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Shock acceleration of cosmic rays
Tony Bell
Imperial College, London
Reynolds, 1986
SNR suitable CR source below 1015eV
Typical max. radius of rapidly expanding SNR ~ 1017m
Radio image of SN1006 x-ray image of SN1006
Long, 2003
Shock in magnetised plasma
Sho
ck
High velocityplasma
Low velocityplasma
Upstream ISM Downstream shocked plasma
B2
B1
B2>B1
Cosmic ray wanders around shock-scattered by magnetic field
High velocityplasma
Low velocityplasma
B2
B1
CR track
Due to scattering, CR recrosses shock many times
Shock acceleration gives right spectrum
High velocityplasma
Low velocityplasma
Upstream ISM Downstream shocked plasma
B2
B1B2>B1
Simple diffusion theory:
Prob of CR crossing shock times is
Shock velocity: vs
= vs/c
m)1( m
Average fractional energy gained at each crossing is
Differential spectrum is 2)( n
Allowing for propagation matches observed spectrum )( 6.2
Cosmic ray wanders around shock-scattered by magnetic field
High velocityplasma
Low velocityplasma
B2
B1
CR track
Due to scattering, CR recrosses shock many times
‘Bohm diffusion’
rg
Mean free path cr ~ rg (proportional to 1/B)
Requires disordered magnetic field: B/B ~ 1
DBohm= crg /3
L= rg c /3vshock
CR distribution near shock
shock
downstreamupstream
Exponential distn
Want small rg (large B) for rapid acceleration to high energy
Balance between advection and ‘Bohm’ diffusion (cr = rg )
Scaleheight must be less than SNR radius
LR
shock
CR pre-cursor
RvshockB must exceed certain value
Need L<R
L=(c/3vshock)cr
(c/3vshock)cr < R
cr=rg , (proportional to 1/B)
Condition on BvR
Get original version
(Hillas, 1984)
Cosmic Ray spectrum arriving at earth
Mainly protons
Reducing the CR mean free path
Magnetic field amplification
CR/Alfven wave interaction (conventional theory)
If CR gyration length matches Alfven wavelength
• CR scattered strongly by waves
• Waves excited by CR
B
CR
Currents driving Alfven waves
BjBBpt
u
)(1
0
B
CR crj
||crj
crj dominates in conventional theory
||crj dominates when CR current is large
k in units of rg-1
in units of vS2/crg
For SNR conditions, instability strongly driven
Dispersion relation
-4
-2
0
2
4
-2 0 2 4log10(k)
log10(omega) Re()
Im()
krg=1
Growth time of fastest growing modeUncertain 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: vs =1.5x107 ms-1 ne~106cm-3
After 9 years: vs =0.9x107 ms-1 ne~104cm-3
jcr
jthermal
jthermal = -jcr
jthermal x B
causes helix expandextends field lines
increases B
Instability mechanism
helical field line
MHD simulations show
magnetic field amplification
BjBBpt
ucr
||0
)(1
Development of previous modelling, Lucek & Bell (2000)
t=0
t=6.4 t=9.5
t=12.4 t=16.8
0.01
0.1
1
10
100
0 5 10 15
Bperp
Bparallel
Brms
Bmax
Evolution of magnetic field
Magnetic field (log) time
linear non-linear
rms field grows 30xmax. field grows 100x
Saturation magnetic field proportional to 1/2vshock3/2
k in units of rg-1
in units of vS2/crg
For SNR conditions, instability strongly driven
Dispersion relation
-4
-2
0
2
4
-2 0 2 4log10(k)
log10(omega) Re()
Im()
krg=1
CR collimate intoFilaments and Beams
Filamentation & self-focussing
proton beam jvelocity vbeam
B
MHD response to beam – mean |B| along line of sight
dyB ||
z
xt=2
t=6
t=4
t=8
Current, j
B (0.71,1.32) (0.76,1.17)
Slices of B and in z at t=2
Magnetic field Density
B (0.40,2.61) (0.54,1.59)
Slices of B and in z at t=4
Magnetic field Density
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 field Density
B (0.,8.59) (0.,4.51)
Slices of B and in z at t=8
Magnetic field Density
MHD response to beam – mean |B| along line of sight
dyB ||
z
xt=2
t=6
t=4
t=8
Current, j
Filamentation & self-focussing
proton beam jvelocity vbeam
E=-uxB
B
R
Energy conservation
Magnetic field growth
jEt
U turb .
t
U
jRR
E
t
B turb
1
~~
Ideal for focussing CR into beam
(focus CR, evacuates plasma)
E=0
E=0
Power carried by filament/beam
Alfven current: Beam radius = Larmor radius
00
22
c
BrI eVg
Alfven
Power in individual filament/beam
eVAlfvenAlfven IP W
=1015eV AlfvenP 1.7x1028 W = 3x10-12 Moc2yr-1
=1021eV AlfvenP 1.7x1040 W = 3 Moc2yr-1
Some questions:
future directions
Acceleration requires large BvR
magnetic fieldvelocity
size
B increases with energy density v2
Puts emphasis on v and
For >1015eV, look at high density, high velocity objects:young SNR expanding into dense mediumsupernovaeAGN
A revised perspective?
Could jets be driven by high energy CR?
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 BMG (vshock/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
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)
Cassiopeia A (Chandra)
jcr
jthermal
jthermal = -jcr
jthermal x B
causes helix expandextends field lines
increases B
Instability mechanism
helical field line