High Energy Cosmic Rays: Fundamentals, Status and Perspectives

1
High Energy Cosmic Rays Fundamentals, Status
and Perspectives
Antonio Insolia Dipartimento di Fisica e
Astronomia INFN Università di Catania
(Italy)
INST International School on Nuclear Physics and
Astrophysics August 26-31, 2005 Hanoi
(Vietnam)
2
Outline

• Brief cosmic ray history
• Electromagnetic interactions in showers
• Shower development the Heitler toy model.
• Hadronic interactions
• The highest energy cosmic rays
  Greisen-Zatsepin-Kuzmin cut-off.
• The energy spectrum the status-of-art.
• Accuracy of direction and problem of energy
  estimates.
• HECR Mass composition elongation rate, Ne/Nµ
  ratio new tools
• Summary of experimental data MACRO/EAS-TOP,
  Kascade,
• AGASA, HiRes
• The Fluorescence Detector of the Pierre Auger
  Observatory
• history, realisation and the first
  preliminary results_at_ICRC
• 2005 (Pune, India).
• The EUSO project.

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2
3
4
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Lecture 1, part A

• Brief cosmic ray history
• b) The key interactions for an Extensive Air
  Shower (EAS)
• c) A simple model for an Extensive Air Shower

4

• Brief cosmic ray history

5
The start of the Cosmic Ray Research

• During a six hours flight with a balloon gondola
  (August 7, 1912) Hess Wolf carefully recorded
  the readings of three electroscopes used to
  measure the intensity of the radiation
• they noted a rise in the radiation level as the
  balloon rose in altitude
• V. F. Hess (1912) the results of these
  observations seem best explained by a radiation
  of great penetrating power entering our
  atmosphere from above...,
• Physikalische Zeitschrift (1912)
• R.A.Millikan (1923-1926) Lake Muir Lake
  Arrowhead experiments
• the radiation is named cosmic rays
• D. Skobeltzyn (1929) using a condensation
  chamber in a magnetic field found that cosmic
  rays were able to produce secondary particles
  able to ionize the matter
• W. Bothe and W. Kolhörster set-up for the
  detection of the first events in coincidence
• B. Rossi makes the first coincidence experiment
  using three GM counters in coincidence the
  first air shower had been detected
• but ..
• The paper by B. Rossi was initially rejected by
  the chosen scientific journal
• and only later on published by an other journal

6
V.F. Hess Data (1912)
W. Kolhoster data (1913,1914)

I(z)I0exp(-µz), with an attenuation coefficient
µ1x10-5cm-1
7
V. F. Hess (1912)
µCR 1x10-5cm-1 while, from experiments on
gamma rays emitted from radium it was known that
µ? 5x10-5 cm-1 The new absorbtion
coefficient was smaller by a factor 5 !!! Gamma
rays hypothesis was almost ruled out !!!
8
W. Bothe and W. Kolhörster set-up for the
detection of the first events in
coincidence(Z. für Physik, 56 (1929) 751)
Fe
Pb
Two GM counters shielded by Pb and Fe produced
a coincidence rate consistent with previous
measurements at the sea level Inserting a gold
slab absorber the coincidence rate reduced in a
way comparable to the rate suppression produced
by the whole atmosphere the measured mass
absorption coefficient ruled out the possibility
that the cosmic radiation could have been gamma
or electrons. They made the hypothesis that the
detected particles were very energetic charged
particles , E ? 10 9 - 1010 eV.
A gold slab
9
B. Rossi set-up for the detection of the first
air shower(1929-1930)
Hypothesis Primary and secondary particles
Pb
Three GM counters in a triangle-like setup were
discharged in coincidence with a measured rate
R 35 events/h, Without the Pb screen, the
coincidence rate was R ? 0 events/h Rossi
made the hypothesis that secondary particles
were produced by the interaction of a primary
particle in the Pb screen. The existence of
Extensive Air Showers was, therefore, postulated
by Rossi and the paper reporting the results
was rejected by the Referee !!!!!
10
The search for geomagnetic effects
The discovery that cosmic radiation is primarily
made of charged particles triggered the search
for effects due to the Hearth magnetic field,
like Est-West effect. Lets consider,
therefore, for simplicity, the case of a uniform
static magnetic field B
11
Charged particle in a uniform static magnetic
field B

• The eq. of motion for a particle of charge Ze and
  rest mass mo is given by
• d/dt (?mov) Ze (E v x B) where ?
  (1-v2/c2) is the Lorentz factor
• the gyroradius of the particle on its spiral path
  with constant pitch
• angle is given by
• r ?mov sin?/ZeB (?mo v/Ze ) (sin?/ B)
  (pc/Ze) (sin?/Bc)
• where R pc/Ze
• is the rigidity , pc-gt joule, Ze -gt
  coulomb, thus R is measured in volt
• or, just for better convenience, in gigavolt
  GV.
• with angular frequency
• ? v / r ZeB/ ?mo

12
Est-West effect

• C. Stoermer (1912) analytical solution of the
  equation of motion for the case of a dipole field
  M
• RStoermer M/2r2 cos4?B / 1 (1-
  cos3?B sin? sinfB) ½ 2 , (1)
• where ? is the particle zenith angle, fB the
  azimuthal angle measured from the direction of
  the magnetic south and ?B is the magnetic
  latitude.
• Eq. (1) is the first prediction for the
  Est-West effect due to the asimmetry introduced
  by the fB angle as
• for positively charged particles at the
  same zenith angle the rigidity cutoff RStoermer
  is higher from the est direction and viceversa
  for negatively charged particles.
• Finally, an excess of particles coming from
  west of the zenith was discovered by
• T. H. Johnson (Mexico City, 1933)
• L. W. Alvarez A. H. Compton (Mexico City,
  1933)
• S. De Benedetti B. Rossi (Asmara , 1933)

13

• The recently discovered cosmic rays
• were
• positively charged particles !
• The measured excess was of order 10

14
Hearth magnetic field pointing North
perpendicular outside the page plane (plane
of the page equatorial plane)
BHearth ? 10-1 gauss the magnetic dipole
moment MHearth?8 x 1025 gauss cm3
Trajectories of negative charged particles
Trajectories of positive charged particles
Est
Est
West
West
15
J. Clay (1927) in a long trip from Leida to
Jakarta using an ionization chamber
Amsterdam
Genoa
Jakarta
16
A.M. Hillas, Cosmic Rays (1972) Pergamon Press
Oxford
Projections onto meridian plane of trajectories
in a dipole field of positive particles with
vertical arrival direction at a selected point
53 N
Lemaître and Vallarta, 1932
Projections onto equatorial plane of
trajectories in a dipole field
17
The problem is still attracting interest the
Vietnam groups contribution

• Pham Ngoc Diep et al., Measurement of the
  est-west asymmetry of the cosmic muon flux in
  Hanoi ,
• where a relative difference between minimum
  and maximum flux of the order of 19 has been
  reported at the zenith angle ? 65o , using an
  orientable scintillator telescope.
• NP B627 (2002) 29
• NP B661 (2003) 3
• NP B(2004)

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19
Pierre Auger, Paris 1981
The conclusion was that extensive air showers
was the reason for the correlated arrival of
particles at widely separated detectors. P.
Auger and collaborators deduced that the primary
energy was about 1015 eV !!!
20
Primaries were interacting in air as much as
particles were interacting inside a cloud
chamber, producing a lot of secondary particles
J G Wilson and C B A Lovell Nature 1938
21
proton interacting with argon in cloud chamber
G R Evans Mt Marmolada Dolomites 1956
22
Still inside a cloud chamber a sort of
Extensive Air Shower
1.3 cm , Pb
Shower initiated by a 10 GeV proton in lead
plates of cloud chamber. The area is O.5 m x 0.3
m
The picture contains all main features of a real
Extensive Air Shower (EAS) as we will discuss
later on.
23
Some major discoveries made with cosmic rays in
the early times
Anderson (1933) the positron Pierre Auger
(1938) Extended Air Shower (postulated by B.
Rossi in 1930) Neddermeyer Anderson the
muon Powell Occhialini (1947) the pion
(postulated by Yukawa) Rochester Butler (1947)
strange particles ? (uds), S(uus,uds,dds) MIT
(1950) the neutral pion Powell (1949)
discovered the process K? ? ? ?-
Experimental evidences for antimatter p-
(eventually discovered by Segre Chamberlain)

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Then, interest in CR decreased so much that
Bruno Rossi made a predictioncompletely
wrong !

• B. Rossi
• ..the cosmic ray physicist is becoming an old
  fashioned role, while the nuclear physicist, the
  geophysicist .. are more and more working on
  cosmic radiation. It seems reasonable that the
  future science historians will close the cosmic
  ray chapter with the 1962 (50 years) anniversary
  of the Hess discovery,
• B. Rossi, Cosmic Rays , McGraw-Hill Inc. (New
  York, 1964).

but .
25
The Volcano Ranch Array J. Linsley , Phys. Rev.
Lett. 10 (1963) 146
In 1963 an event with primary energy E ? 1020eV
was reported by J. Linsley at Volcano Ranch
(New Mexico USA)
A
Shower core
Dots mark the location of 3.3 m2 scintillators
numbers are particle densities (?) in
particles/m2 A is the estimated location of the
core and lines are equal densities contours.
26
Direct CRs detection below ?1014 eV
Indirect CRs detection above ?1014 eV
27
What we are talking about Composition of
cosmic rays

• Typical composition in the region around 100
  GeV
• (direct meas. are possible), 99.8 are
  charged primaries
• 0.2
  are g or neutrinos
• The charged primaries are 98 nuclei, 2
  electrons and positrons
• Finally the nuclear component is made of
• p 87
• a 1 2
• M (Z6 to 9) 0.70
• H (Z10 to 20) 0.20
• VH (Z21 to 30) 0.10
• For larger energies, one has to rely on
  two main different
• procedures
• Measurement of longitudinal development of the
  EAS
• Measurement of electron to muon density ratios
  in the EAS
• (both discussed later on)

Low energy region
Direct measurements energy region
High energy region
28
The CR elemental abundances (measured at Hearth),
compare quite well with the solar system
abundances with a few exceptions (all relative to
Si100), in the energy range 500-1000 MeV/nucleon

• CR Solar system
• Li 136 0.005
• Be 67 0.00008
• B 233 0.0035
• Sc 4.5 0.003
• Ti 10 0.24
• V 6.7 0.025
• Cr 12 1.3
• Mn 8.2 0.93

Two groups of elements
T.K. Gaisser, Cosmic Rays and Particle Physics,
Cambridge Univ. Press (1992)
29
Comparing with abundances of elements in the
solar system

• In cosmic rays two groups of elements Li, Be,
  B and Sc,Ti,V,Cr Mn are many orders of
  magnitude more abundant than in the solar system
  material.
• Those elements (absent as end products of stellar
  nucleosynthesis), are produced as fragmentation
  products of the quite abundant nuclei of carbon
  and oxigen (Li,Be, B ) and of iron (Sc,Ti,V,Cr,Mn
  ) in collisions of cosmic ray proton in the ISM
• This is very important for propagation studies.

30
Gaisser 2002
gt1019 eV 1 km-2 year-1 sr-1
31

• The key interactions for EAS

32
For primary energy larger than 1014 eV we need
to detect an EAS
blu e-/e azure photons red neutronsorange
protons green muons
What about an EAS ?
33
The key interactions for EAS
(1) pleading pN2, O2 ? pleading p
N(? ?- ?o) (2) ?o ? ? ? (3)
(? or ?- ) p ? ? p N(? ?- ?o)
until ? decay is more probable than
interaction, as ? ? µ ?µ
, with tp 2.8 x 10-8 s
µ- ? e- ?e ? µ with tµ 2 x 10-6
s (1) and (3) are strong interactions (2) is
an electromagnetic interaction
Lets start with the electromagnetic part
just follow first the ?o
34
Electromagnetic part

• Two main processes
• Pair production
• Bremmstrahlung
• plus
• Ionisation energy loss

35
Electromagnetic part of the cascade pair
production ? -gt e e-

• opening angle ?mc2/h?
• gamma ray disappears in pair production h?
  2?mec2

?pair    1/n?pair mean free path, n
density ?pair ? ((Z2 re2)/137)(28/9)ln(183/Z1/
3) cm2 ?pair ? 5.7 re2 6 x 10-26 cm2 ,
for air ?pair (7/9)?bremstrahlung
36
Electromagnetic part of the cascade
bremstrahlung, i.e. the radiation associated
with the acceleration of electrons in the
electrostatic field of ions and the nuclei of
atoms

• Non-relativistic bremmstrahlung
• -(dE/dx)brems (constant) Z2 N v
• energy loss proportional to the square root of
  the kinetic energy E, as
• v v(2E/m)

• Relativistic bremmstrahlung
• -(dE/dx)brems E/ Xo
• Thus, energy loss proportional to the energy E.
• Some features of the bremmstrahlung energy
  spectrum
• is flat electron can lose all of
  its energy
• with an energy loss proportional to the
  energy E

37
Bremmstrahlung Energy loss the radiation length
the critical energy
Thus, we can characterise the electron energy
loss with a parameter called radiation length
considering that the energy loss as the electron
traverses a material of thickness x is given by
E Eo exp(-x/Xo), where Xo g cm-2
is the radiation length The radiation length
can be approximated as X0 103 x A /6Z(Z1)
, S. Hayakawa, Cosmic Ray Physics, Wiley (NY,
1969) When the rate of energy loss due to
bremmstrahlung falls below the rate of energy
loss due to ionisation, the electron is said to
be at the critical energy E
ec . Therefore the condition is
-(dE/dx)brem  -(dE/dx)ionisation
Thus, what about ionisation ?
38
Ionisation energy loss of protons p X

• Non-relativistic treatment
• -dE/dx (Z2 e4 Ne )/(4pe2o me v2 ) ln(2 me
  v2)/ltIgt ,
• where Ne is the electron density and ltIgt
  is the mean atomic ionisation potential
• The relativistic case (the famous Bethe-Bloch
  formula) gives
• -dE/dx (Z2 e4 Ne )/(4pe2ov2 me ) ln(2 ?2
  me v2)/ltIgt - v2 /c2

log(-dE/dx)
? 1/v2 ? 1/E
? ln ?2
M. S. Longair, High Energy Astrophysics,
Cambridge Univ. Press (1992)
log(E)
39
Ionisation energy loss of electrons

• The relativistic case gives
• -dE/dx (e4 NZ )/(8pe2o me v2 ) ln( ?2
  me v2 Emax)/2ltIgt2
• - (2/ ? -1/ ?2 )ln2 1/ ?2
  1/8 (1 - 1/ ? )2

Energy loss in air versus momentum a larger
energy loss for protons for the same kinetic
energy
protons
electrons
MeV/c
104
1
102
40
The radiation length and critical energy for
various materials
E Eo exp(-x/Xo)
where x (g cm-2) ?t, the density, ?, in g
cm-3 and the path length, t, in cm.

and E ec when -(dE/dx)brem  -(dE/dx)ionisation
41
Shower initiated by proton in the lead plates
of a cloud chamber
Why is there lateral spread ?
42

• The direction of propagation of an electron
• can be modified in a major way by
  scattering.
• Is there any way to make more quantitave this
• consideration ?

43
The Molière Radius
The lateral spread by which an electron at the
critical energy is SCATTERED while traversing ONE
radiation length (and its energy is being reduced
by a factor 1/e) is called the Molière
radius If the electron has an initial momentum
of p (in units of MeV/c) then   ?rms(21
MeV/p?)?(x/Xo) Scattering Angle Thus, at the
critical energy, an electron undergoes a rms
scatter of about ?14o as it traverses 1
radiation length the Moliere unit is
therefore Ro 21 MeV/?c , in radiation
length.
44
The radiation length, critical energy and Molière
radius for air, water and lead
45
The typical spread on the detection level for
the highest Volcano Ranch event is measured by
the particle densities
E ? 1020 eV
Dots mark the location of 3.3 m2 scintillators
numbers are particle densities (?) in
particle/m2 Thus ? versus core distance
looks like as a crucial quantity The specific
functional form and choice of parameters will
depend on the specific SD features
46
The measured particle density vs core distance
defines the Lateral Distribution Funtion (LDF)

• With the Haverah Park water Cherenkov
  detectors grid, in units of vertical equivalent
  muons per m-2 it was used
• ?(r) k x r (?r/4000)
• where ? is a parameter that depends on
  zenith angle ? and energy E and r is in the
  range 50 lt r lt 800 m
• and
• ?(r) k (1/800)ß x r (?r/ro) ß
• with ß 1.03 0.05 and r in the range r gt
  800 m.
• Different parametrizations were used for
  different detectors, as for plastic scintillators
  in Volcano Ranch, Yakutsk and AGASA.

47
LDF what do we expect to measure at the ground
detector ?

48
LDF for p and Fe
?3 muons /m2
?5 muons /m2
Proton primaries
Iron primaries
Two VERY IMPORTANT features in those LDFs (see
next slide) (from Monte Carlo simulations)
49
Two very important features contained in the
previous results

• a) The ratio Ne/Nµ is variable in the range 100
  1 versus the core distance
• b) The ratio (integrated over the core distance)
  depends on the primary (proton or iron)

Does it provide a tool to discriminate proton
from iron ?
50
Models can be wrong! Hadronic Physics Uncertain
HP Lateral Distribution - models 1978
LDF problem
51
Lets use again our Lab shower for an other
fundamental typical EAS feature N vs
atmospheric depth the longitudinal
development
Number of particles
Xmax
Nmax
Rise and fall of the number of particles
X atmospheric depth
52
Two important points

• So far we have seen, with the help of this
  shower in miniature, the two most prominent
  features of a realistic Extensive Air Shower
  (EAS)
• 1) the raise and fall of the number of particles
  or
• the longitudinal development (more later
  on)
• 2) the particle density versus core distance or
• the lateral distribution function
• The theory of the lateral spread of the
  shower was
• developed by Greisen (1956) and Kamata
  
• Nishimura (1958)

53
Another crucial piece of information The
arrival direction
Fast timing gives the direction
Schematic view
? ? 30 - 1500 m
54
Do we have a simple minded model to describe the
main features of a shower ?
Yes !! The Heitler toy model (RMP, 21 (1949) 113)
55
A very simple model for the e.m. cascade is due
to W. Heitler (RMP, 21 (1949) 113) and it
illustrates some general features of air showers

• In the branching process each line represents a
  particle or a packet of energy.
• A few assumptions
• At any vertex the energy is split in two
• Branching occurs after one collision
  length ?, for whatever the splitting process is
  .
• The cascade continues until the electron has
  reached the critical energy, traversing a
  material of thickness X

?
?
?
56
Thus, within the Heitler toy model, we get

• Number of nodes n X/?
• Number of particles, after X rad. lengths, N(X)
  2X/?
• At depth X the energy per particle is E(X) Eo
  /N(X)
• Splitting process goes on until a critical energy
  is reached
• E(X) Ec (as for instance
  ec )
• The number of particles at the shower maximum
  will be
• N(Xmax) Nmax Eo/Ec Nmax ?
  (constant) x Eo and
• Xmax ? ln (Eo/?c)/ ln 2 Xmax ?
  ln (Eo)
• actually
  the elongation rate

57
Other features of the Heitler model

• Cascade grows until rate of energy loss by
  ionisation exceeds that by bremsstrahlung
• A nucleus as a primary CR
• If the shower is generated by a Nucleus
  lets assume a simple superposition model,
  i.e.
• A nucleus of mass A and total energy E is
  equivalent to A independent nucleons each of
  energy E/A
• Thus, we get
• N(Xmax) Eo/Ec or Nmax ? (constant) x
  Eo (just the same !!!)
• Xmax (constant) x ? ln (Eo/A ?c) or, in
  other words,
• shower generated by heavy primaries
  develop more radiply on
• average (i.e.higher in the
  atmosphere) Xmax is smaller
• Analytical solutions to cascade equations by
  Kamata Nishimura started in
• 1950s, quite soon followed by Monte
  Carlo simulations

58
Lecture 1, part B
a) Hadronic Interactions b) Monte Carlo Shower
simulations
59
Hadronic Interactions
p p ? p p N(? ?-
?o) Over-simplification other particles (like
K, ?, ?, O, etc) omitted Important quantities
are CROSS-SECTIONS INELASTICITY MULTIPLI
CITY
Transverse Momentum
60
Some Useful Numbers and Concepts

• Proton mean free path in air, ?p-air 84 g cm-2
• 12 interactions to sea-level (1000 g cm-2 /84
  g cm-2 )
• FLUCTUATIONS around this number due to
• fluctuations in the point of first interaction
  X1
• INELASTICITY (?)
• fraction of energy NOT retained by leading
  nucleon
• pCR pt ? pLN pt N(? ?- ?o)
• Roughly, mean inelasticity 0.5 BUT.

61
Large systematic uncertainties !!!

• ? (1-Kela) fraction of
• energy loss in a single interaction
• Model dependence
• A quite smooth energy dependence

Mean elasticity ( 1-?) of proton-air and
pion-air collisions as predicted by QGSjet98 and
SIBYLL 2.1
62
Energy contribution into EM cascade

• Charge independence of nuclear forces implies,
  roughly, that in the process
• p p ? p p N(? ?- ?o)
• the energy fraction that goes into neutral pions
  and, hence into the electromagnetic cascade, at
  each collision is (mean inelasticity) x 1/3,
  thus
• 0.5 x 0.33 0.16
• This happens at each and every hadronic
  interaction,
• ON AVERAGE

63
Typical cross-sections
Collisions of interest are with nuclei of
mass A ?pA(inelastic) 45A0.691 mb,
? 84 g cm-2 and ??A
28A0.75 mb, ? 115 g
cm-2 2/3 ratio reflects the number of valence
quarks in pion and baryon But both
cross-sections rise with energy
64
Additional uncertainties from the inelastic
p-air cross-sections from measurements and
models.
1997
2001
65
Still large uncertainties in the atmospheric
physics for the cross section p-Air at the
present time
J. Matthews, ICRC 2005
66
p decay vs p -A interaction
The probability of the two processes occurring in
a given distance interval is equal when
(the mean distance travelled before decay)
?tc is equal to (the mean
distance travelled before interaction) ?/?
??c ?/? where  ?
Lorentz factor of the pion , ? 2.6 x 10-8 s
? the mean free path (in g cm-2) and ?
density (in g cm-3) Example air density 5
x 10-4 g cm-3 at altitude 5000 m Lorentz
factor at which decay and interaction have
equal probability is 380 which means ? pion
energy 50 GeV
67
Different models Monte Carlo Shower simulations

• Longitudinal Development
• Muons electrons in proton and iron induced
  showers
• Model Differences

68
Simulated Longitudinal Development CurvesNumber
of charged particles versus atmospheric depth X

• Xmax is different for different models
• N vs X is different for different models

69
A simple parametrization The Gaisser-Hillas
formula

• A parametrization has been derived by Gaisser
  Hillas for the longitudinal development in the
  form
• Ne (X) Nemax (X-X1)/(Xmax-?) (Xmax-?/?)
  exp-(X-X1)/?
• with 4 parameters Nemax, X1 (the point of first
  interaction),
• Xmax, ? (the mean free path)

See T. K. Gaisser, Cosmic Rays and Particle
Physics, Cambridge Univ. Press (1992) or T.
stanev, High Energy Cosmic Rays, Springer-Verlag
(2004)
70
Main sources of fluctuations

• The depth of first interaction X1 is distributed
  as exp-(X1/?)
• The fluctuations in the Inelasticity
• The net result is that in simulations we get
  
• Fluctuations in the number of charged
  particles in the shower vs X, especially at the
  maximum
• for the quantities Nmax and Xmax

71
A very large number of simulations is required to
deal with these intrinsic fluctuations in Xmax
and Nmax
helium
proton
E 1018 eV and ? 0o
Corsika code, QGSjet98 model
iron
oxigen
Not an easy job !!!!
?Xmax ltXmax, pgt ltXmax, Fegt ? 80 g/cm2
72
At the same time, the overall multiplicity of
secondary particles is very much model dependent,
epsecially at the highest energies.
Almost a factor 2 between different models at
the highest energies
Mean multiplicity of charged particles produced
in inelastic proton-air and pion-air collisions
73
Fluctuations in Xmax the rms sXmax
Solid Sibyll 2.1 dottedSibyll 1.7
dashed QGSJET98
For dots, check original paper ICRC 2001, Engel

• Some comments
• Fluctuations in Xmax are energy dependent
• 20 discrepancy beteween models at the highest
  energies

74
Nmax and Xmax as calculated with two models
of particle interactions
QGSjet model (01) predicts that showers will
maximise a few g cm-2 higher in the atmosphere.
75
Muons in Air Showers

• ?µ 2 x 10-6 s , ? compare with ?p 2.6
  x 10-8 s and
• ?po
  8.4 x 10-17 s
• So muons do not decay until energies are quite
  low (lt 30 GeV)
• Neutrinos from pion and muon decays (not
  detected) are source of
• lost energy from the decay process
• ? ? µ ?µ and µ-
  ? e- ?e ?µ
• Muons produce secondary electrons through
  knock-on reactions
• and bremsstrahlung (as well as muon decay)
• The muon detection plays a crucial for
  observation of inclined showers
• and for the determination the mass of the
  primary via the ratio
• Ne/Nµ (discussed later)

76
What about the muon component in the longitudinal
development of an EAS ?

• We know, from Heitler model superposition
  model, that a iron primary will produce more
  muons at the ground level than a proton if
• Ep-primary
  EFe-primary
• This is because the mean energy of the pions
  is lower in Fe-initiated showers than in the
  proton showers as the energy per nucleon is
  lower.

77
What about the muon component in the longitudinal
development of an EAS ?
Charged Individual event
Muon All events
iron
iron
proton
proton
78
The simulation results may be parametrized as

• N? (Egt1 GeV) kA(E/A??)p
• the muon number is proportional to the primary
  mass and to the energy/nucleon

79
What about the muon number versus muon energy and
primary energy ?
80
Muon numbers above Eµth in proton EAS with zenith
angle 0o
Solid Sibyll 2.1 dottedSibyll 1.7
dashed QGSJET98
Higher contribution
As before Discrepancy between models quite large
81
Sibyll/QGSjet differences

• What this means in practice (see Alvarez-Munez
  et al., astro-ph/0205302)
• Sibyll p/?-air cross-sections are higher (1.4 at
  1019 eV)
• Sibyll secondary pion multiplicity is lower (a
  facter 2 at 1019)
• Xmax for Sibyll is deeper in atmosphere by 30
  g cm-2
• at 1019 eV
• Sibyll generates fewer muons, by 30 - 40 at
  1019 eV
• Other differences plus Monte Carlo codes
• Monte Carlo simulations play a crucial role, but
  still some uncertainties and sistematic
  discrepancies between models

82
In spite of the uncertainties, some typical
numbers for the proton primary Energy
Partition
1018 eV 1020 eV Xmax 890 1069 g
cm-2 Nmax 6x108 5.5x1010 Eem
95.1 97.7 E? 3.2 1.5
E? 1.1 0.5
Hillas 1981
Eµ E? is called missing energy if you
dont measure those two contributions
83
EM component and missing energy what about
iron primary case ?
Fraction of missing energy (Eo Eem)/Eo
1) Iron larger missing energy 2) Other
primaries in between Fe p
40
Fe
30
20
p
T. Stanev , High Energy Cosmic Rays, Springer
(2004)
10
Energy, eV
1015
1016 1017 1018 1019 1020
84

• The End lecture 1

85
Lateral Spread of the hadronic cascade the
Transverse Momentum
The distribution of the transverse momentum of
the secondary particles is well described by
g(pt)dpt ? pt exp(-pt/ltptgt)
with ltptgt 350 MeV/c