1. Supernova Remnants as Cosmic Rays Accelerators Vladimir S. Ptuskin Institute for Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences (IZMIRAN), Troitsk, Moscow region 142190, Russia

2. ulsarulsar N cr ~ 10 -10 cm -3 - total number density w cr ~ 1.5 eV/cm 3 - energy density E max ~ 3×10 20 eV - max. observed energy L cr ~ 5×10 40 erg/s - Galactic luminosity in CR 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 2H flat-halo diffusion model Ginzburg & Ptuskin 1976 Berezinskii et al 1990 Strong & Moskalenko 1998 surface gas density 2.4 mg/cm 2 pure diffusion diffusion + distributed reaccele- ration in ISM Jones et al 2001 Alfven velocity

5. Energy balance local galactic CR energy density 1.5 eV/cm 3 needed source power 3×10 38 erg/s kpc 2 SN kinetic energy 2×10 39 erg/s kpc 2 (W sn =10 51 erg, 50 Myr -1 kpc -2 ) ~ 15% efficiency of CR acceleration + pulsars 2×10 50 (10 ms/τ) 2 erg + stellar winds 2×10 38 erg/s kpc 2 + Galactic GRBs 10 51 erg/10 5 yr + Galactic Center

6. SNR blast waves SN II, SN Ib/c –core collapse of massive stars SN Ia – thermonuclear explosion of white dwarf in binary system Mechanical energy W sn ~ 10 51 erg (10 53 for hypernova) - Free expansion (ejecta-dominated stage): t < 300 yr, u sh = 5×10 8 – 3×10 9 cm/s, R < 2 pc - Adiabatic deceleration (Sedov stage): t = 10 3 - 3×10 4 yr, u sh ~ (W sn /n ism ) 1/5 t -3/5 - Radiation cooling: t > 10 5 yr, R > 20 pc Acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility) b) delay between nuclear synthesis and acceleration high obs. 59Co/56Fe – δt > 10 5 yr Soutoul et al. 1978, Leske 1993

7. Diffusive shock acceleration SNR Fermi 1949, Krymsky 1977, Bell 1978 u sh D(p) shock -average gain of momentum distribution function (test particles) time of acceleration CR intensity resonant diffusion k res ~1/r g Larmor radius

8. Maximum energy condition of acceleration, critical Pecklet number (parameter of modulation) SNR W sn =10 51 erg ism n 0 =1cm -3 -maximum value -typical in interstellar medium 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 2001, VSP & Zirakashvili 2003

9. Nagano & Watson 2000 Bohm limit galactic extra- galactic? knee standard assumption δB ~ B ism Bohm diffusion might be better for SN explosion in progenitor wind Vőlk & Biermann 1988

10. x u(x) u sh u sh / r D(p)/u precursor subshock upstreamdownstream - ∇ P cr Nonlinear shock modification by CR pressure nonmodified shock x sh cosmic ray density

11. Berezhko & Elliison 1999 not power law spectrum for high Mach number shocks Axford 1977, 1981 Eichler 1984 Berezhko et al. 1996 Malkov et al. 2000

12. overall CR spectrum Berezhko & Völk 2000

13. Cassiopeia A is bright at all energies of the electromagnetic spectrum. This composite image shows Cassiopeia A at many different wavelengths: radio polarization in red (VLA), X- rays in green (CHANDRA) and optical in blue (HST). Notice the outer shock, visible only in X-rays, as the thin green rim most visible at the top of the image. Also notice the bright ring which is visible at all three wavelengths, and the many different filamentary structures seen at each wavelength. The compact remains of the exploded star are visible only in X-rays, as the bright green spot slightly below and to the left of the geometric center of the bright ring.

14. observations radio emission ν MHz = 4.6 B μG E e,GeV 2 E = 50 MeV – 30 GeV (100 GeV for IR) γ = 1.9 – 2.5 W e = 10 48 – 10 49 erg Ginzburg & Syrovatskii 1964 Shklovsky 1976 nonthermal X-rays ε keV = 1 B μG (E e /120 TeV) 2 ε max ~ 100 TeV SN1006 Koyama et al. 1995 Cas A Allen et al. 1997 RX J1713-39 Koyama et al. 1997 RX J0852-46 (“Vela jr”) Slane et al 2001 γ-rays (π 0 ) Ε = 30-3000 MeV γ Cygni, IC443 Esposito et al. 1996 Sturner & Dermer 1996 TeV γ – rays electrons/protons ε max ~ 100 TeV SN1006 Tanimori et al 1998 RX J1713 Muraishi et al. 2000 Cas A Aharonian et al. 2001 Only upper limits on TeV γ-rays from many SNRs with ages > 3×10 3 yr Buckley et al. 1998, Aharonian et al. 2002 e γ synchrotron e γ inverse Compton ε γ = ε 0 (E e /m e c 2 ) 2 p π0π0 γ SNR

15. SN1006 Tanimori et al. 2001

16. Problems: - Galactic sources should work up to (1-3)×10 18 eV (Fe ?) (reacceleration may help: Axford 1994, Bell 1992, Bykov & Toptygin 2001, Vőlk & Zirakashvili 2004; dispersion of SN parameters: Sveshnikova 2003) -no VHE gamma-rays from not very young SNRs t snr ≥ 3×10 3 yr (Buckley et al. 1998, Aharonian et al. 2002) -cosmic ray source spectrum γ s = 2.0 - 2.4 (depends on propagation model)

17. VSP & Zirakashvili 2003 W sn = 10 51 erg, B ism = 5 μG, n 0 = 0.4 cm -3 ξ cr = 0.5, κ = 0.04, a = 0.3 strong streaming instability and non-linear wave interactions in shock precursor: under extreme conditions: E max ≈ 10 17 Z(u sh /3×10 4 km/s) 2 ×(κ/0.1)(ξ cr /0.5)M ej 1/3 n 1/6 eV δB max ≈ 10 -3 (u sh /3×10 4 km/s)n 1/2 G maximum momentum of accelerated particles: abandonment of Bohm limit hypotheses

18. Random field produced by cosmic-ray streaming instability in shock precursor Alfven velocity cosmic-ray pressure wave energy density weak random field:strong random field: characteristic velocity of waves Bell & Lucek 2001 VSP & Zirakashvili 2003

19. Average source spectrum spectrum at the shock instantaneous SNR luminosity in run-away cosmic rays average cosmic-ray source spectrum adiabatic stage Q ~ ξ cr ν sn W sn p -4 (Sedov) - universal spectrum ! ejecta-dominated stage SNII in RSG wind: Q ~ p -6.5 at ρ star ~ r -10 SNI in uniform medium: Q ~ p -7 (Chevalier – Nadyozhin) SN rate

20. hot bubble 0.013 cm -3, 3μG ism R=60pc n=1cm -3 RSG wind Weaver et al. 1977 Chevalier & Liang 1989 KASCADE SNII Roth et al. 2003 · E knee ≈ 7×10 15 Z eV, ~ ξ cr W sn M 1/2 (M ej u w ) -1 E max ≈ 4×10 16 Z eV at t min = 7 days ρ star ~ r -10 ∙ M=10 -5 u w =10km/s R w =2pc W sn = 10 51 erg, ξ cr = 0.5 VSP & Zirakashvili 2004

21. Other proposals on acceleration beyond the knee: Reacceleration by multiple shocks Reacceleration in plerions SNR pulsar wind SNR Ω δΦ δΦ = 4×10 15 Z eV – 10 19 Z eV Bell 1991, 2000, Berezhko 1993 u Ｅ θ = B φ u r /c OB association u=3×10 3 km/s B=10 -5 G R=30 pc f ~ 1/p 3 t a ~ R/(F sh u) at D i < uR ~ D/(F sh u 2 ) at D i > uR R u E max ~ 10 17 Z eV Axford & Ip 1991, Bykov & Toptygin 1990, 2001 Klepach et al. 2000 termination shock Crab pulsarfew msec pulsar

22. Galactic wind u R acceleration at termination shock Jokipii & Morfill 1985, 1991 R = 300 kpc, u = 400 km/s E max = 3×10 18 Z eV galactic disk SNR acceleration by traveling shocks and interaction regions Völk & Zirakashvili 2004

23. Nagano & Watson 2000 galactic extra- galactic? knee