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Transcript of Http://hubblesite.org/newscenter/archive/releases/2006/30/image/a/format/xlarge_web/ Particle...
![Page 1: Http://hubblesite.org/newscenter/archive/releases/2006/30/image/a/format/xlarge_web/ Particle Acceleration by Shocks Tony Bell with Brian Reville, Klara.](https://reader036.fdocuments.in/reader036/viewer/2022062314/5697bf6f1a28abf838c7d2e1/html5/thumbnails/1.jpg)
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
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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
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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
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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
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Cosmic ray acceleration
High velocityplasma
Low velocityplasma
B2
B1
CR track
Due to scattering, CR recrosses shock many timesGains energy at each crossing
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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
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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
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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
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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?
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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
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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)
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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
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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
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7.7rg
61rg
Thermal pressure
CR energy density
Magnetic energy density
Section near shock
shoc
k
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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
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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
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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
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How many e-foldings
8.01max
1max5
Condition for CR confinement: 105max dt
(Fixed current simulations 2004)
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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
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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
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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
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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