidate tracks with at least one 3D hit for each inner plane pair
(Layer 3 or 4, 5 or 6, 7 or 8) and at least four 3D hits in total.
• Match the position and direction of the track with those of TOF clusters and
the TRD track to remove the ambiguities on X coordinate.
• Extrapolate the track to Layer 1 and Layer 9, search for 3D hits within a
rigidity-dependent window; if any exists, associate the 3D hit to the track.
The track finding efficiency is estimated to be 90% to 95% for single charged particles
[80]; it is close to 100% for particles with high charge.
The rigidity of a charged particle is determined by a path integral fit on the track
trajectory in the magnetic field [103]. The particle’s motion is driven by the Lorentz
force:
d~p
~ ,
= q~v × B
dt
(3.1)
where p is momentum, q is charge, v is velocity, t is time, and B is magnetic field.
This equation can be rewritten as:
d~u
q
~ ,
= ~u × B
dl
p
70
(3.2)
where dl = v · dt and ~u = d~x/dl = ~v /v is a unitary vector tangent to the track at any
given point. Integrating this equation along the trajectory we obtain
q
~u1 = ~u0 +
p
Z
l1
~ 0 )dl0 ,
~u(l0 ) × B(l
(3.3)
l0
where the subscripts 0 and 1 represent the starting and ending points of the trajectory,
respectively. With the measured trajectory (by the Tracker) and magnetic field map
as inputs, a path integral fit gives the value of rigidity R = p/q.
Figure 3-1: Basic principles of different path integral fitting algorithms used in AMS02 reconstruction.
Three different fitting algorithms are developed for rigidity reconstruction, named
as the Alcaraz fit, the Choutko fit, and the Chikanian fit. As shown in Figure 3-1, the
Alcaraz fit performs the path integral fit along the lines connected between measured
points, while the Choutko fit and the Chikanian fit do so along the expected trajectory
71
with Runge-Kutta tracking. Furthermore, the Chikanian fit (adapted from [104])
improves rigidity resolution for R < 40GV by taking into account multiple scattering
and energy loss. Comparisons between the results from different fitting algorithms can
remove bad reconstructions and purify event samples for data analysis that requires
high quality rigidity reconstruction (e.g., He, C.).
The rigidity resolution is estimated to be ∼ 10% around 10 GV , and it increases
with rigidity. The MDR is ∼ 1 TV for the pattern InnerT racker + Layer1, and
∼ 2 TV for the pattern InnerT racker + Layer1 + Layer9 [84].
3.3
Velocity Reconstruction
A particle’s velocity can be measured by two different sub-detectors, the TOF and
the RICH, with different mechanisms.
The velocity reconstruction by the TOF [88] is based on the time of flight measurement. The time measured by the two sides (T p and T n ) of the counter passed by
a charged particle at time Tl and position X can be expressed as:
X
,
vs
Lc − X
n
= Tl + fslew (An ) + Tdelay
,
+
vs
p
T p = Tl + fslew (Ap ) + Tdelay
+
(3.4)
Tn
(3.5)
where fslew (Ap,n ) are slewing correction factors as functions of measured amplitudes,
p,n
Tdelay
are delays due to electronics and cables, Lc is the length of the counter, and vs is
the propagating velocity of scintillation lights in the counter. Among these variables,
particle’s crossing time Tl and coordinate X are unknown, and all the rest can be
obtained from measurements or calibrations. Therefore, by solving the two equations,
we get Tl and X for each plane. The coordinates measured by the TOF are mostly
used to resolve the X side ambiguities of the Tracker. By associating TOF clusters to
a Tracker track, more accurate coordinates of TOF clusters can be calculated from
extrapolation of the Tracker track to the Z coordinates of TOF clusters. With normal
trigger settings of 4/4 TOF signals, there are four sets of time of flight information
72
(measured by: Layer 1 and 3, Layer 1 and 4, Layer 2 and 3, Layer 2 and 4). The
velocity v is calculated by minimizing a χ2 function which combines all the four
possibilities:
χ2 (v) =
X
[
i=1,2; j=3,4
Lij
− (Tj − Ti )]2 ,
v
(3.6)
where Lij is the distance between the TOF clusters in Layer i and Layer j. The TOF
can measure velocity from 0.4c to c, and the velocity resolution is estimated to be a
few percent (1.2% for Carbon).
The velocity reconstruction by the RICH [90] is based on the measurement of
Cherenkov opening angle θc , which satisfies the formula:
cosθc =
c
,
nv
(3.7)
where n is the radiator refractive index (n = 1.05 for AGL, n = 1.33 for NAF, see
Section 2.1.6), and c is the speed of light. The reconstruction first interpolates the
Tracker track to the Z coordinate of the RICH radiator plane. It then calculates the
impact position and direction, and gets the corresponding local refractive index. Then
a set of velocity (equivalently, opening angle) values are calculated for each PMT hit
with exclusion of the one that is crossed by the particle. A clustering routine runs
over the set, and the largest cluster is taken as the ring candidate. Finally, by fitting
the ring using a likelihood method, the opening angle, and thus the velocity of the
particle, is obtained. The velocity resolution for Carbon is estimated to be ≈ 10−4
[90].
3.4
Charge Measurement
All the five sub-detectors of AMS-02 are able to measure a particle’s charge via electromagnetic interactions, including ionization energy loss and Cherenkov radiation.
• The Tracker [85] measures charge from dE/dx. In addition to nominal Tracker
calibrations, the reconstruction takes into account the dependence of particle’s
energy loss in each sensor on VA chips, βγ (momentum over mass), nonlinear
73
response, inclination angle, and the distance between impact position and readout strips. With these corrections, each layer gives an estimated charge value
based on the Z 2 dependence of dE/dx. A likelihood method is used to estimate
the Inner Tracker charge (Layer 2 to Layer 8).
• The TOF [88] follows similar charge reconstruction principles (dE/dx) as the
Tracker. The reconstruction outputs the estimated charge for each layer after
correcting the dependence on βγ, path length, attenuation and yield saturation
of scintillation lights, and nonlinearity of anode ADC signals. The results from
all the four layers are combined to provide a global estimation of the TOF
charge. The upper and lower two layers are grouped together to give the Upper
TOF charge and Lower TOF charge.
• The TRD [79] uses dE/dx (with βγ and tube path length corrections) to measure charge up to Z = 6 (due to the limitation of the dynamic ADC range). A
novel technique of counting the number of delta rays with TRD tubes in the
vicinity of the particle track is developed to extend the charge measurement up
to Z = 26. Details of the TRD charge reconstruction are presented in Chapter
4.
• The RICH [91] measures charge from Cherenkov radiation, which is also proportional to Z 2 . With the layout of RICH geometry and measured opening angle,
the expected number of photoelectrons for a Z = 1 particle, Nexp , is calculated.
p
The charge is estimated to be Q = Npe /Nexp , where Npe is the number of
collected photoelectrons in the Cherenkov ring.
• The ECAL [94] measures charge in a similar way as the Tracker and the TOF,
but the effective volume for ionization energy loss is just in the top one or two
layers, because the probability of developing a shower increases significantly
with deeper penetration into the ECAL.
The charge spectra of cosmic ray nuclei with charge from 1 to 8 measured by different
sub-detectors are shown in Figure 3-2, together with a typical event display of a
charged particle going through all the sub-detectors.
74
Figure 3-2: Schematic view of AMS-02 sub-detectors measuring charge along the path
of a particle (center) and the charge spectra (from flight data) of each sub-detector
for light cosmic ray elements (from Z=1 to Z=8): (a) Tracker Layer 1; (b) TRD; (c)
Inner Tracker; (d) TOF; (e) RICH; (f) ECAL [15].
Among the five sub-detectors, the TOF and the Inner Tracker have the best charge
resolutions (≈ 0.1 for Carbon, cross migrations of charge are negligible); therefore,
they play major roles in charge identifications. The Tracker Layer 1 and the TRD are
at the top of the detector; therefore, they are important in identifying fragmentations
inside the detector. The RICH and the ECAL charge measurements suffer from low
resolutions and nuclear fragmentations in the material above them.
Figure 3-3 shows an example [15] of the benefits from having multiple charge
measurements along the particle track. The events used in this plot have been selected by the Inner Tracker and the TOF as Boron candidates. The spectrum is
the Tracker Layer 1 charge spectrum for the selected sample. The Boron candidates
75
Figure 3-3: Charge spectrum measured by the Tracker Layer 1 for events identified
as Boron by the Inner Tracker and the TOF, the corresponding template fits clearly
show the charge changing fragmentation processes (C→B, O→B, etc.) happening
inside the TRD [15].
could be genuine incoming Boron, or daughter particles from fragmentations of heavier elements in the TRD. The charge signal in the Tracker Layer 1 can identify the
fragmentation. For example, if a Boron candidate is a fragmentation product from
an incoming Oxygen interacting with the material in the TRD, the charge measured
by the Tracker Layer 1 should be Z = 8. In the spectrum, the tail at the right side
of the Boron peak indicates the fragmentation events. Under the tail, we observe the
fragmentation C → B, O → B, etc. The amount of fragmentation events can be
estimated from template fits on the Tracker Layer 1 charge spectrum. The templates
of particles with different charge values are generated from clean samples selected by
the TRD, the Inner Tracker and the TOF with strong cuts. The templates are plotted
76
in Figure 3-3 under the spectrum. For example, the template of Nitrogen is shown
as a light green area. In physics data analysis, we can either apply cuts to Tracker
Layer 1 charge measurement to remove the fragmentation, or estimate the purity of
the sample by template fits on Tracker Layer 1 charge spectrum. See Section 5.5 for
more details.
77
78
Chapter 4
Charge Measurement by the TRD
4.1
Ionization and Delta Rays
The charge measurement by the TRD is based on ionization of charged high energy
particles in the gas (Xenon). When passing through, a charged particle undergoes
electromagnetic interactions with electrons in atoms along the path, leading to excitation or ionization. The ionization energy [105] for Xenon gas (used in the TRD) is ∼
8.4 eV, but the energy loss needed for the ionization is approximately 30 eV, because
about 70% of the deposited energy leads to non-ionizing excitation [106]. At normal
temperature and pressure (T = 20 ◦ C, P = 1 atm), the energy loss of a minimum
ionizing proton in Xenon gas is ∼ 4.5 keV [107], leading to ∼ 150 primary electrons.
The energy loss for a particular particle in medium is characterized by the quantity
dE/dx (energy loss dE normalized to path length dx), in units of g/cm2 . The energy
loss has a Landau distribution [108]. For particles with 0.1 < βγ < 1000, the mean
value of dE/dx can be described by the Bethe-Bloch formula [18]:
dE
<−
> = 4πNA
dx
e2
4π0 me c2
2
me c2
Z0 Z 2 1 2me c2 β 2 γ 2 Tmax
δ
[ ln
− β 2 − ] . (4.1)
2
2
A β 2
I
2
79
NA : Avogadro’s constant
βc
: velocity of incoming particle
0 : Vacuum permittivity
γ
: Lorentz factor
me : Electron mass
Tmax : Maximum transferable energy
Z0 : Atomic number of absorber
I
: Mean excitation energy
A : Atomic mass of absorber
δ
: Density effect correction
Z
c
: Speed of light
: Charge of incident particle
The strong dependence of energy loss on particle’s charge (dE/dx ∼ Z 2 ) is used for
charge measurement in the TRD.
Electrons that gain sufficiently high energies in ionization are called delta rays.
In the TRD, delta rays are able to travel significant distances (a few mm to a few
cm) away from the track of the primary particle, triggering the tubes in the vicinity
of the tubes passed by the incoming particle. The number of generated delta rays
increases with particle’s charge (see Section 4.4). Charge measurements by counting
the number of generated delta rays were applied in former times with nuclear emulsion
detectors [109], but it is not very often used in modern detectors.
Figure 4-1: Schematic view of ionization and delta rays in the TRD. The red line
indicates the track of the Carbon. The green circle indicates the tube hit by the
Carbon (defined as “dE/dx tube”). The blue circles indicate the tubes hit by the
delta rays generated from the ionization of the Carbon in the TRD (defined as “delta
ray tubes”).
80
Figure 4-1 shows a schematic view of the ionization and delta rays in the TRD.
Shown in the sketch is one of the twenty layers of the TRD (fleece and drift tubes).
An incoming Carbon nucleus passes through the tube indicated by the green circle
(defined as “dE/dx tube”) and leads to ionization in the Xenon gas. Meanwhile, the
delta rays generated from the ionization of the Carbon in the TRD hit the tubes in
the vicinity of the dE/dx tube. Those tubes are indicated by the blue circles in the
sketch, they are defined as “delta ray tubes”.
Figure 4-2 and Figure 4-3 show AMS-02 event displays (side view and front view)
of a typical cosmic ray proton and Carbon. The side view is defined as the view of the
X-Z plane; the front view is defined as the view of the Y-Z plane (see Section 2.1.2).
The fired tube is defined as a tube with signal above pedestal (∼ 700 ADC counts).
In the side view, the red bars in the middle 12 layers show the number of fired tubes,
and the red bars in the top and bottom 4 layers show the amplitude of fired tubes. In
the front view, the red bars in the middle 12 layers show the amplitude of fired tubes,
and the red bars in the top and bottom 4 layers show the number of fired tubes. The
lines linking the red bars are the TRD tracks fitted to the fired tubes (see Section 4.3).
From the event displays we observe that more delta rays are generated by Carbon
than by proton. This phenomenon can be used to provide further information for the
TRD charge reconstruction.
In the TRD drift tubes, a high voltage is applied to the thin wire (with a diameter
of 30 µm) in the center of the tube, generating an electric field E ∝ 1/r, where r is
the distance from the tube center. The high voltage is chosen to be ∼ 1.4 kV to make
the drift tube work in the proportional mode [107]. Primary electrons produced in
the ionization are driven by the electric field and drift towards the wire. The mean
free path is about 4 µm. When close to the wire, the electric field is so strong that
it accelerates the drifting electrons to be energetic enough to ionize the Xenon gas,
producing secondary electrons. This leads to an amplification of the signal. The
electric signals on the wire are generated from the mirror charge of ions; they drift
away from the wire with speeds which are ∼ 1000 times slower than electrons. In the
proportional mode, the signal is proportional to the deposited energy. In the TRD
81
Figure 4-2: Event display of a typical cosmic ray proton in the TRD with side view
(upper) and front view (lower). See text for the explanation of the red bars and lines.
drift tubes, 10% CO2 (quenching gas) is added to Xenon gas to cool down the drifting
electrons and stabilize the drifting process.
82
Figure 4-3: Event display of a typical cosmic ray Carbon in the TRD with side view
(upper) and front view (lower). The 2 hits in the top 4 layers in the side view are
noise.
4.2
Reconstruction Algorithm
Two categories of information recorded by the TRD are used for measuring particle’s
charge:
• The signals of a charged particle in the tubes it passes through (defined as
83
“dE/dx tubes”).
• The signals of the tubes in the vicinity of the dE/dx tubes. These tubes are
not hit by the primary charged particle; the signals originate from the delta
rays produced by the interactions between the primary particle and gas, fleece
and tube walls in the TRD. They are defined as “delta ray tubes”. This is new
compared to conventional methods of charge reconstruction.
Traditionally, charge reconstruction for a gas detector like the TRD is performed
with dE/dx tubes only, using the relationship dE/dx ∝ Z 2 . However, the dynamic
ADC range of the TRD is around 3400 counts above pedestal (∼ 700 counts). This
characterizes a typical signal of minimum ionizing Z = 5 particle with a path length
of 6mm. Therefore, the ADC readout is saturated for particles with Z >= 6. We
need to use additional information from the delta ray tubes for the reconstruction:
the signals in delta ray tubes for particles with Z <= 26 are typically far below the
ADC saturation threshold.
Figure 4-4: Algorithm flowchart of the TRD charge reconstruction.
In order to combine the measurements by dE/dx tubes and delta ray tubes, we
use a likelihood-based algorithm. It is shown in the flowchart in Figure 4-4:
• Dynamic alignment [77] and gain calibration [78] are applied to each tube. The
alignment is critical for calculating particle’s path length in dE/dx tubes. The
84
calibration is to ensure the uniformity of the measurements.
• A track fitting algorithm is designed to improve the separation of dE/dx tubes
and delta ray tubes, which are adjacent to each other. See Section 4.3.
• The distribution of energy loss in each dE/dx tube is parameterized with an
analytical function, which is called the dE/dx Probability Density Function
(dE/dx PDF). Likewise for delta ray tubes: the corresponding function is called
the Delta Ray Probability Density Function (Delta Ray PDF). See Section 4.4.
• The next step is to construct likelihood functions based on dE/dx PDFs and
Delta Ray PDFs, and combine the two likelihood functions into a “global”
likelihood function:
LdE/dx (Z) =
X
i
~ i )] ,
ln[fdE/dx
(Z; X
(4.2)
i
~ ,
LDeltaRay (Z) = ln[fDeltaRay (Z; X)]
LT otal (Z) = LdE/dx (Z) + LDeltaRay (Z) ,
(4.3)
(4.4)
~ i stands for a set of parameters
where f are the probability density functions, X
for a given fired tube (amplitude, path length, and gas gain), and i iterates
through all the tubes passed by the charged particle.
• In the end, the most probable charge value is estimated by maximizing the
likelihood function:
dLT otal (Z)
|Z=Z0 = 0
dZ
⇒
Z0 = M ost P robable T RD Charge .
(4.5)
The likelihood function can be approximated by a parabola function near the
maximum point [18]. Based on this fact, a customized fast maximizing algorithm has been developed. It is orders of magnitude faster than the TMinuit
package in ROOT. The error of the measured charge is calculated by decreasing
the maximum likelihood value by 0.5 and finding the shift in the Z value [18].
85
4.3
TRD Track Fitting
A key in the TRD charge reconstruction is to distinguish delta ray tubes from dE/dx
tubes. The path length, which is sensitive to the position and the angle of the particle
track, is the most effective variable to identify which category a tube belongs to. To
achieve a good separation between the two kinds of tubes, the reconstructed track
must pass the dE/dx tube. The TRD track can be obtained by extrapolation from
the Tracker tracker, but this is not accurate for low energy particles due to strong
multiple scattering. A track fitting algorithm with the TRD has been developed to
overcome this difficulty.
Firstly, we construct a probability density function of the distance between the
TRD track and the center of a fired tube. The probability should be a positive
constant if the absolute value of the distance is smaller than the radius of the tube;
it should be zero if the distance is larger than that. For easier computation, we
approximate this distribution with the following function:
ftrack (d) = arctan[(r − d)/c] + arctan[(r + d)/c] ,
(4.6)
where r = 0.3cm is the radius of the tube, c = 0.03, d is the distance between
the TRD track and the tube center, and is also a function of the parameters of the
reconstructed TRD track: d = d(x, y, θ, φ). The function is plotted in Figure 4-5.
Based on the probability density function in Equation 4.6, we construct a likelihood function to fit the TRD track:
L(x, y, θ, φ) =
X
Ai · ln(ftrack [di (x, y, θ, φ)]) ,
(4.7)
i
where Ai is the amplitude of a tube, and i iterates through every fired tube near the
particle track. Using Ai as weight, the fitting algorithm always pushes the track to
the tubes with large amplitudes, so the bias from delta ray tubes is diminished. By
maximizing the likelihood we get the position and the angle of the fitted TRD track.
Analysis shows that the TRD track accuracy is ∼ 500 µm.
86
Probability
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Distance Between TRD Track and Tube Center (cm)
Figure 4-5: Probability density function of the distance between TRD track and tube
center for a fired tube. This analytical function is to make the TRD track fitting
easier.
4.4
dE/dx and Delta Ray Probability Density Functions (PDFs)
An example of the TRD dE/dx spectrum is shown in Figure 4-6 (protons in the rigidity range 55 GV to 65 GV). An analytical function with a simpler form is “invented”
to approximate the Landau distribution in the parameterization of dE/dx PDF:
fdE/dx (Z) = N · [g(Z, a1 , b1 , c1 ) + d · g(Z, a2 , b2 , c2 )] ,
(4.8)
where g(Z, a, b, c) is:
g(x, a, b, c) = Exp[−
x−a
x−a
− c · Exp(−
)] .
b
bc
(4.9)
The normalization factor N is calculated from the integration of the PDF. The parameters a1 , b1 , c1 , a2 , b2 , c2 , d are fitted with data. They are functions of charge and
rigidity (or effectively βγ). The term g(Z, a1 , b1 , c1 ) describes the peak of the distribution, and g(Z, a2 , b2 , c2 ) describes the tail. Figure 4-6 shows the parameterization
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Figure 4-6: The TRD ADC spectrum of protons in the rigidity range 55 GV to 65 GV,
and the corresponding parameterization with Equations 4.8 and 4.9.
with Equations 4.8 and 4.9 on a typical proton ADC spectrum (55 GV to 65 GV) in
the TRD.
Figure 4-7 shows representative dE/dx PDFs of Helium, Lithium, Beryllium and
Boron. The saturation threshold of electronics is around 3400 ADC (indicated by the
orange line). From the plot we can see the charge measurement of Boron and Carbon
by the TRD is limited by the saturation of electronics. For amplitudes higher than
the saturation threshold, we use the integrated value of the PDF from the threshold
to infinity as the probability. The PDFs can only be fitted at discrete integer charge
values; we use cubic spline interpolation to extend the parameters in the PDFs to be
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Figure 4-7: dE/dx Probability Density Functions of Helium (red), Lithium (green),
Beryllium (blue) and Boron (black), derived from flight data. Saturation of electronics
happens around 3400 ADC, as indicated by the orange line. The saturation influences
charge measurement of Boron and Carbon.
functions of continuous charge values.
The Delta Ray PDF is not as straightforward as the dE/dx PDF; they are represented by the Landau tail of the energy deposition. There is no formula similar to the
Bethe-Bloch formula, especially in our case: the TRD delta ray tubes only collect a
small portion of the generated delta rays. According to the literature [18], delta rays
are mostly keV scale electrons. Therefore, we need to learn by ourselves the behavior
of the delta rays from the flight data of AMS-02.
Figure 4-8 plots the average signal of delta ray tubes as a function of the Tracker
charge. Obvious differences of signals between different ion species are observed, and
there is no saturation up to Z = 26. Figure 4-9 shows the amplitude as a function
of rigidity for Z = 6 particles selected by the Tracker and the TOF. We observe that
the number of detected delta rays increases with rigidity for R < 25 GV; it is almost
89
Figure 4-8: Delta ray amplitudes as functions of the Tracker charge. The amplitudes
have already had pedestals subtracted.
constant in higher rigidity ranges. After the rigidity correction, the parameterization
function used for the Delta Ray PDF is identical to that of the dE/dx PDF.
4.5
Performance of the Reconstruction
The performance of the TRD charge reconstruction is studied with flight data. Figure
4-10 shows the charge distribution of cosmic ray nuclei measured by the TRD only.
From the plot we observe peaks from Z = 1 to Z = 6. For Z > 6, even though the
ADC readouts of dE/dx tubes are saturated, the charge measurement is extended
to Z = 26 with the information from delta ray tubes. In fact, the delta ray tube
amplitudes for Z = 26 particles (∼ 1000 ADC) are still below the saturation threshold
(∼ 3400 ADC); therefore, the TRD is able to identify particles with even higher charge
than Z = 26. However, the quality of Delta Ray PDFs is limited by statistics at this
moment.
The comparisons of charge measurements (Z from 1 to 26) between the TRD and
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Delta Rays Amplitudes / 1000 (ADC)
12.5
12
11.5
11
10.5
10
9.5
9
10
20
30
40
50
60
70
80
90
Rigidity (GV)
Number of Events
Figure 4-9: Delta ray amplitudes as a function of rigidity for Z = 6 particles measured
by the Tracker and the TOF.
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106
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104
103
102
10
1
0
5
10
15
20
25
30
TRD Charge
Figure 4-10: Charge distribution of cosmic ray nuclei, measured by the TRD alone.
the Tracker are plotted in Figure 4-11 and Figure 4-12. The TRD charge reconstruction in Figure 4-11 only uses dE/dx; the one in Figure 4-12 uses both dE/dx and
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5
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0
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25
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Tracker Charge
Figure 4-12: Comparison between charge measured by the TRD and charge measured
by the Inner Tracker. The TRD charge reconstruction uses both dE/dx and delta
rays.
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TRD Charge
Figure 4-11: Comparison between charge measured by the TRD and charge measured
by the Inner Tracker. The TRD charge reconstruction only uses dE/dx. See Figure
4-12 for comparison.
delta rays. In Figure 4-11, the charge mis-reconstructions by the TRD are due to the
electronics saturation. Figure 4-12 shows that the measurement is much improved
with the information from delta rays, and good agreement between the charge values
measured by the Tracker and the TRD is observed. A comparison between these two
plots shows that the new reconstruction method using delta rays is critical for Boron
and Carbon measurement using the TRD.
4.6
Outlook: Future Improvements in TRD Charge
Measurement
By reducing the high voltage of the drift tubes, the gain can be diminished exponentially. Even though such operations decrease the electron-proton separation power,
the charge measurements for particles with Z ≥ 6 with the TRD can be improved
because of less ADC saturation. Besides, transition radiation photons from nuclei can
be measured to determine particle’s energy at an energy scale of 10 TeV. Considering
the large acceptance of the TRD, the long operation time of AMS-02 on the ISS, and
the fact that the maximum detectable rigidity using the Tracker is only about 2 TeV,
this could significantly extend the energy range of the proton and Helium spectra
measured by AMS-02.
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94
Chapter 5
Data Analysis
5.1
Overview
Due to the similarities of Boron and Carbon nuclei’s charges and cross sections, many
systematic uncertainties cancel when taking the ratio of their fluxes.
In literature, the measurement is presented in units of Ek /A (kinetic energy per
nucleon), because in the spallation process C + p → B + X, Boron and Carbon nuclei
have similar Ek /A. AMS-02 measures directly the rigidity, but we decided to convert
it to Ek /A to be able to compare with previous measurements. The cosmic ray flux
in the Field of View of AMS-02 in the energy bin (En1 , En2 ) is defined as:
Φ(En1 , En2 ) =
N (En1 , En2 )
,
AGeo. · PSur. · TExp. · · (En2 − En1 )
(5.1)
where is the product of different efficiencies:
= T rigger · Reconstruction · Selection · ChargeID .
(5.2)
To obtain the Boron to Carbon ratio, we need to analyze all the terms in the Formulas
5.1 and 5.2:
• N (En1 , En2 ) is the raw count of Boron or Carbon in the Field of View of AMS-02.
Four levels of selection are applied to select good Boron and Carbon samples:
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1. Event pre-selection is to use simple cuts to obtain a sample containing
Boron and Carbon. See Section 5.2.
2. Event selection is to clean up the sample and ensure good measurement of
charge, velocity, and rigidity. See Section 5.3.
3. Charge selection is to select Boron and Carbon by their charges. See
Section 5.4.
4. Fragmentation identification is to remove remaining fragmentation events
in the sample. See Section 5.5.
• AGeo. is the geometric acceptance. It can be assumed to be the same for Boron
and Carbon from 1 GeV/n to 670 GeV/n.
• PSur. is the survival probability. It is the probability that a particle does not
have nuclear interactions. This is due to sizable amounts of material in the
TOF and the TRD. See section 5.10.
• TExp. is the exposure time. It is different for particles with different charge
to mass ratios (e.g.,
11
B and
12
C) in units of kinetic energy per nucleon. See
Section 5.7.
• En is the kinetic energy per nucleon. It is calculated from rigidity. It can
also be calculated from velocity, as a cross check of the isotope composition
assumption of Boron (Section 5.8). Rigidity migrations are corrected by the
rigidity unfolding. See Section 5.12.
• is the product of different efficiencies, including: trigger efficiency, reconstruction efficiency, selection efficiency, and charge identification efficiency. Trigger efficiency and reconstruction efficiency are similar for Boron and Carbon,
whereas selection efficiency and charge identification efficiency are different
enough that some corrections must be applied. See Section 5.3, 5.4, 5.6 and
5.9.
The analysis is data driven. MC is also used to understand the performance of
the detector. The analysis takes advantage of redundant measurements of energy and
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Figure 5-1: Charge measurements along particle’s track in AMS-02. ∆Z is the charge
resolution.
charge. A particle’s energy can be measured by the Tracker with different track patterns, as well as the RICH and the TOF in narrow energy ranges. A particle’s charge
can be measured by all the five sub-detectors along the track, as shown in Figure 5-1.
Redundant measurements help to select event samples, estimate efficiencies, remove
bad reconstructions, and control fragmentations inside the detector.
The data sample used in this analysis is taken from May 19, 2011 to November
19, 2013. About 1.1 million Borons and 3.8 million Carbons above 1 GeV/n are
analyzed, among which about 2 thousand Borons and 17 thousand Carbons are above
100 GeV/n.
Five sources of systematic errors are identified and analyzed: (1) Event selection;
(2) Isotope composition; (3) Survival probability; (4) Materials above Tracker Layer
1; (5) Rigidity unfolding.
In this chapter, we will present the procedures used in this analysis, with special focus on the differences of detector responses between Boron and Carbon. The
methods of estimating systematic errors are presented.
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5.2
Event Pre-Selection
The event pre-selection is to use a set of simple cuts to obtain a sample containing
Boron and Carbon. It removes unwanted events due to various factors, such as
hardware error, bad trigger, or origin within the SAA (see Section 1.5.2).
The event pre-selection cuts are:
• The DAQ is in normal operation mode and has no hardware error.
• 4/4 TOF signals are required, and a Tracker track is associated with the 4 TOF
clusters. If there are multiple TOF cluster sets, select the one with the largest
energy deposition.
• The energy deposition in Tracker clusters corresponds to 2<Z<12.
• Remove particles with rigidity below the geomagnetic cutoff.
Pre-selection cuts are independent of particle species, so no correction is needed
for the event pre-selection when taking the ratio between Boron and Carbon.
5.3
Event Selection
The event selection is to clean up the event sample and ensure good measurements of
charge and energy. Three categories of events should be suppressed by the event selection: (1) Large angle scattering; (2) Fragmentation; (3) Massive delta ray production.
Meanwhile, the event selection must keep a high efficiency for good events.
The strategy for determining the selection cuts is to define good samples and bad
samples of Z = 6 events using reconstructed velocity, rigidity and charge. We choose
the cut at the value which keeps a high efficiency for the good sample, while rejecting
as many bad events as possible. Three categories of event samples are used in the
study of selection cuts:
• Good (Bad) TOF Sample: Given that the resolution of TOF β measurement is
1.2% for Carbon, the events with β much larger than 1 must be mis-reconstructed.
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Therefore, we define the Good TOF sample as 0 < β < 1.2, and the Bad TOF
Sample as β > 1.2. See Figure 5-4.
• Good (Bad) Tracker Sample: We don’t expect the existence of anti-Carbon
in cosmic rays, so particles with Z = 6 and negative rigidity must be misreconstructed. Accordingly, we define the Good Tracker Sample as R > 0 GV,
and the Bad Tracker Sample as R < 0 GV. See Figure 5-5.
• (Non) Fragmentation Sample: If we identify an Oxygen at the Tracker Layer
1, and observe Z = 6 in the Inner Tracker, there must be fragmentation in
the TRD or the Upper TOF. Therefore we define the Fragmentation Sample as
5.5 < QT rL1 < 6.5, and the Non-Fragmentation Sample as 7 < QT rL1 < 9,
where QT rL1 is the charge measured by the Tracker Layer 1.
For each cut studied, one of the three categories of samples is used, according to the
detector origin of the signal.
The distributions of selection cut variables for corresponding good and bad Carbon
samples are plotted in Figure 5-2 (TOF-related), Figure 5-3 (Tracker-related). The
cut values and descriptions are:
• TOF Time Chi2/dof. Chi2T < 20.
• TOF Coordinate Chi2/dof. Chi2C < 20.
• TOF Integer Charge Probability. ZP rob > 0.8. It is the probability that charge
measurements in all TOF layers are consistent.
• TOF Cleanliness. T OF Cl > 0.4. It is the ratio between energy deposition of
TOF Clusters on the track and energy deposition of all TOF clusters.
• Tracker Rigidity Chi2/dof. Chi2R < 20.
• Beta Rigidity Agreement. BRAgr < 0.15. It is defined as |(β − βR )/(β + βR )|,
where βR is the velocity calculated from rigidity, and β is the velocity measured
by the TOF. This is a loose cut to remove trivial “junk” events at low energy.
• Inner Tracker Cleanliness. T rCl > 0.4. It is the ratio between energy deposition
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Normalized Entries
Normalized Entries
1
Good TOF Sample
-1
10
Bad TOF Sample
10-2
1
Good TOF Sample
-1
10
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10-2
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0
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90
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30
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50
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TOF Time Chi2/dof
(a) TOF Time Chi2/dof
80
90
100
(b) TOF Coordinate Chi2/dof
1
Normalized Entries
Normalized Entries
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TOF Coordinate Chi2/dof
10-1
10-2
10-3
10-1
10-2
10-3
10-4
10-4
Good TOF Sample
Good TOF Sample
-5
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-5
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-6
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10
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-7
10
0
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0.6
0.7
0.8
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1
0
0.1
0.2
0.3
0.4
TOF Integer Charge Probability
0.5
0.6
0.7
0.8
0.9
1
TOF Cleanliness
(c) TOF Integer Charge Probability
(d) TOF Cleanliness
Figure 5-2: Distributions of TOF-related selection cut variables for good (red, solid)
and bad (black, dashed) samples of Z = 6 events. Both samples are normalized to 1
in the plots. The blue lines indicate the cuts.
of Inner Tracker Clusters on the track and energy deposition of all Inner Tracker
clusters within a 2cm radius cylinder around the track.
• Inner Tracker Energy Deposition Discrepancy. T rAsyE < 0.8. It is defined
as (Emax − Emin )/(Emax + Emin ), where Emax and Emin are the Inner Tracker
clusters with maximum and minimum energy depositions, respectively.
• Number of Energetic Secondary Tracks. N SecT r = 0. The criteria for energetic
secondary tracks is: (1) At least 4 Y-side Inner Tracker hits; (2) Rigidity is larger
than 0.5 GV.
• Inner Tracker Track Pattern. GoodP attern = true. The good pattern is defined
as: (1) At least 5 Y-side Inner Tracker hits; (2) Require at least one Y-side hit
on Layer 2, Layer 3 or 4, Layer 5 or 6, Layer 7 or 8.
The cut values above are not the only options; the final result of the measurement
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Normalized Entries
Normalized Entries
Good Tracker Sample
10-1
Bad Tracker Sample
-2
10
1
Good Tracker Sample
10-1
Bad Tracker Sample
10-2
10-3
10-4
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-5
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-4
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90
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100
0
0.1
0.2
0.3
0.4
0.5
0.6
Tracker Rigidity Chi2/dof
0.8
0.9
1
(b) Beta Rigidity Agreement
Normalized Entries
(a) Tracker Rigidity Chi2/dof
Normalized Entries
0.7
Beta Rigidity Agreement
10-1
10-2
10-3
10-1
10-2
10-3
10-4
Good Tracker Sample
Good Tracker Sample
10-4
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-5
10
0
0.1
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0
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0.2
0.3
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Fragmentation Sample
0.7
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0.6
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1
(d) Inner Tracker Energy Deposition Discrepancy
Normalized Entries
Normalized Entries
(c) Inner Tracker Cleanliness
0.4
Inner Tracker Energy Deposition Discrepancy
Inner Tracker Cleanliness
0.6
0.5
0.9
0.8
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Good Tracker Sample
0.4
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0
0
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0.3
0.2
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2
2.5
3
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4
0
0.2
Number of Energetic Secondary Tracks
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Inner Tracker Track Pattern
(e) Number of Energetic Secondary Tracks
(f) Inner Tracker Track Pattern
Figure 5-3: Distributions of Tracker-related selection cut variables for good (red,
solid) and bad (black, dashed) samples of Z = 6 events. Both samples are normalized
to 1 in the plots. The blue lines indicate the cuts.
should be stable against varying the cuts in the vicinity of the cut values. We check
the stability of the analysis results in Section 6.2.
The effect of the selection cuts is partially shown in Figure 5-4 and Figure 5-5.
We observe that the selection cuts reject almost all the events with mis-reconstructed
velocity and rigidity. In addition, the selection cuts also greatly reduce fragmentation
events, as will be shown in Section 5.5.
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Normalized Entries
10-1
10-2
Before TOF Cuts
After TOF Cuts
10-3
10-4
-5
10
10-6
10-7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Beta
Normalized Entries
Figure 5-4: Beta spectrum of Z = 6 events before (black, dashed) and after (red,
solid) selection cuts on the TOF.
Before Tracker Cuts
-2
10
After Tracker Cuts
10-3
10-4
-5
10
10-6
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1/Rigidity (1/GV)
Figure 5-5: 1/Rigidity distribution of Z = 6 events before (black, dashed) and after
(red, solid) selection cuts on the Tracker.
The event selection causes a small efficiency difference between Boron and Carbon: (1) The cuts that reduce strong delta ray productions and multiple scatterings
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Selection Efficiency
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Boron
Carbon
0.1
0
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10
3
10
Rigidity (GV)
Selection Efficiency Ratio Between B and C
Figure 5-6: Selection efficiency as a function of rigidity estimated by Method One for
Boron (red, solid) and Carbon (black, dashed).
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
Method One
Method Two
0.6
0.5
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10
3
10
Rigidity (GV)
Figure 5-7: Selection efficiency ratio between Boron and Carbon as a function of
rigidity, estimated by Method One (red, solid) and Method Two (black, dashed).
lead to different efficiencies for particles with different charges; (2) The cuts that
remove fragmentations have different efficiencies for particles with different nuclear
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interaction cross sections.
Two methods are used to estimate the selection efficiency:
• Method One: Select Boron (Carbon) using the TRD, the TOF, the Tracker, and
the RICH, and estimate the selection efficiency by counting how many events
pass the selection cuts.
• Method Two: Estimate the selection cuts on the TOF and the Tracker independently, using pure samples selected by other sub-detectors; then multiply
them together to get the total selection efficiency.
The selection efficiency for Boron and Carbon as a function of rigidity is plotted in
Figure 5-6 (using Method One). The selection efficiency ratios between Boron and
Carbon estimated by the two methods are plotted and compared in Figure 5-7. From
these two plots we observe that the selection efficiency drops slightly with increasing
rigidity for R > 10 GV, mainly due to the increasing delta ray production with particle
energy. Also, as expected, Boron’s efficiency is higher than Carbon’s by a few percent
L1 Hit Pickup Efficiency Ratio Between B and C
because of less delta ray production and a smaller fragmentation cross section.
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
102
10
Rigidity (GV)
Figure 5-8: Tracker Layer 1 XY hit pickup efficiency ratio between Boron and Carbon
as a function of rigidity.
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On top of the selection cuts to clean up the event sample, we also require the
existence of a hit at the Tracker Layer 1 with both X-side and Y-side signals. This
cut reduces the geometric acceptance by more than 60%, but the benefit is more
than the cost: It further suppresses fragmentation events from the percent level to
even lower, and increases the MDR from a few hundred GV to more than 1 TV. The
efficiency difference due to this requirement is estimated to be about 1%, as shown
in Figure 5-8.
5.4
Charge Selection by the Tracker
Figure 5-9: Corrected Inner Tracker charge as a function of rigidity for particles with
Z = 1 to Z = 8.
Charge selection is a way to identify Boron and Carbon from the event sample
that was obtained from event pre-selection and selection. Boron and Carbon nuclei
collected by AMS-02 are assumed to be fully ionized. Carbon is created in Stellar
Nucleosynthesis (see Section 1.2.2) in the form of fully ionized nuclei. Boron is created
from spallation of Carbon nuclei (see Section 1.2.3), so it is also fully ionized. Even
if small amounts of incoming Boron and Carbon are partially ionized, a thin layer of
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Normalized Entries
10-1
10-2
10-3
10-4
3
4
5
6
7
8
Inner Tracker Charge
Figure 5-10: Inner Tracker charge spectrum for particles with Z = 3 to Z = 8.
Gaussian fits are applied on each charge peak. The tail cannot be well approximated
by the Gaussian fits. The charge resolutions of Boron and Carbon are approximately
0.1 charge unit.
material on top of AMS-02 could strip out the electrons [110].
The Inner Tracker is used for charge identification (see Section 3.4). It sits in the
center of the detector, and has the best charge resolution among all the sub-detectors.
It contains only a little amount of material (see Section 2.1.4), so it is transparent for
particles in terms of nuclear interactions. The Tracker charge reconstruction removes
the dependence of the Inner Tracker charge on rigidity (velocity), as shown in Figure
5-9. Therefore the charge identification can be achieved with a simple cut on the
reconstructed Inner Tracker charge value. The charge spectrum of the Inner Tracker
is plotted in Figure 5-10 (Z = 3 to Z = 8), with a Gaussian fit around each peak to
estimate the resolution for each element. All the light ions have charge resolutions
of σZ ∼ 0.12 on the Inner Tracker charge spectrum, meaning 3σZ < 0.5; therefore,
a simple cut at Z ± 3σZ (Z = 5, 6) is sufficient to suppress cross migrations from
neighbor elements down to per mil level, while keeping the charge ID efficiencies
larger than 99%.
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Normalized Entries
10-1
Boron
Carbon
-2
10
10-3
10-4
-5
10
3
4
5
6
7
8
Inner Tracker Charge
Figure 5-11: Inner Tracker charge spectrum for Boron (red, solid) and Carbon (black,
dashed) selected by the TOF, the TRD, and the Tracker Layer 1, and corresponding
charge ID cuts (blue line for Boron, green line for Carbon).
From the data we estimate the upper limit of the charge cross migrations. We
select Boron and Carbon samples using the TOF, the TRD and the Tracker Layer
1. The samples are not expected to be 100% pure due to the limited charge identification power of the three sub-detectors. However, using these samples we can get
an upper limit of charge cross migrations. Figure 5-11 plots the Inner Tracker charge
distributions of the selected Boron and Carbon samples. Charge identification cuts
are set at 5.0 ± 0.4 (slightly over 3σZ ) for Boron and 6.0 ± 0.4 for Carbon. The tails
outside the cuts account for 0.1 % of the total events, which is negligible.
5.5
Fragmentation Identification and Purity Estimation
Most fragmentation events are rejected by pre-selection and selection cuts (see Sections 5.2 and 5.3). They usually have multiple tracks or inconsistent signals in different sub-detectors. However, a small portion of fragmentation events look very clean
107
and can pass all the event selection criteria. An example is shown in Figure 5-12.
The event looks very clean, but in fact it is a Carbon fragmentation to a Boron in
the Upper TOF. Thanks to the ability to measure the charge of a particle along all
the sub-detectors that the particle passes by, AMS-02 is able to identify this kind
of “clean” fragmentation by the consistency of charge measurements. For the event
in Figure 5-12, the particle is seen as Carbon in the Tracker Layer 1 and the TRD,
but its charge is measured to be Z = 5 by the Inner Tracker, the Lower TOF, and
the RICH. Moreover, the energy deposition in the Upper TOF is very large, corresponding to a signal of charge 7.6. Therefore, there must have been a fragmentation
process in the Upper TOF.
Figure 5-12: Event display of an incoming Carbon fragmentation to Boron in Upper
TOF.
To estimate the amount of leftover “clean” fragmentation events in the event
sample after event selection and charge identification, we do charge template fits
on the Tracker Layer 1 charge spectra of Boron and Carbon identified by the Inner
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Tracker for each rigidity bin. Figure 5-13 shows examples of the template fits for two
rigidity bins, one around 5 GV and another around 150 GV. The charge spectrum
templates of different charged particles are made from the Tracker Layer 2, which
has exactly the same configurations of Silicon sensors and electronics as the Tracker
Layer 1. With the help of the Inner Tracker, the Upper TOF, and the TRD, much
purer nuclei samples can be selected for the Tracker Layer 2 compared to the Tracker
Layer 1. From Figure 5-13 we have the following observations:
• The contaminations of Z > 6 particles in the Carbon sample are far less than
1% and are similar for low rigidity and high rigidity bins.
• The contaminations of Z > 5 particles in the Boron sample are on the order of a
few percent, and increase with rigidity. The reason for this rigidity dependence
is that the Boron to Carbon ratio decreases with rigidity, while the cross section
of Carbon fragmentation to Boron is almost constant for Ek /A > 1 GeV/n.
To reject the “clean” fragmentation events, especially those that contaminate the
Boron sample by a few percent, a cut on the Tracker Layer 1 charge is applied. The
cut values are shown in Figure 5-13 (4 < Z < 5.5 for Boron, 5 < Z < 6.8 for Carbon).
With this cut, the contaminations for Boron and Carbon samples are both on the
level of 0.1% (as shown in the plots), which is negligible. The efficiency of this cut
can be evaluated on the Tracker Layer 2 charge spectrum of pure Boron and Carbon
samples. The reason for using the Tracker Layer 2 for efficiency estimation is the same
as that for using it to produce charge templates, as described above. The efficiency is
estimated to be ∼ 92% for Boron, and ∼ 98% for Carbon. This difference is corrected
in the final result.
5.6
Trigger Efficiency
Trigger efficiency in physics data analysis means the efficiency of the trigger for all
the good cosmic ray events that pass the pre-selection and selection cuts. There are
two reasons that a small portion of good events are rejected by the trigger:
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Entries
Entries
104
102
10
103
1
102
4
5
6
7
8
10-1
9
4
5
6
7
Tracker Layer 1 Charge
8
9
Tracker Layer 1 Charge
Entries
(b) Boron: 139.2GV − 210.5GV
Entries
(a) Boron: 4.1GV − 5.3GV
103
104
102
103
10
102
1
4
5
6
7
8
9
4
5
6
7
Tracker Layer 1 Charge
8
9
Tracker Layer 1 Charge
(c) Carbon: 4.1GV − 5.3GV
(d) Carbon: 139.2GV − 210.5GV
Figure 5-13: Template fits on the Tracker Layer 1 charge spectra (black dots with
error bars) of Boron (a, b) and Carbon (c, d) identified by the Inner Tracker at two
selected rigidity bins (4.1GV − 5.3GV , 139.2GV − 210.5GV ). The dashed lines are
templates (the red dashed lines are Carbon templates), the solid blue lines are the
fitted results. The purple straight lines correspond to the cuts on Tracker Layer 1
charge to suppress fragmentations.
• The signal in one layer of the TOF does not pass the trigger threshold. This is
possible for Z = 1 particles but very unlikely for Boron and Carbon.
• Too many delta rays are produced and the number of ACC hits is equal to or
larger than 5. This is more significant for particles with higher charge.
We use the unbiased trigger (see Section 2.2.3) to estimate trigger efficiency. In
reality, it is not 100% unbiased, but the settings of the unbiased trigger (3 out of 4
TOF signals and no requirement on the ACC) have an efficiency of almost 100%, so
in practice it can give a good estimate of trigger efficiency. The trigger efficiency is
expressed as:
T rigger (R) =
NP hysics (R)
,
NP hysics (R) + 100 × NU nbiased (R)
110
(5.3)
Trigger Efficiency Ratio Between B and C
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
102
10
3
10
Rigidity (GV)
Figure 5-14: Trigger efficiency ratio between Boron and Carbon as a function of
rigidity.
where NP hysics is the number of events with at least one physics trigger, NU nbiased is
the number of events with only unbiased trigger, and the factor 100 is a scale factor
for the unbiased trigger to reduce the trigger rate to a lower level (see Section 2.2.3).
The ratio between trigger efficiencies of Boron and Carbon is shown in Figure 5-14.
We observe that the trigger efficiency difference between the two species is much less
than 1%.
5.7
Exposure Time
Exposure time is the total effective data-taking time of AMS-02, the time during
which AMS-02 is ready to receive and accessible to the next cosmic ray event. The
calculation of exposure time takes into account trigger rate, detector dead time, and
geomagnetic cutoff. Among these factors, the one that differentiates Boron and Carbon is geomagnetic cutoff. To reject the atmospheric secondary Boron and Carbon,
we apply a cut as R > 1.25RCutof f , where RCutof f = RCutof f (r, θM , φM ) is the maximum cutoff rigidity in the field of view (at the location (r, θM , φM )) below which
111
Normalized Exposure Time
1
0.8
0.6
11
0.4
B
10
B
0.2
0
0.5
1
1.5
2
12
C
2.5
Log (E /A)
10
k
Figure 5-15: Exposure time (normalized to the last bin) as a function of kinetic energy
per nucleon (logarithmic scale) for 10 B, 11 B, and 12 C. The difference is due to the
conversion from rigidity to Ek /A, see Equation 5.4.
charged cosmic rays are screened by the geomagnetic field from reaching AMS-02.
The coefficient 1.25 is to eliminate the influence from limitation of rigidity resolution.
When rigidity is used as a coordinate, all charged particles with the same rigidity
have the same exposure time. However, the unit we are interested in for the Boron
to Carbon ratio is Ek /A, under which particles with different Z/A have different
exposure time (see Section 5.8 for the relationship between Ek /A and rigidity). The
normalized exposure time, as functions of Ek /A, are drawn in Figure 5-15 for
(Z/A = 1/2),
5.8
11
B (Z/A = 5/11), and
12
C (Z/A = 1/2).
Isotope Composition
Isotope composition influences the Boron to Carbon ratio in two ways:
• Exposure time, as presented in Section 5.7.
112
10
B
• Conversion from rigidity to Ek /A, which can be expressed as (in natural units)
Ek /A =
p
(Z/A)2 R2 + Mn2 − Mn ,
(5.4)
where Mn is the mass of a nucleon (1/12 mass of a Carbon nucleus). Different isotopes (different Z/A values) lead to different Ek /A values for the same
measured rigidity.
Carbons collected by AMS-02 are mostly
12
C; they are primary cosmic ray par-
ticles produced from Stellar Nucleosynthesis. Borons are thought to be produced
as secondaries in the ISM; they are mostly in the form of
11
B and
10
B. The ratio
between 11 B and 10 B depends on the cross section ratio between 12 C(16 O) →11 B and
12
C(16 O) →10 B. According to a recent measurement [111], the cross sections of
fragmentation to
11
B and
10
12
C
B are 25.8 ± 3.1mb (26 ± 4mb) and 11 ± 4mb (13 ± 6mb)
at 1.87 GeV/n (2.69 GeV/n). Accordingly, the fraction of 11 B should be around 70%.
The relative abundance of
11
B on the earth is measured to be close to 80% [112].
AMS-02 is, to some extent, capable of determining the fraction of
11
B by itself
from velocity measured by the RICH. Ek /A can be expressed in terms of velocity as
(in natural units):
p
Ek /A = Mn / 1 − β 2 − Mn ,
(5.5)
which does not depend on Z/A. By comparing the B/C spectrum measured by the
Tracker with an assumption on the 11 B fraction and that by the RICH, we can check
whether the 11 B fraction assumption is reasonable. Figure 5-16 shows the comparison
between the two measurements (the range of the RICH measurement is 2.6 GeV/n to
4.9 GeV/n; it is limited by the velocity measurement range of the RICH). We observe
that 11 B/(11 B +10 B) must be between 0.6 and 0.7. We choose 11 B/(11 B +10 B) = 0.65
in this analysis. The 10% difference in the
11
B fraction (from 0.6 to 0.7) corresponds
to about 1% difference in the Boron to Carbon ratio, so we assign 1% systematic
error to the isotope composition assumption.
113
Boron to Carbon Ratio
B/(11B+10B)=0.6
11
B/(11B+10B)=0.7
RICH
11
0.32
0.3
0.28
0.26
0.24
0.22
1
10
Ek/A (GeV/n)
Figure 5-16: The Boron to Carbon ratio (statistical error only) as a function of Ek /A,
with Ek /A measured and calculated in different ways: (1) from rigidity measured
by the Tracker (Inner + Layer 1) with 11 B/(11 B +10 B) = 0.6 (red, dashed) and
11
B/(11 B +10 B) = 0.7 (blue, dotted); (2) from velocity measured by the RICH
(black, solid).
5.9
Reconstruction Efficiency
In the pre-selection we require the existence of reconstructed TOF clusters and a
Tracker track, so we need to take into account the associated efficiencies. Similar to
the definition of the trigger efficiency in the physics analysis (see Section 5.6), the
term “reconstruction efficiency” is not for all incoming cosmic rays, but is only for
good events that have no fragmentation along the particle track.
The TOF is used in charged particle trigger settings; therefore, in principle, whenever there is a trigger for a good charged particle, it is very likely to have a TOF
object being reconstructed. The efficiency should be very close to 100% and the difference between Boron and Carbon can be ignored. This is confirmed by estimating
the TOF reconstruction efficiency using MC simulation.
In comparison, the Tracker reconstruction efficiency is slightly lower, because
sometimes the Tracker clusters include delta rays which confuse the track-finding
114
algorithm. To estimate the efficiency, we use the TOF to select samples of Boron
and Carbon, and count how often a Tracker track is reconstructed with the correct
charge. The rigidity is estimated from the geomagnetic cutoff (see Section 5.10), and
the result is shown in Figure 5-17 (b). We observe that Boron has a higher efficiency
than Carbon by ∼ 1%. This is simply because Boron creates fewer delta rays than
Carbon. The estimation of the Tracker reconstruction efficiency correction will be
Tracker Reconstruction Efficiency
included in the survival probability correction as discussed in Section 5.10.
1.2
Boron
1.15
1.1
Carbon
1.05
1
0.95
0.9
0.85
0.8
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Log10(Rigidity)
Figure 5-17: Tracker reconstruction efficiency, estimated from flight data.
5.10
Survival Probability of Boron and Carbon
Due to the amount of material in AMS-02, the probability for a particle of having
nuclear interactions with the detector is not negligible. It is different for Boron and
Carbon since they have different nuclear cross sections. The interactions can be
identified and removed by comparing signals in different sub-detectors, as presented
in Section 5.5. However, to get the correct counting of the incoming particles, we must
know how many of them are lost; in other words, what is the survival probability for
a particle passing through the detector.
115
Amount of Material Above Z (g/cm2)
20
18
16
14
12
10
8
6
4
2
0
-50
0
50
100
150
Z (cm)
Figure 5-18: Cumulative material distribution of AMS-02 along Z coordinate at (X,
Y) = (5 cm, 5 cm). Particles enter AMS-02 at Z ≈ 170 cm.
The material budget of AMS-02 is shown in Figure 5-18. The gradual rise from
155cm to 65cm in the Z coordinate is due to the material in the TRD. The sudden
rises near 60cm and -70cm are due to the material in the TOF. When reaching the
Lower TOF, the amount of material that a particle has gone through is:
Grammage(Z = −75cm) ≈
18.5
(g/cm2 ) ,
cosθ
(5.6)
where θ is the particle’s inclination angle from Z axis. To get an understanding on
how AMS-02 material leads to different loss rates of Boron and Carbon, we built a
toy model to estimate the survival probability for simple assumptions. The survival
probability can be written as:
PSur. =
Y
e−xi /λi ,
(5.7)
i
where i represents different layers of material, xi is the thickness of the layer, and λi
is the mean free path (or equivalently, nuclear interaction length) for the incoming
116
particle in the material. The mean free path is expressed as:
P
1
1
A
j wj Aj
P
P
= P ρwj NA =
=
,
λ= P
ρN
w
σ
ρN
w
σ
A
j
j
A
j
j
σ
j nj σj
j
j
j
j
(5.8)
A
where j represents different elements in the material, wj is the weight of the element,
Aj is the mass number of the element, ρ is the density of the material, NA is the
Avogadro constant, and σj is the cross section between the incoming particle and
the element. Several models of nuclear interaction cross sections with parameters fit
to experimental measurements can be found in literature. For example, the inelastic
cross section for
12
C interacting with Hydrogen is 238 mb at 1.87 GeV/n [111]. In
our toy model, we use Shen’s model [16] for cross sections. The calculated survival
probabilities at the position of the Lower TOF are shown in Figure 5-19 for 10 B, 11 B,
and 12 C. From the plot we observe that in the GeV region, about half of the incoming
Boron and Carbon nuclei are lost due to nuclear interactions. The difference between
Survival Probability at Z = -75cm
Boron and Carbon is a few percent.
0.55
0.5
0.45
10
B
11
B
0.4
12
C
0.35
10-2
10-1
1
10
102
Ek/A (GeV/n)
Figure 5-19: Survival probability (estimated from hadronic interaction models) at
(X, Y, Z) = (5cm, 5cm, −75cm) as a function of Ek /A for 10 B (red, inverse triangle),
11
B (blue, triangle) and 12 C (green, dot) with an inclination angle of 0◦ , The cross
sections used in the calculation are taken from Shen’s parameterization [16].
117
We estimate the survival probability ratio between Boron and Carbon with two
methods: from full AMS-02 MC and from flight data. There are advantages and
disadvantages for both methods:
1. If using MC, we have absolutely pure samples of incoming particles, but the
interaction models and detector simulations might not be perfect.
2. When using flight data, we select samples which are not 100% pure. This might
lead to some bias.
We studied the survival probability ratio using both methods; the differences between
Entries
these two are taken as systematic errors.
103
12
C: 10.0GV - 12.6GV
102
10
1
0
1
2
3
4
5
6
MC Inner Tracker Charge Estimator
Figure 5-20: Inner Tracker charge distribution for MC generated 12 C at 10.0GV −
12.6GV . The blue curve is a template fit aimed at getting the fraction of survived
Carbon.
For the MC method, we generate particles in a plane above AMS-02, and select particles within the geometric acceptance of the Tracker Layer 1 and the Inner
Tracker. The only pre-selection cut is to require physics triggers (the trigger efficiency
has already been taken care of). Then we use the Inner Tracker to detect how many
particles are intact. An example of this procedure can be illustrated in Figure 5-20.
118
Survival Probability Ratio
1.2
1.15
1.1
1.05
1
0.95
10
B/12C
11 12
B/ C
0.9
0.85
0.8
0.8
1
1.2
1.4
1.6
1.8
Log (Rigidity)
10
Figure 5-21: Survival probability ratio (estimated from MC simulation) as a function
of MC generated rigidity for 10 B and 12 C (red, solid), and 11 B and 12 C (black, dashed).
The generated particles are
12
C (10.0 - 12.6 GV), but in the Inner Tracker charge
spectrum we observe particles with Z ≤ 5, corresponding to secondary particles produced from fragmentation. A template fit on Z = 6 is performed to estimate the
number of survived Carbons. Dividing this number by the total number of incoming Carbons, we can obtain the survival probability. The survival probability ratio
between Boron and Carbon as a function of rigidity is plotted in Figure 5-21. We
observe that the survival probability difference between Boron and Carbon is about
4%. The reason that 11 B and 10 B show similar survival probabilities is that the fragmentation from 11 B to 10 B cannot be identified by the Inner Tracker, so the observed
survival probability of
11
B is slightly higher.
For the estimation with flight data, we use the Tracker Layer 1 to select samples of
incoming Boron and Carbon. We select the cluster with the largest energy deposition
at the Tracker Layer 1. To remove obvious noise, we require the Tracker Layer 1
cluster to be within a 10 cm cylinder defined by the TOF clusters.
These samples are not pure; it is critical to understand the purity and background
of the samples. Given that the Tracker Layer 1 has a charge resolution of σZ ≈ 0.3,
119
we select Boron and Carbon very close to their charge peaks, so the contaminations
from the nearby charged particles (such as Beryllium and Nitrogen) are negligible.
However, the background from Z ≤ 2 particles is still significant: Hydrogen and
Helium nuclei are far more abundant than Boron and Carbon, and their charge spectra
on the Tracker Layer 1 have long tails (see Figure 5-22). The tails have two main
origins:
• A Hydrogen or Helium nucleus scatters with a Silicon nucleus in the Tracker
Layer 1, leading to large energy deposition inside the Silicon.
• A Hydrogen or Helium nucleus interacts with the material above the Tracker
Layer 1, producing lots of low energy secondaries which create Tracker clusters
with large energy deposition on the Tracker Layer 1.
To estimate the background from proton and Helium tails, we select Z ≤ 2 particles
using the TRD, the Upper TOF and the Tracker, and use their charge distributions
on the Tracker Layer 1 as the background templates. As shown in Figure 5-22, the
red solid curve is the Tracker Layer 1 charge distribution of all particles, and the
black dashed curve corresponds to Z ≤ 2 particles.
With an estimation of the background, the next step is to estimate the survival
probability. We select Boron and Carbon samples according to the cuts shown in
Figure 5-22 (the plot also shows the background from Z ≤ 2 particles). Then we
count how many Borons or Carbons are left using the charge measurement of the
Inner Tracker. For instance, the case for the Carbon sample is shown in Figure 5-23.
Let the number of survived Carbon be NSur. , the total number of events in the Carbon
sample be NT ot. , and the number of background proton and Helium nuclei be NBkg. ,
then the survival probability can be estimated as:
PSur. =
NSur.
.
NT ot. − NBkg.
(5.9)
Another difficulty for the flight-data method is the energy dependence of the survival probability ratio. Since the samples from the flight data are not pure, particle’s
energy cannot be estimated from the Tracker measured rigidity or the TOF measured
120
Entries
106
5
10
104
All Particles
Z = 1 or 2
103
0
1
2
3
4
5
6
7
8
9
Tracker Layer 1 Charge
Entries
Figure 5-22: Tracker Layer 1 charge spectrum for all particles (red, solid) and Z ≤ 2
particles (black, solid). The blue and green lines correspond to the cuts to select
Boron and Carbon samples, with non-negligible backgrounds from Z ≤ 2 particles.
104
103
102
10
1
-2
0
2
4
6
8
Inner Tracker Charge
Figure 5-23: Inner Tracker charge distribution for the Carbon sample selected by the
Tracker Layer 1, as shown in Figure 5-22. The negative charge bin represents the
events without a Tracker track being reconstructed.
121
Survival Probability Ratio Between B and C
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Log (Rigidity)
10
Figure 5-24: Survival probability ratio (estimated from flight data) between Boron
and Carbon as a function of rigidity (estimated from geomagnetic cutoff).
velocity: neither is reliable due to bad reconstructions. However, we can take advantage of the geomagnetic cutoff (see also Section 1.5.2) to have a rough estimation of
rigidity. The spectra of cosmic rays decrease with rigidity following a power law. At
a position with a geomagnetic cutoff Rcutof f , most charged cosmic ray particles have
rigidity values close to Rcutof f . Therefore, Rcutof f can be used as an approximation
of the true rigidity.
The survival probability ratio estimated from flight data is plotted in Figure 524. The survival probability difference between Boron and Carbon is about 4% to
6%. This is in agreement with that estimated by MC. Therefore, we apply a survival
probability correction of 4% to the Boron to Carbon ratio, and assign a 2% systematic
error for the correction.
5.11
Top of Instrument Correction
Before a Carbon nucleus reaches the Tracker Layer 1, it might interact with the
material above (< 1 g/cm2 , see Figure 5-18) and produce an energetic Boron nucleus.
122
Frac(C->B) (%)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
20
30
40
50
60
70
80
90
100
Rigidity (GV)
Figure 5-25: Fraction of Carbon spallation into Boron when transversing the material
above the Tracker Layer 1, estimated from MC. The blue line indicates the average
value.
In high energy region (Ek /A > 100 GeV/n), Carbon is more than 10 times as abundant
as Boron; therefore, a small fraction of the interaction C → B leads to a big bias in
the measured Boron to Carbon ratio. The relationship between the Boron to Carbon
ratio normalized to the Tracker Layer 1 ([NB /NC ]L1 ) and that normalized to the top
of instrument ([NB /NC ]T OI ) can be expressed as:
[NB /NC ]L1
NT OI (B) + NTL1OI (C → B)
= [NB /NC ]T OI + F rac(C → B) , (5.10)
≈
NT OI (C)
where NT OI (B) and NT OI (C) are the numbers of incoming Boron and Carbon nuclei,
NTL1OI (C → B) is the number of Boron nuclei which are produced from spallation of
Carbon nuclei transversing the material above the Tracker Layer 1, and F rac(C → B)
is the ratio between NTL1OI (C → B) and NT OI (C). To get the Boron to Carbon ratio
at the top of instrument ([NB /NC ]T OI ), we need to estimate F rac(C → B).
The fraction of interaction C → B is estimated from full AMS-02 MC simulation. F rac(C → B) is estimated to be about 0.45%, as shown in Figure 5-25. The
123
fluctuation of about 0.1% is taken as systematic error.
5.12
Rigidity Unfolding
Due to the limited resolution of the rigidity measurement, a particle with true rigidity
Rt might be measured to have a different rigidity value Rm . The probability of rigidity
migration is represented by resolution matrix M (Rm , Rt ), using which the measured
flux spectrum can be expressed as:
Z
+∞
Φt (Rt )M (Rt , Rm )dRt .
Φm (Rm ) =
(5.11)
−∞
Therefore, to obtain the true flux spectrum Φt (Rt ), we need to unfold from the
measured flux spectrum Φm (Rm ) using the resolution matrix.
The effects of rigidity migration are largely canceled out between Boron and Carbon because of their similar spectral shapes and almost identical rigidity resolutions.
However, the remaining difference between the two is not negligible at a few hundred
GV (close to the MDR), where it can account for ∼ 10%.
The most important factor in rigidity unfolding is the rigidity resolution function.
It is estimated from MC simulation, which is tuned to match flight data on Tracker
cluster residuals and χ2 of reconstructed rigidity [84]. An example of rigidity resolution spectrum (at R = 256 GV) for Helium is shown in Figure 5-26, along with a
parameterization using a double Gaussian function:
f (x) = A[ √
1
(x − µ1 )2
ω21
(x − µ2 )2
√
Exp(−
)
+
Exp(−
)] ,
2σ12
2σ22
2πσ1
2πσ2
(5.12)
where x = (1/Rm − 1/Rt )/(1/Rt ).
Carbon has a slightly worse rigidity resolution than Helium. To show this from
data, we construct the relative rigidity resolution:
|RigL1 − RigL9|
,
RigL9
124
(5.13)
Normalized Entries
10-1
10-2
10-3
10-4
10-5
-5
-4
-3
-2
-1
0
1
2
3
4
5
∆R/R
Figure 5-26: Rigidity resolution spectrum at R = 256 GV and corresponding parameterization using double Gaussian fit. This is from MC data.
where RigL1 is the rigidity measured by the L1 configuration (Inner Tracker + Layer
1), and RigL9 is the rigidity measured by the L9 configuration (Inner Tracker + Layer
1 + Layer 9). The relative rigidity resolutions as functions of RigL9 are plotted
in Figure 5-27 for Helium and Carbon. In Figure 5-28, we take the ratio of the
two curves in Figure 5-27. We observe that the rigidity resolution of Carbon is
systematically 5% worse than that of Helium (indicated by the blue line in Figure
5-28). Therefore, we implement Carbon’s rigidity resolution function by degrading
the parameterized Helium rigidity resolution function by 5%. The ratio in Figure
5-28 shows a fluctuation of ∼ 8%. This is taken into account in the estimation of
the systematic error due to unfolding. We generate the resolution matrix as shown
in Figure 5-29, covering both positive and negative rigidity ranges.
An unfolding algorithm based on the Bayesian theorem [113] [114] [115] is applied
as follows:
• Take an arbitrary initial guess of the true spectrum Φ0t (Rt ), a spectrum with a
single power law.
125
Relative Rigidity Resolution
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
Helium
Carbon
102
10
RigL9 (GV)
Resolution Ratio C/He
Figure 5-27: Relative rigidity resolution (defined as |RigL1 − RigL9|/RigL9) for
Helium and Carbon as a function of RigL9. This is from flight data. We observe
that Helium has a slightly better rigidity resolution than Carbon.
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
1
102
10
RigL9 (GV)
Figure 5-28: Rigidity resolution ratio between Carbon and Helium (the ratio between
the two curves in Figure 5-27) as a function of RigL9. We take the fluctuation of 8%
as systematic error.
126
Figure 5-29: Resolution matrix for rigidity unfolding.
• Calculate Φ0m (Rm ), the folded spectrum of Φ0t (Rt ).
• Update the guessed true spectrum as: Φ1t (Rt ) = Φ0t (Rt ) × Φ0m (Rm )/Φm (Rm ).
• Go back to the first step, but use the updated true spectrum Φ1t (Rt ).
• Loop N times, stop the loop when the difference between ΦN
m (Rm ) and Φm (Rm )
is smaller than a threshold.
The unfolding is applied on raw counts spectrum without corrections of efficiencies,
exposure time, and survival probability. The results of the unfolding are shown in
Figure 5-30 (flux) and Figure 5-31 (ratio). We observe that the Boron to Carbon ratio
is not much influenced by the unfolding at low rigidity. However, at high rigidity (close
to the MDR), the unfolding corrections are at the level of ∼ 10%.
To estimate the systematic error due to unfolding, we varied the width of rigidity
resolution function by 8% (the uncertainty already mentioned before, see Figure 528). The result is plotted in Figure 5-32. The systematic uncertainty is small in low
rigidity region, and it increases with rigidity.
127
Raw Counts of Boron and Carbon
105
104
Before Unfolding
3
10
After Unfolding
102
10-3
10-2
10-1 1/R (1/GV)
Raw Boron to Carbon Ratio
Figure 5-30: Boron and Carbon raw counts spectra (without any corrections, statistical error only) before (black, dashed) and after (red, solid) rigidity unfolding.
Before Unfolding
10-1
After Unfolding
10-3
10-2
10-1 1/R (1/GV)
Figure 5-31: Raw Boron to Carbon ratio spectra (without any corrections, statistical
error only) before (black, dashed) and after (red, solid) rigidity unfolding.
5.13
Summary
This chapter presented the analysis procedure of the Boron to Carbon ratio measurement by AMS-02. Four levels of selections have been applied to obtain pure samples
128
Raw Boron to Carbon Ratio
0.4
0.3
0.2
0.1
widen resolution function by 8%
nominal resolution function
shrink resolution function by 8%
0.04
10-3
10-2
10-1
1/R (1/GV)
Figure 5-32: Estimation of systematic error due to unfolding: varying the width of
rigidity resolution function by 8%, as already mentioned before (see Figure 5-28), and
observe the influences on the unfolded result.
of Boron and Carbon nuclei: (1) Event pre-selection; (2) Event selection; (3) Charge
selection; (4) Fragmentation rejection.
Different efficiencies have been discussed and estimated: (1) Trigger efficiency;
(2) Reconstruction efficiency; (3) Selection efficiency; (4) Charge selection efficiency.
The influence of Boron isotope composition has also been explored. The survival
probability has been studied and estimated with both MC simulation and flight data.
A rigidity unfolding procedure has been finally applied to overcome bin to bin event
migration due to the finite resolution of the Tracker rigidity measurement.
Five sources of systematic errors have been analyzed and estimated: (1) Event selection; (2) Isotope composition; (3) Survival probability; (4) Materials above Tracker
Layer 1; (5) Rigidity unfolding.
The results of the analysis are presented in Chapter 6.
129
130
Chapter 6
Results
6.1
The Energy Spectrum of the Boron to Carbon
Ratio
With the event selection criteria described in Sections 5.2 and 5.3, we obtain about 1.1
million Borons and 3.8 million Carbons above 1 GeV/n (kinetic energy per nucleon)
in the 30 months of data collection. Among the 4.9 million selected events, about 2
thousand Borons and 17 thousand Carbons are above 100 GeV/n. The purity of the
event sample is about 99.9%.
Table 6.1 lists the result of the Boron to Carbon ratio as a function of kinetic
energy per nucleon. The binning is evaluated according to 3σ rigidity resolution of
the Tracker. The statistical error of the Boron to Carbon ratio, σstat , is calculated
B
C
from the statistical errors of Boron (σstat
) and Carbon (σstat
):
s
σstat = RB/C
B
σstat
NB
2
+
C
σstat
NC
2
,
(6.1)
B
C
where RB/C is the Boron to Carbon ratio. σstat
and σstat
are estimated from the raw
counts NB and NC , using Poisson statistics.
The systematic error, σsys , is calculated as a sum in quadrature of uncorrelated
131
Ek /A(GeV/n)
0.9-1.3
1.3-1.9
1.9-2.6
2.6-3.6
3.6-4.9
4.9-6.6
6.6-8.9
8.9-12.0
12.0-16.4
16.4-22.8
22.8-32.2
32.2-46.6
46.6-68.7
68.7-104.2
104.2-166.0
166.0-287.6
287.6-669.7
NB
110935
167989
168556
152942
124710
97241
76085
55862
37230
22336
12240
6686
3600
2028
1002
496
251
B/C
0.3178
0.3077
0.2926
0.2775
0.2625
0.2472
0.2304
0.2117
0.1936
0.1758
0.1556
0.1369
0.1191
0.1089
0.0956
0.0850
0.0743
σstat
0.0010
0.0009
0.0009
0.0008
0.0009
0.0009
0.0010
0.0010
0.0012
0.0013
0.0016
0.0019
0.0022
0.0027
0.0034
0.0043
0.0053
σsys
0.0072
0.0070
0.0066
0.0063
0.0060
0.0056
0.0053
0.0048
0.0045
0.0041
0.0037
0.0033
0.0030
0.0034
0.0042
0.0075
0.0146
Table 6.1: Energy spectrum of the Boron to Carbon ratio between 0.9 GeV/n and
669.7 GeV/n. The columns are: kinetic energy per nucleon, raw counts of Boron, the
Boron to Carbon ratio, statistical error, systematic error.
contributions:
σsys
v
u 5
uX
i )2 ,
= t (σsys
(6.2)
i=1
i
where σsys
(i = 1, ..., 5) are the five sources of systematic errors that are described and
estimated in Chapter 5: (1) Event selection; (2) Isotope composition; (3) Survival
probability; (4) Materials above Tracker Layer 1; (5) Rigidity unfolding.
The result is plotted in Figure 6-1. Statistical errors are shown in red error bars;
systematic errors are shown in blue error bars. We observe that the Boron to Carbon
ratio is slightly above 0.3 at 1 GeV/n and decreases with energy. The ratio is less
than 0.1 for energies above 100 GeV/n.
A comparison with previous measurements is shown in Figure 6-2. Following
the tradition in literature [116] [11], the error bars represent statistical errors and
systematic errors summed in quadrature. Below 20 GeV/n, the results are compatible
with previous measurements within their error bars. For energies above 20 GeV/n,
132
Boron-to-Carbon Ratio
0.4
0.3
0.2
0.1
AMS02 (2014)
Statistical Error
Systematic Error
0.04
1
102
Kinetic Energy (GeV/n)
10
Figure 6-1: The Boron to Carbon ratio measured by AMS-02 with the first 30 months
of flight data. Statistical errors are shown in red error bars, and systematic errors are
shown in blue error bars. The measured results are listed in Table 6.1.
the errors are one order of magnitude smaller than previous measurements. This
allows for an improved understanding of cosmic ray propagation.
With the precision measurements at high energy, we find that the B/C spectrum
for Ek /A > 20 GeV/n can be described by a power law:
y = a · xb ,
(6.3)
where y is the Boron to Carbon ratio, x is kinetic energy per nucleon, and a and b
are free parameters. The fit shown in Figure 6-3 gives:
6.2
a = 0.417 ± 0.045 ,
(6.4)
b = −0.302 ± 0.028 .
(6.5)
Result Stability
To ensure the stability of the results, we performed further checks.
133
Boron-to-Carbon Ratio
0.4
0.3
0.2
AMS02 (2014)
HEAO (A&A 1990)
0.1
CRN (ApJ 1990)
ATIC-2 (ICRC 2007)
CREAM (Astropart. Phys. 2008)
AMS01 (ApJ 2009)
TRACER (ApJ 2011)
0.04
1
102
Kinetic Energy (GeV/n)
10
Boron-to-Carbon Ratio
Figure 6-2: Comparison of the Boron to Carbon ratio measured by AMS-02 to previous experiments [6] [7] [8] [9] [10], [11]. Statistical and systematic errors are summed
in quadrature (for comparison with literature). The statistical and systematic errors
for AMS-02 are listed in Table 6.1.
0.4
0.3
0.2
0.1
AMS02 (2014)
0.04
1
102
Kinetic Energy (GeV/n)
10
Figure 6-3: The Boron to Carbon ratio spectrum in the energy range 20 - 670 GeV/n
can be described by a power law. The power law index is fitted to be −0.302 ± 0.028.
134
Figure 6-4: Stability of the results against selection cuts: by varying the cuts in a
wide phase space and doing the analysis 500 times, the number of selected Borons is
changed by ∼ 20%, but the B/C value is only changed by a few per mil. Shown in
the figure is an example for energy bin 8.4-10.2 GeV/n.
Selection Cuts Dependence. We varied the cut values in wide ranges and
performed the analysis 500 times. An example (energy bin 8.4-10.2 GeV/n) is shown
in Figure 6-4. In the left plot we observe that even though the number of selected
Borons is changed by about 20%, the Boron to Carbon ratio is stable within a few
per mil. The right plot is a projection of the left plot on the X axis. A Gaussian fit
on the B/C distribution shows that the B/C value varies only on the order of 4 × 10−4
with the vast changes on selection cuts. The result appears stable against selection
cuts. The systematic error due to selection is accordingly estimated to be a few per
mil. This is negligible compared to other systematic errors.
Time Dependence. We divided the 30 months of data taking into 5 periods.
We then compared the spectrum of Boron to Carbon ratio (raw counts, without
unfolding) in each period. Figure 6-5 shows that the measurements in different periods
are statistically compatible.
Unfolding Dependence. We compared the B/C measured using the L9 configuration without unfolding and that using the L1 configuration with unfolding. The
L9 configuration has a longer lever arm, thus higher rigidity resolution; therefore, the
135
B/C (Raw Counts)
1st Period
0.3
2nd Period
0.25
3rd Period
4th Period
0.2
5th Period
0.15
0.1
1
102
Kinetic Energy (GeV/n)
10
Boron-to-Carbon Ratio
Figure 6-5: Stability of the measurement over time: Comparison of the Boron to
Carbon ratio (raw counts, without unfolding) of 5 different periods (6 month for each
period) in the first 30 months of data collection.
0.4
0.3
0.2
0.1
L1 - With unfolding
L9 - Without unfolding
0.04
1
102
Kinetic Energy (GeV/n)
10
Figure 6-6: Check of unfolding: Comparison between B/C measurement with the
L1 configuration with unfolding applied (Red) and that with the L9 configuration
without unfolding applied (Blue). Errors are statistical only.
136
(L1 - L9) / σ21 + σ29
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
1
102
Kinetic Energy (GeV/n)
10
p
Figure 6-7: Check of unfolding: The test variable (L1 − L9)/ σ12 + σ92 shows similar
fluctuations in the low and high energy regions, demonstrating the correctness of the
unfolding for the L1 configuration.
B/C measured by the L9 configuration is not much influenced by rigidity migration
up to a few hundred GeV/n. To some extent, it reflects the “true” rigidity. Figure
6-6 shows a good agreement between the two spectra. To further investigate this
p
agreement, we plotted the quantity of (L1 − L9)/ σ12 + σ92 (see Figure 6-7), where
L1 and L9 represent the two measurements in Figure 6-6, respectively, and σ1 and
σ9 are the corresponding statistical errors. The difference between the two spectra
is within ±1σ, and is evenly distributed. We take this result as a validation of our
unfolding procedure.
Further investigations of the errors for different Tracker configurations are shown
in Figure 6-8. For the L1 configuration, the systematic error is larger than the statistical error. At low energy, systematic error is dominated by survival probability
correction. At high energy, systematic error is dominated by rigidity unfolding. With
30 months of data taking, the statistical error of the L9 configuration alone is already
greater than the total error of the L1 configuration; therefore, to take advantage of
the higher rigidity resolution of the L9 configuration, more data is needed.
137
Relative Error
0.3
0.25
0.2
L1 Stat. Err.
L1 Sys. Err.
0.15
L1 Stat. + Sys. Err.
0.1
L9 Stat. Err.
0.05
0
1
102
10
Kinetic Energy (GeV/n)
Figure 6-8: Relative errors as functions of energy: L1 configuration, statistical error
only (Red); L1 configuration, systematic error only (Orange); L1 configuration, statistical error and systematic error summed quadratically (Blue); the L9 configuration,
statistical error only (Black).
6.3
Constraints on Cosmic Ray Propagation Model
We fit the Boron to Carbon ratio measured by AMS-02 with the GalProp model [12].
As presented in Section 1.6.4, the parameters in the GalProp model that are sensitive
0
and the Alfven velocity
to the Boron to Carbon ratio are the diffusion coefficient Dxx
VA .
We use least χ2 method to perform the fit. The χ2 function is constructed as
0
, VA ) =
χ2 (Dxx
X [yi (D0 , VA ) − y 0 ]2
xx
i
,
2
σ
i
i
(6.6)
where i represents different energy bins, yi0 is the measured B/C value, σi is the
0
error associated with the measurement, and yi (Dxx
, VA ) is the B/C value calculated
0
from GalProp with given values of Dxx
and VA . We use default values for all the
other parameters in GalProp (the parameter settings are listed in Appendix C). To
avoid the influence of solar modulation, we only fit the data with Ek /A > 10 GeV/n
138
Figure 6-9: χ2 of the GalProp fit (represented by color code) as a function of
0
and Alfven velocity VA , showing the correlation between
diffusion coefficient Dxx
these two parameters. The correlation can be approximated with a linear function
0
0
in units of 1028 cm2 /s, VA in units of km/h), as indicated
− 85.9 (Dxx
VA = 19.7Dxx
by the red line on the plot. See Figure 6-9 for the zoomed-in version.
(effectively R > 20 GV).
0
The χ2 as a function of Dxx
and VA is plotted in Figure 6-9 (see Figure 6-10 for
the zoomed-in version.). From the plot we can identify the best fitted values at the
0
minimum χ2 value. The plot shows a strong correlation between Dxx
and VA . The
correlation can be approximated by a linear function (shown as the red line in Figure
6-9):
0
VA = 19.7Dxx
− 85.9 ,
(6.7)
0
where Dxx
is in units of 1028 cm2 /s and VA is in units of km/h. This linear function is
indicated by the red line in Figure 6-9. The error on each fit parameter is evaluated
by varying the parameter value until χ2 is incremented by 1 [18]. The B/C spectrum
calculated from GalProp with the best fitted parameter values is plotted in Figure
139
Figure 6-10: Zoom-in of Figure 6-9.
6-11, along with the measurement by AMS-02. The fitting results are:
0
Dxx
= (6.05 ± 0.05) × 1028 cm2 /s ,
VA = (33.9 ± 1.0) km/s .
6.4
(6.8)
(6.9)
Improvement of P̄ /P Background Prediction
in Dark Matter Search
As described in Section 1.6.5, prediction of P̄ /P background in dark matter search
is a good example to show the importance for physics of the precision measurement
of the Boron to Carbon ratio. Using the same fitting procedure and energy range
as Section 6.3, we perform the fit using the B/C ratio measured by a few recent
experiments (AMS-01 [11], TRACKER [10], CREAM [9]).
140
Boron-to-Carbon Ratio
0.25
AMS02 Measurement
GalProp Fit
0.2
0.15
0.1
0.05
102
10
Kinetic Energy (GeV/n)
Figure 6-11: Best χ2 fit of GalProp on the Boron to Carbon ratio measured by AMS02 (see also Figure 6-3). The fit is performed above 10 GeV/n to avoid influences of
solar modulation at low energy.
0
Table 6.2 shows a comparison between Dxx
fitted from AMS-02 data and from
previous measurements. They are compatible with each other, but the error is much
0
0
, we predict
obtained in this analysis. Using the fitted value of Dxx
smaller for the Dxx
the secondary anti-proton background.
The secondary anti-proton background prediction needs several inputs:
• Primary proton and Helium nuclei flux spectra.
• Cross sections of reactions which produce anti-protons.
• Diffusive propagation of charged cosmic rays in our galaxy, which is determined
by the Boron to Carbon ratio and related nuclear cross sections.
Among these items, we study the uncertainty from the diffusion coefficient (determined by the measured B/C ratio). The results are plotted in Figure 6-12, the bands
0
correspond to ±1σ variations, corresponding to ∆Dxx
in Table 6.2. A comparison
between the two bands shows that the precision measurement of the Boron to Carbon
ratio by AMS-02 significantly improves the prediction of the secondary anti-proton
141
background in dark matter search.
B/C Data Source
AMS-02
AMS-01, TRACER, CREAM
0
(1028 cm2 /s)
Dxx
6.05
5.91
0
(1028 cm2 /s)
∆Dxx
0.05
0.23
0
in the GalProp model,
Table 6.2: The fitted results of the diffusion coefficient Dxx
with the Boron to Carbon ratio measured by AMS-02 and three recent experiments
(AMS-01 [11], TRACER [10], CREAM [9]).
0.18 ×10
P/P
-3
0.16
0.14
0.12
AMS01+TRACER+CREAM
0.1
AMS02
0.08
103
Kinetic Energy (GeV/n)
102
10
Figure 6-12: Prediction of anti-proton background in anti-proton to proton ratio for
anti-protons produced from interactions between cosmic rays and interstellar medium.
0
The bands correspond to ±1σ variations. The red solid band uses Dxx
constrained
0
by AMS-02 B/C measurement, and the blue textured band uses Dxx constrained by
B/C measurements of AMS-01 [11], TRACER [10], and CREAM [9].
6.5
Galactic Magnetic Field and Plasma Density
Alfven waves are generated from magnetic tension (B 2 /µ0 ) on the plasma in the ISM.
The velocity of the wave (VA ) can be expressed as [117]:
VA =
tension
density
1/2
=
142
B2
µ0 ρ
1/2
,
(6.10)
where B is the galactic magnetic field, µ0 is the permeability of the vacuum, and ρ
is the total mass density of the charged plasma particles. Assuming all the charged
plasma ions in the ISM are protons, Formula 6.10 becomes:
VA ≈ (2.18 × 105 cm/s)(n/cm−3 )−1/2 (B/µG) ,
(6.11)
where n is the ion number density. In Section 6.3, we estimate VA ≈ 33.9 km/s in
the ISM. Using this in Formula 6.11, we get the relationship between n and B:
n ≈ 15/
B
µG
2
cm−3 .
(6.12)
Using the magnetic field measurement by Voyager 1 (B ≈ 4µG [42]), we obtain:
n ≈ 14 cm−3 .
(6.13)
Using the magnetic field measurement by Faraday rotation (B ≈ 10µG [41]), we
obtain instead:
n ≈ 2.3 cm−3 .
(6.14)
The measured average ion density in the ISM is ∼ 1 cm−3 [38] [39], suggesting the
magnetic field measured by Voyager 1 might only reflect the local field close to the
Solar system, but not the average field strength of our galaxy.
143
144
Conclusion
The Boron to Carbon ratio is measured in the range 1 GeV/n to 670 GeV/n with
AMS-02. Above 20 GeV/n, this is the first precision measurement. From the first 30
months of flight data, 1.1 million Boron and 3.8 million Carbon nuclei are identified
and analyzed. A high resolution charge measurement of σZ ∼ 0.1 is achieved. Rejecting fragmentation events leads to a purity of ∼ 99.9%. The B/C ratio is measured
to be ∼ 0.32 at 1 GeV/n, and it decreases to be ∼ 0.08 at 500 GeV/n. The B/C
spectrum follows a falling power law. This agrees with the assumption that Boron is
a secondary particle from spallation of heavier elements in collision with interstellar
medium.
This measurement determines two parameters necessary for diffusive galactic propagation models, diffusion coefficient and Alfven velocity, to be:
0
Dxx
= (6.05 ± 0.05) × 1028 cm2 /s ,
VA = (33.9 ± 1.0) km/s .
(6.15)
(6.16)
Using these parameters, the prediction of the secondary anti-proton background in
dark matter search is one order of magnitude more accurate.
AMS-02 will be taking data for another ∼ 10 years; the B/C measurement will be
improved with additional data and extended to higher energy. The analysis methods
developed in this thesis can also be used in other important measurements, including
O/C,
10
Be/9 Be, 6 Li/7 Li and Sub–F e/F e.
145
146
Appendix A
Search for anti-Carbon
Section 2.4 describes the importance of primordial anti-matter search, and shows that
most efforts of anti-matter search so far are on primordial anti-Helium search.
A byproduct of this thesis is a search for anti-Carbon. Using the event selection
criteria described in Chapter 5, no anti-Carbon is observed. The upper limit of the
anti-Carbon to Carbon ratio, RC/C , is defined as
R
RC/C < R
3.09 / C (E) dE
,
NC (E) / C (E) dE
(A.1)
where C (E) and C(E) are the efficiencies of Carbon and anti-Carbon, NC (E) is
the energy spectrum of Carbon, and 3.09 is the maximum number of hypothetical
anti-Carbon consistent at 95% confidence with a null detection and no background
[118]. Assuming anti-Carbon has the same acceleration and propagation mechanism
as Carbon, C (E) and C(E) should be the same and cancel with each other in Formula
A.1, then RC/C can be simplified as
RC/C < R
where NC =
R
3.09
3.09
=
,
NC
NC (E) dE
(A.2)
NC (E) dE is the total count of Carbon. With the selection cuts in
Chapter 5, NC = 3, 848, 255 for 0.9 GeV/n < Ek /A < 669.7 GeV/n; therefore, we
obtain the upper limit of the anti-Carbon to Carbon ratio at 95% confidence in the
147
energy range 0.9-669.7 GeV/n:
RC/C <
3.09
' 8.03 × 10−7 .
3848255
(A.3)
No other measurement on the anti-Carbon to Carbon ratio has been found in literature. Given that AMS-02 has much more data compared to all the other cosmic ray
experiments combined, this should be the best upper limit of RC/C so far.
148
Appendix B
Production Mechanism of Cosmic
Ray Boron
As addressed in Chapter 1, cosmic ray Boron is a secondary particle produced from
nuclear interactions between primary cosmic rays and the ISM. There are two possible
production mechanisms:
1. High energy proton (or Helium) collides with a nucleus (such as Carbon) in the
ISM, producing a secondary Boron.
2. High energy Carbon (or Nitrogen, Oxygen, etc.) collides with a proton (or
Helium) in the ISM, producing a secondary Boron.
In practice, however, only the second production mechanism can provide sufficient
high energy Borons. The relative abundance of Carbon in the ISM (O(10−15 ), see
Section 1.2.1) is much smaller than that in the cosmic rays (O(10−4 ), see Section
1.2.2), so the reactions in the second mechanism happen far more frequently.
149
150
Appendix C
GalProp Parameters
The default parameters of GalProp Version 54 are as follows:
n_spatial_dimensions = 2
r_min
= 0.0
min r
r_max
= 25.0
max r
dr
= 1.0
delta r
z_min
= -04.0
min z
z_max
= +04.0
max z
dz
= 0.2
x_min
= -20.0
min x
x_max
= +20.0
max x
dx
= 1.0
y_min
= -20.0
min y
y_max
= +20.0
max y
dy
= 1.0
p_Ekin_grid
= Ekin
p||Ekin alignment
p_min
= 1000
min momentum (MV)
p_max
= 4000
max momentum (MV)
p_factor
= 1.3
Ekin_min
= 1.0e1
delta z
delta x
delta y
momentum factor
min kinetic energy per nucleon (MeV)
151
Ekin_max
= 1.0e8
max kinetic energy per nucleon (MeV)
Ekin_factor
= 1.2
gamma_rays
= 0
1=compute gamma rays 2=compute HI, H2 skymaps
= 3
1= old formalism 2=Blattnig et al. 3=Kamae
= 1
1=compute isotropic IC: 1=compute full; 2=store
IC_anisotropic
= 0
1=compute anisotropic IC
bremss
= 1
1=compute bremsstrahlung
integration_mode
= 0
integr.over part.spec.: =1-old E*logE; =0-PL
kinetic energy per nucleon factor
separately.
pi0_decay
et al.
IC_isotropic
skymaps components
analyt.
E_gamma_min
= 100
min gamma-ray energy (MeV)
E_gamma_max
= 1.0e6
E_gamma_factor
= 1.5
ISRF_factors
= 1.0,1.0,1.0
max gamma-ray energy (MeV)
gamma-ray energy factor
ISRF factors for IC calculation:
optical, FIR, CMB
synchrotron
= 0
1=compute synchrotron
nu_synch_min
= 1.0e6
nu_synch_max
= 1.0e10
nu_synch_factor
= 2.0
long_min
= 0
min synchrotron frequency (Hz)
max synchrotron frequency (Hz)
synchrotron frequency factor
gamma-ray intensity skymap longitude minimum
(deg)
long_max
= 360
gamma-ray intensity skymap longitude maximum
= -90
gamma-ray intensity skymap latitude minimum
= +90
gamma-ray intensity skymap latitude maximum
= 1.0
gamma-ray intensity skymap longitude binsize
(deg)
lat_min
(deg)
lat_max
(deg)
d_long
152
(deg)
d_lat
= 1.0
gamma-ray intensity skymap latitude binsize
(deg)
healpix_order
= 6
order for healpix skymaps. 6 gives ~1.0 degree
resolution and it changes by an order of 2.
lat_substep_number
= 1
latitude bin splitting (0,1=no split, 2=split
in 2...)
LoS_step
= 0.01
LoS_substep_number
= 1
kpc, Line of Sight (LoS) integration step
number of substeps per LoS integration step
(0,1=no substeps)
D0_xx
= 6.10e28
D_rigid_br
= 4.0e3
diffusion coefficient at reference rigidity
reference rigidity for diffusion coefficient,
MV
D_g_1
= 0.33
diffusion coefficient index below reference
= 0.33
diffusion coefficient index above reference
rigidity
D_g_2
rigidity
diff_reacc
= 1
v_Alfven
= 30.0
damping_p0
= 1.0e6
1=include diffusive reacceleration
Alfven speed in km s^{-1}
some rigidity, MV, (where CR density is
low)
damping_const_G
= 0.02
a const derived from fitting B/C
damping_max_path_L
= 3.0e21
convection
= 0
v0_conv
= 0.0
V0 convection in km s^-1
dvdz_conv
= 7.0
dV/dz=grad V in km s^-1 kpc^-1
nuc_rigid_br
= 1.0e2
reference rigidity for primary nucleus
= 2.43
nucleus injection index below reference
Lmax~1 kpc, max free path
1=include convection
injection index in MV
nuc_g_1
rigidity
153
nuc_g_2
= 2.43
nucleus injection index above reference
rigidity
inj_spectrum_type
= rigidity
rigidity||beta_rig||Etot nucleon injection
spectrum type
electron_g_0
= 2.50
electron_rigid_br0
= 1.0e3
electron injection index below electron_rigid_br0
reference rigidity0 for electron injection
index in MV
electron_g_1
= 2.50
electron injection index between electron_rigid_br0
and electron_rigid_br
electron_rigid_br
= 1.0e3
reference rigidity for electron injection
index in MV
electron_g_2
= 2.50
electron injection index above reference
He_H_ratio
= 0.11
He/H of ISM, by number
n_X_CO
= 9
an option to select functional dependence of
n_X_CO_values
= 0
only for n_X_CO=3, number of values in X_CO_values
X_CO_values
= 0
only for n_X_CO=3
X_CO_radius
= 0
only for n_X_CO=3
propagation_X_CO
= 0
not used
X_CO
= 1.9E20
rigidity
X_CO=X_CO(r)
CO to H2 conversion factors, used both
in propagation and skymap genergation
X_CO_parameters_0
= 1.0E20
Parameter X0 for n_X_CO = 2
X_CO_parameters_1
= 1
Parameter A for n_X_CO = 2
X_CO_parameters_2
= 0
Parameter B for n_X_CO = 2
X_CO_parameters_3
= 0
Parameter C for n_X_CO = 2
nHI_model
= 1
an option to select analytical HI model
nH2_model
= 1
an option to select analytical CO model
nHII_model
= 1
an option to select analytical HII model
COR_filename
= rbands_co10mm_v2_2001_qdeg.fits
154
HIR_filename
= rbands_hi12_v2_qdeg_zmax1_Ts125.fits
GCR_data_filename
= GCR_data_1.dat
fragmentation
= 1
1=include fragmentation
momentum_losses
= 1
1=include momentum losses
radioactive_decay
= 1
1=include radioactive decay
K_capture
= 0
1=include K-capture
ionization_rate
= 0
1=compute ionization rate
start_timestep
= 1.0e9
end_timestep
= 100
timestep_factor
= 0.50
timestep_repeat
= 20
timestep_repeat2
= 0
timestep_print
= 10000
timestep_diagnostics = 10000
H I maps
(years)
(years)
number of repeats per timestep in timestep_mode=1
number of repeats per timestep in timestep_mode=2
number of timesteps between printings
number of timesteps between diagnostics
control_diagnostics
= 0
control details of diagnostics
network_iterations
= 2
number of iterations of entire network
network_iter_compl
= 2
number of iterations of entire network
network_iter_sec
= 1
number of iterations for secondary particles
prop_r
= 1
1=propagate in r (2D)
prop_x
= 1
1=propagate in x (3D)
prop_y
= 1
1=propagate in y (3D)
prop_z
= 1
1=propagate in z (2D, 3D)
prop_p
= 1
1=propagate in p (2D, 3D)
use_symmetry
= 0
0=no symmetry, 1=optimized symmetry, 2=xyz
with A&lt;=1
symmetry by copying (3D)
vectorized
= 0
source_specification = 0
0=unvectorized code, 1=vectorized code
2D::1:r,z=0 2:z=0
3D::1:x,y,z=0 2:z=0 3:x=0
4:y=0
source_model
= 1
0=zero 1=parameterized 2=case-B 3=pulsars 5=S-Mattox
155
6=S-Mattox with cutoff 7=Gaussian 8=Table 9=HI+H2 10=H2 11=HII
source_parameters_0
= 0
not used
source_parameters_1
= 0.5
model 1:alpha
source_parameters_2
= 1.0
model 1:beta
source_parameters_3
= 20.0
model 1:rmax
source_parameters_4
= 20.0
model 1:rmax
source_parameters_5
= 0.0
source_parameters_6
= 0
not used
source_parameters_7
= 0
not used
source_parameters_8
= 0
not used
source_parameters_9
= 0
not used
source_model_elec
= 1
source model for electrons, definitions as
source_pars_elec_0
= 0
not used
source_pars_elec_1
= 0.5
model 1:alpha
source_pars_elec_2
= 1.0
model 1:beta
source_pars_elec_3
= 20.0
model 1:rmax
source_pars_elec_4
= 20.0
model 1:rmax
source_pars_elec_5
= 0.0
source_pars_elec_6
= 0
not used
source_pars_elec_7
= 0
not used
source_pars_elec_8
= 0
not used
source_pars_elec_9
= 0
not used
n_source_values
= 0
only used with source_model/source_model_elec=8
source_values
= 0
list of source ring values for source_model=8
source_radius
= 0
list of source ring values for source_model=8
SNR_events
= 0
handle stochastic SNR events
SNR_interval
= 1.0e4
time interval in years between SNR in 1
= 1.0e4
CR-producing live-time in years of an SNR
model 1:rmax
for nuclei
model 1:rmax
kpc^-3 volume
SNR_livetime
156
SNR_electron_sdg
= 0.0
delta electron source index for Gaussian
= 0.0
delta nucleus source index for Gaussian sigma
sigma
SNR_nuc_sdg
SNR_electron_dgpivot = 5.0e3
delta electron source index pivot rigidity
(MV)
SNR_nuc_dgpivot
= 5.0e3
delta nuclei source index pivot rigidity
(MV)
ISRF_file
= ISRF/Standard/Standard.dat
ISRF_filetype
= 3
ISRF_healpixOrder
= 3
B_field_name
= galprop_original
n_B_field_parameters = 10
B_field_parameters
input ISRF file
the name of the B-field model
number of B-field parameters
= 0,0,0,0,0,0,0,0,0,0
parameters of the model specified
by B_field_name
B_field_model
= 050100020
bbrrrzzz bbb=10*B(0) rrr=10*rscale
zzz=10*zscale
proton_norm_Ekin
= 1.0e5
proton kinetic energy for normalization
electron_norm_Ekin
= 3.45e4
electron kinetic energy for normalization
proton_norm_flux
= 4.90e-9
flux of protons at normalization energy
(cm^-2 sr^-1 s^-1 MeV^-1)
electron_norm_flux
= 4.0e-10
flux of electrons at normalization energy
(cm^-2 sr^-1 s^-1 MeV^-1)
source_norm
= 1.0
absolute normalization for proton CR source
function (only if electron_norm_flux=proton_norm_flux=0)
electron_source_norm = 1.0
absolute normalization for electron CR source
function (only if electron_norm_flux=proton_norm_flux=0)
rigid_min
= 0.0
rigid_max
= 1.0E38
max_Z
= 28
min rigidity for sources
max rigidity for sources
the largest atomic number (Z) in the nuclear
reaction network
157
iso_abundance_01_001 = 1.06e6
iso_abundance_01_002 = 34.8
H
H
iso_abundance_02_003 = 9.033
He
iso_abundance_02_004 = 7.199e4
He
iso_abundance_03_006 = 0.0
Li
iso_abundance_03_007 = 0.0
Li
iso_abundance_04_007 = 0.0
Be
iso_abundance_04_009 = 0.0
Be
iso_abundance_04_010 = 0.0
Be
iso_abundance_05_010 = 0.0
B
iso_abundance_05_011 = 0.0
B
iso_abundance_06_012 = 2819
C
iso_abundance_06_013 = 5.268e-07
iso_abundance_07_014 = 182.8
C
N
iso_abundance_07_015 = 5.961e-5
iso_abundance_08_016 = 3822
N
O
iso_abundance_08_017 = 6.713e-7
iso_abundance_08_018 = 1.286
O
O
iso_abundance_09_019 = 2.664e-8
iso_abundance_10_020 = 312.5
F
Ne
iso_abundance_10_021 = 0.003556
Ne
iso_abundance_10_022 = 100.1
Ne
iso_abundance_11_023 = 22.84
Na
iso_abundance_12_024 = 658.1
Mg
iso_abundance_12_025 = 82.5
Mg
iso_abundance_12_026 = 104.7
Mg
iso_abundance_13_027 = 76.42
Al
iso_abundance_14_028 = 725.7
Si
iso_abundance_14_029 = 35.02
Si
iso_abundance_14_030 = 24.68
Si
158
iso_abundance_15_031 = 4.242
P
iso_abundance_16_032 = 89.12
S
iso_abundance_16_033 = 0.3056
S
iso_abundance_16_034 = 3.417
S
iso_abundance_16_036 = 0.0004281
S
iso_abundance_17_035 = 0.7044
Cl
iso_abundance_17_037 = 0.001167
iso_abundance_18_036 = 9.829
Cl
Ar
iso_abundance_18_038 = 0.6357
Ar
iso_abundance_18_040 = 0.001744
Ar
iso_abundance_19_039 = 1.389
K
iso_abundance_19_040 = 3.022
K
iso_abundance_19_041 = 0.0003339
K
iso_abundance_20_040 = 51.13
Ca
iso_abundance_20_041 = 1.974
Ca
iso_abundance_20_042 = 1.134e-6
Ca
iso_abundance_20_043 = 2.117e-6
Ca
iso_abundance_20_044 = 9.928e-5
Ca
iso_abundance_20_048 = 0.1099
Ca
iso_abundance_21_045 = 1.635
Sc
iso_abundance_22_046 = 5.558
Ti
iso_abundance_22_047 = 8.947e-06
Ti
iso_abundance_22_048 = 6.05e-07
Ti
iso_abundance_22_049 = 5.854e-09
Ti
iso_abundance_22_050 = 6.083e-07
Ti
iso_abundance_23_050 = 1.818e-5
V
iso_abundance_23_051 = 5.987e-09
iso_abundance_24_050 = 2.873
iso_abundance_24_051 = 0
iso_abundance_24_052 = 8.065
V
Cr
Cr
Cr
159
iso_abundance_24_053 = 0.003014
Cr
iso_abundance_24_054 = 0.4173
Cr
iso_abundance_25_053 = 6.499
Mn
iso_abundance_25_055 = 1.273
Mn
iso_abundance_26_054 = 49.08
Fe
iso_abundance_26_055 = 0
Fe
iso_abundance_26_056 = 697.7
Fe
iso_abundance_26_057 = 21.67
Fe
iso_abundance_26_058 = 3.335
Fe
iso_abundance_27_059 = 2.214
Co
iso_abundance_28_058 = 28.88
Ni
iso_abundance_28_059 = 0
Ni
iso_abundance_28_060 = 11.9
Ni
iso_abundance_28_061 = 0.5992
Ni
iso_abundance_28_062 = 1.426
Ni
iso_abundance_28_064 = 0.3039
total_cross_section
= 2
Ni
=0 -Letaw83; =1 - WA96 Z.gt.5 and BP01 Z.lt.6;
=2 -BP01 (2-best)
cross_section_option = 012
100*i+j i=1: use Heinbach-Simon C,O->B j=kopt
j=11=Webber, 21=ST
t_half_limit
= 1.0e4
year - lower limit on radioactive half-life
for explicit inclusion
primary_electrons
= 1
secondary_electrons
= 1
knock_on_electrons
= 0
1,2 1=compute knock-on electrons (p,He) 2=
use factor 1.75 to scale pp,pHe
secondary_positrons
= 1
secondary_protons
= 1
secondary_antiproton = 2
1=uses nuclear scaling; 2=uses nuclear factors
by Simon et al. (1998)
160
tertiary_antiproton
= 1
skymap_format
= 0
fitsfile format: 0=old format (the default),
1=mapcube for glast science tools, 2=both, 3=healpix
output_gcr_full
= 0
output full galactic cosmic ray array
warm_start
= 0
read in nucle file and continue run
verbose
= 0
verbosity: -1=min,10=max
test_suite
= 0
test suite instead of normal run
161
162
Bibliography
[1] A. Coc et al. Standard Big Bang Nucleosynthesis up to CNO With an Improved
Extended Nuclear Network. ApJ, 744:158, 2012.
[2] E. Komatsu et al. Seven-Year Wilkinson Microwave Anisotropy Prob (WMAP
Observations: Cosmological Interpretation). ApJS, 192:18, 2011.
[3] K. Cunha. Boron Abundances in the Galactic Disk. In IAU Symposium, number
268, 2010.
[4] J. George et al. Elemental Composition and Energy Spectra of Galactic Cosmic
Rays During Solar Cycle 23. ApJ, 698:1666, 2009.
[5] V. Ptuskin. Propagation of galactic cosmic rays. Astropart. Phys., 39:44, 2012.
[6] J. Engelmann et al. Charge composition and energy spectra of cosmic-ray nuclei
for elements from Be to Ni. Results from HEAO-3-C2. Astron. Astrophys.,
233:96, 1990.
[7] S. Swordy et al. Relative Abundances of Secondary and Primary Cosmic Rays
at High Energies. ApJ, 349:625, 1990.
[8] A. Panov et al. Relative abundances of cosmic ray nuclei B-C-N-O in the energy
region from 10GeV/n to 300 GeV/n. Results from ATIC-2 (the science flight of
ATIC). In 30th International Cosmic Ray Conference, 2007.
[9] H. Ahn et al. Measurements of cosmic-ray secondary nuclei at high energies
with the first flight of the CREAM balloon-borne experiment. Astroparticle
Physics, 30:133, 2008.
[10] A. Obermeier et al. Energy Spectra of Primary and Secondary Cosmic-Ray
Nuclei Measured with TRACER. ApJ, 742:14, 2011.
[11] M. Aguilar et al. Relative Composition and Energy Spectra of Light Nuclei in
Cosmic Rays: Results from AMS-01. ApJ, 724:329, 2010.
[12] A. Strong et al. Cosmic-Ray Propagation and Interactions in the Galaxy. Annu.
Rev. Nucl. Part. Sci., 57:285, 2007.
[13] O. Adriani et al. PAMELA results on the cosmic-ray antiproton flux. Phys.
Rev. Lett., 105:121101, 2010.
163
[14] M. Aguilar et al. First Result from the Alpha Magnetic Spectrometer on the
International Space Station: Precision Measurement of the Positron Fraction
in Primary Cosmic Rays of 0.5-350 GeV. Phys. Rev. Lett., 110:141102, 2013.
[15] N. Tomassetti et al. Identification of Light Cosmic-Ray Nuclei with AMS-02.
In 33rd International Cosmic Ray Conference, number 896, 2013.
[16] W. Shen et al. Total Reaction Cross Section for Heavy-Ion Collisions and Its
Relation to the Neutron Excess Degree of Freedom. Nucl. Phys. A, 130:146,
1989.
[17] F. Iocco et al. Primordial nucleosynthesis: From precision cosmology to fundamental physics. Phys. Rep., 472:1, 2009.
[18] K. Olive et al (Particle Data Group). The Review of Particle Physics. Chin.
Phys. C, 38:090001, 2014.
[19] M. Pettini et al. Deuterium abundance in the most metal-poor damped Lyman
alpha system: converging on Ωb,0 h2 . Mon. Not. R. Astron. Soc., 391:1499, 2008.
[20] T. Bania et al. The cosmological density of baryons from observations of 3 He+
in the Milky Way. Nature, 415:54, 2002.
[21] L. Sbordone et al. The metal-poor end of the Spite plateau: I. Stellar parameters, metallicities, and lithium abundances. A&A, 522:A26, 2010.
[22] D. Ostile et al. An introduction to modern stellar astrophysics. Pearson AddisonWesley, 2007.
[23] F. Hoyle. On Nuclear Reactions Occurring in Very Hot Stars. I. The Synthesis
of Elements from Carbon to Nickel. ApJS, 1:121, 1954.
[24] E. Anders et al. Solar-system abundances of the elements. Geochimica et
Cosmochimica Acta, 46:2363, 1982.
[25] K. Kaufer. Observations of light elements in massive stars. In IAU Symposium,
number 268, 2010.
[26] K. Nakamura. Boron Synthesis in Type Ic Supernovae. ApJL, 718:L137, 2010.
[27] W. Baade et al. Cosmic Rays From Super-Novae. Proc. N. A. S, 20:259, 1934.
[28] R. Diehl et al. Radioactive
439:45, 2006.
26
Al from massive stars in the Galaxy. Nature,
[29] S. Smartt. Progenitors of Core-Collapse Supernovae. Annu. Rev. Astron. Astrophys., 47:63, 2009.
[30] A. Strong et al. Global Cosmic-Ray-Related Luminosity and Energy Budget of
the Milky Way. ApJL, 722:L58, 2010.
164
[31] M. Ackermann et al. Detection of the Characteristic Pion-Decay Signature in
Supernova Remnants. Science, 339:807, 2013.
[32] A. Bell. The acceleration of cosmic rays in shock fronts - I. Mon. Not. R. Astr.
Soc., 182:147, 1978.
[33] A. Bell. The acceleration of cosmic rays in shock fronts - II. Mon. Not. R. Astr.
Soc., 182:443, 1978.
[34] T. Gaisser. Cosmic Rays and Particle Physics, chapter 11. Cambridge University Press, 1973.
[35] E. Fermi. On the Origin of the Cosmic Radiation. Phys. Rev., 75:1169, 1949.
[36] D. Gaggero. Cosmic Ray Diffusion in the Galaxy and Diffuse Gamma Emission,
chapter 2. Sprinter, 2012.
[37] J. Bennett et al. The Cosmic Perspective, chapter 19. Addison-Wesley, 2010.
[38] A. Strong et al. Propagation of Cosmic-Ray Nucleons in the Galaxy. ApJ,
509:212, 1998.
[39] G. Gilmore et al. Kinematics, Chemistry, and Structure of the Galaxy. Annu.
Rev. Astron. Astrophys., 27:555, 1989.
[40] R. Beck et al. Galactic and Extragalactic Magnetic Field. AIP Conf. Proc.,
1085:83, 2008.
[41] R. Beck. Galactic and extragalactic magnetic fields - a concise review. Astrophys. Space Sci. Trans., 5:43, 2009.
[42] L. Burlaga et al. Magnetic Field Observations as Voyager 1 Entered the Heliosheath Depletion Region. Science, 341:147, 2013.
[43] H. Alfven. Existence of Electromagnetic-Hydrodynamic Waves.
150:405, 1942.
Nature,
[44] J. Armstrong et al. Electron Density Power Spectrum in the Local Interstellar
Medium. ApJ, 443:209, 1995.
[45] A. Kolmogorov. The local structure of turbulence in incompressible viscous
fluid for very large Reynolds numbers. Proc. R. Soc. Lond. A, 434:9, 1991.
[46] M. Haverkorn et al. The Outer Scale of Turbulence in the Magnetoioinzed.
ApJ, 680:362, 2008.
[47] S. Ter-Antonyan. Sharp knee phenomenon of primary cosmic ray energy spectrum. Phys. Rev. D, 89:123003, 2014.
[48] J. Philibert. One and a Half Century of Diffusion: Fick, Einstein, before and
beyond. Diffusion Fundamentals, 2:1, 2005.
165
[49] J. Wallace. A Diffusion Model for Cosmic Ray Propagation in the Galaxy.
Astrophys. & Space Sci., 68:27, 1980.
[50] V. Ginzburg et al. On the origin of cosmic rays: Some problems in high energy
astrophysics. Rev. Mod. Phys., 48:161, 1976.
[51] T. Gaisser. Cosmic Rays and Particle Physics, chapter 9. Cambridge University
Press, 1973.
[52] F. Jones. Examination of the ”Leakage-Lifetime” Approximation in CosmicRay Diffusion. Phys. Rev. D, 2:2787, 1970.
[53] V. Ptuskin. On Using the Weighted Slab Approximation in Studying the Problem of Cosmic-Ray Transport. ApJ, 465:972, 1996.
[54] V. Berezinkii et al. Astrophysics of Cosmic Rays. North Holland, 1990.
[55] C. Evoli et al. Cosmic ray nuclei, antiprotons and gamma rays in the galaxy:
a new diffusion model. JCAP, 10:018, 2008.
[56] T. Cravens. Physics of Solar System Plasmas, chapter 6. Cambridge University
Press, 1997.
[57] L. Svalgaard et al. Structure of the extended solar magnetic field and the
sunspot cycle variation in cosmic ray intensity. Nature, 262:766, 1976.
[58] S. Solanki et al. The solar magnetic field. Rep. Prog. Phys., 69:563, 2006.
[59] L. Gleeson et al. Solar Modulation of Galactic Cosmic Rays. ApJ, 154:1011,
1968.
[60] E. Parker. The Passage of Energetic Charged Particles Through Interplanetary
Space. Planet. Space Sci, 13:9, 1965.
[61] I. Usoskin et al. Solar modulation parameter for cosmic rays since 1936 reconstructed from ground-based neutron monitors and ionization chambers. J.
Geophys. Res., 116:A02104, 2011.
[62] G. Hulot et al. The Magnetic Field of Planet Earth. Space Sci. Rev., 152:159,
2010.
[63] M. Abdu et al. South Atlantic magnetic anomaly ionization: A review and
a new focus on electrodynamic effects in the equatorial ionosphere. JASTP,
67:1643, 2005.
[64] C. Finlay et al. International Geomagnetic Reference Field: the eleventh generation. Geophys. J. Int., 183:1216, 2010.
[65] C. Stormer. The Polar Aurora. Clarendon Press, 1955.
166
[66] D. Smart. A review of geomagnetic cutoff rigidities for earth-orbiting spacecraft.
Adv. Space Res., 36:2012, 2005.
[67] A. Strong et al. A Galactic Cosmic-Ray Database. In 31st International Cosmic
Ray Conference, 2009.
[68] G. Bertone et al. Particle dark matter: evidence, candidates and constraints.
Phys. Rep., 405:279, 2005.
[69] P. Kiraly et al. Antiprotons in the cosmic radiation. Nature, 293:120, 1981.
[70] S. Hawking. Black hole explosions? Nature, 248:30, 1974.
[71] I. Cholis et al. Constraining the origin of the rising cosmic ray positron fraction
with the boron-to-carbon ratio. Phys. Rev. D, 89:043013, 2014.
[72] I. Cholis et al. Dark matter and pulsar origins of the rising cosmic ray positron
fraction in light of new data from the AMS. Phys. Rev. D, 88:023013, 2013.
[73] M. Cirelli et al. PPPC 4 DM ID: a poor particle physicist cookbook for dark
matter indirect detection. JCAP, 03:051, 2011.
[74] M. Cirelli et al. Antiprotons from Dark Matter: current constraints and future
sensitivities. JCAP, 04:015, 2013.
[75] A. Kounine. The Alpha Magnetic Spectrometer on the International Space
Station. Int. J. Mod. Phys. E, 21:1230005, 2012.
[76] M. Aguilar et al. The Alpha Magnetic Spectrometer (AMS) on the International
Space Station: Part I - results from the test flight on the space shuttle. Phys.
Rep., 366:331, 2002.
[77] M. Heil et al. Operations and alignment of the AMS-02 Transition Radiation
Detector. In 33rd International Cosmic Ray Conference, number 1232, 2013.
[78] H. Gast et al. Identification of cosmic-ray positrons with the transition radiation
detector of the AMS experiment on the International Space Station. In 33rd
International Cosmic Ray Conference, number 359, 2013.
[79] W. Sun et al. Measurement of the absolute charge of cosmic ray nuclei with
the AMS Transition Radiation Detector. In 33rd International Cosmic Ray
Conference, number 940, 2013.
[80] G. Ambrosi et al. In-flight operations and efficiency of the AMS-02 Silicon
Tracker. In 33rd International Cosmic Ray Conference, number 849, 2013.
[81] J. Alcaraz et al. The Alpha Magnetic Spectrometer Silicon Tracker: Performance results with protons and Helium nuclei. Nucl. Instr. Meth. Phys. Res.
A, 593:376, 2008.
167
[82] P. Zuccon. The AMS Silicon Tracker: Construction and performance. Nucl.
Instr. Meth. Phys. Res. A, 596:74, 2008.
[83] G. Ambrosi et al. Alignment of the AMS-02 Silicon Tracker. In 33rd International Cosmic Ray Conference, number 1260, 2013.
[84] G. Ambrosi et al. AMS-02 Track reconstruction and rigidity measurement. In
33rd International Cosmic Ray Conference, number 1064, 2013.
[85] G. Ambrosi et al. Nuclear Charge Measurement With the AMS-02 Silicon
Tracker. In 33rd International Cosmic Ray Conference, number 789, 2013.
[86] V. Bindi et al. The scintillator detector for the fast trigger and time-of-flight
(TOF) measurement of the space experiment AMS-02. Nucl. Instr. Meth. Phys.
Res. A, 623:968, 2010.
[87] V. Bindi et al. The AMS-02 time of flight (TOF) system: construction and
overall performances in space. In 33rd International Cosmic Ray Conference,
number 1046, 2013.
[88] V. Bindi et al. Calibration and Performance of the AMS-02 Time of Flight
Detector. In 33rd International Cosmic Ray Conference, number 1097, 2013.
[89] J. Casaus. The AMS RICH detector. Nucl. Phys. B (Proc. Suppl.), 113:147,
2002.
[90] W. Gillard et al. High precision measurement of the AMS-RICH aerogel refractive index with cosmic ray. In 33rd International Cosmic Ray Conference,
number 742, 2013.
[91] F. Giovacchini et al. In-flight determination of the AMS-RICH photon yield.
In 33rd International Cosmic Ray Conference, number 1028, 2013.
[92] C. Adloff et al. The AMS-02 lead-scintillating fibres Electromagnetic Calorimeter. Nucl. Instr. Meth. Phys. Res. A, 714:147, 2013.
[93] S. Falco et al. Performance of the AMS-02 Electromagnetic Calorimeter in
Space. In 33rd International Cosmic Ray Conference, number 1028, 2013.
[94] L. Basara et al. Energy calibration with MIP in space and charge measurement
with AMS-02 Electromagnetic Calorimeter. In 33rd International Cosmic Ray
Conference, number 917, 2013.
[95] Ph. von Doetinchem et al. The AMS-02 Anticoincidence Counter. Nucl. Phys.
B (Proc. Suppl.), 197:15, 2009.
[96] A. Basili et al. The TOF-ACC flight electronics for the fast trigger and time
of flight of the AMS-02 cosmic ray spectrometer. Nucl. Instr. Meth. Phys. Res.
A, 707:99, 2013.
168
[97] F. Cadoux et al. The Electromagnetic Calorimeter Trigger System for the
AMS-02 Experiment. IEEE Trans. Nucl. Sci., 55:817, 2008.
[98] S. Agostinelli et al. GEANT4 - a simulation toolkit. Nucl. Instr. Meth. Phys.
Res. A, 506:250, 2003.
[99] A. Capella et al. Dual parton model. Phys. Rev. Lett., 236:225, 1994.
[100] Y. Galaktionov. Antimatter in cosmic rays. Rep. Prog. Phys., 65:1243, 2002.
[101] A. Sakharov. Violation of CP invariance, C asymmetry, and baryon asymmetry
of the universe. Sov. Phys. Usp., 34:392, 1991.
[102] K. Abe et al. Search for Antihelium with the BESS-Polar Spectrometer. Phys.
Rev. Lett., 108:131301, 2012.
[103] J. Alcaraz. Track fitting in slightly inhomogeneous magnetic fields. Nucl. Instr.
Meth. Phys. Res. A, 553:613, 2005.
[104] A. Chikanian et al. A momentum reconstruction algorithm for the PHENIX
spectrometer at Brookhaven. Nucl. Instr. Meth. Phys. Res. A, 371:480, 1996.
[105] E. Aprile et al. Noble Gas Detectors, chapter 2. Wiley-VCH, 2006.
[106] J. Bushberg et al. The Essential Physics of Medical Imaging, chapter 3. Lippincott Williams & Wilkins, 2006.
[107] W. Blum et al. Particle Detection with Drift Chambers. Springer, 2008.
[108] L. Landau. On the energy loss of fast particles by ionization. J. Phys. (USSR),
8:201, 1944.
[109] D. Reames et al. Observation on the Elemental Abundances of Low-Energy
Cosmic Rays in July 1964. Phys. Rev., 149:991, 1964.
[110] D. Mueller et al. Multiple electron stripping of heavy ion beams. Laser and
Particle Beams, 20:551, 2002.
[111] A. Korejwo et al. Isotopic cross section of 12 C fragmentation on hydrogen
measured at 1.87 and 2.69 GeV/nucleon. J. Phys. G: Nucl. Part. Phys., 28:1199,
2002.
[112] P. Bentley et al. Boron-10 Abundance in Nature. Nature, 182:1156, 1958.
[113] W. Richardson. Bayesian-Based Iterative Method of Image Restoration. Journal
of the Optical Society of America, 62:55, 1972.
[114] L. Lucy. An iterative technique for the rectification of observed distributions.
The Astronomical Journal, 79:745, 1974.
169
[115] G. D’Agostini. A multidimensional unfolding method based on Bayes’ theorem.
Nucl. Instr. Meth. Phys. Res. A, 362:487, 1995.
[116] J. Childers et al. Expected Boron to Carbon at TeV energies. In 30rd International Cosmic Ray Conference, number 585, 2007.
[117] J. Howard. Introduction to Plasma Physics, chapter 7. Australian National
University, 2002.
[118] G. Feldman et al. Unified approach to the classical statistical analysis of small
signals. Phys. Rev. D, 57:3873, 1998.
170