PHYSICS OF EXTREMELY HIGH ENERGY COSMIC RAYS 0 0 0 XAVIERBERTOU,MURATBORATAV,ANTOINELETESSIER-SELVON 2 Laboratoire de Physique Nucl´eaire et des Hautes Energies (IN2P3/CNRS), n Universit´esParis 6&7, 4 place Jussieu 75005 Paris, France a J Overthelastthirdofthecentury,afewtensofevents,detectedbyground-basedcosmic 9 raydetectors,haveopenedanewwindowinthefieldofhigh-energyastrophysics. These 2 events have macroscopic energies - exceeding 5×1019 eV -, unobserved sources - if supposed to be in our vicinity -, an unknown chemical composition and a production and transport mechanism yet to be explained. With a flux as low as one particle per 1 century per square kilometer, only dedicated detectors with huge apertures can bring v in the high-quality and statistically significant data needed to answer those questions. 6 Inthis article,wereview the presentstatus ofthe fieldboth froman experimental and 1 theoretical point of view. Special attention is given to the next generation of detectors 5 devoted tothethoroughexplorationofthehighestenergyranges. 1 0 1. Introduction 0 0 This review article will mainly concern the problems raised by the existence and / h observation of cosmic rays whose energies are above 5 1019 eV. Such cosmic rays p × - for whichwe shalluse the term “extremelyhighenergycosmic rays”orEHECR- - o are exceptional for the following reasons: r st TheGreisen-Zatsepin-Kuzmin(GZK)cutoff1 correspondstothethresholdfor • a inelasticcollisionsbetweenthecosmicmicrowavebackground(CMB)andpro- : v tons (photo-pion production) or heavy nuclei (photo-disintegration). Similar i X cutoffs exist at lower energies for gammas interacting with background pho- r tons(CMB,infra-redorradiowaves). Consequently,andexceptforneutrinos, a if the EHECR observed on Earth are due to the known stable particles, they must be produced in our vicinity. At the GZK cutoff, the “visible” universe shrinkssuddenlytoasphereofafewtensofmegaparsecs(Mpc).aThisshould be reflected on the energy spectrum of cosmic rays as a sharp drop around 5 1019 eV. The available data show no such drop. On the contrary, if a × structure exists in the energy spectrum, it is in the sense of a softening of the power law, possibly suggesting a new component rising from under an otherwise steeply falling spectrum. There are very few conventional astrophysical sources considered by the ex- • perts as being able to accelerate particles at energies exceeding those of the aThe megaparsec is the cosmological unit of distance that we shall use throughout this article. 1Mpc=3.26×106light-years≈3×1019km 1 most energetic EHECR that have been observed in the past. Atsuchenergies,thebendingeffectofthegalacticandextragalacticmagnetic • fields arequite weakonthe EHECR.Thus,eveniftheyarechargedparticles, theirreconstructedincidentdirectionshouldpointtowardtheirsourceswithin a few degrees. This distinguishes the EHECR from their counterparts in the lower energy regions: one can use them for point-source-searchastronomy. The widely shared excitement about the EHECR comes from the above consid- erations and from the study of the scarce data available. The EHECR exist. They have to be produced somewhere and with a mechanism we do not understand up to now: to explain the observation of the highest energy events, the energy at the source should probably be in the ZeV range (Z is for zetta, i.e. 1021), namely at least150joules! Iftheseextraordinaryacceleratingenginesareastrophysicalmacro- scopic objects, they must be visible through some counterpart that e.g. optical- or radio-astronomyshoulddetect. Butnosuchremarkableobjectisvisibleinthedirec- tions fromwhere the EHECRcome. Thereis evenno convincing evidence thatone can find any correlation between the incoming directions and the inhomogeneous distribution of matter in our vicinity. During the 35 years where the EHECR puzzle was fed by a slow input of ex- perimental data, many models and theories were put forward to try to explain it. In the following, we shall develop in detail the facts and arguments briefly men- tioned in this introduction. In section 2 we discuss the cosmic ray interactions in the atmosphere and the detection techniques. In section 3 we review our current knowledge of the subject while section 4 is devoted to transport problems and to candidate source characteristics. Finally section 5 describes the next generation of detectors devoted to EHECR studies. There is no doubt that for the scientists working in the field of what is now called “Particle Astrophysics” the near future will be a thrilling period where a large variety of models or theories will be confronted with high-quality and high- statistical data brought by a new generation of detectors. To avoid repetitive use of large powers of ten, the energy units in the following willmostly be inzetta-electron-volts(ZeV,seeabove)andexa-electron-volts(EeV, i.e. 1018 eV). 2. The detection of the EHECR Whenthe cosmicrayfluxbecomessmallerthan1particleperm2 peryear,satellite bornedetectorsarenotappropriateanymore. Thishappensabove1016 eV(theso- called “knee” region). Then large surfaces are needed. The detectors then become ground-based. What they detect is not the incident particle itself but the cascade ofsecondaryparticlesinitiatedbythe cosmicrayinteractionswiththe moleculesof the atmosphere. The object of study is therefore this cascade or shower called the Extensive Air Shower (EAS). 2 Another distinction has to be made between the techniques used at lower and higher energies. Air showers can actually be observed at much lower energies than the knee region. Gamma ray astronomy, for example, uses the properties of the EAS (production of Cerenkov light by charged secondaries in the atmosphere) to detectandmeasurecosmicphotonsfromafewtensofGeVup. Themaindifference with the higher energies is that above a few hundreds of TeV and up to 1020 eV, cosmic rays are mainly charged particles which cannot be associated with a point source as is the case with photons. Therefore a ground-based cosmic ray detector must survey the whole sky and not point at a defined source. There are two major techniques used in the detection of the highest energy cosmic rays. The first, and the most frequent, is to build an array of sensors (scintillators,waterCerenkovtanks,muondetectors)spreadoveralargearea. The detectors countthe particle densities atany givenmoment, thus sampling the EAS particles hitting the ground. The surface of the array is chosen in adequation with the incident flux and the energy range one wants to explore (large array surfaces for weak fluxes, large density of sensors for lower energies). From this sampling of the lateral development of the shower at a given atmospheric depth one can deduce the direction, the energy and possibly the identity of the primary CR. The second technique, until recently the exclusivity of a group from the University of Utah, consists in studying the longitudinal development of the EAS by detecting the fluorescence light produced by the interactions of the the charged secondaries. 2.1. The Extensive Air Showers Onanincidentcosmicraytheatmosphereactsasacalorimeterwithvariabledensity, averticalthickness of26radiationlengths andabout11interactionlengths. In the following, we will describe the properties of a vertical EAS initiated by a 10 EeV proton and mention how some of these properties are modified with energy and with the nature of the initial cosmic ray (CR). At sea level (atmospheric thickness of 1033 g/cm2) the number of secondaries reachinggroundlevel(withenergiesinexcessof200keV)isabout3 1010particles. × 99% of these are photons and electrons/positronsin a ratio of 6 to 1. Their energy ismostlyintherange1to10MeVandtheytransport85%ofthetotalenergy. The remaining 1% is shared between mostly muons with an average energy of 1 GeV (and carrying about 10% of the total energy), pions of a few GeV (about 4% of the total energy) and, in smaller proportions, neutrinos and baryons. The lateral development of the shower is represented by its Moli`ere radius (or the distance within which 90% of the total energy of the shower is contained) which, in the standardairis70m. However,the actualextensionoftheshoweratgroundlevelis of course much larger. As an example, at a distance of 1 km from the shower axis, the average densities of photons/electrons/muonsare 30/2/1 per m2. ThelongitudinaldevelopmentoftheEASwillbedescribedtosomeextentinthe next section. Let us just mention that the maximum size of the shower is reached at an atmospheric depth of 830 g/cm2 (or an altitude of about 1800 meters) and 3 containsabout7 109electrons(whichproducethefluorescencelightdetectedwith × the Fly’s Eye telescopes, see below). Showers initiated by heavier nuclei can be described by making use of a super- position principle: a heavy nucleus of mass number A and energy E can be in a firstapproximationconsideredasasuperpositionofAshowersinitiatedbynucleons each with an energy of E/A, therefore less penetrating than a nucleon with energy E (roughly 100 g/cm2 higher in the atmosphere for iron). Agroundarraymakesuseoftwomaineffectstoseparateheavyfromlightnuclei (and from photons): the proportion of muons compared to the electromagnetic componentofthe showerandthe risetime of the detected signal. Both parameters are due to the way the muons are produced during the shower development. The muonsinashowercomefromthedecayofchargedpionswhentheyreachanenergy lowenoughsothattheirdecaylengthbecomessmallerthantheirinteractionlength. Since this happens earlier in the case of a primary heavy nucleus, the resulting showerisricherinmuonsthanaprotonshower. Atthesametime,andsincemuons are producedearlier in the shower development,they reachthe groundalso earlier, compared to the electromagnetic component which undergoes many interactions before reaching the detector array. For a photon shower the proportion of muons will be even smaller and at the highest energies and another physical process will have important consequences on the EAS detection and characterization. This is the Landau-Pomeranchuk-Migdal (LPM) effect2 which describes the decrease of the photon/electron nucleus cross- sections with energy and with the density of the medium with which they interact. Even in the upper atmosphere, the LPM effect becomes appreciable at energies in the EeV range so that it is possible for a photon of 100 EeV to develop an EAS very deep in the atmosphere, yielding less than 109 particles at ground level. Such a shower would have an extension of only a few km2. These effectsarestudiedthroughheavyuseofEASMonteCarloprogramssuch as AIRES,3 CORSIKA,4 HEMAS5 or MOCCA.6 At the EHECR ranges, where the center-of-massenergiesaremuchhigher (almosttwo ordersofmagnitude) than thoseattainableinthe future(andthe mostpowerful)acceleratorLHC,thecorrect modelling of the EAS in these programsbecomes delicate. Some data are available from accelerator experiments such as HERA,7 and showers of about 1016 eV are now being well studied through experiments such as KASCADE.8 The models are thus constrained at lower energies and then extrapolated at higher ranges. The most commonly used models for the high energy hadronic interactions of the simulation programs are SIBYLL,9 VENUS,10 QGSJet11 and DPMJet.12 In- teractions at lower energies are either processed through internal routines of the EAS simulation programs or by well-known packages such as GHEISHA.13 Some detailed studies of the different models are available.14 A clear conclusion is that the simulation results are never identical, even when the same theoretical models are used in different programs. However, when simulating a shower, these models are only used for the first few interactions and an EAS yields about 1010 or 1011 4 particlesatgroundlevel. Thereforethemainshowerparameters,suchastherecon- structed direction and energy of the primary CR, are never strongly dependent on the chosen model. However, the identification of the primary is more problematic. Whatever technique is chosen (see Section 3.4 for details) the parameters used to identify the primary cosmic ray undergo large physical fluctuations which make an unambiguous identification difficult. A complete analysis done by the KASCADE group on the hadronic core of EAS8 has put some constraints on interaction models beyond accelerator energies. Variousstudiesseemto indicateQGSJetasbeing the modelwhichbestreproduces the data14,15 with still some disagreement at the knee energies (1016 eV). For the highest energies, additionnal work (and data) is needed to improve the agreement between the available models. 2.2. The optical fluorescence technique The idea that one could use the fluorescence light produced in the atmosphere to detect and characterize the EAS was first suggested independently by Greisen and Suga16 and then by a few other authors in the early sixties. The basic principle is simple17(althoughthedetectoritselfandthemeasuringtechniquesarequitesophis- ticated): the charged particles produced in the development of the EAS excite the nitrogen atoms of the atmosphere which then emit, very quickly and isotropically, fluorescence light which can be detected by a photo-multiplier. The emission effi- ciency(ratiooftheenergyemittedasfluorescencelighttothedepositedone)ispoor (less than 1%), therefore observations can only be done on clear moonless nights (whichresults inanaverage10%duty cycle)andlow energyshowerscanhardly be observed. At higher energies, the huge number of particles in the showerb produce enough light to be detected even at large distances. The fluorescence yield is 4 photons per electron per meter at ground level. The emitted light is typically in the 300-400 nm UV range to which the atmosphere is quite transparent. Under favorable atmospheric conditions an EHECR shower can be detected at distances as large as 20 km (about two attenuation lengths in a standard desert atmosphere at ground level). The first successful detectors based on these ideas were built by a group of the University of Utah, under the name of “Fly’s Eyes”, and used with the Volcano Ranch ground array (see Section 3.2). A complete detector was then installed at Dugway (Utah) and started to take data in 1982. An updated version, the High- Resolution Fly’s Eye, or HiRes, is presently running on this same site. Figure 1 shows the geometry of the detection of an air shower by Fly’s Eye type detectors (which are usually given the more generic name of “fluorescence detectors”or “fluorescencetelescopes”). The detector sees the showeras a variable lightbulbcmovingatthe speedoflightalongthe showeraxis. The detectoritselfis bThe highest energy shower ever detected (320 EeV) was observed by the Fly’s Eye detector: at theshowermaximum,thenumberofparticleswaslargerthan2×1011. cAroughestimateoftheequivalentradiatedpowerwouldbe3E18 wattsattheshowermaximum, 5 Shower axis Zenith Detector Impact point Detection plane Fig.1. Theprincipleofthedetection ofanEASbyafluorescencetelescope.17 asetofphototubes mountedona“camera”setatthefocalplaneofamirror. Each phototubeseesasmallportionofthesky(typically1◦). Afitonthepatternoftubes hit by the fluorescence photons determines with a precision better than one degree the plane containing the detector and the shower axis. In the stereo mode (EAS seenby twotelescopes installeda few kmapart),two planesare thus reconstructed andtheir intersectiongivesthe incidentdirectionwithgoodprecision. Inthemono mode (EAS seen by a single telescope), one has to rely on the the time of arrival of the photons on the tubes. A good reconstruction of the direction (the Ψ angle) thenneedsalargenumberofpixelstobehit,enoughtomeasuresimultaneouslythe angular velocity and the angular acceleration of the shower development. Finally, in the hybrid mode, i.e. simultaneous detection of the EAS with a fluorescence telescope and a ground array, the knowledge of the intersection of the shower axis with the array plane (reconstructed by the array) allows the selection of the right direction in the family of lines in the detector-shower axis plane. For 100 EeV showers,a precision of 0.2◦ can then be reached. The fluorescence technique is the most appropriate way to measure the energy oftheincidentcosmicray: itisapartialcalorimetricmeasurementwithcontinuous longitudinal sampling. The amount of fluorescence light emitted is proportional to the number of charged particles in the shower. The EAS has a longitudinal developmentusuallyparametrizedbytheanalyticGaisser-Hillasfunctiongivingthe size N of the shower (actually the number of the ionizing electrons) as a function e whereE18 istheprimaryenergyinEeV. 6 of atmospheric depth x: x x (Xmax−x0)/λ N (x)=N − 0 e(Xmax−x)/λ e max (cid:18)X x (cid:19) max 0 − whereλ=70g/cm2,x isthedepthatwhichthefirstinteractionoccurs,andX 0 max thepositionoftheshowermaximum. Thetotalenergyoftheshowerisproportional to the integralof this function, knowing that the averageenergy loss per particle is 2.2 MeV/g cm−2. In practice severaleffects have to be taken into accountto properly convertthe detectedfluorescencesignalintotheprimaryCRenergy. Theseincludethesubtrac- tion of the direct or diffused Cerenkov light, the (wavelength dependent) Rayleigh and Mie (aerosol) scatterings, the dependence of the attenuation on altitude (and elevation for a given altitude) and atmospheric conditions, the energy transported by the neutral particles (neutrinos), the hadrons interacting with nuclei (whose energy is not converted into fluorescence) and penetrating muons whose energy is mostly dumped into the earth. One also has to take into account that a shower is never seen in its totality by a fluorescence telescope: the Gaisser-Hillas function parameters are measured by a fit to the visible part of the shower, usually cut at the beginning (interaction point) and the end (tail absorbed by the earth). All these effects contribute to the systematic errors in the energy measurement which needs sophisticated monitoring and calibration techniques, e.g the use of powerful laser beams shot through the atmosphere. The overall energy resolution one can reach with a fluorescence telescope is of course dependent on the EAS energy but also on the detection mode (mono, stereo or hybrid). The HiRes detector should havearesolutionof25%orbetter above30 EeVinthemono mode. This improves significantly in the stereo or hybrid modes (about 3% median relative error at the same energy in the latter case). The identification of the primary cosmic ray with a fluorescence telescope is based on the shower maximum in the atmosphere (X ) which depends on the max nature and the energy of the incident cosmic ray. At a given energy, and on the average,a showergenerated by a heavy nucleus reaches its maximum higher in the atmospherethanthatofalightnucleusoraproton. Simulationsshowtypicalvalues of (respectively for iron nuclei and protons) 750 and 850 g/cm2. Unfortunately, physicalfluctuationsofthe interactionpointandoftheshowerdevelopment(larger than the precision on the shower reconstruction) blur this ideal image. As an example,at10EeVthetypicalfluctuationontheX positionis50g/cm2. Thus, max when the fluorescence technique is used alone, it is practically impossible to define the primary composition on a shower-by-shower basis. Therefore, one must look for statistical means of studying the chemical composition and/or use the hybrid detection method where a multi-variable analysis becomes possible. The former method uses the so-called elongation rate measured for a sample of showerswithinsomeenergyrange. Thedepthoftheshowermaximumasafunction 7 of the energy for a given composition is given by19: E X =D ln max el (cid:18)E (cid:19) 0 where E is a parameter depending on the primary nucleus mass. Therefore, inci- 0 dentsamplesofpurecompositionwillbedisplayedasparallelstraightlineswiththe same slope D (the elongation rate) on a semi-logarithmic diagram. The results of el such an analysis in the highest energy range will be mentioned in Section 3. 2.3. The ground array technique A ground array is a set of particle detectors distributed as a more or less regular matrix over some surface. The surface of the array is a direct function of the expectedincidentflux andofthe statistics neededtoanswerthe questionsathand. The100km2 AGASAarray(seeSection3.2)isappropriatetoconfirmtheexistence oftheEHECRwithenergiesinexcessof100EeV(whichitdetectsatarateofabout one event per year). To explore the properties of these cosmic rays and hopefully answerthe open question of their origin,the relevantdetector will no doubt be the Auger Observatory with its 6000 km2 surface over two sites. The array detectors count the number of secondary particles which cross them as a function of time. Therefore, they sample the non-absorbed part of the shower which reaches the ground. The incident CR’s direction and energy are measured by assuming that the shower has an axial symmetry. This assumption is valid for not too large zenith angles (usually θ < 60◦). At larger angles the low energy secondaries are deflected by the geomagnetic fields and the analysis becomes more delicate. The direction of the shower axis (hence of the incident CR) is reconstructed by fitting an analytical function (the “lateral distribution function” or LDF) to the measured densities. The LDF explicit form depends on each experiment. The Haverah Park experiment20 (an array of water-Cerenkov tanks) used the function: ρ(r,θ,E)=kr−[η(θ,E)+r/4000] as the LDF for distances less than 1 km from the shower core. Here r is in meters, and η can be expressed as: η(θ,E)=a+bsecθ+clog(E/E ) 0 withappropriatevaluesforalltheparameterstakenfromshowertheoryandMonte Carlo studies at a given energy range. At larger distances (and highest energies), this function has to be modified to take into account a change in the rate at which the densities decreasewith distance. A muchmorecomplicatedformis usedby the AGASA group.21 However, the principle remains the same. Once the zenith angle correction is made for the LDF, an estimator of the primary CR energy is extracted from this function. At energies below 10 EeV, this 8 estimator is usually taken as the particle density (whatever particles detected by the array stations) at 600 m from the shower core, ρ . The density at 600 m is 600 chosen for the following reason. Because of variations on the primary interaction point(andthe positionofthe showermaximum),therearelargefluctuationsinthe ground densities close to the core. At the same time, the statistical fluctuations in the measured densities are important at large distances where the densities are low. Monte Carlo studies show that somewhere in between, the overall fluctuation reaches a minimum. This happens to be at 600 m from the core, a value slowly increasing when one goes to the highest energies. In the EHECR range, a more appropriate density is ρ . Once this value is determined, the primary energy is 1000 related to it by a quasi-linear relation: E =kρα 600 where α is a parameter close to 1. Of course, to be able to reconstruct the LDF, many array stations have to be hit at the same time by a shower. The spacing between the stations determines the threshold energy for a vertical shower: the 500 m spacing of the Haverah Park triggering stations corresponds to a threshold of a few 1016 eV, while the 1.5 km separation of the Auger Observatory stations makes this array almost 100% efficient for energies above 10 EeV. Inagroundarray,theprimarycosmicray’sidentityisreflectedintheproportion ofmuonsamongthesecondariesatgroundlevel. Hereaproperestimatoristherefore the ratio of muons to electrons - and eventually photons, if they are detected - (see Section2.1). Whenagroundarrayhasmuondetectingcapabilities(waterCerenkov tanks, buried muon detectors), one measures directly the muon to electron ratio. Otherwise, an indirect method consists in measuring the rise-time of the signal in the detectors: the faster this time, the higher the muon content. 2.4. The detection of neutrinos EHEneutrinosmayalsobedetectedbytheirEAS.Thisisimportantfortworeasons. The firstis that the detection of neutrinos (together with an importantcomponent ofphotons)inthehigherenergyrangeofthespectrumisasolidsignatureofthetop- down mechanisms (see Section 4.3). The second is that the projected high energy neutrino telescopes (under-water or under-ice km scale detectors) are ineffective at energies above 1016 eV at which the Earth becomes opaque to upward going neutrinos. Therefore large ground arrays (or fluorescence telescopes) for which the interaction medium is not the earth but the atmosphere, and which could become efficient enough at 1017 eV and above, would be complementary to the neutrino telescopes in the exploration of the whole spectrum. The neutrino cross-sections at these ultra-high energies become non-negligible (about10−32 cm2 at1EeV).22 Theneutrinocanthereforeinitiateashoweratsome point in the atmosphere where the density is high enough. The main difficulty for anobserveristoidentifytheEASascomingfromaneutrino. Withthefluorescence technique(whichcanlocatewithsomeprecisionthe interactionpoint), aclearneu- 9 trinosignaturewouldbetoseeashowerstartingdeepintheatmosphere. However, the expected low fluxes of neutrinos combined with the low cross-sections result in veryloweventrates. The10%dutycycleofthefluorescencedetectorswilltherefore hinder their use for this purpose. Analternativeandpromisingwayofdetectingultra-highenergyneutrinoswould be to use horizontal air showers,23 i.e. showers generated by cosmic rays with incidentzenithangleslargerthan60◦. Attheselargeangles,hadronicshowershave their electromagneticpartextinguishedas they havegonethrougha few equivalent verticalatmosphere (2 at 60◦, 3 at 70◦, 6 at 80◦). Only high energy muons survive past 2 equivalent verticalatmospheres. These muons are created in the first stages of the shower development, are of very high energy, and therefore the shape of the shower front is quite specific: it is very flat (curvature of more than 100 km), and its time extension is very short (less than 50 ns!). On the other hand, a neutrino shower which would have been initiated a few kilometers before hitting the array wouldappearas a “normal”shower,with a curvedfront(curvature of afew km), a largeelectromagnetic component, and a signalwith a width of a few microseconds. With such important differences between neutrino and background (hadronic) showers,particularlyatlargezenithangles,wecanassumethatifthefluxesarehigh enough, the next generation of experiments will detect neutrino induced showers. Therealbackgroundwouldcome,butonlyatthehighestenergies,frompenetrating photonshowerswhosedevelopmentisdelayedduetotheLPMeffect. However,such showers would show a strong correlation in direction with the geomagnetic field, a helpful effect to distinguish them from neutrinos. A large amount of ongoing work is exploring this very promising and exciting field. 3. What do we know about the EHECR? It is outside the scope of this review to present the full history of the cosmic ray detection and studies. This would cover the whole century (1912 is the year of the first decisive balloon experiments by Victor Hess). If we want a starting point for the genesis of the EHECR physics, we need to go back to the end of the thirtieswiththefirstobservationsofPierreAugerandcollaborators.24Theystudied the coincidence rates between counters with increasing separation (up to 150 m in their first experiments in Paris, more than 300 m when they repeated them at the Jungfraujoch in Switzerland). They inferred from this very modest measurement the existence of primary cosmic rays with energies as large as 1 PeV (1015 eV). Today’sgroundarraysusedto detectthe highestenergycosmicrays(someofthem more than five orders of magnitude beyond the energies Auger considered as being extraordinary in his times) are actually based on this same technique, however sophisticated they may be: time coincidences between distant counters to identify a giant shower, and then the lateral profile of the densities of the particles hitting the counters to measure the total energy. Figure 2 is a compilation25 of the differential spectrum of cosmic ray flux as a function of energy. On this figure, integrated fluxes above three energy values are 10