Acceleration of Cosmic Rays
E.G.Berezhko Yu.G.Shafer Institute of Cosmophysical Research and Aeronomy Yakutsk, Russia
• Introduction• General properties of Cosmic Ray (CR) acceleration• Diffusive shock acceleration• Acceleration of CRs in Supernova Remnants (SNRs)• Nonthermal emission of individual SNRs• SNRs as Galactic CR source• Some aspects of UHECR production in GRBs and extragalactic jets• Conclusions
Cosmic Rays
Earth
Atmosphere
V.Hess (1912)
I ≈ 1 particle/(cm2s)
I ~ ε-γ
γ ≈ 2.7
LCR ≈ 3×1041 erg/s
CR origin problem:i) CR source (?)ii) Acceleration mechanism (?)
• Cosmic Rays (CRs) = atomic nuclei = charged particles
• Electric field is needed to generate (accelerate) CR population
• High value large scale electric field is not expected in space plasma
• Electric field in space plasma is created due to the movement of magnetized clouds
• For efficient CR production (acceleration) the system, which contains strong magnetic field and sufficient number of rapidly moving clouds, is needed
General remarks
vf
vi
Elastic scattering:Elastic scattering:
vi
vf
CRvi
vf
E wscattering center
w
E
Head-on collision:
Δv = vf – vi >0
Overtaken collision:
Δv = vf – vi <0
ww = 0
vf = vi
vf > vi
w = 0Δv = 0
Larger rate of head-on then overtaken collisions efficient CR acceleration
×B
B
E = -[w B]/c
CR scattering on moving magnetized clouds
v >> w
General remarks
• CR acceleration, operated in the regions of powerful sources, are the most meaningful
• The main form of energy available in the space is kinetic energy of large scale supersonic plasma motion (stellar winds, expanding supernova remnants, jets)
• Most relevant acceleration mechanisms are those, which directly transform the energy of large scale motion into the population of high energy particles
• Intense formation of CR spectra are expected to take place at the shocks and in shear flows
Solar wind
Diffusive shock acceleration of CRs
log NCR
log p
p-
= ( + 2)/( -1)
shock compression ratio
Krymsky 1977Bell 1978
Δp
scattering centers
y
x
w
Frictional Acceleration of Cosmic RaysBerezhko (1981)
acc
dp p
dt
2
1acc
dw
dy
mean scattering time
Shear plasma flow
acceleration rate
CR
Frictional CR acceleration is expected to be very efficientin relativistic/subrelativistic jets
scattering center
Energetic requirements to CR sources
Requirements to the CR acceleration mechanism
Jobs ~ ε –γobs ~ Js/τesc
γobs = 2.7
Τesc ~ ε-μ ( μ = 0.5 - 0.7)
JS ~ε-γS
γS = γobs – μ = 2 – 2.2
observed CR spectrum
CR residence time inside the Galaxy
source CR spectrum
Supernova explosions
Supernova explosions supply enough energy to replenish GCRs against their escape from the GalaxyIf there is acceleration mechanism which convert ~10% of the explosion energy into CRS
Cosmic Ray Flux
knee
ankle
GZK cutoff (?)
Possible GCR sources:
SNRs
Reacceleration (?)
Extragalactic (?)
SNRs (?)
Cosmic Ray diffusive acceleration in Supernova Remnants
shock compression ratio
Krymsky 1977Bell 1978
2
1
for strong shock 4 2
ESN ~ 1051erg
Nonlinear kinetic (time-dependent) theory of
CR acceleration in SNRs
•Gas dynamic equations
•CR transport equation
•Suprathermal particle injection
•Gas heating due to wave dissipation
•Time-dependent (amplified) magnetic field
Applied to any individual SNR theory gives at any evolutionary phase t>0 :nuclear Np(p,r), NHe(p,r), … and electron Ne(p,r) momentum and spatial
distributions, which in turn can be used for determination of the expectednonthermal emissions Fγ(εγ)
3
f f
f f p Qt p
ww
c g
gg g g a g a c
0,
,
1 ,
t
P Pt
PP P c P
t
w
ww w
w w
3e e
e e e21
1
3
f f pf f p f
t p p p
ww
Nonlinear kinetic model: basic equations
4
2 2 20
4
3
c
c p fP dp
p m c
Hydrodynamicequations
CR transport equationsfor protons and electrons
CR pressure 1 12
( ) ( )4
inj sinj
uQ p p r R
mpsource term
ρ(r, t) – gas density
w(r, t) – gas velocity
Pg(r, t) – gas pressure
f (p, r, t) – CR distribution function
Berezhko, Yelshin, Ksenofontov (1994)
( )3
pcp
eB CR diffusion
coefficient
2 2
1 2 20
9
4 em c
r B p Synchrotron loss time
(Krymsky, 1964)
u = Vs - w
Particle spectrum in/near acceleration region
/injN N injection rate (parameter)
η > 10-5 → efficient CR production
Nonlinear effects due to accelerated CRs
• Modification of the shock structure due to CR pressure gradient
Non power law (concave) CR spectrum
• Magnetic field amplification (Lucek & Bell, 2000)
Increase of maximum CR energy
Increase of π0-decay gamma-ray emission over IC emission
CR spectrum inside SNRlg N
lg p
N p 2 2
2ptest particle limit
p
pm c maxpp
maximum CR momentumdue to geometrical factors (Berezhko 1996)
ppmax ~ RSVSB
Main nonthermal emission produced by Cosmic Rays(how one can “see” CR sources)
• Synchrotron radiationB
e
radio 0.1 10e GeV
X-ray 1 100e TeV
• Inverse Compton scattering
e
gamma-rays 1 100e TeV
• Nuclear collisions
p
N
0
gamma-rays
10 1510 10p eV
Nonthermal emission of SNRs
• Test for CR acceleration theory
• Determination of SNR physical parameters: - CR acceleration efficiency - Interior magnetic field B
Relevant SNR parameters SNR age t known for historical SNRs
ISM density NH influences SNR dynamics andgamma-ray production;deduced from thermal X-rays
magnetic field B influences CR acceleration & synchrotron losses;deduced from fit ofobserved synchrotron spectrum;
expected to be strongly amplifiedB >> BISM
injection rate η(fraction of gas particles,involved in acceleration)
influences accelerated CR number,shock modification,CR spectral shape;deduced from observed shapeof radio emission
CR spectrum inside SNRlg N
lg p
N p 2 2
2ptest particle limit
p
e
10B G
10B Gradio X-ray
pm c maxep max
pp
due to synchrotron losses
lp1 2
lp t B 1/ 2maxe
sp V B
/14
/10e
GHzGeV
B G
Steep radio-synchrotron spectrum Sν ~ν -α
(>0.5, >2) is indirect evidence ofi) efficient proton acceleration andii) high magnetic field B>>10G
3p
α = (γ – 1)/2
Cassiopeia A
Tuffs (1986), VLA
Type Ib
Distance 3.4 kpc
Age 345 yr
Radius 2 pc
Circumstellar medium: free WR wind + swept up RSG wind + free RSG wind
Circumstellar medium
1 2 r, pc
10
1
Ng, cm-3
BSG wind RSG wind
shell
MS → RSG → BSG → SNBorkowski et al. (1996)
d = 3.4 kpc Mej = 2 MSun ESN = 0.4×1051 erg
current SN shockposition
CSM number density
Berezhko et al. (2003)
Synchrotron Emission from Cassiopeia AExperiment: radio (Baars et al. 1977), 1.2 mm data (Mezger et al. 1986), 6 m data (Tuffs et al. 1997), X-ray data (Allen et al. 1997)
α ≈ 0.8
Proton injection rate η = 3×10--3
Interior magnetic field Bd ≈ 0.5 mG
Strong SN shock modification
Steep concave spectrum at ν < 1012 Hz
Smooth connection with X-ray region (ν > 1018 Hz)
Magnetic field inside SNRs
5d ISMB B G 0.1 SL R
d ISMB Bρ
Rs
Line
of
sigh
t
0-Rs Rs
J
J
Emission (X-ray, γ-ray) due to high energy electrons
L
0.1 SL R
3 / 2dL B
Low field
High (amplified)field
Unique possibility
of magnetic field determination!
ρ
ρ
ChandraCassiopeia A
ChandraSN 1006Filamentary structure of X-ray emission
of young SNRs-consequence of strongly amplified magnetic field,
leading to strong synchrotron losses
Experiment (Vink & Laming 2003)confirms high internal magnetic field extracted from the fit of volumeIntegrated synchrotron flux(Berezhko, Pühlhofer & Völk 2003)
Theory: Berezhko & Völk (2004)
0.5dB mG
L
Projected X-ray brightness of Cassiopeia A
2/316100.5d
cmB mG
l
3/ 7 10 sl L R
For strong losses
emissivity scale
brightness scale
( )acc loss
angular distance
Bd = 500 μG
Bd = 10 μG
direct evidence for magnetic field amplification
Integral gamma-ray energy spectrum of Cas A
Components:
Hadronic (π0)
Inverse Compton (IC)
Nonthermal bremsstrahlung (NB)
Confirmation of HEGRA measurement is very much neededAlready done by Magic (ICRC, Merida 2007)!
SNR RX J1713.7-3946X-rays (nonthermal) ROSAT (Pfeffermann & Aschenbach 1996) ASCA (Koyama et al. 1997; Slane et al. 1999)
XMM (Cassam-Chenai et al. 2004; Hiraga et al. 2005)
Radio-emission ATCA (Lazendic et al. 2004)
VHE gamma-rays CANGAROO (Muraishi et al. 2000)
CANGAROO II (Enomoto et al. 2002)
HESS (Aharonian et al. 2005)
Gamma-ray image (HESS) Aharonian et al. (2005)
Spatially integrated spectral energy distribution of RX J1713.7-3946
required interiormagnetic field
Bd = 126 μG
Experiment: Aharonian et al. (2006)Theory: Berezhko & Völk (2006)
BISM
Beff
Magnetic field amplification
Results of modeling (Lucek & Bell, 2000) +
Spectral properties of SNR synchrotron emission +
Fine structure of nonthermal X-ray emission
SNR magnetic field is considerably amplified
Beff2/8π ≈ 10-2ρISMVS
2
Bd = Beff >> BISM
VS
ρISM
L
SNR magnetic field
• Influences synchrotron emission
• Determines CR diffusion mobility:
Κ ~ p/(ZBd) CR diffusion coefficient (Bohm limit)
pmax ~ Z e Bd RS VS
• Influences CR maximum momentum pmax:
nuclear charge number
Berezhko & Völk (2007)
Energy spectrum of CRs, produced in SNRs
Amplified magnetic field
Bd2/(8π) ≈ 10-2ρ0VS
2
Bd >> BISM
Cosmic Ray Flux
knee 1
GZK cutoff (?)
CR sources:
Supernova remnants
Extragalactic (?)
Supernova remnants
knee 2
Energy spectrum of CRs
CR spectrum,produced in SNRs
CR spectrum from JEG~ε -2.7
extragalactic sources(Berezinsky et al.2006)
Dip scenario Dipp + γ → p + e+ + e-
GZK cutoffp + γ → N + π
Experiment:Akeno-AGASA (Takeda et al. 2003)HiRes (Abbasi et al. 2005)Yakutsk (Egorova et al. 2004)
SNRs
SNRs + reacceleration
Extragalactic(AGNs, GRBs…) JEG~ε -2
Berezinsky et al.(2006)
Energy spectrum of CRsAnkle scenario
Mean logarithm of CR atomic number
Ankle scenario
Dip scenario
Experiment:KASKADE (Hörandel 2005)Yakutsk (Ivanov et al.2003)HiRes (Hörandel 2003)
Precise measurements of CR composition is needed to discriminate two scenarios
Fireball model of Gamma-ray bursts
dΩ ~ 10-2 π
Forward Shock
ISM
Fireball Γ ≈ 100Lorentz factor
Energy release (supernova ?) E
Rees & Meszaros (1992)
E ≈ 1051 erg (?)
ESS
≈ 3×1053 erg
spherically symmetric analog
R
Γ ~ (ESS/NISM
)1/2 R-3/2
R ~ t1/4
CR acceleration in GRBs
εmax ≈ e BuΓ R c
Achterberg et al. (2001)
Bu = BISM = 10 μG
relativistic shock (Γ >> 1)
assumption: isotropic CR diffusion in downstream region
maximum proton energy
εmax ≈ 5 × 107mpc2
Bu2/8π = 0.1Γ2 ρISMc2 εmax ≈ 5 × 1013mpc
2
amplified magnetic field
unamplified magnetic field
NCR(ε)~ ε-γ γ ≈ 2.2
GRBs are powerful extragalactic sources of CRs (?)
Problem
upstreamdownstream
Bu
Bd
Bd ~ Γ2 Bu >> Bu
strongly anisotropic CR diffusion
low chance for CRs to recross shock from downstream to upstream
inefficient CR production
(e.g. Ostrowski & Niemiec, 2006)
VS
shock
Bdll >> Bd┴&
CR acceleration at late evolutionary stage(nonrelativistic shock)
εmax ≈ e Bu R c
R(Γ = 1) =(ESS/3ρISMc2)1/3
Bu2/8π = 0.1ρISMc2
For ESS= 3× 1053 erg, NISM = 1 cm-3 εmax = 3 × 1010 mpc2
then ESS≈1055 erg εmax ≈ 1011 mpc2
amplified magnetic field
ρISM = NISMmpInterStellar Medium density
However assumption Lγ = Qe , Pe ~ Γ2ρISM c2 seems to be unrealistic
Realistic numbers: Pp ~ Γ2ρISM c2 Pe = 10-2Pp
Active Galactic Nuclei Jets
Γ ≈ 10 Lorentz factor
Powerful source of nonthermal emission
Powerful source of Cosmic Rays
Shear flowEffective frictional acceleration(e.g. Ostrowski, 2004)
ShockDiffusive shock acceleration
Conclusions
• CR acceleration in SNRs is able to provide the observed Galactic CR spectrum up to the energy ε ≈ 1017 eV
• Two possibility for Galactic CR spectrum formation: - Dip scenario ( CRs from Galactic SNRs at ε < 1017 eV + Extragalactic CRs at ε > 1018 eV ) - Ankle scenario ( CRs from Galactic SNRs at ε < 1017 eV + Reaccelerated CRs at 1017 < ε < 1018 eV + Extragalactic CRs at ε >019eV)
• Precise measurements of CR spectrum and composition at ε > 1017 eV are needed to discriminate the above two possibilities
• Acceleration by subrelativistic/nonrelativistic shocks in GRBs (or AGN jets) and frictional acceleration in AGN jets are potential sources of Ultra High Energy CRs
Supernovae
0 100 200 300
t, day
lg( Luminosity) = star explosions
SN I
SN II
H lines
H lines
0
-4
-8
MCO<1.4MSun
MCO>1.4MSun
No central objects
pulsar / black hole
SN Ia
SN II/Ib
SNR in uniform ISM
SNR in CSM, modified by progenitor star wind
( 15 % )
( 85 %)
ν
detected from SN1987 A
thermonuclear explosion
core collapse
Cosmic Ray Flux
knee 1
GZK cutoff (?)
CR sources:
Supernova remnants
Extragalactic (?)
Supernova remnants (?)Reacceleration (?)
knee 2
Structure of the shock modified due to CR backreaction
u
xshock front
classical (unmodified)
shock σ = u0/u2 = σS = u1/u2 =4
modified
shock σ > 4, σS < 4
cP CR pressure0u
1u
2u
Flow speed
subshock
precursor
upstream downstream
Accelerationsites
p < mpc γ > 2
p >> mpc γ < 2
E = 1030 eV E=6×1019 eV
CR source
π0
π±
Zatcepin, Kuzmin (1966)Greisen (1966)
Galaxy
Cosmic microwavebackground (CMB) radiation
Cutoff of CR spectrum due to CR interaction with CMB
Projected radial profile of TeV-emission (normalized to a peak values)
Smoothed with GaussianPSF of widthΔψ = 0.1o
Jγmax/Jγ
min ≈ 2.3consistent withHESS value
LL = 0.07 RS
Jγmax/Jγ
min ≈ 8
Spatially integrated spectral energy distribution of RX J1713.7-3946 (Vela Jr)
Low (inefficient) protons injection/acceleration, Bd = 15μG
Projected radial profile of 1 keV X-ray emission (normalized to a peak values)
smoothed with PSFof XMM-Newton(Δψ = 15’’)
test-particle limitBd = 20 μG
inconsistent with experiment
L
Experiment: L=1.2×1018 cm(Hiraga et al. 2005)
Theory: L=1.15×1018 cm(Bd = 126 μG)
wind bubble
shell
Interstellar medium
Rsh lg r
lg Ng
Nb << NISM
σshNISM
NISM
CSM structure
SN
current SN shock position
CSM number density