1. Shock acceleration of cosmic rays Tony Bell Imperial College, London

2. Reynolds, 1986 SNR suitable CR source below 10 15 eV Typical max. radius of rapidly expanding SNR ~ 10 17 m Radio image of SN1006 x-ray image of SN1006 Long, 2003

3. Shock in magnetised plasma Shock High velocity plasma Low velocity plasma Upstream ISMDownstream shocked plasma B2B2 B1B1 B 2 >B 1

4. Cosmic ray wanders around shock -scattered by magnetic field High velocity plasma Low velocity plasma B2B2 B1B1 CR track Due to scattering, CR recrosses shock many times

5. Shock acceleration gives right spectrum High velocity plasma Low velocity plasma Upstream ISM Downstream shocked plasma B2B2 B1B1 B 2 >B 1 Simple diffusion theory: Prob of CR crossing shock times is Shock velocity: v s  = v s /c Average fractional energy gained at each crossing is Differential spectrum is Allowing for propagation matches observed spectrum

6. Cosmic ray wanders around shock -scattered by magnetic field High velocity plasma Low velocity plasma B2B2 B1B1 CR track Due to scattering, CR recrosses shock many times

7. ‘Bohm diffusion’ rgrg Mean free path cr ~ r g (proportional to 1/B) Requires disordered magnetic field:  B/B ~ 1 D Bohm = cr g /3

8. L= r g c /3v shock CR distribution near shock shock downstreamupstream Exponential dist n Want small r g (large B) for rapid acceleration to high energy Balance between advection and ‘Bohm’ diffusion ( cr = r g )

9. Scaleheight must be less than SNR radius L R shock CR pre-cursor Rv shock B must exceed certain value Need L<R L=(c/3v shock ) cr (c/3v shock ) cr < R cr =r g, (proportional to 1/B)

10. Condition on BvR Get original version (Hillas, 1984)

11. Cosmic Ray spectrum arriving at earth Mainly protons

12. Reducing the CR mean free path Magnetic field amplification

13. CR/Alfven wave interaction (conventional theory) If CR gyration length matches Alfven wavelength CR scattered strongly by waves Waves excited by CR B CR

14. Currents driving Alfven waves B CR dominates in conventional theory dominates when CR current is large

15. k in units of r g -1  in units of v S 2 /cr g For SNR conditions, instability strongly driven Dispersion relation Re(  ) Im(  ) kr g =1

16. Growth time of fastest growing mode Uncertain efficiency factor SNR expand rapidly for ~1000 yrs Acceleration favoured by high velocity and high density Look to very young SNR for high energy CR eg SN1993J in M81 (Bartel et al, 2002) After 1 year: v s =1.5x10 7 ms -1 n e ~10 6 cm -3 After 9 years: v s =0.9x10 7 ms -1 n e ~10 4 cm -3

17. j cr j thermal j thermal = -j cr j thermal x B causes helix expand extends field lines increases B Instability mechanism helical field line

18. MHD simulations show magnetic field amplification Development of previous modelling, Lucek & Bell (2000)

19. t=0

20. t=6.4t=9.5 t=12.4t=16.8

22. Evolution of magnetic field Magnetic field (log) time linearnon-linear rms field grows 30x max. field grows 100x Saturation magnetic field proportional to  1/2 v shock 3/2

23. k in units of r g -1  in units of v S 2 /cr g For SNR conditions, instability strongly driven Dispersion relation Re(  ) Im(  ) kr g =1

24. CR collimate into Filaments and Beams

25. Filamentation & self-focussing proton beam j velocity v beam B

26. MHD response to beam – mean |B| along line of sight z x t=2 t=6 t=4 t=8 Current, j

27. B (0.71,1.32)  (0.76,1.17) Slices of B and  in z at t=2 Magnetic field Density

28. B (0.40,2.61)  (0.54,1.59) Slices of B and  in z at t=4 Magnetic field Density

29. B (0.11,8.53)  (0.03,4.13) Slices of B and  in z at t=6 Low density & low B in filament Magnetic fieldDensity

30. B (0.,8.59)  (0.,4.51) Slices of B and  in z at t=8 Magnetic field Density

31. MHD response to beam – mean |B| along line of sight z x t=2 t=6 t=4 t=8 Current, j

32. Filamentation & self-focussing proton beam j velocity v beam E=-uxB B R Energy conservation Magnetic field growth Ideal for focussing CR into beam (focus CR, evacuates plasma) E=0

33. Power carried by filament/beam Alfven current: Beam radius = Larmor radius Power in individual filament/beam W =10 15 eV1.7x10 28 W = 3x10 -12 M o c 2 yr -1 =10 21 eV 1.7x10 40 W = 3 M o c 2 yr -1

34. Some questions: future directions

35. Acceleration requires large BvR magnetic field velocity size B increases with energy density  v 2 Puts emphasis on v and  For >10 15 eV, look at high density, high velocity objects: young SNR expanding into dense medium supernovae AGN A revised perspective? Could jets be driven by high energy CR?

36. Limits on shock acceleration at high density p-p loss time:  pp ~ 3x10 -9  gm/cc -1 sec Max CR energy:  ~ 25  gm/cc -1 B MG (v shock /c) 2 GeV p-p Loss length: pp ~ 0.8  gm/cc -1 m (Aharonian, 2004) p-p loss limit Can CR escape dense plasma? Other (larger?) losses

37. a natural explanation for CR Recent theory: 1) removes doubts about acceleration to the knee 2) acceleration beyond knee a possibility 3) directs attention to young SNR 4) filament/beaming intriguing 5) application to accretion systems/compact objects Shock acceleration Lucek & Bell, MNRAS 314, 65 (2000) Bell, MNRAS 353, 550 (2004) Bell, MNRAS in press (2005)

38. Cassiopeia A (Chandra)

39. j cr j thermal j thermal = -j cr j thermal x B causes helix expand extends field lines increases B Instability mechanism helical field line