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