Shock Waves in the Large Scale Structure of the Universe and Cosmic Rays Accelerated Dongsu Ryu (Chungnam National U, Korea) Hyesung Kang (Pusan National U, Korea) cosmic rays: observations and theory a possible origin of cosmic rays in large scale structure: cosmological shocks waves in an adiabatic simulation effects of detailed physics (cooling/heating, feedback) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea 12 orders of magnitude 32 orders of magnitude direct measurements air shower E-2.7 E-3.1 extragalactic origin CRs observed at Earth particle energy spectrum power-law spectrum knee energy: 1015 eV ankle energy: 1018.5 eV N(E) ~ E-2.7 below the knee and steeper above E: up to ~1021 eV “universal” acceleration mechanism working on a wide range of scales → shock acceleration UHECRs: above the ankle May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Extra Galactic? Galactic? C,O,… GZK cutoff He Fe p knee 2 knee 1 ankle E-2.7 extra-Galactic component Galactic component May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Nagano & Watson 00

Observational evidences for CRs in large scale structure - diffuse radio halos and relics in over 30 clusters radio synchrotron (CR electrons + magnetic field) (Govoni, Feretti, Giovannini) - hard X-ray & EUV (?) emission in excess of thermal radiation inverse Compton scattering of CBR by CR electrons (Fusco-Feminao, Colafrancesco, Blasi, Lieu, Sarazin) - g-rays yet to be observed CR p + p → po decay → GeV g-ray CBR photons inverse Compton e- up to g-ray pp po g-ray CR protons Pion decay gamma May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea diffuse raiod sources in clusters of galaxies prove the existence of relativistic electrons of energy  GeV and of magnetic fields  G on scales of Mpcs !! Coma cluster X-ray: ROSAT (White et al. 1993) thermal: X-ray 500 kpc RADIO: WSRT, 90 cm (Feretti et al.1998) nonthermal: radio May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea A 2319: 1.4 Mpc CR e’s & magnetic fields COMA: 1.1 Mpc A 2255: 1.2 Mpc CL0016+16: 1.1 Mpc z = 0.5545 A 2163: 2.9 Mpc May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

radio arcs in A3376 (Bagchi 2003) observational evidence for accretion shocks or merger shocks ? 2.6 h50 -1 Mpc May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

nonthermal hard X-ray emission from clusters possible detections of hard X-ray excesses from clusters with BeppoSAX & RXTE Coma, A2319, A2256, … CR e’s Coma HXR BeppoSAX (Fusco-Femiano et al.) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Why do we care about the CRs? - CRs are ubiquitous in astrophysical plasma. heliosphere (solar system) solar wind, interplanetary shocks - ISM of our Galaxy ECR ~ EB ~ Egas ~ ECMBR ~ 10-12 erg/cm3 dynamically important in the ISM of galaxies sources: SNRs, stellar wind (OB stars), pulsars - ICM inside clusters of galaxies (and large scale structure) ECR,e ~ 0.01 Ethermal , ECR,p ~ Etheremal , EB ~ Ekinetic ~ 0.1 Ethermal sources: AGNs, galactic winds, turbulence, structure shocks May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

Origins of cosmic rays in large scale structures * cosmological shock waves - fresh injection/acceleration of protons and electrons (diffusive shock acceleration (DSA): Fermi first order process) - re-acceleration of CR electrons and protons (pre-existing or ejected by radio galaxies and etc …) (in relic radio ghosts) secondary electrons generated by CR protons + ICM (CR p + p → p + p + p, p± → m± → e± & po → g-rays ) * stochastic acceleration by the ICM turbulence * AGNs, galatic winds, and etc May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

“Hillas Plot” for Emax = Z ba B R B R = Emax /(Z ba ) = 1020 eV some plausible accelerators (after Hillas 1984) confinement and acceleration: Emax = Z ba B R B Emax: highest possible energy Z: charge of the CR particle Va/c = ba : speed of accelerator B: magnetic field strength R: size of accelerator B R = Emax /(Z ba ) = 1020 eV R May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Collisionless astrophysical shocks - collisionless shocks form in low density astrophysical plasmas via EM viscosities (i.e. collective interactions btw 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 May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea the key ideas behind DSA (diffusive shock acceleration) - Alfven waves in a converging flow act as converging mirrors → particles are scattered by waves → cross the shock many times “Fermi first order process” u1 u2 shock front particle upstream downstream shock rest frame energy gain at each crossing converging mirrors May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea simplest prediction of DSA theory - when non-linear feedback due to CR pressure is insignificant test particle theory: f(p) ~ p-q or N(E) ~ E-q+2 universal power-law 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 M): r → 4 (g = 5/3 for gas adiabatic index) q → 4, f(p) dp= f0 p-4 dp or N(E)dE = N0 E-2 dE synchrotron jn ~ n-a , a = (q - 3)/2 → 0.5 spectral index ~ similar to observed values of “q” and “a” But DSA is very efficient, CR pressure is significant → nonlinear feedback of diffusive CRs to the shock structure May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea 1D Plane Shock simulations of DSA acceleration t=0 CR modified shocks - presusor + subshock - reduced Pg enhanced compression time evolution of the Ms = 5 shock structure at t = 0, pure gasdynamic shock with Pc = 0. no simple shock jump condition → need numerical simulations to calculate the CR acceleration efficiency precursor (Kang, Jones & Gieseler 2002) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Thermal E CR E - kinetic energy flux through shocks Fk = (1/2)r1Vs3 - net thermal energy flux generated at shocks Fth = (3/2) [P2-P1(r2/r1)g] u2 = d(M) Fk - CR energy flux emerged from shocks FCR= h(M) Fk Egas r1 Vs= u1 thermalization efficiency: d(M) CR acceleration efficiency: h(M) ECR May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

Shock waves in the large scale structure of the universe (Ryu, Kang et al 2003, 2004) Numerical simulations - L cold dark matter cosmology L = 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 10243 cells for gas and gravity, 5123 DM particles, Dx = 97.7 h-1Mpc X-ray emissivity shock speed vsh = 15 - 1500 km s-1 and higher

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea X-ray emissivity distribution: time evolution (100 h-1 Mpc)3 10243 cells full box spinning May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea X-ray emissivity shock waves sheet cluster filament (100 Mpc/h)2 2D slice rich, complex shock morphology: shocks “reveal” filaments and sheets (low density gas) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

velocity field and shocks in a cluster complex Lx rgas T Ms (25 h-1Mpc)2 2D slice May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea distribution of shock Mach no. May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea time evolution of shocks around a cluster complex 28 x 37 (h-1 Mpc)2 slice 150 < vsh< 700 km/s vsh< 150 km/s vsh> 700 km/s external shocks internal shocks external shocks: high Mach no. outer surfaces of nonlinear struct. internal shocks: low Mach no. inside nonlinear structure May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

statistics of Mach number distribution (S Sshock/V, 1/S mean comoving distance btw shock surfaces) shock frequency 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-1Mpc with M > 1.5 at z = 0 → average inverse comoving distance between shock surfaces May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

kinetic energy flux per unit comoving volume through shock surfaces internal shocks are energetically more important than external shocks! May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Thermal E CR E - kinetic energy flux through shocks Fk = (1/2)r1Vs3 - net thermal energy flux generated at shocks Fth = (3/2) [P2-P1(r2/r1)g] u2 = d(M) Fk - CR energy flux emerged from shocks FCR= h(M) Fk Egas r1 Vs= u1 thermalization efficiency: d(M) CR acceleration efficiency: h(M) ECR May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

energies passed through and produced at shocks: integrated from z = 2 to 0 3 - CR acceleration  shocks with M = 2~5 - ECR accelerated at shocks = ~1/2 x Eth generated at shocks May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

Effects of other processes? (Kang, Ryu et al 2006 in preparation) three homogeneous simulations of L cold dark matter cosmology (data from R. Cen) L = 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 10243 cells for gas & gravity, 5123 DM particles - adiabatic (gravity and gas pressure only) cooling/heating (heating mostly due to the UV background) cooling/heating+feedback (Efeedback = 3x10-6 Mgalaxyc2 as kinetic energy) (intended to be galactic winds, not jets) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

density-temperature plane adiabatic cooling/heating rgas/rmatter T 108 104 106 102 100 10-2 May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

temperature distribution cooling/heating cooling/heating+feedback (21.2 h-1Mpc)2 2D slice May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

evolution of WHIM (warm-hot intergalactic medium) WHIM in cooling/heating+feedback WHIM in cooling/heating Mass weighted volume filling factorof about 0.05, then with density of 10 times The mean, we get 50% of mass in WHIM (Cen and Ostriker 2006) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

distribution of shock waves (100 h-1Mpc)2 2D slice adiabatic May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

distribution of shock waves adiabatic cooling/heating (21.2 h-1Mpc)2 2D slice cooling/heating+feedback wind shock only May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

statistics of shock waves adiabatic shock frequency log(M) cooling/heating cooling/heating+feedback May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea log(v)

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

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) tacc 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, B = 1 mG diff. 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 <1019 eV cluster accretion shocks (Ostrowski & Siemieniec-Ozieblo 2002) May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Averaged energy spectrum of CRs produced at shocks at z = 0 E-2.2 thermal leakage & test particle models adopted E-2.1 3 109 eV 1019 eV May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Summary - shock waves are common in the large scale structure of the Universe, which are consequences of structure formation V/Sshock = ~3h-1Mpc with M >1.5 at z=0 (V/Sshock = ~1h-1Mpc with M >1.5 at z=0 inside structures) - CRs are natural byproducts of dissipation at collisionless shocks Eth  shocks ECR/Eth ~ 1/2 at shocks => ECR ~ Eth 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 ~1019 eV May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea

May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea Thank you ! May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea