Cosmic Ray Acceleration Beyond the Knee up to the Ankle in the Galactic Wind Halo

1. Cosmic Ray Acceleration Beyond the Knee up to the Ankle in the Galactic Wind Halo V.N. Zirakashvili1,2 1Institute for Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Russian Academy of Sciences, 142190 Troitsk, Moscow Region, Russia 2Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany • Enhanced Star/CR formation in spiral arms and recurrent wind compressions • Production of CRPopulation beyond the “knee” • Shock formation in wind halo • Reacceleration of disk CRs at large distance from Galaxy • Role of termination shock

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

3. CR spectrum

4. Astrophysical reasons of the “knee”: CR sourcesversusCR propagation “knee” in CR spectrum at 1016 eV Kulikov & Khristiansen 1958 Drift velocity VdE, CR diffusion coefficient DEm, m=0.20.7 in the standard diffusion model Drift of CR particles in inhomogeneous galactic magnetic field Ginzburg, Syrovatsky 1963 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 Change in energy dependence of diffusion can produce the same effect Power-low CR source spectrum up to 1017 eV was assumed

5. CR sources: Diffusive Shock Acceleration Very attractive feature: power-low spectrum of particles accelerated, =(+2)/(-1), where  is the shock compression ratio, for strong shocks =4 and =2 Krymsky 1977; Axford, Leer, & Scadron 1977; Bell 1978 Maximum energy for SN: D0.1ushRsh, in the Bohm limit D=DB=crg/3 and for interstellar magnetic field Magnetic field amplification by CR streaming instability (Bell & Lucek 2001) Emax=Z•1017 eV However, rather steep spectrum beyond the knee =4.5, Ptuskin & Zirakashvili 2005 A&A 429, 755

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

7. 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 Mean Galactic Wind Flow • Rda(1 TeV) ≃ 15 kpc Ipavich, 1975 Breitschwerdt, McKenzie, & Völk, 1991 Zirakashvili, Breitschwerdt, Ptuskin, & Völk, 1996 • Knee particles diffusive • Rda(1 PeV) ≃ 150 kpc • Strong Termination shock: energy independent CR escape

8. Kinetic energy power in the Galactic wind Distance to the Termination Shock, u2 PIG, PIG –is the intergalactic pressure Magneticfield 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: DBuRs, DB=crg/3-Bohm diffusion coefficient

9. Cosmic Ray Acceleration on the Termination Shock was introduced by Jokipii and Morfill in 1987 PROBLEMS • The condition of efficient acceleration on the • Termination Shock D<<uRs 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‖1027 p/(Zmpc) cm2 s-1

11. Cosmic Ray Propagation in the Galactic Wind Flow Equation for CR momentum distribution N. It is normalized as nCR=4p2dpN Reacceleration by spiral shocks advection Adiabatic energy gain or losses diffusion

12. CR Reacceleration on the Galactic Wind Termination Shock Numeric results Zirakashvili, & Völk 2004 u=500 km s-1 =4 Q(p)p-4exp(-p2/p2max) Pmax=3•106 Zmpc Wind velocity Termination shock compression ratio galactic CR source spectrum • Spherical termination shock, • Rs=300 kpc, D‖=2.5•1025 p/(Zmpc) 2) Nonspherical termination shock (possible since CR sources are concentrated near galactic center) Rs=150(1+3cos2)1/2 kpc, D‖=1026 p/(Zmpc(1+3cos2)) cm2s-1

13. Not very good but the simplest model CR proton spectrum in the Galaxy CR proton spectrum at the spherical termination shock modulation Rs=300 kpc, D‖=2.5•1025 p/(Zmpc)(a factor 40 smaller in order to get effective acceleration)

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

15. Spiral shocks: Solar Wind-Galactic Wind analogy 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. Corotating Interaction Region Spiral arms play the role of active regions in the Galaxy, since massive young stars and correspondent SN explosions are concentrated there. 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). Difference:

16. M51 Spiral Arms HST

17. Reacceleration by spiral shocks in the galactic wind flow 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 Particles with energies smaller then Z•1017eV are locked inside the Termination Shock and reaccelerated by almost perpen-dicular spiral shocks.

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

19. velocity CR pressure Gas pressure

20. ---- velocity Bt2/4 CR pressure Gas pressure

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

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

23. Disk-CR sources with Q(p)  p-4 exp(-p/pmax) • Reacceleration by about factor 30 in rigidity From pmax = 3 x Z x 106mpc, up to ∼ Z x 1017Volt. C All-particle spectrum Fe (Kampert et al. 2001) He p Chemical composition fixed at energy 9 x 1014 eV

24. Summary • Supersonic Galactic Wind flow is bounded by a so-called Termination Shock that can accelerate or confine CR particles up to energies Z•1017 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).