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