Cosmic Ray Astrophysics and Hadronic Interactions

16 Pages·0.47 MB·English

by  Paolo Lipari

1
Cosmic Ray Astrophysics and Hadronic Interactions
3
0 Paolo Lipari a
0
2 aINFN sez. Roma 1, and Dipartimento di Fisica, Universit`a di Roma, “La Sapienza”.

n
a Research in cosmic rays is now nearly a century old, but most of the fundamental questions in this field
J remainunanswered,ontheotherhandtheperspectivesoffuturestudiesinthenextdecadeareverybright. New
2 detectors will provide higher quality data in the entire energy range from 108 to 1020 eV (or more if particles
1 of higher energy havenon negligible fluxes), moreover cosmic ray astrophysics must now be considered, together
withgamma, neutrinoandgravitational waveastronomy,asoneofthesubfieldsofhigh energyastrophysics,and
1
using information from these four “messengers” there is the potential of a detailed understanding of the origin
v
of the high energy radiation in the universe. High energy cosmic rays are measured indirectly observing the
6
showers they generate in the atmosphere, and a correct and detailed interpretation of these measurements will
9
requireanimprovedunderstandingof thepropertiesofhadronicinteractions. Thenewcolliderexperiments,and
1
1 in particular the LHC project at CERN offer the unique possibility to perform measurements of great value for
0 cosmic ray astrophysics. It is of great importance for cosmic research that this possibility is fully exploited with
3 theappropriate instrumentation and analysis.
0
/
h
p 1. High Energy Astrophysics mentinHighEnergyAstrophysics,andhasapar-
- and Fundamental Science ticular deep relation with Particle Physics. This
o
relationishistoricalandmethodological. Thetwo
r
t Progress in fundamental science requires the fields started essentially at the same time, at the
s
study of “extreme physical systems”, where the
a beginning of the last century, and the measure-
: deeper structure of the physical laws can be-
v mentofthefluxesofcosmicraysclearlyrequired,
comevisible,such“extremesystems”canbecon-
i and at the same time made possible an under-
X structed in the laboratory, or can be found in
standing of the interaction properties of high en-
r nature. Particle accelerators can be seen as in-
ergy elementary particles. Research in cosmic
a
struments for the construction of extreme sys-
rays in the years between1930 and1960resulted
tems (composed of few very high energy parti-
in the discovery of the first elementary particles
cles) to study the properties of interactions at (after the electron): the positron e+, the second
very small distances. The history of astrophysics charged lepton µ±, the charged and neutral pi-
can also be seen as the discovery and the study ons π±, π◦, the strangeparticlesΛ,K±, K ,K
L S
of more and more “exotic” objects (or events):
(the θ–τ puzzle). Also the discovery of the anti–
normal stars, white dwarfs, neutron stars, super-
proton in 1955 happened essentially simultane-
nova explosions, Active Galactic Nuclei, Gamma
ously at the BerkeleyBevatron,and in emulsions
Ray Bursts, ..., whose understanding requires a
exposedtocosmicrays. Then, inthe 1950’s,par-
deeper and more refined description of the phys-
ticle physics entered in the era of big machines
ical laws. Cosmology [1] allows the study of the
and big detectors. An extraordinary experimen-
early universe, and going back in time explores
tal and intellectual effort culminated in the con-
progressivelymore and more extreme conditions,
struction of the “Standard Model”, based on the
in fact of “arbitrary extremeness”, and consti-
gauge group SU(3) SU(2) U(1), with great
tutestheultimatelaboratoryforfundamentalsci- ⊗ ⊗
predictivepowerandasetofopenquestionsthat
ence. The three fields of Particle Physics, Astro-
have inspired new and very complex experimen-
physicsandCosmologyappeartodayasmoreand
talprojectssuchasLHC.Duringthe“accelerator
more strictly interconnected fields.
era”thedirectionofscientificinputflowedmostly
The research on Cosmic Rays is a crucial ele-
2
in the other direction, from particle physics to ticles above the GZK cutoff; on the other hand
cosmicrayresearch. ExperimentsattheISR,the italsohassome“requests”,addressedinparticu-
SppSandtheTevatroncollidersmeasuredthein- lartothecommunityofphysicistsworkingonthe
teractionpropertiesofhighenergyprotons,allow- hadroncolliders. Therequestistomeasureatac-
ing amoreaccurateinterpretationofthe showers celerators (and especially at the LHC) the main
produced high energy cosmic rays. features of the very high energy hadronic colli-
Progress in cosmic ray research has been slow sions,inorderto interpretaccuratelythe present
and after nearly a century of intense efforts, it and future data on the highest energy hadronic
is fair to say that the most important questions showers. This is in fact a difficult and costly
in the field remain without (unambiguous) an- experimental challenge, but the motivations are
swers. Thenearfuture ofcosmicrayreserachap- strong and clear.
pear however as extraordinarily interesting, and
itseemslikelythatinthe nextdecadewewillsee 2. Cosmic Ray Measurements
dramatic advances in our understanding of the
In fig. 1 we show some measurements of the
highenergyradiation. Amainreasonfor this ex-
energyspectrumofcosmicrays. Onecanidentify
pectationisthatcosmicrayresearchhasmatured
several energy regions:
into one component of high energy astrophysics,
together with γ–astronomy [2], that in the last
decade has produced a set of remarkable results,
and ν –astronomy[3]that, after the observations
ofthe sunandSN1987a,isnowaimingatthede-
tectionofhighenergysourcesusingnewlargevol-
ume ν–telescopes. Hopefully gravitational waves
willalsobesoonobservedandwewillreceivefour
different “messengers” (γ, ν, c.r. and g.w.) from
astrophysical objects. With the combined efforts
ofthesefourfields,theidentificationanddetailed
understanding of sources of galactic and extra–
galacticcosmicraysappearspossible afternearly
a century of efforts.
Cosmicraymeasurementsarealsogiving(con-
troversial) indications of the existence of unex-
pected phenomena. The most interesting results
is the suggestion that there are significant fluxes
of particles with energy as large as several times
1020 eV, in contrast with the expectation that Figure1. Somerecentmeasurementsofthec.r. spec-
particle ofsuchhighenergycannotpropagatefor tra. The p and He spectra were taken in june 1998.
long distances. If this result is confirmed by the Thelinesareextrapolationsoffitstothedirectmea-
surements [12] using theansatz (1) for theknee.
future experiments (and we will soon know) the
consequences can be extraordinarily deep.
The series of the ISVHECRI (Internationall
Symposia on Very–High Energy Cosmic Ray in-
teraction) discuss the science at the intersection [i]Alowerenergyregion(E < 30GeV)wherethe
∼
of the two fields of Particle Physics and Cos- energyspectrumisnotasimplepowerlawbuthas
mic Ray Astrophysics. Research in cosmic rays “curvature” in a log–log plot. In this region the
is offering to particle physics some exciting (but fluxesofc.r. haveatimedependenceduetomod-
again controversial) hints of “new physics” such ulationsproducedbythe time varyingsolarwind
as the existence of centauros events and of par- intensity. The new measurements with magnetic
3
spectrometers have reduced significantly the un- describedbyasimplepowerlaw(φ (E) E−α).
A
∝
certainties of the flux below 100 GeV, and mea- In this region there are only few measurements
surements takenatdifferent times allowto study mostly obtained with calorimeter on balloons,
the solar modulation, extracting the interstellar such as JACEE[9] and RUNJOB [10]. There are
flux. There is still a significant difference of some indications that index α of the spectra of
differentcomponentsdifferandinparticularthat
the helium spectrum is slighly harder than p one
(α(p) > α(He)). This is an important point and
need to be confirmed by new more precise mea-
surements. Data of an upgraded version of the
BESS detector (BESS–TeV) should soon become
available possibly resolving this question.
[iii]At the so called“knee”(atE 3 1015 eV)
∼ ×
the all–particlespectrumsteepens,withachange
in slope ∆α 0.35. The measurements of the
≃
spectrum in this region are only obtained with
indirect measurements1. A subset of recent mea-
surementsisshowninfig.3,wherewecanseethat
significantdiscrepanciesexistamongthedifferent
measurements. It is still a matter of debate how
muchofthedifferencesisduetoexperimentalsys-
tematicerrors,andhowmuchisduetouncertain-
Figure 2. Recent simultaneous measurements of the ties in the modeling of the shower development.
p spectrum by magnetic spectrometers. Infig.1thedifferentlinesaretheextrapolationof
afit[12]ofdirectmeasurementsofthecosmicray
fluxes. There is some tension between the results
of suchextrapolations with the highestestimates
order 15–20% between quasi–simultaneous mea- ofthefluxinthekneeregionbyEASexperiments.
surements performed by the BESS [4] and AMS A significant amount of energy has gone into
[5]detectors(withhigherflux)andCAPRICE[6] thedeterminationofthemasscompositionofcos-
(lower flux) see fig. 2 that need to be resolved. mic rays below and above the knee. Perhaps the
The main goal of the AMS detector [7] is the simplest model for such an evolution is the as-
search for anti–nuclei in the cosmic ray fluxes. sumption that the knee corresponds to a fixed
The discovery of these particle would clearly be value of the rigidity p/Ze, and therefore for the
ofprofoundsignificanceforbothastrophysicsand nuclear component of electric charge Z:
particle physics [8]; the detector will soon start
E (Z)=ZE (p). (1)
knee knee
three years of data–taking aboard the Interna-
tionalSpace Station, using a high field supercon- Equation (1) is predicted in a very wide range
ductingmagnet,obtainingdataofunprecedented of models, where the knee is the consequence of
accuracy. The detailed study of the shape of the therigiditydependenceoftheaccelerationratein
energy fluxes of different particle species (p, nu- the sources,or the galactic containementproper-
clei, e∓, p) in the this low energy region has the ties of cosmic rays. The ansatz (1) is used in
potentialtogiveveryvaluableinformationabout the extrapolation of the spectra shown in fig. 1.
the injection, acceleration and galactic and solar 1Clearlyanimportantdirectionofprogressistopushthe
environment propagation of the cosmic rays. direct measurements to the highest possible energy, ap-
proaching the knee. Ultra long duration (60–100 days)
[ii]Intheregion(3 1011 eV < E < 1015 eV)the
∼ ∼ ballon flights in the Antartics offer this possibility. The
×
cosmic rays fluxes to a good approximation are Creamdetector [11]isdesignedforthispurpose.
4
number asafunctionoftheN andthe unknown
e
mass A as:
N K′ A1−β/αNβ/α (3)
µ ≃ e
with a mass dependence A1−β/α A0.2, and the
∼
heavy primaries can in principle can be selected
choosing muon rich showers. An example of this
is shown in fig. 4 from the Kascade air shower
experiment [13]. The detector can measure si-
multaneously N and N . In the bottom panel
e µ
of fig. 4 the showers are selected in a fixed in-
terval of N , and the distribution in N is anal-
e µ
ysed to obtain the mass composition. Showers
with a small muon number N are associated to
µ
proton primaries, while the highest µ multiplic-
Figure 3. Recentmeasurementsofthec.r. spectrum ities are associated with iron nuclei. A quanti-
at the knee. tative analysis clearly requires a precise knowl-
edge (including fluctuations) of the shower prop-
erties for primaries of different energy and mass.
The results of fig. 4 have been fitted, using the
There is mounting evidence [13,14] that the av- QGSJET model [15], with a composition domi-
erage mass of cosmic rays increases with energy nated by helium nuclei and smaller contributions
across the knee, and more precisely that equa- of p, 16O and 56Fe. It can be seen that the
tion (1) is valid, however large systematic uncer- resolution in the measurement of A is not suf-
tainties are still existing, and are mostly due to ficient to separate the different components, and
uncertainties inthe modeling ofcosmicrayinter- therefore the determination of the mass compo-
actions. sition depends critically of the Montecarlo pre-
Inverysimplifiedterms the determinationofa diction, and one needs to consider a systematic
the mass composition is obtained with the mea- error in the estimate of the energy spectrum
surement of (at least) two quantities per shower, and mass composition due to theoretical uncer-
suchastheelectromagneticsizeNe andthemuon tainties in the modeling of shower development
number Nµ. These quantities have different de- (that is in the description of the hadronic inter-
pendencesontheenergyandmassoftheprimary, action properties). Similar considerations apply
andthereforethisallowsinprincipletoobtaines- also to all other techniques for the determina-
timatesofE andAforeachshower. Forexample, tion of spectrum and compositionin the knee re-
for the case of Ne and Nµ qualitatively one has: gion and above. For example the DICE experi-
N K A E α with α>1 ment [16] measures with two imaging telescopes
Ne ≃ Ke A(cid:0)AE(cid:1)β with β <1. (2) the Cherenkov light produced by c.r. showers,
µ ≃ µ A obtaining two quantities per shower, then total
(cid:0) (cid:1)
The esponentαis largerthanunity becausewith number of Cherenkov photons N and the po-
Cher
increasing energy the N size at maximum grows sition of Shower maximum X , showers with
e max
linearly with energy while the shower maximum deep (shallow) X are attributed to protons
max
position approaches the detector level, while β is (iron nuclei). The BLANCA detector [17] op-
lessthanunitybecausemuonsareproducedinthe erating in 1997–1998 measured the distribution
decayofmesonsinprocessessuchasπ+ µ+ν , of Cherenkov photons at the ground with a sys-
µ
→
and the decay probability of high energy mesons temof144angleintegratingphotondetectors,ex-
isreducedbecauseoftheLorentztimeexpansion. tracting two parameters per shower, the photon
One can use equations (2) to express the muon densityat120metersfromtheshoweraxis(C )
120
5
g Ne 7 104 wers 1.51.5 preliminary spurmot oonf all
l 6.5 103 er of sho -1-1 GeVs GeVs hciraeolrnibuomn
6 102 numb -1-2-1-2 srm srm 110033
5.5 10 2.52.5 E E

53.5 4 4.5 5 5.5 6 1 (cid:215)(cid:215)) x I(E) x I(E00110022
lg Ntmr fluflu
s 110066 110077
nt data
cou103 - fit He pprriimmaarryy eenneerrggyy EE00 GGeeVV
p
O
102 Figure5. Fitofthecompositionatthekneeobtained
Fe by Kascade [13].
10
1
ing, and the hadronic component is larger. The
0.65 0.75 0.85 0.95 analysis of the data in terms of different pairs of
log(Ntmr)/log(Ne) variables, for example (Ne, Nµ) and (Ne, Nhad),
will give consistent results only if the modeling
Figure 4. The top panel shows the 2-D distribution of the shower development is correct. Similarly
in N , N of Kascade [13]. The bottom panel show (barringtheexistenceofexperimentalsystematic
e µ
an example of a composition fit. errors) the interpretation in terms of spectrum
and composition of different experiments will be
compatibleonlyifthemodelingofhadronicinter-
actions is sufficiently accurate. This requirement
of consistency (within and between experiments)
and the exponential slope s of the photon den-
sity in the 30–120 meters range (ρ(r) Ke−sr); allows in principle to obtain at the same time in-
≃ formationaboutthespectrumandcompositionof
steep (flat) slopes correspondto light (heavy pri-
primaryc.r. andaboutthepropertiesofhadronic
maries). The energy spectrum and composition
interactions. This bootstrap philosophy has been
can be obtained from the analysis of the distri-
atthecenterofconsiderableeffortsinrecentyears
bution of events in the (N ,X ) or (C ,s)
Cher max 120
planes2. (seforexample[18]foracontributionatthiscon-
ference). Acriticalanalysisofallavailabledatais
Some detectors can measure more than two
beyondthescopeofthissummary(see[21,22]for
quantities per shower, for example Kascade can
a review and critical analysis). In a nutshell the
measurenotonlytheelectronandmuonsizes(N
e
main points are the following: (a) significant in-
and N ), but also the hadronic component N
µ had
consistenciesstillexistwithinandbetweenexper-
in its central calorimeter[20]. For the a fixed en-
iments, pointing to the necessity of an improved
ergy, light primaries showers are more penetrat-
modeling of hadronic interactions; (b) a consis-
2The “unfolding” of the spectrum and composition from tent picture is however beginning to emerge, the
the data is a non–trivial statistical problem, even under
existenceofthe“knee”isfirmlyestablished,even
theassumptionofno–systematical errors,andseveralap-
if the precise shape and location are still uncer-
prochesarepossible. Seeforexamplethecontributionsof
Kascadeatthisconference[13,19]. tainmaybebyafactoraslargeastwo,andmost
6
experiments extract a composition that becomes
heavier across the knee, in agreeement with the
assumption of the knee as a rigidity dependent
feature (see fig. 5 for an example)3; (c) the gen-
eral features of the hadronic interactions incor-
poratedinthe Regge–Gribovmodelscurrentlyin
use are at least qualitatively correct.
Theenergyregionabovethe knee (1016 E
≤ ≤
1018 eV), is still relatively poorly known. The
Kascade–Grande detector is planning to explore
it,withthemainaimtoidentifyan“ironknee”at
an energy E 6 1016 eV [23]. A detailed anal-
∼ ×
ysis of the size spectrum of 7 different air shower
arrays [24] already gives some qualitative indica-
tionsoftheexistenceofasecondknee,thatcould
be attributed to the bending of the iron compo-
Figure6. Recentmeasurementsofthec.r. spectrum
nent. Some authors [25] see evidence as a more at the highest energy.
detailed structure in the knee energy spectrum,
that are attributed to the contributions of a re-
cent nearby supernova explosions.
[iv] The highest energy points in fig. 1 and 6
disintegration(suchasA+γ (A 1)+N). The
are from the Agasa [26] and Hires [27] detec- → −
detailed shape of UHE cosmic rays flux will de-
tors,thedataoftheYakutskarraycanbeseenin
pend on the shape of the spectrum at the source
[28]. The Agasa spectrum extends up to an en-
(in particular on the maximum acceleration en-
ergy E 3 1020 eV. It is well known [29] that
∼ × ergy E ), the distribution in space–time of the
oneexpectstheexistenceofa(Greisen–Zatsepin– max
sources, and the structure of the extra–galactic
Kuzmin or GZK) cutoff in the energy spectrum
magnetic fields, that control the propagation of
of cosmic rays due to interactions with the cos-
charged particles from the source to our galaxy.
mic microwave background. The dominant pro-
The energy determination of an EAS detec-
cess is pion photoproduction on the photons of
tor as Agasa (see [30] for a full discussion) is
the (2.7◦K) Cosmic Microwave Background Ra-
based on a measurement of the particle density
diation: p+γ p(n)+π +..., with an
CMBR
→ at the ground at a distance 600 meters from
energy threshold of order Ethr mpmπ/ ǫ ∼
≃ h i ≃ the shower core. It has been demonstrated [31]
few 1019 eV. Particles above the GZK cutoff
× that this measurement is relatively insensitive to
should only arrive from near (on a cosmological
boththemassoftheprimaryparticleandthede-
case) sources. Since the γ targetis veryprecisely
tails of the interaction model, however in princi-
known and the interactioncross sectionhas been
ple somemodeldependence is possibleandneeds
accuratelymeasuredinexperimentswithprotons
to be very carefully investigated.
at rest, it is possible to compute with very good
New results of the High Resolution Fly’s Eye,
precisiontheinteractionlengthandenergylossof
based on the fluorescence technique [27] show a
Ultra High Energy (UHE) protons. Similar con-
spectrum that is well described assuming the ex-
siderationscanalsobemadeforcompositenuclei,
istence of the GZK cutoff. In principle the mea-
when the dominant energy loss process is photo-
surement based of the detection of fluorescence
lighemittedbynitrogenmoleculesexcitedbythe
3There are however significant discrepancies between ex-
shower, represents a nearly completely model in-
periments. Analysis of the Cherenkov data suggests a
dependent method for the energy determination.
composition becoming lighter. See [21] for a critical dis-
cussion. If N(X) is the number of charged particle in a
7
shower at depth X and dY /dE is the yield of tures that should be clearly demonstrated with
fluo
fluorescencephotonsproducedafterthereleaseof the higher statistics obtained from future experi-
the energy dE in ionization, then the number of ments.
fluorescence photons generated by the shower in (iii)Thehighestenergyparticlesaregeneratedin
the depth interval (X, X +dX) is: the vicinity of our galaxy by the interactions of
a more weakly interacting “carrier”. This is the
dN dE dY
fluo =N (X) fluo(X) (4) so called “Z–burst” scenario [32] where the car-
e
dX (cid:28)−dX(cid:29) dE riersareultra–highenergyneutrinos. Theseneu-
trinos are created in “standard” sources, propa-
the X dependence of the yield reflects a (strong)
gateinintergalacticspacewithnegligibleabsorp-
dependence on the air pressure. The number
tion, produce the observed UHE particles inter-
received at the detector, can be obtained from
acting with a postulated neutrino galactic halo.
simple geometry (the fluorescence emission is
This scenario implies that there are neutrinos
isotropic)andaknowledgeofthe showeraxispo-
with energy E at least a few times E (and
sition if one has good control of the trasparency ν GZK
therefore at the source protons must be accel-
of the atmosphere for the fluorescence photons.
erated up to an energy several times E ). To
This technique in principle allows to measure ν
obtain a sufficiently large probability for inter-
the profile of the fluorescence emission along
actions with the galactic halo this scenario as-
the shower axis, and therefore the profile of the
sumes that the cross section is enhanced by the
shower energy loss, and by integration the total
s–channelresonantproductionofZ0 (theprocess
energy dissipated in ionization by a c.r. shower.
ν +ν Z0 final state). This requires a neu-
Thetotalenergyoftheprimaryparticlecanthen → →
trino mass of order
beobtainedapplyingsmallcorrectionsfortheen-
ergy that reaches the ground in the form of neu- M2 M2
m = Z Z few eV (5)
trinos,muons,hadronsandthetailoftheelectro- ν 2E ∼ (few 1021 eV) ≃
ν
magneticshower. Inthiscasethemainsourcesof
that could be the correctnumber consistent with
systematic uncertainties are the correct descrip-
the existence of the halo.
tion of the fluorescence yield and of the atmo-
(iv)TheexistenceofUHEparticles,comingfrom
spheric transparency.
“invisible” sources can be naturally explained in
2.1. Particles beyond the GZK cutoff ? the framework of the so called Top–Down [33]
The question of the existence of a significant models. In these models the UHE particles are
flux of particles particles with energy above the not produced by acceleration (the Down–Top
expected GZK cutoff is certainly the question mechanism)butaretheresultofthedecayofvery
thas has attracted more excitement and contro- large mass particles. The mass scale M is re-
X
versyin cosmic rayphysics in the lastdecade. In lated to a unification mass scale. In particular
the following there is a list of possible solutions itisimportanttonotethatthegrand–unification
for this puzzle: massscale(M 1024eV)isoftherightorder
GUT
∼
(i) There are no particles above the GZK cut- of magnitude so that the decay of particles with
off. The present results of Agasa, Fly’s Eye, mass M M can produce the super–GZK
X GUT
∼
Haverah Park and othe detectors are the effect particles. TheTop–Downmodelsrequirethatthe
of a combination of incorrect energy calibration, dark matter in the universe is provided by such
larger than predicted fluctuations in shower de- super–heavy particles, or by topological defects
velopment, non gaussian tails in mesasurements (suchasmagneticmonopoles,cosmicstrings,...)
etc. that can decay into such particles.
(ii) The highest energy particles are produced in (v)Finallyoneextraordinarypossibilityistheex-
few “standard” sources at small distances. The istenceofviolationsofLorentzinvariance. Inthis
energyspectrumandtheangulardistributionex- case the GZK cutoff is not observed because it
pected in this scenario will then have strong fea- does not exist ! The statement that protons of
8
energy 1020 eV produce pions interacting with small).
photons of ε 10−3 eV is based on the obser- In diffusive shock acceleration a charged par-
≃
vations of the interactions properties of photons ticle moving in a turbolent magnetic field of av-
with ε 108 eV with protons at rest, and on eragestrengthB performs“cycles”crossingback
r.f.
∼
the assumptionofLorentz invarianceand the va- and forth across the shock discontinuity. Dur-
lidity of Lorentz invariance. The two frames are ing each cycle the particle acquires an energy
connected by a transformation with a Lorentz ∆E 4/3 β E (where cβ = v v is the
sh sh 2 1
≃ −
γ factor of order 1011. If Lorentz invariance is differencebetweenthevelocityofthefluidonthe
violated the statement can become false. This two sides of the shock. The time for performing
apparently outrageous possibility is actually pre- a cycle is of order T D/(β c2), where D
cycle sh
≃
dicted [34] in the framework of quantum gravity isthediffusioncoefficientthatdependsonthein-
or in models where the space manifold has addi- tensity and structure ofthe magnetic field. For a
tional large extra dimensions. diffusion coefficient linear in E:
Itshouldbe possibletodetermine whichoneis 1 1 E
D r c c (6)
the truetruesolutionofthis puzzlethankstothe L
≃ 3 ≃ 3 ZeB
new detectors in construction (as Auger [35]) or
theaccelerationratedE/dt ∆E/T becomes
in the planning stage (as Euso [36], based on the ≃ cycle
a constant, and the maximum energy obtainable
detection of fluorescence light from space.)
is a Supernova can be estimated (using R
SNR
∼
ct β ) as:
SNR sh
3. Cosmic Ray Astrophysics
dE
E t R Z B β (7)
max SNR SNR sh
A list of fundamental questions for c.r. astro- ∼ dt ∼ × × ×
physics can be simply formulated as following: This energy is similar to the energy of the knee.
(A) What if the dominant source for cosmic rays Thesimple“standard”scenariooutlinedabove
below the “knee” ? predicts an exponential cutoff of the cosmic ray
(B) What is the origin of the knee ? flux at the maximum energy. This is very differ-
(C) What is the origin of the particles beyond ent from the simple moderate steepening of the
the knee ? energyspectrumobservedinthedata,andthere-
(D) At what energy the fluxes of extra–galactic fore the identification of the knee with the maxi-
and galactic cosmic rays are equal ? mum energy in SNR remains unclear.
(E) Which are the sources of extra–galactic cos- A problem that still waits for a clear answer
mic rays ? is the determination of the energy at which the
(F) Are there particles beyond the GZK cutoff ? fluxes of galactic and extragalactic particles are
equal. There is a general consensus that this en-
Itis surprisingthat we still do nothave unam- ergy must exist. The gyroradius of charged par-
biguous answersto any ofthese questions. There ticles in a magnetic field is
is a general (but non universal) consensus that
p p (1018 eV)
SuperNova Remnants (SNR’s) are the source of R = ⊥ 1.1 ⊥ Kpc (8)
gyro
ZeB ≃ ZB(µGauss)
the galactic cosmic rays. This consideration is
essentially based on two considerations: (i) SNR The galactic radius is r 15 Kpc, and the
gal
∼
canprovidethepower(L 1040erg/s)needed typical strength of the magnetic field is B
c.r.
∼ ∼
tomantaintheobservedenergydensityofcosmic 3 µGauss, therefore very likely the highest en-
rays, taking into account the measured (rigidity ergycosmicraycannotremainconfinedinsidethe
dependent) confinement time of the cosmic rays; Galaxy. It is possible that the energy where the
(ii) the mechanism of diffusive first order Fermi fluxes of particles of galactic and extra–galactic
acceleration at a shock can naturally produce a originare equalcorrespondsto the so called“an-
powerlawsourceenergyspectrum(q(E) E−α) kle” (E 1019 eV) in the c.r. spectrum, how-
∝ ∼
with a (differential) esponent α 2+ε (with ε ever it is also claimed [37] that the ankle is an
≃
9
asorptionfeature due to the process p+γ (Aisthemassoftheprimaryparticle). Thehigh-
cmbr
→
p+e+ +e− and that the crossing point for the est energy collisions produced in an accelerator
two population is at lower energy. This is clearly have√spp 1.8TeVatthe Tevatron,andthere-
≃
animportantpoint that canbe clarifiedwith ad- forecorrespondscloselytotheknee;theLHCcol-
ditionaldataontheenergyspectrumandangular lider at CERN will reach √spp 14 TeV, that is
≃
anistropy of cosmic rays. still approximately 30 times lower than the GZK
Equation(7)canbe usedto constraintthe size energy. Howeverthesituationismuchworstthan
and magnetic field of any source of cosmic rays what appears from these simple considerations.
where the acceleration mechanism is first order The measurements at the hadron colliders have
Fermi acceleration. This implies that very few been limited to an angular region that excludes
objects in the known universe can have a suffi- the beam pipe, and therefore a very large ma-
cientylargeproductR Btobeacandidate jority of the high energy particles that are emit-
source
×
for the acceleration of the UHE cosmic ray [38]. ted at small angles are unobservable (see fig. 9).
AGN and GRB are perhaps the best candidates These particles carry more than 90% of the en-
for this purpose. ergy in a collision and are clearly those crucial
in determining the properties of air showers. It
should also be noted that the study of hadron–
4. Hadronic Interactions
nucleus interactionsis stilllimited to fixedtarget
The study of high energy cosmic rays requires energies (√sNN)hA ∼< 0.027 TeV). The new data
“indirect methods” that is the measurement of fromtheRHICdetectoraboutgold–golddetector
theshowerproducedbytheprimaryparticle. The at (√sNN)AA ∼< 0.2 TeV) presented at this con-
uncertaintiesinthepredictionofthedevelopment ferencebyS.Klein[39]havethereforegreatvalue
of the shower produced by a primary cosmic ray intestingtheaccuracyofthetreatmentofnuclear
are the consequence of uncertainties in the cal- effects used in the existing montecarlo codes. In
culation of hadronic interactions. The problem factacomparisonhasshowntheexistenceofnon–
is the following: one has a “projectile” particle trivialdiscrepancies(15–20%inthecentralregion
(a proton, a nucleus (A,Z), or a weakly decaying rapidity density, see [40,41,42]).
meson such as a pion or kaon) and one needs to At fixed target energies the inclusive distribu-
knowtheinteractioncrosssectionwiththeairnu- tionoffinalstateparticlesexhibitinfirstapprox-
clei (mostly nitrogen and oxygen), and the prop- imation the property of Feynman scaling:
ertiesofthefinalstateproducedinsuchaninter-
dσ
action, namely the multiplicity, flavor composi- pp→a (p ,p ,√s) f (p ,√s) G (p )
dp d2p k ⊥ ≃ a k a k
tionandmomentumdistributionofthefinalstate k ⊥
particles, with a correct estimate of the fluctua- Fa(xF)
G (p ) (10)
tions. It is well knownthat now and for the fore- ≃ E a ⊥
seablefeaturewearenotintheconditiontocom-
where x = 2p∗/√s and the functions F (x )
pute from first principles these needed quantities F k a F
from the fundamental QCD Lagrangian. More- and Ga(p⊥) e−bp2⊥ are independent from √s.
∝
overthe existing datadonotcoverallthe “phase Clearly the assumption of Feynman scaling al-
space”necessaryforpurelyphenomenologicalde- lows to extrapolate the low energy results and
scription. The c.m. energy on nucleon–nucleon to predict the properties of showers of arbitrary
interactions for cosmic rays in the knee region energy. However the data of the hadron collid-
(E 3 1015 eV) and and near the GZK cutoff ers (ISR, SppS,TevatronandRHIC) haveshown
∼ ×
energy (E 1020 eV) are: that Feynman scaling is violated. As an exam-
∼
ple the scaling function F for pion production
π
(√sNN)knee 2.5/√A TeV in pp interactions has approximately the form
∼ (9) Fπ(xF) C(1 xF )n with n 3–4. This form
≃ −| | ∼
(√sNN)GZK 400/√A TeV indicates that pions are approximately produced
∼
10
witha spectrumdn/dE 1/E peakedatlowen- tween partons, that can be treated in perturba-
∼
ergy. At collider energy the quantity C (that is tive QCD, while another fraction is “soft”. The
the value of F near x 0 or the height of the growthof the crosssection with energy is related
π F
∼
rapidityplateau)ismeasuredtogrowlogarithmi- to the increase of the number of sub–interactions
callywithincreasing√s. Theformofscalingvio- with increasing √s. This approach can be nat-
lationsforlarge x (fornucleonsandmesons)is urally implemented into montecarlo algorithms.
F
| |
known much more poorly, however it is essential The “topological structure” of one event, that is
for shower development. the number and type of sub–interaction is trans-
The spectrum of the nucleons produced in lated into the formation of a set of color strings
hadronic interactionsplays a fundamentalrole in (closedloopsorobjectswithq,qorqq “endings”)
the development of c.r. showers. At fixed tar- conserving exactly 4–momentum and all quan-
get energy a fraction 20% of the pp inelastic tum numbers. Thesestringsarethen fragmented
∼
interactions is due to “single diffraction” where into observable hadrons using algorithms simi-
one if the incident protons is excited into a state lar (or identical) to the algorithms developed by
X with the sameinternalquantumnumbers that the LUND group. Several montecarlo implemen-
scatters elastically with small transfer momen- tation of this philosophy (QGSJET, Sibyll, DP-
tum with the other proton and ( 5% of the MJET, VENUS, NEXUS) have been developed
∼
inelastic interactions can be attributed to dou- and are used in the montecarlo simulation of c.r.
ble diffraction). Note that in a target diffrac- showers. A discussion of the differences between
tion event the projectile protonretains nearly all these MC implementations can be found in [15].
the initial energy, while in projectile diffraction, Itisencouragingthatthedifferencesbetweenthe
the decay of the excited state X result in a fi- latest versions of the models are smaller than in
nalstatenucleonthatcarriesaverylargefraction the past. The size of these differences has been
(> 50%)oftheinitialpenergy. Innon–diffractive used to estimate the importance of systematic
∼
interactions the final state nucleons have a hard– uncertainties in hadronic interactions modeling.
spectrum (dn/dE const) and carry approxi- It should be noted that the use of this method
∼
mately 40% of the initial state energy4. These has the danger to underestimate systematic er-
∼
highenergynucleonsinthefinalstatefeedenergy rors, because all of these codes share the same
deeperintotheshowerandclearlyplayaveryim- basic theoretical assumptions, and therefore nat-
portant role in the shower development. At the urally converge to similar results. It should not
hadroncollidersmostofthesenucleonsareunob- be forgotten that despite of their sophisticated
served, and their spectrum must be infered with language the theoretical basis for this models is
a large amount of uncertainty. not rock solid, and significant uncertainties still
exist. In fact several important problems do not
4.1. Montecarlo Modeling have an unambiguous answer in the framework
A general framework to compute the proper- of the Regge–Gribov approach. In particular it
tiesofhadronic(hp,hAandAA)interactionshas is not clear how diffraction fits in the theoreti-
been developed in the last 10 years [44]. In this cal scheme; there is also significant arbitrariness
frameork, the so called “Regge–Gribov effective in the shape (and evolution with energy) of the
theory”,thatisformallyverysimilartoaneikon- inclusive particle distribution in the fragmenta-
alizedpartonmodel,anhadroniccollisionisanal- tion regions (x > 0.1). It is significant that
F ∼
ysed as a set of sub–interactions, or “Pomeron eachtime new|acc|eleratordatahasbecomeavail-
exchanges”, between the participant particles. A able (from ISR to the recent RHIC data) sig-
fraction of these sub–interactions can be simply nificant differences with the available predictions
understoodashardorsemi–hardinteractionsbe- were found. New data is clearly required to vali-
date (or correct) the existing models.
4Traditionallytheenergyfractioncarriedbynucleonshas
beed called by comsmic ray physicists the “elasticity” of
theinteraction.