- Email: [email protected]
Investigations of Muons in EAS with KASCADE-Grande
Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357 www.elsevierphysics.com
Investigations of Muons in EAS with KASCADE-Grande A. Haungsa∗ , W.D. Apela , J.C. Arteagaa† , A.F. Badeaa‡ , K. Bekka , A. Bercucib , M. Bertainac, J. Bl¨ umerad , H. Bozdoga , I.M. Brancusb, M. Br¨ uggemanne, P. Buchholze , A. Chiavassac, d a c F. Cossavella , K. Daumiller , F. Di Pierro , P. Dolla , R. Engela , J. Englera, P.L. Ghiaf , H.J. Gilsa , R. Glasstetterg , C. Grupene , D. Hecka , J.R. H¨ orandeld , T. Huegea , P.G. Isara§ , K.-H. Kampertg , a e h H.O. Klages , Y. Kolotaev , P. Luczak , H.J. Mathesa , H.J. Mayera , C. Meurera , J. Milkea , B. Mitricab , C. Morellof , G. Navarrac, S. Nehlsa , R. Obenlanda , J. Oehlschl¨ agera, S. Ostapchenkoa¶ , e b a a a h S. Over , M. Petcu , T. Pierog , S. Plewnia , H. Rebel , A. Risse , M. Rotha , H. Schielera , O. Simab , M. St¨ umpertd , G. Tomab , G. Trincherof , H. Ulricha , J. van Burena , W. Walkowiake, A. Weindla , J. Wochelea , J. Zabierowskih, D. Zimmermanne a
Institut f¨ ur Kernphysik, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany National Institute of Physics and Nuclear Engineering, P.O. Box Mg-6, RO-7690 Bucharest, Romania c Dipartimento di Fisica Generale dell’Universit` a,10125 Torino, Italy d Institut f¨ ur Experimentelle Kernphysik, Universit¨ at Karlsruhe, D-76021 Karlsruhe, Germany e Fachbereich Physik, Universit¨at Siegen, 57068 Siegen, Germany f Istituto di Fisica dello Spazio Interplanetario, INAF, 10133 Torino, Italy g Fachbereich Physik, Universit¨at Wuppertal, 42097 Wuppertal, Germany h Soltan Institute for Nuclear Studies, PL-90950 Lodz, Poland b
KASCADE-Grande is a multi detector setup for the investigation of extensive air showers in the primary energy range of the knee including energies around the so-called second knee. With the data of the 700 · 700 m2 large Grande array shower core position, shower direction, and the total number of electrons are reconstructed for events with primary energy above 1016.5 eV. In addition, the experiment consists of different detector setups for measuring muons at various energy thresholds between 230 MeV and 2.4 GeV. These informations are used to estimate the muon shower size as well as observables sensitive to differences of hadronic interaction models embedded in shower simulation codes. We report the goals and the status of the different muon measurements at KASCADE-Grande.
1. Introduction KASCADE-Grande is a multi-detector setup to get redundant information on single air shower basis. The information is used to perform multiparameter analyses to solve the threefold problem of the reconstruction of the unknown primary energy, the primary mass, and to quantify the characteristics of the hadronic interactions in the air-shower development. The KASCADE-Grande experiment [1] located at the Forschungszentrum Karlsruhe, Germany, ∗ corresponding
author, e-mail: [email protected] address: CINVESTAV, Mexico D.F., Mexico ‡ on leave of absence from b § on leave of absence from Nat.Inst.Space Sc., Romania ¶ on leave of absence from Moscow State University, Russia † permanent
0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.11.030
extends the original extensive air shower experiment KASCADE [2] by an array of 37 detector stations spread over an area of 0.5 km2 (Fig. 1). Its major goal is to measure the possible knee of the heavy component in the primary cosmic ray energy spectrum, expected at ≈ 1017 eV. In order to infer the energy spectra of the primary cosmic ray particles for different mass groups with unfolding techniques (like with KASCADE data [3,4]) using the two dimensional electron-muon size spectrum, both particle numbers, i.e. total electron and muon number, have to be known. For measuring muons in KASCADE-Grande registered showers, the field array of the original KASCADE experiment provides 192 detector stations with 622 m2 of shielded scintillators providing an energy thresh-
355
error in muon number [Δ lg(Nμ ]
y/m
A. Haungs et al. / Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357
100
KASCADE array -100
w/o muon detectors
-200
Muon Tracking Detector
-300
Central Detector
-400
Piccolo
-500
KASCADE-Grande
-600
Grande rande DAQ G
-700 -700
protons iron
0.3
0
-600
-500
-400
-300
-200
-100
0
16
10 eV
0.2
0.1
0
-0.1 4.5 4.
100
5
x/m
old for vertical incidence of Eµ > 230 MeV. In addition, KASCADE-Grande consists of a muon tracking detector, which measures with high precision the incidence angles of individual muons (Eµ > 800 MeV). Also, at the KASCADE central detector further components are installed multiwire proportional chambers (MWPC), and limited streamer tubes (LST) - which offer valuable information on the penetrating muonic component at 2.4 GeV energy threshold. Whereas the information of the KASCADE array muon detectors are preferentially used to estimate the total muon number, the redundant information of the showers measured by the Central Detector and the Muon Tracking Detector is prevailingly used for tests and improvements of the hadronic interaction models. 2. The KASCADE muon array The Grande array measures the densities and arrival times of the charged particles, from what the shower core and the arrival direction of the EAS are reconstructed. The total muon number is obtained in a likelihood fit to the densities measured by KASCADE muon detectors. To describe the lateral distribution of the muons a Lagutinlike function is used [5]. In order to obtain stable fit results, the curvature of the lateral muon densities is kept constant and only the muon num-
6
Figure 2. Inaccuracies in KASCADE-Grande reconstruction of the total muon number. muon density [m -2]
Figure 1. The main components of the KASCADE-Grande experiment: the KASCADE, the Grande and the Piccolo arrays, the Muon Tracking Detector and the Central Detector.
5.5
muon number lg Nμ
iron hydrogen
log (E /GeV) range : 10 10
7.9-8.2
data fit
7.6-7.9 1
(Lagutin function)
7.3-7.6 7.0-7.3
°
0 -18
°
10 -1
10 -2 0
100
200
300
400
500
600
700
core distance [m]
Figure 3. Lateral density distributions of muons measured with KASCADE-Grande compared with simulated distributions. ber Nµ is estimated. The systematics and uncertainties have been studied with Monte Carlo simulations using CORSIKA [6] and the interaction model QGSJet 01 [7] and a detailed GEANT based detector simulation (Fig. 2). Figure 3 shows measured and simulated LDFs for different primary energies, where the energy has been roughly estimated by a linear combination of reconstructed total electron and muon numbers [5]. Generally, the agreement between data and MC is very good and the LDF describes the data reasonable well up to ≈ 1017 eV. The shown differential muon size spectra (Fig. 4 upper panel) are corrected for their systematic errors in reconstruction, derived from
356
dI/dN μ m -2s -1sr -1
A. Haungs et al. / Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357
10
-9
preliminary
10 -10 10 -11 10 -12 10 -13 10 -14 10 -15
KASCADE-Grande 0°-18 °
10 -16
KASCADE-Grande 18 °-25 °
10 -17 10
-18
KASCADE 0 °-18 °
10
-19
KASCADE 18° -25 °
10 -20
4
4.5
5
5.5
6
6.5
7
preliminary
KASCADE KASCADE-Grande
o
| τ | < 23 o | ρ | < 23 log10(sizeG) > 5.8 log10(sizeA) > 5.0 o o 0 ≤ Θ ≤ 18 100
200
300
400
1.5
]
muon number lg(Nμ)
<η> 4.4 4.2 4 3.8 3.6 3.4 3.2 3 2.8 2.6
GeV 10
Figure 5. Mean pseudorapidity of muons measured by the MTD versus the lateral distance of the muons to the shower axis.
3
[m -2 s -1 sr
-1
600 R [m]
preliminary
2.5
dI/dE × E
500
10 2
KASCADE e+ μ unfolded KASCADE-Grande μ unfolded systematic uncertainty
15
15.5
16
16.5
17
17.5
Energy log10(E/eV)
Figure 4. Upper part: KASCADE-Grande reconstructed muon size spectra for two zenith angle ranges compared with reconstructed KASCADE muon size spectra. Lower part: Unfolded allparticle spectrum of KASCADE-Grande compared to data of KASCADE from Ref. [3].
Monte Carlo studies. As one can see there is good agreement between the two measured fluxes in the overlap area in both zenith angle ranges. In Ref. [3] we have emphasized the importance of unfolding algorithms for the reconstruction of the energy and mass of cosmic rays. Because of the preliminary nature of the present data, we have not attempted a 2-dimensional unfolding of the electron and muon numbers such as in Ref. [3], but since the primary energy is mostly determined by the muon number with only a weak dependence on the primary mass, an unfolding of the muon size spectrum can be used as a first step to determine the all-particle energy spectrum at energies beyond the KASCADE range. The lower
panel of Fig. 4 shows the results of such an unfolding for the zenith angle range below 18◦ compared with results from KASCADE. One observes a very good overlap above 1016 eV. For more detailed statements on the shapes of the muon size spectrum and the primary energy spectrum the statistics is still too poor. 3. Muon Tracking Detector The Muon Tracking Detector (MTD) [8] allows a precise measurement of muon directions in EAS due to its excellent angular resolution (≈0.35◦ ). Measuring the relative angles τ and ρ between single shower muons and shower axis the mean muon production heights [9] and the pseudorapid2p ity η = ln pt ≈ −ln( τ 2 + ρ2 /2) of the muons can be calculated [10]. The first parameter improves the conventional separation into light and heavy primaries by means of the Ne /Nµ -ratio. The latter, being highly correlated with pseudorapidities and momenta of parent hadrons, is a very good probe of high-energy hadronic interactions and thus serves as a tool to test and improve existing hadronic interaction models. At KASCADE-Grande muons arriving up to 700 m from the shower core can be tracked, comparing to 160 m maximum distance in KASCADE. As an example, the mean pseudorapidity lateral distribution of muons registered up to 600 m from
probability
A. Haungs et al. / Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357
procedures at ultra-high energies.
KASCADE-Grande data
0.14
100m < Rcore < 250m Eest > 1016eV 5o < Θ < 35o
0.12 0.1
5. Summary
Rρ2.4/0.23
0.08 0.06 0.04 0.02 0 0
0.5
1
1.5
2
2.5
357
3
Rρ
Figure 6. Example for a measured distribution of the muon density ratio. the shower core is shown in Fig. 5 and compared to the distribution calculated out of KASCADE data up-to 150 m. In the KASCADE sample a lower primary energy was selected which is the reason for the downward shift of the results with respect to the Grande ones. It is seen, however, that the slopes of the pseudorapidity distributions are consistent. 4. Muon Density Measurements The local muon density of the EAS is measured for various muon energy thresholds by separate detector set-ups of KASCADE. Two of them are installed in the basement of the central detector building, enabling an estimate of the muon density, ρ2.4GeV , for each single EAS. A second µ local muon density is reconstructed using the KASCADE array data. Here, the fitted LDF is used to estimate the densities of muons at the place of the central detector (ρ0.23GeV ). The raµ tios of the measured local muon densities at fixed core distances are determined by the muon energy spectrum in air-showers, which is a different approach to test the models [11]. Fig. 6 displays the ratio exemplarily. Comparing such distributions with predictions (including full detector response and reconstruction procedures) will test various high-energy and low energy model combinations. Such tests of the validity of the muon component will be of high relevance for shower simulation
Measurements with the multi-detector setup KASCADE-Grande provide plenty of high quality data to investigate the physics of the possible second knee in the cosmic ray energy spectrum. The multi-detector concept allows the reconstruction of energy spectra of single mass groups as well as comprehensive tests of the simulation procedures in the Monte Carlo codes underlying the shower analysis. In particular, the detailed measurements of muons at various energy thresholds are the basis of sophisticated analysis procedures. At KASCADE-Grande, observables describing the muon component are reconstructed for showers in the primary energy range up to 1 EeV and in radial distances up to 700 m. Acknowledgment: This work is partly supported by PPP-DAAD/KBN project for 2005-2006.
REFERENCES 1. G. Navarra et al. - KASCADE-Grande Coll., Nucl. Instr. Meth. A 518 (2004) 207. 2. T. Antoni et al. - KASCADE Collaboration, Nucl. Instr. Meth. A 513 (2003) 429. 3. T. Antoni et al. - KASCADE Collaboration, Astropart. Phys. 24 (2005) 1. 4. H. Ulrich et al. - KASCADE-Grande Coll., (2006) these proceedings. 5. J. van Buren et al. - KASCADE-Grande Coll., Proc. of 29th ICRC Pune 6 (2005) p.301. 6. D. Heck et al., Report FZKA 6019, Forschungszentrum Karlsruhe (1998). 7. N.N. Kalmykov, S.S. Ostapchenko, Phys. Atom. Nucl. 56 (1993) 346. 8. P. Doll et al., Nucl. Instr. Meth. A 488 (2002) 517. 9. C. B¨ uttner et al. - KASCADE-Grande Coll., 28th ICRC Tsukuba 1 (2003) p.33. 10. J. Zabierowski et al. - KASCADE-Grande Coll., 28th ICRC Tsukuba 1 (2003) p.29. 11. A. Haungs et al. - KASCADE-Grande Coll., Proc. of 29th ICRC Pune 6 (2005) p.281.
Investigations of Muons in EAS with KASCADE-Grande A. Haungsa∗ , W.D. Apela , J.C. Arteagaa† , A.F. Badeaa‡ , K. Bekka , A. Bercucib , M. Bertainac, J. Bl¨ umerad , H. Bozdoga , I.M. Brancusb, M. Br¨ uggemanne, P. Buchholze , A. Chiavassac, d a c F. Cossavella , K. Daumiller , F. Di Pierro , P. Dolla , R. Engela , J. Englera, P.L. Ghiaf , H.J. Gilsa , R. Glasstetterg , C. Grupene , D. Hecka , J.R. H¨ orandeld , T. Huegea , P.G. Isara§ , K.-H. Kampertg , a e h H.O. Klages , Y. Kolotaev , P. Luczak , H.J. Mathesa , H.J. Mayera , C. Meurera , J. Milkea , B. Mitricab , C. Morellof , G. Navarrac, S. Nehlsa , R. Obenlanda , J. Oehlschl¨ agera, S. Ostapchenkoa¶ , e b a a a h S. Over , M. Petcu , T. Pierog , S. Plewnia , H. Rebel , A. Risse , M. Rotha , H. Schielera , O. Simab , M. St¨ umpertd , G. Tomab , G. Trincherof , H. Ulricha , J. van Burena , W. Walkowiake, A. Weindla , J. Wochelea , J. Zabierowskih, D. Zimmermanne a
Institut f¨ ur Kernphysik, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany National Institute of Physics and Nuclear Engineering, P.O. Box Mg-6, RO-7690 Bucharest, Romania c Dipartimento di Fisica Generale dell’Universit` a,10125 Torino, Italy d Institut f¨ ur Experimentelle Kernphysik, Universit¨ at Karlsruhe, D-76021 Karlsruhe, Germany e Fachbereich Physik, Universit¨at Siegen, 57068 Siegen, Germany f Istituto di Fisica dello Spazio Interplanetario, INAF, 10133 Torino, Italy g Fachbereich Physik, Universit¨at Wuppertal, 42097 Wuppertal, Germany h Soltan Institute for Nuclear Studies, PL-90950 Lodz, Poland b
KASCADE-Grande is a multi detector setup for the investigation of extensive air showers in the primary energy range of the knee including energies around the so-called second knee. With the data of the 700 · 700 m2 large Grande array shower core position, shower direction, and the total number of electrons are reconstructed for events with primary energy above 1016.5 eV. In addition, the experiment consists of different detector setups for measuring muons at various energy thresholds between 230 MeV and 2.4 GeV. These informations are used to estimate the muon shower size as well as observables sensitive to differences of hadronic interaction models embedded in shower simulation codes. We report the goals and the status of the different muon measurements at KASCADE-Grande.
1. Introduction KASCADE-Grande is a multi-detector setup to get redundant information on single air shower basis. The information is used to perform multiparameter analyses to solve the threefold problem of the reconstruction of the unknown primary energy, the primary mass, and to quantify the characteristics of the hadronic interactions in the air-shower development. The KASCADE-Grande experiment [1] located at the Forschungszentrum Karlsruhe, Germany, ∗ corresponding
author, e-mail: [email protected] address: CINVESTAV, Mexico D.F., Mexico ‡ on leave of absence from b § on leave of absence from Nat.Inst.Space Sc., Romania ¶ on leave of absence from Moscow State University, Russia † permanent
0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.11.030
extends the original extensive air shower experiment KASCADE [2] by an array of 37 detector stations spread over an area of 0.5 km2 (Fig. 1). Its major goal is to measure the possible knee of the heavy component in the primary cosmic ray energy spectrum, expected at ≈ 1017 eV. In order to infer the energy spectra of the primary cosmic ray particles for different mass groups with unfolding techniques (like with KASCADE data [3,4]) using the two dimensional electron-muon size spectrum, both particle numbers, i.e. total electron and muon number, have to be known. For measuring muons in KASCADE-Grande registered showers, the field array of the original KASCADE experiment provides 192 detector stations with 622 m2 of shielded scintillators providing an energy thresh-
355
error in muon number [Δ lg(Nμ ]
y/m
A. Haungs et al. / Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357
100
KASCADE array -100
w/o muon detectors
-200
Muon Tracking Detector
-300
Central Detector
-400
Piccolo
-500
KASCADE-Grande
-600
Grande rande DAQ G
-700 -700
protons iron
0.3
0
-600
-500
-400
-300
-200
-100
0
16
10 eV
0.2
0.1
0
-0.1 4.5 4.
100
5
x/m
old for vertical incidence of Eµ > 230 MeV. In addition, KASCADE-Grande consists of a muon tracking detector, which measures with high precision the incidence angles of individual muons (Eµ > 800 MeV). Also, at the KASCADE central detector further components are installed multiwire proportional chambers (MWPC), and limited streamer tubes (LST) - which offer valuable information on the penetrating muonic component at 2.4 GeV energy threshold. Whereas the information of the KASCADE array muon detectors are preferentially used to estimate the total muon number, the redundant information of the showers measured by the Central Detector and the Muon Tracking Detector is prevailingly used for tests and improvements of the hadronic interaction models. 2. The KASCADE muon array The Grande array measures the densities and arrival times of the charged particles, from what the shower core and the arrival direction of the EAS are reconstructed. The total muon number is obtained in a likelihood fit to the densities measured by KASCADE muon detectors. To describe the lateral distribution of the muons a Lagutinlike function is used [5]. In order to obtain stable fit results, the curvature of the lateral muon densities is kept constant and only the muon num-
6
Figure 2. Inaccuracies in KASCADE-Grande reconstruction of the total muon number. muon density [m -2]
Figure 1. The main components of the KASCADE-Grande experiment: the KASCADE, the Grande and the Piccolo arrays, the Muon Tracking Detector and the Central Detector.
5.5
muon number lg Nμ
iron hydrogen
log (E /GeV) range : 10 10
7.9-8.2
data fit
7.6-7.9 1
(Lagutin function)
7.3-7.6 7.0-7.3
°
0 -18
°
10 -1
10 -2 0
100
200
300
400
500
600
700
core distance [m]
Figure 3. Lateral density distributions of muons measured with KASCADE-Grande compared with simulated distributions. ber Nµ is estimated. The systematics and uncertainties have been studied with Monte Carlo simulations using CORSIKA [6] and the interaction model QGSJet 01 [7] and a detailed GEANT based detector simulation (Fig. 2). Figure 3 shows measured and simulated LDFs for different primary energies, where the energy has been roughly estimated by a linear combination of reconstructed total electron and muon numbers [5]. Generally, the agreement between data and MC is very good and the LDF describes the data reasonable well up to ≈ 1017 eV. The shown differential muon size spectra (Fig. 4 upper panel) are corrected for their systematic errors in reconstruction, derived from
356
dI/dN μ m -2s -1sr -1
A. Haungs et al. / Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357
10
-9
preliminary
10 -10 10 -11 10 -12 10 -13 10 -14 10 -15
KASCADE-Grande 0°-18 °
10 -16
KASCADE-Grande 18 °-25 °
10 -17 10
-18
KASCADE 0 °-18 °
10
-19
KASCADE 18° -25 °
10 -20
4
4.5
5
5.5
6
6.5
7
preliminary
KASCADE KASCADE-Grande
o
| τ | < 23 o | ρ | < 23 log10(sizeG) > 5.8 log10(sizeA) > 5.0 o o 0 ≤ Θ ≤ 18 100
200
300
400
1.5
]
muon number lg(Nμ)
<η> 4.4 4.2 4 3.8 3.6 3.4 3.2 3 2.8 2.6
GeV 10
Figure 5. Mean pseudorapidity of muons measured by the MTD versus the lateral distance of the muons to the shower axis.
3
[m -2 s -1 sr
-1
600 R [m]
preliminary
2.5
dI/dE × E
500
10 2
KASCADE e+ μ unfolded KASCADE-Grande μ unfolded systematic uncertainty
15
15.5
16
16.5
17
17.5
Energy log10(E/eV)
Figure 4. Upper part: KASCADE-Grande reconstructed muon size spectra for two zenith angle ranges compared with reconstructed KASCADE muon size spectra. Lower part: Unfolded allparticle spectrum of KASCADE-Grande compared to data of KASCADE from Ref. [3].
Monte Carlo studies. As one can see there is good agreement between the two measured fluxes in the overlap area in both zenith angle ranges. In Ref. [3] we have emphasized the importance of unfolding algorithms for the reconstruction of the energy and mass of cosmic rays. Because of the preliminary nature of the present data, we have not attempted a 2-dimensional unfolding of the electron and muon numbers such as in Ref. [3], but since the primary energy is mostly determined by the muon number with only a weak dependence on the primary mass, an unfolding of the muon size spectrum can be used as a first step to determine the all-particle energy spectrum at energies beyond the KASCADE range. The lower
panel of Fig. 4 shows the results of such an unfolding for the zenith angle range below 18◦ compared with results from KASCADE. One observes a very good overlap above 1016 eV. For more detailed statements on the shapes of the muon size spectrum and the primary energy spectrum the statistics is still too poor. 3. Muon Tracking Detector The Muon Tracking Detector (MTD) [8] allows a precise measurement of muon directions in EAS due to its excellent angular resolution (≈0.35◦ ). Measuring the relative angles τ and ρ between single shower muons and shower axis the mean muon production heights [9] and the pseudorapid2p ity η = ln pt ≈ −ln( τ 2 + ρ2 /2) of the muons can be calculated [10]. The first parameter improves the conventional separation into light and heavy primaries by means of the Ne /Nµ -ratio. The latter, being highly correlated with pseudorapidities and momenta of parent hadrons, is a very good probe of high-energy hadronic interactions and thus serves as a tool to test and improve existing hadronic interaction models. At KASCADE-Grande muons arriving up to 700 m from the shower core can be tracked, comparing to 160 m maximum distance in KASCADE. As an example, the mean pseudorapidity lateral distribution of muons registered up to 600 m from
probability
A. Haungs et al. / Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 354–357
procedures at ultra-high energies.
KASCADE-Grande data
0.14
100m < Rcore < 250m Eest > 1016eV 5o < Θ < 35o
0.12 0.1
5. Summary
Rρ2.4/0.23
0.08 0.06 0.04 0.02 0 0
0.5
1
1.5
2
2.5
357
3
Rρ
Figure 6. Example for a measured distribution of the muon density ratio. the shower core is shown in Fig. 5 and compared to the distribution calculated out of KASCADE data up-to 150 m. In the KASCADE sample a lower primary energy was selected which is the reason for the downward shift of the results with respect to the Grande ones. It is seen, however, that the slopes of the pseudorapidity distributions are consistent. 4. Muon Density Measurements The local muon density of the EAS is measured for various muon energy thresholds by separate detector set-ups of KASCADE. Two of them are installed in the basement of the central detector building, enabling an estimate of the muon density, ρ2.4GeV , for each single EAS. A second µ local muon density is reconstructed using the KASCADE array data. Here, the fitted LDF is used to estimate the densities of muons at the place of the central detector (ρ0.23GeV ). The raµ tios of the measured local muon densities at fixed core distances are determined by the muon energy spectrum in air-showers, which is a different approach to test the models [11]. Fig. 6 displays the ratio exemplarily. Comparing such distributions with predictions (including full detector response and reconstruction procedures) will test various high-energy and low energy model combinations. Such tests of the validity of the muon component will be of high relevance for shower simulation
Measurements with the multi-detector setup KASCADE-Grande provide plenty of high quality data to investigate the physics of the possible second knee in the cosmic ray energy spectrum. The multi-detector concept allows the reconstruction of energy spectra of single mass groups as well as comprehensive tests of the simulation procedures in the Monte Carlo codes underlying the shower analysis. In particular, the detailed measurements of muons at various energy thresholds are the basis of sophisticated analysis procedures. At KASCADE-Grande, observables describing the muon component are reconstructed for showers in the primary energy range up to 1 EeV and in radial distances up to 700 m. Acknowledgment: This work is partly supported by PPP-DAAD/KBN project for 2005-2006.
REFERENCES 1. G. Navarra et al. - KASCADE-Grande Coll., Nucl. Instr. Meth. A 518 (2004) 207. 2. T. Antoni et al. - KASCADE Collaboration, Nucl. Instr. Meth. A 513 (2003) 429. 3. T. Antoni et al. - KASCADE Collaboration, Astropart. Phys. 24 (2005) 1. 4. H. Ulrich et al. - KASCADE-Grande Coll., (2006) these proceedings. 5. J. van Buren et al. - KASCADE-Grande Coll., Proc. of 29th ICRC Pune 6 (2005) p.301. 6. D. Heck et al., Report FZKA 6019, Forschungszentrum Karlsruhe (1998). 7. N.N. Kalmykov, S.S. Ostapchenko, Phys. Atom. Nucl. 56 (1993) 346. 8. P. Doll et al., Nucl. Instr. Meth. A 488 (2002) 517. 9. C. B¨ uttner et al. - KASCADE-Grande Coll., 28th ICRC Tsukuba 1 (2003) p.33. 10. J. Zabierowski et al. - KASCADE-Grande Coll., 28th ICRC Tsukuba 1 (2003) p.29. 11. A. Haungs et al. - KASCADE-Grande Coll., Proc. of 29th ICRC Pune 6 (2005) p.281.