1. Cosmic Ray Transport in the Galaxy Vladimir Ptuskin IZMIRAN, Russia

2. ulsarulsar N cr ~ 10 -10 cm -3 - total number density w cr ~ 1.5 eV/cm 3 - energy density E max ~ 3x10 20 eV - max. observed energy δ cr ~ 10 -3 at 10 12 - 10 14 eV - anisotropy r g ~ 1E/(Z×3×10 15 eV) pc - Larmor radius

3. source spectrum N cr T Q cr E -2.7 cosmic ray density escape time E -(0.3 … 0.6) source spectrum E -(2.0 … 2.4) two power laws: source spectrum + propagation secondary species: Q cr,2 = nvσ 21 N 1 d, 3 He, Li, Be, B … p, e + escape length: X = ρvT ~ 10 g/cm 2 at 1 GeV/nucleon

4. SNR Sun cosmic-ray halo galactic disk r =20 kpc 2H basic empirical diffusion model Ginzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998 (GALPROP code) surface gas density 2.4 mg/cm 2 - plain diffusion break of D at 5 GV - diffusion + reacceleration V a = 30 km/s escape length:

5. convective transport Jones 1979 XeXe E distributed reacceleration Simon et al. 1986; Seo & Ptuskin 1994 D pp ~ p 2 V a 2 /D, D ~ vR 1/3 - Kolmogorov spectrum of turbulence v R -0.6 wind or turbulent diffusion resonant diffusion I cr E strong reaccele- ration weak reacceleration ΔEΔE some explanations of peak in sec./prim. ratio: problem: too broad sec/prim peak problem: low flux of secondary antiprotons wave damping on cosmic rays VSP, Moskalenko et al. 2004 W(k) Iroshnikov - Kraichnan cascade D 0 ~ vR 1/2 damping nonlinear cascade W(k) ~ k -3/2 D ~ vR 1/2 1/10 20 cm1/10 12 cm k problem: cascade availability

6. Sina et al. 2001

7. radioactive secondaries 10 Be (2.3 Myr) 26 Al (1.3 Myr) 36 Cl (0.43 Myr) 54 Mn (0.9 Myr) 14 C (0.0082 Myr) decay time at rest d gas density primaries D = (2 – 5)×10 28 cm 2 /s at 0.5 GeV/n H ~ 4 kpc, T esc ~ 70 Myr Ptuskin & Soutoul 1998

8. flat component of secondary nuclei produced by strong SNR shocks Wandel et al. 1987, Berezhko et al. 2003 Berezhko et al. 2003 production by primaries inside SNRsreacceleration in ISM by strong shocks volume filling factor of SNRs grammage gained in SNR grammage gained in interstellar gas standard plain diff. reacceleration plain diff. reacceleration n ism = 0.003…1 cm -3 Bohm diffusion T SNR = 10 5 yr RUNJOB 2003 preliminary

9. “microscopic” theory of cosmic-ray diffusion p + δB resonant interaction r g ~ 1 / k Larmor radius resonant wave number parallel diffusion Jokipii 1966 anomalous perpendicular diffusion Jokipii & Parker 1970 Chuvilgin & Ptuskin 1993 Giacolone & Jokipii 1999 Casse et al 2001 Hall diffusion Armstrong et al 1995 W(k) ~ k -5/3 … k -3/2 hot topic: anisotropic Alfvenic turbulence Shebalin et al. 1983, Higdon 1984, Bieber et al. 1994, Montgomery & Matthaeus 1995, Goldrreich & Shridhar 1995, Lazarian et al. 2003 Kolmogorov Kraichnan 10 9 eV10 17 eV

10. galactic wind driven by cosmic rays Ipavich 1975, Breitschwerdt et al. 1991, 1993 cosmic ray streaming instability with nonlinear saturation CR emissivity of Galactic disk per unit area u inf = 500km/s R sh = 300 kpc effective halo size H(p/Z) stable secondaries : radioactive secondaries : Zirakashvili et al. 1996, 2002 Ptuskin et al. 1997

11. empirical spectrum of galactic cosmic ray sources: problem for theory of diffusive shock acceleration R -2.35 Davis et al. 2000 R -2.50 Moskalenko et al. 2004 plane diffusion D ~ βR 0.54 diffusion with reacceleration D ~ βR 0.3 high energy asymptotic R -2.15 low energies, R < 30 GV R -2.40 (1+( 2/R GV ) 2 ) -1/2 Jones et al. 2001 concave spectrum flattened at low energy Q E Q E

12. spectrum of very high energy electrons Shen 1970, Cowsik & Lee 1979, Nishimura et al. 1979, 1997, Dorman et al. 1985, Aharonian et al. 1995, Kobayashi et al. 2004 Golden et al. 1984 Tang et al. 1984 Barwick et al.1998 Kobayashi et al. 1999 Boezio et al. 2000 Tori et al. 2001 plain diffusion reacceleration Vela Cygnus Monogem G65.3 HB21 Vela Cygnus S147 Monogem G65.3 HB21 SN185 G347.3 t loss = 2.3×10 5 yr(E TeV ) -1 E max = 100 TeV TeV

13. data: l = 1 Z kpc

14. knee as effect of propagation Hall diffusion in average Galactic magnetic field Ptuskin et al.1993 Kalmykov & Pavlov 1999 Candia et al. 2003 Galactic disk Candia et al 2003

15. alternative at ultra-high energies two components: Galactic (heavy) + extragalactic (protons ?) Bird et al. 1993 pure Galactic origin: Pochepkin et al. 1998 p Fe p extragalactic p 10 15 10 17 10 19 10 15 10 17 10 19 E, eV knee switch to free exit from the Galaxy limit for acceleration In Galactic sources problems with acceleration and anisotropy J·E 3 TUNKA collaboration 2005

16. trajectory calculations Zirakashvily et al. 1998 simple magnetic field structure: T disk kyr p p B 0 = 1 μG, a = 1.5 kpc, r 1 = 0.5 kpc B r /B 0 = 3, L = 100 pc, R = 20 kpc average field random field

17. 3x10 19 eV pure Galactic mixed

18. Nagano & Watson 2000 galactic extra- galactic? knee dispersion of SNs? reacceleration? early transition to extragalactic CRs? diffusion approximation (protons) 2 nd knee trajectory claculations

19. Conclusion Diffusion model provides reasonably good description of cosmic ray propagation in the Galaxy even under simplified assumptions on cosmic ray transport coefficients and geometry of propagation region. The choice between plain diffusion model and the model with reacceleration is difficult to make: Plain diffusion model predicts too large anisotropy at E > 100 TeV. Diffusion model with reacceleration is bearably compatible with data on cosmic ray anisotropy. Source spectrum in the plain diffusion model is close to prediction of diffusive shock acceleration theory. Source spectrum in the model with reacceleration is considerably steeper.