1. Pasquale Blasi INAF/Arcetri Astrophysical Observatory 4th School on Cosmic Rays and Astrophysics UFABC - Santo André - São Paulo – Brazil

2. WHAT NEXT? We have found the elegant results of the theory of DIFFUSIVE SHOCK ACCELERATION in the TEST PARTICLE approximation and also found some of its limitations: 1.TOO LARGE EFFICIENCIES TO EXPECT TEST PARTICLES 2.THE EXPECTED DIFFUSION COEFFICIENT LEADS TO TOO LOW E MAX 3.IF PARTICLES DIFFUSE THEY ALSO LEAD TO WAVE GROWTH ALL THESE PHENOMENA SUGGEST THAT WE NEED TO MOVE BEYOND THE TEST PARTICLE APPROXIMATION NON LINEAR THEORY OF DIFFUSIVE SHOCK ACCELERATION

3. Dynamical Reaction of Accelerated Particles PRECURSOR Undisturbed Medium Shock Front v subshock Precursor Conservation of Momentum Transport equation for cosmic rays SUBSHOCK Velocity Profile

4. WHAT SHOULD BE EXPECT? High p UPSTREAM Velocity SUBSHOCK PRECURSOR 1.PARTICLES WITH HIGH P FEEL LARGER COMPRESSION FACTOR THEN LOW P PARTICLES 2. THE TOTAL COMPRESSION BECOMES LARGER THAN 4 3. THE SPECTRUM SHOULD BE NO LONGER A POWER LAW! 4. AT HIGH P THE SLOPE SHOULD BE FLATTER THAN 2 !!! 5. THE GAS BEHIND THE SHOCK SHOULD BE COOLER THAN FOR AN ORDINARY SHOCK R tot R sub

5. INJECTION Ideal Collisionless Shock (More) Real Collisionless Shock rL rL WHICH PARTICLES AND HOW MANY PARTICLES ENTER THE ACCELERATION CYCLE? THIS IS THE LEAST UNDERSTOOD ASPECTS OF ALL !

6. INJECTION…cont’d f(p) p Maxwellian for the Downstream gas P inj =  p th,2 Relation between R sub, ξ and η T 2 T 1 OUTPUT OF THE CALCULATIONS

7. SHOCK HEATING and SPECTRA PB, Gabici & Vannoni 2005 SHOCK MODIFICATION REDUCED HEATING

8. Particle Diffusion  Wave Growth Remember that we showed that a particle diffuses along a direction z where there is an ordered magnetic field B 0 because of a small perturbation d B perpendicular to B 0. In this process the particles lose momentum in the z direction and this p Is transferred to the d B waves. This equals the momentum gained by the waves: And imposing a perfect balance: In the ISM this is ~10 -3 yr -1 but close to a shock front the grow can be even larger!!! d B IS AMPLIFIED BY PARTICLES

9. SMALL PERTURBATIONS IN THE LOCAL B-FIELD CAN BE AMPLIFIED BY THE SUPER-ALFVENIC STREAMING OF THE ACCELERATED PARTICLES Particles are accelerated because there is High magnetic field in the acceleration region High magnetic field is present because particles Are accelerated efficiently Without this non-linear process, no acceleration of cr to High energies (and especially not to the knee!) Bell 2004, Amato & PB 2009

10. Successes of the SNR paradigm 1. Observation of X-ray rims TYPICAL THICKNESS OF FILAMENTS: ~ 10 -2 pc The synchrotron limited thickness is:

11. Chandra Cassiopeia A Chandra SN 1006

13. Successes of the SNR paradigm 2. Max energy and the knee p max /mc 10 7 10 6 10 5 10 4 50 100 150 200 M0 M0 MAXIMUM MOMENTUM PROTON KNEE Bohm Diff without B-amplification PB, Amato & Caprioli, 2007 Magnetic field amplification leads to higher values of the Maximum energy

14. Observed proton spectrum Data from Bertaina et al. 2008

15. Successes of the SNR paradigm 3. evidence for a CR precursor ? PRECURSOR REGION RIM Morlino, Amato, PB & Caprioli 2010

16. Successes of the SNR paradigm 4. Balmer dominated shocks DOWNSTREAM ION Temperature LOWER because of CR acceleration NEUTRAL Temperature HIGHER because of charge exchange ++ BROAD BALMER LINE IS NARROWER NARROW BALMER LINE IS WIDER

17. Observations of Balmer dominated shocks Helder et al. 2009 INFERRED EFFICIENCY of CR ACCELERATION 50-60% !!!

18. Observation of Balmer dominated shocks broader narrow Balmer line Sollerman et al. 2003 Broadening of the narrow line hints to a mechanism for heating of the neutrals upstream on scales shorter than ionization scales TURBULENT HEATING CHARGE EXCHANGE UPSTREAM

19. Observation of Balmer dominated shocks: Possible evidence for a CR precursor in the narrow Balmer line A broadened narrow Ha line from upstream shows that the neutrals and ions have some level of charge exchange  different bulk velocities and/or T’s between the two components  CR precursor

21. HADRONIC LEPTONIC Morlino, Amato & PB 2009 RXJ1713

22. RXJ1713 with fermi data 1.e/p Equilibration downstream? (Morlino et al. 2009) 2.Very low value of K ep at given time 3.Lines from non-equilibrium ionization ? (Ellison et al. 2010) 4.What are those Fermi data points telling us?

23. A Puzzling situation Courtesy of S. Funk Most SNR detected by Fermi have steep spectra (some exceptions, such as RXJ1713) The predicted spectra would naively require steep diffusion D(E)~E 0.7 in conflict with anisotropy measurements

24. A small print in the theory of DSA: a point as important as poorly known Velocity of scattering centers in the shock frame NOT velocity of the plasma In general the velocity of scattering centers is small and there is no problem BUT AMPLIFIED MAGNETIC FIELD  high velocity ??? VERY MACROSCOPIC CONSEQUENCES ON SPECTRA!

25. ROLE OF NUCLEI Caprioli, PB, Amato 2010 The dynamical reaction of nuclei on the shock structure turns out to be VERY IMPORTANT

26. ROLE OF NUCLEI: The knee Caprioli, PB, Amato 2010

27. WHERE DO GALACTIC CR end? 1.The SNR paradigm hints to a galactic CR spectrum ending at ~a few 10 17 eV 2.Observations of chemical composition also suggest the same trend ?

28. PROPAGATION OF PROTONS from extragalactic sources 100 Mpc GZ K DIP

29. HOW DOES THE SPECTRUM LOOK LIKE? THE DIP Berezinsky et al. 2005 Aloisio et al. 2007 Dip structure

30. HISTORICAL INTERPRETATION OF THE TRANSITION: THE ANKLE

31. ALTERNATIVE INTERPRETATION OF THE TRANSITION: MIXED COMPOSITION Allard et al. 2005-2008

32. UNDERSTANDING THE DIFFERENCE: DIP VS MIXED From Kampert 2008

33. UNDERSTANDING THE DIFFERENCE: DIP VS ANKLE Aloisio, Berezinsky, PB & Ostapchenko 2008 DIP ANKLE

34. X MAX and RMS OF X MAX Auger HiRes