Yuri V. Stenkin Institute for Nuclear Research of Russian Academy of Sciences, Moscow, RUSSIA

1. Remarks on astrophysical origin of the knee in cosmic ray spectrum Yuri V. StenkinInstitute for Nuclear Research of Russian Academy of Sciences, Moscow, RUSSIA 13 ISVHECRI, Pylos, Greece

2. The astrophysical origin of the so-called “knee” in primary cosmic ray spectrum in PeV region is very popular and is widely exploited in practice for a long time of about 50 years. This hypothesis seems to begin a new life in the recent years after discovering some new Supernova remnants... But, experimental data accumulated up to now in cosmic ray physics seed some doubt to the “knee” existence. One could argue that there is no one theory capable to explain pure power law spectrum in a very wide energy range of 1010 - 1020 eV.

3. But, such a theory does exist [Trubnikov B.A., Vlasov V.P. and Zhdanov. S.K., JETP, 1989, v.49, p.581; B.A.Trubnikov, Uspekhi -Physics, v.160, issue 12, 1990; Trubnikov B.A., Zhdanov S.K. And S.M.Zverev. “Hydrodynamics of unstable media”., CRC Press, 1996, p.114]. There was proposed a universal mechanism of cosmic ray acceleration in the cosmic plasma pinches. This theory can explain not only power law spectrum but even the value of its power law index . This mechanism can generate cosmic rays up to the highest energy with integral exponent 1.73. Another remarkable feature of this mechanism is following: the index does not depend on a particle mass or charge. It is really the universal and possibly a fundamental value.

4. Very breifly this process of matter acceleration can be illustratedby an analogy with water stream: here water drops are produced and accelerated by the force of the surface tension. Cosmic plasma also produces pinches and can accelerate the matter (plasma itself) up to the highest energy (pinch-mechanism). water stream

5. Brief review of the experimental data Let us look to the problem from the experimental point of view [Yu.V.Stenkin, 2003]. If primary spectrum index is  and a secondary x-component depends on primary energy E0 as Nx~ E0 than the EAS-size distribution on Nx is P(Nx)~Nx-, where =/ .If the “knee” in primary spectrum does exist (let it be =0.6) one can predict a relationship between the “knees” in all detectable secondary components: electromagnetic, muonic and hadronic. e =1.15-1.25 (so e=/e0.5) ,h=0.8-0.9 (,h1.7/0.85=0.71) ,h <1 while e >1 and ,h > e !!! e-m knee h & m knee

6. What experiments give us? 1. KASKADE (hadrons) CORSIKA simulations measurements

7. KASKADE (hadrons) Db=0.110.02

8. 2. KASKADE (muons) Result: m0.2

9. Interpretation of KASKADE muon data made by the MSU group (N.P.Il’ina, N.N.Kalmykov et al. 28th ICRC, p.123) Result: the data disagree with calculations made with a knee... To explain this they introduced some unknown fluctuations...

10. 3. MSU ( EAS muons) (Yu.A.Fomin, N.N.Kalmykov et al. Proc. 27th ICRC, Hamburg, p. 80) Result: the «knee» is not visible in direct measured muon number spectrum! It is visible only in a spectrum recalculated (!) from electron size spectrum. Yu.A.Fomin, N.N.Kalmykov et al. Proc. 27th ICRC, p. 80

11. 4. Underground muons 4.1 Baksan data • (Stenkin Yu.V. and Tsyabuk A.L. Proc. 28th ICRC, Tsukuba, 2003, p. 1151)) Result: muon number spectrum measured in very wide range has no «knee»!

12. 4.2. Comparison with other experiments (Stenkin Yu.V. and Tsyabuk a.L. Izvestia RAN, ser. Fizich., 2004, (in press)) Em> 3.1 Tev Result: No knee

13. Em> 1.3 TeV Result: no visible knee

14. 5. Cosmic ray experiments in CERN

15. Results: measured spectra are much flatter than expectations assumed a knee

16. Experimental data summary References • 2. Yu.V.Stenkin. Mod. Phys. Lett. A, 18(18), (2003), p. 1225 • 3. T.Antoni, W.D.Apel et al. (KASKADE Collaboration). Astropart. Phys., v.16, (2002), 373-386 • 4. J.R.Horandel, T.Antoni et al. (KASKADE Collaboration). Proc. 27th ICRC, Hamburg, (2001), p. 137 • 5. Yu.A.Fomin, N.N.Kalmykov et al. Proc. 28th ICRC, Tsukuba, (2003), p. 119 • 6. Yu.V.Stenkin and A.L.Tsyabuk. Izvestia RAN, ser. Fizich., in press (underground muons) • 7. N.M.Budnev, D.V.Chernov et al.(Tunka) Izvestia RAN, ser. Fizich., (2002), No 11, p.1563 • 8. R.Glasstetter et al. (KASKADE Collaboration). Nucl. Phys. B, (Proc. Suppl.), (1999), 75A, 251 • 9. P.Travnicek and J.Ridky (DELPHI collaboration). Epiphani 2004, Krakov (talk)

17. Conclusion • The question “Does the knee in primary spectrum exist or not?” is still open. • Therefore, the main efforts should be now directed not to explanations of the “knee” but to the above question answering. • I incline to a negative answer for this question, because only in this case we could understand the muon experimental data. • There exist a natural explanation of the visible “disagreement” of the experimental data shown in Table 1 in a frame of a new approach to EAS development predicting the absense of a knee in hadronic and muonic components. • And finally: if the answer is negative then we probably have a natural universal theory of cosmic ray acceleration in plasma pinches. To confirm or to reject this theory we have to measure the spectral index  with high accuracy and answer the question: • “Does it equal to  3=1.73 or not?”

18. Continued...