Astroparticle Physics 15 72001) 149±165 www.elsevier.nl/locate/astropart

Time structure of the extensive air shower muon component measured by the KASCADE experiment KASCADE Collaboration T. Antoni a, W.D. Apel a, A.F. Badea b, K. Bekk a, K. Bernlohr a,1,H.Blumer a,c, E. Bollmann a, H. Bozdog b, I.M. Brancus b,*, A. Chilingarian d, K. Daumiller c, P. Doll a, J. Engler a, F. Feûler a, H.J. Gils a, R. Glasstetter c, R. Haeusler a, W. Hafemann a, A. Haungs a, D. Heck a, T. Holst a, J.R. Horandel a,2, K.H. Kampert a,c, J. Kempa e, H.O. Klages a, J. Knapp c,3, D. Martello a,c, H.J. Mathes a, H.J. Mayer a, J. Milke a,D.Muhlenberg a, J. Oehlschlager a, M. Petcu b, H. Rebel a, M. Risse a, M. Roth a, G. Schatz a, F.K. Schmidt a, T. Thouw a, H. Ulrich a, A. Vardanyan d, B. Vulpescu b, J.H. Weber c, J. Wentz a, T. Wiegert a, J. Wochele a, J. Zabierowski f, S. Zagromski a

a Institut fur Kernphysik, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany b Institute of Physics and Nuclear Engineering, 7690 Bucharest, Romania c Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, 76021 Karlsruhe, Germany d Cosmic Ray Division, Yerevan Physics Institute, Yerevan 36, Armenia e Department of Experimental Physics, University of Lodz, 90236 Lodz, Poland f Soltan Institute for Nuclear Studies, 90950 Lodz, Poland Received 11 May 2000; received in revised form 10 August 2000; accepted 12 September 2000

Abstract

The temporal structure of the extensive air shower 7EAS) muon component 7Ethres ˆ 2:4 GeV) is studied at sea level by measurements of the muon arrival time distributions using the muon detection facilities of the KASCADE central detector. Data have been analysed for EAS core distances up to 110 m for primary energies around the knee region. The time structure of the EAS muon component is represented by the distributions of the mean, median, ®rst quartile and the third quartile of the muon arrival time distributions relative to the foremost muon. The EAS time pro®les 7variation with the distance from the EAS center) are studied along their dependencies on the angle of incidence and the energy- tr indicative muon number Nl . E€ects of the ¯uctuation of the arrival time of the ®rst registered muon are scrutinised and corrected. The experimental results are compared with EAS Monte Carlo 7CORSIKA±GEANT) simulations, fully

* Corresponding author. E-mail addresses: [email protected] 7I.M. Brancus), [email protected] 7H. Rebel). 1 Present address: University of Hamburg, Hamburg. 2 Present address: University of Chicago, Enrico Fermi Institute, Chicago, IL 60637, USA. 3 Present address: University of Leeds, Leeds LS2 9JT, UK.

0927-6505/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S0927-6505700)00148-1 150 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 including the detector responses and illustrating the phenomenological features. The comparisons, though generally in fair global agreement, revealed that the simulations underestimate the shower thickness and show nearly no dependence on the mass composition if the time resolution of the apparatus is realistically taken into account. Ó 2001 Elsevier Science B.V. All rights reserved.

PACS: 96.40.Pq; 96.40.Tv Keywords: Cosmic rays; Air shower; Arrival time distribution

1. Introduction Agnetta et al. [7] and Ambrosio et al. [8,9] pre- sented detailed results on the temporal structure The particles of extensive air shower 7EAS) of EAS charged particles based on measure- move nearly in the direction of the primary parti- ments with the GREX/COVER-PLASTEX set-up cles with velocities close to the velocity of light. [7]. Transverse momenta of particles emitted in strong Simple kinematics arguments [10±13] show that interactions and multiple scattering in the air pro- the time spread, in particular of the muon com- duce a lateral dispersion. Di€erences in the ve- ponent carries some information about the height locities 7``Lorentz e€ects'') and, in particular, in of production i.e. the longitudinal EAS pro®le, via the path lengths, when travelling through the at- the time-of-¯ight e€ects. This feature arises from mosphere, are the origin of a longitudinal disper- the fact that high-energy muons above a few GeV sion 7thickness) of the shower disk and of time travel through the atmosphere in a relatively un- delays of the arrival of the shower front, approx- disturbed way. The aspect has been pursued by imately represented by the relative arrival time of detailed investigations of the temporal structure the ®rst particle, relative to the arrival time of the of the muon component with the Chacaltaya core. The EAS thickness is manifested by the air shower array [14] and with a set-up of lead variation of the arrival times of particles, observed shielded liquid scintillators of the Haverah Park at a particular ®xed location of the EAS lateral experiment by Blake et al. [15]. They explored the extension while the variation of the delays with the dependence of the time delay on the inclination h distance from the shower centre re¯ects the shape of the shower axis, on the primary energy E0 7or 7curvature) of the EAS front and the direction of shower sizes Ne and Nl), and on the distance Rl the incidence. from the shower core. Linsley et al. [1,2] and Thielert and Wiedecke [3] This speci®c kind of EAS investigations con- systematically explored the lateral dependence of siders suitable shower observables which represent the shower thickness, expressed by the median the arrival time distributions, e.g., the distributions delay time relative to the arrival time of the shower of various characteristic quantities like mean val- core. An increase of the time dispersion with the ues, median values of the individual distributions distance from the shower centre has been found. etc. and their dispersions. The variation of the Since these early studies the time structure of mean of these quantities with the distance from the the charged particle/photon component has been shower core Rl represents the EAS time pro®le experimentally studied under various aspects. [16]. It depends on the energy E0, the mass M of Walker and Watson [4,5] directed the interest to the primary particle 7re¯ected by suitable shower the time spread of the shower disk, whose origin variables like Ne, Nl), on the zenith angle h of could be interpreted as ¯uctuations of the height of shower incidence and additionally on biasing trig- maximum of the shower development due to dif- ger and observation conditions: energy threshold ferent masses of the primaries, as consequence of Ethres and multiplicity n of the muon detection. di€erent interaction lengths of the primaries and Knowing the time pro®le may thus help to identify the multiplicities, energy and momentum distri- the primary particle and improve the energy de- butions of the secondaries [6]. Most recently, termination. T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 151

The present experimental studies of the time of particles penetrating through the absorber structure of the EAS muon component are based above [24]. The MWPC system is arranged in on data measured with the KASCADE detector double layers with a telescope e€ect, improving the system [17±19]. The investigation explores phe- reconstruction quality of the particle hits and nomenological features, and studies empirical pa- giving information about the mean direction. Be- rameterisations of the observed time pro®les, low the third iron layer, at a depth of 30X0 and rather than the speci®c sensitivity to the mass of with a mean energy threshold for muons of 490 the primary particles. The experimental results are MeV, plastic scintillators provide a fast trigger compared with results of detailed EAS Monte signal [25] and are used for timing measurements. Carlo simulations, using the program CORSIKA This timing layer is composed of 456 detector el- [20,21] and taking into account the response and ements, covering e€ectively 64% of the total cen- timing qualities of the detectors. tral detector area of 16  19 m2. Each detector consists of two quadratic scintillator sheets of 3 cm thickness and 0.45 m2 in total area, with a readout 2. The timing and muon identi®cation facilities of by a wavelength shifter bar and an 1.5-in. pho- the KASCADE central detector tomultiplier. Two of these elements are housed, optically separated, in a light-tight detector box. The KASCADE ®eld covers an array of 252 The average time resolution has been deter- detector stations, measuring the EAS electron± mined to be 1.7 ns. In addition, this detector layer photon and muon components with a threshold of is used as dE=dx detector for 7muons and other)

5 and 230 MeV, respectively 7for details see Refs. charged particles 7Ethres ˆ 0:49 GeV). Two di€er- [17,18]). The central detector [22] 7Fig. 1) is com- ent thresholds of the electronic readout allow to posed of several di€erent detector components. discriminate the energy loss of minimum-ionising Basically the set-up is an iron sampling calorimeter particles 7m.i.p.) and of hadrons 750 m.i.p.) [25]. to identify hadrons and to measure their energy, The contribution of punch-through events of the position and angle of incidence, in particular in the electromagnetic component to muons events, iden- shower core. Eight active detector layers measure ti®ed with the low-energy threshold, becomes the energy loss of the traversing hadrons in ioni- negligible for distances >30 m from the shower sation chambers. In the basement of the set-up centre. For studies of the high-energy muons a there is an installation of large area position sen- correlated measurement of the MWPC and the sitive multiwire proportional chambers 7MWPC) trigger layer detectors is performed. Due to the for the identi®cation of muons of energies larger good angular resolution of the MWPC 7<1° than 2.4 GeV [23]. They exploit the relatively good for El > 10 GeV) it is possible to use them to spatial resolution to study the lateral distribution identify high-energy muons. For ®ltering, every

Fig. 1. Sketch of the KASCADE central detector. 152 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 reconstructed muon is traced back through the central detector up to the trigger layer. In case that the track is hitting a trigger detector with a valid signal the time is used for further analysis. With this procedure one is able to suppress eciently the low energy muons. The MC simulations show that about 75% of the 2.4 GeV muon tracks in the MWPC have a correlated signal in the trigger layer. This corresponds to the coverage of the trigger layer of the active area of the MWPC. On the other hand only about 26% of the trigger de- tectors have a correlated signal with the MWPC. This is smaller than the active area 743%) of the MWPC. The central detector system allows to study lateral and time distributions of the muon Fig. 2. Characterisation of the EAS temporal structure by component with two di€erent energy thresholds global and local arrival times. [26]. Measurements of the relative muon arrival times refer to an experimentally de®ned zero time 7Fig. 2). In many studies the arrival time of the 3. General procedures shower core scor has been used as reference [11±13], also in the ®rst analysis of relative muon arrival 3.1. De®nition of the observables times with KASCADE data [29]. In that analysis the distributions of the arrival time of the foremost The present investigation explores the temporal muon s1l, of the mean sl of the single event dis- features of the muon component of EAS events at tributions, and the corresponding standard devia- muon energies above 2.4 GeV. An event can be tions r have been regarded: characterised by the shower core position Rcor e.g., glob measured from the centre of the central timing Ds1 Rl†ˆs1l Rl†Àscor 1† layer, the direction of shower incidence 7with the zenith angle h and azimuth angle U), by the shower glob Ds Rl†ˆsl Rl†Àscor 2† size Ne, the muon number Nl or the ``truncated'' muon number N tr. The quantity N tr is the number l l Time quantities referring to s are further on of muons with E P 230 MeV, integrated in a cor l called ``global'' times. Experimentally, it turned limited range of 40±200 m from the shower centre. out [29] that s is not well determined from the As Monte Carlo simulations show [27,28], due to cor arrival time of the electromagnetic component various fortunate features of the lateral distribu- near the shower core with the present reconstruc- tion, log N tr proves to be nearly proportional to 10 l tion procedures, and it introduces an additional log E and is almost independent of the primary 10 0 jitter of some nanoseconds. Hence, for the present mass at the KASCADE observation level. There- studies we prefer to consider ``local'' times, which fore, we prefer a classi®cation according to N tr l refer to the arrival of the foremost muon, regis- instead of the shower size N . The latter would e tered in the timing detector at the particular dis- prepare samples of mixed energies, dominated by tance from the centre R ˆR in case of vertical proton-induced showers [24]. For showers located l cor showers): within 90 m from the array centre, the recon- loc struction accuracy is about 3 m for the location of Ds Rl†ˆsl Rl†Às1l Rl† 3† the shower centre, 0:5° for the angle of incidence tr and 10±20% for Ne and Nl . 7The label ``loc'' is omitted further on.) T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 153

It should be immediately noted that the ®rst tematically fake early ``®rst muons'' in the scintil- detected muon does not well de®ne the shower lation detector, which distort the relative arrival front. This approximation is mainly dependent on time distributions. In order to suppress muon the multiplicity of the sample 7taken from the signals faked by hadrons, a veto for a large energy particle population in the shower disk) and needs deposit in the scintillator detectors Edep P 20 MeV at low multiplicities a correction of the observed 7c. 3 m.i.p.) has been applied. This procedure delay distribution with respect of the true arrival remedies the distortion e€ect in the shower centre time distribution 7see Section 3.4). In general, Rl is as displayed in Fig. 4. Previous studies [31] have de®ned in a plane perpendicular to the shower shown that by use of a cut on the arrival time of axis, which is speci®ed by zenith angle h and the the ®rst muon the analysis could be safely per- azimuth angle U of the direction of incidence. formed up to radii Rl < 110 m. In fact, the muon For a detailed discussion of the time structure arrival times at large radii are of particular interest we use speci®c quantiles Dsa of the distributions, for mapping the time structure to production the ®rst quartile 7Ds0:25), the median value 7Ds0:50) heights since the path-length e€ects become more and the third quartile 7Ds0:75) which exhibit di€er- pronounced [11,12]. ent features of the time structure of the muon component. For ordered statistics of measured 3.3. EAS and detector response simulations times Ds1 6 Ds2 6 ÁÁÁ 6 Dsn and k :ˆ na ‡ n, k in- teger and n 2‰0; 1†, the a-quantile Dsa a 2 0; 1†† The observed muon arrival time distributions is the following [30]: are compared with simulations of the air shower  development, calculated with the Monte Carlo Dsk ‡ Dsk‡1†=2 : for n ˆ 0 air shower simulation program CORSIKA Dsa ˆ 4† Dsk : for n 2 0; 1† 7ver. 5.621) [20,21]. This program includes the GHEISHA code [32] and various packages of That means: in the case of large n, a fraction a of high-energy interaction models like VENUS [33] muons has arrival times less than Dsa. and QGSJET [34] as generators of the hadronic interactions. The electron±photon component is 3.2. Measurements simulated by the EGS4 Monte Carlo procedure [35]. The in¯uence of the Earth's magnetic ®eld on The experimental data have been accumulated the muon propagation has been taken into ac- in the period January 1998±April 1999 and the count. As density pro®le of the atmosphere the US data sample comprises more than 3.4 millions of standard atmosphere is chosen [20,21]. reconstructed showers. The EAS reconstruction The actual calculations are based on the procedures are described elsewhere [26]. For the QGSJET model and cover an energy range of 5  arrival time analysis, at least three detectors of the 1014±3:06  1016 eV 7divided in seven energy bins) trigger layer are required to have a signal which and a zenith angle range of 0±40°. They are per- can be correlated with three muon tracks in the formed for three mass groups: H ˆ light group, MWPC. Generally measurements of the muon O ˆ CNO group, Fe ˆ heavy group with an en- component at small core distances could be af- ergy distribution of a spectral index of À2:7. They fected by the electromagnetic punch through and comprise a set of '2000 showers for each case, by the hadrons in the shower core. Due to the except for the bins of the highest energies 15 16 selection of muons with El P 2:4 GeV by the 76:51  10 ±1:82  10 eV with '1000 simulated MWPC positioned below the iron sampling calo- showers and 1:09  1016±3:06  1016 eV with rimeter, a disturbance by electromagnetic punch '500 simulated showers). The response of the through is found to be negligible. There are no KASCADE detector system and the timing qual- deviations visible from the Landau distribution of ities have been simulated using a program, devel- the energy deposits of the identi®ed muons, even at oped on the basis of the GEANT code [36]. The small Rl ˆ 10 m [38]. But cascading hadrons sys- particles of the simulated EAS are tracked through 154 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165

tr the detector set-up and the timing response of the density distributions. For example, for log10 Nl ˆ detectors are recorded for various core distances 4:0±4:25 and 40 m < Rl 6 50 m the mean value of from the central detector facilities. Particularly, it the multiplicity n is about 16 with a distribution should be noted that the timing depends on the extending to n ' 40, while for the range 100 m < energy deposit in the scintillation detectors. This Rl 6 110 m the value n is about 8. Thereby in the e€ect has been corrected by introducing an ade- experiment we observe EAS events of di€erent quate procedure. primaries, which exhibit di€erent lateral muon densities and di€erent arrival time distributions. This implies that the particular mixture of contri- 3.4. Multiplicity e€ects butions of di€erent EAS primaries to the observed arrival time distributions is also varying with R . The present studies consider time distributions l The e€ect that the arrival time of the foremost relative to the arrival time of the foremost muon muon is deviating from the ideal shower front, and with muon multiplicities n P 3. Fig. 3 displays ¯uctuating with the sample multiplicity is rela- the average single muon arrival time distribution tively small in the pure CORSIKA simulations. as observed experimentally in the distance of 60± But it seriously distorts the experimental arrival 70 m from the shower core for '2000 EAS events. time distributions as well as the simulated distri- In an event-by-event consideration intriguing sta- butions, when the smearing due to the ®nite time tistical e€ects enter in the estimate of the proper- resolution [38] is taken into account. Though in ties 7like the median) of the probability density principle a comparison of the data could be made function 7p.d.f.) from small samples of muons. with simulations including the e€ect, we do pre- Following the considerations of Ref. [37] it can be fer to remove the distortions arising from the shown that the arrival time s of the foremost 1l measuring apparatus by an adequate correction muon 7relative to a ®ctive time zero, representing procedure. Such an procedure by a ``local time the muon front and approximated with a sample correction function'' invokes EAS simulations and of very large n), its ¯uctuations and the estimated is described in Appendix A. The e€ect of the cor- median value, e.g. of Dsloc ˆ s À s depend on l 1l rection procedure is indicated in Fig. 4. the particular value of the multiplicity n, system- atically increasing the mean values of the quanti- ties with increasing n. The actual observed pro®les 4. The time pro®le of the EAS muon component are derived from samples s1l, s2l, ..., snl of dif- ferent muon multiplicities, with the average mul- The experimental distributions of the quantiles tiplicities depending on R and decreasing with the l are considered in di€erent intervals of the core core distance, for the case of di€erent log N tr 10 l distance R ˆ 10±20 m, up to 100±110 m, for ze- values di€erently, according to the lateral muon l nith angles in di€erent ranges from 0° to 40° and tr for ®ve di€erent Nl ranges.

4.1. Shape of the arrival time distributions

Simple kinematics arguments lead to a quali- tative understanding of the gross shape of the arrival time distributions, which also imply a variation 7broadening) with increasing distance from the shower centre. Fig. 5 compares the ex- perimental and simulated muon arrival time dis- Fig. 3. Averaged single muon arrival time distribution ob- tr tributions of di€erent quantiles for the radial range served at Rl ˆ 70±80 m with 3:6 < log10 Nl 6 4:8 7corre- sponding to 8  1014±3  1016 eV) for the angular range of Rl ˆ 90±100 m. At a ®rst glance it displays a 5° < h 6 30°. fair overall agreement between experimental and T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 155

tr Fig. 4. Observed EAS median time pro®les hDs0:50i for the sample with 3:6 < log10 Nl 6 4:8 for the angular range 5° < h 6 30° without and with correction procedures applied. The corrected pro®le is displayed with EAS simulations.

tr Fig. 5. Distributions of di€erent time quantities for the particular sample with 4:25 < log10 Nl 6 4:45 for the angular range 5° < h 6 30° and the radial range: 90 m < Rl 6 100 m. The simulations adopt a mass composition: H:O:Fe ˆ 4:1:2. simulated data. For the simulations a mass com- ni®cantly the results [40]. The simulated mean position suggested by Ref. [39] has been adopted, muon arrival time and standard deviation values but other composition choices have been also are smaller than the experimental ones. In both considered and are shown to change only insig- cases, the fast component 7Ds0:25) is narrower than 156 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165

tr Fig. 6. Distributions of the median muon arrival time for di€erent log10 Nl ranges displayed for the angular range 5° < h 6 30° and the radial range: 90 m < Rl 6 100 m. The simulations adopt a mass composition: H:O:Fe ˆ 4:1:2.

b the median 7Ds0:50), the latter suppresses the in- C T †ˆaT exp ÀcT†; T ˆ Dsa† 5† ¯uence of large ¯uctuations a€ecting the mean 7Ds). Fig. 6 presents the dependence of the exper- with a mean value hT iˆ 1 ‡ b†=c and the stan- 1=2 imental and simulated median time values on the dard deviation rC ˆ 1 ‡ b† =c. We do not apply tr Nl range 7indicating the primary energy), exhib- the parameterisation by the C-form as arising from iting narrower distributions for higher energies. a speci®c mathematical model of the EAS devel- The data have been processed for all radial ranges opment, but it is empirically justi®ed. It can be by determining the mean values and the variances shown that the shape with a fast increase and a r2 7standard deviations of r) of the mean 7Ds), the longer decreasing slope re¯ects just the gross lon- median 7Ds0:50), and of the quartiles 7Ds0:25)and gitudinal development of the muon component 7Ds0:75). Figs. 7 and 8 show the observed variations [16], but any other parameterisation of this type of the distributions of the quartiles 7Ds0:25)and may be of similar convenience for ®tting the bulk 7Ds0:75) of the muon arrival time distributions with of data. Figs. 7 and 8 show as examples experi- the distance from the shower core 7for a particular mental and correspondingly simulated distribu- tr Nl range). With increasing radial distances both tions ®tted by the C-form 7further examples are types of distributions become broader and shifted given in Ref. [40]). Only the tails of the experi- to larger mean values of the local delay times 7local mental distributions are less well described by the pro®les). In studies of the charged-particle EAS C-form 7Fig. 9). This feature of ``delayed showers'' component [7] it has become customary to para- has been noticed and stressed in the shape of the meterise the observed distributions by a C p.d.f. time distributions of the EAS charged particle [41,42] given by: component [8,9] and has been associated to ¯uc- T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 157

Fig. 7. The variation of the shape of the experimental distributions of the ®rst and third quartiles with the core distance. The lines display ®ts by the C-form. tuations of the shower development, insuciently muon disk. This feature is displayed in Fig. 10 tr accounted for in the simulations. A considerable showing the log10 Nl dependence of the mean part of these ``delayed'' tails may be accounted to values 7and their uncertainties) of the median and uncorrelated particles triggering the zero time too third-quartile distributions at two distances from early. In our case the contribution arising from the shower core. Like above the simulations are uncorrelated muons is estimated to be less than based on an adopted particular primary mass 20% of the observed excess in Fig. 9, and com- composition: H:O:Fe ˆ 4:1:2, but the gross fea- pletely negligible for the total distribution at all. tures do not depend very much on that. A par- Nevertheless, we cannot follow the conclusions of ticular feature, especially pronounced with the Ref. [9] that these ``delayed'' tails are a specially third quartile, is the tendency of a decreasing time interesting feature in the arrival time distributions. spread of the local pro®le with increasing primary tr In fact, an alternative heuristic parameterisation energy 7Nl ), roughly beyond the knee position tr by a logarithmic Gauss distribution [43] does suf- 7log10 Nl ' 4:1). The origin of this feature has not ®ciently well reproduce such tails as pointed out by been explored in detail. The observation can be Battistoni et al. [44]. associated with the energy variation of the lateral When comparing the variation of the experi- muon contribution, i.e. with varying local contri- mental and simulated muon arrival time distribu- butions from di€erent muon production heights, tr tions for di€erent Nl ranges, there appears a and thus of EAS induced by di€erent kind of systematic tendency that the distributions of the primaries. Since the simulations 7with a ®xed pri- simulated data underestimate the thickness of the mary mass composition) exhibit similar features, a 158 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165

Fig. 8. Corresponding to Fig. 7 the variation of the shape of the simulated distributions of the ®rst and third quartiles with the core distance. The lines display ®ts by C-form.

change of the mass composition with the primary pro®les: hDsi, r; hDs0:25i, r0:25; hDs0:50i, r0:50; energy cannot be considered to be a main reason hDs0:75i, r0:75† represents the time structure of the of e.g. the decreasing spread of the third quar- EAS muon disk. Figs. 13 and 14 present experi- tile. Fig. 11 displays the shapes of the median ar- mental pro®les for the time distributions for dif- tr rival time distributions for three di€erent 7broad) ferent Nl ranges and angular ranges of EAS ranges of the EAS zenith angle and shows no incidence, respectively, and compare with EAS signi®cant variation. The decrease of the time simulations. The uncertainty in the mean valuesp dispersion of the local pro®le with the EAS age, and in thep standard deviations, given by r= N shown for two ranges of Rl 7Fig. 12), may be and r= 2 N À 1†, respectively, 7N being the qualitatively understood as the correspondence number of events) are indicated by the vertical between age and the depth of the EAS maximum. bars 7so far visible). In general a good overall

It should be noted that Fig. 12 shows averages agreement 7except for larger Rl) for the mean tr over the total Nl range which may explain the values can be noticed, while the variances ap- good agreement as compared to Fig. 10. pear distinctly smaller in case of the simulations. As compared to the total charge particle compo- 4.2. Time pro®les nent [8] the width of the muon component is signi®cantly smaller. This ®nding is in contrast to

The Rl-dependence of distributions of the var- the conclusions of Ref. [8]. The shape of the ious time quantities, or expressed in a more concise EAS time pro®les may be approximated by the way, of the mean values and their dispersion time form [7]: T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 159

Fig. 9. Tails of the experimental and simulated distributions for various time quantities for 70 m < Rl 6 80 m, ®tted with the C-form. The simulations adopt a primary mass composition: H:O:Fe ˆ 4:1:2.

b equivalent samples of simulated events for inclined T Rl†ˆt1 ‡ t2 Rl=Rm† ; T ˆ Dsa† 6† showers, for the sake of simplicity the multiplicity corrections have been done on basis of the cor- with R the scaling radius for the muon lateral m rection function for vertical showers. This might distribution function 7determined for E P 2:4 l a€ect the systematic accuracy of the results of Fig. GeV to be R ˆ 100 m [45]). Such an empirical m 14, shown without simulations, which nevertheless formula 7whose parameters for the muon compo- reproduce the gross features of the observations nent have been determined for di€erent depen- 7see also Fig. 6). dencies on basis of a smaller data sample in Ref. [31]) accounts for the increasing width of the charge particle component at larger distances from the core. It was suggested [46] that a parameteri- 5. Concluding remarks and summary sation of the observed feature could be used to determine the core location. At a closer look the The present paper studies the phenomenologi- muon component, whose time structure is di€erent cal features of the time structure of the EAS muon and with the muon disk walking ahead the elec- component 7El P 2:4 GeV) based on experimental tromagnetic component [47], shows some devia- observations with the KASCADE detector. The tions from the quasi-parabolic shape 7b ' 2:0). As investigations are focussed to observables cha- obvious in Fig. 14, the variation of the pro®le with racterising the time spread of the muon shower the EAS angle of incidence is relatively weak for disk and its variation with the distance from the the considered distances from the shower cen- centre. For that purpose the local arrival time tre, though not completely negligible. It should distributions of muons relative to the arrival time be noted that because of lack of statistically of the ®rst registered muon are measured, event by 160 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165

Fig. 10. Energy dependence of the mean values and their uncertainties of the experimental and simulated median and third-quartile distributions observed at two di€erent ranges of the distance from the shower core 75° < h 6 30°). event and correlated with a number of other ob- characteristic quantities from the muon multiplic- tr servables specifying the shower 7Ne, Nl , age, ...). ity of the sample, as discussed in Refs. [10,37]. Various time parameters are inferred to characte- Since the average multiplicity varies with the lat- rise the single arrival time distributions: mean 7Ds), eral distance from the EAS core, the observed median 7Ds0:50), ®rst 7Ds0:25) and third 7Ds0:75) local time distributions are superpositions for quartiles. Because of the relatively small number of di€erent multiplicities. Intriguing features arising muons 7sample multiplicity) de®ning the observed from the e€ect that the time zero reference does single distributions, these quantities are subject of not always re¯ect the extreme shower front, have various ¯uctuations, in particular of the ¯uctua- already pointed out with KASCADE data in Ref. tion of the arrival of the ®rst muon used as zero [31] and become more pronounced, when the ®nite calibration point. As compared with the time delay time resolution of the detectors is taken into ac- distributions determined with respect to the well- count. Hence, for a reasonable discussion of the de®ned arrival of the light front in the shower core arrival time distributions a correction procedure 7``global'' arrival time distributions), this ¯uctua- has been applied in the observed data as well as tion leads to a noticeable dependence of the local in the detector simulations, removing the experi- T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 161

Fig. 11. Experimental and simulated median time distributions for three di€erent angular ranges 7equal sec h ± bins) of EAS incidence,

®tted with the C-form 790 m < Rl 6 100 m). The simulations adopt a primary mass composition: H:O:Fe ˆ 4:1:2. mentally induced distortions by the ¯uctuations 73) Regarding the shower pro®les the mean around the ``true'' reference point. The arrival time delays and the thickness are increasing with in- distributions exhibit following features: creasing Rl, whereby the variation of the third- 71) In general, there is a good overall agreement quartile distribution is more pronounced than of between the experimental distributions and the the ®rst quartile. In agreement with analyses of predictions by Monte Carlo simulations of the Monte Carlo simulations, the variations, which EAS development by the CORSIKA code, and it show that the muon disk is ¯atter than that of con®rms that the code describes well observables electrons, can be fairly well approximated by a sensitive to the longitudinal EAS development. quasi-parabolic shape in the radial range close the

72) The shapes of the experimental and simu- EAS center up to Rl ˆ 110 m. While the simu- lated arrival time distribution can be suciently lations reproduce even some deviations of the well described by a phenomenological parame- local mean delays from parabolic shape, which terisation in terms of the C p.d.f., with some presumably re¯ect the original in¯uence of vary- additional tails observed in the experimental dis- ing sample multiplicities 7also present in pure tributions. But these tails are much less pro- CORSIKA simulations), they underestimate the nounced than observed with the charged particle ¯uctuations of the thickness of the muon disk. distributions [7]. A closer look reveals a signi®cant This ®nding may indicate a general underestima- tendency that the theoretical distributions, based tion of ¯uctuations of the EAS development by the on a particular adopted primary mass composi- 7CORSIKA) simulations. tion, predict smaller time delays relative to the 74) The dependence of the EAS time pro®le tr local front and a smaller spread of the muon disk, from the energy 7Nl ) and the zenith angle appears especially at larger distances Rl from the EAS to be weak, but signi®cant 7especially at larger core. Nevertheless, the thickness of the muon disk Rl). We observe a tendency that the shower disk 7El P 2:4 GeV) is signi®cantly smaller than of the get less curved and thinner with rising primary electron component 7Ee P 4 MeV). This ®nding is energy. in disagreement to conclusions of the analysis of The present studies are focussed to explore phe- the GREX/COVER-PLASTEX experiment [8]. nomenological features of the temporal structure 162 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165

Fig. 12. Age dependence of the average values and their uncertainties of the experimental and simulated median and third-quartile distributions observed at two di€erent ranges of the distance from the shower core 75° < h 6 30°). of the EAS muon component, with the question to tential of such investigations. We thank M. Duma which extent Monte Carlo simulations do repro- for his ecient help in preparing adequate ®les duce the observations. The experimental results from the collected data samples for the analysis. are a basis for further analyses and interpretations, We acknowledge the exploratory contributions of exploring in multivariate analyses the sensitivity Dr. M. Foller and Dr. U. Raidt who participated to various di€erent hadronic interaction models in an early stage of the investigations. The authors 7used as generators of the Monte Carlo calcula- would also like to thank the members of the en- tions) or to the mass composition of primary gineering and technical sta€ of the KASCADE cosmic rays. collaboration who contributed with enthusiasm and engagement to the success of the experiment. The work has been supported by the Ministry for Acknowledgements Research of the Federal Government of Germany and, in addition, by a grant of the Romanian We acknowledge the clarifying discussions with National Agency for Science, Research and Prof. Dr. A.A. Watson on the information po- Technology as well as by a research grant T. Antoni et al. / Astroparticle Physics 15 72001) 149±165 163

tr Fig. 13. Experimental and simulated time pro®les for two di€erent Nl ranges 7corresponding to energy ranges of the primary cosmic ray spectrum before and after the ``knee'') and for 5° < h 6 30°. The simulations adopt a primary mass composition: H:O:Fe ˆ 4:1:2.

For the Rl-dependence of hDs0:75i the results of ®ts with the quasi-parabolic form 7Eq. 76)) are given.

Fig. 14. Experimental time pro®les for the median distributions for di€erent angular ranges 7equal sec h ± bins) of EAS incidence for tr 3:6 < log10 Nl 6 4:8. 164 T. Antoni et al. / Astroparticle Physics 15 72001) 149±165

7no. 94964) of the Armenian Government and by the ISTC project A116. The collaborating group of the Cosmic Ray Division of the Soltan Institute of Nuclear Studies in Lodz and of the University of Lodz is supported by the Polish State Com- mittee for Scienti®c Research. The KASCADE collaboration work is embedded in the frame of scienti®c-technical cooperation 7WTZ) projects between Germany and Romania 7no. RUM-014- 97), Poland 7no. 92-94) and Armenia 7no. 002-98).

Appendix A. Local time correction procedure

The observed 7local) arrival time distributions are a superposition of distributions of di€erent muon multiplicities. This feature combined with the time resolution and detection eciency of the Fig. 15. Multiplicity dependence of the average median of the apparatus, leads to distortions of the true shower local arrival time distribution of 2.4 GeV EAS muons registered pro®le, which mainly arise from the ¯uctuations of with the KASCADE central detector. The inset indicates how the registered arrival time of the foremost muon the expectation values hDs1i of the arrival time of the ®rst muon 7used as reference for local distributions). The inset depends on the multiplicity. of Fig. 15 displays schematically the 7global) ar- rival time distribution and the multiplicity depen- m, is practically insensitive to the primary energy dence of the mean arrival time of the ®rst muon. and the mass composition. Small in¯uences appear Nevertheless comparison of the experimental ob- with the variation of the zenith angle of EAS in- servations with simulated distributions, taking se- cidence, but for sake of simplicity only EAS of riously into account the experimental responses, vertical incidence have been taken into account for would be reasonable and could indicate the agree- the present correction procedure. In order to ap- ment or disagreement. However, the distortions proximate the true shower front, the global arrival by the speci®c response of the particular experi- time distributions 7i.e. relative to the arrival of the mental apparatus, do hamper the comparisons light front in the core) have been calculated for all with results of other detector arrays. Thus it ap- muons 7of the chosen energy threshold), cumu- pears desirable to display the time pro®les as cor- lating all simulated showers. According to this rected for the multiplicity-dependent ¯uctuations distribution 7taken as estimate of the p.f. of the of the arrival time of the foremost muon and to muon arrival times) for each radial bin n individ- relate the measured and simulated distributions ual arrival times have been randomly selected and with a certain, arbitrarily chosen value ncal of the the local quartiles 7i.e. of distributions relative to multiplicity. This can be done by invoking EAS the arrival time of the earliest muon) have been simulations using the CORSIKA program. We calculated. The dependence of the local time quan- sketch brie¯y the procedure of such a ``local time tity from a particular value of n has been gener- correction''. The appearance of proton and iron ated by repeating the procedure 5000 times. Fig. initiated EAS of vertical incidence and of the pri- 15 displays an example: the variation of the ob- 15 mary energy E0 ˆ 3  10 eV has been simulated served average median of the local arrival time for the time resolution of 1.7 ns. A sample with a distributions with the multiplicity, calculated for

1:1 mass composition has been considered. The three di€erent Rl ranges. Using such curves, Dsa n† local time correction, which has been estimated for observed with the actual multiplicity n can be

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