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

2. Lecture 1 - plan Short historical introduction to CRs Some observational data Basics of Cosmic Ray Transport – Interaction of particles and waves: why particles diffuse – Diffusion Model and Leaky Box model – Bases of the Supernova paradigm for the origin of CR

3. Lecture 2 - plan Particle Acceleration – Second order Fermi particle acceleration – First order Fermi acceleration at non-relativistic shocks – Bell’s approach – Transport equation approach – The limitations of the test-particle approach Do charged particles act on the waves? – Simple arguments for wave growth

4. Lecture 3 – plan (research oriented) Modern aspects of diffusive shock acceleration – DSA as a non-linear problem – The SNR paradigm for the origin of CRs Magnetic field amplification Maximum energy of accelerated particles Balmer dominated shocks Transport of CR in the Galaxy – Chemical composition – Anisotropy

5. Early History of Cosmic Rays

6. Ionized by what? 1895: X-rays (Roengten) 1896: Radioactivity (Becquerel) But ionization remained, though to a lesser extent, when the electroscope was inserted in a lead or water cavity

7. Victor F. Hess: the 1912 flight Wulf Electroscope (1909) + + 6am August 7, 1912 Aussig, Austria

8. COSMIC Rays

9. The Spectrum of Cosmic Rays Knee 2 nd knee? Dip/Ankle GZK? 140 GeV 2.5 TeV 20 TeV 100 TeV 450 TeV

10. The Chemical Composition of Cosmic Rays

11. Unstable Elements Simpson and Garcia-Munoz 1988 Balloon flights For Cosmic Rays Laboratory Experiment Age of Cosmic Rays about 10-15 million years

12. PROPAGATION OF COSMIC RAYS PROPAGATION TIME IN THE DISC PROPAGATION TIME ALONG THE ARMS OF THE GALAXY PROPAGATION TIME IN THE HALO ALL THESE TIME SCALES ARE EXCEEDINGLY SHORT TO BE MADE COMPATIBLE WITH THE ABUNDANCE OF LIGHT ELEMENTS DIFFUSIVE PROPAGATION

13. A qualitative look at the diffusive propagation of CR If is the mean distance between two scattering centers, then the time necessary for a particle to travel a distance R is Mean distance between Scattering centers From the measured abundance of light elements and from the decay time of Unstable elements we know that the diffusion time on scales of about 1 kpc Must be about 5 million years. It immediately follows that Diffusion Coefficient

14. The Leaky Box Model The diffusion of CR can be described through an equation similar to that of Heat transfer Ignorance of Diffusion + Assumption of stationarity H Since D(E) grows with E the observed spectrum n(E) is always steeper than the injected spectrum q(E) injection Leakage

15. Primary/Primary and Secondary/Primary ratios (CREAM 2008)

16. Dependence of the Diffusion Coefficient on energy – a leaky box approach From the previous plot we see that at low energies P/S ~ 0.1 which implies X(E) ~ 5 g cm -2 As a function of energy:

17. Electrons (and positrons)

18. Leaky Box with Energy Losses When the propagating particles are electrons, energy losses may become important:

19. Positron ratio Positrons are only produced as secondary products: While CR propagate from their sources to Earth throughout the Galaxy

20. Quick look at the positron excess PRIMARY PROTONS: PRIMARY ELECTRONS: (b= d for diffusion, b=1 for losses) SECONDARY POSITRONS INJECTION: SECONDARY POSITRONS EQUILIBRIUM: CANNOT GROW!

21. - SUBTLETIES OF PROPAGATION (Shaviv et al. 2009) - REACCELERATION OF SECONDARY PAIRS IN SNR (Blasi 2009, Blasi&Serpico2009, Alhers et al. 2009) - PULSARS (Hooper, Blasi & Serpico 2008, Grasso et al. 2009, BUT see pre-PAMELA work from Bueshing et al. 2008)

23. COSMIC RAY TRANSPORT: Basic Concepts CHARGED PARTICLES IN A MAGNETIC FIELD DIFFUSIVE PARTICLE ACCELERATION COSMIC RAY PROPAGATION IN THE GALAXY AND OUTSIDE

24. Charged Particles in a regular B-field In the absence of an electric field one obtains the well known solution: LARMOR FREQUENCY

25. A few remarks… THE MAGNETIC FIELD DOES NOT CHANGE PARTICLE ENERGY -> NO ACCELERATION BY B FIELDS A RELATIVISTIC PARTICLE MOVES IN THE z DIRECTION ON AVERAGE AT c/3

26. Motion of a charged particle in a random magnetic field z ┴ THIS CHANGES ONLY THE X AND Y COMPONENTS OF THE MOMENTUM THIS TERM CHANGES ONLY THE DIRECTION OF P Z =Pμ

27. SITTING IN THE REFERENCE FRAME OF THE THE WAVE, THERE IS NO ELECTRIC FIELD…AND IF THE WAVE IS SLOW COMPARED WITH THE PARTICLE (THIS IS GENERALLY THE CASE) THEN THE WAVE IS STATIONARY AND Z=v μ t RATE OF CHANGE OF THE PITCH ANGLE IN TIME

28. Diffusive motion ONE CAN EASILY SHOW THAT BUT:

29. Many waves IN GENERAL ONE DOES NOT HAVE A SINGLE WAVE BUT RATHER A POWER SPECTRUM: THEREFORE INTEGRATING OVER ALL OF THEM: OR IN A MORE IMMEDIATE FORMALISM: RESONANCE!!!

30. DIFFUSION COEFFICIENT THE RANDOM CHANGE OF THE PITCH ANGLE IS DESCRIBED BY A DIFFUSION COEFFICIENT FRACTIONAL POWER (δB/B 0 ) 2 =G(k res ) THE DEFLECTION ANGLE CHANGES BY ORDER UNITY IN A TIME: PATHLENGTH FOR DIFFUSION ~ vτ SPATIAL DIFFUSION COEFF.

31. PARTICLE SCATTERING EACH TIME THAT A RESONANCE OCCURS THE PARTICLE CHANGES PITCH ANGLE BY Δθ ~ δ B/B WITH A RANDOM SIGN THE RESONANCE OCCURS ONLY FOR RIGHT HAND POLARIZED WAVES IF THE PARTICLES MOVES TO THE RIGHT (AND VICEVERSA) THE RESONANCE CONDITION TELLS US THAT 1) IF k >1/rL PARTICLES HARDLY FEEL THE WAVES

32. The Diffusion Equation In its simplest version, the diffusion of CR from a source can be described through an equation similar to that of Heat transfer The Green function of this partial differential equation is simple to calculate if D(E,r)=D(E):

33. H 2h RdRd disc Halo Particle escape In general: R d > H >> h ASSUMPTIONS: 1.Instantaneous injection of particles in a point in the disc 2.Infinitely thin disc, h  0 and infinitely extended disc, R d  ∞ 3. Free escape of the particles from above and below the halo In order to fulfill this boundary condition the correct Green function is

34. Contribution of many sources Integral in tau is analytical In the limit H/R d <<1 Diffusion time You can compare this result with the less fundamental leaky box model

35. The Diffusion Model is not fully equivalent to the Leaky Box Model Diffusion Leaky Box CR primary CR electrons (with dominant Losses) Similar situation for nuclei when spallation dominates

36. The Supernova remnant paradigm in numbers Let us assume that the rate of SN in the Galaxy is R and each produces a power law spectrum of protons N(E)=K (E/E 0 ) - g and we take E 0 ~m~1 GeV and energies are taken to be normalized to E 0. The observed spectrum of protons at Earth is and taking D(E)~( r /3GV) d where r is the rigidity: and comparing with the observed spectrum Order 10 51 erg Relatively large efficiencies required

37. A curiosity Life on Earth is based on CNO elements, as well as heavier elements such as Fe (your blood is red!) All of these elements are formed ONLY in stars and liberated into space by the explosion of supernovae… But supernovae are usually formed in regions of star formation, or molecular Clouds… These clouds form by gravitational collapse…BUT their gravitational collapse time would be too short to form stars in the first place… UNLESS… the clouds are very weakly ionized (remember the electroscopes?) and this allows magnetic fields in the ISM to oppose and slow down collapse COSMIC RAYS, produced in SN explosions, also create the conditions for the stars to be created and later explode