1. PARTICLE ACCELERATION IN STRONG SHOCKS: INFLUENCE ON THE SUPERNOVA REMNANT EVOLUTION IN RADIO
Dejan Urošević
Department of Astronomy, Faculty of Mathematics, University of Belgrade
VII BSAC, 1- 4 June, 2010, CHEPELARE

2. particle acceleration

3. particle acceleration
first order Fermi acceleration (“Type A” in Fermi (1949))
ΔE / E ~ v / c

4. particle acceleration
second order Fermi acceleration (“Type B” in Fermi (1949)) – affirmed in this paper
ΔE / E ~ (v / c)2

5. particle acceleration
Cosmic rays
Ultra-relativistic electrons
Synchrotron emission, gamma-ray emission by inverse Compton scattering and pion decay
SNRs, AGNs

6. particle acceleration (SNRs and AGNs)
diffuse shock acceleration – first order Fermi acceleration
Bell (1978a,b), Blandford & Ostriker (1978, 1980), Drury (1983a,b), Malkov & Drury (2001)

7. particle acceleration (SNRs and AGNs)
second order Fermi acceleration – turbulences in downstream region
Scott & Chevalier (1975), Galinsky & Shevchenko (2007)

8. DSA – diffuse shock acceleration
Microscopic approach (Bell 1978a)

9. DSA – diffuse shock acceleration
Probability of escape at a large distance downstream
η = 4 v2/ v
v – test particle velocity (v ≈ c) ↓↓
PROBABLE RECROSSING FROM DOWNSTREM TO UPSTREAM
scattering induced by magnetic turbulence in downstream region

10. DSA – diffuse shock acceleration
Scattering in upstream region is induced by turbulence in the form of Alfven waves excited by energetic particles which pass through the shock and attempt to escape upstream
(quasi-non-linear effect) ↓↓
RECROSSING FROM UPSTREAM TO DOWNSTREM

11. DSA – diffuse shock acceleration
After N cycles particle is
“diffuse shocked”
Particle “loses memory” about its initial spectrum

12. DSA – diffuse shock acceleration
Resulting spectrum of the cosmic ray particles in DSA theory is power law:
N(E) dE ~ E-μ dE, where μ=(2v2+v1)/(v1-v2), for strong non-modified shocks (v1=4v2)
μ=2

13. DSA – diffuse shock acceleration
Macroscopic approach
(Krymsky 1977, Axford et al. 1977, Blandford & Ostriker 1978)
f(t,x,p) - distribution function of the phase space density
again the power-law form f(p) ~ p-4
for the ideal gas (γ = 5/3), and Mach number M → ∞ ↓↓
N(p)dp = 4πp2f(p)dp

14. DSA – diffuse shock acceleration
MODIFIED SHOCKS
Non-linear effects
Including of cosmic ray (CR) pressure
γ = 4/3 → compression ratio r = 7!!!

15. DSA - SNRs (Blandford & Ostriker 1978)
* SNRs are energetically capable to accelerate CRs by DSA mechanism!!!
(Blandford & Ostriker 1978)
* Still, the particle injection stays as an open problem

16. DSA - SNRs
Injection (Bell 1978b) → Einj = 4(1/2mpvs2)

17. DSA - SNRs 4(1/2mpvs2) = 2mec2 → vs ≈ 7000 km/s
For SNRs in energy conserving phase, the radio (synchrotron) surface brightness (for vs << 7000 km/s) to diameter relation:
Σ ~ D-3.5 (Duric & Seaquist 1986)

18. DSA - SNRs
Non-linear kinetic theory for CR acceleration in SNRs (Berezhko & Völk 2004)
Modified shocks by CR pressure

20. DSA - SNRs
Early free expansion phase vs ≈ const, shock is slightly modified (PCR ≈ const. → B ≈ const.) → Σ ~ D
Late free expansion phase, vs ≠ const, shock is slightly modified (PCR ~ vs + equipartition → B ~ vs1/2) → Σ ~ D-0.3

21. DSA - SNRs

22. DSA - SNRs (linear theory Σ ~ D-3.5)
early energy conserving (Sedov) phase, vs ~ D-1.5, shock is significantly modified (PCR ~ vs2 → B ~ vs) ↓↓
Σ ~ D-4.25
(linear theory Σ ~ D-3.5)

23. DSA - SNRs
late energy conserving (Sedov) phase, shock decelerates, DSA and mag. Field amplification are irrelevant (PCR ~ vs2 → B ≈ const.) ↓↓
Σ ~ D-2

25. DSA - SNRs
Injection (Berezhko & Völk 2004 – B&V)

26. Conclusions
1. Bell’s and B&V models are not in contradiction (in order of used injection models).
2. Different results for energy conserving phase are relics of different models and using of different assumptions.
3. Bell’s model has physically better foundations.

27. Future work
1. Free expansion evolution in “Bell’s environment” and corresponding radio evolution – preliminary results: Σ ~ D for early free expansion
2. Evolution of an SNR in radio – excluding phases of evolution
3. Searching for different injection models

28. Future work DSA – diffusion only in pinch angle
second order acceleration – diffusion in velocities
↓↓↓
modeling of both processes in the same time

29. Regards from the Belgrade ISM gang!!!!!

30. THANK YOU VERY MUCH FOR ATTENTION!!!