1. Diffusive Shock Acceleration
of Cosmic Rays
Hyesung Kang
Pusan National University, Korea
Feb. 23, 2007
APCTP2007

2. Particle energy spectrum N(E): power-law spectrum
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
Feb. 23, 2007
APCTP2007

3. 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 ~ erg/cm3 ~1 eV/cm3
- sources: SNRs, stellar wind (OB stars), pulsars
-ICM inside Clusters of Galaxies
- ECR,p Egas , EB ~ (0.1-1) Egas , ECR,e~ 0.01 Egas
- sources: AGN jets, galactic winds, structure shocks, turbulence
Feb. 23, 2007
APCTP2007

4. Direct measurements of particle acceleration
at collisionless shocks inside heliosphere
Earth’s Bow shock
interplanetary
magnetic field
, flares
energized particles
M.A. Lee, Rev. Geophys. Space Phys. 21, (1983)
Sun
Solar Wind
adapted from Lee 1983

5. 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 CR
gas
Feb. 23, 2007
APCTP2007

6. 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
Feb. 23, 2007
APCTP2007

7. CRs below the knee energy (E<1015eV) 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 ?
Feb. 23, 2007
Shock wave=blast wave
APCTP2007

8. Galactic Supernova Remnants: collisionless shocks
SN1006
Cas A
Tycho
Chandra X-ray images
- X-ray Synchrotron from CR electrons
- Clear Evidences for ~100 TeV = 1014 eV electrons :
- CR nuclei up to Knee energy ?
Feb. 23, 2007
APCTP2007

9. 2) 100 TeV electrons  IC scattering  g-ray ?
SNR RX J (G ):
- 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 ?
Feb. 23, 2007
APCTP2007

10. Emax = Z ba B R Astrophysical accelerators: Hillas Diagram (1984)
confinement condition:
for DSA to be effective
diffusion length < size of accelerator
l d = k B/Vs = r g v /Vs < R
p max c / (ZB Vs) = R
 E max = Z ba BR
Magnetic field is important in acceleration and confinement of CRs
Astrophysical accelerators:
Hillas Diagram (1984)
Emax = Z ba B R
Nakar B
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)
The red line shows the relation btw B and R of accelerators that can achieve E max=1020 eV
Ryu & Inoue
Feb. 23, 2007
APCTP2007 R

11. 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 (QBn< 45)
Shock Drift Acceleration: drift along the shock surface dominant at quasi-perpendicular shocks (QBn> 45)
Second-order Fermi mechanism: Stochastic process, turbulent acceleration  add momentum diffusion term
 Diffusive Shock Acceleration
Feb. 23, 2007
APCTP2007

12. Shock Drift Acceleration
Magnetic Field direction: Parallel vs. Perpendicular shock
Shock Drift Acceleration
Fermi st Order Process
Slide from Jokipii (2004): KAW3
Feb. 23, 2007
APCTP2007

13. Drift Acceleration in perpendicular shocks with weak turbulences yx 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”
Feb. 23, 2007
APCTP2007

14. 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
Feb. 23, 2007
APCTP2007

15. Plasma simulations at oblique shocks : Giacalone (2005)
thermal
CRs
(DB/B)2=1
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.
Feb. 23, 2007
APCTP2007

16. “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-q power-law with a slope
q = 3r/(r-1) (r = r2/r1=u1/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:
Feb. 23, 2007
APCTP2007

17. DSA numerical simulations : M=10 shock
“CR modified shocks”
- presusor + subshock
- reduced Pg
enhanced compression Pg r
- a fraction of x= of the incoming particles become CRs.
- about % of shock kinetic E can be transferred to CRs at strong shocks
PCR
f(p)p4
Feb. 23, 2007
APCTP2007

18. 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 : 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.
Feb. 23, 2007
APCTP2007

19. Feb. 23, 2007
APCTP2007