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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)
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
FeHe
C,O,…
p
Nagano & Watson 00
E-2.7
Galactic component
extra-Galactic component
Galactic?Extra
Galactic?
knee 2knee 1
ankle
GZKcutoff
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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
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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
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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, …
Coma HXR BeppoSAX (Fusco-Femiano et al.)
CR e’s
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
- 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.
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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 + , ± → ± → e± & o → -rays )
* stochastic acceleration by the ICM turbulence
* AGNs, galatic winds, and etc
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
“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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
- 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
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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
upstreamdownstream
shock rest frame
u
u
p
p ||~
energy gainat each crossing
converging mirrors
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
- 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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
- 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
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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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
(100 h-1 Mpc)3
10243 cells
full box spinning
X-ray emissivity distribution:time evolution
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May 17-19, 2006 4th Korean Astrophysics Workshop 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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
velocity field and shocks in a cluster complex
(25 h-1Mpc)2 2D slice
Lxgas
T Ms
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
distribution of shock Mach no.
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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
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
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May 17-19, 2006 4th Korean Astrophysics Workshop 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 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
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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!
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
- 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
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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
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May 17-19, 2006 4th Korean Astrophysics Workshop 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 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)
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
density-temperature plane
gas/matter
T
108
104
106
102
100 102 10410010-2 102 104
adiabatic cooling/heating
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
temperature distribution
(21.2 h-1Mpc)2 2D slice
cooling/heating cooling/heating+feedback
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
evolution of WHIM (warm-hot intergalactic medium)
WHIM in cooling/heatin
g
WHIM in cooling/heating+feedback
(Cen and Ostriker 2006)
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
distribution of shock waves
(100 h-1Mpc)2 2D slice
adiabatic
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
distribution of shock waves
(21.2 h-1Mpc)2 2D slice
adiabatic cooling/heating
cooling/heating+feedback wind shock only
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
statistics of shock waves
shock frequency
log(M)
log(v)
adiabatic
cooling/heating
cooling/heating+feedback
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energetics of shock waves
adiabatic
cooling/heating
cooling/heating+feedback
energy fluxes per unit comoving volume through shoc
k surfaces
the effcts of cooling/heating and feedback on shock energetics are not important!
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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)
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
- 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
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May 17-19, 2006 4th Korean Astrophysics Workshop KASI, Korea
Thank you !