1. Nuclei As Ultra High Energy Cosmic Rays Oleg Kalashev* UCLA, INR RAS GZK 40: The 3rd International Workshop on THE HIGHEST ENERGY COSMIC RAYS AND THEIR SOURCES INR RAS, Moscow, 17 May 2006 * e-mail: kalashev@physics.ucla.edu

2. Overview Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Motivation Propagation of protons and nuclei compared Typical propagated spectrum of protons and nuclei Fitting AGASA and HiRes spectra Conclusion

3. GZK problem Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 All experiments have registered events above 100 EeV HiRes is claimed to be consistent with GZK cutoff provided that UHECR sources are close enough, however no evident sources has been found yet within GZK sphere

4. Possible solutions Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006

5. Possible solutions Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models: Topological defects Z-burst

6. Possible models Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst AGASA muon measurements γ -ray fraction predicted is close to experimental bounds! Gelmini, Kalashev, Semikoz astro-ph/0506128 Current experimental limitations on γ ray flux on 95% CL: AGASA, Yakutsk combined (astro-ph/0601449 G.I.Rubtsov et al) 36% above 100EeV Pierre-Auger (M.Risse, ICRC 2005) 26% above 10EeV

7. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst Acceleration (bottom-up) models: Possible models

8. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst Acceleration (bottom-up) models: + Don’t require new physics

9. Possible models Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst Acceleration (bottom-up) models: + Don’t require new physics Hard to achieve energies above 100 EeV (possibly extreme astrophysics needed) _

10. Possible models Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst Acceleration (bottom-up) models: protons nuclei

11. Possible models Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst Acceleration (bottom-up) models: protons Most natural UHECR candidate as most abundant element in the universe nuclei

12. Possible models Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Top-Down models (disfavored?) : Topological defects Z-burst Acceleration (bottom-up) models: protons Most natural UHECR candidate as most abundant element in the universe nuclei More efficient acceleration and isotropisation

13. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Propagation of Ultra High Energy Cosmic Rays

14. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Propagation of Ultra High Energy Cosmic Rays A. Uryson – next talk

15. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Main Factors influenc ing UHECR propagation Microwave Photon Background (MWB) Random Extragalactic Magnetic Field (EGMF) 10 -12 -10 -9 G IR/Optic radiation e, γ p, n Nuclei photodisintegration Pair production synchrotron ICS, e + e - production  & e + e - production , e+e-, photodisintegration deflection ? Radio background (RB) ?

16. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Simulating UHECR propagation Photodisintegration e+e- pair production  production F.Stecker et al. Astrophys.J. 512 (1999) 521-526. E.Khan et al. Astropart.Phys. 23 (2005) 191-201 M.J.Chodorowski et al. Astrophys.J.400,181(1992) A.Mucke et al.,Comp.Phys.Comm.124,290(2000) Extragalactic magnetic field K.Dolag et al., ICRC 2003 proceedings Infrared background Sigl et al. astro-ph/0309695 F.Stecker et al. astro-ph/0510449

17. Energy loss length - Fe Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006

18. Energy loss length – Fe and p Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006

19. Phenomenological source model Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) ParameterName Values Power of the Injection Spectrum, E -   1.0 - 3.0 End point of the Energy Spectrum Σ max 10 19 - 10 22 Evolution factor: (1+z) 3+m m0 ± 3 Red shift of the nearest sourcez min 0 - 0.1 Maximal source redshift z max 3 z – red shift, Θ(x)- step function, E max = Z Σ max, Z- electric charge

20. Dependence on  Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Protons E max = 6 x 10 20 eV m = 0 z min = 0 Best fit (HiRes) α= 2.6

21. Dependence on  Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Fe primaries Σ max = 6 x 10 20 eV m = 0 z min = 0 Best fit (HiRes) α= 2.4

22. Dependence on E max Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Protons α = 2 m = 0 z min = 0

23. Dependence on E max Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Fe primaries α = 2 m = 0 z min = 0 E max =26 x

24. Dependence on Z min Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Protons α = 2.65 m = 0 E max = 3 x 10 20 eV

25. Dependence on m Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) He primaries α = 2.3 E max = 5 x 10 21 eV z min = 0

26. Composition of the propagated cascade Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Nuclei with E > 10-100 EeV are subjected to photodisintegration Even if primary source composition consisted of single atomic number the propagated spectrum should contain products of photodisintegration Photodisintegration kinematics E A` = E A A`/A m A, m A’, m p >> k ~ 10 MeV k – background photon energy in the nucleus rest frame γ = const k th =f( γ, A) γ = const -photodisintegration chain continues

27. Composition dependence on E max Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Fe primaries α = 2 m = 0 z min = 0 Mean atomic number in the cascade Fe ≡ Σ A i F i / F tot F i – flux of A i Σ max

28. Composition dependence on E max Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Fe and O primaries α = 2 m = 0 z min = 0 Fe O Mean atomic number in the cascade ≡ Σ A i F i / F tot F i – flux of A i Σ max

29. Composition dependence on E max Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Fe and O primaries α = 2 m = 0 z min = 0 Fe O Mean atomic number in the cascade ≡ Σ A i F i / F tot F i – flux of A i Σ max

30. Fitting experimental spectra* Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 F(E, z) = f E - α (1+z) 3+m Θ(E max - E) Θ(z-z min ) Θ(z max -z) Source model Lower energy component (LEC) if needed F LEC (E) = f o (E/E o ) - β exp(-E/E o ) where β = 2.7, E o = 10 EeV, f o – free normalization parameter Here we assume that LEC has galactic origin and so we neglect propagation effects, however one can show that spectrum of the form close to (2) can be obtained as a result of propagation of extragalactic protons or nuclei from the source like (1). + (2) (1) * O. Kalashev, J. Lee, K. Arisaka, G. Gelmini work in preparation The fit is done above 3 EeV

31. HiRes stereo and mono combined fit Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 α = 2.6 ; E max = 10 22 eV; m=0; z min =0 Proton source + LEC

32. HiRes stereo and mono combined fit Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 α = 2.6 ; E max = 10 22 eV; m=0; z min =0 Proton source + LEC α = 2.1÷2.7 (α = 2.5÷2.7 if no LEC assumed) E max ≥ 10 20.2 eV m ≤ 0 Z min <0.01 (50Mpc)

33. HiRes stereo and mono combined fit Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 He source + LEC α = 2.3 ; E max = 5x10 21 eV; m=0; z min =0 α = 2.2÷2.3 E max > 10 20.5 eV Z min <0.02 (100Mpc) -2≤ m ≤ 2 lg(Σ max /eV)

34. HiRes stereo and mono combined fit Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 α = 1.4 ; E max = 2.6x10 20 eV; m=0; z min =0 Fe source + LEC lg(Σ max /eV) α = 1.0÷2.0 E max =10 19.8 - 10 20.5 eV -3≤ m ≤ 3 works fine Z min <0.05 (250Mpc)

35. HiRes stereo and mono combined fit Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 α = 1.4 ; E max = 2.6x10 20 eV; m=0; z min =0 Fe source + LEC lg(Σ max /eV) α = 1.0÷2.0 E max =10 19.8 - 10 20.5 eV -3≤ m ≤ 3 works fine Z min <0.05 (250Mpc) More heavy elements

36. HiRes stereo and mono combined fit Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 α = 1.4 ; E max = 2.6x10 20 eV; m=0; z min =0 Fe source + LEC lg(Σ max /eV) α = 1.0÷2.0 E max =10 19.8 - 10 20.5 eV -3≤ m ≤ 3 works fine Z min <0.05 (250Mpc) More protons

37. Conclusions Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Nuclei-reach sources may explain UHECR spectrum as well as pure proton sources. + Nuclei sources models with low enough E max may be less limited in terms of distance to the closest source (250 Mpc compared to 50 Mpc for HiRes) +/- Lot of parameters to play with _ LEC is normally required _ Composition study made so far by AGASA and HiRes does not support heavy nuclei as primaries for the showers More accurate composition study will clear the picture

38. Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006

39. Protons versus nuclei Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 AGASA, ICRC 2005, K.Shinozaki at al Experimental limitations

40. Appendix Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006

41. AGASA fitting attempts Oleg Kalashev GZK 40, INR RAS, Moscow, 17 May 2006 Iron Iron E max = 2.6x10 20 eV; m=0; z min =0 Protons Protons E max = 10 22 eV; m=0; z min =0