1. Particle Acceleration by Shocks Brian Reville, Klara Schure,
Tony Bell
with
Brian Reville, Klara Schure,
Gwenael Giacinti
University of Oxford

2. Cassiopeia A Radio (VLA) Infrared (Spitzer) NASA/JPL NASA/JPL Optical
chandra.harvard.edu/photo/
0237/0237_radio.jpg
NASA/ESA/
Hubble Heritage
(STScI/AURA))
NASA/CXC/MIT/UMass
Amherst/
M.D.Stage et al.
NASA/JPL
NASA/JPL
NASA/JPL-Caltech/
O Krause(Steward Obs)
Optical
(Hubble)
X-ray
(Chandra)

3. Historical shell supernova remnants
Chandra observations
Kepler 1604AD
Tycho 1572AD
SN1006
Cas A 1680AD
HESS observation
SNR RX J
Aharonian et al
Nature (2004)
NASA/CXC/Rutgers/
J.Hughes et al.
NASA/CXC/Rutgers/
J.Warren & J.Hughes et al.
NASA/CXC/NCSU/
S.Reynolds et al.
NASA/CXC/MIT/UMass Amherst/
M.D.Stage et al.

4. Cosmic Ray (CR) acceleration
This talk:
How do CR escape SNR?
Can SNR accelerate CR to 1 PeV – and when?
Importance of magnetic field amplification for the above
Observations: TeV emission outside SNR
For related discussion :
Drury (2011) MNRAS
Malkov, talk on Weds
Reville, talk on Weds

5. Cosmic ray acceleration
High velocity
plasma
Low velocity B2 B1
CR track
Due to scattering, CR recrosses shock many times
Gains energy at each crossing

6. CR acceleration time shock u ncr upstream L=D/ushock L~R/8 R
Time needed for acceleration (Lagage & Cesarsky)
D increases with CR energy
L~R/8
Max CR energy set by t = R/ushock R
Shock moves distance R = 8L during CR acceleration time t
SNR CR
precursor
If so, CR never escape upstream
shock
Theory is simplistic

7. Maximum CR energy Conclusion: Need amplified magnetic field,
Magnitude of the problem: CR Larmor radius:
parsec
Max CR energy set by t = R/ushock
Bohm is minimum diffusion coefficient:
Maximum CR energy:
Young SNR: age=300yrs, B=3mG, ushock=5000 km s-1
Max CR energy = 1013eV
Tycho
Conclusion: Need amplified magnetic field,
D varies with time, space, CR energy

8. Streaming CR excite instabilities
L~R/8 CR
precursor
Streaming CR excite instabilities R
SNR
shock
Shock
CR streaming ahead of shock
Excite instabilities
Amplify magnetic field
upstream
downstream
Amplify magnetic field
Lucek & Bell (2000)

9. Conditions for PeV acceleration
Equipartition magnetic field
Maximum CR energy: 20PeV
Theoretical saturation, matches observation (Vink 2006,2008)
h = CR efficiency factor
Maximum CR energy: 0.5 PeV (young SNR)
Within error bars, but tough!
Are Tycho, Kepler already too old and too slow?

10. Time for magnetic field amplification?
Growth rate of fastest growing mode:
CR electric current density:
Upstream energy fluxes:
Energy of CR carrying current
Shortest growth time:
CR efficiency/0.03
Density in cm-3
ushock in 10,000 km s-1
Cannot assume instability reaches saturation

11. The scalelength issue CR Larmor radius:
Wavelength of fastest growing mode:
for ushock=10,000 km s-1 and n =1 cm-3
Fortunately: instability grows non-linearly by spatial expansion
Routes to large-scale structure with CR response included:
1) Filamentation (Brian Reville)
2) Include scattering (Klara Schure)

12. Numerical simulation of interacting physics
Coupled questions:
Does the instability have time to grow?
Does the instability saturate?
How large is the magnetic field?
What is the maximum CR energy?
Do CR escape upstream of the shock?
Simulation code:
MHD background plasma coupled to kinetic CR treatment through jxB
Include shock, precursor & escape
Self-consistent magnetic field generation
CR respond to magnetic field (not diffusion model)
2D or 3D with momentum-dependent beyond-diffusion CR treatment
Time-dependent
CR model:
isotropic
drift
off-diagonal part of stress tensor
CR distribution defined in local fluid rest frame
See Schure & Bell (2011) for instability analysis with stress tensor

13. Flow into reflecting wall (2D simulation)
Parallel magnetic field
370rg (3104 cells)
Flow at 0.1c
7.7rg
(64 cells)
shock
wall
Thermal pressure
expansion
CR free
CR energy density B0
Magnetic energy density
Perpendicular magnetic field

14. Section near shock Thermal pressure shock CR energy density
Magnetic energy density
7.7rg
61rg

15. Momentum dependence Two populations at low CR energy
Confined by magnetic field
Freely escaping, excite instability
High energy CR escape freely:
Large mean free path
Generated once low energy CR confined

16. Escape and confinement (t=2t0/3)
3D simulation
240rg
7.7rg
shock
Thermal pressure
Confined CR
escaping CR
CR energy density
Perpendicular magnetic field
Perpendicular field
Perpendicular slices

17. Instability growth CR only confined if enough CR escaped upstream
CR energy density
Perpendicular magnetic field
Stationary box in upstream plasma
Max growth rate
Number of e-foldings:
Number of CR passed through box (times charge)
CR only confined if enough CR escaped upstream

18. How many e-foldings Condition for CR confinement:
(Fixed current simulations 2004)
Condition for CR confinement:

19. Instability growth Make a guess: c = 3 CR energy density
Perpendicular magnetic field
(matches simulation)
Condition for CR confinement:
Upstream energy fluxes:
Mean energy of escaping CR:
in 300 yrs
Max CR energy a few times larger:
in 10,000 km s-1
Make a guess: c = 3
in cm-3

20. Compare with saturation limit on CR energy
Instability growth time (depends on CR escaping upstream)
emax = cej c = 3
Instability saturation + acceleration time
in 300 yrs
in cm-3
in 10,000 km s-1
Suggests:
PeV acceleration lies on limit for both growth times and saturation
High energy CR escape upstream (with efficiency ~h almost by definition)
Growth time limit
Saturation limit

21. Evolution of max CR energy as limited by growth times
assume c = 3
1987A after 6 years
Cas A
During Sedov phase
Blast wave energy in 1044J

22. Conclusions Instability growth/saturation limits acceleration
Some CR must escape/get ahead of main precursor to excite magnetic field
Energy of escaping CR determined by
Pre-Sedov SNR reach PeV, but only just
Max CR energy drops during Sedov
Young high velocity SNR into high density might exceed PeV