2. Particle Acceleration At Astrophysical Shocks Particle Acceleration At Astrophysical Shocks And Implications for The Origin of Cosmic Rays Pasquale Blasi Arcetri Astrophysical Observatory, Firenze - Italy INAF/National Institute for Astrophysics

3. Outline 1. Phenomenological Introduction: Open Problems in Cosmic Ray Astrophysics 1. Reminder of the basics of particle acceleration at shock waves 2. Maximum energy of accelerated particles and need for self-generated magnetic fields 3. Non linear effects: 3.1 Shock modification due to accelerated cosmic rays: the failure of the test particle approach 3.2 Self-generated magnetic turbulence 3.3 Both Ingredients together 4. Recent developments in the investigation of the self-generated field

4. A Phenomenological Introduction Some Open Problems in Cosmic Ray Astrophysics

5. All Particle Spectrum of Cosmic Rays Knee 2 nd Knee Dip GZK?

6. Proton knee Helium knee Iron Kascade data Hoerandel Astro-ph 0508014

7. A lot of uncertainties depending upon the simulations used for the interpretation of the chemical composition ?

8. The Transition from Galactic to Extra-Galactic Cosmic Rays Two Schools of Thought: THE ANKLE THE TRANSITION TAKES PLACE AT ENERGY AROUND 10 19 eV WHERE THE FADING GALACTIC COMPONENT IS SUBSTITUTED BY AN EXTRA-GALACTIC COMPONENT WHICH CORRESPONDS TO A FLAT INJECTION SPECTRUM THE TWISTED ANKLE THE TRANSITION TAKES PLACE THROUGH A SECOND KNEE AND A DIP WHICH ARE PERFECTLY INTERPRETED AS PARTICLE PHYSICS FEATURES OF BETHE-HEITLER PAIR PRODUCTION. Berezinsky, Gazizov & Grigorieva 2003 Aloisio, Berezinsky, Blasi, Gazizov & Grigorieva 2005

9. The Ankle and The Twisted Ankle The Ankle and The Twisted Ankle

10. The Twisted Ankle Model The Twisted Ankle Model 2 nd knee Dip Depends on the IG magnetic field Galactic CR’s (mainly Iron)

11. The Elusive GZK feature...

12. De Marco, PB & Olinto (2005) It is absolutely reasonable that with current statistics there are large uncertainties on the existence of the GZK feature The spectrum at the end is VERY MODEL DEPENDENT. We might see a suppression that is due to Emax rather to the photopion production The GZK feature and its statistical volatility...

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

14. Statistical Volatility of the SSA signal De Marco, PB & Olinto 2005 THE SSA AND THE SPECTRUM OF AGASA DO NOT APPEAR COMPATIBLE WITH EACH OTHER (5 sigma)

15. Common lore on the origin of the bulk of CRs  Cosmic Rays are accelerated at SNR’s  The acceleration mechanism is Fermi at the 1 st order at the SN shock  If so, we should see the gamma’s from production and decay of neutral pions  Diffusion in the ISM steepens the spectrum: Injection Q(E) -> n(E)~Q(E)/D(E)

16. Reminder of the basics of Particle Acceleration at Shocks

17. x x=0 Test Particle The particle is always advected back to the shock The particle may either diffuse back to the shock or be advected downstream First Order Fermi Acceleration: a Primer Return Probability from UP=1Return Probability from DOWN<1 P Total Return Probability from DOWN G Fractional Energy Gain per cycle r Compression factor at the shock

18. The Return Probability and Energy Gain for Non-Relativistic Shocks Up Down At zero order the distribution of (relativistic) particles downstream is isotropic: f(µ)=f 0 Return Probability = Escaping Flux/Entering Flux Newtonian Limit Close to unity for u 2 <<1! The extrapolation of this equation to the relativistic case would give a return probability tending to zero! The problem is that in the relativistic case the assumption of isotropy of the function f loses its validity. SPECTRAL SLOPE

19. The Diffusion-Convection Equation: A more formal approach The solution is a power law in momentum The slope depends ONLY on the compression ratio (not on the diffusion coef.) Injection momentum and efficiency are free param. SPATIAL DIFFUSION ADVECTION WITH THE FLUID ADIABATIC COMPRESSION OR SHOCK COMPRESSION INJECTION TERM

20. 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 !!! Particle Acceleration at Parallel Collisionless Shocks works ONLY if there is additional magnetic scattering close to the shock surface!

21. A second CRUCIAL issue: the energetics About 10% of the Kinetic energy in the SN must be converted To CRs Summary 1. Particle Acceleration at shocks generates a spectrum E -  with  ~2 2. We have problems achieving the highest energies observed in galactic Cosmic Rays 3. The Cosmic Rays must carry about 10% of the total energy of the SNR shell 4. Where are the gamma rays from pp scattering? 5. Why so few TeV sources? 6. Anisotropy at the highest energies (10 16 -10 17 eV)

22. The Need for a Non-Linear Theory The relatively Large Efficiency may break the Test Particle Approximation…What happens then? The relatively Large Efficiency may break the Test Particle Approximation…What happens then? Non Linear effects must be invoked to enhance the acceleration efficiency (problem with Emax) Non Linear effects must be invoked to enhance the acceleration efficiency (problem with Emax) Cosmic Ray Modified Shock Waves Self-Generation of Magnetic Field and Magnetic Scattering

23. Particle Acceleration in the Non Linear Regime: Shock Modification

24. Why Did We think About This?  Divergent Energy Spectrum At Fixed energy crossing the shock front ρu 2 tand at fixed efficiency of acceleration there are values of Pmax for which the integral exceeds ρu 2 (absurd!)

25.  If the few highest energy particles that escape from upstream carry enough energy, the shock becomes dissipative, therefore more compressive  If Enough Energy is channelled to CRs then the adiabatic index changes from 5/3 to 4/3. Again this enhances the Shock Compressibility and thereby the Modification

26. Approaches to Particle Acceleration at Modified Shocks  Two-Fluid Models The background plasma and the CRs are treated as two separate fluids. These thermodynamical Models do not provide any info on the Particle Spectrum The background plasma and the CRs are treated as two separate fluids. These thermodynamical Models do not provide any info on the Particle Spectrum  Kinetic Approaches The exact transport equation for CRs and the coservation eqs for the plasma are solved. These Models provide everything and contain the Two-fluid models The exact transport equation for CRs and the coservation eqs for the plasma are solved. These Models provide everything and contain the Two-fluid models  Numerical and Monte Carlo Approaches Equations are solved with numerical integrators. Particles are shot at the shock and followed while they diffuse and modify the shock Equations are solved with numerical integrators. Particles are shot at the shock and followed while they diffuse and modify the shock

27. The Basic Physics of Modified Shocks Undisturbed Medium Shock Front v subshock Precursor Conservation of Mass Conservation of Momentum Equation of Diffusion Convection for the Accelerated Particles

28. Main Predictions of Particle Acceleration at Cosmic Ray Modified Shocks Formation of a Precursor in the Upstream plasma Formation of a Precursor in the Upstream plasma The Total Compression Factor may well exceed 4. The Compression factor at the subshock is <4 The Total Compression Factor may well exceed 4. The Compression factor at the subshock is <4 Energy Conservation implies that the Shock is less efficient in heating the gas downstream Energy Conservation implies that the Shock is less efficient in heating the gas downstream The Precursor, together with Diffusion Coefficient increasing with p-> NON POWER LAW SPECTRA!!! Softer at low energy and harder at high energy The Precursor, together with Diffusion Coefficient increasing with p-> NON POWER LAW SPECTRA!!! Softer at low energy and harder at high energy

29. Spectra at Modified Shocks Spectra at Modified Shocks Very Flat Spectra at high energy Amato and PB (2005)

30. Efficiency of Acceleration (PB, Gabici & Vannoni (2005)) Note that only this Flux ends up DOWNSTREAM!!! This escapes out To UPSTREAM

31. Suppression of Gas Heating PB, Gabici & Vannoni (2005) Increasing Pmax Rankine-Hugoniot The suppressed heating might have already been detected (Hughes, Rakowski & Decourchelle (2000))

32. CR frac Mach number M 0 R sub R tot CR frac P inj /mc  4 3.19 3.57 0.1 0.035 3.4 10 -4 10 3.413 6.57 0.47 0.02 3.7 10 -4 50 3.27 23.18 0.85 0.005 3.5 10 -4 100 3.21 39.76 0.91 0.0032 3.4 10 -4 300 3.19 91.06 0.96 0.0014 3.4 10 -4 500 3.29 129.57 0.97 0.001 3.4 10 -4 Summary of Results on Efficiency of Non Linear Shock Acceleration Amato & PB (2005) Be Aware that the Damping Of waves to the thermal plasma Was neglected (on purpose) here! When this effect is introduced The efficiencies clearly decrease BUT still remain quite large

33. Going Non Linear: Part II Coping with the Self-Generation of Magnetic field by the Accelerated Particles

34. The Classical Bell (1978) - Lagage-Cesarsky (1983) Approach Basic Assumptions: 1. The Spectrum is a power law 2. The pressure contributed by CR's is relatively small 3. All Accelerated particles are protons The basic physics is in the so-called streaming instability: of particles that propagates in a plasma is forced to move at speed smaller or equal to the Alfven speed, due to the excition of Alfven waves in the medium. C V A Excitation Of the instability

35. 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 Strong Turbulence F(p)~1

36. 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 10 6 GeV We recall that the knee in the CR spectrum is at 10 6 GeV and the ankle at ~ 3 10 9 GeV. The problem of accelerating CR's to useful energies remains... BUT what generates the necessary turbulence anyway? Wave growth HERE IS THE CRUCIAL PART! Wave damping Bell 1978

37. Standard calculation of the Streaming Instability (Achterberg 1983) There is a mode with an imaginary part of the frequency: CR’s excite Alfven Waves resonantly and the growth rate is found to be:

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

39. Non Linear DSA with Self-Generated Alfvenic turbulence (Amato & PB 2006) Non Linear DSA with Self-Generated Alfvenic turbulence (Amato & PB 2006)  We Generalized the previous formalism to include the Precursor!  We Solved the Equations for a CR Modified Shock together with the eq. for the self-generated Waves  We have for the first time a Diffusion Coefficient as an output of the calculation

40. Spectra of Accelerated Particles and Slopes as functions of momentum Amato & PB (2006)

41. Magnetic and CR Energy as functions of the Distance from the Shock Front Amato & PB 2006

42. Super-Bohm Diffusion Super-Bohm Diffusion Amato & PB 2006 Spectra Slopes Diffusion Coefficient

43. Recent Developments in The Self-Generation of Magnetic Scattering

44. Some recent investigations suggest that the generation of waves upstream of the shock may enhance the value of the magnetic field not only up to the ambient medium field but in fact up to Lucek & Bell 2003 Bell 2004 UPSTREAM SHOCK B B NON LINEAR AMPLIFICATION OF THE UPSTREAM MAGNETIC FIELD Revisited

45. Generation of Magnetic Turbulence near Collisionless Shocks Upstream vsvs SHOCK In the Reference frame of the UPSTREAM FLUID, the accelerated particles look as an incoming current: The plasma is forced by the high conductivity to remain quasi-neutral, which produces a return current such that the total current is Assumption: all accelerated particles are protons

46. The total current must satisfy the Maxwell Equation Clearly at the zero order J ret = J CR Next job: write the equation of motion of the fluid, which now feels a force:

47. In addition we have the Equation for conservation of mass and the induction equation: SUMMARIZING: Linearization of these eqs in Fourier Space leads to 7 eqs. For 8 unknowns. In order to close the system we Need a relation between the Perturbed CR current and the Other quantities

48. Perturbations of the VLASOV EQUATION give the missing equations which defines The conductivity σ (Complex Number) Many pages later one gets the DISPERSION RELATION for the allowed perturbations. There is a purely growing Non Alfvenic, Non Resonant, CR driven mode if k v A < ω 0 2 Bell 2004

49. Re(ω) and Im(ω) as functions of k

50. Saturation of the Growth The growth of the mode is expected when the return current (namely the driving term) vanishes: The growth of the mode is expected when the return current (namely the driving term) vanishes:

51. Bell 2004 Hybrid Simulations used to follow the field amplification when the linear theory starts to fail For typical parameters of a SNR we get δB/B~300

52. Some Shortcomings of this Result 1. Bell (2004) uses the approximation of power law spectra, which we have seen is NOT VALID for modified shocks, as Bell assumes the shock to be. 2. The calculations also assume spatially constant spectra and diffusion properties, which again are not applicable. 3. The maximum energy is fixed a priori, but for modified shocks this is not allowed, because that is the place where most pressure is present.

53. How do we look for NL Effects in DSA? Curvature in the radiation spectra (elentrons in the field of protons) Curvature in the radiation spectra (elentrons in the field of protons) Amplification in the magnetic field at the shock Amplification in the magnetic field at the shock Heat Suppression downstream Heat Suppression downstream

54. Possible Observational Evidence for Amplified Magnetic Fields 240 µG 360  G Volk, Berezhko & Ksenofontov (2005) Rim 1 Rim 2 Lower Fields But may be we are seeing the scale of the Damping (Pohl et al. 2005) ???

55. CONCLUSIONS CONCLUSIONS  Crucial steps ahead are being done in the understanding of the origin of CRs through measurements of spectra and composition of different components  We understood the if shock acceleration is the mechanism of acceleration, NON LINEAR effects have to be taken into account. These effects are NOT just CORRECTIONS.  The CR reaction enhances the acceleration efficiency, hardens spectra at HE, suppressed heating  The maximum energies observed in galactic CRs can be understood only through efficient NL self generation of turbulent fields