1. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea Shock Waves and Cosmic Rays in the Large Scale Structure of the Universe Dongsu Ryu (Chungnam National U, Korea) Hyesung Kang (Pusan National U, Korea) - review of previous work: cosmological shocks waves and cosmic rays in large scale structure - effects of detailed physics such as cooling/heating, feedback

2. Shock waves in the large scale structure of the universe Numerical simulations -  cold dark matter cosmology   = 0.73,  DM = 0.27,  gas = 0.043, h=0.7, n = 1,  8 = 0.8 (no gas cooling, no heating, no feedbacks) - computational box: (100h -1 Mpc) 3 1024 3 cells for gas and gravity, 512 3 DM particles,  x = 97.7 h -1 Mpc (Ryu, Kang et al 2003, 2004) shock speed v sh = 15 - 1500 km s -1 and higher X-ray emissivity

3. (100 h -1 Mpc) 3 1024 3 cells full box spinning X-ray emissivity distribution: time evolution

4. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea (100 Mpc/h) 2 2D slice cluster sheet filament shock waves rich, complex shock morphology: shocks “reveal” filaments and sheets (low density gas) X-ray emissivity

5. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea velocity field and shocks in a cluster complex (25 h -1 Mpc) 2 2D slice LxLx  gas TMsMs

6. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea distribution of shock Mach no.

7. time evolution of shocks around a cluster complex 28 x 37 (h -1 Mpc) 2 slice 150 < v sh < 700 km/s v sh < 150 km/s v sh > 700 km/s v sh < 150 km/s external shocks internal shocks external shocks: high Mach no. outer surfaces of nonlinear struct. internal shocks: low Mach no. inside nonlinear structure

8. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea statistics of Mach number distribution S (external) / S(internal) = ~2 at z = 0 and larger in the past → external shocks are more common than internal shocks S = ~1/3 h -1 Mpc with M > 1.5 at z = 0 ( S = ~1 h -1 Mpc with M > 1.5 at z = 0 inside nonlinear structures) → average inverse comoving distance between shock surfaces (S S shock /V, 1/S mean comoving distance btw shock surfaces) shock frequency

9. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea kinetic energy flux per unit comoving volume through shock surfaces internal shocks are energetically more important than external shocks!

10. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea - collisionless shocks form in low density astrophysical plasmas via EM viscosities (i.e. collective interactions between particles and underlying B field) - incomplete “thermalization” → non-Maxwellian tail → suprathermal particles : leak upstream of shock → streaming CRs induce MHD waves - accelerated to higher E via Fermi first order process - CRs are byproducts of collisionless shock formation Collisionless astrophysical shocks

11. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea - CR energy flux emerged from shocks F CR =  (M) F k Thermal E CR E thermalization efficiency:  (M) CR acceleration efficiency:  (M)  1 V s = u 1 E gas - kinetic energy flux through shocks F k = (1/2)   V s 3 - net thermal energy flux generated at shocks F th = (3/2) [P 2 -P 1        u 2 =  (M) F k E CR

12. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea energies passed through and produced at shocks: integrated from z = 2 to 0 3 - CR acceleration  shocks with M = 2~5 - E CR accelerated at shocks = ~1/2 x E th generated at shocks

13. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea - three homogeneous simulations of  cold dark matter cosmology (data from R. Cen)   = 0.69,  matter = 0.31,  gas = 0.048, h=0.69, n = 0.97,  8 = 0.89 computational box (85 h -1 Mpc) 3 with 1024 3 cells for gas & gravity, 512 3 DM particles - adiabatic (gravity and gas pressure only) cooling/heating (heating mostly due to the UV background) cooling/heating+feedback (E feedback = 3x10 -6 M galaxy c 2 as kinetic energy) (intended to be galactic winds, not jets) Effects of other processes? (Kang, Ryu et al 2006 in preparation)

14. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea density-temperature plane  gas /  matter T 10 8 10 4 10 6 10 2 10 0 10 2 10 4 10 0 10 -2 10 2 10 4 adiabaticcooling/heating

15. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea temperature distribution (21.2 h -1 Mpc) 2 2D slice cooling/heatingcooling/heating+feedback

16. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea evolution of WHIM (warm-hot intergalactic medium) WHIM in cooling/heating WHIM in cooling/heating+feedback (Cen and Ostriker 2006)

17. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea distribution of shock waves (100 h -1 Mpc) 2 2D slice adiabatic

18. distribution of shock waves (21.2 h -1 Mpc) 2 2D slice adiabaticcooling/heating cooling/heating+feedbackwind shock only

19. statistics of shock waves shock frequency log(M) log(v) adiabatic cooling/heating cooling/heating +feedback dashed lines – differential dis. solid lines – cumulative dis.

20. energetics of shock waves adiabatic cooling/heating cooling/heating +feedback energy fluxes per unit comoving volume through shock surfaces the effcts of cooling/heating and feedback on shock energetics are not important!

21. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea CRs observed at Earth particle energy spectrum - power-law spectrum - knee energy: 10 15 eV ankle energy: 10 18.5 eV - N(E) ~ E -2.7 below the knee and steeper above - E: up to ~10 21 eV - “universal” acceleration mechanism working on a wide range of scales → shock acceleration UHECRs: above the ankle 12 orders of magnitude 32 orders of magnitude direct measurements air shower measurements E -2.7 E -3.1 extragalactic origin

22. Fe He C,O,… p Nagano & Watson 00 E -2.7 Galactic component extra-Galactic component Galactic? Extra Galactic? knee 2 knee 1 ankle GZK cutoff

23. “Hillas Plot” for some plausible accelerators (after Hillas 1984) confinement and acceleration: E max = Z  a B R E max : highest possible energy Z: charge of the CR particle V a /c =  a : speed of accelerator B: magnetic field strength R: size of accelerator B R = E max /(Z  a ) = 10 20 eV R B

24. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea  acc (p)~ 8  p  /V s 2 mean acceleration time  loss = e. loss time scale due to CBR  acc =  loss  E max ~ 10 18.5 eV for Bohm E max ~ 10 19.7 eV for Jokipii (Kang, Rachen, Biermann 1997)  acc V s = 1000 km/s, B = 1  G Highest Energy accelerated at cluster accretion shocks Bohm diffusion in parallel shocks    B = r g v / 3 Jokipii diff. in perpendicular shocks    J ~ r g V s = 3(V s /c)  B ~ 0.01  B diff. along field lines and drift across field are limited by the finite size  E max = Z b a BR : return back to “Hillas” constraint, so E < a few x 10 19 eV cluster accretion shocks (Ostrowski & Siemieniec-Ozieblo 2002)

25. - shock waves are common in the large scale structure of the Universe, which are consequences of structure formation V/S shock = ~3h -1 Mpc with M >1.5 at z=0 (V/S shock = ~1h -1 Mpc with M >1.5 at z=0 inside structures) - the effects of cooling/heating and feedbacks on shock energetics are negligible - CRs are natural byproducts of dissipation at collisionless shocks E th & E CR  shocks E CR /E th ~ 1/2 at shocks => E CR ~ E th at present - weaker internal shocks => heat gas and accelerate CR protons & electrons shocks with M = 2~4 contribute most - stronger external shocks => produce higher energy CRs up to ~ a few x 10 19 eV Summary

26. November 1 - 3, 2006 2 nd East Asia Numerical Astrophysics Meeting KASI, Korea Thank you !