1. Cosmic Ray Acceleration Beyond the Knee up to the Ankle in the Galactic Wind Halo V.N. Zirakashvili 1,2 1 Institute for Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Russian Academy of Sciences, 142190 Troitsk, Moscow Region, Russia 2 Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany Enhanced Star/CR formation in spiral arms and recurrent wind compressions Production of CR Population beyond the “knee” Shock formation in wind halo Reacceleration of disk CRs at large distance from Galaxy Role of termination shock

2. CR sources in Galactic disk short-lived / small-scale p max  p knee Energy spectrum steepens beyond knee Continuity problem for spectrum Problems: Proposed Solution: Reacceleration in extended Galactic Wind beyond knee Spiral Arms generate Galactic Wind Interaction Regions Shocks Large spatial and temporal Scales Spectral Continuity possible Shocks in the Galactic Wind Flow: Termination Shock

3. CR spectrum

4. Astrophysical reasons of the “knee”: CR sources versus CR propagation “knee” in CR spectrum at 10 16 eV Kulikov & Khristiansen 1958 Drift of CR particles in inhomogeneous galactic magnetic field Ginzburg, Syrovatsky 1963 Drift velocity V d  E, CR diffusion coefficient D  E m, m=0.2  0.7 in the standard diffusion model Drift motion is negligible at small energies, but becomes essential at larger energies and can explain the “knee” Ptuskin et al 1993, Kalmykov & Pavlov, 1999 Power-low CR source spectrum up to 10 17 eV was assumed Change in energy dependence of diffusion can produce the same effect

5. CR sources: Diffusive Shock Acceleration Krymsky 1977; Axford, Leer, & Scadron 1977; Bell 1978 Very attractive feature: power-low spectrum of particles accelerated,  =(  +2)/(  -1), where  is the shock compression ratio, for strong shocks  =4 and  =2 Maximum energy for SN: D  0.1u sh R sh, in the Bohm limit D=D B =cr g /3 and for interstellar magnetic field Magnetic field amplification by CR streaming instability (Bell & Lucek 2001) E max =Z10 17 eV However, rather steep spectrum beyond the knee  =4.5, Ptuskin & Zirakashvili 2005 A&A 429, 755

6. One can conclude that 1.It seems that Supernovae are the best candidate for CR acceleration. 2.However, at present we can expect that SN effectively produce CR particles up to the “knee” region. For larger energies acceleration is ineffective. 3.In this case some mechanism is needed for producing CRs beyond the knee. We suggest reacceleration by shocks in the Galactic Wind flow.

7. Mean Galactic Wind Flow Cosmic rays are produced in the Galactic disk.  CR   gas   mag  1 eV cm -3 Gas is confined by gravity, CRs are not CR scale height is larger then the scale height of thermal gas Galactic Wind flow driven by CR pressure gradient R da (1 TeV) ≃ 15 kpc Knee particles diffusive R da (1 PeV) ≃ 150 kpc Strong Termination shock: energy independent CR escape Ipavich, 1975 Breitschwerdt, McKenzie, & Völk, 1991 Zirakashvili, Breitschwerdt, Ptuskin, & Völk, 1996

8. Kinetic energy power in the Galactic wind Distance to the Termination Shock,  u 2  P IG, P IG –is the intergalactic pressure Magnetic field in the Wind is almost azimuthal at large distances,  is the galactic colatitude,  is the angular velocity of Galactic rotaion Maximum energy of accelerated (or confined) particles in the Bohm limit: D B  uR s, D B =cr g /3-Bohm diffusion coefficient

9. Cosmic Ray Acceleration on the Termination Shock was introduced by Jokipii and Morfill in 1987 PROBLEMS 1.The condition of efficient acceleration on the Termination Shock D<<uR s coinsides with condition of strong CR modulation in the Galactic Wind flow. So it is difficult to observe particles accelerated near the Terminaination Shock in the Galaxy. 2. If the Termination Shock reaccelerates galactic CRs, their number density near the shock is smaller in comparison with the density in the Galaxy. Thus it is difficult to obtain continiuty of the CR spectrum.

10. Cosmic ray propagation in the galactic wind flow CR scattering and diffusion is determined by the spectrum of Alfven waves Self-consistent CR diffusion coefficient Ptuskin, Völk, Zirakashvili, & Breitschwerdt 1997 Cosmic ray streaming instability of Alfven waves is balanced by nonlinear damping Exact value depends on CR galactic sources power and nonlinear Alfven wave damping D ‖  10 27 p/(Zm p c) cm 2 s -1

11. Cosmic Ray Propagation in the Galactic Wind Flow Equation for CR momentum distribution N. It is normalized as n CR =4  p 2 dpN diffusion Adiabatic energy gain or losses advection Reacceleration by spiral shocks

12. CR Reacceleration on the Galactic Wind Termination Shock Numeric results u=500 km s -1  =4 Q(p)  p -4 exp(-p 2 /p 2 max ) P max =310 6 Zm p c Wind velocity Termination shock compression ratio galactic CR source spectrum 1)Spherical termination shock, R s =300 kpc, D ‖ =2.510 25 p/(Zm p c) 2) Nonspherical termination shock (possible since CR sources are concentrated near galactic center) R s =150(1+3cos 2  ) 1/2 kpc, D ‖ =10 26 p/(Zm p c(1+3cos 2  )) cm 2 s -1 Zirakashvili, & Völk 2004

13. CR proton spectrum at the spherical termination shock CR proton spectrum in the Galaxy modulation Not very good but the simplest model R s =300 kpc, D ‖ =2.510 25 p/(Zm p c)(a factor 40 smaller in order to get effective acceleration)

14. CR proton spectrum in the Galaxy CR proton spectra at different colatitudes of nonspherical termination shock  =0  =  /4  =  /2 CR spectrum in the Galaxy is continuous because maximum energy depends on colatitude

15. Galaxy fast rotator, no backward shocks. Spiral pattern = Wave, rotates with angular velocity that differs from Galactic one. Spiral shocks are slipping across B-field. Wind CR-dominated:  no injection (only reacceleration). Fast wind from the active region on the Sun surface overtakes slow wind. Compression region and forward and backward shocks are formed at large distances. Spiral arms play the role of active regions in the Galaxy, since massive young stars and correspondent SN explosions are concentrated there. Difference: Spiral shocks: Solar Wind-Galactic Wind analogy Corotating Interaction Region

16. HST M51 Spiral Arms

17. Reacceleration by spiral shocks in the galactic wind flow Particles with energies smaller then Z10 17 eV are locked inside the Termination Shock and reaccelerated by almost perpen- dicular spiral shocks. Relatively fast CR diffusion inside the termination shock. Strong turbulence and slow CR diffusion beyond the Termination Shock. Völk, & Zirakashvili 2004 A&A 417, 807

18. velocity Gas pressure Results of numeric 2D MHD calculations of Slipping Interaction Region (SIR) shocks Spiral modulation of CR sources in the Galactic disk results in modulation of G.Wind velocity Nonlinear steepening produces shocks

19. CR pressure velocity Gas pressure

20. ---- velocity CR pressure Gas pressure B t 2 /4 

21. forward shocks (Sawtooth) = Slipping Interaction Regions (SIRs) velocity Reacceleration in

22. Reacceleration by saw-tooth shock system Adiabatic losses between shocks Reacceleration on the shock fronts  u – velocity jump on the shock front,  s – shock compression ratio, L – distance between neighboring shocks

23. Disk-CR sources with Q(p)  p -4 exp(-p/p max ) Reacceleration by about factor 30 in rigidity From p max = 3 x Z x 10 6 m p c, up to ∼ Z x 10 17 Volt. All-particle spectrum Chemical composition fixed at energy 9 x 10 14 eV (Kampert et al. 2001) p He Fe C

24. Summary 1.Supersonic Galactic Wind flow is bounded by a so- called Termination Shock that can accelerate or confine CR particles up to energies Z10 17 eV. 2. Spiral structure of our Galaxy results in spiral shocks formation at large distances. 3. Shocks in the Galactic Wind flow can provide CR reacceleration beyond the “knee”. 4. Acceleration at the Termination Shock can be effective if CR diffusion coefficient is small enough. 5. It is easy to obtain the spectral continuity in the spiral shock reacceleration model (Völk, & Zirakashvili 2004).