1. Acceleration of Cosmic Rays E.G.Berezhko Yu.G.Shafer Institute of Cosmophysical Research and Aeronomy Yakutsk, Russia Introduction General properties of Cosmic Ray (CR) acceleration Diffusive shock acceleration Acceleration of CRs in Supernova Remnants (SNRs) Nonthermal emission of individual SNRs SNRs as Galactic CR source Some aspects of UHECR production in GRBs and extragalactic jets Conclusions

2. Cosmic Rays Earth Atmosphere V.Hess (1912) I ≈ 1 particle/(cm 2 s) I ~ ε -γ γ ≈ 2.7 L CR ≈ 3×10 41 erg/s CR origin problem: i) CR source (?) ii) Acceleration mechanism (?)

3. Cosmic Rays (CRs) = atomic nuclei = charged particles Electric field is needed to generate (accelerate) CR population High value large scale electric field is not expected in space plasma Electric field in space plasma is created due to the movement of magnetized clouds For efficient CR production (acceleration) the system, which contains strong magnetic field and sufficient number of rapidly moving clouds, is needed General remarks

4. vfvf vivi Elastic scattering: vivi vfvf CR vivi vfvf E w scattering center w E Head-on collision: Δv = v f – v i >0 Overtaken collision: Δv = v f – v i <0 w w = 0 v f = v i v f > v i w = 0 Δv = 0 Larger rate of head-on then overtaken collisions efficient CR acceleration × B B E = -[w B]/c CR scattering on moving magnetized clouds v >> w

5. General remarks CR acceleration, operated in the regions of powerful sources, are the most meaningful The main form of energy available in the space is kinetic energy of large scale supersonic plasma motion (stellar winds, expanding supernova remnants, jets) Most relevant acceleration mechanisms are those, which directly transform the energy of large scale motion into the population of high energy particles Intense formation of CR spectra are expected to take place at the shocks and in shear flows

6. Solar wind

7. Diffusive shock acceleration of CRs log N CR log p p-p-  = (  + 2)/(  -1) shock compression ratio Krymsky 1977 Bell 1978 ΔpΔp scattering centers

8. y x w Frictional Acceleration of Cosmic Rays Berezhko (1981) mean scattering time Shear plasma flow acceleration rate CR Frictional CR acceleration is expected to be very efficient in relativistic/subrelativistic jets scattering center

9. Energetic requirements to CR sources

10. Requirements to the CR acceleration mechanism J obs ~ ε – γ obs ~ J s /τ esc γ obs = 2.7 Τ esc ~ ε -μ ( μ = 0.5 - 0.7) J S ~ε - γ S γ S = γ obs – μ = 2 – 2.2 observed CR spectrum CR residence time inside the Galaxy source CR spectrum

11. Supernova explosions Supernova explosions supply enough energy to replenish GCRs against their escape from the Galaxy If there is acceleration mechanism which convert ~10% of the explosion energy into CRS

12. Cosmic Ray Flux knee ankle GZK cutoff (?) Possible GCR sources: SNRs Reacceleration (?) Extragalactic (?) SNRs (?)

13. Cosmic Ray diffusive acceleration in Supernova Remnants shock compression ratio Krymsky 1977 Bell 1978 for strong shock E SN ~ 10 51 erg

14. Nonlinear kinetic (time-dependent) theory of CR acceleration in SNRs Gas dynamic equations CR transport equation Suprathermal particle injection Gas heating due to wave dissipation Time-dependent (amplified) magnetic field Applied to any individual SNR theory gives at any evolutionary phase t>0 : nuclear N p (p,r), N He (p,r), … and electron N e (p,r) momentum and spatial distributions, which in turn can be used for determination of the expected nonthermal emissions F γ (ε γ )

15. Nonlinear kinetic model: basic equations Hydrodynamic equations CR transport equations for protons and electrons CR pressure source term ρ(r, t) – gas density w(r, t) – gas velocity P g (r, t) – gas pressure f (p, r, t) – CR distribution function Berezhko, Yelshin, Ksenofontov (1994) CR diffusion coefficient Synchrotron loss time (Krymsky, 1964) u = V s - w

16. Particle spectrum in/near acceleration region injection rate (parameter) η > 10 -5 → efficient CR production

17. Nonlinear effects due to accelerated CRs Modification of the shock structure due to CR pressure gradient Non power law (concave) CR spectrum Magnetic field amplification (Lucek & Bell, 2000) Increase of maximum CR energy Increase of π 0 -decay gamma-ray emission over IC emission

18. CR spectrum inside SNR test particle limit p maximum CR momentum due to geometrical factors (Berezhko 1996) p p max ~ R S V S B

19. Main nonthermal emission produced by Cosmic Rays (how one can “see” CR sources) Synchrotron radiation B e radio X-ray Inverse Compton scattering e   gamma-rays Nuclear collisions p N   gamma-rays

20. Nonthermal emission of SNRs Test for CR acceleration theory Determination of SNR physical parameters: - CR acceleration efficiency - Interior magnetic field B

21. Relevant SNR parameters SNR age t known for historical SNRs ISM density N H influences SNR dynamics and gamma-ray production; deduced from thermal X-rays magnetic field B influences CR acceleration & synchrotron losses; deduced from fit of observed synchrotron spectrum; expected to be strongly amplified B >> B ISM injection rate η (fraction of gas particles, involved in acceleration) influences accelerated CR number, shock modification, CR spectral shape; deduced from observed shape of radio emission

22. CR spectrum inside SNR test particle limit p e radio X-ray due to synchrotron losses Steep radio-synchrotron spectrum S ν ~ν -α (  >0.5,  >2) is indirect evidence of i) efficient proton acceleration and ii) high magnetic field B>>10  G α = (γ – 1)/2

23. Cassiopeia A Tuffs ( 1986), VLA Type Ib Distance 3.4 kpc Age 345 yr Radius 2 pc Circumstellar medium: free WR wind + swept up RSG wind + free RSG wind

24. Circumstellar medium 1 2 r, pc 10 1 N g, cm -3 BSG wind RSG wind shell MS → RSG → BSG → SN Borkowski et al. (1996) d = 3.4 kpc M ej = 2 M Sun E SN = 0.4×10 51 erg current SN shock position CSM number density

25. Berezhko et al. (2003)

26. Synchrotron Emission from Cassiopeia A Experiment: radio (Baars et al. 1977), 1.2 mm data (Mezger et al. 1986), 6  m data (Tuffs et al. 1997), X-ray data (Allen et al. 1997) α ≈ 0.8 Proton injection rate η = 3×10 --3 Interior magnetic field B d ≈ 0.5 mG Strong SN shock modification Steep concave spectrum at ν < 10 12 Hz Smooth connection with X-ray region (ν > 10 18 Hz)

27. Magnetic field inside SNRs ρ RsRs Line of sight 0 -R s RsRs J J Emission (X-ray, γ-ray) due to high energy electrons L Low field High (amplified) field Unique possibility of magnetic field determination! ρ ρ

28. Chandra Cassiopeia A Chandra SN 1006 Filamentary structure of X-ray emission of young SNRs -consequence of strongly amplified magnetic field, leading to strong synchrotron losses

29. Experiment (Vink & Laming 2003) confirms high internal magnetic field extracted from the fit of volume Integrated synchrotron flux (Berezhko, Pühlhofer & Völk 2003) Theory: Berezhko & Völk (2004) L Projected X-ray brightness of Cassiopeia A For strong losses emissivity scale brightness scale angular distance B d = 500 μG B d = 10 μG direct evidence for magnetic field amplification

30. Integral gamma-ray energy spectrum of Cas A Components: Hadronic (π 0 ) Inverse Compton (IC) Nonthermal bremsstrahlung (NB) Confirmation of HEGRA measurement is very much needed Already done by Magic (ICRC, Merida 2007)!

31. SNR RX J1713.7-3946 X-rays (nonthermal) ROSAT (Pfeffermann & Aschenbach 1996 ) ASCA (Koyama et al. 1997; Slane et al. 1999) XMM (Cassam-Chenai et al. 2004; Hiraga et al. 2005) Radio-emission ATCA (Lazendic et al. 2004 ) VHE gamma-rays CANGAROO (Muraishi et al. 2000) CANGAROO II (Enomoto et al. 2002) HESS (Aharonian et al. 2005) Gamma-ray image (HESS) Aharonian et al. (2005)

32. Spatially integrated spectral energy distribution of RX J1713.7-3946 required interior magnetic field B d = 126 μG Experiment: Aharonian et al. (2006) Theory: Berezhko & Völk (2006)

33. B ISM B eff Magnetic field amplification Results of modeling (Lucek & Bell, 2000) + Spectral properties of SNR synchrotron emission + Fine structure of nonthermal X-ray emission SNR magnetic field is considerably amplified B eff 2 /8π ≈ 10 -2 ρ ISM V S 2 B d = B eff >> B ISM VSVS ρ ISM L

34. SNR magnetic field Influences synchrotron emission Determines CR diffusion mobility: Κ ~ p/(ZB d ) CR diffusion coefficient (Bohm limit) p max ~ Z e B d R S V S Influences CR maximum momentum p max : nuclear charge number

35. Berezhko & Völk (2007) Energy spectrum of CRs, produced in SNRs Amplified magnetic field B d 2 /(8π) ≈ 10 -2 ρ 0 V S 2 B d >> B ISM

36. Cosmic Ray Flux knee 1 GZK cutoff (?) CR sources: Supernova remnants Extragalactic (?) Supernova remnants knee 2

37. Energy spectrum of CRs CR spectrum, produced in SNRs CR spectrum from J EG ~ε -2.7 extragalactic sources (Berezinsky et al.2006) Dip scenario Dip p + γ → p + e + + e - GZK cutoff p + γ → N + π Experiment: Akeno-AGASA (Takeda et al. 2003) HiRes (Abbasi et al. 2005) Yakutsk (Egorova et al. 2004)

38. SNRs SNRs + reacceleration Extragalactic (AGNs, GRBs…) J EG ~ε -2 Berezinsky et al.(2006) Energy spectrum of CRs Ankle scenario

39. Mean logarithm of CR atomic number Ankle scenario Dip scenario Experiment: KASKADE (Hörandel 2005) Yakutsk (Ivanov et al.2003) HiRes (Hörandel 2003) Precise measurements of CR composition is needed to discriminate two scenarios

40. Fireball model of Gamma-ray bursts dΩ ~ 10 -2 π Forward Shock ISM Fireball Γ ≈ 100 Lorentz factor Energy release (supernova ?) E Rees & Meszaros (1992) E ≈ 10 51 erg (?) E SS ≈ 3×10 53 erg spherically symmetric analog R Γ ~ (E SS /N ISM ) 1/2 R -3/2 R ~ t 1/4

41. CR acceleration in GRBs ε max ≈ e B u Γ R c Achterberg et al. (2001) B u = B ISM = 10 μG relativistic shock (Γ >> 1) assumption: isotropic CR diffusion in downstream region maximum proton energy ε max ≈ 5 × 10 7 m p c 2 B u 2 /8π = 0.1Γ 2 ρ ISM c 2 ε max ≈ 5 × 10 13 m p c 2 amplified magnetic field unamplified magnetic field N CR (ε)~ ε - γ γ ≈ 2.2 GRBs are powerful extragalactic sources of CRs (?)

42. Problem upstream downstream BuBu BdBd B d ~ Γ 2 B u >> B u strongly anisotropic CR diffusion low chance for CRs to recross shock from downstream to upstream inefficient CR production (e.g. Ostrowski & Niemiec, 2006) VSVS shock B dll >> B d ┴ &

43. CR acceleration at late evolutionary stage (nonrelativistic shock) ε max ≈ e B u R c R(Γ = 1) =(E SS /3ρ ISM c 2 ) 1/3 B u 2 /8π = 0.1ρ ISM c 2 For E SS = 3× 10 53 erg, N ISM = 1 cm -3 ε max = 3 × 10 10 m p c 2 then E SS ≈ 10 55 erg ε max ≈ 10 11 m p c 2 amplified magnetic field ρ ISM = N ISM m p InterStellar Medium density However assumption L γ = Q e, P e ~ Γ 2 ρ ISM c 2 seems to be unrealistic Realistic numbers: P p ~ Γ 2 ρ ISM c 2 P e = 10 -2 P p

44. Active Galactic Nuclei Jets Γ ≈ 10 Lorentz factor Powerful source of nonthermal emission Powerful source of Cosmic Rays Shear flow Effective frictional acceleration (e.g. Ostrowski, 2004) Shock Diffusive shock acceleration

45. Conclusions CR acceleration in SNRs is able to provide the observed Galactic CR spectrum up to the energy ε ≈ 10 17 eV Two possibility for Galactic CR spectrum formation: - Dip scenario ( CRs from Galactic SNRs at ε < 10 17 eV + Extragalactic CRs at ε > 10 18 eV ) - Ankle scenario ( CRs from Galactic SNRs at ε < 10 17 eV + Reaccelerated CRs at 10 17 < ε < 10 18 eV + Extragalactic CRs at ε >0 19 eV) Precise measurements of CR spectrum and composition at ε > 10 17 eV are needed to discriminate the above two possibilities Acceleration by subrelativistic/nonrelativistic shocks in GRBs (or AGN jets) and frictional acceleration in AGN jets are potential sources of Ultra High Energy CRs

46. Supernovae 0100200 300 t, day lg( Luminosity) = star explosions SN I SN II H lines 0 -4 -8

47. M CO <1.4M Sun M CO >1.4M Sun No central objects pulsar / black hole SN Ia SN II/Ib SNR in uniform ISM SNR in CSM, modified by progenitor star wind ( 15 % ) ( 85 %) ν detected from SN1987 A thermonuclear explosion core collapse

48. Cosmic Ray Flux knee 1 GZK cutoff (?) CR sources: Supernova remnants Extragalactic (?) Supernova remnants (?) Reacceleration (?) knee 2

49. Structure of the shock modified due to CR backreaction u x shock front classical (unmodified) shock σ = u 0 /u 2 = σ S = u 1 /u 2 =4 modified shock σ > 4, σ S < 4 CR pressure Flow speed subshock precursor upstream downstream Acceleration sites p 2 p >> m p c γ < 2

50. E = 10 30 eVE=6×10 19 eV CR source π0π0 π±π± Zatcepin, Kuzmin (1966) Greisen (1966) Galaxy Cosmic microwave background (CMB) radiation Cutoff of CR spectrum due to CR interaction with CMB

51. Projected radial profile of TeV-emission (normalized to a peak values) Smoothed with Gaussian PSF of width Δψ = 0.1 o J γ max /J γ min ≈ 2.3 consistent with HESS value L L = 0.07 R S J γ max /J γ min ≈ 8

52. Spatially integrated spectral energy distribution of RX J1713.7-3946 (Vela Jr) Low (inefficient) protons injection/acceleration, B d = 15μG

53. Projected radial profile of 1 keV X-ray emission (normalized to a peak values) smoothed with PSF of XMM-Newton (Δψ = 15’’) test-particle limit B d = 20 μG inconsistent with experiment L Experiment: L=1.2×10 18 cm (Hiraga et al. 2005) Theory: L=1.15×10 18 cm (B d = 126 μG)

54. windbubble shell Interstellar medium R sh lg r lg N g N b << N ISM σ sh N ISM N ISM CSM structure SN current SN shock position CSM number density