Hyesung Kang

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Diffusive Shock Acceleration of Cosmic Rays
Hyesung Kang Pusan National University, Korea
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• CRs observed at Earth
• Particle energy spectrum
• N(E) power-law spectrum
• Universal power-law
• by a universal acceleration
• mechanism working on
• a wide range of scales
• and environments.
• Diffusive Shock
• Acceleration

E-2.7
32 orders of magnitude
E-3.1
12 orders of magnitude
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CRs Shocks are ubiquitous in astrophysical
plasmas.
-Heliosphere (solar system) - direct
measurements of particle acceleration at shocks
- source solar flare, CME, solar wind,
interplanetary shocks -ISM of our Galaxy filled
with galactic CRs - ECR Egas EB ECMBR
10-12 erg/cm3 1 eV/cm3 - sources SNRs,
stellar wind (OB stars), pulsars -ICM inside
Clusters of Galaxies - ECR,p 0.2 Egas ,
EB (0.1-1) Egas , ECR,e 0.01 Egas -
sources AGN jets, galactic winds, structure
shocks, turbulence
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Direct measurements of particle acceleration at
collisionless shocks inside heliosphere
Earths Bow shock
interplanetary
magnetic field
, flares
energized particles
Sun
Solar Wind
adapted from Lee 1983
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Direct measurements of particle spectra in the
Solar wind (Mewaldt et al 2001) - Thermal
(Maxwellian) CRs (power-law tail) ?
suprathermal particles leak out of thermal
pool into CR population
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Radiation from Cosmic Rays in the ISM of our
Galaxy
radio synchrotron (408MHz) CR electrons
magnetic field
Sources of these galactic cosmic rays
Supernova Blast Waves.
Gamma ray above 100 MeV CR protons ISM
collision ? p0 decay ? g ray
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CRs below the knee energy (Elt1015eV) are
accelerated by SNRs.
- CR Galactic luminosity 1041 erg/s 10
LSNe (1051 erg x 1/(30years) x 10 ) energy of
escaping CRs from our Galaxy ? only possible
acceleration sites inside our Galaxy
Observational Evidences ?
Shock waveblast wave
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Galactic Supernova Remnants collisionless shocks
Chandra X-ray images

• - X-ray Synchrotron from CR electrons
• - Clear Evidences for 100 TeV 1014 eV
  electrons
• - CR nuclei up to Knee energy ?

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SNR RX J1713.7 - 3946 (G347.3 - 0.5) -
discovered by ROSAT in the X-ray spectrum - TeV
g-rays by EGRET.
HESS atmospheric Cerenkov g-ray telescope (2005)
TeV g-ray image by HESS (color) X-ray shell
(contour map) similar morph.
1) CR protons ? p0 ? g-ray ? 2) 100 TeV
electrons ? IC scattering ? g-ray ?
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Astrophysical accelerators Hillas Diagram (1984)
confinement condition for DSA to be effective
diffusion length lt size of accelerator
l d k B/Vs r g v /Vs lt R p max c /
(ZB Vs) R ? E max Z ba BR Magnetic
field is important in acceleration and
confinement of CRs
Emax Z ba B R
Nakar
Emax highest possible energy (ZeV) Z charge of
the CR particle Va/c ba speed of
accelerator B magnetic field strength (Gauss) R
size of accelerator (pc)
B
The red line shows the relation btw B and R of
accelerators that can achieve E max1020 eV
Ryu Inoue
R
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CRs are known to be accelerated at astrophysical
shocks.

• Three Shock Acceleration mechanisms work
  together.
• First-order Fermi mechanism scattering across
  the shock dominant at quasi-parallel shocks (QBnlt
  45)
• Shock Drift Acceleration drift along the shock
  surface dominant at quasi-perpendicular shocks
  (QBngt 45)
• Second-order Fermi mechanism Stochastic process,
  turbulent acceleration ? add momentum diffusion
  term
• ? Diffusive Shock Acceleration

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Magnetic Field direction Parallel vs.
Perpendicular shock
Shock Drift Acceleration
Fermi 1st Order Process
Slide from Jokipii (2004) KAW3
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Drift Acceleration in perpendicular shocks with
weak turbulences
B
Particle trajectory in weakly turbulent fields
Jokipii (2004)

• Energy gain comes mainly from drifting in the
  convection electric field along the shock surface
  (Jokipii, 1982), i.e. De q E L,
• Drift acceleration

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Diffusive Shock Acceleration in quasi-parallel
shocks Fermi first order process Alfven waves
in a converging flow act as converging mirrors
? particles are scattered by waves ? cross the
shock many times
Shock front
mean field
B
particle
energy gain at each crossing
U2
U1
upstream
downstream
shock rest frame
Converging mirrors
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Plasma simulations at oblique shocks Giacalone
(2005)
thermal
CRs
(DB/B)21
parallel
parallel
perp.
perp.
Injection rate weakly depends on QBn for fully
turbulent fields. 10 reduction at
perpendicular shocks
The perpendicular shock accelerates particles to
higher energies compared to the parallel shock.
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Universal slope of CR energy spectrum ? ?
prediction of DSA theory in test particle limit

• -When non-linear feedback due to CR pressure is
  insignificant
• N(E) E-q2 power-law with a slope
• q 3r/(r-1) (r r2/r1u1/u2
  compression ratio across the shock)
• determined solely by the shock Mach
  number
• - for strong gas shock (large Ms) r ? 4 (g
  5/3 gas adiabatic index)
• q ? 4,
  (source spectrum)
• this may explain the universal power-law,
  independent of shock parameters

• - momentum dependent transport/confinement/escape
  lead to steepening
• nonlinear feedback of CR pressure to the flow
  can flatten the spectrum
• ? observed spectrum

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DSA numerical simulations M10 shock

• CR modified shocks
• - presusor subshock
• - reduced Pg
• enhanced compression

Pg
r
- a fraction of x 10-4 - 10-3 of the incoming
particles become CRs. - about 10-50 of shock
kinetic E can be transferred to CRs at strong
shocks
PCR
f(p)p4
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Summary

• - CRs turbulent B fields are natural byproducts
  of the collisionless shock formation process
  they are ubiquitous in cosmic plasmas .
• - DSA produces a nearly universal power-law
  spectrum with the correct observed slopes.
• - With turbulent fields, thermal leakage
  injection works well 10-4 - 10-3 of the
  incoming particles become CRs
• - Up to 50 of shock kinetic E can be
  transferred to CRs at strong collisionless
  shocks DSA is very efficient.

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