1. Open Problems with Very High Energy Cosmic Rays Pasquale Blasi National Institute for Astrophysics Arcetri Astrophysical Observatory Firenze, Italy TeV Workshop, Madison, August 2006

2. Outline Some observational facts –Spectrum –Chemical Composition –Anisotropies Where do CRs become extragalactic? –The dip –The Ankle –Mixed Composition Open issues with acceleration of CRs –Non linear Fermi Acceleration –Relativistic shocks Help of multifrequency observations

3. Observations I: Spectrum Knee 2 nd Knee Dip GZK? Observations – I: Spectrum

4. The actual discrepancy is at 1-2 standard deviations

5. De Marco, PB and Olinto 2006

6. Chemical Composition

7. Proton knee Helium knee Iron ?

8. From A. Watson (2006) Knee Region TRANSITION ? DIP ANKLE

9. Anisotropies

10. Observations – III: Anisotropy HiRes-I data with E>10 19.5 eV with mono (52 events versus 47 of AGASA) The banana-shaped error boxes are [4.9-6.1]x[0.4-1.5] degrees HiRes stereo data (271 events with E>10 19 eV versus about 900 of AGASA). The error boxes are about 0.6 degrees wide. Only 27 events above 4 10 19 eV

11. Small Scale Anisotropies PB & De Marco 2003 10 -5 Mpc -3

12. Statistical Volatility of the SSA signal De Marco, PB & Olinto 2006 THE SSA AND THE SPECTRUM OF AGASA DO NOT APPEAR COMPATIBLE WITH EACH OTHER (5 sigma)

13. De Marco, PB and Olinto 2006 >4 10 19 eV >10 20 eV 10 5 km 2 sr yr

14. De Marco, PB and Olinto 2006 15 years of Operation of Auger South

15. Transition from Galactic to Extragalactic Cosmic Rays The Ankle scenario The Dip scenario The mixed Composition scenario

16. Transition at the Ankle 1.A steep GAL spectrum encounters a flat EX-GAL spectrum 2.The GAL spectrum should extend to >10 19 eV and is expected to be Fe dominated 3.The chemical composition of the EX-GAL part can have heavy nuclei Aloisio, Berezinsky, PB, Gazizov, Grigorieva, Hnatyk 2006

17. Transition at the Dip 1.STILL TRUE that a STEEP GAL spectrum meets a FLAT EX-GAL spectrum 2. The Low energy flattening due to either pair prod. or most likely magnetic horizon 3.The GAL spectrum is expected to END at <10 18 eV (mainly Fe) 4.The EX-GAL spectrum is predicted to be mainly protons at E>10 18 eV (No more that 15% He allowed) 5. Steep injection spectrum unless complex injection Aloisio, Berezinsky, PB, Gazizov, Grigorieva, Hnatyk 2006 A DIP IS GENERATED DUE ONLY TO PAIR PRODUCTION. ITS POSITION IS FIXED BY PARTICLE PHYSICS INTERACTIONS

18. Kachelriess and Semikoz 2005 Aloisio, Berezinsky, PB, Grigorieva and Gazizov 2006

19. Transition due to Mixed Composition Allard et a. 2006 1.Particles at injection have an arbitrary chemical composition 2.Relatively flat spectra at injection are required 3.The inferred galactic spectrum has a cutoff at energies about the same as in the DIP scenario 4. At 10 19 eV there is still an appreciable fraction of heavy elements 5. At 10 20 eV, as in all other models, there are mainly protons

20. Some Open Problems with Acceleration of Cosmic Rays The lesson we can learn from galactic cosmic rays…

21. maximum energy A CRUCIAL ISSUE: the maximum energy of accelerated particles 1. The maximum energy is determined in general by the balance between the Acceleration time and the shortest between the lifetime of the shock and the loss time of particles 2. For the ISM, the diffusion coefficient derived from propagation is roughly For a typical SNR the maximum energy comes out as FRACTIONS OF GeV !!! Similar numbers would be obtained for galactic sources of similar age and in similar conditions. PARTICLE ACCELERATION AT ASTROPHYSICAL SHOCKS IS EFFICIENT ONLY IF PARTICLES GENERATE THEIR OWN SCATTERING CENTERS!!! NON-LINEAR PARTICLE ACCELERATION

22. Pitch angle scattering and Spatial Diffusion The Alfven waves can be imagined as small perturbations on top of a background B-field The equation of motion of a particle in this field is In the reference frame of the waves, the momentum of the particle remains unchanged in module but changes in direction due to the perturbation: The Diffusion coeff reduces To the Bohm Diffusion for F(p)~1

23. Maximum Energy a la Lagage-Cesarsky In the LC approach the lowest diffusion coefficient, namely the highest energy, can be achieved when F(p)~1 and the diffusion coefficient is Bohm-like. For a life-time of the source of the order of 1000 yr, we easily get E max ~ 10 4-5 GeV Wave growth HERE IS THE CRUCIAL PART! Wave damping Bell 1978

24. Maximum Level of Turbulent Self- Generated Field Stationarity Integrating Breaking of Linear Theory… For typical parameters of a SNR one has δB/B~20. UPSTREAM SHOCK B B

25. Possible Observational Evidence for Amplified Magnetic Fields 240 µG 360  G Volk, Berezhko & Ksenofontov (2005) Rim 1 Rim 2 Lower Fields Add to all this, the enourmous Predictions of Non-linear Diffusive Shock Acceleration!!! 1.Curved spectra 2.Heating suppression downstream 3.B-field amplification

26. Bell 2004 Hybrid Simulations (PIC+MHD) used to follow the field Amplification when the linear theory starts to fail For typical parameters of a SNR we get δB/B~300 The Max energy for a SNR becomes ~10 17 eV for protons and 3 10 18 eV for Iron nuclei (for Bohm diffusion)

27. General lesson and concerns The max energy as estimated through Hillas-like plots may well be incorrect by orders of magnitude if the ambient field is used instead of the self-generated field δB/B>>1 is predicted by a quasi-linear approach, though confirmed by PIC PIC carried out in very simple approach. No nonlinear effects taken into account in these PIC simulations… THERE ARE NO such calculations in the case of RELATIVISTIC SHOCKS

28. Particle Acceleration At Relativistic Shocks

29. Peculiar Aspects of Particle Acceleration at relativistic shocks we find that p 2 = (1/3)  2 and  2 = 1/3 No equipartition ultrarelativistic pressureless For a homogeneous magnetic field downstream NO PARTICLE is expected to return back to the shock. The turbulent structure of the B-field is crucial! Taub’s relations

30. E ~4  2 E Reflection at the relativistic mirror works ONLY at the first interaction. After that Relativistic mirror vs Fermi acceleration

31. Universal or non-universal… Most calculations of particle acceleration at relativistic shocks lead to the so-called UNIVERSAL SPECTRUM This important result is obtained by solving the same equation: ASSUMPTIONS: the scattering is diffusive and in the so-called Small Pitch Angle Scattering (SPAS) regime (D µµ is constant ONLY for the isotropic case)

32. The transport equation in the most general case is Vietri 2003 PB & Vietri 2005 Arbitrary Scattering Function For instance, in the case of Large Angle Scattering: Blasi & Vietri 2005 Universal

33. More non-universality… Isotropic turbulence Anisotropic Turbulence Lemoine et al. 2006 Again, one ends up again in a situation of quasi-coherent perpendicular Field downstream: PARTICLES DO NOT RETURN → SPECTRUM STEEPENS Caveat: what if the field upstream does not have a coherence length? (e.g. Scale invariant spectrum 1/k)

34. The role of multifrequency observations For Galactic CRs the role of Multi-ν observations is obvious (e.g. gamma, X, radio from SNR,…) A similar role would be desirable for UHECRs –Interactions inside the source during the acceleration –Interactions during the propagation from source to observer The sources of UHECRs might be identified through the SSA of the arrival directions, but this depends on Extra-Gal B- field, chemical composition, Gal B-field, etc... Correlations with Large Scale Structures (Longo et al. 2006) would also be helpful.

35. A simulated Auger South Sky De Marco

36. CONCLUSIONS A lot of indirect evidence is accumulating in favor of SNRs being sources of CRs in the Galaxy, up to <10 18 eV…but no iron solid proof The transition between Gal to Extra-Gal CRs takes place either at the second knee or at the ankle (very important for the origin of UHECRs; crucial the composition) Acceleration at shock fronts presents us with exciting new developments and challenges to reach high E max even of relevance for UHECRs The spectrum of UHECRs is being investigated by Auger…just some patience is needed. It would be precious to gather information about the composition in the transition region UHECRs are still orphans…may be something even bigger than Auger South will be needed to “see” the sources (Auger North, Super Auger, EUSO-like?)