Cosmic Ray Transport in the Galaxy Vladimir Ptuskin IZMIRAN, Russia

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

2. Ncr ~ 10-10 cm-3- total number density wcr ~ 1.5 eV/cm3- energy density Emax ~ 3x1020 eV - max. observed energy δcr ~ 10-3 at 1012 - 1014 eV - anisotropy rg ~ 1E/(Z×3×1015 eV) pc - Larmor radius ulsar

3. source spectrum E-2.7 cosmic ray density Ncr T source spectrum E-(2.0 … 2.4) Qcr escape time E-(0.3 … 0.6) two power laws: source spectrum + propagation secondary species:Qcr,2 = nvσ21N1 d, 3He, Li, Be, B … p, e+ escape length:X = ρvT ~ 10 g/cm2at 1 GeV/nucleon

4. basic empirical diffusion model Ginzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998 (GALPROPcode) surface gas density 2.4 mg/cm2 cosmic-ray halo Sun escape length: SNR 2H galactic disk r =20 kpc - plain diffusion break of D at 5 GV - diffusion + reacceleration Va = 30 km/s

5. some explanations of peak in sec./prim. ratio: Xe v • convective transport • Jones 1979 problem: too broad sec/prim peak R-0.6 wind or turbulent diffusion resonant diffusion E • distributed reacceleration • Simon et al. 1986; Seo & Ptuskin 1994 • Dpp~ p2Va2/D, D ~ vR1/3 • - Kolmogorov spectrum of turbulence Icr ΔE problem: low flux of secondary antiprotons weak reacceleration strong reaccele- ration E • wave damping on cosmic rays nonlinear cascade W(k) problem: cascade availability VSP, Moskalenko et al. 2004 damping W(k) ~ k-3/2 D ~ vR1/2 Iroshnikov - Kraichnan cascade D0 ~ vR1/2 k 1/1020cm 1/1012cm

6. Sina et al. 2001

7. radioactive secondaries 10Be (2.3 Myr) 26Al (1.3 Myr) 36Cl (0.43 Myr) 54Mn (0.9 Myr) 14C (0.0082 Myr) decay time at rest d gas density primaries D = (2 – 5)×1028 cm2/s at 0.5 GeV/n H ~ 4 kpc, Tesc ~ 70 Myr Ptuskin & Soutoul 1998

8. flat component of secondary nuclei produced by strong SNR shocks Wandel et al. 1987, Berezhko et al. 2003 production by primaries inside SNRs reacceleration in ISM by strong shocks grammage gained in SNR volume filling factor of SNRs grammage gained in interstellar gas Berezhko et al. 2003 RUNJOB 2003 preliminary plain diff. reacceleration nism = 0.003…1 cm-3 Bohm diffusion TSNR = 105 yr standard plain diff. reacceleration

9. “microscopic” theory of cosmic-ray diffusion resonant interaction rg~ 1 / k p 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 < B > + δB 1017 eV 109 eV 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. 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 Zirakashvili et al. 1996, 2002 Ptuskin et al. 1997 uinf = 500km/s Rsh = 300 kpc stable secondaries: radioactive secondaries: effective halo size H(p/Z)

11. empirical spectrum of galactic cosmic ray sources: problem for theory of diffusive shock acceleration high energy asymptotic R-2.15 low energies, R < 30 GV plane diffusion D ~ βR0.54 R-2.35Davis et al. 2000 R-2.50Moskalenko et al. 2004 Q concave spectrum E diffusion with reacceleration D ~ βR0.3 R-2.40(1+(2/RGV)2)-1/2Jones et al. 2001 Q flattened at low energy E

12. spectrum of very high energy electronsShen 1970, Cowsik & Lee 1979, Nishimura et al. 1979, 1997, Dorman et al. 1985,Aharonian et al. 1995, Kobayashi et al. 2004 plain diffusion Vela S147 Cygnus SN185 HB21 G65.3 Monogem G347.3 reacceleration Golden et al. 1984 Tang et al. 1984 Barwick et al.1998 Kobayashi et al. 1999 Boezio et al. 2000 Tori et al. 2001 Vela tloss = 2.3×105yr(ETeV)-1 Cygnus Emax = 100 TeV Monogem G65.3 HB21 TeV

13. l = 1Zkpc data:

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

15. alternative at ultra-high energies J·E3 TUNKA collaboration 2005 extragalactic p Fe p two components: Galactic (heavy) + extragalactic (protons ?) Bird et al. 1993 E, eV limit for acceleration In Galactic sources knee 1015 1017 1019 J·E3 Fe pure Galactic origin: Pochepkin et al. 1998 p problems with acceleration and anisotropy switch to free exit from the Galaxy knee E, eV 1015 1017 1019

16. Tdisk kyr trajectory calculations Zirakashvily et al. 1998 simple magnetic field structure: average field random field B0 = 1 μG, a = 1.5 kpc, r1 = 0.5 kpc Br/B0 = 3, L = 100 pc, R = 20 kpc p p

17. 3x1019 eV pure Galactic mixed

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

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.