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Spectrum and mass composition of the high energy galactic radiation
Nuclear Physics B (Proc. Suppl.) 136 (2004) 265–272 www.elsevierphysics.com
Spectrum and mass composition of the high energy galactic radiation G. Navarra for the EAS-TOP Collaborationa a
Dipartimento di Fisica Generale dell’Universita’ and INFN, Torino, Italy via P. Giuria, 1, 10125 Torino, Italy We summarize the experimental data on the cosmic radiation in the energy range 1012 − 1016 eV obtained from the EAS-TOP experiment (Campo Imperatore, 2005 m a.s.l., 820 g/cm2 ; National Gran Sasso Laboratories, 1989-2000). The energy range covers the transition from the direct measurements through balloons and satellites to the ground based (EAS) ones, and a comparison of the data is presented. The region of the ”knee” (1015 − 1016 eV) is studied. It is found that the ”knee” is characterized by changes in slopes of the spectra of the lighter components. No break is observed in the iron spectrum. The generality of the results with respect to the hadron interaction models used for the interpretation are discussed.
1. INTRODUCTION The energy region 1015 − 1016 eV is usually considered to characterize the high energy cosmic ray galactic radiation, since it represents both the upper limit to the energy reachable by the most credible sources (SNR) [1] and to the magnetic confinement inside the Galaxy [2,3]. Experimentally this is supported by the observation [4] of the ”knee” in the primary spectrum (deduced from the EAS size spectrum). Understanding the evolution of the spectra of the different components of the primaries, and of the related anisotropy is therefore a clue for the understanding of the galactic c.r. sources. The study suffers from two main experimental constraints: a) the low fluxes, and the difficulties of calorimetric measurements, limit the observations that cannot be ”direct”, but have to be performed by means of ground arrays based on the detection of the secondaries produced by the primary particles in the atmosphere (the Extensive Air Showers, EAS) 1 , and b) accelerator measurements of the hadronic cross sections are still not available in this energy range and in the relevant kinematic region. The EAS-TOP experiment has therefore been planned to connect the measurements to the ”direct” ones, and to exploit observables that can 1 The indirect measurements combined with a steep primary spectrum enhance the influence of fluctuations.
0920-5632/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2004.10.032
constrain the uncertainties due to the hadronic interaction cross sections.
2. EAS-TOP The basic detector configuration, relevant for the present discussion, is shown in figs. 1-2 together with the array location with respect to the underground Gran Sasso Laboratories, and consisted of: - the e.m. detector: 35 scintillator modules, 10 m2 each, fully efficient for Ne > 105 , for the measurement of the shower size (Ne ), the core location and the arrival direction [5]; - the muon-hadron detector: 140 m2 calorimeter with 9 layers of 13 cm iron absorbers and Iarocci tubes as active elements, operating in ”quasi proportional” mode for hadron calorimetry at Eh > 50 GeV, and in streamer mode for muon counting at Eµ > 1 GeV [6]; - the Cherenkov light detector: 8 telescopes loading 0.5 m2 area light collectors equipped with imaging devices and wide angle optics (7 photomultipliers for a total field of view of 0.16 sr) [7]. Moreover, EAS-TOP operated in coincidence with the underground MACRO and LVD muon detectors (Eµ > 1.3 TeV; full effective area ATeV ≈ 1000 m2 ). µ
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Figure 1. The EAS-TOP array.
Figure 2. The EAS-TOP location with respect to the underground Gran Sasso laboratories.
3. THE CONNECTION WITH THE DIRECT MEASUREMENTS a) The primary proton spectrum [8] in the energy range 0.5 - 50 TeV has been deduced from the hadron spectrum measured in the calorimeter, after: i) simulating the propagation of primary protons and nuclei from the top of the atmosphere to the observation level, ii) checking the validity of the code used (CORSIKA/QGSJET) [9,10] by comparing with the sea level spectrum measured by KASCADE [11], iii) correcting for the contribution from the heavier nuclei. The results are shown in fig. 3, showing good agreement with the direct data, and constancy of the slope of the p-spectrum: S(E0 ) = (9.8 ± 1.1 ± 1.6sys ) × E0 (−2.80±0.06) 10−5 ( 1000 ) m−2 s−1 sr−1 GeV−1 . b) The fraction of He and CNO primaries is obtained from the atmospheric Cherenkov light density measurements at the surface (which is proportional to the total energy of the primary, E0 ) combined with the TeV muons recorded by MACRO [12] (providing the detection geometry and a ”trigger” based on the energy/nucleon). In fig. 4, showing the average number of muons
Figure 3. The primary proton spectrum obtained from the hadron flux (continuous line). The dotted lines represent the 1 s.d. statistical and systematic errors. Results from different experiments are shown for comparison.
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1
-1
10
-6
10
-2
10 10
2
Figure 4. Average muon numbers at the MACRO depth, from primary protons (full circle), He (open circle) and CNO (open cross) as a function of energy.
3.4
3.6
3.8
4
4.2
4.4
Figure 5. Comparison between the experimental C.l. photon numbers and the expectations from the JACEE and RUNJOB spectra.
4. THE KNEE
reaching the MACRO depth for different primaries we deduce that at primary energy E0 ≈ 80 TeV the muon contributions from p and He primaries coincide (the same holds at E0 ≈ 250 TeV also for CNO), so that by selecting C.l. signals corresponding to such energy the p+He (or p+He+CNO) flux is obtained. The C.l. photon numbers for events observed in coincidence with MACRO are shown in fig. 5: photon densities between 103.55 and 103.75 /m2 (268 events) correspond to primary energies about 80 TeV, and between 104.15 and 104.35 /m2 (125 events) to about 250 TeV (for core distances 125 < r < 145 m). By subtracting from the (p+He) and the (p+He+CNO) fluxes the p-flux we can derive the He and CNO ones, their relative ratio at 250 TeV being: J(p):J(He):J(CNO)=(0.20 ± 0.08):(0.58 ± 0.19):(0.22 ± 0.17). Also in fig. 5, the expectations from the JACEE [13] and RUNJOB [14] spectra are given. The data are in much better agreement with the JACEE spectra, due to the larger He flux measured in such experiment.
a) The ”knee”, as observed in the Ne size spectrum, is shown in fig. 6 [15]. Since compatible breaks (concerning spectral indexes and intensities) are observed in the e.m., Ne , and muon, Nµ , spectra [16] 2 , we can work on the hypothesis that in such region we are observing, in both spectra, the same component. In such case it can be identified. In fig. 7, the experimental muon number spectrum is compared with the expectations from individual primaries, whose fluxes I(E0 ) reproduce the shower size spectrum in the region of the 2 This is shown in tab. 1, in which the parameters of the spectral fits are reported, following expression:
dI = Ske,µ dNe,µ
Ne,µ Nke,µ
1,2 −γe,µ
(1)
where Nke,µ is the ”knee” position in the e.m. and muon 1,2 1 ) are the spectral indexes below (γe,µ size spectra, γe,µ 2 and above (γe,µ ) the ”knee” and Ske,µ the intensity corresponding to Nke,µ . γe and γµ are connected through the relation: (γe -1)/(γµ -1)=α, where α is the exponent of the relation: Nµ ∝ Ne α .
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γe1
γe2
2.56 2.56 2.56 2.56 2.56 2.56 γµ1
2.96 ± 0.06 2.86 ± 0.05 2.86 ± 0.04 2.82 ± 0.08 2.92 ± 0.09 2.75 ± 0.07 γµ2
3.21 ± 0.06 3.18 ± 0.08 3.18 ± 0.09 3.12 ± 0.15
3.42 ± 0.10 3.45 ± 0.10 3.4 ± 0.2 3.4 ± 0.1
∆ sec θ
1.00 − 1.05 1.05 − 1.10 1.10 − 1.15 1.15 − 1.20 1.20 − 1.25 1.25 − 1.30 ∆ sec θ 1.00 − 1.05 1.05 − 1.10 1.10 − 1.15 1.15 − 1.20 Table 1 Parameters of
I(> Nek ) × 107 m−2 s−1 sr−1 1.1 ± 0.1 1.3 ± 0.2 1.0 ± 0.1 0.8 ± 0.2 0.5 ± 0.1 1.4 ± 0.4 I(> Nµk ) × 107 m−2 s−1 sr−1 1.2 ± 0.3 1.1 ± 0.2 0.6 ± 0.2 1.6 ± 0.5
M [f d (i) − f s (i)]2 i=1
χ2 /d.f.
6.08 ± 0.03 5.95 ± 0.04 5.95 ± 0.01 5.92 ± 0.06 5.94 ± 0.05 5.62 ± 0.07 Log(Nµk )
7.8/11 8.4/11 5.3/11 7.6/11 4.6/11 2.8/11 χ2 /d.f.
4.65 ± 0.10 4.65 ± 0.10 4.75 ± 0.15 4.55 ± 0.15
10.4/10 9.3/10 6.9/10 5.9/10
the Ne and Nµ size spectra in different intervals of zenith angles.
”knee” following QGSJET. The upper and lower limits resulting from the uncertainties related to the hadronic interaction model are given (higher values for VENUS, lower for NEXUS). Such analysis lead to the conclusion of helium primaries dominating at the ”knee”, in agreement with the previously reported EAS-TOP and MACRO results (a conclusion that, as we see from fig. 7, can hardly be modified using a different interaction model). b) The spectra of light (p,He), intermediate (CNO), and heavy (Fe) primaries are obtained by fitting the muon number distributions in intervals of Ne . The expression minimized to perform such fit is: χ2 =
Log(Nek )
σ(i)2
(2)
where: f d (i) is the experimental fraction of events falling in the Ne channel i; f s (i) = αL fL (i) + αI fI (i) + αH fH (i) is the theoretical expression in which αL , αI and αH are the fit parameters representing the relative abundances of the light, intermediate and heavy mass groups; fL (i), fI (i) and fH (i) are obtained through simulations based on QGSJET for primary spectra with slopes γ = 2.75, and σ(i) is the error on the theoretical expression. Results of the fits as relative abundances (vs. Ne ) and fluxes (vs. E0 ) are
reported in figs. 8 and 9. It results that the energy range between 1015 and 1016 eV is characterized by a steepening spectrum of the lighter, and then of the medium components, while the heaviest one (Fe) is unchanged. The spectra are consistent with the extrapolations from direct measurements. 5. ABOUT HADRON INTERACTIONS The measurements have been interpreted by means of QGSJET as implemented in CORSIKA. Some main features of the conclusions result however independent from the model used (as already mentioned for the helium ”dominance” in the ”knee” region). a) Average values of muon numbers in intervals of shower size are shown in fig. 10 for the experimental data and simulated single elements spectra: the increasing average primary mass is seen from the shift of the experimental data from average helium to CNO. In fig. 11 the slopes of the Nµ -Ne relations for different interaction models implemented in CORSIKA [17–19] are compared for primary protons with the expectations of QGSJET. The properties of the interaction model can be represented in terms of the parameter α characteristic of the Nµ -Ne relation: Nµ ∝ Ne α . While the experimental value of α is αexp = 0.907 ± 0.004, for the different models we have:
G. Navarra / Nuclear Physics B (Proc. Suppl.) 136 (2004) 265–272
269
Figure 6. Differential shower size spectra measured at different zenith angles (i.e. atmospheric depths), showing the ”knee” position, and its shift with zenith angle.
Figure 7. Experimental muon number spectrum compared with the expectations from individual primaries, whose fluxes I(E0 ) reproduce the shower size spectrum in the region of the ”knee”.
αQGSJET = 0.792 ± 0.007, αV EN U S = 0.820 ± 0.007, αN EXU S = 0.77 ± 0.02, αDP M JET = 0.789 ± 0.008. The increasing mass with primary energy up to 1015 eV reported e.g. by JACEE would increase the quoted values of α of about 0.006. These are therefore the slopes expected following the different models for a ”constant” (and ”direct measurement based”) primary composition. None of the models can therefore explain the experimental value of α without requiring an additional increasing of the average primary mass around the ”knee”. b) Since the main changes in the hadronic interactions would finally manifest into different energy distributions of the secondaries, a check of the reported change in composition can be obtained by means of a similar muon number analysis vs shower size performed by means of the Eµ > 1.3 TeV muons recorded by MACRO. The relative spectra of the light and heavy components obtained through the quoted analysis are
reported in fig. 12 [20]. The interpretation is again performed through simulations exploiting QGSJET, and the results agree with the ones obtained through the GeV muon analysis. A comparison of the results in terms of < ln(A) > vs. primary energy is shown in fig. 13. 6. THE ANISOTROPY A crucial test of the possibility that the ”knee” feature is due to the decreasing galactic containment could be provided by the anisotropy data. The anisotropy is measured at primary energy E0 ≈ 100-200 TeV, with amplitude A(δ=0) = (3.7 ± 0.6) 10−4 and phase φ = (1.8 ± 0.5) hrs LST, fully compatible with the lower energy data (1-100 TeV). The lower statistics does not allow measurements with equal accuracy at higher energies. Upper limits have been obtained, that exclude an increasing amplitude of the anisotropy with energy dependence stronger than A ∝ E00.3
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Figure 8. Relative abundances of the three mass groups in different intervals of shower sizes.
(see fig. 14 [21]). A systematic search for γ-ray sources has been performed, looking for different candidates [22]: Pulsars, SNRs, X-ray binaries, the BL Lac objects Mrk421 and Mrk501, and over the whole visible sky, for steady and transient emissions. No DC emission has been detected; the values of the energy thresholds and the obtained upper limits depend on the source declination. As examples, the 90% c.l. upper limits obtained from the Crab Nebula are Φ(> 20TeV) < 2.6 · 10−13 cm−2 s−1 , and Φ(> 100TeV) < 3.9 · 10−14 cm−2 s−1 . 7. CONCLUSIONS The connection with the direct measurements is well described; the proton spectrum obtained from the hadron measurements agrees with both the JACEE and RUNJOB ones. The total light component (p + He) flux (from TeV muons and C.l. data) is in better agreement with the higher values reported by JACEE. This implies a primary flux dominated by helium above 1014 eV,
Figure 9. Energy spectra of the three mass groups. The direct measurement data are also reported for comparison.
and is in agreement with the analysis of the muon and e.m. size spectra above 1015 eV. A break in the spectrum of He primaries is therefore the best candidate for the explanation of the most prominent ”knee” in the e.m. size spectrum. The study of the evolution of the average spectra of the light, intermediate and heavy mass groups through the 1015 − 1016 eV region leads to: a) a steep spectrum of the light component (γp,He > 3.1); b) a spectrum harder for the intermediate one (γCN O 2.75), c) a constant slope for the spectrum of the heavy primaries (γF e 2.3 ÷ 2.7), consistent with the direct measurements. The increasing average logarithmic mass in one decade of primary energy (1.5 1015 ÷ 1.5 1016 eV), amounts to ∆ < lnA >= 1.5 ± 0.5. The general conclusion of increasing average primary mass with primary energy does not depend on the interaction model used for the analysis. The result is in good agreement with the one obtained from the combined EAS-TOP (Ne ) and
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Log(Nµ)-Log(NµQGSJET)
-2
<ρµ180> [m ]
0.25
10
Experimental data p He CNO
0.15
Mg -1
Experimental Data
0.2
Fe
0.1
VENUS
0.05
QGSJET
0
-0.05
DPMJET -0.1
NEXUS -0.15
10
-2
-0.2
5.4
5.6
5.8
6
6.2
6.4
6.6
-0.25
5.5
5.75
6
6.25
Figure 10. < ρµ > at rcore between 180 and 210 m vs Ne relation (measured and expected from QGSJET for individual elements).
MACRO (Nµ ) data, in which the detected muons (Eµ > 1.3 TeV) are produced above the central rapidity region. This demonstrates the consistency of QGSJET in describing the hadron interactions over a wide energy range of the secondaries 3 . The observed evolution of the composition is therefore in general agreement with the expectations from the standard acceleration and propagation models of galactic cosmic rays, predicting rigidity dependent breaks in the spectra of the different primaries. Following such idea, the detection of the iron break requires a measurement extending up to about 1018 eV. An array (KASCADE-Grande) with such acceptance, realized as an extension of KASCADE with the e.m. detectors of EAS-TOP, is now in operation [24]. 3 The agreement with the KASCADE results [23] is also quite significant in such context, due to the different atmospheric depth of the two arrays (of about 200 gr/cm2 ) and therefore different stage of development of the cascades.
6.5
6.75
7
7.25
7.5
7.75
8
Log(Ne)
Log(Ne)
Figure 11. Comparison between the Nµ -Ne relationships obtained for different interaction models (proton primaries). Data are normalized to QGSJET. The slope of the Nµ -Ne relationship for the experimental data is also plotted.
The collaboration with MACRO has been determinant for reaching part of these results. REFERENCES 1. E.G. Berezhko et al, J.E.P.T., 82 (1996) 1 2. B. Peters, Proc. 6th ICRC, Vol. 3, (1960), 157 3. G.T. Zatsepin et al., Izv. Akad. Nauk USSR S.P. 26 (1962) 685 4. G.V. Kulikov and G.B. Khristiansen, Sov. Phys. JEPT, 35 (8) (1959) 441 5. EAS-TOP Coll, N.I.M., A 336 (1993) 310 6. EAS-TOP Coll, N.I.M., A 420 (1999) 117 7. EAS-TOP Coll, Il Nuovo Cimento, 105A (1992) 1807 8. EAS-TOP Coll, Astrop. Phys., 19 (2003) 329 9. N.N. Kalmykov et al., Nucl. Phys. B, 52B (1997) 17 10. D. Heck et al, FZK-Report 6019 (1998) 11. KASCADE Coll., J.Phys.G: Nucl.Part.Phys,
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Figure 12. Light (p+He) and heavy (Mg+Fe) primary spectra as obtained from the fits to the TeV muon multiplicity distributions (by MACRO) in different bins of Ne (by EAS-TOP).
20 (1994) 637 12. EAS-TOP and MACRO Colls, Astrop. Phys., 21 (2004) 223 13. K. Asakimori et al., Ap.J., 502 (1998) 278 14. A. V. Apanasenko et al., Astrop. Phys., 16 (2001) 13 15. EAS-TOP Coll, Astrop. Phys., 10 (1999) 1 16. EAS-TOP Coll, Nucl. Phys. B, 85 (2000) 318; Proc. 28th ICRC, 1 (2003) 147 and 151 17. H.J. Drescher et al., Phys. Rep. 350 (2001) 93 18. J. Ranft, Phys. Rev. D51 (1995) 64 ; hepph/9911232 (1999) 19. K. Werner, Phys. Rep. 232 (1993) 87 20. EAS-TOP and MACRO Colls, Astrop. Phys., 20 (2004) 641 21. EAS-TOP Coll, Ap. J., 470 (1996) 501; Proc. 28th ICRC, 1 (2003) 183 22. EAS-TOP Coll, Astrop. Phys., 3 (1994) 1; Proc 26th I.C.R.C., 4 (1999) 68 23. KASCADE Coll, Astrop. Phys., 16 (2002) 373 24. KASCADE-Grande Coll, Nucl. Phys. B, 122 (2003) 422, and F. Badea, this volume.
Figure 13. Average logaritmic mass vs primary energy in the ”knee” region, as obtained from Ne and Nµ (GeV and TeV muons).
E 0.7 10 Amplitude
272
-3
E 0.5 E 0.3
Energy (TeV) 500
1000
Figure 14. The amplitude of the measured anisotropy at 100-200 TeV, and the upper limits at higher energies.
Spectrum and mass composition of the high energy galactic radiation G. Navarra for the EAS-TOP Collaborationa a
Dipartimento di Fisica Generale dell’Universita’ and INFN, Torino, Italy via P. Giuria, 1, 10125 Torino, Italy We summarize the experimental data on the cosmic radiation in the energy range 1012 − 1016 eV obtained from the EAS-TOP experiment (Campo Imperatore, 2005 m a.s.l., 820 g/cm2 ; National Gran Sasso Laboratories, 1989-2000). The energy range covers the transition from the direct measurements through balloons and satellites to the ground based (EAS) ones, and a comparison of the data is presented. The region of the ”knee” (1015 − 1016 eV) is studied. It is found that the ”knee” is characterized by changes in slopes of the spectra of the lighter components. No break is observed in the iron spectrum. The generality of the results with respect to the hadron interaction models used for the interpretation are discussed.
1. INTRODUCTION The energy region 1015 − 1016 eV is usually considered to characterize the high energy cosmic ray galactic radiation, since it represents both the upper limit to the energy reachable by the most credible sources (SNR) [1] and to the magnetic confinement inside the Galaxy [2,3]. Experimentally this is supported by the observation [4] of the ”knee” in the primary spectrum (deduced from the EAS size spectrum). Understanding the evolution of the spectra of the different components of the primaries, and of the related anisotropy is therefore a clue for the understanding of the galactic c.r. sources. The study suffers from two main experimental constraints: a) the low fluxes, and the difficulties of calorimetric measurements, limit the observations that cannot be ”direct”, but have to be performed by means of ground arrays based on the detection of the secondaries produced by the primary particles in the atmosphere (the Extensive Air Showers, EAS) 1 , and b) accelerator measurements of the hadronic cross sections are still not available in this energy range and in the relevant kinematic region. The EAS-TOP experiment has therefore been planned to connect the measurements to the ”direct” ones, and to exploit observables that can 1 The indirect measurements combined with a steep primary spectrum enhance the influence of fluctuations.
0920-5632/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2004.10.032
constrain the uncertainties due to the hadronic interaction cross sections.
2. EAS-TOP The basic detector configuration, relevant for the present discussion, is shown in figs. 1-2 together with the array location with respect to the underground Gran Sasso Laboratories, and consisted of: - the e.m. detector: 35 scintillator modules, 10 m2 each, fully efficient for Ne > 105 , for the measurement of the shower size (Ne ), the core location and the arrival direction [5]; - the muon-hadron detector: 140 m2 calorimeter with 9 layers of 13 cm iron absorbers and Iarocci tubes as active elements, operating in ”quasi proportional” mode for hadron calorimetry at Eh > 50 GeV, and in streamer mode for muon counting at Eµ > 1 GeV [6]; - the Cherenkov light detector: 8 telescopes loading 0.5 m2 area light collectors equipped with imaging devices and wide angle optics (7 photomultipliers for a total field of view of 0.16 sr) [7]. Moreover, EAS-TOP operated in coincidence with the underground MACRO and LVD muon detectors (Eµ > 1.3 TeV; full effective area ATeV ≈ 1000 m2 ). µ
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Figure 1. The EAS-TOP array.
Figure 2. The EAS-TOP location with respect to the underground Gran Sasso laboratories.
3. THE CONNECTION WITH THE DIRECT MEASUREMENTS a) The primary proton spectrum [8] in the energy range 0.5 - 50 TeV has been deduced from the hadron spectrum measured in the calorimeter, after: i) simulating the propagation of primary protons and nuclei from the top of the atmosphere to the observation level, ii) checking the validity of the code used (CORSIKA/QGSJET) [9,10] by comparing with the sea level spectrum measured by KASCADE [11], iii) correcting for the contribution from the heavier nuclei. The results are shown in fig. 3, showing good agreement with the direct data, and constancy of the slope of the p-spectrum: S(E0 ) = (9.8 ± 1.1 ± 1.6sys ) × E0 (−2.80±0.06) 10−5 ( 1000 ) m−2 s−1 sr−1 GeV−1 . b) The fraction of He and CNO primaries is obtained from the atmospheric Cherenkov light density measurements at the surface (which is proportional to the total energy of the primary, E0 ) combined with the TeV muons recorded by MACRO [12] (providing the detection geometry and a ”trigger” based on the energy/nucleon). In fig. 4, showing the average number of muons
Figure 3. The primary proton spectrum obtained from the hadron flux (continuous line). The dotted lines represent the 1 s.d. statistical and systematic errors. Results from different experiments are shown for comparison.
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1
-1
10
-6
10
-2
10 10
2
Figure 4. Average muon numbers at the MACRO depth, from primary protons (full circle), He (open circle) and CNO (open cross) as a function of energy.
3.4
3.6
3.8
4
4.2
4.4
Figure 5. Comparison between the experimental C.l. photon numbers and the expectations from the JACEE and RUNJOB spectra.
4. THE KNEE
reaching the MACRO depth for different primaries we deduce that at primary energy E0 ≈ 80 TeV the muon contributions from p and He primaries coincide (the same holds at E0 ≈ 250 TeV also for CNO), so that by selecting C.l. signals corresponding to such energy the p+He (or p+He+CNO) flux is obtained. The C.l. photon numbers for events observed in coincidence with MACRO are shown in fig. 5: photon densities between 103.55 and 103.75 /m2 (268 events) correspond to primary energies about 80 TeV, and between 104.15 and 104.35 /m2 (125 events) to about 250 TeV (for core distances 125 < r < 145 m). By subtracting from the (p+He) and the (p+He+CNO) fluxes the p-flux we can derive the He and CNO ones, their relative ratio at 250 TeV being: J(p):J(He):J(CNO)=(0.20 ± 0.08):(0.58 ± 0.19):(0.22 ± 0.17). Also in fig. 5, the expectations from the JACEE [13] and RUNJOB [14] spectra are given. The data are in much better agreement with the JACEE spectra, due to the larger He flux measured in such experiment.
a) The ”knee”, as observed in the Ne size spectrum, is shown in fig. 6 [15]. Since compatible breaks (concerning spectral indexes and intensities) are observed in the e.m., Ne , and muon, Nµ , spectra [16] 2 , we can work on the hypothesis that in such region we are observing, in both spectra, the same component. In such case it can be identified. In fig. 7, the experimental muon number spectrum is compared with the expectations from individual primaries, whose fluxes I(E0 ) reproduce the shower size spectrum in the region of the 2 This is shown in tab. 1, in which the parameters of the spectral fits are reported, following expression:
dI = Ske,µ dNe,µ
Ne,µ Nke,µ
1,2 −γe,µ
(1)
where Nke,µ is the ”knee” position in the e.m. and muon 1,2 1 ) are the spectral indexes below (γe,µ size spectra, γe,µ 2 and above (γe,µ ) the ”knee” and Ske,µ the intensity corresponding to Nke,µ . γe and γµ are connected through the relation: (γe -1)/(γµ -1)=α, where α is the exponent of the relation: Nµ ∝ Ne α .
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γe1
γe2
2.56 2.56 2.56 2.56 2.56 2.56 γµ1
2.96 ± 0.06 2.86 ± 0.05 2.86 ± 0.04 2.82 ± 0.08 2.92 ± 0.09 2.75 ± 0.07 γµ2
3.21 ± 0.06 3.18 ± 0.08 3.18 ± 0.09 3.12 ± 0.15
3.42 ± 0.10 3.45 ± 0.10 3.4 ± 0.2 3.4 ± 0.1
∆ sec θ
1.00 − 1.05 1.05 − 1.10 1.10 − 1.15 1.15 − 1.20 1.20 − 1.25 1.25 − 1.30 ∆ sec θ 1.00 − 1.05 1.05 − 1.10 1.10 − 1.15 1.15 − 1.20 Table 1 Parameters of
I(> Nek ) × 107 m−2 s−1 sr−1 1.1 ± 0.1 1.3 ± 0.2 1.0 ± 0.1 0.8 ± 0.2 0.5 ± 0.1 1.4 ± 0.4 I(> Nµk ) × 107 m−2 s−1 sr−1 1.2 ± 0.3 1.1 ± 0.2 0.6 ± 0.2 1.6 ± 0.5
M [f d (i) − f s (i)]2 i=1
χ2 /d.f.
6.08 ± 0.03 5.95 ± 0.04 5.95 ± 0.01 5.92 ± 0.06 5.94 ± 0.05 5.62 ± 0.07 Log(Nµk )
7.8/11 8.4/11 5.3/11 7.6/11 4.6/11 2.8/11 χ2 /d.f.
4.65 ± 0.10 4.65 ± 0.10 4.75 ± 0.15 4.55 ± 0.15
10.4/10 9.3/10 6.9/10 5.9/10
the Ne and Nµ size spectra in different intervals of zenith angles.
”knee” following QGSJET. The upper and lower limits resulting from the uncertainties related to the hadronic interaction model are given (higher values for VENUS, lower for NEXUS). Such analysis lead to the conclusion of helium primaries dominating at the ”knee”, in agreement with the previously reported EAS-TOP and MACRO results (a conclusion that, as we see from fig. 7, can hardly be modified using a different interaction model). b) The spectra of light (p,He), intermediate (CNO), and heavy (Fe) primaries are obtained by fitting the muon number distributions in intervals of Ne . The expression minimized to perform such fit is: χ2 =
Log(Nek )
σ(i)2
(2)
where: f d (i) is the experimental fraction of events falling in the Ne channel i; f s (i) = αL fL (i) + αI fI (i) + αH fH (i) is the theoretical expression in which αL , αI and αH are the fit parameters representing the relative abundances of the light, intermediate and heavy mass groups; fL (i), fI (i) and fH (i) are obtained through simulations based on QGSJET for primary spectra with slopes γ = 2.75, and σ(i) is the error on the theoretical expression. Results of the fits as relative abundances (vs. Ne ) and fluxes (vs. E0 ) are
reported in figs. 8 and 9. It results that the energy range between 1015 and 1016 eV is characterized by a steepening spectrum of the lighter, and then of the medium components, while the heaviest one (Fe) is unchanged. The spectra are consistent with the extrapolations from direct measurements. 5. ABOUT HADRON INTERACTIONS The measurements have been interpreted by means of QGSJET as implemented in CORSIKA. Some main features of the conclusions result however independent from the model used (as already mentioned for the helium ”dominance” in the ”knee” region). a) Average values of muon numbers in intervals of shower size are shown in fig. 10 for the experimental data and simulated single elements spectra: the increasing average primary mass is seen from the shift of the experimental data from average helium to CNO. In fig. 11 the slopes of the Nµ -Ne relations for different interaction models implemented in CORSIKA [17–19] are compared for primary protons with the expectations of QGSJET. The properties of the interaction model can be represented in terms of the parameter α characteristic of the Nµ -Ne relation: Nµ ∝ Ne α . While the experimental value of α is αexp = 0.907 ± 0.004, for the different models we have:
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Figure 6. Differential shower size spectra measured at different zenith angles (i.e. atmospheric depths), showing the ”knee” position, and its shift with zenith angle.
Figure 7. Experimental muon number spectrum compared with the expectations from individual primaries, whose fluxes I(E0 ) reproduce the shower size spectrum in the region of the ”knee”.
αQGSJET = 0.792 ± 0.007, αV EN U S = 0.820 ± 0.007, αN EXU S = 0.77 ± 0.02, αDP M JET = 0.789 ± 0.008. The increasing mass with primary energy up to 1015 eV reported e.g. by JACEE would increase the quoted values of α of about 0.006. These are therefore the slopes expected following the different models for a ”constant” (and ”direct measurement based”) primary composition. None of the models can therefore explain the experimental value of α without requiring an additional increasing of the average primary mass around the ”knee”. b) Since the main changes in the hadronic interactions would finally manifest into different energy distributions of the secondaries, a check of the reported change in composition can be obtained by means of a similar muon number analysis vs shower size performed by means of the Eµ > 1.3 TeV muons recorded by MACRO. The relative spectra of the light and heavy components obtained through the quoted analysis are
reported in fig. 12 [20]. The interpretation is again performed through simulations exploiting QGSJET, and the results agree with the ones obtained through the GeV muon analysis. A comparison of the results in terms of < ln(A) > vs. primary energy is shown in fig. 13. 6. THE ANISOTROPY A crucial test of the possibility that the ”knee” feature is due to the decreasing galactic containment could be provided by the anisotropy data. The anisotropy is measured at primary energy E0 ≈ 100-200 TeV, with amplitude A(δ=0) = (3.7 ± 0.6) 10−4 and phase φ = (1.8 ± 0.5) hrs LST, fully compatible with the lower energy data (1-100 TeV). The lower statistics does not allow measurements with equal accuracy at higher energies. Upper limits have been obtained, that exclude an increasing amplitude of the anisotropy with energy dependence stronger than A ∝ E00.3
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Figure 8. Relative abundances of the three mass groups in different intervals of shower sizes.
(see fig. 14 [21]). A systematic search for γ-ray sources has been performed, looking for different candidates [22]: Pulsars, SNRs, X-ray binaries, the BL Lac objects Mrk421 and Mrk501, and over the whole visible sky, for steady and transient emissions. No DC emission has been detected; the values of the energy thresholds and the obtained upper limits depend on the source declination. As examples, the 90% c.l. upper limits obtained from the Crab Nebula are Φ(> 20TeV) < 2.6 · 10−13 cm−2 s−1 , and Φ(> 100TeV) < 3.9 · 10−14 cm−2 s−1 . 7. CONCLUSIONS The connection with the direct measurements is well described; the proton spectrum obtained from the hadron measurements agrees with both the JACEE and RUNJOB ones. The total light component (p + He) flux (from TeV muons and C.l. data) is in better agreement with the higher values reported by JACEE. This implies a primary flux dominated by helium above 1014 eV,
Figure 9. Energy spectra of the three mass groups. The direct measurement data are also reported for comparison.
and is in agreement with the analysis of the muon and e.m. size spectra above 1015 eV. A break in the spectrum of He primaries is therefore the best candidate for the explanation of the most prominent ”knee” in the e.m. size spectrum. The study of the evolution of the average spectra of the light, intermediate and heavy mass groups through the 1015 − 1016 eV region leads to: a) a steep spectrum of the light component (γp,He > 3.1); b) a spectrum harder for the intermediate one (γCN O 2.75), c) a constant slope for the spectrum of the heavy primaries (γF e 2.3 ÷ 2.7), consistent with the direct measurements. The increasing average logarithmic mass in one decade of primary energy (1.5 1015 ÷ 1.5 1016 eV), amounts to ∆ < lnA >= 1.5 ± 0.5. The general conclusion of increasing average primary mass with primary energy does not depend on the interaction model used for the analysis. The result is in good agreement with the one obtained from the combined EAS-TOP (Ne ) and
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Log(Nµ)-Log(NµQGSJET)
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Figure 10. < ρµ > at rcore between 180 and 210 m vs Ne relation (measured and expected from QGSJET for individual elements).
MACRO (Nµ ) data, in which the detected muons (Eµ > 1.3 TeV) are produced above the central rapidity region. This demonstrates the consistency of QGSJET in describing the hadron interactions over a wide energy range of the secondaries 3 . The observed evolution of the composition is therefore in general agreement with the expectations from the standard acceleration and propagation models of galactic cosmic rays, predicting rigidity dependent breaks in the spectra of the different primaries. Following such idea, the detection of the iron break requires a measurement extending up to about 1018 eV. An array (KASCADE-Grande) with such acceptance, realized as an extension of KASCADE with the e.m. detectors of EAS-TOP, is now in operation [24]. 3 The agreement with the KASCADE results [23] is also quite significant in such context, due to the different atmospheric depth of the two arrays (of about 200 gr/cm2 ) and therefore different stage of development of the cascades.
6.5
6.75
7
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8
Log(Ne)
Log(Ne)
Figure 11. Comparison between the Nµ -Ne relationships obtained for different interaction models (proton primaries). Data are normalized to QGSJET. The slope of the Nµ -Ne relationship for the experimental data is also plotted.
The collaboration with MACRO has been determinant for reaching part of these results. REFERENCES 1. E.G. Berezhko et al, J.E.P.T., 82 (1996) 1 2. B. Peters, Proc. 6th ICRC, Vol. 3, (1960), 157 3. G.T. Zatsepin et al., Izv. Akad. Nauk USSR S.P. 26 (1962) 685 4. G.V. Kulikov and G.B. Khristiansen, Sov. Phys. JEPT, 35 (8) (1959) 441 5. EAS-TOP Coll, N.I.M., A 336 (1993) 310 6. EAS-TOP Coll, N.I.M., A 420 (1999) 117 7. EAS-TOP Coll, Il Nuovo Cimento, 105A (1992) 1807 8. EAS-TOP Coll, Astrop. Phys., 19 (2003) 329 9. N.N. Kalmykov et al., Nucl. Phys. B, 52B (1997) 17 10. D. Heck et al, FZK-Report 6019 (1998) 11. KASCADE Coll., J.Phys.G: Nucl.Part.Phys,
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Figure 12. Light (p+He) and heavy (Mg+Fe) primary spectra as obtained from the fits to the TeV muon multiplicity distributions (by MACRO) in different bins of Ne (by EAS-TOP).
20 (1994) 637 12. EAS-TOP and MACRO Colls, Astrop. Phys., 21 (2004) 223 13. K. Asakimori et al., Ap.J., 502 (1998) 278 14. A. V. Apanasenko et al., Astrop. Phys., 16 (2001) 13 15. EAS-TOP Coll, Astrop. Phys., 10 (1999) 1 16. EAS-TOP Coll, Nucl. Phys. B, 85 (2000) 318; Proc. 28th ICRC, 1 (2003) 147 and 151 17. H.J. Drescher et al., Phys. Rep. 350 (2001) 93 18. J. Ranft, Phys. Rev. D51 (1995) 64 ; hepph/9911232 (1999) 19. K. Werner, Phys. Rep. 232 (1993) 87 20. EAS-TOP and MACRO Colls, Astrop. Phys., 20 (2004) 641 21. EAS-TOP Coll, Ap. J., 470 (1996) 501; Proc. 28th ICRC, 1 (2003) 183 22. EAS-TOP Coll, Astrop. Phys., 3 (1994) 1; Proc 26th I.C.R.C., 4 (1999) 68 23. KASCADE Coll, Astrop. Phys., 16 (2002) 373 24. KASCADE-Grande Coll, Nucl. Phys. B, 122 (2003) 422, and F. Badea, this volume.
Figure 13. Average logaritmic mass vs primary energy in the ”knee” region, as obtained from Ne and Nµ (GeV and TeV muons).
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Figure 14. The amplitude of the measured anisotropy at 100-200 TeV, and the upper limits at higher energies.