1. Cosmic Ray Acceleration in Supernova Remanants 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. energy balance Ginzburg & Syrovatskii 1964 required source power 3×10 38 erg/(s kpc 2 ) SN kinetic energy 2×10 39 erg/(s kpc 2 ) (W sn =10 51 erg, ν Gal = 0.03 yr -1 local SN rate 50 Myr -1 kpc -2 ) ~ 15% - efficiency of CR acceleration in SNRs other Galactic accelerators: 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], micro quasars, Galactic Center … acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility) b) delay between nuclear synthesis and acceleration (Soutoul test: 59 Ni 59 Co, high obs. 59 Co/ 56 Fe gives δt > 10 5 yr Leske 1993 )

4. 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 diffusio n k res ~1/r g Larmor radius

5. 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 2000, 2001

6. Nagano & Watson 2000 Bohm limit galactic extra- galactic? knee standard assumption δB ~ B ism Bohm diffusion

7. Berezhko & Elliison 1999 nonlinear shock modification by cosmic ray pressure for high Mach shocks Axford 1977, 1981 Eichler 1984 Berezhko et al. 1996 Malkov et al. 2000 not power law spectrum at the shock

8. 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.

9. 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 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 Aharonian et al. 2004 Cas A Aharonian et al. 2001 RX J0852-46 (“Vela jr”) G338.3-0.0; G23.3-0.3; G8.7-0.1 Aharonian et al. 2005 e γ synchrotron e γ inverse Compton ε γ = ε 0 (E e /m e c 2 ) 2 p π0π0 γ SNR not confirmed by HESS (2004) !

10. confrontation with observations problems: -Galactic sources should work up to (1-3)×10 18 eV (Fe ?) -no VHE gamma-rays from not very young SNRs t snr ≥ 3×10 3 yr -average cosmic ray source spectrum γ s = 2.1 - 2.4 (depending on propagation model)

11. Ptuskin & 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 under extreme conditions: E max ≈ 10 17 Z(u sh /3×10 4 km/s) 2 ×(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 μG -strong cosmic-ray streaming instability (δB B 0 ), Bell & Lucek 2000, 2001 - non-linear wave interactions of Kolmogorov type in shock precursor Ptuskin & Zirakashvili 2003, 2005 δB > B 0 δB < B 0 maximum momentum of accelerated protons abandonment of Bohm limit hypotheses < >

12. 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 -7.0 ( Chevalier – Nadyozhin ) SN rate step function delta function

13. hot bubble 0.013 cm -3, 3μG ism R=60pc n=1cm -3 dense RSG wind Weaver et al. 1977 Chevalier & Liang 1989 KASCADE SNII Roth et al. 2003 · E knee ≈ 6×10 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 Ptuskin & Zirakashvili 2004 expected break of all particle spectrum δγ = 0.5

14. Nagano & Watson 2000 galactic extra- galactic? knee dispersion of SNs? reacceleration? early transition to extragalactic CRs? 2 nd knee

15. 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

16. Summary Maximum energy of accelerated particles strongly depends on SNR age in the presence of cosmic-ray streaming instability accompanied by non-linear wave dissipation. E max can reach 10 17 Z eV in very young SNRs (with corresponding increase of random magnetic field to up to 10 -3 G) and may fall down to less than 10 11 Z eV at the end of Sedov stage. Standard estimate of E max based on the Bohm limit calculated for interstellar magnetic filed strength is not justified. This gives a clue to understanding why SNRs are not bright in very high energy γ-rays at t > 3×10 3 yr. Average source spectrum ~ p -4 up to ~ 6×10 15 Z eV is formed during adiabatic (Sedov) stage of SNR evolution provided constant fraction of incoming gas momentum flux goes to cosmic ray pressure at the shock. Steep power-law spectrum above this energy is produced at the preceding ejecta-dominated stage. The knee observed at 4×10 15 eV may mark the transition from ejecta- dominated to adiabatic evolution of SNR shocks which accelerate cosmic rays.

17. strong streaming instability and non-linear wave interactions in shock precursor ( ): abandonment of Bohm limit hypotheses Ptuskin & Zirakashvili 2003 eq. for cosmic rays (1D, u=const) eq. for mhd waves (w k is spectral energy density) supersonic convection growth rate …D ∇ f in agreement with Bell & Lucek 2001 linear damping nonlinear wave interactions of Kolmogorov type ~ kδB(>k)/(4πρ) 1/2 Verma et al. 1996 eq. for maximum momentum

18. diffusion coefficient: growth rate:

19. streaming instability in shock precursor (no damping) Alfven velocity cosmic-ray pressure wave energy density weak random field:strong random field: characteristic velocity of waves ~ 0.5 for very strong shock