1. Proton Injection & Acceleration at Weak Quasi-parallel ICM shock
 Hyesung Kang (Pusan National University)
Dongsu Ryu, Ji-Hoon Ha (UNIST, Korea)
SN1006
Supernova remnant shock
Solar wind bow shock
Radio Relic shocks
Galaxy clusters

2. ICM: IntraCluster Medium
𝑸 ⊥ :
𝑸 ∥ :
2-3
20-30
Previous studies on collisionless shocks focus mainly on low b (<1) plasma (e.g. solar wind & ISM). Physics of weak shocks in b=100 ICM could be quite different (e.g. various microinstabilities).

3. : Requirement for shock crossing
DSA: Fermi first order process at 𝑸 ∥ shocks U2 U1
Shock front
particle
downstream
upstream B
mean field
: Requirement for shock crossing
Kinetic plasma processes are crucial for pre-acceleration/injection problem Focus of this talk

4. Particle Energy Spectrum: Injection Problem
Maxwellian
DSA power-law spectrum
Kinetic processes
PIC/Hybrid simulations
𝑃 𝑖𝑛𝑗

5. Q: Can weak ICM shocks accelerate CR protons/electrons ?
Shocks in Structure Formation Simulations
(Ryu et al 2003)
Shocks in ICM
Weak internal shocks with Ms<3 are dominant and energetically important inside hot ICM.
Cosmic-rays are accelerated via Fermi-I just like Earth’s bow shock & supernova remnants
Q: Can weak ICM shocks accelerate CR protons/electrons ?
25h-1 Mpc
Quasi-parallel ( 𝑸 ∥ ) shocks in the ICM
 CR protons collision with ICM
 p0 decay g rays (not detected)
Quasi-perpendicular ( 𝑸 ⊥ ) shocks in the ICM
CR electrons radio synchrotron emiss (observed)
Ji-Hoon’s talk
Accretion Shocks
ICM= Intracluster Medium (𝑇= K)

6. subcritical supercritical Low 𝑴 𝑨 𝑸 ∥ shocks 1D hybrid simulations
𝑴 𝑨 = 1.5 : shock is steady & smooth.
𝑴 𝑨 > 2.8 : shock is unsteady &
undergoes self-reformation.
Subcritical weak shocks:
shock transition is smooth, lacking an overshoot.
Ion reflection is inefficient,
maybe no particle acceleration
supercritical
1994

7. Earth Bow shock: Q-perp shock
-relative drift between reflected ions and incoming particles excites various waves via micro-instabilities in the shock foot.
upstream
Shock criticality & ion reflection are crucial for the shock structure & particle acceleration.
Collisionless shock is not a simple MHD jump.
Dissipation is mediated by collective EM interactions instead of inter-particle collisions.  complex kinetic processes are involved, e.g. microinstabilities.

8. Two ways to reflect protons/electrons at the shock
(1) magnetic mirror reflection due to compressed magnetic fields B n
QBn
shock
mirror force due to gradient of B
dominant at 𝑸 ⊥ shock
Caprioli & Spitkovsky
(2) Shock potential barrier:
-decelerates ions
but accelerates electrons
-ions are reflected by overshoot
dominant at 𝑸 ∥ shock
Both magnetic field compression & shock potential drop depends on 𝑴 𝒔
 Reflection fraction increases with increasing 𝑴 𝒔

9. Kinetic Plasma Simulations: PIC (Particle In Cell)
-can follow kinetic plasma processes: e.g. wave-particle interactions
-provide the most complete pictures, but very expensive / =
Large mass ratio  large time scale ratio

10. 1D/2D PIC simulations for 𝑸 ∥ shocks (proton injection to DSA)
Ha et al. 2018
downstream
upstream
B in x-y plane
Simulation frame = downstream rest frame

11. First critical Mach number : 𝑀 𝑓 ∗ ≈2.3
Time evolution of shock structure: Stack plot
Supercritical
subcritical
-Time-varying overshoot in eF & B
-cyclic reformation of the shock
-No overshoot, smooth transition
First critical Mach number : 𝑀 𝑓 ∗ ≈2.3

12. Ms=3.2 supercritical with a beam of reflected ions
Ms=2.0 subcritical without reflected ions
Overshoot
~ 200

13. Time Evolution of energy spectrum Injection to DSA
DSA power-law spectrum extends to higher energy in time.
Obliquity dependence
Early stage of DSA
in Q-par shocks
Only SDA (no DSA)
in Q-perp shocks
q=63
q13

14. Mach number dependence
Injection momentum
Injection fraction
Ms~2.25
𝑝 𝑚𝑖𝑛 = 2 𝑝 𝑖𝑛𝑗

15. SUMMARY
1. internal shocks driven by mergers and chaotic flows: 𝑀 𝑠 ≤3,
2. In high b ICM, only supercritical 𝑸 ∥ shocks with 𝑴 𝒔 ≥𝟐.𝟑
may inject suprathermal protons to DSA and accelerate CR protons.
So most of ICM shocks do not accelerate CR protons.
3. The injection fraction, x(t), decreases with time.
Long-term evolution of x(t) can be studied with other methods.
Key words:
Shock criticality, 𝑴 𝒇 ∗ ≈𝟐.𝟑, Ion Reflection,
Ion Injection to Fermi-I process, Weak ICM Shock

17. 𝑸 ∥ 𝑸 ⊥ Key elements for proton injection to DSA at 𝑸 ∥ shocks
(1) Reflection at the shock & energy gain near the front via SDA
(2) Backstreaming of ions upstream along B0
relative drift between reflected ions & incoming particles: free E source
(3) Self-excitation of upstream waves: e.g. whistlers or Alfven waves
 Scattering leads to Injection to Fermi I acceleration
𝑸 ∥
𝑸 ⊥
(3) self-excitation of waves
(2)
(1)
after 1/2 gyro-orbit, advect downstream
Scattering by upstream waves
Backstreaming
upstream

18. Particle Acceleration Processes operating at collisionless shocks
Diffusive Shock Acceleration (DSA): Fermi 1st order process
- effective at quasi-parallel ( 𝑸 ∥ ) shocks
- scattering off MHD waves in the upstream and downstream region
(2) Shock Drift Acceleration (SDA)
- effective at quasi-perpendicular ( 𝑸 ⊥ ) shocks
- drifting along the convective E field (grad B) at the shock front
(3) Shock Surfing Acceleration (SSA)
- reflected by shock potential, scattered by upstream waves
- moving along the convective E field, while being trapped at the shock foot
(4) Turbulent Acceleration: Fermi 2nd order process, stochastic acceleration
- much less efficient than DSA
- could be important only in turbulent plasma
(5) Magnetic Reconnection
There are three main acceleration processes operating at collisionless shocks.

19. Shock Drift Acceleration (SDA) at 𝑸 ⊥ shocks
downstream
Electrons drift anti-parallel
to E field.
upstream
shock surface
in x-y plane
upstream
Trajectory of an electron
upstream
From Guo, Sironi, & Narayan 2014
SDA
drift along - z
-perpendicular component of B is compressed at shock
-motional Electric field is induced
-grad(B) drift of electron in -z direction (anti-parallel to E)
protons in +z direction (parallel to E)
in the shock transition layer  gain energy
pre-acceleration of protons/electrons
 multi-cycles of SDA  injection to DSA
reflected

20. CR proton acceleration efficiency from Hybrid simulations
Caprioli & Spitkovsky 2014
𝑸 ∥
𝑸 ⊥
No proton acceleration at 𝑸 ⊥ shocks
High beta cases
𝛽 𝑝 ~36
Caprioli (KAW9)

21. according to hybrid simulations, b~1
2016
Fermi LAT upper limits on gamma-ray flux
from individual clusters
To be compatible with Fermi upper limits, the CR proton acceleration efficiency should be h <0.1% for 2<M<5.
according to hybrid simulations, b~1
Different DSA efficiency models

22. Signatures of shocks in ICM: X-ray shocks in merging clusters
The Bullet Cluster
Markevitch 2006
Shimwell et al. 2015
Cluster A665
Dasadia et al. 2016
shock
Structure formation shocks have been detected by temperature or surface brightness discontinuities in X-ray observations, as shown in this Bullet cluster and also in the cluster A665. These are among the strongest X-ray shocks detected in the ICM, with the sonic Mach number ranging from 2.5 to 3.

23. Radio relics: diffuse radio sources in merging clusters
1RXS J
PLCKG
shock
Sausage relic
Shock Mach numbers estimated from spectral index, based on DSA model, 𝑴 𝒔 ~𝟐−𝟑
ZwCl0008.8
Radio relics are diffuse radio source found in the outskirts of merging clusters. They are interpreted as synchrotron emission….
The shock Mach number can be estimated from the radio spectral index, based on diffusive shock acceleration model.

24. Key Physical Processes in ICM: shocks, turbulence, magnetic fields,
& particle acceleration nonthermal radiation
Gravitational energy
X-ray shocks: observed
supersonic flows
Heat
Shock
Quasi-perpendicular shocks:
CR electrons (Radio relics): observed
Relativistic particles
Quasi-parallel shocks: CR protons
pp collision  p0 decay g rays (not detected)
DSA (Fermi I)
Ji-Hoon’s talk
Heat
turbulence decay
Vorticity
Turbulence
turbulent acceleration (Fermi II)
turbulence dynamo
MHD/Plasma waves
CR 2ndary electrons (Radio halos)
Magnetic fields
CR protons  secondary ptls
merging clusters
dissipation scale

25. Hybrid simulation: Proton acceleration at shocks
Caprioli & Sptikovsky 2014
upstream
downstream
At Q-par shocks:
stream of accelerated ions into upstream
self-generated waves
B amplification B n
At Q-perp shocks:
No backstreaming ions into upstream
No turbulent waves n B

26. DSA beyond injection ?
Amplitude of the DSA power-law should decrease in time.
𝛾 𝑚𝑎𝑥 ~1
The injection fraction, x(t), decreases with time.
Long-term evolution of x(t) can be studied with other methods such as hybrid simulations.

27. Ion reflection at super-critical shocks:
Edmiston & Kennel (1984)
High beta plasma (IPM or ICM)
Low beta plasma (solar flare)
For ICM shocks with b~50,