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Shower properties relevant to large arrays
Nuclear PhysicsB (Prec. Suppl.) ~B (1992)67-73 North-Holland
SUPP
MS
Shower properties relevant to large arrays A. M. Hillas Physics Deparunent, University of leeds, ~s LS2 9]T, United Kingdom If a giant detector army is used to observe showers "above 1 EeV, measurements of the ~ scin,~~ light and its ratio to Cerenkov light might usefully indicate the depth of shower development. The p t ~ of muons remains a useful indicator of primary mass: their height of origin appears to be a less sensi~ve indicator of mass.
1. GROSS FEATURES OF AN AIR SHOWER
In this section the gross features of an extensive air shower will be reviewed very briefly, with emphasis on those features which are expected to carry information about the energy and nature of the primary particle. The next section will then concentrate on what we expect to see in the parts of the shower far distant from the axis, as these are the regions where the shower will probably be sampled in a giant sparse array of detectors. L I Longitudinal development The number of charged particles in the cascade builds up to a maximur, and then decays, as illustrated in Figure 1. This curve was calculated using the author's Monte-Carlo cascade simulation, MECCA, for a light nucleus (Z=8) of energy 1 EeV B
10e 6 4 2
0
0
200
t,O0
600
BOO ,3000 1200
depth/g ¢m"~ Figure 1. Average number of charged particles as function of depth in atmosphere, for I EeV oxygen primaries (from simulation)
(i.e. 1018 eV) and shows the averdge shower development. It is not yet known reliably what is the typical mass of primary particles, which, as mentioned later, makes scme difference to the of maximum, but this seems a reasonable ~erage, and the depth of maximum is close to that e s ~ ~ by various experiments for showers of this er~tgy. The shape seems to be consistent with Fly's Eye observations. Although there is an nns f [ u c ~ of 30 g cm-2 in depth of maximum even for oxygen-induced showers, the average d e v ~ curve for individual showers, if displaced to have unvarying depths of maximum, is virtually the same as the curve shown. The shower maximum becomes deeper by about 63 g cm-2 per decade of primary energy (the "elongation rate" as def'med by Linsley), and it becomes less by the same amount per decade of increase in mass of the primary particle, as the energy-per-nucleon is the factor determining the average development of showers. In the first few hundred g cm-2 one has a cascade of high energy hadrons, which gradually pass most of the energy into the e|ectron-phoum cascade, and some of it into muons, as follows. To a reasonable degree of approximation, after the first i n ~ c t i o n of the primary nucleon, half the primary energy remains in the nucleon, one third is carried by charged pions, and one sixth by gamma rays (from decay of neutral pions) The games ~ y s initiate an electron-photon cascade. The charged pions of this first generation have such high Lorentz factors that their decay is suppressed, and they practically all make nuclear collisions. If one third of the energy of these collision products
0920-5632/92/$05.00 O 1992- Elsevier Science Publishers B.V. All rights reserved.
68
A.M. Hillas I Shower properties relevant to large arrays
(secoad generate) is carried by gamin rays (from reua-al pion decay), and two thirds by charged one sees that at each successive stage of mul~Id~ of the cascade, one Ihird of the pionic energy is drained away into the electron-photon component. Each successive generation of pions in the cascade contains only about 2/3 of the energy of its predecessor, and the individual pious have succe~ively lower energy. Eventually, when tim individual pions have energies as low as about 20 GcV, the time dilation allows ~c, ay to muons to occur, ~ the amount of energy left in the pions at this poim is dumped into muons (and neutrinos). In a 1019 eV ~ - i a ~ t i a t e d shower, there have been so many steps in the pion cascade to reach 20 GeV that only 2.4% of the primary energy goes into m ~ s , 0.8% into neutrinos, and 96% has been put into the electron-photon cascade. (A very small amount remains in hadrons at sea level.) However, a 1015 eV proton primary requires fewer steps to degrade the pion energies to 20 GeV, and so 13% remains for the muons, and 81% goes into the e l e c t r o n - ~ component. If fl~ is the fraction of the total energy put into muons (not all of which reach the ground), the calculations indicate that fl~ 0¢ Ep -0-18, and this relationship can be understood crudely as follows, from the process described above. If each successive generation of pious has an effective energy reduced by a factor 10, and the energy in the pion cascade is multiplied by 2/3 at each step, due to losses to the electron-photon cascade, the exponent -0.18 is obtained from ln(2/3)/ln(10). Although the dependence is obtained from a detailed Mome-C~lo calculation, rather than from this simple approximation, it can be seen that the proportion of muons will hence be altered if the energy carried by neutral pions (and direct gammas) from pion collisions in air is not exactly 1/3, or if the secondary pion ener~ spectnnn becomes harder of softer than assumed in the present model. This provides one of the favourite methods for at~mpting to distinguish between heavy and light nuclei as primary particles: lighter primaries (with consequently higher energy per nucleon) should put a smaller fraction of their total energy into muons: the ratio Ntt to Ep should be lower. Coming to more readily observable quantities, th~ ratio of Ntt to
He should be lower. If observations are made far beyond shower maximum (as at 1015 eV, for example), the fact that the light-nucleus showers reach maximum N later also increases He at ground level, relative to Ep, further increasing the difference in the Np]Ne ratio for different primary masses, but wtth the great disadvantage of a large fluctuation in we. As already indicated, the cascade reaches its maximum later for higher energy-per-nucleon, as the cascade continues to multiply until the individual particle energies fall below the critical energy. In summary, the useful diagnostic features of the gross (longitudinal) structure of the shower are (a) The total ionization produced, proportional to the area under the N(x) curve, x being atmo~heric depth, gives the total energy. (Above 1019 eV there is only a small correction for the energy in more penetrating particles n muons, neutrinos
and neutrons). Co)Concerning the nature of the primary particle - Fluctuations in starting points m larger for protons, smaller for very heavy nuclei - - may give information about the comosition in a statistical sense. High mass implying lower E/A leads to an earh'er shower maximum. more muons.
The difference in average depth of maximum per decade of mass, A, is about 63 g cm-2 and the nns fluctuation in depth of maximum is expected to be about 30 g cm-2 for A=I6, and 72 g cm-2 for A=I. The separation per decade of A is therefore about equal to the typical fluctuation in depth for protons, so that many individual protons would be mistaken for heavy nuclei, though if protons were absent, the separation would be more reasonable. For a given total energy (gauged, perhaps by optical radiation), logl0Ntt would differ by about 0.18 per decade of A (as outlined above)~ whereas the fluctuation in logl0Np should be about 0.09, 0.13, for A=16, 1, (at 1 EeV) according to the simulations. This is not less favourable than the depth of maximum, although one must consider
A.M. Hillas/Shower propet6es relevant to large re'rays
fluctuations in muon numbers in the observable part of the shower, rather than the gross Ntt for reliable evaluations. Also, one must note that, as Ep is unknown, one would have to observe either the ratio of muons to electrons or muons to optical photons, and the fluctuations in logl0Ne would be about 0.05 and 0.13 for the masses considered above, at sea level (less at 800 g cm-2). Very energetic hadrons near the axis may retain information about the primary particle, but this is not of much practical interest in a giant array.
seen immediately that ~ the ~ within 30 m of the shower axis.
69
~ ~
N
003
002 001 f/m
1.2 Lateral spread of shower In the main part of the shower, the spread of the electron component is due to multiple coulomb scattering, whereas the muon spread is determined largely by the angle of emission of the parent pion (usually much bigger than the angles involved in earlier generations) with a small additional effect of coulomb scattering and geomagnetic deflection. If the particle density at a distance r from the shower axis is denoted by p(r). the spread of the charged panicles is best conveyed by plotting r2p(r) against a logarithmic scale of r . Since the total number of charged particles, N --- ~ 2m" p dr - 2g ~ (r2p) dlnr, the area under such a graph represents the number of particles, and displays directly hhe relative numbers of particles in different radial ranges. Fig. 2 shows such a plot for vertical showers of N = 4.75x108 at an atmospheric depth of 920 g cm-2 (Akeno). This shower size correspond~ to a primary energy of 1 EeV, both accoraing to me Akeno group I and to figure 1 (A--16). The lateral distribution plotted is that derived by experiments at Akenol, and it should be noted that the apparent particle densities recortied by scintillators of normal thickness do not correspond exactly to a count of charged particles made with a very thin scintillator, because of photon conversion and short-range electrons, so the integral of the apparent density may not agree exactly with a correct count of particle numbers, N. The graph plotted above has been normalized to agree with the quoted N. At these energies, the experiments do not cover distances of a few metres from the shower axis, but the full graph is plotted, as it can thus be
Figure 2. Density p of charged par~les a t ~ r from shower axis, in shower of N = 4.75x108 particles(E= I EeV) at Akeno. Tbe a r e a ~ t h e curve in any interval of r, in this form of reWesentation, is proportional to the number of particles in that range. The stippled r e ~ ~ be sampled in a large array.
If scintillators are laid out on a grid spacing which ensures that there are a few of them smrmw_,dingthe shower axis, at distances of about 3Ore, then fluctuations in shower "age', resulting in lateral displacements o~ the curve in figure 2, would not much affect ~ e observed densities, and a good measure of shower size (N) would be abtained just from these well-placed scintillators. (At PeV energies, where such small arrays are practical, N is actually not a very good measure of wimm3r energy, because of large fluctuations in the deep tail of the shower; and at EeV energies, where f ~ vertical showers N would be a good measure, observations at such small distances are impractical.) With an array suitable for the largest showers, having very widely spaced detectors, particles are only sampled beyond about 600m from the shower axis m in the region stippled in the diagram. This is only the outer fringe of a shower, and as the curve fluctuates sideways somewhat with change in shower age from shower to shower, one cannot deduce the shower size N with much certainty. Hence "P600", the panicle density ~ from the shower axis, is commonly used to describe shower sizes. This usage was introduced at the Haverah
70
A.M. Hig~ / ~
lro~
Park array, in which deep water tanks detected par~ and in which the particle deputy at-400m t ~ axis was ~p~:ted to be ~ ~..-estmeasure of Ep, as in fluctuations w~.lich proOuced younger showers, for examp~, the increase in N was offset by the steeper lateral distribution, so that at 400m the ~nsity fluctuated much less than N did. P600 was ~m~ewhat less we~. ~eimved but mor~ :oracfical than P400. However, " ~ chara~teristics,~ shallow scintillators are different, and P600 will be somewhat less closely tie~ to Ep.
2. PARTICLES AND PHOTONS FROM THE SHOWER AXIS
FAR
What gets out to large distances (say 0.7 to 2 lun) - - where the detectors of a large array would be p ~ - - and how? By far the most numerous particle~quanta out hen~ae Air f l ~ photons, Cerenkov photons; and thereme gamma rays and electrons, non-relativistic neutrons, and antineutrons (and protons), muons. The sub-relativistic nucleons are not particularly useful, but they can cause problems, as one such particle can cause a large pulse (say 200 MeV) in a scintillator, due to a recoil proton. They occur distinctly later than the normal relativistic particles.
relevant to large arrays
tracks acctntely without introducing deflections or, in the case of optical photons, if one focuses an optical image (as in the Fly's E y e ) - or (2) by ~ ~ g delays in arrival of particles, time delays being deteanined by path length if v = c, and in this case deflection in or near the detector is u n i m g ~ n t . However. one needs enough detectors to define a plane tangent f~nt to ~ e shower if absolute delays are to be used, otherwise one has to use the somewhat less direct information of the spread in arrival times. (This approach has been successfully applied by Watson and colleagues2.3 to the pulse width of the mixed electron-photon-muon component, although the simple geometrical picture may be a little misleading when applied to this mixed component measurement, as noted below.)
The question of how accurately the axis needs to be known in case (1) will not be discussed.
t
2.1 Heights of origin of particles: track
projection or timing. The other distant particles have an important characteristic in common: most of them have travelled with very little deflection from the main shower core (according to a trace-back of particle histories in a Monte-Carlo simulation program MOCCA, used by the author). Hence we might attempt to find the height at which most particle interactions occurred by tracing back the particle trajectories (Figure 3): (1) by geometrical projection of particle tracks - - if one has elaborate detectors which define muon
~/
///
Figure 3. Muons arriving at a distant cletectcr.
If one does project tracks back to the shower axis by some method, does this give us useful information? Testing such back-projection of muon tracks which reach the ground beyond 500m in Monte Carlo shower simulations (unpublished), two things were found--
A,M. Hillas I Shower propenies relevant to large ~
(a) The appment height of erigin of that panicle which reached the ground - - defined by the nearest approach of its back-projected trajectory to the axis (i,cSlecthtg any inaccuracy in the knowledge of the axis) - - is good, showing little bias and almost the correct spw.ad ,~",~m-"-- !80 g c.m_-2 ). The spread, o , shows how many muon tracks are needed to define their mea~ height of origin to some specified accuracy. Thus 25 muon tracks would not be capable of giving this height to better than 180 g cm -2 1 ~ 2 5 ffi 36 g cm-2 . If timing gives essentially the same heights as geometrical re-tracing of the tracks, the same limitation would apply to measurements based on a suitable average of time delay. (Pulse width measurements without imowledge of the absolute time of passage of the tangent plane would presumably be not as good as this.) ('0) However, these heights of "origin" (or ejection from the shower axis) do not give a very good overall picture of the cascade. In the case of muons there is a bias against detecting muons at large distances if they are emitted low down, because of the emission angle required. Figure 4 shows, for showers of several energies (1015 to 1019 eV per nucleon), the number of pi-mu decays cccuring per g cm-2 as a function of depth, for several primary energies.
~30 LL!
5
c•20 ~o "I=3
g 2OO
600 ' 600 depth/g 8~
1000
Figure ~. Number of muons generated at ~gifferent depths. Also (circled crosses), mean depthsof origin of parents of muons reaching the ground beyond 500m.
71
Each number has been s c a ~ ~ to ~ energy, being multiplied by (I Pev /El,), to the curves easy to c o m ~ , The c~rc~ed Ooined by a dotted line) ~ the ~ ~ origin of the pica i m r e ~ of mucus ~ ~ groundat O.5-3km. O n e n o t i c e s ~ ~ ~ l-,eights of origin shift down with ~ ' ~ energy at a rate of ~ y 31 g cm-2 ~ ~
of
of
primary energy (or of energy per nttdeea)--- so observations seem to be only weaHy m t ~ m changes in ~:e cascade. ( M e ~ ~ i s ~ ~ amount of rouen production, per PeV of
energy,as F~ rises,) These figures may not apply to the ~ "rise time" measurements of Walker, Watson Wilson 1.2.3, which have been used to changes in depth of maximum, as these were made on the rouen-electron mixture in their detectors, were sensitive to the muon/elecutm ratio to at least as great an extent as to the time spread of m ~
(Watson, privatecommunication). 2.2 Sensitivity of optical phcP.ons to depth of development of shower One does not need a Fly's Eye to obtain information from optical photons. Figure 5 shows the density of Cerenkov photons (in the S11 waveband) and of air fluorescence photons at 0.4 to 3 km from the shower axis, calculated for a vertical womngenerated s~ower of I EeV. The first interaction of the proton was made to occur at specificdepths - 60, 200 and 400 g cm-2 - - to show the effect of variations in the depth of shower development (though many showers were simulated for each depth). The ratio F/C of fluorescent to scintillation light is clearly sensitive to the depth of shower development . This is primarily because the fluorescent radiation is entitled isotmpically, whilst the Cerenkov radiation is mostly concentrated in a small cone of angles (the scattered radiation not much alie~ingthe picture), so the ratio of the two depends on the distance to the main light source. Hence, if optical fdters in front of a photomultiplier can greatly change its relative sensitivity to fluorescent and Cerenkov emission spectra, the ratio
~M, Hilhrs/ ~ h ~
72
propen~s rd~a~ to~
sig~ls in two s ~ h detectors might give a good of beight of s1~owerm a x i m . Hence one ra~ht be able ~ monitor the anmunt of f l ~ , estimate the p t a ~ component from the deep tail of the disu-ibuzion. The dotted line gives an
emimmeof the ~
sky ~ise in a 2ps ga~
~ n g a 5-inch phototube (no filter) for a 1 F..eV shower, indicating the ~ g e of axial distances in
w-hich su.eh~ me~sureme.ntcould be made. (it is
assumed that in g ~ ~,'k-sky conditions the Poisson fluctuations on 10 photoelectrons per nanosenond from a 5-inch photocathode form the ~ g r o u n d noL~) I~ 13
,
i
~
~
~
arrays
photons (Cerenkov plus fluorescent) observed at three axial dimances, and for verdcal proton showers constrained to start at normal depths or at 200 g cm-2, as illustrated before. Clearly, one would have to know the distance r rather well in order to make use of these didfferences in pulse delay or width, as there is a rapid dependence on r as well as on height of maximum. 20~
10~ 9 !
=
;i
1
10%i ~ o 0 ~-:
2
r= lO00m , ~
.,Jr"~ ' - - " ' - ' - ~ I
\
1
2
h.s
N
N I
Figure 6. Sensitivity of time profile of optical photons to depth of maximum of shower, illustrated by calculated time profiles of optical photons received at specified distances r from shower axis, for I EeV proton shower having its first interaction at 60 or 200 g cm-2. "N" indicates the probable magnitude of the sky noise in a 50 ns channel.
I# I
~5
..... ;
3
km
P
Figure 5. Comparison of density of Cerenkov (c) and fluore.scent (f) photons due to vertical proton showers initialed at depths 60, 200 and 400 g cm-2, at large distances from the shower axis (sea level). Note: To obtain numbers of photoelectrons in a phozomultiplier, the photon densities quoted should be multiplied by the phott~athode area and the peak quantum conversion efficiency. Altern~.tively, one could measure the pulse shape of the optical photon signal (as ou'Jined in the previous section) to deduce heights of origin. This is a crude alternative to the Fly's Eye approach. Figure 6 shows calculated pulse shapes for optical
3. SUMMARY If measurements are possible of Fiuorescence/Cerenkov ratio Optical rise time Muon rise time muon density I fluorescence signal or muon density I total particle density. a multi-parameter classification of showers could possibly lead to a more reliable measure of "depth of maximum" and its fluctuations, as ~ method of investigating at least the proportion of protons amongst the primary particles, and possibly a better separation of masses.
A.M. Hillas / Showerpropertiesrelevantto large~ REFERENCES
1. M. Nagano, M. Teshima, Y. l~Lsubara, H. Y. Dai, T. Hara, N. Hayashida, M. Honda, H. Ohoka and S. Yoshida, J. Phys. G, Nucl. Phys., 18: 423. (1992) 2 A. A. Watson and J. G. Wilson, J. Phy. A, Math., Nucl., Gen., 7:1199 (1974). 3. R. Walker and A. A. Watson,J. Phys. G., Nucl. Phys., 7, 1297 (1981) andJ. Phys. G.,Nucl. Phys., 8, 1131 (1982).
SUPP
MS
Shower properties relevant to large arrays A. M. Hillas Physics Deparunent, University of leeds, ~s LS2 9]T, United Kingdom If a giant detector army is used to observe showers "above 1 EeV, measurements of the ~ scin,~~ light and its ratio to Cerenkov light might usefully indicate the depth of shower development. The p t ~ of muons remains a useful indicator of primary mass: their height of origin appears to be a less sensi~ve indicator of mass.
1. GROSS FEATURES OF AN AIR SHOWER
In this section the gross features of an extensive air shower will be reviewed very briefly, with emphasis on those features which are expected to carry information about the energy and nature of the primary particle. The next section will then concentrate on what we expect to see in the parts of the shower far distant from the axis, as these are the regions where the shower will probably be sampled in a giant sparse array of detectors. L I Longitudinal development The number of charged particles in the cascade builds up to a maximur, and then decays, as illustrated in Figure 1. This curve was calculated using the author's Monte-Carlo cascade simulation, MECCA, for a light nucleus (Z=8) of energy 1 EeV B
10e 6 4 2
0
0
200
t,O0
600
BOO ,3000 1200
depth/g ¢m"~ Figure 1. Average number of charged particles as function of depth in atmosphere, for I EeV oxygen primaries (from simulation)
(i.e. 1018 eV) and shows the averdge shower development. It is not yet known reliably what is the typical mass of primary particles, which, as mentioned later, makes scme difference to the of maximum, but this seems a reasonable ~erage, and the depth of maximum is close to that e s ~ ~ by various experiments for showers of this er~tgy. The shape seems to be consistent with Fly's Eye observations. Although there is an nns f [ u c ~ of 30 g cm-2 in depth of maximum even for oxygen-induced showers, the average d e v ~ curve for individual showers, if displaced to have unvarying depths of maximum, is virtually the same as the curve shown. The shower maximum becomes deeper by about 63 g cm-2 per decade of primary energy (the "elongation rate" as def'med by Linsley), and it becomes less by the same amount per decade of increase in mass of the primary particle, as the energy-per-nucleon is the factor determining the average development of showers. In the first few hundred g cm-2 one has a cascade of high energy hadrons, which gradually pass most of the energy into the e|ectron-phoum cascade, and some of it into muons, as follows. To a reasonable degree of approximation, after the first i n ~ c t i o n of the primary nucleon, half the primary energy remains in the nucleon, one third is carried by charged pions, and one sixth by gamma rays (from decay of neutral pions) The games ~ y s initiate an electron-photon cascade. The charged pions of this first generation have such high Lorentz factors that their decay is suppressed, and they practically all make nuclear collisions. If one third of the energy of these collision products
0920-5632/92/$05.00 O 1992- Elsevier Science Publishers B.V. All rights reserved.
68
A.M. Hillas I Shower properties relevant to large arrays
(secoad generate) is carried by gamin rays (from reua-al pion decay), and two thirds by charged one sees that at each successive stage of mul~Id~ of the cascade, one Ihird of the pionic energy is drained away into the electron-photon component. Each successive generation of pions in the cascade contains only about 2/3 of the energy of its predecessor, and the individual pious have succe~ively lower energy. Eventually, when tim individual pions have energies as low as about 20 GcV, the time dilation allows ~c, ay to muons to occur, ~ the amount of energy left in the pions at this poim is dumped into muons (and neutrinos). In a 1019 eV ~ - i a ~ t i a t e d shower, there have been so many steps in the pion cascade to reach 20 GeV that only 2.4% of the primary energy goes into m ~ s , 0.8% into neutrinos, and 96% has been put into the electron-photon cascade. (A very small amount remains in hadrons at sea level.) However, a 1015 eV proton primary requires fewer steps to degrade the pion energies to 20 GeV, and so 13% remains for the muons, and 81% goes into the e l e c t r o n - ~ component. If fl~ is the fraction of the total energy put into muons (not all of which reach the ground), the calculations indicate that fl~ 0¢ Ep -0-18, and this relationship can be understood crudely as follows, from the process described above. If each successive generation of pious has an effective energy reduced by a factor 10, and the energy in the pion cascade is multiplied by 2/3 at each step, due to losses to the electron-photon cascade, the exponent -0.18 is obtained from ln(2/3)/ln(10). Although the dependence is obtained from a detailed Mome-C~lo calculation, rather than from this simple approximation, it can be seen that the proportion of muons will hence be altered if the energy carried by neutral pions (and direct gammas) from pion collisions in air is not exactly 1/3, or if the secondary pion ener~ spectnnn becomes harder of softer than assumed in the present model. This provides one of the favourite methods for at~mpting to distinguish between heavy and light nuclei as primary particles: lighter primaries (with consequently higher energy per nucleon) should put a smaller fraction of their total energy into muons: the ratio Ntt to Ep should be lower. Coming to more readily observable quantities, th~ ratio of Ntt to
He should be lower. If observations are made far beyond shower maximum (as at 1015 eV, for example), the fact that the light-nucleus showers reach maximum N later also increases He at ground level, relative to Ep, further increasing the difference in the Np]Ne ratio for different primary masses, but wtth the great disadvantage of a large fluctuation in we. As already indicated, the cascade reaches its maximum later for higher energy-per-nucleon, as the cascade continues to multiply until the individual particle energies fall below the critical energy. In summary, the useful diagnostic features of the gross (longitudinal) structure of the shower are (a) The total ionization produced, proportional to the area under the N(x) curve, x being atmo~heric depth, gives the total energy. (Above 1019 eV there is only a small correction for the energy in more penetrating particles n muons, neutrinos
and neutrons). Co)Concerning the nature of the primary particle - Fluctuations in starting points m larger for protons, smaller for very heavy nuclei - - may give information about the comosition in a statistical sense. High mass implying lower E/A leads to an earh'er shower maximum. more muons.
The difference in average depth of maximum per decade of mass, A, is about 63 g cm-2 and the nns fluctuation in depth of maximum is expected to be about 30 g cm-2 for A=I6, and 72 g cm-2 for A=I. The separation per decade of A is therefore about equal to the typical fluctuation in depth for protons, so that many individual protons would be mistaken for heavy nuclei, though if protons were absent, the separation would be more reasonable. For a given total energy (gauged, perhaps by optical radiation), logl0Ntt would differ by about 0.18 per decade of A (as outlined above)~ whereas the fluctuation in logl0Np should be about 0.09, 0.13, for A=16, 1, (at 1 EeV) according to the simulations. This is not less favourable than the depth of maximum, although one must consider
A.M. Hillas/Shower propet6es relevant to large re'rays
fluctuations in muon numbers in the observable part of the shower, rather than the gross Ntt for reliable evaluations. Also, one must note that, as Ep is unknown, one would have to observe either the ratio of muons to electrons or muons to optical photons, and the fluctuations in logl0Ne would be about 0.05 and 0.13 for the masses considered above, at sea level (less at 800 g cm-2). Very energetic hadrons near the axis may retain information about the primary particle, but this is not of much practical interest in a giant array.
seen immediately that ~ the ~ within 30 m of the shower axis.
69
~ ~
N
003
002 001 f/m
1.2 Lateral spread of shower In the main part of the shower, the spread of the electron component is due to multiple coulomb scattering, whereas the muon spread is determined largely by the angle of emission of the parent pion (usually much bigger than the angles involved in earlier generations) with a small additional effect of coulomb scattering and geomagnetic deflection. If the particle density at a distance r from the shower axis is denoted by p(r). the spread of the charged panicles is best conveyed by plotting r2p(r) against a logarithmic scale of r . Since the total number of charged particles, N --- ~ 2m" p dr - 2g ~ (r2p) dlnr, the area under such a graph represents the number of particles, and displays directly hhe relative numbers of particles in different radial ranges. Fig. 2 shows such a plot for vertical showers of N = 4.75x108 at an atmospheric depth of 920 g cm-2 (Akeno). This shower size correspond~ to a primary energy of 1 EeV, both accoraing to me Akeno group I and to figure 1 (A--16). The lateral distribution plotted is that derived by experiments at Akenol, and it should be noted that the apparent particle densities recortied by scintillators of normal thickness do not correspond exactly to a count of charged particles made with a very thin scintillator, because of photon conversion and short-range electrons, so the integral of the apparent density may not agree exactly with a correct count of particle numbers, N. The graph plotted above has been normalized to agree with the quoted N. At these energies, the experiments do not cover distances of a few metres from the shower axis, but the full graph is plotted, as it can thus be
Figure 2. Density p of charged par~les a t ~ r from shower axis, in shower of N = 4.75x108 particles(E= I EeV) at Akeno. Tbe a r e a ~ t h e curve in any interval of r, in this form of reWesentation, is proportional to the number of particles in that range. The stippled r e ~ ~ be sampled in a large array.
If scintillators are laid out on a grid spacing which ensures that there are a few of them smrmw_,dingthe shower axis, at distances of about 3Ore, then fluctuations in shower "age', resulting in lateral displacements o~ the curve in figure 2, would not much affect ~ e observed densities, and a good measure of shower size (N) would be abtained just from these well-placed scintillators. (At PeV energies, where such small arrays are practical, N is actually not a very good measure of wimm3r energy, because of large fluctuations in the deep tail of the shower; and at EeV energies, where f ~ vertical showers N would be a good measure, observations at such small distances are impractical.) With an array suitable for the largest showers, having very widely spaced detectors, particles are only sampled beyond about 600m from the shower axis m in the region stippled in the diagram. This is only the outer fringe of a shower, and as the curve fluctuates sideways somewhat with change in shower age from shower to shower, one cannot deduce the shower size N with much certainty. Hence "P600", the panicle density ~ from the shower axis, is commonly used to describe shower sizes. This usage was introduced at the Haverah
70
A.M. Hig~ / ~
lro~
Park array, in which deep water tanks detected par~ and in which the particle deputy at-400m t ~ axis was ~p~:ted to be ~ ~..-estmeasure of Ep, as in fluctuations w~.lich proOuced younger showers, for examp~, the increase in N was offset by the steeper lateral distribution, so that at 400m the ~nsity fluctuated much less than N did. P600 was ~m~ewhat less we~. ~eimved but mor~ :oracfical than P400. However, " ~ chara~teristics,~ shallow scintillators are different, and P600 will be somewhat less closely tie~ to Ep.
2. PARTICLES AND PHOTONS FROM THE SHOWER AXIS
FAR
What gets out to large distances (say 0.7 to 2 lun) - - where the detectors of a large array would be p ~ - - and how? By far the most numerous particle~quanta out hen~ae Air f l ~ photons, Cerenkov photons; and thereme gamma rays and electrons, non-relativistic neutrons, and antineutrons (and protons), muons. The sub-relativistic nucleons are not particularly useful, but they can cause problems, as one such particle can cause a large pulse (say 200 MeV) in a scintillator, due to a recoil proton. They occur distinctly later than the normal relativistic particles.
relevant to large arrays
tracks acctntely without introducing deflections or, in the case of optical photons, if one focuses an optical image (as in the Fly's E y e ) - or (2) by ~ ~ g delays in arrival of particles, time delays being deteanined by path length if v = c, and in this case deflection in or near the detector is u n i m g ~ n t . However. one needs enough detectors to define a plane tangent f~nt to ~ e shower if absolute delays are to be used, otherwise one has to use the somewhat less direct information of the spread in arrival times. (This approach has been successfully applied by Watson and colleagues2.3 to the pulse width of the mixed electron-photon-muon component, although the simple geometrical picture may be a little misleading when applied to this mixed component measurement, as noted below.)
The question of how accurately the axis needs to be known in case (1) will not be discussed.
t
2.1 Heights of origin of particles: track
projection or timing. The other distant particles have an important characteristic in common: most of them have travelled with very little deflection from the main shower core (according to a trace-back of particle histories in a Monte-Carlo simulation program MOCCA, used by the author). Hence we might attempt to find the height at which most particle interactions occurred by tracing back the particle trajectories (Figure 3): (1) by geometrical projection of particle tracks - - if one has elaborate detectors which define muon
~/
///
Figure 3. Muons arriving at a distant cletectcr.
If one does project tracks back to the shower axis by some method, does this give us useful information? Testing such back-projection of muon tracks which reach the ground beyond 500m in Monte Carlo shower simulations (unpublished), two things were found--
A,M. Hillas I Shower propenies relevant to large ~
(a) The appment height of erigin of that panicle which reached the ground - - defined by the nearest approach of its back-projected trajectory to the axis (i,cSlecthtg any inaccuracy in the knowledge of the axis) - - is good, showing little bias and almost the correct spw.ad ,~",~m-"-- !80 g c.m_-2 ). The spread, o , shows how many muon tracks are needed to define their mea~ height of origin to some specified accuracy. Thus 25 muon tracks would not be capable of giving this height to better than 180 g cm -2 1 ~ 2 5 ffi 36 g cm-2 . If timing gives essentially the same heights as geometrical re-tracing of the tracks, the same limitation would apply to measurements based on a suitable average of time delay. (Pulse width measurements without imowledge of the absolute time of passage of the tangent plane would presumably be not as good as this.) ('0) However, these heights of "origin" (or ejection from the shower axis) do not give a very good overall picture of the cascade. In the case of muons there is a bias against detecting muons at large distances if they are emitted low down, because of the emission angle required. Figure 4 shows, for showers of several energies (1015 to 1019 eV per nucleon), the number of pi-mu decays cccuring per g cm-2 as a function of depth, for several primary energies.
~30 LL!
5
c•20 ~o "I=3
g 2OO
600 ' 600 depth/g 8~
1000
Figure ~. Number of muons generated at ~gifferent depths. Also (circled crosses), mean depthsof origin of parents of muons reaching the ground beyond 500m.
71
Each number has been s c a ~ ~ to ~ energy, being multiplied by (I Pev /El,), to the curves easy to c o m ~ , The c~rc~ed Ooined by a dotted line) ~ the ~ ~ origin of the pica i m r e ~ of mucus ~ ~ groundat O.5-3km. O n e n o t i c e s ~ ~ ~ l-,eights of origin shift down with ~ ' ~ energy at a rate of ~ y 31 g cm-2 ~ ~
of
of
primary energy (or of energy per nttdeea)--- so observations seem to be only weaHy m t ~ m changes in ~:e cascade. ( M e ~ ~ i s ~ ~ amount of rouen production, per PeV of
energy,as F~ rises,) These figures may not apply to the ~ "rise time" measurements of Walker, Watson Wilson 1.2.3, which have been used to changes in depth of maximum, as these were made on the rouen-electron mixture in their detectors, were sensitive to the muon/elecutm ratio to at least as great an extent as to the time spread of m ~
(Watson, privatecommunication). 2.2 Sensitivity of optical phcP.ons to depth of development of shower One does not need a Fly's Eye to obtain information from optical photons. Figure 5 shows the density of Cerenkov photons (in the S11 waveband) and of air fluorescence photons at 0.4 to 3 km from the shower axis, calculated for a vertical womngenerated s~ower of I EeV. The first interaction of the proton was made to occur at specificdepths - 60, 200 and 400 g cm-2 - - to show the effect of variations in the depth of shower development (though many showers were simulated for each depth). The ratio F/C of fluorescent to scintillation light is clearly sensitive to the depth of shower development . This is primarily because the fluorescent radiation is entitled isotmpically, whilst the Cerenkov radiation is mostly concentrated in a small cone of angles (the scattered radiation not much alie~ingthe picture), so the ratio of the two depends on the distance to the main light source. Hence, if optical fdters in front of a photomultiplier can greatly change its relative sensitivity to fluorescent and Cerenkov emission spectra, the ratio
~M, Hilhrs/ ~ h ~
72
propen~s rd~a~ to~
sig~ls in two s ~ h detectors might give a good of beight of s1~owerm a x i m . Hence one ra~ht be able ~ monitor the anmunt of f l ~ , estimate the p t a ~ component from the deep tail of the disu-ibuzion. The dotted line gives an
emimmeof the ~
sky ~ise in a 2ps ga~
~ n g a 5-inch phototube (no filter) for a 1 F..eV shower, indicating the ~ g e of axial distances in
w-hich su.eh~ me~sureme.ntcould be made. (it is
assumed that in g ~ ~,'k-sky conditions the Poisson fluctuations on 10 photoelectrons per nanosenond from a 5-inch photocathode form the ~ g r o u n d noL~) I~ 13
,
i
~
~
~
arrays
photons (Cerenkov plus fluorescent) observed at three axial dimances, and for verdcal proton showers constrained to start at normal depths or at 200 g cm-2, as illustrated before. Clearly, one would have to know the distance r rather well in order to make use of these didfferences in pulse delay or width, as there is a rapid dependence on r as well as on height of maximum. 20~
10~ 9 !
=
;i
1
10%i ~ o 0 ~-:
2
r= lO00m , ~
.,Jr"~ ' - - " ' - ' - ~ I
\
1
2
h.s
N
N I
Figure 6. Sensitivity of time profile of optical photons to depth of maximum of shower, illustrated by calculated time profiles of optical photons received at specified distances r from shower axis, for I EeV proton shower having its first interaction at 60 or 200 g cm-2. "N" indicates the probable magnitude of the sky noise in a 50 ns channel.
I# I
~5
..... ;
3
km
P
Figure 5. Comparison of density of Cerenkov (c) and fluore.scent (f) photons due to vertical proton showers initialed at depths 60, 200 and 400 g cm-2, at large distances from the shower axis (sea level). Note: To obtain numbers of photoelectrons in a phozomultiplier, the photon densities quoted should be multiplied by the phott~athode area and the peak quantum conversion efficiency. Altern~.tively, one could measure the pulse shape of the optical photon signal (as ou'Jined in the previous section) to deduce heights of origin. This is a crude alternative to the Fly's Eye approach. Figure 6 shows calculated pulse shapes for optical
3. SUMMARY If measurements are possible of Fiuorescence/Cerenkov ratio Optical rise time Muon rise time muon density I fluorescence signal or muon density I total particle density. a multi-parameter classification of showers could possibly lead to a more reliable measure of "depth of maximum" and its fluctuations, as ~ method of investigating at least the proportion of protons amongst the primary particles, and possibly a better separation of masses.
A.M. Hillas / Showerpropertiesrelevantto large~ REFERENCES
1. M. Nagano, M. Teshima, Y. l~Lsubara, H. Y. Dai, T. Hara, N. Hayashida, M. Honda, H. Ohoka and S. Yoshida, J. Phys. G, Nucl. Phys., 18: 423. (1992) 2 A. A. Watson and J. G. Wilson, J. Phy. A, Math., Nucl., Gen., 7:1199 (1974). 3. R. Walker and A. A. Watson,J. Phys. G., Nucl. Phys., 7, 1297 (1981) andJ. Phys. G.,Nucl. Phys., 8, 1131 (1982).