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Physics at the End of the Cosmic-Ray Spectrum

Physics at the End of the Cosmic-Ray Spectrum. Theory Summary Talk. J. R. Jokipii and Frank Jones. First, look at the general background physics:. basic empirical diffusion model. Ginzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998 ( GALPROP code ).

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Physics at the End of the Cosmic-Ray Spectrum

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  1. Physics at the End of the Cosmic-Ray Spectrum Theory Summary Talk J. R. Jokipii and Frank Jones

  2. First, look at the general background physics:

  3. 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

  4. energy balanceGinzburg & Syrovatskii 1964 • required source power3×1038 erg/(s kpc2) • SN kinetic energy 2×1039 erg/(s kpc2) • (Wsn=1051 erg, νGal = 0.03 yr-1 • local SN rate 50 Myr-1kpc-2) ~ 15% - efficiency of CR acceleration in SNRs acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility) b) delay between nuclear synthesis and acceleration (Soutoul test: 59Ni 59Co, high obs. 59Co/56Fe gives δt > 105yr Leske 1993) other Galactic accelerators: pulsars [2×1050 (10 ms/τ)2 erg], stellar winds [2×1038 erg/s kpc2], Galactic GRBs [1051 erg/105 yr], micro quasars, Galactic Center …

  5. Basic Theoretical Themes or Issues: 1. Acceleration Mechanisms 2. Sources and Knees 3. The Sharpness of the Knee (s)

  6. Acceleration Mechanisms: Diffusive Shock Acceleration

  7. maximum energy condition of acceleration, critical Pecklet number (parameter of modulation) SNR Wsn=1051erg • maximum value -typical in interstellar medium ism n0=1cm-3 diffusion should be anomalously slow near the shock (upstream and downstream) cosmic ray streaming instability in shock precursor Bell 1978, Lagage & Cesarsky 1983, McKenzie & Vőlk 1982, Achterberg 1983, Vőlk et al. 1988, Fedorenko 1990, Bell & Lucek 2000, 2001

  8. MHD simulations demonstratemagnetic field amplification Development of previous modelling, Lucek & Bell (2000)

  9. Filamentation & self-focussing B E=0 R proton beam j velocity vbeam E=-uxB E=0 Magnetic field growth Focuses CR, evacuates cavity Ideal for focussing CR into beam

  10. Non-spherical aspects of SNRs Ion injectiononly for instantane-ously quasi-parallel shocks nB«π/2  Stochastic self-limitation of injection rate through nonlinear wave pro –duction: from ηװ ≈ 10-2 to ηeff ≈ 10-4  Plus systematic reduction of ion injection. Strong wave production only locally in “polar” regions Confirmation by Rothenflug et al. 2004using XMM on SN 1006  Hadronic -rayemission dipolar for uniform external B1Renormalization of spherically symmetric flux  Synchrotron emission also overall dipolar for uniform external B1 Völk et al.(2003)

  11. Magnetic field amplification by accelerating particles in shocks • Accelerated particles tend to stream ahead upstream  Instability (A.R. Bell 1978) • Nonlinear evolution  Bohm limit of scattering •  Mean field amplification(Bell & Lucek 2001; Bell 2004, 2005) • High field Beff Depression of IC emission •  Faster scattering  Increase of pmax for nuclei • Instabilities driven by dominant nuclear component

  12. SN 1006 • Accreting White Dwarf (Type Ia): Mej≈ 1.4 M • Age = 999 yr • Angular diameter ≈ 0.5 degrees Koyama et al. (1995) ASCA Extended source for-ray instruments: H.E.S.S. upper limit < 0.02 Crab From other measurements: NH = 0.3 – 0.05 cm-3Distance = 1.8 – 2.2 kpc Winkler et al. (2003)

  13. The Importance of the Magnetic-Field Angle • Acceleration to high energies: • Parallel Shocks • Very slow • Efficient • Perpendicular Shocks • Much faster • Also efficient (we point out in this talk that there is no injection problem) • New numerical simulations • Hybrid simulations (self consistent) show efficient acceleration of thermal ions by a perpendicular shock

  14. What about Injection and the limit of diffusive shock acceleration? • An often-invoked injection criterion is • This assumes, for no good reason, that there is NO motion normal the average magnetic field • In general, particles move normal to the field, and this is important for the injection problem

  15. 2. Different Sources:

  16. Lessons from the heliosphere • ACE energetic particle fluences: • Smooth spectrum • composed of several distinct components: • Most shock accelerated • Many events with different shapes contribute at low energy (< 1 MeV) • Few events produce ~10 MeV • Knee ~ Emax of a few events • Ankle at transition from heliospheric to galactic cosmic rays R.A. Mewaldtet al., A.I.P. Conf. Proc. 598 (2001) 165

  17. 1st Tooth Fairy 2nd Tooth Fairy Two Component CR Spectrum 1 0 Flux X E2.7 -1 10 11 12 13 14 15 16 17 18 19 20 21 Log E (eV)

  18. 2nd knee knee ankle CR flux evolution from a local GRB: simple power-low D(E) (conservs the number of particles in rdif3) Injected CR energy: 1052 ergs at 1 kpc Emax=1021 erg,  = 2.2 D(1 PeV)= 1029 cm2 s-1,  =0.6 Galactic halo size: 10 kpc

  19. 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

  20. “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

  21. x 0.1 x 0.01 Tibet EE/1.23 All-particle spectrum:Knee ~3 PeV

  22. SECOND KNEE and EXTRAGALACTIC PROTONS Second knee automatically appears in the total spectrum (galactic +extragalactic) due to low-energy flattening of extragalactic spectrum, which appears at Ec~ 1×1018 eV.This energy is universal for all propagation modes (rectilinear or diffusive) and it is determined by transition from adiabatic to e+e- -energy losses . g diffusive propagationLemoine 2004, Aloisio, V.B. 2004 rectilinear propagation

  23. Unusually High Maximum p Energies at Sgr A East • With 4mG field Sgr A East shock can accelerate particles to 1019(R/10pc) Z eV in a perpendicular shock configuration (Jokipii 1982 & ApJ 1987) • p-p cooling-limited p energy is ~1021 eV • Time-limited p energy is ~1020 eV (given 10 000 year age)

  24. 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

  25. 3. How Sharp is a Knee ?

  26. Conclusions: Theory is in good shape, but there are too many alternatives. Need more observations, chosen specifically to distinguish between theories!

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