Cosmic Ray Lithium Isotope Measurement with AMS-01
by
Feng Zhou
Bachelor of Science, Shanghai Jiaotong University (2001)
Master of Science, Shanghai Jiaotong University (2004)
Submitted to the Department of Physics
in Partial Fulfillment of the Requirements for the Degree of
MASSACHUSETTS t INSTITUTE
TocCH
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?Y
IOF
Doctor of Philosophy
NOV 18 2010
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
~~~1V~
ARCHVES
September 2009
© Massachusetts Institute of Technology 2009.
LIBRARIES
All rights reserved.
-7T
Author
Departoent of Physics
September, 2009
Certified by
Ulrich J. Becker
Professor of Physics
Thesis Supervisor
Accepted by_
Th 9 'as J. Greytak
Associate Department H atlfor Education
2
Cosmic Ray Lithium Isotope Measurement with AMS-0 1
by
Feng Zhou
Submitted to the Department of Physics
on July 30th, 2009 in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy
Abstract
The AMS-01 detector measured charged cosmic rays during 10 days on the Space Shuttle
Discovery in 1998 and collected 108 events. By identifying 8349 Lithium and 22709 Carbon
nuclei from the raw data, this thesis presents the measurement of cosmic ray Lithium to
Carbon ratio of presently highest statistics and momentum resolutions in the rigidity range of
2 GV to 100 GV. The 7Li to 6Li ratio is measured to be 1.07±0.16 in the rigidity region
achieved from 2.5 GV to 6.3 GV. The experimental results are used to provide constraints
on cosmic ray propagation models and address the "Lithium Problems".
Thesis Supervisor: Ulrich J. Becker
Title: Professor
4
Acknowledgments
First and foremost I would like to express my gratitude to my advisor, Professor Ulrich
Becker, for his initial idea for this work, and invaluable support, supervision and useful
suggestions through the analysis. Without his guidance, this thesis would not have been
possible. I would also like to thank Professor Samuel Ting for providing me the wonderful
opportunity of studying at MIT and working on the AMS experiment. I am also particularly
grateful to Professor Peter Fisher for showing me the essence of data analysis and providing
incredible advice throughout my study. A great deal of gratitude also goes to my committee
members for a careful reading of my thesis: Professor John Belcher and Professor lain
Stewart.
In addition, I am highly thankful to many students who have assisted me throughout the
years: Benjamin Monreal, Gianpaolo Carosi and Gray Rybka for patiently explaining to me
the details of the AMS-01 experiment and data analysis techniques; Sa Xiao for her valuable
assistance on data analysis, especially the GALPROP program; Yue Zhou for showing me the
Tracing program; Scott Hertel for his help on my English and editing the thesis; and Wei Li
for nice discussion on Physics. I wish them endless success in their careers.
I would like to thank the entire AMS collaboration. Their successful completion on
AMS-0I flight makes this work possible.
I deeply appreciate my parents. I would not be writing this thesis if it weren't for their
love and continuous support.
Finally I would like to dedicate this thesis to my wife, Jianhong Zhang, for her love and
for believing in me.
6
Contents
1 Introduction ............................................................................................................................
2 M ysteries of C osm ic L ithium .....................................................................................
17
2.1.2
Galactic Cosm ic Ray Production.............................................................................
19
2.1.3
Stellar Production......................................................................................................
22
Lithium Problem ..................................................................................................................
......................................
Proposed M odel Explanations................... ...............................
24
2.2
2.3
C harged C osm ic Rays ..................................................................................................
18
25
29
Cosm ic Ray Origin and A cceleration.............................................................................
Galactic Cosmic Ray Propagation............. ............................ ...................................
29
3.2.1
Galactic Structure......................................................................................................
32
3.2.2
Propagation M odels...................................................................................................
33
3.2.3
34
GALPROP Properties.................................................................................................
.. 36
. -----------...............................----Li/C Ratio Constraints on Dxx and V A---- ...
3.1
3.2
3.2.4
32
38
3.4
Solar M odulation...............................................................................................................
Geom agnetic Field .............................................................................................................
3.5
M easurem ent of Cosm ic Ray Lithium ...........................................................................
40
The Alpha M agnetic Spectrometer (AM S-01).................................................
42
The A M S-01 Detector .....................................................................................................
42
4 .1.1 M a g ne t.............................................................................................................................
42
4 .1.2
T ra c ke r.............................................................................................................................
44
4.1.3
Tim e of Flight.............................................................................................................
46
4.1.4
Anticoincidence Counter..........................................................................................
47
4.1.5
A erogel Threshold Cerenkov Counter (A TC).......................................................
48
3.3
4
17
Origin of Lithium Isotopes...................................................................................................
2.1.1 Big Bang N ucleosynthesis (BBN )..........................................................................
2.1
3
15
4.1
4 .2
T h e F lig h t ...............................................................................................................................
7
38
48
4.3
Trigger and Livetime............................................49
4.4
Event R econstruction ............................................................................................................
4.4.1
Velocity Reconstruction.........................................................................
4.4.2
....... 51
Track Reconstruction and Rigidity Measurement......................52
4.4.3
Charge Reconstruction ............................................................................
4.4.4
Mass Reconstruction
Isotopesdi.M........
5 Data Analysis...............................
............
.................................................
.............................................................
5.1
Event Preselectionre.......
5.2
R igidity M easurem ent............................................................................................
...............
Velo city S election .................................................................................................................
5.3
5 .4
54
55
56
58
56
5.4.1
Energy Loss of Charged Particles..........
.................................................................
59
5.4.2
Cluster Selection and Velocity Dependence ...........................................................
Charge Identification by Gaussian Fit.....................................................................
61
5.5
63
Eliminate Atmospheric Secondary Particles.................................................................
64
Monte Carlo Simulation for Detector Acceptance.......................................................
5.6.1 Monte Carlo Simulation...................
....................................................................
71
71
5.6.2
71
5.6
5.6.3
Acceptance and Efficiency ......
....................................................................
Rigidity Unfolding .........................................................................................................
73
Results...............................................77
6.1
6 .2
Li/C Abundance R atio .....................................................................................................
7L i to 6L i R atio .......................................................................................................................
77
6.3
Constraints on GALPROP Parameters ..........................................................................
84
6.4
Constraint on the Lithium Problems ...................................................................................
Fu ture O u tloo k .......................................................................................................................
86
6 .5
7
53
....................................................................................
...........................................................................................................
5.4.3
6
51
C o n c lu sio n s .............................................................................................................................
79
86
89
A F ermi A ccelera tio n ..............................................................................................................
91
B T h e A M S-02 D etector ........................................................................................................
C GALPROP Parameter Setting ......................................................................................
95
97
List of Figures
2.1
2.2
2.3
2.4
2.5
3.1
3.2
3.3
3.4
The nuclides involved in Big Bang Nucleosynthesis and the most important
* The beta decay of 7Be occurs late in the time of
reactions that relate them.
18
recombination and ultimately contributes to the 7Li observation ...............................
7
The primary abundances of 4He, 2H, 3He, and Li as predicted by the standard
model of BBN [4]. The bands show the 95% CL range. Boxes indicate the
observed light element abundances (smaller boxes: ±2G statistical errors; larger
boxes: ±2a statistical and systematic errors). The narrow vertical band indicates the
CMB measure of the cosmic baryon density, while the wider band indicates the
BBN concordance range (both at 95% CL). The 5-year WMAP study [19] reports
20
- = 6.23 + 0.17 x 10-' 0 , see section 2.2...................................................
The relative chemical abundances for GCRs (solid line) and within the solar system
(dashed line) [20]. The differences between these two regimes are most evident
for the secondary particles (LiBeB) and the sub-Iron group.............................. 21
Lithium production cross section measurements: (a) a fusion [21]. The lines
are simple exponential fits. (b) Spallation of CNO [22]. Solid circle symbols are
accumulated data and dashed lines are evaluated cross sections in [22]................. 21
Observed logarithmic abundances of 7Li (open triangles) and 6Li (filled circles) as
a function of [Fe/ H] for UVES. The large circle corresponds to the solar system
meteoritic 6Li abundance [43], while the solid line is the predicted 7Li abundance
from WMAP+BBN prediction [19]. The dotted line is zero metallicity 7 Li
abundance [36] and dashed line is the average 6Li abundance for UVES. logE(Li)
26
is defined as logE(Li) = log(Li/H) + 12.....................................................
30
Major components of the primary cosmic radiation from [4]............................
Side view of the Milky Way and schematic propagation of cosmic rays............... 32
Beryllium isotope ratio measurements from [24]. The listed experiments will be
discussed in section 3.5. The solid line is the GALPROP model and the dashed
35
lines are two Leaky Box models [59].......................................................
The effects of diffusion coefficient and Alfven velocity on the Li/C ratio, simulated
3.5
3.6
3.7
4.1
4.2
4.3
4.4
4.5
4.6
5.1
5.2
5.3
5.4
5.5
5.6
by GALPROP. The red curve represents the theoretical Li/C ratio prediction from
the default GALPROP parameter set Dxx=5.75cm 2 s' and VA=36kms-' [6, 75].
In (a) we fix VA and change the D, while in (b) we make opposite parameter
adju stm ents........................................................................................
Schematic view of motion of charged particles in Earth magnetic field [80]...........
Li/C ratio versus kinetic energy (GeV/nucleon). The solid curve is from the
GALPROP prediction assuming low solar modulation (potential D=500MV). See
the table 3.1 for the corresponding reference...............................................
7Li/ 6Li ratio versus
kinetic energy (GeV/nucleon)........................................
The AMS-01 schmetic and sketch [1].......................................................
AMS-01 magnet dimensions and field orientation [1]. 64 groups of Nd-Fe-B block
are arranged such that a uniform 0. 15T dipole field is created inside the bore, and
less than 60 G outside to prevent interference with electronics..........................
An exploded view of AMS-01 tracker ladder.............................................
The tw o upper TO F planes......................................................................47
AMS-01 in the space shuttle Discovery....................................................
Zenith angle of AMS-01 in ten-day flight, from [69]. The cartoon on the right
illustrates the definition of zenith angle......................................................
Rigidity resolution as a function of rigidity for Li, B and C..............................
Scintillator paddle occupancy for each TOF plane........................................
Schematic view of residual distance calculation..............................................
Mean energy loss for pions in liquid hydrogen, gaseous helium, Aluminum, iron,
tin and lead [4]...................................................................................
Occupancy level for ladder 9 on the second layer of Tracker. The red line
indicates the level of 65% of average occupancy in that ladder.........................
Average energy deposition on Tracker as a function of velocity from 0.6 to 0.95.
37
39
42
42
44
44
45
50
51
57
58
59
60
61
The function for solid curves is - = A - p--", where A is a constant..................... 62
dx
5.7
5.8
5.9
Mean energy deposition on Tracker for Charge from 3 to 8. Red curve is the fit to
six Gaussians. Nitrogen and Oxygen are suppressed due to the ACC triggering by
6 ray s.........................................................................................
. . .. 6 3
The longitude and latitude coverage of AMS-01 flight. (a) is in the Geographic
Coordinate system and (b) is in the Geomagnetic Coordinate system. The South
Atlantic Anomaly (SAA) is labeled. The discontinuities are due to the trigger
suppression of proton data......................................................................
65
AMS-01 proton spectra at different geomagnetic latitudes. The apices in the low
rigidity region of low geomagnetic latitude spectra consist of mostly Albedo
6
666...........................
proton s
5.10 (a) Full trace-back track of the proton from the birth in the atmosphere (10 s) to the
detection by AMS-01 (0 s). The altitude is measured from the Earth's center.
(b) shows its partial track, which demonstrates the three motions in the Earth's
67
magnetic field: cyclotron, bounce and drift.................................................
5.11 Proton spectrum at geomagnetic latitude less than 0.1. Red curve represents the
proton spectrum after removing the Albedo and Trapped protons....................... 68
5.12 (a) Lithium and (b) Carbon spectra. Black histogram is the AMS-01 data after
selection cuts discussed in section 5.1-5.4. Blue and green histograms are the
69
identified atmospheric events after back tracing............................................
5.13 Spectra after selection cuts of (a) Lithium and (b) Carbon. 8349 Lithium and
70
22709 Carbon events are kept after selection cuts..........................................
5.14 Acceptance for Lithium and Carbon. Efficiency correction has been included........ 72
5.15 Resolution Matrices for (a) Lithium and (b) Carbon. The darkness represents the
probability. Notice that Lithium has better rigidity resolution than Carbon.
74
Squares are due to calculation coarseness in domains.....................................
5.16 Unfolded (a) Lithium and (b) Carbon spectra, compared with folded spectra.
Notice that Carbon spectrum has larger correction due to the worse rigidity
. 75
resolution ........................................................................................
6.1 Lithium to carbon ratio measured by AMS-01. Errors include statistical errors of
data, and a 3.5% detector efficiency (see section 5.6.2), summed in quadrature since
they are uncorrelated. The solid curve is the best fit from GALPROP including
solar modulation (CD=580MV for AMS-01 flight), see section 6.3. The other six
experiment data sets were converted from kinematic energy to rigidity for
comparison, refer to table 3.1 for the corresponding references. The reason these
measured values lie below the prediction curve is that the solar activity was much
smaller when these measurements were carried out than during the AMS-0 1 flight
. . 78
in 199 8..........................................................................................
6.2 Lithium Mass distribution fit assuming 7 Li/ 6Li= 12.1. The black dots are the
AMS-01 lithium data, two shadowed histograms represent the Monte Carlo 6 Li
(brown) and 7Li (blue), and the red histogram is the sum of Monte Carlo 6Li and 7 Li
80
as the best fit to the data.......................................................................
6.3 Lithium Mass distribution fit. Normalization factors for Monte Carlo 7Li and 6Li
81
are both free param eters.......................................................................
6.4 Confidence intervals for the Monte Carlo 6Li and 7Li normalization factors. The
two normalization factors are negatively correlated. The correlation has been
82
taken into the error analysis of the 7Li/ 6Li ratio..............................................
6.5
7Li/ 6Li
ratio versus rigidity. The previous experimental data have been converted
from the kinetic energy to rigidity, refer to table 3.1 for the corresponding
references. Because of the conversion, the results have upward trend compared to
Figure 3.7. The blue curve is from the GALPROP prediction.........................
6.6 Confidence intervals for diffusion coefficient Dxx and Alfven velocity VA. The
color code represents the value of Chi Square x2 . Inner contour is for 50%
confidence level and the outer one is for 68.3% (1) confidence level.................
6.7 Projected ratio measurements [72]: (a) B/C results from 6 months of AMS-02 and
(b) 10Be/ 9Be results from 1 year of AMS-02...............................................
A. 1 Schematic view of one cycle of shock wave acceleration...................................92
B.l The schematic view of AMS-02 detector..................................................
83
85
87
96
List of Tables
2.1
2.2
3.1
5.1
6.1
Li/H abundance ratio measurements. Refer to section 2.2 for details of the MPH
23
stars and CMB measurements.................................................................
7Li/ 6Li isotope ratio measurements...........................................................
24
Summary list of previous experiments which measured cosmic ray lithium isotopes
41
with energy < 1TeV/nucleon....................................................................
71
Selection cuts on Lithium and Carbon data....................................................
83
AM S-01 7Li/ 6 Li ratio results......................................................................
14
Chapter 1
Introduction
In June of 1998 the Alpha Magnetic Spectrometer (AMS-01) [1, 2] launched on the Space
Shuttle Discovery for a 10 day mission at an altitude between 320 and 390km, a suitable place
for cosmic ray measurement because of the absence of atmosphere. The AMS experiment is
designed primarily to search for dark matter and antimatter by studying cosmic rays. During
the flight, 100 million events with kinetic energies at MeV to TeV scales were collected and
precisely measured. This thesis presents the results of cosmic ray lithium to carbon ratio and
lithium isotope ratio using the AMS-0 1 data.
For more than thirty years lithium isotopes (6Li and 7Li) have been recognized as an
efficient probe of nueclosynthesis in the universe [3]. The primordial lithium isotopes
produced in the Big Bang Nucleosynthesis (BBN) retain the footprint of the early universe
and provide tight constraints on cosmological constants [4, 5]. The lithium isotopes in
cosmic rays, stellar atmospheres, and the interstellar medium record subsequent stages of
evolution [3, 6, 7, 8]. Even with the large number of observations at different astrophysical
regions, there are still many unsolved questions on lithium isotopes: the reason for large
discrepancy of 7Li/ 6 Li ratio between solar system and cosmic rays is not yet clear [9, 10], and
the recent two "Lithium Problems" [11, 12] for primordial lithium isotopes have spurred
many new hypotheses on stellar models, BBN and cosmological/galactic cosmic rays. The
precise experimental characterization of cosmic ray lithium isotopes is essential for solving
these problems.
The cosmic ray lithium to carbon ratio, so-called 'secondary to primary' ratio, has long
been used to probe models of cosmic ray propagation within the Milky Way, because most
cosmic ray lithium isotopes are expected to be produced by the spallation of carbon, nitrogen
and oxygen during their propagation through the galaxy. GALPROP [6], a diffusive galactic
propagation model, has been widely used by many cosmic ray experiments, such as AMS,
PAMELA, Fermi/GLAST, etc. to interpret their observations. The cosmic ray lithium to
carbon ratio can provide good constrains on the propagation parameters in GALPROP, and
thus further assist in the interpretation of these many experiments' results.
Since 1970's, the direct measurement of cosmic ray lithium isotopes, especially the Li/C
and 7 Li/6 Li ratios, has been achieved through both balloon-borne and space-bome
experiments. But most measurements are done in the energy region below 1 GeV/nucleon.
Only a very small amount of data is available above 1 GeV/nucleon with low statistics and
energy resolutions.
From the AMS-01 data, about 4 thousand lithium and 20 thousand carbon nuclei have
been identified using the combined information of the silicon tracker and the scintillators,
which allows us to measure the Li/C and 7 Li/ 6Li ratio in the high energy region with an
unprecedented level of statistics. The Li/C ratio versus rigidity, defined as momentum over
charge, can then be used to constrain two critical Galaxy propagation parameters, the
diffusion coefficient D xx and the Alfven velocity VA.
The outline of the thesis is as follows,
Chapter 2: Mysteries of Cosmic Lithium describes the origin and production mechanism of
lithium isotopes, and briefly reviews the "Lithium Problems" and proposed model
explanations.
Chapter 3: Charged Cosmic Rays presents a general overview of characteristics of cosmic
rays: their origin, acceleration and propagation in the Galaxy. Previous results for other
cosmic ray lithium isotope experiments are summarized.
Chapter 4: The AMS-01 describes the details of the experiment, mission, design, flight, and
constructions of sub-detector components relevant to the data analysis in the following
chapter.
Chapter 5: Data Analysis lays out the specific analysis techniques used to obtain the lithium
and carbon events from the AMS-0 1 raw data.
Chapter 6: Results presents the final results of the Li/C and 7Li/ 6 Li ratio and the best fit to
the propagation parameters in GALPROP.
Chpater 7: Conclusions: summarizes the experimental results and interpretations.
Chapter 2
Mysteries of Cosmic Lithium
The abundance of lithium isotopes (6Li and 7Li) provides important information about the
early universe, galactic evolution, stellar formation and cosmic ray propagation and
interactions [3]. Unlike other heavy (Z>2) nuclei, which are synthesized in stellar formation,
lithium isotopes are fragile and can be easily destroyed in the hot star centers. They are
produced in many other ways, such Big Bang Nucleosynthesis (BBN), cosmic ray nuclear
reactions, and non-equilibrium stellar processes such as supernova or giant star explosions.
The specific mechanisms of stellar production are still under debate.
Recently, two so-called "Lithium Problems" have arisen regarding the disagreement of
the primordial lithium abundance between the experimental observations and the predictions
of the standard BBN model. Many speculative resolutions have been proposed, but the
actual resolution of the Lithium Problems is still far from clear.
Cosmic ray lithium isotopes play an important role in attempts to resolve the above
problems.
In this chapter, we introduce present knowledge of the origins and the production
mechanisms of lithium isotopes. The "Lithium Problems" and possible solutions are briefly
reviewed.
2.1 Origin of Lithium Isotopes
The stellar formation of chemical elements was first proposed by Fred Hoyle and his
collaborators in 1957 [13]. While this idea proved to be correct for heavy nuclei, from
carbon to uranium, it encountered big difficulties when trying to account for the abundances
of light elements such lithium, beryllium and boron (LiBeB), which are very fragile and
rapidly consumed by radiative capture reactions in the stellar center.
Lithium has two stable isotopes, Lithium 6 (6Li) and Lithium 7 (7Li). Since they have
low binding energies, 5.3MeV/nucleon for 6Li and 5.6 MeV/nucleon for 7Li, they are both
destroyed in stellar interiors via 6 Li(p, 3He) 4 He at ~2 million K and 7Li(p,a) 4He at ~2.5 million
K respectively. Significant abundances of lithium can only be produced in regions of rapid
expansion and cooling, e.g., the Big Bang or explosive nucleosynthesis, or in cool rarefied
matter such as the interstellar medium (ISM).
2.1.1
Big Bang Nucleosynthesis (BBN)
The origin of 7Li can be traced back to the very beginning of the universe, at the end of the
"First Three Minutes" after the Big Bang, when the BBN started [14]. At that time the
temperature dropped to 109K which allowed the neutrons and protons to start to form
deuterons. In sequence, more reactions took place for roughly 20 minutes until the
temperature and density of the universe fell below what is required for nuclear fusion. The
nuclear reactions of BBN are illustrated in the Figure 2.1. The specific reactions involved in
the production and destruction of Li are emphasized by the red rectangle.
7 Be
12
11
P-
3He
He
13
1H <
11.
7i3.
2. 'H +n
22H +,y
2H + 'H + He + y
4. 2H + 2 H - He +n
5. 2H + 2 H
[1 2
2H
5
3H
n
+ 3H +'H
6.
7.
+2nH
3He
He~n-) 3+H+H1 H
8.
3He+2H
44He +'H
3He
+ 4 He 4 7 Be+y
3H + 4He
7
'Li + y
11. 7Be + e7Li +Ve*
12. 7Be +n *Li7 +'H
13. 7 Li+ 'H- 4 He + 3He
9.
110.
HFy
n
Figure 2.1: The nuclides involved in Big Bang Nucleosynthesis and the most important
reactions that relate them. *The beta decay of 7Be occurs late in the time of recombination
and ultimately contributes to the 7Li observation.
BBN hypothesis has been a reliable probe of the early universe, and depends on only one
free parameter: baryon density or baryon to photon ratio (9) [4, 15]. The concordance
7
4
between theory and observation of the abundance of the light elements 2H, 3He, He and Li
provides a powerful tool for obtaining the baryon to photon density and a consistency check
for the model itself. Figure 2.2 shows the abundance of the light elements as a function of 1
[4].
produced in BBN, so-called "primordial" 7Li, has abundance of 7Li/H -10 10. The
complicated shape of the abundance curve results from two competing processes, reaction 9
7
and 10. At high rj, the bulk of 7Li is produced as 7Be, which will be converted to Li after
BBN. The sum of these two processes results in the shape of abundance curve.
Deuterium abundance is always taken as the best "baryometer" to constrain the value of
,i, because it is highly sensitive to i and has no other astrophysical source. For comparison,
primordial 7Li abundance was also measured with old halo stars and globular clusters. This
direct measurement is in significant disagreement with a 7Li abundance derived from
measurements of the Cosmic Microwave Background (CMB) radiation shown in Figure 2.2.
The details will be discussed in the later section as one of the two famous "Lithium
7Li
Problems".
In addition to the light elements listed in Figure 1.1, trace amount of 6 Li, Be and B are
4
also produced in the BBN. 6Li abundance is estimated to be of 6 Li/H~10-1 [8]. The
nuclear reactions for the production and destruction are:
4
He+ 2 H - 6Li+y
6Li
'H4He
+
+3 He
2.1.2 Galactic Cosmic Ray Production
The Lithium abundance in the solar system and galactic disk has been measured to be
Li/H~1-2x10- 9 [8, 16, 17], which appears enriched by factor of 10 since BBN. Therefore
there must be other mechanisms which generate the major part of lithium isotopes during the
galactic evolution, such as cosmic ray nuclear reaction.
The idea of Galactic Cosmic Ray (GCR) production of lithium, as well as beryllium and
boron, was introduced in 1970 by Reeves [18], who conjectured that the light elements were
made by the interaction of fast GCRs with the interstellar medium. The enrichment of light
elements can be illustrated by the comparison of the element abundance in cosmic rays and
the solar system as shown in Figure 2.3. Lithium abundance in cosmic rays is 4 orders of
magnitude larger than the solar system abundances, proving GCR production to be an
important, perhaps dominant, mechanism.
0.005
0.27
Baryon density UBh2
0.02
0.01
0.03
0.26
0.25
0.24
0.23
10-3
10-9
5
7Li/H
Ip
10-10
1
3
4
5
6
7
8 9 10
Baryon-to-photon ratio q x 1010
Figure 2.2: The primary abundances of 4He, 2H, 3He, and 7Li as predicted by the standard
model of BBN [4]. The bands show the 95% CL range. Boxes indicate the observed light
element abundances (smaller boxes: +2G statistical errors; larger boxes: +2G statistical and
systematic errors). The narrow vertical band indicates the CMB measure of the cosmic baryon
density, while the wider band indicates the BBN concordance range (both at 95% CL). The
5-year WMAP study [19] reports -1= 6.23 + 0.17 x 10-10, see section 2.2.
10
i
10
C' 0
10
Fe
I()
10
10
10
+
V)
s
10
Sc
La B
Be
10
-6
10
10
25
Charge Z
Figure 2.3: The relative chemical abundances for GCRs (solid line) and within the solar
system (dashed line) [20]. The differences between these two regimes are most evident for
the secondary particles (LiBeB) and the sub-Iron group.
p+N -+LI
0.01
0 100
I
%
I
I
200 30D 400 500 600 700
Ekin (MeV)
.1
1
GeVinuceon
Ekin,
ID
01
1
Ekin, GeV/nucleon
10
(b)
Figure 2.4: Lithium production cross section measurements: (a) a fusion [21]. The lines
are simple exponential fits. (b) Spallation of CNO [22]. Solid circle symbols are
accumulated data and dashed lines are evaluated cross sections in [22].
Lithium isotopes are generated by two GCR production processes: spallation of carbon,
nitrogen and oxygen (CNO) and a fusion [1, 21]. Spallation occurs when energetic cosmic
CNO nuclei interact with interstellar protons and a particles (or vise versa) and split into light
elements. Most cosmic ray LiBeB, so-called secondary particles, are produced in this way.
The secondary to primary abundance ratio plays an important role for cosmic ray propagation
in the galaxy which will be discussed in next chapter.
The a fusion produces only 6Li and 7Li, through reactions 4He + He 4 6 Li _ 2H and 4He
+ 4He 4 7Li + H. It plays a major role in production of 6Li and 7Li in the early galaxy when
the interstellar medium contains very little CNO. But a fusion does not contribute much to
the present cosmic rays above 600 MeV, because the production cross section falls rapidly,
essentially exponentially, with the increasing energy [21]. The production cross sections for
both processes are shown in Figure 2.4.
The 6Li abundance in the solar system and ISM is 6Li/H~10* [20], which is by four
orders of magnitude larger than the BBN production. Therefore GCR production of 6Li
accounts for almost the entirety of the 6 Li in the universe.
2.1.3 Stellar Production
Problems arose when comparing the GCR lithium isotope ratio to the ratios in solar system
and galactic gas composition. As we can see form Figure 2.4, GCR produces almost equal
amount of 6Li and 7Li, a result that has been observed by many cosmic ray experiments [23,
24]. But the measurements on protosolar meteorites [25, 26], Earth [27] and the present ISM
[28] yield a value for 7Li/ 6Li ratio -12, indicating that this ratio has remained nearly constant
during the last 4.5-5 Gyr. Therefore, there must be some extra sources able to produce large
amounts of 7Li without generating 6 Li.
The Asymptotic Giant Branch (AGB) star 7Li production has been studied intensively
since 1970's [29]. The AGB stars are post 4He-core burning objects with a C-O core, around
which a H-burning shell operates, and a deep outer convective envelope. The 3He(a,y) 7 Be
reaction takes place in the deep interior of a star and then 7Be is transported via the
convection zone to outer regions where the temperature is much cooler. The reaction
7
Be(e~,v) 7 Li can then produce 7Li under conditions where the lithium is not rapidly destroyed.
This beryllium transport mechanism was first suggested by Cameron in 1955 [30].
Now
more and more lithium-rich stars have been experimentally discovered [7, 9]. However, it is
hard to estimate their total contribution since it depends on the estimated number of such stars,
which are hidden from observation by their own wind [9]. The estimated contribution is
roughly 10-50% of total 7Li in the universe.
Another major 7Li production mechanism is the neutrino nucleosynthesis in Type II
supernovae (SNII) [31, 32]. When the core of a massive star collapses into a neutron star,
the flux of neutrinos is so great that despite the small cross section they may still induce
considerable nucleosynthesis. The neutrino process in the helium shell is responsible for the
most of the 7Li production in SNII through the following reactions.
v + 4 He 4 3He +v'+n
3 He + 4He
7+ 7 Be
7Be + e- + 7Li + ve
Eventually, 7Li is injected into the ISM by the Supernova explosions. Like the AGB star
case, there are also large uncertainties on the total yields of the SNII [10]. Other stellar
mechanisms, such as explosive hydrogen burning in nova explosions, may also contribute to
the 7Li enrichment [33].
In conclusion, while 6Li only has one simple source, GCR production, 7Li owes its
abundance to three different mechanisms: BBN, GCR spallation and fusion, and stellar
nucleosynthesis. None of the stellar mechanisms has been quantitatively and accurately
estimated nor strongly constrained by observations.
Observations of lithium isotope abundance at different astrophysical local sites are listed
in tables 2.1 and 2.2.
Sample
High energy
cosmic rays
Population I Stars
and interstellar gas
Super Li-Rich stars
(7Li only)
Metal-poor halo
(MPH) stars
WMAP+BBN
Li/H ratio
~10-4
1-3x10_9
10-_107
Method
Direct cosmic ray
nuclei measurement
Li I X=670.7nm
Doublet
Reference
4
[16, 34]
Li I X=670.7nm
Doublet
[9, 35]
1.23x10~10
(6Li) -6.3x10-1 2
Li I X=670.7nm
doublet
[11, 36]
('Li) 5.24x10~"'
(6Li) ~ 10-"
CMB measurement
[4, 19]
Table 2.1: Li/H abundance ratio measurements.
MPH stars and CMB measurements.
Refer to section 2.2 for details of the
Sample
Cosmic rays
(1GeV/n)
Earth
Meteorites (pre-solar)
7Li/ 6Li
ratio
093
-12.1
-12.5
Method
Reference
Direct cosmic ray
nuclei measurement
Mass spectrometer
Mass spectrometer
[24]
[27]
[25]
ISM (present)
-12.5
Li IX670.7nm
doublet
[28]
MPH stars
-20
Li IX670.7nm
doublet
[11]
Table 2.2:
7
Li/ 6Li isotope
ratio measurements.
2.2 Lithium Problems
The lithium problems arise from the significant discrepancy between the primordial 7Li and
6Li abundance as inferred from the observations of metal-poor halo (MPH) stars and predicted
by BBN theory and the Wilkinson Microwave Anisotropy Probe (WMAP) [37] baryon
density.
The first lithium problem: the latest WMAP-based analysis [11] predicts a primordial
7Li abundance of 7Li/H=5.24i07 x 10-10, which is by factor of 4.3 larger than the MPH
stellar observations of Li/H=1.23to+.3 x 10-10 [36]
The observation of primordial Li was promoted first by Spite and Spite in 1982 [3], who
showed that lithium abundance (>95% is 7Li) in the MPH (Population II) stars was
independent of metallicity for [Fe/H]<-1.5*. The constant lithium abundance, commonly
called "the Spite plateau", was interpreted as resulting from a pre-galactic origin, from BBN.
In subsequent years, a voluminous literature has accumulated on the lithium abundance in
MPH stars, but the published lithium abundance varied little from the initial plateau
measurements [11, 38, 39]. In 2000, Ryan reported a slight dependence of lithium
abundance on the metallicity in MPH stars [36], which was attributed to enrichment of
galactic cosmic ray lithium. The primordial lithium abundance is then identified with the
extrapolation of the observed lithium abundance to zero metallicity, commonly cited as
Li/H= 1.230.34x 10-10. This value is recently confirmed by Ultraviolet and Visual Echelle
Spectrograph (UVES) on VLT telescopes [11], which has the highest spectral resolution of
any telescope for this wavelength.
This simple but beautiful picture has been shaken by recent observations from WMAP.
By precisely measuring the CMB anisotropies and mapping these anisotropies to the "acoustic"
peaks in angular power spectrum of the CMB, the WMAP 5-year study has determined the
baryon density, as the only free parameter for BBN, to unprecedented accuracy to be
fiBh2 = 0.02273 + 0.00062 or equivalent to baryon to photon density 11 = 6.23 + 0.17 x
10-10 [40]. Adopting this baryon density in the standard BBN model, Figure 2.2 shows the
7
7
predicted abundance of 4He, 2H, 3He, and Li. The primordial Li abundance is expected to
be 4.3 times larger than the plateau value. Additional support for the reliability of baryon
density comes from the excellent agreement of 2H abundance achieved from the WMAP
prediction and the measured value from quasar absorption systems [41]. This perfect
agreement makes the discrepancy between WMAP predictions and measured values of
lithium abundance even harder to explain.
The second lithium problem is even more serious: a 6Li plateau of 6 Li/H~6.3 X 10-4
has been found [42, 43] and recently confirmed by UVES/VLT, on the MPH stars which
favors the primordial origin, but Standard BBN should only produce trace amounts of 6 Li,
with an abundance of 6Li/H ~10-14; a two orders of magnitude discrepancy.
The 7 Li and 6 Li plateaus measured by UVES/VLT are shown in Figure 2.5.
2.3 Proposed Model Explanations
Many mechanisms have been invoked to explain these two lithium isotope problems.
For 7Li, systematic errors on lithium spectra measurements and nuclear reaction rate
models cannot account for such a significant discrepancy [19], and discarding WMAP
estimation of baryon density will introduce more problems. Therefore the depletion of 7Li
during stellar evolution seems presently the most favored solution. 7Li are assumed to be
destroyed by Li(pa) 4 He when transported deep into the stellar center due to atomic diffusion
or rotationally-induced mixing. Many so-called non-standard stellar models have been
developed by including the rotation, diffusion and mass loss effect to reconcile the 7Li
reduction [44, 45]. But the depletion has only been observed on the main sequence stars,
and may fail on the requirement to deplete 7Li in different stars of different surface
temperature, mass and rotation velocity without introducing large dispersion in the plateau.
Since 6Li are assumed to be only produced in the cosmic rays, the excessive Li
abundance found on MPH stars has been mostly attributed to cosmological/galactic cosmic
rays. The pre-galactic large-scale structure formation [46] or the explosion of Population III
stars [47] produced cosmological cosmic rays which consisted of mostly protons and a
particles. As we discussed in section 2.1.2, 6Li and 7Li were then produced by cosmic ray a
fusion and brought to the atmosphere of MPH stars. Galactic cosmic rays are also expected
to provide extra 6Li and 7Li by CNO spallation to MPH stars [48].
To reconcile the potential depletion of both lithium isotopes during the stellar evolution,
the production of 6Li by the interaction of in situ solar-like flares [49] with MPH stellar
atmosphere is also proposed as one explanation.
3.0
WMAP+BBN
2.5
Li
Sun
2.0
1.5
6Li
0
Jft-
1.0
0.5
0.0
-
-3.0
,
~
i
-2.5
-2.0
III
-1.5
[Fe/H]
-
-1.0
-0.5
0.0
Figure 2.5: Observed logarithmic abundances of 7Li (open triangles) and 6Li (filled circles)
as a function of [Fe/ H] for UVES. The large circle corresponds to the solar system
meteoritic 6Li abundance [43], while the solid line is the predicted 7Li abundance from
WMAP+BBN prediction [19]. The dotted line is zero metallicity 7Li abundance [36] and
dashed line is the average 6Li abundance for UVES. loge(Li) is defined as logE(Li) =
log(Li/H) + 12.
A mechanism that can solve the two lithium problems simultaneously has been proposed
by incorporating non-standard model particles, such as the neutralino or gravitino [12]. The
decay or annihilation of these particles (as relics of the very early universe) will inject thermal
neutrons into BBN. Neutrons will reduce the primordial 7Li by destroying the 7Be which is
expected to be converted to 7Li after BBN. Thermal neutrons will also develope a nuclear
cascade to produce more Deuterium which results in excessive 6Li production. But the
existence of such particles is not yet experimentally proven.
Nevertheless, cosmic ray lithium isotopes may play an important role for the excessive
To solve the 6Li plateau problem, both a better understanding
6Li abundance on MPH stars.
of cosmic rays and a more accurate measurement of cosmic ray lithium isotopes are
necessary.
In astrophysics, metallicity is defined as the proportion of matter made up
of chemical elements other than hydrogen and helium. It is usually expressed by [Fe/H] =
*
logo10 (Ne)
NH
star
-
log 1 0 (
-)
NH
sun
where NFe and NH are the number of iron and hydrogen
atoms per unit of volume respectively. The metallicity provides an indication of age since
older stars have lower metallicities than younger one, e.g. Sun is one of the metal-rich
Population I stars.
28
Chapter 3
Charged Cosmic Rays
Nearly 100% of the galaxy's 6 Li and 10-20% of the 7Li is conjectured to be produced through
cosmic ray spallation and fusion during galactic propagation. The direct measurement of
cosmic ray lithium isotopes therefore provides an essential probe of the nature of
characteristics of these propagation processes.
A general overview of the features of cosmic rays, including their origin and acceleration,
will be given in the first part of this chapter. Then we will focus on the details of the galactic
propagation of cosmic rays. The propagation of cosmic rays through the local solar
environment and the Earth's magnetic field will also be discussed. Finally, we will discuss
previous cosmic lithium ratio experiments and summarize their results.
3.1
Cosmic Ray Sources and Acceleration
Cosmic rays are energetic charged particles reaching the Earth's atmosphere from all
directions. The discovery of cosmic rays came in 1912 with the first pioneering balloon
measurements of an increasing ionization rate with altitude [50]. Since then, cosmic ray
composition and intensity have been measured by many satellites, balloons, and ground-based
experiments.
Cosmic ray energies span more than 20 orders of magnitude, from several eV to 102 eV
and above, and the rough composition of cosmic rays is 86% protons, 11% ionized helium, 2%
electrons and positrons, and trace amounts of heavier elements [4]. Hydrogen and helium
are produced in the Big Bang Nucleosynthesis (BBN) and heavier elements from carbon to
nickel are synthesized in the stellar evolution by the nuclear fusion. The elements above
iron are typically produced in supernova (SN) explosions. The nuclei generated before
propagation are called primary cosmic rays. Secondary cosmic rays, such as lithium,
beryllium and boron (LiBeB), are generated by spallation of primary nuclei in the interstellar
medium during propagation. Therefore, the LiBeB nuclei provide important information of
Galaxy chemical evolution and cosmic ray propagation [3, 6].
the primary cosmic ray nuclei are given in Figure 3.1.
The major components of
10
1 I 1rr
1 F TJ----1--rrrrrq
H
SHe xI 10-2
%IbA~,-
10
c x 10 lc*,*.
OX 10-6
10-0
80T
p.-
0000
Nex 10- 8
0
10
Mg X 10-11*)
12
-
Si X 10-12
a
10-16-16X
Sx0
Ca x 10-
o AMS
t
*
X 1L-21
10-4Fe
-29
*
W40
* BESS
0 CAPRICE
o HEAO-3
o CRN
@CREAM
c JACEE
* TRACER
*
-
e HESS
10--32
L
ATIC
a RUNJOB
1i11111 1, 111al' ''"'nal
0.1
1.0
10.0
100.
1n
103
10)4
105
106
Kinetic energy per particle (nucleus) [GeV]
Figure 3.1:
Major components of the primary cosmic radiation from [4].
In the intermediate energy range from 0.1 GeV to 106 GeV, the cosmic ray flux can be
described by a single power law distribution [2],
nucleons
IN(E) ~ 1.8 x 10 4 E -Y muces
m 2 sec sr GeV
(3.1)
The spectra index y is 2.7 for over all flux and takes value from 2.5 to 3 for individual species.
The cosmic rays in this energy range are believed to be produced primarily within the galaxy.
A strong support to this local source hypothesis comes from the observed power-law spectrum
for high energy electrons.
Inverse-compton scattering with the Cosmic Microwave
Background (CMB) would destroy this spectrum, if they were produced at distances greater
than 300 kpc [51].
The cosmic ray acceleration mechanism was first proposed by Fermi in 1949 [52].
He
assumed that the charged particles were randomly scattered by the moving magnetized clouds,
which resulted in net energy gain per bounce proportional to the square of the velocity of the
magnetized clouds. That is why the mechanism is called Second Order Fermi Acceleration.
Although such a process can explain the power-law spectrum, it is unable to accelerate
particles to GeV energy.
The First Order Fermi Acceleration in Supernova Remnant (SNR) shock wave is now a
widely accepted mechanism for the efficient acceleration of cosmic ray particles to energies
up to 106 GeV [53]. The model has been supported by recent observations of X-ray and
gamma ray emissions near SNs, which has revealed the presence of energetic electrons
accelerated in the SN shock waves. Assuming a galactic rate of 3 supernovae per century
and an explosion energy of 10 erg, less than 10% of the energy is needed to channel into
3
acceleration to sustain the average cosmic ray energy density, estimated to be ~1eV/cm .
The details of the first-order and second-order Fermi acceleration mechanisms will be
discussed in the Appendix A. In summary, each time the particle up-scatters off the SNR
shock front, it gains energy proportional to the velocity of the shock wave. Higher and
higher energies are achieved when the particle repeatedly crosses and re-crosses the shock
front. Meanwhile, the particles' probability of escaping the SN magnetic field altogether
increases with velocity. The combination of these two effects would result in a power law
spectrum with index ~ -2.1 [54]. The observed much steeper cosmic ray spectral index of
-2.7 can be achieved by accounting for the energy dependence of the probability of a cosmic
ray particle to escape to infinity during galactic propagation.
The upper limit for the accelerated energy comes from the increasing gyroradii of the
charged particles compared to the size of the shock wave. The steepening at 106 GeV in the
cosmic ray spectrum, usually called the Knee, is believed to represent the maximum energy
transferable from the SNR shock waves. The spectrum above the Knee flattens again at the
109 Gev, the so-called Ankle [55]. The particles observed at this energy have gyroradii of
the order of the galaxy's size. Therefore they are still speculated to be of the galactic origin
and accelerated at the termination of galactic wind [56]. The particles with energy above
1010 GeV are called Ultra High Energy Cosmic Rays (UHECRs). Their origin and
acceleration mechanism are still debated. The gyroradii indicate extragalactic source, i.e.
Gamma Ray Burst (GRB) [57]. But the extragalactic UHECRs should have been highly
suppressed by the "GZK-cutoff' [58] due to the energy losses of protons by
photon-pion-production with the Cosmic Microwave Background.
Cosmic rays with energy below 1GeV/n are mostly from the solar wind as discussed
later in section 3.3.
3.2
Galactic Cosmic Ray Propagation
Once accelerated by supernova shocks, cosmic rays spend ~107 years diffusing through the
galaxy, confined by magnetic fields. During this propagation, cosmic rays spiral around
This
magnetic field lines, frequently scattered by magnetic irregularities and turbulence.
process has long been interpreted as slow diffusion [54], which results in an isotropic
distribution of charged cosmic rays as observed at Earth.
halo
PPP_
CRS
15 kpc
Figure 3.2:
8.5 kpc
Side view of the Milky Way and schematic propagation of cosmic rays.
3.2.1 Galactic Structure
A cartoon representation of our galaxy and the propagation of cosmic rays is shown in Figure
The Milk Way has a form of a flat disk with a radius of -15 kpc (1 kpc= 3.086x
3.2.
102 1cm) and a thickness of approximately 100 pc. The luminous matter of the galaxy is
mainly distributed in the center bulge and the spiral arms on the disk. The galactic disk is
surrounded by a spheroid halo of old stars and globular clusters, of which 90% lie within 30
kpc. The solar system lies at a distance of 8.5 kpc away from the galactic center. The
cosmic rays will be confined inside the halo for ~107 years depending on their energies [59].
While traveling through the galaxy, cosmic rays interact with the Interstellar Medium
(ISM), which consists of clouds of gas and dust, magnetic fields both coherent and turbulent,
radiation fields from starlight, and CMB radiation. Interaction processes include energy loss
through ionization, synchrotron radiation and inverse-Compton scattering; energy gain by the
stochastic acceleration; and nuclear reactions such as radioactive decay and fragmentation.
The interstellar gas and dusts have important effects for the secondary production. The
gas consists mostly of hydrogen in the form of atomic neutral hydrogen (HI) and molecular
hydrogen (H2), and small portion (about 10%) of Helium. The average density of interstellar
matter is estimated to be 1 nucleon/cm 3 [60], from various measurements [61, 62, 63].
The average magnetic field in the Galaxy is on the order of 10-6 Gauss. Magnetic
turbulence and irregularities play important roles to confine and reaccelerate the energetic
particles.
The Interstellar Radiation Field (ISRF) includes photons emitted from stars and CMB
radiation. The latter is well-known by its black body spectrum.
3.2.2 Propagation Models
Two general classes of models have been proposed to describe the propagation of cosmic rays
in the galaxy: the Leaky Box Model (LBM) and the Diffusion Halo Model (DHM). The
LBM uses the simple picture of an equilibrium system, in which the cosmic ray sources,
interstellar gas, and radiation field are uniformly distributed in a confinement volume (the
galaxy), and these sources are constant in time [54, 64]. The diffusion is approximated by
the mean escape time (-esc), the mean time spent by a cosmic ray in the containment volume.
The recent modified LBMs are quite compatible with data [64, 65, 66], but the escape
mechanism and the physical size of the volume are still not well addressed [67].
The DHM model accounts for the actual structure of the galaxy, cosmic ray source
distributions, and interactions of cosmic rays with the interstellar medium, which are all
incorporated into the transportation equation [6],
adt
0
U4, p. t
=q(i,p,t)
ap
2
p
V(DxVxi$-Y$)
3
-(V1-
a1
0
-A$Tr
A$
(3.5)
Tr
Note that in [6]
.
.
.
.
.
$(r, p, t) is the density per unit of total particle momentum at position r with
$p(p)dp = 4Trp 2 f() in terms of the phase-space density f().
q(r, p, t) is the source term including the primary sources and contributions from
spallation and decay.
DXX is the spatial diffusion coefficient.
V is the convection velocity. Since there is no direct observational support for the
convection, we will not use this term in the later analysis.
Dpp is the momentum space diffusion coefficient which contains the Alfven velocity VA.
=p
is the momentum gain/loss rate.
.
Tf is the timescale for fragmentation.
*
Tr
is the timescale for radioactive decay.
A variety of analytical and numerical approaches to the transportation equation can be
found in the literature [68]. GALPROP [6] is a widely used numerical simulation code
developed by Igor Moskalenko and Andrew Strong. It has been applied towards indirect
Dark Matter signature searches in AMS-01 [69], PAMELA [70] and FERMI/GLAST [71],
and will also be used for AMS-02 experiment [72]. Understanding of this program becomes
important interpreting future cosmic ray data.
3.2.3 GALPROP Properties
The GALPROP model is three-dimensional, with cylindrical symmetry in the Galaxy;
the basic coordinates are R (Galactocentric radius), z (distance from the galactic plane) and p
(particle total momentum). The propagation region is bounded by a cylinder with Rh=30 kpc
and Zh=1-20 kpc, with free escape assumed. The input source is the primary cosmic rays
after the SNR acceleration. Once the input source distribution and the boundary condition
are determined, GALPROP solves the time-dependent equation 3.5 for all species by
advancing the solution in time until a steady state is achieved.
There are three basic parameters which govern the GALPROP model: halo size Zh,
diffusion coefficient Dxx, and Alfven velocity VA. The halo size determines how long the
cosmic rays will be contained in the galaxy, and the diffusion coefficient and Alfven velocity
characterize the essential diffusive reacceleration process in the propagation.
Halo height Zh and the radioactive clocks
Long-lived unstable secondaries are good probes of confinement of cosmic rays in the galaxy.
Several of the best of these so-called radioactive clocks are 10Be, 14C, 2 6Al and 54 Mn.
Among these nuclei, 10Be is the best measured and longest lived, with a half life of 1.5 million
years, comparable to the confinement time. The data on energy dependence of ' 0 Be/9Be
abundance ratio and the prediction from different propagation models are shown in Figure
3.3.
9Be (stable) and '0 Be (unstable) are both secondaries and produced with similar cross section.
In the low energy range with negligible relativistic time-dilation, 10Be is much depleted (in
relation to 9Be) due to beta decay. Therefore, the larger the halo size, the less ' 0 Be will be
observed. The best fit suggests the halo height of 4 kpc [6].
## i i
0 .6
-
0.5
0
0.3
ISOMAX TOF
ISOMAX CK
-
0.4
0
<1
0
[>
ACE
Ulysses
Voyager 1-2
IMP 7/8
ISEE-3
0.2
0
.1----
0
.0
T
-
0.01
I I II 1 l
i
lIIk
0.1
-
-
l
1
-
10
Ekin [GeV nucleon']
Figure 3.3: Beryllium isotope ratio measurements from [24]. The listed experiments will be
discussed in section 3.5. The solid line is the GALPROP model and the dashed lines are two
Leaky Box Models [59].
Diffusion and Reacceleration
The concept of cosmic ray diffusion explains why energetic particles are "mixed" efficiently
and are retained rather well within the galaxy. In the GALPROP model, diffusion terms
include the spatial diffusion and momentum space diffusion through reacceleration. On the
microscopic level, both diffusion types are the result of scattering on random moving
magnetic fields, Alfven waves [73]. Alfven waves are transverse magnetic tension waves
which propagate along magnetic field lines and can be excited in magnetized plasma in
response to perturbations. The velocity with which Alfven waves propagate along the
1
magnetic field is called Alfven velocity VA. It is estimated to be VA = B/(4Trp-), where B
is the magnetic field strength and p is the interstellar medium density.
The wave-particle scattering is of a resonant character so that a particle with Larmor
radius r mainly interacts with waves which have a wave number of k = 1/r. Assuming a
Kolmogorov spectrum for the MHD turbulence [6], the spatial diffusion coefficient has a
power-law dependence on the rigidity and can be expressed as
1
D. = D0 P(R/Ro)3
(3.6)
where Do is the diffusion constant to be determined, and R is the rigidity, Ro is the reference
rigidity (see Appendix C).
A rough estimation of the value of the diffusion coefficient can be obtained by picturing
diffusion in a macroscopic level (in pc) [74]. Cosmic ray particles are scattered by the
sudden change of magnetic field due to the presence of stars and other objects. In our
neighborhood of the galaxy, the distribution of stars is roughly 1 per cubic parsec, therefore
the mean free path of a charged particle Xcan be estimated about 3x 10' 8cm.
Supposing the
particle has a velocity close to the speed of light, the propagation velocity is v = c/V,
because it spirals along the magnetic field line. Then the diffusion coefficient can be
calculated as D = v x A ~ 5 x 10 2 8 cm2 s-1. This value is close to the one predicted by the
GALPROP at 3GV (3 - 5 x 10 28 cm2 s-1) [6].
In addition to diffusion, charge particles are also accelerated by stochastically scattering
off random MHD Alfven waves. To distinguish it from the primary acceleration in SNR
shock waves, scattering off such Alfven waves is called reacceleration, which shares the same
mechanism with second-order Fermi acceleration. In the transportation equation 3.5 the
reacceleration is presented by diffusion in the momentum space and the diffusion coefficient
is estimated as
D pp
=
p2V2
(3.7)
9DXX
where the Alfven velocity VA is the only free parameter. The ISM Alfven velocity is
approximately 30 km/s [6, 73] and the exact value needs to be determined with the help of
fitting the model to specific cosmic ray observations.
3.2.4 Li/C Ratio---Constraints on Dx and VA
Secondary particles are produced by the interaction of primary particles with the ISM during
galactic propagation. Therefore, their spectra encode information about the propagation
processes. The secondary to primary ratio, which cancels out the uncertainty on primary
spectra, provides a good probe to the propagation parameters. The boron to carbon (B/C)
ratio is often used because of its well-measured cross sections and abundant cosmic ray data.
The Li/C ratio is particular interesting since its production depends not only on the
interaction of CNO, but also on tertiary interactions (Be-Li, B4Li), and therefore the Li/C
ratio is more sensitive to variations between propagation models and provides further
constrains on them. As we can see in Figure 3.4, the ratio (red curve) is featured by a
characteristic peak at ~GeV/nucleon, which can be explained by the diffusive reacceleration
process. In the low energy region, the reacceleration is strongest, which means that the
particles with higher energy have spent longer time in the galaxy and produced more
secondaries. When energy becomes larger, diffusion dominates. Particles have more
chance to escape with higher energy, which results in less interaction of ISM and less
secondary production.
These two processes balance at the peak position.
The overall height of the Li/C ratio determines the diffusion coefficient, while the Alfven
velocity determines the peak position, as illustrated in Figure 3.4.
0 0.22,-
.2
.2~----.-----
28om-s-t
),,=5.75x 10 Cm s'
D =6.00
28
.
.
-
..
0.18m
0.14
0.120.1
0.08
0.06[
0.04
0.02F
1
10
Kinetic Energy (GeV/nucleon)
0.1
100
(a)
0 0.22
A
-.
VA=20
S0.18..
km s
VA= 3 6 km s'
-0.2
-
... VA=50 km s
0.16
0.12
0.1
0.08
0.06
0.040.02
.i110
100
Kinetic Energy (GeV/nucleon)
(b)
Figure 3.4: The effects of diffusion coefficient and Alfven velocity on the Li/C ratio,
simulated by GALPROP. The red curve represents the theoretical Li/C ratio prediction from
the default GALPROP parameter set Dx.=5.75cm 2s~1 and VA=36kms-1 [6, 75]. In (a) we fix
VA and change the Dxx, while in (b) we make opposite parameter adjustments.
3.3
Solar Modulation
After cosmic rays propagate through the galaxy and near our star, they must penetrate the
solar wind to reach Earth. The solar wind is a stream of charged particles ejected from
the upper atmosphere of the sun with velocity about 400 km/s, carrying magnetic field
irregularities. The interaction, known as solar modulation, will decrease the intensity of
cosmic ray flux below 10GeV/nucleon as particles are blown away by the solar wind.
Cosmic rays are scattered by the magnetic irregularities from the solar wind, resulting in
diffusion in space and momentum, which is similar to that of the galactic propagation.
Transport within the solar regime can be approximated by the Fokker-Planck equation,
including the effects of diffusion, convection and energy loss due to scattering [76].
Va
2V
-- (r2U)-rzoar
3r aT (TU)
-
rzar
r
)
ior
=0
(3.8)
Where U(r,T) is the density of the flux of cosmic rays at radial distance r from the sun. T is
the kinetic energy and a is defined as (Eo+E)/E with EO the rest energy (mass) and E the total
energy. V is the speed of solar wind assumed to be spherically symmetric and K is the
isotropic diffusion coefficient.
This equation can be solved by an approximation method, generally known as "ForceField Approximation" suggested by Gleeson and Axford [77]. The cosmic ray flux inside
the solar system turns out to be distorted from the interstellar flux according to the equation,
U(r, E)
E2
E
-2E
E
U(rooE + |Z|$)
(3.9)
where Z is the charge of the cosmic ray particle, and D is the so-called "Force Field potential"
ranging from 400MV to 1000 MV during the eleven year solar cycle.
2.4
Geomagnetic Field
For cosmic rays to be detected in low earth orbit, they must penetrate one more shield, the
Earth's magnetic field. This field can be described, to first order, as a magnetic dipole tilted
with respect to the rotation axis by -11.5' and displaced ~400 km with respect to the Earth's
center and with a magnetic moment M = 8.1 x 1025 Gcm 3. Low energy particles will be
deflected by the field depending on their latitude, height and direction, and the lowest rigidity
accessible to a detector is given by [78],
Cos*4X
Rcutoff = (59.6[GeV/c])
COSX2
(1 +
where Rcutoff is the cutoff rigidity,
Q
Qcos3AcospEW
(3.10)
(3.10
is the sign of the particle's charge, X is the
i1
-
geomagnetic latitude of the detector and <pEW is the east-west component of the zenith angle
of the incident trajectory (see reference [74] for the details).
Both particles with rigidity above and below the local geomagnetic cutoff have been
found in many balloon and satellite experiments. The latter ones have no galactic origin, and
are usually called cosmic ray Albedo [79]. They are the secondary particles produced by the
interaction of cosmic rays with the upper atmosphere. Once produced, the motion of the
Albedo particle in the Earth's magnetic field can be decomposed into three components as
shown in Figure 3.5: a very fast gyration around a guiding center, a fast oscillation (or
"bouncing") around the magnetic equatorial plane, and a slow drift in longitude. Positively
charged particles will drift westwards, and negatively charged particle will drift eastwards.
Albedo particles are either absorbed again by the atmosphere, most probably at the mirror
points and with very short lifetimes, or they keep drifting in the Van Allen Radiation Belt for
a long time [79], and are referred to as "trapped".
Trapped Protons and
Inner Electron Belt
Outer Electron Belt
Cyclotror Motion
Bounce Motion
Mirror Poirt
Electron Drift Motion
Magnetic Field Line/ Guiding Center
Figure 3.5:
Schematic view of motion of charged particles in Earth magnetic field [80].
From an experimental standpoint, the geomagnetic cutoff can provide an energy scale
useful for the differentiation of the Albedo particles and trapped radiation from the primary
cosmic rays. But a simple cut in energy is only a very simplified approximation. An
alternative method to provide a clear separation is to trace the trajectory of a detected particle
backward in time in the actual geomagnetic field to find its origin. The details will be
discussed in the chapter 5 of data analysis.
One important irregularity in the earth's magnetic field is the South Atlantic Anomaly
(SSA). In this region the earth's magnetic field is weakest and the Inner Van Allen
Radiation Belt, usually above 700 km, makes the closest approach to the earth surface. Any
satellite or spacecraft at several hundred kilometer altitude will be exposed to high radiation
in the SSA. This high flux can overwhelm the trigger of the detector, the AMS events
collected in this region were removed.
3.5
Measurement of Cosmic Ray Lithium
Since the 1960's, the direct measurement of cosmic rays have been extensively studied in
balloon-borne, space-borne and ground-based experiments with an energy range covered from
MeV/nucleon to 1019eV/nucleon. At low energies (below 1GeV), where the cosmic ray flux
is relatively high, solid state detectors with small acceptance can achieve high statistics.
Such detectors are usually light enough to be carried by satellites and spacecrafts. In the
GeV-TeV energy domain, the measurement has been taken by both balloon-borne and
space-borne experiments. Balloon-borne experiments have the advantage of flexibility, a
higher mass budget and a larger geometrical acceptance compared to space-borne experiments.
But the systematic uncertainties caused by atmospheric corrections could potentially spoil the
expected accuracies due to the relative low altitude the balloon can reach. Ground based
experiments are designed for ultra high energy particles.
In table 3.1, we summarize the previous experiments which measured the cosmic ray
lithium isotopes. The experimental observations of Li/C ratio and 7Li/ 6Li ratio are shown in
Figure 3.6 and Figure 3.7.
As we can see, above 1GeV/nucleon, most Li/C ratio
measurements have either large uncertainties due to the low statistics, or low energy
resolutions by the detector limitation. Accurate cosmic ray Li/C data in the intermediate
energy region (1GeV/nucleon -100GeV/nucleon) is still missing.
The measurement of Li/C ratio in the intermediate energy region and 7Li/ 6Li ratio above
1 GeV/nucleon can be fulfilled by the AMS-01 experiment. In the next chapter, we will
introduce the details of the detector and its ten-day flight.
Year
Experiments
Experimental metod
Carrier
Elements
EZ)
Energy
(GeV/n)
Cosmic Ray Nuclei Abundance Measurement
1970
Cerenkov counter and scintillator
Balloon
2-30
0.1-2
1971-1972
Cerenkov counter
Balloon
3-28
20-120
Orth et al. [831
1972
Magnet spectrometer
Balloon
3-26
2-150
Lezniak et al. [84]
1974
Cerenkov counters
Balloon
3-28
0.3-50
Buffington et al. [85]
1977
Magnet spectrometer
Balloon
3-8
0.2-1.5
Webber et al. (2) [861
1977
Cerenkov counter and scintillator
Balloon
3-8
0.2-3
Garcia-Munoz et al. [64]
1972-1978
Solid state detector
Satellite IMP-7 &8
1-28
0.01-0.28
MEH on ISEE-3 1871
1978-1982
Cerenkov counters
Spacecraft
3-8
0.5-20
HET on Voyager 1 &2 [881
1977-now
Solid state detector
Spacecraft
1-28
0.001-0.5
CRIS on ACE [89]
1997-now
Solid state detector
Spacecraft
2-30
0.05-0.5
Webber et al. (1) [811
Juliusson et al.
1821
Cosmic Ray Light Element Isotope Measurement
Garcia-Munoz et al. [90]
1972-1978
Solid state detector
Satellite IMP-7 &8
3-5
0.035-0.15
Buffington et al. [95]
1977
Magnet spectrometer
Balloon
3-8
0.2-1
Webber et al. [91]
1977
Cerenkov counter and scintillator
Balloon
3-5
0.04-0.4
HET on Voyager 1 &2 [88]
1977-now
Solid state detector
Spacecraft
3-5
0.001-0.5
SMILI-II [921
1991
Magnetic spectrometer
Balloon
2-5
0.1-1.7
CRIS on ACE [23]
1997-now
Solid state detector
Spacecraft
2-30
0.05-0.5
ISOMAX [24]
1998
Magnetic spectrometer
Balloon
3-8
0.2-2
Table 3.1:
Summary list of previous experiments which measured cosmic ray lithium isotopes with energy < 1TeV/nucleon.
o0.25
*
*
A
T
o
WehhAr 1
Buffington
Wobber 2
CRIS
Garcie-Munoz
El Voyager
A Ort
) Jutiusson
" 0.2
c)
VEH
Tk
0.15
0.1
0.05k-
lI
I 10100...
10
1
Kinetic Energy (GeV/nucleon)
0.11
|
0.1
Figure 3.6:
i
I
l
,
.
.
100
The solid curve is from the
Li/C ratio versus kinetic energy (GeV/nucleon).
GALPROP prediction assuming low solar modulation (potential <D=500MV).
3.1 for the corresponding reference.
1.6
A ISOMAX
1.4
A SMILI-Il
V Buffington
1.2
[ Webber
* Voyager
o ACE
~
I=r~
1
0.8
0.6
0.4
0.200.01
I
I
I
I
I I I I
,
I
I
I
I
I I I
I
-
I
I
I
0.1
1
Kinetic Energy (GeV/nucleon)
Figure 3.7:
7 Li/ 6Li
ratio versus kinetic energy (GeV/nucleon).
I
I
I I
See the table
Chapter 4
The Alpha Magnetic Spectrometer (AMS-01)
The AMS experiment is designed primarily to search for dark matter and antimatter by
studying the charged cosmic rays in low-earth orbit [1].
AMS-01 flew onboard the space
shuttle Discovery in June 2 1998 for 10 days and recorded over 100 million cosmic ray events.
AMS-01 was an engineering model to demonstrate the feasibility of AMS-02, which is
intended to be mounted on the International Space Station (ISS) for three years running in
2010.
4.1 The AMS-01 Detector
The AMS-01 detector basically is a large aperture magnetic spectrometer.
It consists of five
core components, a Nd-Fe-B permanent magnet, a silicon tracker within the magnet volume, a
time of flight (TOF) hodoscope, a plastic scintillator anticoincidence counter (ACC), and an
array of aerogel threshold Cerenkov counter (ATC).
The layout of the assembled detector is shown in Figure 4.1.
The AMS-01 coordinate
system defines the Z axis as "up" along the magnet axis, the X axis as parallel to the B-field
and the Y axis in such a way as to form the usual right-handed coordinate system.
4.1.1
Magnet
The design of AMS-01 permanent magnet has two major considerations: (1) providing largest
possible geometrical acceptance and bending power within the maximum allowed weight, (2)
minimizing the fringe field to be lower than the shuttle and ISS allowance (60 Gauss).
The magnet is of cylindrical geometry, with a height of 800 mm and inner and outer
diameters of 1115 mm and 1298 mm respectively, as shown in Figure 4.2. The magnetic
material, 1024 blocks of high grade Nd-Fe-B, is divided into 64 groups and carefully arranged
with varying field directions to create a dipole field of 0.15 T, which is fairly uniform inside
the bore and quickly drops off to the level of a few gausses outside the bore.
The final magnet weights 1.92 tons and has bending power of BL 2 =0. 14 Tm 2 .
information of the magnet can be found in [2].
Further
Particle trajectory
I~O
Low Energy Particle Shield
k!!rsx
S1:
Tracker TI
PtanasT2
--
0
'
I
-
j
0
Waftrs
13
T40
:®~=*~4TS
4To
-q.---~
I'
S3'
Arogel
Cerenkov
y
Figure 4.1:
The AMS-01 schematic and sketch [1].
x 41 2
y
11000
n
Outer
uShrll
YT
-- -- -- -- ---
- -- -- ----
-*-
1 M
L,0,Inner Inere
Nd-Fe-B4.
BL2=0. 15 TMW
Acceptance =0.82 misrX
Weight = 1900 kg
Figure 4.2:
t
tI
AMS-01 magnet dimensions and field orientation [1]. 64 groups of Nd-Fe-B
block are arranged such that a uniform 0.15T dipole field is created inside the bore, and less
than 60 G outside to prevent interference with electronics.
4.1.2 Tracker
The central part of the detector is the silicon tracker, which measures the trajectory of each
charged particle in the magnetic field. The silicon tracker is composed of 6 layers of
double-sided microstrip sensors.
Each sensor has dimensions of 40 mm x 72 mm and a
thickness of 300 ptm, based on the design used for L3 microvertex detectors at the Large
Electron-Positron collider (LEP) at CERN [92]. The strips on one side of each layer are
orthogonal to the strips on the other side of the layer, so as to measure the two coordinates at
the same time. The sensors use capacitive charge coupling [93]. The p-doped side (S side)
measures position in the bending plane with a readout pitch of 110 pm, and the n-doped side
(K side) measures position in the non-bending plane with a readout pitch of 208 pim.
7 to 15 sensors are chained together with front-end electronics and support structures to
form a single "ladder" up to 60cm long, as shown in Figure 4.3. The ladders are arranged
parallel to the B-field such that the S-side strips are orthogonal to the field to maximize the
position resolution in the bending plane.
Silicon Sensors
S side
K side
Hybrids
n-side Kapton Cable
Figure 4.3:
An exploded view of AMS-0 1 tracker ladder.
The passage of a charged particle through a tracker plane is recorded as a cluster of strips
characterized by position and amplitude. The cluster reconstruction algorithm requires the
selection first of a "seed" strip (size of 110 [tm for s side and 208ptm for k side) [94], which
has a signal larger then 3 Gped (with Gped defined as the strip's pedestal width). Subsequently,
up to two strips are chosen on the two sides of the seed strip to form a cluster. This leads to
a position resolution of 10 pm in the bending plane and 30 ptm in the non-bending plane,
which translates to a momentum resolution of 9% for protons in the 1-10 GeV range.
resolution is degraded at lower momenta due to multiple scattering.
This
The amplitude of the cluster is a direct measurement of the total energy deposition, and
that information is used to determine the absolute charge of the particle passing through the
tracker. At most six energy deposition measurements can be obtained from either the S side
or K side for a single event.
For the flight mission in 1998, 38% of the tracker was instrumented (58368 channels),
which lead to an acceptance of 0.31 m2 -str for events that passed through at least 4 of the 6
planes. During the flight, the tracker alignment calibration was constantly monitored with a
laser alignment system with accuracy within 5um.
plane is 0.65% of one radiation length.
The average thickness of each tracker
More information on the AMS-01 tracker can be
found in [95].
4.1.3
Time of Flight
The TOF measures the time of flight of incoming particles. It also provides the fast trigger
signal, and gives an estimation of absolute charge of a particle. TOF consists of 4 planes of
plastic scintillator, two above and two below the tracker as illustrated in Figure 3.4. Each
plane has 14 plastic scintillator paddles of 10 mm thick, 110 mm wide and 720-1360 mm long.
The paddles are wrapped with aluminized mylar and arranged within a two-shell, 0.6 mm
thick carbon fiber cover. The paddles in each plane are staggered together with an overlap at
each junction of 1cm to avoid dead space.
Planes 1 (the top) and 4 run along the X direction
while planes 2 and 3 are along the Y direction.
photomultiplier tubes (PMT) on both ends.
Each scintillator paddle is viewed by three
By measuring the arrival time of light at the two
ends of the scinillaor and knowing effective velocity of light within the scintillator, the time
of flight and long-dimension position where a particle passes through the paddle can be
The detail of velocity reconstruction will be discussed in section 4.4.1. The
spatial resolution of the TOF is ~ 2cm. The temporal resolution (100 ps) is much smaller
than the minimum time of flight 5 ns for a particle with pz1, which results in an
obtained.
upward/downward going particles separation of 1 in 1011 [96].
The TOF also measure the energy deposition and provide a measurement of the absolute
The coincidence of fast signals from four planes is used to trigger the
precise readout of all detector elements. Further information on the TOF can be found in
charge of particles.
[96].
Photornultiplier
Support Foot
Figure 4.4: The two upper TOF planes.
4.1.4
Anticoincidence Counter
The 16 Anticoincidence Counters (ACC), made of 10 cm thick plastic scintillator material, are
arranged between the magnet inner wall and the tracker support structure. A signal in the
ACC indicates a particle which passes through the side of the detector. As these particles
can not be fully analyzed, the signals from these counters are used for event rejection.
4.1.5
Aerogel Threshold Cerenkov Counter (ATC)
Since the ATC is not used in this analysis, it will not be discussed further.
of the ATC is in [97].
4.2
A full description
The Flight
The AMS-01 was flown on the space shuttle Discovery during flight STS-91 in June 1998 in a
51.70 orbit at altitudes between 320 and 390 km. Figure 4.5 shows the location of the
AMS-01 in the payload bay of Discovery. Data taking started on 3 June 1998 and can be
separated in four periods,
(a)
25 hours before docking with the MIR space station, during which the shuttle attitude
was constrained to keep the AMS longitudinal axis (z-axis) pointing within 450 of the
zenith.
(Zenith is defined as the point in the sky directly perpendicular to the plane of
the earth's surface. The angle between the AMS Z-axis and the zenith direction is
defined as zenith angle and will be used in the analysis, see Figure 4.6.)
(b) Four days while docked to MR.
frequently during this period.
The zenith angle varied between 400 to 1450 very
During this time, part of the view of the detector was
obscured by the MIR station, and large amount of the secondary particles from the
interaction of cosmic rays and the station material impinged on the detector. Thus the
data from this period is excluded in the analysis.
(c) After MIR undocking. Within a degree, the pointing was kept within 00, 200 and 450 of the
zenith for 19, 25 and 20 hours respectively.
(d) Before descending, the shuttle was turned over for approximately 9 hours and the pointing
was toward the nadir (zenith angle =1800) to study particle interaction with the shuttle
bottom.
The data is excluded with the same reason as in the period of docking with MIR.
During the ten days flight about 100 millions cosmic particles passing through AMS-01
were recorded.
Figure 4.6 shows the zenith angle of AMS-01 as a function of mission
time.
4.3
Trigger and Livetime
Since the incoming rate of signals is much higher than the AMS data acquisition rate,
AMS-01 uses three stages of triggers to record only the useful events which traverse the
detector and can be well measured.
Fast trigger The fast trigger requires that at least one signal from one or more PMTs on
each of the four TOF planes goes above the voltage threshold, all within 200 ps.
hardware trigger indicates that a particle passes through the magnet volume.
Level-i Trigger (Matrix)
This
Since the tracker is only partially instrumented, mostly in
the innermost region (see Figure 4.1), this software trigger applies the correlation matrix
between paddles in the TOF planes 1 and 4 to reject events which do not pass through at least
4 tracker planes.
Level-1 trigger (Anti trigger) This trigger discards the events with any signals recorded
It cuts large scattering particles, interacting particles and particles which pass
through the side of AMS. It degrades the detection efficiency for high Z nuclei providing
the energy deposition dependence on Z2
in the ACC.
Level-3 Trigger (TOF)
To select events which have a good time of flight, this trigger
requires a signal on both ends of one or two adjacent scintillators on planes 1 and 4. But
during the flight this restriction was only applied to the plane 1 because plane 4 delivered
unreliable information.
Level-3 Trigger (Tracker) A straight fiducial path of 6.2cm width connecting the TOF
clusters is then generated in the tracker bending plane.
Tracker clusters in the bending
plane are selected if the strip with the highest measured signal has a signal-to-noise ratio (S/N)
greater than 4.
are selected.
This trigger requires that at least three clusters in the different tracker planes
A higher level trigger was applied only before the docking with MIR and
disabled due to the lower than anticipated rate thereafter.
We don't consider this trigger in
this analysis.
During the flight, events passing all three levels of triggers were recorded.
To study the
trigger efficiency, a group of "prescaled" events, constituting about 0.1% of the total dataset,
are recorded with only a Fast trigger requirement. Further information of trigger can be
found in [98] and the efficiency will be discussed in section 5.6.2.
The trigger rate varied in the 10 day flight between 100 and 1600Hz as a function of
The readout time is approximately 85 is at the highest
position relative the magnetic poles.
trigger rates.
The dead time must be taken into account for the analysis.
Th
Spa-d
nice Shus te,+ X
The AM,,IS Experrrimen
F-
st
X/u~
Ilk ..
.
.I
Disovr y
hi~
u/~
t~n
a ifrn
......
1ade tthemgn:L l
Figure 4.5
AMS-0Olin the space shuttle Discovery.
rgn
180
160 -Dock
WZenithanl
angle
with MIR
140
120
E100
Ole
2
N
0
-
40
-
20-
Earth
50
0
Figure 4.6:
100
150
Time in hours
200
Zenith angle of AMS-0 lin ten-day flight, from [69].
250
The cartoon on the right
illustrates the definition of zenith angle.
4.4
Event Reconstruction
The raw AMS-01 data was analyzed by the event reconstruction software to produce the
physical information of the passing particles, such as charge, velocity, rigidity and mass etc.
4.4.1
Velocity Reconstruction
The velocity is reconstructed by fitting the time measurement of the TOF clusters found in the
vicinity of the reconstructed track with the assumption of the constant speed.
A mean time
(tm) of a cluster is calculated by averaging the two time measurements from the each end of
the paddle.
tm =
ti
+ t2
2
(4.1)
Meanwhile, the position of the cluster along the paddle can be obtained by measuring the
difference of the two arrival times, given the effective velocity of light in the scintillator,
veff=15.5cm/ns.
ti
td= -
-
t2
(4.2)
2
The time measurements are corrected for time slewing (The TOF timing electronics
record the time when the signal from PMT reaches certain threshold, which causes the large
signal to be recorded earlier than the small signal given the same arrival time),
k
tcorr = tm -
where a is the integrated anode signal in pC and k = 7.5 ns
(4.3)
'Jjc
is a constant.
Since the effective of the bending of the charged particle in the magnetic field is
negligible with respect to the detector length, roughly speaking, the velocity P = v/c is
determined by P-1 = ct/d where d is the track length at the crossing point of the paddle.
The measurement of p-1 follows a Gaussian distribution with 6p1~0.03 [1].
4.4.2 Track Reconstruction and Rigidity Measurement
As we described in section 4.1.2, the first step of track reconstruction is to locate the "seed
strip" and then add the adjacent strips to form a cluster. The onboard compression is done
by selecting the "seed strip" on the S-side (bending plane) with S/N>3.5 and S/N>2.75 for the
K-side (non-bending plane). The adjacent strips and adjacent to adjacent are added only if
the S/N>1. The Offline Clustering adds higher threshold for the "seed strip" finding,
S/N>4.5 for the S-side and S/N>3.75 for the K-side.
A series of 3-D hit positions can be formed by combining all the possible S and K clusters
belonging to the same ladder. Due to the fact that for K cluster one readout channel
corresponds 6 to 8 geographical positions equally spaced, a single S, K cluster pair creates 6
to 8 3-D hits.
The ambiguity is somewhat resolved by comparing the clusters in the outer
and inner tracker planes which are relatively offset, and also by using the track from the TOF.
To reconstruct the track, a straight line fit is first done with at least four hits. Then a
helical fit is performed for the hits which have the lowest x2 from the straight line fit. The
helical fit is based on a spatially constant magnetic field. If the helical fit yield a 7 less than
the preset threshold (typically 1000), the hits are passed on to more complicated fitting
algorithm taking into account the real magnetic field.
It should be noted that sometimes no track can be found by using this method. This can
happen when the K cluster S/N is so low that not enough K clusters are selected to satisfy the
requirement of at least 4 hits to be included in the track. In this case, a false K cluster will be
added according to the prediction from the track to continue the reconstruction.
Two different advanced algorithms have been used:
2
Fast Fit based on 5x5 matrix inversion that iteratively minimizes a X between actual hits
and the hits from simulation [99]. This algorithm provides the best rigidity measurement at
high rigidity.
GEANE Fit based on Kalman filter [100, 101] using the GEANE CERN Library program.
It uses the GEANT 3 detector simulator to calculate a hit-by-hit fit. In principle it should
provide better rigidity, but in practice it's only better than the Fast Fit in the low rigidity
region [69].
Finally, track reconstruction provides the information of incident angle and the rigidity of
a particle.
4.4.3
Charge Reconstruction
The energy deposition in the detector material where a particle passes through is proportional
to the square of the charge. The charge of the cosmic ray particle is determined by the
maximum likelihood method based on the energy deposition on the TOF and tracker after the
correction for incident angle and velocity. The TOF provides a reliable energy deposition
measurement up to Z=2.
Z>2.
Therefore, only the Tracker is used for charge measurement for
We will discuss this in detail in section 5.4.
4.4.4
Mass Reconstruction-Isotopes
Mass reconstruction is essential for separating isotopes.
Knowing the Charge Z, rigidity R and velocity p, the mass of a particle can be calculated
via
m=|ZRC-'
p-2_1
(4.4)
where C is the speed of light.
Supposing we can measure the charge with high confidence, the uncertainty of the mass
can be estimated from the uncertainty in rigidity measurement (6R) and velocity (6Pf),
assuming they are uncorrelated.
(6m)2
=
_
(p-2 -
1)(6R) 2 +
-2
p1)2
(4.5)
Due to the limited accuracy of velocity measurements, the mass resolution is >0.5GeV
for the lithium isotopes. The details will be discussed in Chapter 6.
Chapter 5
Data Analysis
This chapter describes the procedure used to obtain the lithium (charge 3) and carbon (charge
6) spectra from the raw detector data. The particle's rigidity, velocity, and charge are the
three most important properties we will focus on in this analysis.
A Monte Carlo simulation
is used to determine the detector acceptance.
5.1
Event Preselection
After the AMS-01 flight, the raw data of 108 events, which consisted of various ADC/TDC
channel numbers from each part of the detector, were reconstructed to generate the charge,
velocity, rigidity, and direction for each event. We need to apply first a series of
preselection cuts to remove the events that were measured incorrectly or poorly understood.
During the time the Discovery shuttle was docked with MIR, the particle spectra were
contaminated by secondary particles generated by the spallation of cosmic rays off the MIR
material. Therefore all events taken in these four days were rejected.
When the shuttle passed over the South Atlantic Anomaly (SAA), the trigger rate
saturated due to the overwhelming incoming particles in the inner Van Allen Radiation Belt.
Events collected during that time were removed to avoid errors from pileup in the electronics.
For the same reason, events during detector livetime less than 35% were also removed from
further analysis.
Events with no track reconstruction were removed.
To ensure accurate rigidity and
velocity measurements, at least four Tracker plane hits and three TOF plane hits were
required.
Events were cut whenever the Anti-coincidence Counters was triggered, which indicated
that cosmic rays passed through the side or secondary particles were generated when energetic
cosmic rays interacted with detector material.
Events were only accepted when the detector zenith angle (see section 4.2) was less than
500 and particles came from the top of detector. This partially eliminates secondary particles
generated in the atmosphere or trapped in the Earth's magnetic field. The further selection
cut on atmospheric secondary particles from primary cosmic ray particles will be discussed in
section 5.5.
Protons and Helium ions have much larger abundance than all other species, and
therefore we only select events with reconstructed charge larger than 2. After the
preselection cut, about 15 thousand charge 3 particles and 40 thousand charge 6 particles are
selected as the lithium and carbon candidates for further analysis. The data is generally
binned in the variable log(Rigidity) with a bin width of 0.1. Rigidity is defined as
R=-
(5.1)
where p is the magnitude of the momentum and Z is the charge of the particle.
5.2
Rigidity Measurement
There are four different ways to describe the spectra for the cosmic rays [4],
(1) by number of particles per rigidity interval
(2) by number of particles per energy-per-nucleon interval
(3) by number of nucleons per energy-per-nucleon interval
(4) by number of particles per energy-per-nucleus interval.
The
second one is widely used in cosmic ray measurements, because the
energy-per-nucleon is approximately conserved when a nucleus breaks up by interaction with
interstellar gas during the cosmic ray propagation.
In this analysis, we will use the first spectrum representations, particles per rigidity,
because:
(1)
Rigidity is directly measured by the Tracker.
(2)
The Earth's magnetic field will modulate the flux of cosmic rays depending on the
rigidity, incident angle, and geomagnetic coordinates of the incoming particles.
AMS-01 has always the same geometric rigidity acceptance for all particles at the same
time. By measuring the lithium to carbon ratio against rigidity, the largest systematic
error, that of rigidity acceptance, will be cancelled.
(3)
Rigidity determines the gyroradius of charged particles propagating in the cosmic
magnetic fields, which is essential for "back tracing".
(4)
Rigidity is directly determined, all other spectra imply knowledge of isotope mass.
The quality of the rigidity measurement is determined by how well the trajectory
reconstruction has been done. As we discussed in section 4.4.2, there are two reconstruction
algorithms, and between the two, the Fast Fit Algorithm provides the better fit for the majority
of events. In addition to measuring the rigidity of a full trajectory of at least four hits, the
Fast Fit also measures the rigidity of the first 3 hits and the last 3 hits separately.
events if both of these fits are non-zero and have the same sign.
We select
A different sign of the
rigidity fit will indicate a different curvature of upper half trajectory and the lower half,
probably induced by scattering.
The resolution of rigidity inevitably becomes lower for larger values.
The rigidity
resolution becomes worse also in the low rigidity region due to the multiple scattering (each
tracker layer represents 0.65% Xo). Figure 5.1 shows the resolution dependence on rigidity
for lithium, boron and carbon.
The best resolution is at around 2GV.
Therefore we select
the particles with rigidity from 2 GV to 100 GV.
e 0.5
0
i 0.45
-Li Z=3
0.4
0.4-
-B Z=5
-C Z=6
0.35
00.3
0.25
0.2
0.15
0.10.05
0
1
Figure 5.1:
10
Rigidity (GV)
Rigidity resolution as a function of rigidity for Li, B and C.
5.3
Velocity Selection
Velocity is measured by the TOF with at least 3 planes hit requested in the preselection.
We
applied further selection cuts to guarantee the well reconstructed dynamic property for
particles. It is essential for lithium isotope ratio measurement in the later chapter.
During the flight, paddle No. 8 in layer 2 and paddle No. 10 in layer 2 provided
inaccurate timing information [94, 102] and also displayed low efficiency as shown in Figure
5.2.
Events passing through these two paddles were thus rejected.
4000
2500 -
40002000
3000
1500
2000
1000
500-
1000
TOF Paddle Number (Layer 2)
TOF PaddleNumber (Layer 1)
t
00-
53 5 0 0
3000
20002500
1500-
2000-
1000 --
'1500
10
1000
500
2
4 6
6
14
12
10
TOF PaddleNumber(Layer 3)
Figure 5.2:
2
4
6
6
14
12
0
TOF Paddle Number (Layer 4)
Scintillator paddle occupancy for each TOF plane.
The trajectory measured in the tracker will be extrapolated back to TOF to compare with
the TOF plane hits.
These two position measurement provide a consistency check.
5.3 shows how the comparison of two measurements is done.
Figure
The residual distance, rl or r2,
are both required to be less than 5 cm [102], which corresponds to a 2.5a TOF position
measurement error, see section 4.1.3.
Reconstructed
TOF hit
Residual
distance r
Extrapolated
TOF hit
TOF
Tracker
Residual
distance r2
Figure 5.3:
5.4
Schematic view of residual distance evaluation.
Charge Identification
Charge identification is essential in this analysis.
charge information.
Either the TOF or Tracker can provide the
But the dynamic range of the TOF does not permit to distinguish
particles of Z>2 with great accuracy.
Therefore, only information from the Tracker is
adopted for analysis.
5.4.1
Energy Loss of Charged Particles
Moderately relativistic charged particles other than electrons lose energy in matter mainly by
inelastic collision with the atomic electrons of the material.
The mean rate of energy loss
per unit path length has quadratic dependence on the particle charge, described by the
Bethe-Bloch equation [4],
dE
2z
1 1
- - = KZ
- n
dx
A @2 -2
2mc2
2 2Tmax
2
6
- @In-
(5.2)
2
V2
where
A
atomic mass of absorber
Z = charge of incident particle
z
atomic number of absorber
p
velocity of incident particle
me = mass of electron
y = Lorentz factor
I = mean excitation energy
K = 4rrNareme c 2 = 0.307MeV cm2
6 = density effect correction to ionization energy loss
Tmax
= the maximum energy transfer in a single collision
10
8
C\3
1L
0.1
Figure 5.4:
1.0
10
100
7 = p/Mc
1000
10000
Mean energy loss for pions in liquid hydrogen, gaseous helium, Aluminum, iron,
tin and lead [4].
Figure 5.4 shows the mean energy loss for pions in different materials.
curve for silicon is expected to be near the Al curve.
The energy loss
The rate of energy loss has minimum at
py=3 and only slightly depends on energy in the py range from 3 to 10000. Above this range
the energy loss increases dramatically by radiative losses.
The property of energy loss being
dependent on the square of particle's charge is used in our charge measurement.
5.4.2 Cluster Selection and Velocity Dependence
The energy deposition in each tracker layer is collected from the total energy of the cluster in
that layer.
Each cluster contains 5 strips, and at least 4 clusters are requested at the bending
plane (S side) for reconstruction.
A large amount of low energy deposition clusters have
been found due to the inefficient collection of total energy on that spot.
Therefore we only
choose the "good" clusters from the S side layer for the average energy loss evaluation.
A
"good" cluster should have two main characteristics [94]:
1) It contains no "dead strips".
All the strips with occupancy level less than 65% of the average over all strips on a given
ladder are considered as "dead strips".
Figure 5.5 gives examples of occupancy level for two
ladders on the second Tracker layer.
Any cluster containing "dead strips" should be
removed.
010,3
104
0
Figure 5.5:
100
200
300
400
500
600
Channel number
Occupancy level for ladder 9 on the second layer of Tracker.
indicates the level of 65% of average occupancy in that ladder.
The red line
2)
It is far enough from the silicon wafer border.
A "good" cluster has a Gaussian energy deposition distribution, with a maximum at the
center and the energy deposition decreases when the strip is away from the center.
Any
abnormal strip signal may indicate the cluster is near the wafer border.
The energy deposition in Bethe-Bloch formula has P-" dependence at low energies when
py=1-10. When py is larger than 10, this disappears due to the relativistic effect from the
radiactive losses. Therefore we have to take into account of p-" dependence for corrections
on energy deposition for particles with P < 0.95 (py<10). Figure 5.6 gives the average
energy deposition in the tracker against P and the best fit for the index n for each charge.
The average energy deposition here is evaluated by the truncated mean built from up to six
tracker measurements. The energy deposition is also corrected by the incident angle 0
measured on the first tracker layer.
-
ANADCICos(O)|
(5.3)
where A is the constant relating ADC channel numbers to energy.
~2200
S2000
00
<-. 1600
11400
10
Figure 5.6:
Average energy deposition on Tracker as a function of velocity from 0.6 to 0.95.
The function for solid curves is dx- = A -
where A is a constant.
5.4.3 Charge Identification by Gaussian Fit
The Bethe Bloch formula only gives the mean rate of energy loss in a unit path length. The
real energy loss has a Landau distribution featured by a long tail towards the high energy loss
side resulting from a large energy transfer for a single collision [103].
Fortunately, for Z>2
particles passing through 300 pm silicon sensor, the Landau effect is minor.
By discarding
the highest value of total 4 to 6 energy deposition measurements, the average energy loss in
the tracker can be approximated by the Gaussian distribution.
The average energy deposition spectrum is shown in Figure 5.7 for velocity from 0.6 to
1.0 and fit by six Gaussians. The incident angle and beta dependence correction for
[3< 0.95 is included in equation 5.4.
dEp
dx
dx
=
ANADCICOS ()|
0.95 )
"
(for P < 0.95)
(5.4)
Proton and helium events are removed due to their overwhelming statistics. Lithium
events are selected with the energy deposition within the two a range of the first Gaussian
peak in Figure 5.7 and Carbon within the two a range of the forth Gaussian peak.
C
250
Li
200
150-
B
100-
800
1000 1200 1400 1600 1800 2000
Energy Deposition (ADC channel)
Figure 5.7: Mean energy deposition on Tracker for Charge from 3 to 8. Red curve is the fit
to six Gaussians. Nitrogen and Oxygen are suppressed due to the ACC triggering by 6 rays.
5.5
Eliminate Atmospheric Secondary Particles
As described in section 3.4, primary cosmic rays are affected by Earth's magnetic field. At
low geomagnetic latitudes, cosmic ray particles with low energy are turned away by the field
and atmospheric secondary particles dominate the low energy region of observed spectra.
AMS-01 covered a wide range of geomagnetic latitude and longitude during its 10 day
flight. The 160 orbits of AMS-01 are shown in Figure 5.8. Protons have the largest
statistics and therefore provide a very good demonstration for how the Earth's magnetic field
and Albedo particles distort the cosmic ray spectra.
In Figure 5.9, proton spectra are
plotted for different geomagnetic latitudes. At the highest latitude (|rag|>1), the proton
spectrum keeps the "normal" power law shape. In contrast, the proton spectra at low
latitudes have a second apex in the low energy region, which is composed of Albedo particles
mostly [1]. These can be further investigated by tracing the trajectory of the particle
backward to see its origin.
The tracing algorithm is based both on precise measurement of incident direction,
location, and rigidity of a particle, as measured by AMS-0 1; and also an accurate model of the
Earth's magnetic field. The most widely used model for the Earth's field is called the
International Geomagnetic Reference Field (IGRF), produced by the International Association
of Geomagnetism and Aeronomy (IAGA) [104].
The IGRF model describes the internal magnetic field as the negative gradient of a scalar
potential,
B(p', ,r, t) = -VV(p', A, r, t)
And the potential V(p', A,r, t) can be expanded in terms of spherical harmonics:
V(p',Xr,t) = a
W(gf(t) cos(mA) + hm(t)sin (mA))
"nm(sintpl)
(5.5)
(5.6)
where a is the standard Earth's radius (6371.2km) and <p', A,r are the latitude, longitude and
radius in a spherical frame, and gm (t), hm (t) are the time-dependent Gauss coefficient of
degree n and order m, and Pnm(sinp') is the Schimdt semi-normalized Associated Legendre
Function. The latest version has degree and order up to 13. For the details of the model
please refer to the reference [104]. The Earth's magnetic field during the AMS-01 flight can
be obtained by extrapolating the 1995 data to June 1998.
(a
60
40
0
s0
100
.-J
ISO
200
Longitude
260
300
360
150
200
250
Geomagnetic Longitude
300
350
(a)
.o
0
20
-40-60
0
50
100
(b)
Figure 5.8: The longitude and latitude coverage of AMS-01 flight. (a) is in the Geographic
Coordinate system and (b) is in the Geomagnetic Coordinate system. The South Atlantic
Anomaly (SAA) is labeled. The discontinuities are due to the trigger suppression of proton
data.
102
010
4--
0~.-
10
- '
'
<0.6
0.6<J1e .g<0.8
'
'
'
'
'
'
'
''
'
' ' '
10
1
10
Rigidity (GV)
100
The apices in the
Figure 5.9: AMS-0 1 proton spectra at different geomagnetic latitudes.
low rigidity region of low geomagnetic latitude spectra consist of mostly Albedo protons.
A program has been developed to trace the particle trajectory backward by numerically
integrating the motion equation in the Earth's magnetic field [105]. A particle is rejected as
"Albedo" if the trajectory once approached the atmosphere (40 km above the earth surface).
Additionally, if a particle did not reach a distance of 10 earth radii and stayed within the Van
Allen Radiation Belt for more than 20 seconds [105], it is rejected as a trapped particle, which
may originate from "Albedo" but has been trapped in the radiation belt for relatively long
time.
Figure 5.10 (a) illustrates the trace-back track of an Albedo proton recorded by AMS-0 1.
The proton originated from the atmosphere with 0.7 GeV kinetic energy, then it traveled for
about 10 seconds before it was detected by AMS-01. The motions in the Earth's magnetic
The cyclotron
field, as we discussed in section 3.4, can be seen from Figure 5.10 (b).
motion along the magnetic field lines results in Albedo protons having equal likelihoods to
enter AMS-0 1 from either top or bottom. Almost the same amount of upward and
downward protons with kinetic energy below geomagnetic cutoff has been detected by
AMS-0 1 in the low geomagnetic latitude region, which also proved their Albedo origin. But
this phenomenon has not be seen in lithium and carbon, because only very few Albedo
lithium and carbon ions are generated compared to protons and electrons.
6400-6200
0
2
1
3
4
5
7
8
9
10
Trace Back Time (s)
6
0.3
Cyclotron + bounce motion
0.25F-
~--~-I~
0.2
0.15
C-
)
-~
-~
)
-- ".
-~
c~
-~
-"5
-
'C
5,
)
-~
-
~
0.05
gj
'C
5?
5?
0.1
5?
)
~cQ
)
~
'5
(~
(
-
~
(~4~
(3
~
C
Drift westward
0
-0.05 F-0.1'
-
0
1
LI
0.05
0.1
0.15
0.2
(b)
I
0.25
0.3
I
0.35
0.4
Geo-longitude
(a) Full trace-back track of the proton from the birth in the atmosphere (10 s) to
the detection by AMS-01 (0 s). Altitude is measured from the Earth's center. (b) shows its
partial track, which demonstrates the three motions in the Earth's magnetic field: cyclotron,
bounce and drift.
Figure 5.10:
To demonstrate how the tracing cut affects cosmic ray spectra, we use AMS-01
In Figure 5.11, the black histogram is the selected
low-latitude proton data as an example.
All these events are then traced back to
proton data with geomagnetic latitude below 0.1.
identify their origins. The atmospheric protons, shown by blue and green histograms,
compose the second spectrum in the low rigidity region. A primary cosmic ray proton
spectrum (red histogram) is then achieved by rejecting these secondary protons. It should be
noted that the excessive trapped proton flux around 1OGV is due to misidentified primary
protons. These protons represent less than 1% of the total proton events, therefore they are
negligible.
The tracing cut was then applied on both lithium and carbon to select the primary cosmic
ray particles, as shown in Figure 5.12. The count rate can be calculated by dividing the
Since we are
counts per rigidity bin by the time the detector was exposed to that rigidity.
interested in the Li/C ratio against rigidity, the exposure time which causes large systematic
error, will be cancelled out. Therefore only a count-per-rigidity spectrum is used in this
analysis. Figure 5.13 shows the final spectra compared to spectra before selection cuts. As
we can see, the spectrum shape is not biased by selection cuts. Each event is corrected by
livetime and the errors assigned for each rigidity bin is from the statistic uncertainty
Table 5.1 lists the effects of all the selection cuts on AMS-0 1 events.
Nunts .
-
Total proton
-Tracing Cut
Al bedlo proton
EJTrappedl proton
103
102
10
101
110
Rigidity (GV)
Figure 5.11: Proton spectrum at geomagnetic latitude less than 0.1.
the proton spectrum after removing the Albedo and Trapped protons.
Red curve represents
E
-
-Total Li
(~Albedo Li
0 13 0 10
Trapped Li
102
10
10
Rigidity (GV)
100
(a)
e104
-Total
C
[ ] Albedo C
o
ETrapped C
103
102
10
'1
10
100
Rigidity (GV)
(b)
Figure 5.12: (a) Lithium and (b) Carbon spectra. Black histogram is the AMS-01 data
after selection cuts discussed in section 5.1-5.4. Blue and green histograms are the identified
atmospheric events after back tracing.
.
(0
.
.
.. . .. . .
efore selection cut
-
_...
-- Li t
after selection cut
o103
-I---
-
. I
102
--H
10
1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
100
10
Rigidity (GV)
(a)
104
_-
- -- - -
------- C before selection cut
--
C after selection cut
103
102
+
10
Rigidity (GV)
100
(b)
Figure 5.13: Spectra after selection cuts of (a) Lithium and (b) Carbon.
22709 Carbon events are kept after selection cuts.
8349 Lithium and
Selection Cuts
%of cut (Li)
Events kept (Li)
Preselection
%of cut (C)
15665
Events kept (C)
39777
Fast Fit rigidity
3.7%
15085
3.7%
38358
Rigidity range
21.2%
11878
16.5%
32009
Bad TOF Paddles
9.3%
10776
8.1%
29402
Residual distance
2.6%
10501
2.5%
28677
Charge selection
12.4
9201
10.9%
25564
Tracing back
9.3%
8349
11.2%
22709
Table 5.1:
5.6
Selection cuts on Lithium and Carbon data.
Monte Carlo Simulation for Detector Acceptance
Once the counting rate is known, the cosmic ray flux can be determined by evaluating the
geometric acceptance, detection efficiency, and rigidity resolution of the detector. These are
estimated using a Monte Carlo Simulation.
5.6.1
Monte Carlo Simulation
The AMS-01 detector simulation was based on GEANT 3 package and incorporated many
important physics processes [106]. Generated were 5.8 million 6Li and 5.9 million 7Li with
rigidity from 1 GV to 1000 GV, and 27.7 million Carbon with rigidity from 0.5 GV to 500
GV in the Monte Carlo simulation. These events were generated over a rectangle 250 cm by
90 cm, 100 cm above the detector in simulation with momentum directions distributed
isotropically over the half-sphere towards the detector. Events that would trigger the
detector were recorded for analysis.
5.6.2 Acceptance and Efficiency
The "recorded" Monte Carlo events were run through the same analysis chain to generate the
detector acceptance, A(R), with unit of (m2-sr)
A(R) (M2sr)
2TrS Nrec(R)
Ngen (R)
(5.7)
where S is the surface area over which the Monte Carlo particles are generated.
the number of reconstructed particles that pass all the cuts, binned by rigidity.
Nrec(R) is
Ngen(R) is
the number of generated events. The acceptances are shown in Figure 5.14. Carbon has a
significantly lower acceptance because when it passes through the tracker it will generate
more 6 rays, which then trigger the veto. The 6 ray effect has been included in the GEANT
3 package.
The acceptance needs to be corrected first by the detector efficiency. By comparing the
Monte Carlo detector simulation with "prescaled" events (see section 4.3), the simulation
generally overestimates the efficiency by 13 ± 3.5 percent [69], mostly due to uncertainties in
trigger efficiency and particle interactions in various sub-detectors [1, 107]. The absolute 13%
efficiency correction is found to be only weakly dependent on rigidity and will cancel in Li/C
ratio calculation. The 3.5% system error is added on the detector acceptance to the statistic
errors.
-
Lithium
-Carbon
N 0
I
-
I
0-
10 Rigidity (GV)
Figure 5.14:
Acceptance for Lithium and Carbon.
102
Efficiency correction has been included.
5.6.3
Rigidity Unfolding
Due to the finite rigidity resolution of the instrument, a particle with a given rigidity R' is
generally detected at a different rigidity R with probability P(R, R'). This problem is
usually stated as a Fredholm equation of the first kind,
oM (R) =
f P(R, R')DT (R')dR'
(5.8)
where IM(R) is the spectrum measured by the detector and c-T(R') is the true spectrum
which needs to be determined. Since our data is binned discretely in the variable log(R),
equation 5.8 can also be written in the matrix form,
(5.9)
Dm -- NPT
and P is called resolution matrix. Figure 5.15 shows the resolution matrices for lithium and
carbon which are generated from the Monte Carlo events that passed all cuts.
A simple inversion of the resolution matrix is usually instable due to the negative matrix
terms. Several methods exist to solve equation (5.9). The one widely used in previous
AMS-01 analysis is the Method of Convergent Weights [1, 108, 109], which uses an iterative
At each step, the iterative approximation that converges to the true spectrum,
procedure.
gJ(R), is calculated by
f wi (R')P(R, R')dR'
(5.10)
g)(R)
fP(RR')dR'
gj+'(R) =
where the weight function wJ (R')
wJ(R')
is defined as
q m(R')
-
f P(R', R")gi(R)dR"
The iteration starts with g0 (R) = Im (R) and the corresponding cIj (R)
through
cPj(R) =
P(R, R')gJ(R')dR'
(5.11)
is evaluated
(5.12)
Generally after several steps, cIj (R) will converge to the measured spectrum (Dm (R) and
the corresponding gi (R) is a good approximation for the true spectrum.
Figure 5.16 shows the unfolded lithium and carbon spectra after 7 iterations of this
algorithm, compared with the folded spectra. The count rate for each bin is corrected by the
acceptance and efficiency.
Resolution Matrix for Lithium
102
102
Reconstructed Rigidity (GV)
Resolution Matrix for Carbon
102
102
Reconstructed Rigidity (GV)
Figure 5.15: Resolution Matrices for (a) Lithium and (b) Carbon. The darkness represents
the probability Notice that Lithium has better rigidity resolution than Carbon. Squares are
due to calculation coarseness in domains.
.
104
o
0
-
Folded Li Spec.
0
Unfolded Li Spec.
-
0
103
102
Rigidity (GV)
100
105:
0
0
04
Rigidity (GV)
100
(b)
Figure 5.16: Unfolded (a) Lithium and (b) Carbon spectra, compared with folded spectra.
Notice that Carbon spectrum has larger correction due to the worse rigidity resolution.
76
Chapter 6
Results
6.1
Li/C Abundance Ratio
In chapter 5, we obtained 8349 lithium events and 22709 carbon events with strict selection
rules, and then corrected the spectra with acceptance and resolution effects. Here we address
the Li/C ratio. Figure 6.1 shows the Li/C ratio from AMS-01 measurement together with the
previous experiment results below 1GeV/ nucleon.
The previous experimental data are converted from the kinetic energy per nucleon to
rigidity by the equation,
(AEk ) 2 + 2mAEk
z
(6.1)
where R is the rigidity, Ek is the kinetic energy per nucleon, A is the atomic number, m is the
total mass, and Z is the charge, assuming the speed of light C=1. For example, 1
GeV/nucleon is equivalent to 3.38 GV for carbon.
For kinetic energies above 1 GeV/nucleon, the previous measurements have either large
uncertainties due to low statistics, or low energy resolutions by detector limitation. Since the
conversion will introduce larger uncertainties for these data, they are not shown in Figure 6.1.
Our experiment achieves an unprecedented energy resolution and statistics on the cosmic
ray Li/C ratio measurement in the rigidity region between 2GV and 100 GV (equivalent to
kinetic energy between -0.5 GeV/nucleon and ~50 GeV/nucleon). A characteristic peak
from the diffusive reacceleration propagation process can be clearly seen from our data and
previous measurements in the low energy region.
-
o0.222
S
0.2
-
A Webber 1
Buffington
_
A Webber 2
0
T
0.16
0.14
V CRIS
0 Garcia-Munoz
E Voyager
* AMS-O1
-
0.12
0.1
0.087
1
0.06
0.040.02
0-
1
10
Rigidity [GV]
100
Figure 6.1: Lithium to carbon ratio measured by AMS-01. Errors include statistical errors
of data, and a 3.5% detector efficiency (see section 5.6.2), summed in quadrature since they
are uncorrelated. The solid curve is the best fit from GALPROP including solar modulation
(D=580MV for AMS-01 flight), see section 6.3. The other six experiment data sets were
converted from kinematic energy to rigidity for comparison, refer to table 3.1 for the
corresponding references. The reason these measured values lie below the prediction curve
is that the solar activity was much smaller when these measurements were carried out than
during the AMS-0I flight in 1998.
6.2
7
Li to 6Li ratio
Mass reconstruction is critical for isotope ratio measurement. Mass is determined from the
particle's relativistic momentum P, measured by the tracker and its velocity p, measured by
the TOF, via the following relation:
m =PC- @-2 - 1
(6.2)
The uncertainty of the mass can be estimated from the uncertainty in the measurement of
curvature q = P and unit-less time of flight P-', assuming they are uncorrelated.
p-2
2
_ 1
C274
(62
+(p 2
C (1
P2
-
2
(6.3)
P2)
The uncertainty in the curvature is caused by the finite resolution of the silicon tracker
In the low energy regime, multiple scattering
and also the effects of multiple scattering.
dominates the uncertainty in curvature.
As we discussed in section 5.2, rigidity
measurements become worse below -2GV; we thus set the lower rigidity limit to 2.5 GV.
In the high energy region, the uncertainty of mass is mostly caused by the finite
resolution of time of flight, the last term in (6.3). The uncertainty in the time of flight
measurement is approximately Gaussian with 8P-1 = 0.03, as we discussed in section 4.4.1.
When p is larger than 0.9, the mass resolution is >>1GeV. Therefore, the upper rigidity limit
is set to be 6.3 GV, corresponding to P=0.9.
Even with the strict selection of rigidity and velocity as we showed in chapter 5, the mass
resolution of AMS-01 is still too low to clearly separate the two lithium isotopes from each
other. One method to obtain the lithium isotope ratio is by fitting the mass distribution of
lithium with Monte Carlo simulations, which has been used for the measurements of proton to
deuterium ratio [110], and Helium 3 to Helium 4 ratio [1] with AMS-01.
The mass distribution of lithium and comparisons with Monte Carlo simulations are
shown in Figure 6.2. Four rigidity regions are selected to ensure enough statistics. The
shadowed histograms represent the mass distributions of Monte Carlo 6Li and 7Li events
respectively. For comparison, we first assume that the cosmic ray lithium isotope ratio is the
same as what we observed at Earth, 7Li/ 6Li 12.1. We float only the normalization factor
for 6Li and fix the one for 7Li such that the ratio of Monte Carlo 7Li to 6Li is 12.1. The Least
Chi Square method is used to fit the Monte Carlo simulation to the AMS-0 1 Lithium mass
distribution. The fitted histogram (red line in Figure 6.2) clearly deviates from the measured
data in each rigidity region and the corresponding chi square is large. In conclusion, the
cosmic ray lithium isotope ratio is far from the Earth value.
LU2.5<R<3.2 GV
140
0 120-
140-
100 -
120 -
SUm of
80 -C
Li
100
80 -
60-
MC7
60
40-
40--
20
0
Li 3.2<R<4.0 GV
0160-
20
/N
2
2
=
6
,
8
I/Nddo= 136.5/35
Mass (
Mass (GeVc
4G
2
)
2/Ndo=
4
2
x /Ndoo=
Figure 6.2:
138.3/43
Z2 /NdO=
Lithium mass distribution fit assuming 7Li/ 6Li~ 12.1.
183.9/39
6
Mass (GeVfc2)
8
100.1/43
The black dots are the
AMS-01 lithium data, two shadowed histograms represent the Monte Carlo 6Li (brown) and
7Li (blue), and the red histogram is the sum of Monte Carlo 6Li and 7Li as the best fit to the
data.
We then free both normalization factors to make the best fit to the lithium mass
6
7
distribution. The fitting results are shown in Figure 6.3. The Monte Carlo Li and Li
histograms have similar height and width, which indicates a ratio close to 1.
Since we use the
The confidence intervals for normalizations are shown in Figure 6.4.
sum of the overlapped histograms to fit the data, these two normalizations are negatively
correlated. The correlation is included in the error analysis of the 7Li/ 6Li ratio.
6
Taking into account the rigidity resolution effect, we obtain the 7Li/ Li ratio in each
rigidity region. The results are shown in Figure 6.5 with the previous experimental data.
The exact values are listed in the table 6.1. Our 7 Li/ 6Li ratio measurement covers the largest
rigidity range (2.5GV-6.3GV), the average ratio is 1.07 ±0.16.
.
Li 3.2< R<4.0 GV
160
140
120
100
80 -
-I
60
40
20
a
2
4
6
8
10
12
X2 /Ndof= 46.1/38
X2/Ndof 41.2/42
Figure 6.3:
Lithium Mass distribution fit.
14
Mass (GeVc)
x2/Ndof= 42.6/42
Normalization factors for Monte Carlo 7Li and 6 Li are both free parameters.
3.2<R<4.0
2.5<R<3.2
0.24r-
2a
0. 3
$2a
0,23
0.22
0.281
0.21!
0.21
0.26
0.19
0.24
0.17
0.220.16~
0.15 0.16 0.17 0.18 0.19 0,2 0.21 0.22 0.23
7Li Normalization
0.22
7
0,26
0,28
Li Normalization
0.3
5.0<R<6.3
4.0<R<5.0
0.38
0.24
1_
Ji
0.36-
0.361
1c
0.34r'-
0,341-
0.32 !7
0.321
0.3
0.281
0.3
0.26k
0.28
0.24[
0.22e-
0.24
0.26
0.32
0.3
0.28
7Li Normalization
0.34
0.36
0.22 0.24 0.2$ 0.28 0.3 0,32 0,34 0,36 0.38
7
Li Normalization
Confidence intervals for the Monte Carlo 6Li and 7Li normalization factors.
The two normalization factors are negatively correlated. The correlation has been taken into
Figure 6.4:
the error analysis of the 7 Li/ 6 Li ratio.
0
1.6 -.
9
AMS01
A
ISOMAX
SMILI-Il
1
o Buffingtor
ACE
(U
1.2
[ Webber
-
A
0.8
*
T
Voyager
1
0.6
0.40.2
0
1
2
3
4
5
6
7
Rigidity (GV)
7
Figure 6.5:
Li/ 6Li ratio versus rigidity.
The previous experimental data have been
converted from the kinetic energy to rigidity, refer to table 3.1 for the corresponding
references.
Because of the conversion, the results have upward trend compared to Figure 3.7.
The blue curve is from the GALPROP prediction.
Rigidity (GV)
7Li/6 Li
ratio
2.5-3.2
3.2-4.0
4.0-5.0
5.0-6.3
1.11±0.16
1.02±0.13
1.10±0.16
1.03 ±0.18
7 Li/ 6Li
Average Ratio
Table 6.1:
= 1.07±0. 16
AMS-0 1 7Li/ 6Li ratio results.
6.3
Constraints on GALPROP Parameters
The secondary to primary cosmic ray ratio has long been taken to constrain the Galaxy
propagation models, as we discussed in chapter 2.
The B/C ratio is the most quoted ratio
because their cosmic ray abundance and production cross section have been well measured by
many experiments.
The Li/C ratio is more sensitive to the propagation parameters but it is
not used as often as the B/C ratio.
One reason for this (as has been shown in Figure 3.6) is
that only a few cosmic ray data above 1 GeV/nucleon are available, and with only low
statistics.
The AMS-01 measurement provides a Li/C data set which covers the energy range
between 0.5GeV/nucleon and 50 GeV/nucleon.
With the latest version of GALPROP program [111], we are able to use the AMS-01
Li/C ratio to constrain the Galaxy propagation parameters, the diffusion coefficient Dx and
Alfven velocity VA.
The sensitivity of Li/C ratio to the two propagation parameters has been
demonstrated in Figure 3.4.
Because GALPROP does not include the Solar Modulation, we have to apply the "Force
Field Approximation", see section 3.3, on the predicted Li/C ratio from GALPROP.
The
force field potential <D for solar modulation is 580MV at the time period of AMS-01 flight in
June 1998 [74].
The best fit from Least Chi Square analysis [112] yields,
Diffusion coefficient DXX = 5.73 + 0.46 x 1028 cm 2 /s
and Alfven velocity
with &=22 and Ndor= 14.
VA = 33.4 + 6.1 km/s
The GALPROP Li/C ratio from the best fit is shown in Figure 6.1
as the blue curve and the confidence contour used for error analysis is shown in Figure 5.5.
The best fit results from B/C ratio are DXX = 5.75 x 1028 cm2 /s and VA = 36 km/s,
provided by GALPROP [6, 111]. They are within the 1la constraints of our measurement.
The large uncertainties on Alfven velocity in our analysis are mostly caused by the high
correlation between these two propagation parameters, as we can see in Figure 6.6.
Most
data are collected at the right hand side of the characteristic peak, where the slope of curve
can be adjusted by both parameters and not so sensitive to the Alfven velocity.
A much
better fitting can be achieved when more lithium and carbon data from several MeV/nucleon
to 1000 GeV/nucleon become available, from AMS-02 (Appendix B) or other experiments.
40;7
150%
V..
68.3% 1l
E
.33
1
> 36
34'
32
30
8C
28
26C
24
5
5.2
5.4
5.6
6.2
6
5.8
D
Figure 6.6:
6.4
x 108 (cm 2sI)
Confidence intervals for diffusion coefficient Dxx and Alfven velocity VA.
color code represents the value of Chi Square
x.
The
Inner contour is for 50% confidence level
and the outer one is for 68.3% (la) confidence level.
6.4
Constraint on the Lithium Problems
As we discussed in section 2.4 of the Lithium Problems, cosmological/galactic cosmic ray 6Li
production may be a plausible solution for the 6Li plateau found on the MPH stars.
Here we
will not show how solid the speculation is, which of course needs further experimental
evidence.
We will discuss how the 6Li plateau and the cosmic ray production mechanism
may affect the first Lithium Problem, the
7Li
discrepancy.
The AMS-01 measurement gives an average 7Li to
6Li
ratio of 1.07, which indicates
almost same amount of lithium isotopes produced in cosmic rays.
If we assume the galactic
cosmic ray origin of 6Li plateau, the "primordial" Li abundance around the plateau value must
have been contaminated from cosmic rays.
The observed the 6Li plateau abundance is 6Li/H=6.3x10-1 [11].
Assuming the galactic
cosmic ray (GCR) origin for all 6Li, the cosmic ray Li abundance on MPH stars is
i)
=
HGCR =
(L
6
Li7U)
H
=
1.30 x 10-11
(6.4)
GCR
which accounts for 10.6% of the observed Spite plateau [36].
Removing cosmic ray contamination, the discrepancy between 7Li plateau observations
and the WMAP+BBN prediction can be revised as,
7
Liplateau
-
LiBBN
7
= 4.8
(6.5)
LiGCR ~ 6LiGCR
The magnitude of the discrepancy is enlarged by 11.6% from [19].
The cosmic ray 'Li
contamination is not negligible and should be taken into account for the 7Li stellar depletion
mechanisms.
6.5
Future Outlook
AMS-02, to be installed on the International Space Station in 2010, will perform a 3 year
mission on study of cosmic rays.
The expectations for Li/C and 7Li/ 6Li ratio measurements
are:
(1) 107- 108 events for carbon and 106-107 events for lithium.
(2) Li/C measured in the range of 0.1 GeV/nucleon to 1-2 TeV/nucleon with high
precision.
(3) 7 Li/ 6 Li measured in the range of 0.1 GeV/nucleon to 10 GeV/nucleon with high
precision.
Figure 6.7 shows the projected B/C ratio and '0 Be/ 9Be ratio from the AMS-02 Monte
Carlo simulation [72].
The statistics and energy range for Li/C ratio and 7Li/ 6Li ratio
measurement are expected to be similar. More details about the detector are discussed in
Appendix B.
0.
0.6
0.5
0.4
0.1
Co 0.3
000.
0.
Q)
I3 0.2
0.
-1
10
1
10
10
2
Kinetic Energy (GeV/n)
0.1
0.09
0.08
0.07
10 ,
1
10
Kinetic Energy (GeVIn)
(b)
Figure 6.7: Projected ratio measurements [72]: (a) B/C results from 6 months of AMS-02 and
(b) '0 Be/ 9Be results from 1 year of AMS-02.
88
Chapter 7
Conclusions
Combining the information from the Tracker, the TOF and the ACC, we have identified 8349
lithium and 22709 carbon nuclei from the total 108 events collected by AMS-01 10-day flight.
The cosmic ray lithium to carbon ratio has measured with unprecedented statistics and energy
resolutions in the intermediate rigidity region from 2 GV to 100 GV.
The 7 Li/ 6Li ratio has
measured to be 1.07±0. 16 in the rigidity range from 2.5 GV to 6.3 GV by fitting the lithium
mass distribution with Monte Carlo data.
7Li/ 6Li
The result extends the measurement of cosmic ray
ratio to the highest rigidity achieved by any experiment.
The Li/C measurement provides an essential probe to the cosmic ray Galaxy
propagations.
Two basic propagation parameters
necessary for diffusive galactic
propagation models, diffusion coefficient and Alfven velocity, have been constrained by this
measurement:
DXX = 5.73 + 0.46 x 1028 cm2/s
VA= 3 3 .4 + 6 .1 km/s
By using cosmological/galactic cosmic ray models to explain the 6Li plateau on the MPH
stars, the cosmic ray 7 Li/ 6Li ratio result enlarges the primordial 7Li discrepancy by 11.6%.
90
Appendix A
Fermi Acceleration
The Fermi acceleration mechanism was first proposed by Fermi [52] in 1949 as a stochastic
means by which charged particles colliding with the moving magnetized clouds could be
accelerated to high energies.
In his origin picture, particles are reflected by the "magnetic
mirrors" associated with irregularities of galactic magnetic field.
move randomly with typical velocity V.
The magnetic mirrors
Particles with velocity v will either gain energy or
loss energy after each collision, depending on whether they experience a head-on or
overtaking collision.
Statistically, head-on collisions are more frequent than overtaking
collisions, assuming v>>V.
Averaged over many collisions, the mean energy gain is
positive and proportional to the square of the velocity of the magnetic clouds.
the mechanism is also called the Second Order Fermi Acceleration.
That is why
Unfortunately, this
process was quickly recognized to be too inefficient to account for the observed spectra.
In 1978, it was shown [113] that non-relativistic shock waves, such as those generated in
Supernova remnants (SNR) expanding into the ISM, will accelerate particles at a rate
proportional to the velocity of the shock wave (First Order Fermi Acceleration).
The acceleration scenario is illustrated in the Figure A.l.
A particle diffuses through
the material on either side of the shock by scattering on the magnetohydrodynamic (MHD)
Alfven waves.
Assuming the Alfven velocity is much less than the shock velocity and the
medium in both sides is collisionless, the scattering will not change the particle energy in the
local rest frame.
A particle has initial energy El at the rest frame of downstream medium
may cross the shock front and escape into infinity or re-cross the shock into the downstream
again.
After one cross cycle, the energy of the particle Ef can be calculated by performing
two successive Lorentz transforms,
Ef = Eiyei(1 -
reicos6)(1 + f#re cos 6)
(A.1)
where fl,,, and y,,, are the relative velocity and Lorentz factor of upstream to downstream
media, and Oi (in the rest frame of upstream), and 0,, (in the rest frame of downstream) are
the incident angles shown in Figure A. 1.
Assuming isotropic angular distribution of the scattering, the flux-weighted averages of
the direction angle cosines, over the relevant ranges -Tr/2 ! Oi !! 0 and 0!! 00 !< -a/2, are
respectively (cos0i) = -2/3
<< 1.
and (cosO.) = 2/3.
For non-relativistic SNR shock waves,
Therefore the average energy gain per cross cycle can be approximated as
4
(Ef
(Ei) (1 + 3 Nei)
(A. 2)
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Shock front
Figure A. 1:
Schematic view of one cycle of shock wave acceleration.
After n cross cycles, particles having initial energy Eo will be accelerated to E
EO(j +4
3
Assuming P is the probability that the particles stay at teach cycle, the
number of particles remains after N cycles is N = NOP'
This yields the power-law
spectrum
dN(E)
dE
where a =
"n(
spectral index of -2.
)
(A.3)
~1 for the strong non-relativistic shock wave acceleration giving a
94
Appendix B
AMS-02 Detector
In the year 2010, AMS-02 will be installed on the International Space Station to begin a 3
year mission to perform a high statistics study of cosmic rays.
Based on the same core
design of its prototype, AMS-01, AMS-02 has made tremendous improvements. Figure B.1
shows a schematic drawing of AMS-02.
From top to the bottom, it contains the following
main sub-detectors:
(1) A 20 layers Transition Radiation Detector (TRD) to discriminate positrons from protons,
up to 300GeV to search for dark matter signals.
(2) Four layers Time of Flight System (TOF) to provide velocity and charge measurement,
and faster trigger for the whole apparatus.
(3) The superconducting magnet to develop a dipolar magnetic field of ~0.87 T in the center,
providing the Bending power of BL 2 = 0.87 T m2 .
2
(4) Eight layers of double-sided silicon tracker of a global active area of 6.6 m2. The
measured 10.7 pm spatial resolution on the bending plane gives a maximum detectable
rigidity of a few TV.
(5) An Anti-Coincidence Counter (ACC) to veto high inclination particles.
(6) A Ring Imaging Cerenkov Counter (RICH) to provide high precision velocity
measurement and also the charge of the incoming particles.
(7) An Electromagnetic Calorimeter (ECAL) which provides 3-dimensional image of EM
shower development to distinguish electrons and positrons from hadrons with a rejection
of_10 4 in the range of 1.5 GeV to 1 TeV.
With all these improvements, the cosmic ray lithium to carbon ratio and 7Li to 6Li ratio can be
measured at an unprecedentedly accurate level.
AMS-02 are summarized as following:
Compared to AMS-01, the advantages of
(1) 3 years mission will provide a statistics by at least 3 orders of magnitude larger than the
AMS-01 measurement.
(2) The bending power of superconducting magnet is 6 times larger than the AMS-01's
magnet, which allows cosmic ray abundance measurement (Li/C ratio) up to a few
TeV/nucleon with high precision.
(3) Velocity measurement is highly improved by the RICH with 0.1% accuracy (3% for
AMS-01 TOF). The 7Li/ 6Li ratio and the 10 Be/9Be ratio are predicted to be measured up to
10 GeV/nucleon.
(4) Charge can be measured independently by the TOF, the Silicon Tracker and the RICH.
AMS 02
Figure B. 1:
The schematic view of AMS-02 detector.
Appendix C
GALPROP Parameter Setting
1234567890123456789012
-=====================value
Title
conventional/2D 4 kpc tuned to agree with ACE
Title
source isotopic distr. of an element = solar isot. abund. distr.
n spatial dimensions = 2
r min
=00.0
min r
r max
=20.00
max r
dr
= 1.0
delta r
z min
=-4.0
min z
z max
=+4.0
max z
dz
= 0.1
delta z
x min
= 0.0
min x
x max
=+15. 0
max x
dx
-
0.2
delta x
y_min
-
0.0
min y
y max
=+15. 0
max y
dy
= 0.2
delta y
p min
=1000
min momentum (MV)
p_max
=4000
max momentum
p factor
=1. 50
Ekin min
=1. Oel
min kinetic energy per nucleon (MeV)
Ekin max
=1. 0e7
max kinetic energy per nucleon
Ekin factor
=1. 3
p Ekin grid
Ekin
momentum factor
kinetic energy per nucleon factor
pH Ekin alignment
E gamma min
1. e0
-
E gamma max
S1. e8
min gamma-ray energy (MeV)
max gamma-ray energy (MeV)
1.4
E gamma factor
gamma-ray energy factor
integr.over part.spec.: =1-old E*logE; 0=1-PL analyt.
integration-mode
nusynch_min
1.0e6
min synchrotron frequency (Hz)
nusynch_max
= 1.0e10
nu synch_ factor
= 2.0
long_min
=
longmax
=359. 50
lat min
=-89. 50
gamma-ray intensity skymap longitude maximum (deg)
gamma-ray intensity skymap latitude minimum (deg)
lat max
=+89. 50
gamma-ray intensity skymap latitude
d_long
=
1.00
gamma-ray intensity skymap longitude binsize (deg)
d lat
-
1.00
gamma-ray intensity skymap latitude
DOxx
=5.75e28
diffusion coefficient at reference rigidity
D rigid -br
=4.0e3
reference rigidity for diffusion coefficient in MV
D_g_1
= 0.34
diffusion coefficient index below reference rigidity
D g_2
= 0.34
=1
diffusion coefficient index above reference rigidity
O=no reacc.; 1,2=incl.diff.reacc.; -1==beta^3 Dxx;
diff reacc
0.50
max synchrotron frequency (Hz)
synchrotron frequency factor
gamma-ray intensity skymap longitude minimum (deg)
maximum (deg)
binsize (deg)
11=Kolmogorov+damp ing; 12=Kraichnan+damping
vAlfven
=36.
Alfven speed in km s-1
dampingp0
= 1.e6
MV -some rigidity (where CR density is low)
dampingconst_G
= 0.02
a const derived from fitting B/C
damping maxpath L
= 3.e21
Lmax'1 kpc, max free path
convection
=0
1=include convection
vO conv
=0.
km s-1
v conv=vO conv+dvdz conv*dz
dvdz conv
=10.
km s-1 kpc-1
v conv=v0_conv+dvdz conv*dz
nucrigid br
=9. 0e3
nucg 1
=1. 82
nucleus injection index below reference rigidity
nuc g 2
=2. 36
nucleus injection index index above reference rigidity
inj_spectrum type
= rigidity
electron g_0
=1. 60
reference rigidity for nucleus injection index in MV
rigidity
lbeta rigH Etot nucleon injection spectrum type
electron injection index below electronrigid brO
electron rigid brO
=4. 0e3
reference rigidity0 for electron injection index in MV
electron_g_1
=2. 50
electron rigid br
=1. 0e9
reference rigidity for electron injection index in MV
electron_g_2
=5. 0
electron injection index index above reference rigidity
HeH ratio
=0.11
X CO
=0.4E20,0.4E20,0.6E20,0.8E20,1.5E20,10.0E20,10.0E20,10.0E20,10.0E20
electron injection index below reference rigidity
He/H of ISM, by number
conversion factor from CO integrated temperature to H2 column density
for CO rings
0.0 - 1.5 - 3.5
-
5.5 -
7.5 - 9.5
-
11.5 -
13.5 -
fragmentation
=1
1=include fragmentation
momentum losses
=1
1=include momentum losses
radioactive decay
=1
1=include radioactive decay
K capture
=1
1=include K-capture
start timestep
=1. 0e7
end timestep
=1. 0e2
timestepfactor
=0. 25
timestep repeat
=20
number of repeats per timestep in timetepmode=1
timestep repeat2
=0
number of timesteps in timetepmode=2
timestep print
=10000
timestep diagnostics =10000
control diagnostics =0
network iterations
prop r
prop_x
prop y
prop_z
= 1
=-1
=1
=-1
prop p
15.5
-
50 kpc
number of timesteps between printings
number of timesteps between diagnostics
control detail of diagnostics
number of iterations of entire network
1=propagate in r (2D)
1=propagate in x (2D,3D)
1=propagate in y (3D)
1=propagate in z (3D)
1=propagate in momentum
use symmetry
= 0
0=no symmetry, 1=optimized symmetry, 2=xyz symmetry by copying(3D)
vectorized
= 0
0=unvectorized code, 1=vectorized code
source specification
source model
0
-
2D::1:r,z=0 2:z=0
1 0=zero 1=parameterized
with cutoff
source parameters_1
source parameters 2
-
3D::1:x,y,z=0 2:z=0
0.
=1.
model 1:alpha
model 1:beta
3
:x=0 4:y=0
2=Case&B 3=pulsars 4= 5=S&Mattox 6=S&Mattox
source parameters_3
20.0
n cr sources
0
number of pointlike cosmic-ray sources
cr source x_01
= 10.0
cr sourcey 01
= 10.0
x position of cosmic-ray source 1 (kpc)
y position of cosmic-ray source 1
cr-source z 01
= 0.1
z position of cosmic-ray source 1
cr source w 01
= 0.1 sigma width
cr sourceL 01
= 1.0
luminosity of cosmic-ray source 1
cr-source x 02
3.0
x position of cosmic-ray source 2
cr sourcey 02
= 4.0
y position of cosmic-ray source 2
cr-source z 02
0.2
z position of cosmic-ray source 2
cr source w 02
model 1:rmax
= 2.4 sigma width
2.0
cr source L 02
3D only!
of cosmic-ray source 1
of cosmic-ray source 2
luminosity of cosmic-ray source 2
SNR_ events
= 0
SNR_ interval
= 1.0e4 time interval in years between SNR in 1 kpc^-3 volume
SNR_ livetime
= 1.0e4 CR-producing live-time in years of an SNR
SNR_ electron sdg
= 0.00
delta electron source index Gaussian sigma
SNR nuc sdg
= 0.00
delta nucleus
handle stochastic SNR events
SNR_ electrondgpivot = 5.0e3
source index Gaussian sigma
delta electron source index pivot rigidity (MeV)
SNR nuc dgpivot
= 5.0e3
delta nucleus
HI survey
= 9
HI survey 8=orig 8 rings
9=new 9 rings
CO survey
9
CO survey 8=orig 8 rings
9=new 9 rings
B field model
050100020
ISRF file
MilkyWayDRO.5_DZO.1_DPHI1ORMAX20 ZMAX5_galpropformat.fits
bbbrrrzzz
source index pivot rigidity (MeV)
bbb=10*B(0)
rrr=10*rscale zzz=10*zscale
input ISRF file
ISRF factors
= 1.0,1.0, 1.0
proton norm Ekin
= 1.00e+5 proton kinetic energy for normalization (MeV)
protonnorm-flux
= 4. 90e-9 to renorm nuclei/flux of protons at norm energy (cm^-2 sr^-1 s'-1
ISRF factors for IC calculation: optical, FIR, CMB
MeV^-1)
electron norm Ekin
= 34.5e3
electron kinetic energy for normalization (MeV)
electron norm flux
=.40e-9
flux of electrons at normalization energy (cm^-2 sr'-l s^-1 MeV^-1)
max Z
-
28
maximum number of nucleus Z listed
100
useuse-
=1
useuse-
=-1
=1
use-
=-1
useuse-
=-1
=21
use-
=:1
=:1
=1
useuse-
=:1
use-
=-1
use-
=-1
use-
=:1
use-
=1
use-
=-1
useuse-
=-1
=1
use-
=1
use-
=-1
use-
=1
use-
=-1
=1
use
useuse
=1
=21
use-
=-1
use-
=-1
useuse-
=-1
useuseiso- abundance 01 001
S1. 06e+06
iso abundance 01 002
iso abundance 02 003
34.8
=
9.033
iso- abundance 02 004 = 7.199e+04
iso- abundance 03 006
=
0
iso abundance 03 007
=
0
iso- abundance 04 009
=
0
iso abundance 05 010
=
0
iso abundance 05 011
=
0
iso abundance 06 012 =
2819
C
iso abundance 06 013 = 5.268e-07
iso abundance 07 014 =
182.8
N
iso abundance 07 015 = 5.961e-05
iso abundance 08 016 =
3822
0
iso abundance 08 017 = 6.713e-07
iso abundance 08 018 =
1.286
iso abundance 09 019 = 2.664e-08
iso abundance 10 020 =
312.5
F
Ne
iso abundance 10 021 = 0.003556
iso abundance 10 022 =
100.1
iso abundance 11 023 =
22.84
Na
iso abundance_12_024 =
658.1
Mg
iso abundance 12 025 =
82.5
iso abundance 12 026 =
104.7
iso abundance 13 027 =
76.42
Al
iso abundance 14 028 =
725.7
Si
iso abundance 14 029 =
35.02
iso abundance 14 030 =
24.68
iso abundance 15 031 =
4.242
P
iso abundance 16 032 =
89.12
S
iso abundance 16 033 =
0.3056
iso abundance 16 034 =
3.417
iso abundance 16 036 = 0.0004281
iso abundance 17 035 =
0.7044
iso abundance 17 037 = 0.001167
Cl
iso abundance 18 036 =
9.829
Ar
iso abundance 18 038 =
0.6357
iso abundance 18 040 = 0.001744
iso abundance 19 039 =
1.389
iso abundance 19 040 =
3.022
K
iso abundance 19 041 = 0.0003339
iso abundance 20 040 =
51.13
iso abundance 20 041 =
1.974
Ca
iso abundance 20 042 = 1.134e-06
iso abundance 20 043 = 2.117e-06
iso abundance 20 044 = 9.928e-05
iso abundance 20 048 =
0.1099
iso abundance 21 045 =
1.635
Sc
iso abundance 22 046 =
5.558
Ti
iso abundance-
047 = 8.947e-06
iso- abundance-
048 = 6.05e-07
iso- abundance-
049 = 5.854e-09
iso- abundance-
050 = 6.083e-07
iso- abundance-
050 = 1.818e-05
iso abundance-
051 = 5.987e-09
iso abundance-
050 =
2.873
iso- abundance-
052 =
8.065
iso abundance
053 = 0.003014
iso- abundance-
054 =
0.4173
iso- abundance-
053 =
6.499
iso abundance-
055 =
1.273
iso abundance-
054 =
49.08
iso abundance-
056 =
697. 7
iso abundance-
057 =
21.67
iso- abundance
058 =
3.335
iso- abundance-
059 =
2.214
iso abundance
058 =
28.88
iso- abundance-
060 =
iso- abundance-
061 =
0.5992
abundance-
062 =
1.426
064 =
0.3039
iso
iso abundance
total cross section
11.9
= 2
cross section option = 012
total cross section option: 0=L83 1=WA96 2=BP01
100*i+j
i=i: 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
primaryelectrons
= 1
secondarypositrons
1
secondaryelectrons
1
secondaryantiproton
2
tertiaryantiproton
secondary protons
gamma rays
pi0_decay
-
0 1 2
1
1
-0
0
1=compute gamma rays, 2=compute HI,H2 skymaps separately
1= old formalism 2=Blattnig et al.
IC isotropic
1,2= compute isotropic IC: 1=compute full, 2=store skymap components
IC anisotropic
1,2,3= compute anisotropic IC: 1=full, 2=approx., 3=isotropic
bremss
-0
1=compute bremsstrahlung
synchrotron
= 0
comment
DM positrons
= the dark matter (DM) switches and user-defined parameters
=
1=compute DM positrons
DM electrons
= 0
1=compute DM electrons
DM antiprotons
= 0
1=compute DM antiprotons
DM gammas
= 0
1=compute DM gammas
DM_ double0
= 2.8
DM doublel
= 0.43
core radius, kpc
local DM mass density, GeV cm-3
DM_ double2
= 80.
neutralino mass, GeV
DM_ double3
= 40.
positron width distribution, GeV
DM double4
= 40.
positron branching
DM_ double5
= 40.
electron width distribution, GeV
electron branching
1=compute synchrotron
DM_ double6
30.
DM_ double7
50.
DM_ double8
40.
DM double9
=3.e-25
DM_ intO
=1
DM_ intl
=-1
DM_ int2
=-1
DM int3
=-1
DM_ int4
=1
pbar width distribution, GeV
pbar branching
<cross sec*V>-thermally overaged, cm3 s-1
isothermal profile
DM_ int5
DM int6
DM_ int7
DM_ int7
DM int9
output_gcr_full
output full galactic cosmic ray array
read in nuclei file and continue run
warm start
verbose
-0
test suite
-0
verbosity: 0=min,10=max <0: selected debugs
run test suite instead of normal run
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