http://hubblesite.org/newscenter/archive/releases/2006/30/image/a/format/xlarge_web/

Particle Acceleration by ShocksTony Bell

withBrian Reville, Klara Schure,

Gwenael GiacintiUniversity of Oxford

Cassiopeia A

Radio(VLA)

Infrared(Spitzer)

Optical(Hubble)

X-ray(Chandra)

NASA/JPL NASA/JPL

NASA/JPL-Caltech/O Krause(Steward Obs)

NASA/CXC/MIT/UMass Amherst/M.D.Stage et al.

NASA/ESA/Hubble Heritage (STScI/AURA))

chandra.harvard.edu/photo/0237/0237_radio.jpg

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.

SNR RX J1713.7-3946

Aharonian et alNature (2004)

HESS observation

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

For related discussion :

• Drury (2011) MNRAS 415 1807

• Malkov, talk on Weds

• Reville, talk on Weds

Observations: TeV emission outside SNR

Cosmic ray acceleration

High velocityplasma

Low velocityplasma

B2

B1

CR track

Due to scattering, CR recrosses shock many timesGains energy at each crossing

CR acceleration timeshock

upstream

ncru

L=D/ushock

222

8

)4/(

44

shock

upstream

shock

downstream

shock

upstream

u

D

u

D

u

D

Time needed for acceleration (Lagage & Cesarsky)

Shock moves distance R = 8L during CR acceleration time

D increases with CR energy

shock CR precursor

SNR

Max CR energy set by = R/ushock

R

L~R/8

Theory is simplistic

If so, CR never escape upstream

Maximum CR energy

222

8

)4/(

44

shock

upstream

shock

downstream

shock

upstream

u

D

u

D

u

D

Max CR energy set by = R/ushock

Bohm is minimum diffusion coefficient: Tesla

eVgBohm B

crD

33

Magnitude of the problem: CR Larmor radius: G

PeVg Br

parsec

Young SNR: age=300yrs, B=3G, ushock=5000 km s-1

Maximum CR energy: BRushock83

Max CR energy = 1013eV

Conclusion: Need amplified magnetic field, D varies with time, space, CR energy

Tycho

Shock

downstreamupstream

CR streaming ahead of shock

Excite instabilities

Amplify magnetic field

Streaming CR excite instabilities

Amplify magnetic field

Lucek & Bell (2000)

shock

CR precursor

SNR

R

L~R/8

Equipartition magnetic field

BRushock83

Conditions for PeV acceleration

2

0

2

shockuB

Maximum CR energy: 20PeV

Theoretical saturation, matches observation (Vink 2006,2008)

2

0

2

shockshock uc

uB

= CR efficiency factor03.0

Maximum CR energy: 0.5 PeV (young SNR)

Within error bars, but tough!

Are Tycho, Kepler already too old and too slow?

Time for magnetic field amplification?

Growth rate of fastest growing mode: 0

21

max j

CR electric current density:

Shortest growth time: years50

3703.0

1max

cm

PeV

nu

ushock in 10,000 km s-1

Density in cm-3CR efficiency/0.03

Cannot assume instability reaches saturation

Upstream energy fluxes:3v shockjdriftCR uen

j

shockuj

3

jEnergy of CR carrying current

The scalelength issue

CR Larmor radius: m103 16

G

PeVg Br

Wavelength of fastest growing mode: m102/2 14max GBk

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)

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: 0..3

1.).(

3

2

pBv

rvuu

r

fe

f

p

fp

pf

t

f

jiijii pptpfptpftpff ),,(),,(),,(0 rrr ji 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

Magnetic energy density

CR energy density

Perpendicular magnetic field

7.7rg

(64 cells)

370rg (3104 cells)

shoc

k

CR

fre

e ex

pans

ion

Flow into reflecting wall (2D simulation)

Thermal pressure

Flow at 0.1c

wal

l

Parallel magnetic field

7.7rg

61rg

Thermal pressure

CR energy density

Magnetic energy density

Section near shock

shoc

k

Momentum dependence

injectpp

injectpp 10

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

CR energy density

Perpendicular magnetic field

7.7rg

Thermal pressure

240rg

shoc

k

escaping CR ConfinedCR

Perpendicular field

Perpendicular slices

Escape and confinement (t=2t0/3)3D simulation

Instability growth

Stationary box in upstream plasma

Max growth rate 0

21

max j

Number of e-foldings: jdtdt 0

21

max

Number of CR passed through box (times charge)

CR only confined if enough CR escaped upstream

CR energy density

Perpendicular magnetic field

How many e-foldings

8.01max

1max5

Condition for CR confinement: 105max dt

(Fixed current simulations 2004)

Instability growth

Condition for CR confinement: 100 jdt

Upstream energy fluxes:3v shockjdriftCR uen

j

shockuj

3

PeV10 300

37

2/130 tuntu cmshockj

Mean energy of escaping CR:

Max CR energy a few times larger:

in 300 yrs

in 10,000 km s-1

in cm-3

j max

Make a guess: = 3

(matches simulation)

CR energy density

Perpendicular magnetic field

Compare with saturation limit on CR energy

Instability saturation + acceleration time

Instability growth time (depends on CR escaping upstream)

2

0

2

shockshock uc

uB

PeV5 3002/7

72/1

max tuncm

PeV3 30037

2/13max tuncm 5max dt

in 300 yrs

in 10,000 km s-1in cm-3

Suggests:

• PeV acceleration lies on limit for both growth times and saturation

• High energy CR escape upstream (with efficiency ~ almost by definition)

max = j = 3

tushock3

0max 3.0

Growth time limit Saturation limit

tuc

ushock

shock 30max 4.0

Evolution of max CR energy as limited by growth times

)(PeV2.0 3/428.0300

1.06.044max shockcm uRtnE

Blast wave energy in 1044J

During Sedov phase

PeV30037

2/1max tuncm

1987A after 6 years

PeV3 2/1max cmn5.37 u

Cas A

1,1,6.0 3007 cmntu PeV6.0max

assume = 3

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

1j