shock waves in the large scale structure of the universe and cosmic rays accelerated

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

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)


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 ankle12 orders of magnitude

32 o

rder

s of

mag

nit

ud

e

direct measurements

air showermeasurements

E-2.7

E-3.1

extragalactic origin


FeHe

C,O,…

p

Nagano & Watson 00

E-2.7

Galactic component

extra-Galactic component

Galactic?Extra

Galactic?

knee 2knee 1

ankle

GZKcutoff


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)

- -rays yet to be observed CR p + p → o decay → GeV -ray

CBR photons

h

h2

inverse Compton

e-

up to -ray

p

o

-ray

CR protons

Pion decay gamma


Coma cluster

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 !!

500 kpc

RA

DIO

: W

SR

T,

90

cm

(Fere

tti et

al.

19

98

)

nonthermal: radio

X-r

ay:

RO

SA

T (

Wh

ite e

t al.

19

93

)

thermal: X-ray


COMA: 1.1 Mpc

A 2255: 1.2 Mpc

CL0016+16: 1.1 Mpcz = 0.5545

A 2319: 1.4 Mpc

A 2163: 2.9 Mpc

CR e’s &

magnetic fields


radio arcs in A3376 (Bagchi 2003)

observational evidence for accretion shocks or merger shocks ?

2.6 h50 -1 Mpc


nonthermal hard X-ray emission from clusters

possible detections of hard X-ray excesses from clusters with BeppoSAX & RXTE

Coma, A2319, A2256, …

Coma HXR BeppoSAX (Fusco-Femiano et al.)

CR e’s


- 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

Why do we care about the CRs? - CRs are ubiquitous in astrophysical plasma.


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 + , ± → ± → e± & o → -rays )

* stochastic acceleration by the ICM turbulence

* AGNs, galatic winds, and etc


“Hillas Plot” for some plausible accelerators (after Hillas 1984)

confinement and acceleration:

Emax = Z a B REmax: highest possible energyZ: charge of the CR particle

Va/c = a : speed of accelerator B: magnetic field strengthR: size of accelerator

B R = Emax /(Z a ) = 1020 eV

R

B


- 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

Collisionless astrophysical shocks


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

upstreamdownstream

shock rest frame

u

u

p

p ||~

energy gainat each crossing

converging mirrors


- 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 = 2/1=u1/u2 compression ratio across the shock) determined solely by the shock Mach number

- for strong gas shock (large M): r → 4 ( = 5/3 for gas adiabatic index) q → 4, f(p) dp= f0 p-4 dp or N(E)dE = N0 E-2 dE synchrotron j = (q - 3)/2 → 0.5spectral index ~ similar to observed values of “q” and “”

simplest prediction of DSA theory

But DSA is very efficient, CR pressure is significant

→ nonlinear feedback of diffusive CRs to the shock structure


time evolution of the Ms = 5 s

hock structure

at t = 0, pure gasdynamic shock with Pc = 0.

t=0

(Kang, Jones & Gieseler 2002)

1D Plane Shock simulations ofDSA acceleration

CR modified shocks- presusor + subshock- reduced Pg

- enhanced compression

precursor

no simple shock jump condition→ need numerical simulations to calculate the CR acceleration efficiency


- CR energy flux emerged from shocks FCR= (M) Fk

Thermal E

CR E

thermalization efficiency: (M)CR acceleration efficiency: (M)

1

Vs= u1

Egas

- kinetic energy flux through shocks

Fk = (1/2)Vs3

- net thermal energy flux generated at shocks

Fth = (3/2) [P2-P1u2

= (M) Fk

ECR

Shock waves in the large scale structure of the universeNumerical 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

10243 cells for gas and gravity, 5123 DM particles, x = 97.7 h-1Mpc

(Ryu, Kang et al 2003, 2004)

shock speed

vsh = 15 - 1500 km s-1 and higher

X-ray emissivity


(100 h-1 Mpc)3

10243 cells

full box spinning

X-ray emissivity distribution:time evolution


(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


velocity field and shocks in a cluster complex

(25 h-1Mpc)2 2D slice

Lxgas

T Ms


distribution of shock Mach no.


time evolution of shocks around a cluster complex

28 x 37 (h-1 Mpc)2 slice

150 < vsh< 700 km/s

150 < vsh< 700 km/s

vsh< 150 km/s

vsh> 700 km/s

vsh> 700 km/s

vsh< 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


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 shocksS = ~1/3 h-1Mpc with M > 1.5 at z = 0 → average inverse comoving distance between shock surfaces

(S Sshock/V, 1/S mean comoving distance btw shock surfaces)

shock frequency


kinetic energy flux per unit comoving volume through shock surfaces

internal shocks are energetically more important than external shocks!


- CR energy flux emerged from shocks FCR= (M) Fk

Thermal E

CR E

thermalization efficiency: (M)CR acceleration efficiency: (M)

1

Vs= u1

Egas

- kinetic energy flux through shocks

Fk = (1/2)Vs3

- net thermal energy flux generated at shocks

Fth = (3/2) [P2-P1u2

= (M) Fk

ECR


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


- 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 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)

Effects of other processes?

(Kang, Ryu et al 2006 in preparation)


density-temperature plane

gas/matter

T

108

104

106

102

100 102 10410010-2 102 104

adiabatic cooling/heating


temperature distribution

(21.2 h-1Mpc)2 2D slice

cooling/heating cooling/heating+feedback


evolution of WHIM (warm-hot intergalactic medium)

WHIM in cooling/heatin

g

WHIM in cooling/heating+feedback

(Cen and Ostriker 2006)


distribution of shock waves

(100 h-1Mpc)2 2D slice

adiabatic


distribution of shock waves

(21.2 h-1Mpc)2 2D slice

adiabatic cooling/heating

cooling/heating+feedback wind shock only


statistics of shock waves

shock frequency

log(M)

log(v)

adiabatic

cooling/heating


energetics of shock waves

adiabatic

cooling/heating


energy fluxes per unit comoving volume through shoc

k surfaces

the effcts of cooling/heating and feedback on shock energetics are not important!


acc (p)~ 8 p/Vs

2 mean acceleration time

loss = e. loss time scale due to CBR

acc = loss Emax ~ 1018.5 eV for Bohm

Emax ~ 1019.7 eV for Jokipii (Kang, Rachen, Biermann 1997)

acc

acc

Vs = 1000 km/s, B = 1 G

Highest Energy accelerated at cluster accretion shocks

Bohm diffusion in parallel shocks

B = rg v / 3Jokipii diff. in perpendicular shocks

J ~ rg Vs = 3(Vs /c) B ~ 0.01 B

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)


Averaged energy spectrum of CRs produced at shocks at z = 0

3

E-2.1

E-2.2

1019 eV109 eV

thermal leakage & test particle models adopted


- 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

Summary


Thank you !

shock waves in the large scale structure of the universe and cosmic rays accelerated

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