Particle Acceleration

1
Particle Acceleration at Cosmic Shocks
Hyesung Kang Pusan National University, Korea

• Basics of Diffusive Shock Acceleration
• CR Acceleration at Supernova Remnants
• CR Acceleration at Cosmic Shocks on LSS

2
The origin of Cosmic Rays
astrophysical problem - acceleration
mechanisms bottom-up models
physical problem - decays of heavy particles
top-down models
vs.

• Well established facts for the Shock Acceleration
  theory
• Collisionless shocks form via EM viscosities in
  tenuous magnetized
• astrophysical plasmas.
• - CRs turbulent B fields are key elements of
  collisionless shocks.
• Diffusive shock acceleration provides a natural
  explanation for CRs. - CRs turbulent B fields
  are ubiquitous in astrophysical plasmas.

3
CRs, B fields, shocks are ubiquitous in
astrophysical plasmas.
-Heliosphere solar wind, interplanetary
shocks -ISM of our Galaxy - ECR Egas EB
ECMBR 10-12 erg/cm3 dynamically
important in the ISM of galaxies - sources
SNRs, stellar winds (OB stars), pulsars -ICM
inside Clusters of Galaxies radio, EUV, HXR
observations - ECR,p 0.2 Egas , EB
(0.1-1) Egas , ECR,e 0.01 Egas - sources
AGN, galactic winds, structure shocks, turbulence
4
Field configuration Parallel (QBn0) vs.
Perpendicular (QBn90) shock
Slide from Jokipii (2004) KAW3
energy gain at each crossing
Fermi first order process
Injection is less efficient at perpendicular
shocks, compared to parallel shocks
5

• 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

6
Diffusive Shock Acceleration in quasi-parallel
shocks Alfven waves in a converging flow act
as converging mirrors ? particles are scattered
by waves ? cross the shock many times Fermi
first order process
Shock front
mean field
B
particle
energy gain at each crossing
U2
U1
upstream
downstream
shock rest frame
Converging mirrors
7
Drift Acceleration in perpendicular shocks with
weak turbulences
B
Particle trajectory in weakly turbulent fields

• 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

8

• CRs observed at Earth
• N(E) power-law spectrum
• universal acceleration
• mechanism working on
• a wide range of scales
• DSA in the test particle limit predicts a
  universal power-law

This explains the universal power-law,
independent of shock parameters ! Propagation,
loss, Nonlinear CR feedback
E-2.7
f(p) p-q N(E) E-q2 q
3r/(r-1) 2 r r2/r1u1/u2 4 for strong
shocks
E-3.1
9
DSA beyond the test particle limit Recent (
old) Developments in DSA model 1. Amplification
of B field in the precursor due to CR streaming
? higher B gt BISM 3 mG 2. Efficient CR
injections at perpendicular shocks 3. Reduction
of CR acceleration efficiency due to wave drift
10

• streaming CRs upstream of the shock
• - drive large-amplitude Alfven waves
• - amplify B field (Lucek Bell 2000)

Voelk Berezhko, 2003 CR streaming in CR
dominated shocks? Higher B ? higher Emax
beyond the Knee ?
11
Synchrotron emission in radio
X-ray Determination of B amplification factor,
ion injection rate, proton-to-electron number
ratio with SNR observations
x
Slide from Voelk (2006)
12
CR injection at perpendicular shock Giacalone
(2005)

• - acceleration of thermal protons by
  perpendicular shocks (hybrid simulations)
• - Field line meandering due to large scale
  turbulent B fields ? increased cross-field
  transport ? efficient injection at shock
• thermal particles can be efficiently accelerated
  to high energies by a perpendicular shock
• Acceleration efficiency does not depend strongly
  on QBn (comparable of 10-20 of the efficiency
  at parallel shocks)
• injection problem for perpendicular shocks
  solved !

Particles are injected where field lines cross
the shock surface ? efficient injection
density of particles with energies E gt 10Ep
dotted lines field lines
13
Parallel vs. Perpendicular Shocks for Type Ia
SNRs ion injection
SNR expanding into uniform BISM
14

• Recent Observations of SNRs in X-ray and radio
• Cas A, SN 1006, Tyco, RCW86, Kepler,
  RXJ1737,
• B field amplification through streaming of CR
  nuclear component into upstream plasma is
  required to fit observations
• - thin shell of X-ray emission (strong
  synchrotron cooling)
• - amplification factors of B O(10) (Voelk
  2006)
• - Observational proof for dominance of
  hadronic CRs at SNRs
• ?Dipolar radiation consistent with uniform ISM B
  field configuration
• Ion injection rate at shocks x10-4
• Proton/electron ratio Kp/e 50-100
• 50 of SN explosion energy is transferred to
  CRs at parallel shocks. Considering the fraction
  of parallel portion of remnants (20), so about
  10 of SN explosion energy becomes CR energy.

15
Alfven wave drift heating in the precursor due
to Streaming CRs

• - Streaming CRs generate waves upstream
• - Waves drift upstream with
• Waves dissipate energy and heat the gas.
• CRs are scattered and isotropized in the wave
  frame rather than the fluid frame
• ? u u w instead of u
• ? smaller velocity jump and less efficient
  acceleration

streaming CRs
upstream
16
moderate nonlinear modification precursor
CR spectrum at the shock
Kang Jones 2006
17
Evolution of CR modified SNR (Sedov Solution)
18
Volume Integrated CR spectrum for SNR
N p power-law like G p non-linear concave
curvature q 2.2 near pinj q 1.6 near pmax
2.2
1.6
19
CR acceleration efficiency F vs. Ms for
plane-parallel shocks

• - The CR acceleration efficiency
• is determined mainly by Ms
• - It increases with Ms
• but it asymptotes to a limiting
• value of F 0.5 for Ms gt 30.
• - Weak dependence on the
• injection, wave dissipation model
• at high Mach numbers.
• - pre-existing CRs help for low
• Mach number shocks.

Kang Jones 2006
DSA Numerical Simulation Results
20
E max highest energy ? Hillas Plot for
astrophysical accelerators (after Hillas 1984)
Emax Z ba B R
B
Emax highest possible energy (ZeV 1021
eV) Z charge of the CR particle Va/c ba
speed of accelerator B magnetic field strength
(Gauss) R size of accelerator (pc)
R
slide from T.W. Jones
21
X-ray emissivity
Shocks on LSS Mach Number
pancake
cluster
filament
rich, complex shock morphology Shocks reveal
filaments and sheets
(100 Mpc/h)2 2D slice
LCDM simulation with 10243 cells, computational
box (100h-1 Mpc)3 , TVD grid-based Eulerian
hydro code (Ryu et al 2003)
22
Cosmic shocks in ICM
velocity field in x-y plane
rgas
Lx
T
Ms
external shocks high Mach no. outer surfaces of
nonlinear structure internal shocks low Mach
no. inside nonlinear structure
(25Mpc/h)2 slice
23
Highest Energy accelerated at cluster accretion
shocks

• acc (p) 8 k(p)/Vs2 mean acceleration time
• loss e. loss time scale due to CBR
• tacc tloss ? Emax 1018.5 eV for Bohm
  
• Emax 1019.7 eV for Jokipii
• (Kang, Rachen, Biermann 1997)

• Bohm diffusion in parallel shocks
• ? kB rg v / 3
• Jokipii diff. in perpendicular shocks
• kJ rg Vs 3(Vs /c) kB 0.01 kB

Vs 1000 km/s, B1 mG

• Ostrowski Siemieniec-Ozieblo 2002
• diffusion along field lines and drift across
  field are limited by the finite size
• E max Z ba BR return back to Hillas
  constraint,
• so E lt1019 eV cluster accretion shocks

24
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 slopes.
• - With turbulent fields, thermal leakage
  injection works well even at perpendicular shocks
  as well as parallel shocks.
• a fraction of x 10-4 - 10-3 of the incoming
  particles become CRs.
• - About 50 of shock kinetic E can be
  transferred to CRs for strong shocks with Ms gt
  30.
• - At low Mach numbers 10-20 with
  pre-existing CRs
• - Cosmological shocks on LSS can accelerate CR
  protons up to 1019eV, providing that 1mG field is
  present.

25
Thank you !
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Magnetic field is important in acceleration and
confinement of CRs
- in the ISM of our Galaxy mean field 5-8 mG -
Observed Cluster magnetic fields Faraday
Rotation Measures thru the ICM? 1-40 mG
Synchrotron radio halos of clusters ? 0.4-1 mG
Inverse Compton of CMBR in the ICM? 0.2-1 mG
(Carilli Taylor 2002, Clark et al. 2001)

ECR,p 0.2 Egas , EB (0.1-1) Egas ,
ECR,p (10-100) ECR,e CRs and mag. fields could
be dynamically important in the ICM, as in the
ISM of our Galaxy. ( ECR E gas EB 10-12
erg/cm3)
27

• CR modified shocks
• presusor subshock
• (just like MHD J-shock)
• - reduced Pg
• enhanced compression

t0
-1D Plane Shock simulations DSA acceleration
Time evolution of the M0 5 shock structure. At
t0, pure gasdynamic shock with Pc0.

• No simple shock jump condition
• Need numerical simulations to calculate the CR
  acceleration efficiency

precursor
Kang, Jones Gieseler 2002
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Evolution of CR distribution function in DSA
simulation f(p) number of particles in the
momentum bin p, pdp, g(p) p4 f(p)

• CR feedback effects
• gas cooling (Pg decrease)
• thermal leakage
• power-law tail
• concave curve at high E

initial Maxwellian
thermal
power-law tail (CRs)
f(p) p-q
Particles diffuse on different ld(p) and feel
different Du, so the slope depends on p.
g(p) f(p)p4
Concave curve
injection momenta