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Diffusive shock acceleration & magnetic field amplification Tony Bell University of Oxford Rutherford Appleton Laboratory. SN1006: A supernova remnant 7,000 light years from Earth - PowerPoint PPT Presentation
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Diffusive shock acceleration
& magnetic field amplification
Tony Bell
University of OxfordRutherford Appleton Laboratory
SN1006: A supernova remnant 7,000 light years from EarthX-ray (blue): NASA/CXC/Rutgers/G.Cassam-Chenai, J.Hughes et al; Radio (red): NRAO/AUI/GBT/VLA/Dyer, Maddalena & Cornwell;Optical (yellow/orange): Middlebury College/F.Winkler. NOAO/AURA/NSF/CTIO Schmidt & DSS
magnetic field amplification 1) Basic theory
2) Observational indicators
Diffusive shock acceleration and magnetic field amplification
DIFFUSIVE SHOCK ACCELERATIONCosmic ray wanders around shock
-scattered by magnetic field
High velocityplasma
Low velocityplasma
B2
B1
CR track
Due to scattering, CR recrosses shock many timesGains energy on each crossing
Idealised shock acceleration: diffusion, no magnetic field
Upstream Downstream
Uniform density nCR
Probability of escape = u/c
shock velocity: u
Rate CR cross shock = nCRc/4
fluid velocity = u fluid velocity = u/4
Rate CR escape downstream = nCRu/4
Idealised shock acceleration: diffusion, no magnetic field
Upstream Downstream
Uniform density nCR
Probability of escape = u/c
shock velocity: u
Rate CR cross shock = nCRc/4
fluid velocity = u fluid velocity = u/4
Rate CR escape downstream = nCRu/4
On each crossing
Fractional CR loss N/N = -u/c
Fractional energy gain on each crossing E/E=u/c
N/E = -N/EEdN/N = - EdE/E
N f E-1
differential spectrum n(E) dE f E -2 dE
L
Maximum CR energy
u
cL
3
1
23
88
u
c
u
Laccel
u
RSNR
Shock (velocity u)
downstreamupstream
Exponential distn
Balance between advection and diffusion
Acceleration time:
Precursor scaleheight:
LR
shock
CR pre-cursor
Shock expansion time:
mfp
shock vel
(Lagage & Cesarsky)
L
Maximum CR energy
u
cL
3
1
23
88
u
c
u
Laccel
u
RSNR
Shock (velocity u)
downstreamupstream
Exponential distn
Balance between advection and diffusion
Acceleration time:
Precursor scaleheight:
LR
shock
CR pre-cursor
Shock expansion time:
SNRaccel Rc
u
8
3
eB
prg uBR
E
8
3
eVmax
u = 5000 kms-1, R = 1017 m, B = 3 G Emax < 6x1013 eV
mfp
shock vel
rg
1) Bohm diffusion: mean free path ~ rg
Disordered magnetic field: B/B ~ 1
2) Magnetic field amplification
Need B ~ 100 G to reach few x 1015eV
CR path
How to increase CR energy
uBRE
8
3
eVmax
B/B>>1 scatters energetic particles
Cavity forms inside spirals
Streaming instability driven by cosmic raysLucek & Bell 2000
CR
Linear instability
B0, jCR
zBx, vx
By, vy
MHD equation of motion Bjv
CRdt
d
Model
Thermal plasma as MHD fluid
CR as fixed uniform current jCR
Flux freezing BvB
t
Purely growing, circularly polarised transverse mode:
2/1
0
CRjkB
B
Slices through |B| - time sequence (fixed CR current)
Non-linear growth – expanding loops
Cavities and wallsin |B| &
Instability must be strongly driven (large CR electric current)
Condition for unstable growth:
BBj 0
1
CR
driving force tension in magnetic field line
Back-of-envelope:0LB
jCR
scalelength
Growth only if scalelength L shorter than CR Larmor radius:(otherwise CR tied to field lines) eB
pL
0
2
B
p
ejCR
Saturation magnetic field
0
2
B
p
ejCR
venj CRCR
CR energy flux in precursor: vpcnQ CRCR )(
CR electric current:
CR efficiency : 321 uQCR
Growth condition
3
0
2
42u
c
B
Allowing for compression of B (~times 2) at shock
2
0
2
2u
c
uBdownstream
Observations
Shock thickness & synchrotron losses
Good evidence for field amplification
(Vink & Laming, Voelk et al)
Historical shell supernova remnants
Kepler 1604ADTycho 1572AD
SN1006 Cas A 1680AD
Chandra observations
NASA/CXC/NCSU/S.Reynolds et al.
NASA/CXC/Rutgers/J.Warren & J.Hughes et al.
NASA/CXC/MIT/UMass Amherst/M.D.Stage et al.
NASA/CXC/Rutgers/J.Hughes et al.
Observations
Scale length of turbulence
Can we observe structure of magnetic field?
Estimate shock structure scale L
jcrxB moves upstream plasma a distance
R
shock CR precursor
jcr
2
2
1t
BjL CR
vshock
h
01.02
R
h
D
D
R
L
Bohm
~0.01 1 1
Using scaling arguments for jCR, B,& t
SNR in historical order (CHANDRA)
Tycho 1572ADSN1006
Chandra observations
Kepler 1604AD Cas A 1680AD
Cas A, CHANDRA (Patnaude et al 2008)
Cas A radio (VLA)
High speed shrapnel?Clumpy ambient medium? CR-driven instability?
NASA/CXC/NCSU/S.Reynolds et al.
NASA/CXC/Rutgers/J.Warren & J.Hughes et al.
NASA/CXC/MIT/UMass Amherst/M.D.Stage et al.
NASA/CXC/Rutgers/J.Hughes et al.
Shock structure maps outpre-shock features (B, …)
RX J1713.7-3946 (SN of 393AD)HESS, Aharonian et al 2007
Direct evidence for 100TeV CR
Uchiyama et al 2007
CHANDRA (0.1-10keV)
Changes in ~1 yearimply mG magnetic field
HESS Cerenkov telescope(0.3-100TeV)
Conclusions
Magnetic field amplification an important part of shock acceleration
Opportunity to bring theory & observation closer together
Potential diagnostics of physical environment & CR origin
• Magnetic field (from shock thickness) gives u3
• Time-dependent shock structure maps out ambient medium