Download ppt

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
V.Hess (1912)
I ≈ 1 particle/(cm2s)
I ~ ε-γ
γ ≈ 2.7
Earth
LCR ≈ 3×1041 erg/s
Atmosphere
CR origin problem:
i) CR source (?)
ii) Acceleration mechanism (?)
General remarks
• 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
CR scattering on moving magnetized clouds
E = -[w B]/c
scattering center
vi
E
B×
CR
w
vf
Head-on collision:
Δv = vf – vi >0
w=0
Δv = 0
v >> w
E
B
w
Overtaken collision:
Δv = vf – vi <0
vi
vi
w=0
w
vf
vf
Elastic scattering: vf = vi
Elastic scattering: vf > vi
Larger rate of head-on then overtaken collisions
efficient CR acceleration
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
Krymsky 1977
Bell 1978
log NCR
Δp
p-
log p
scattering centers
 = ( + 2)/( -1)
shock compression ratio
Frictional Acceleration of Cosmic Rays
Berezhko (1981)
y
dp
p

dt  acc
Shear plasma flow
w
CR
2

scattering center
1
acc
 dw 

 
 dy 
acceleration rate
mean scattering time
x
Frictional CR acceleration is expected to be very efficient
in relativistic/subrelativistic jets
Energetic requirements to CR sources
Requirements to the CR acceleration mechanism
Jobs ~ ε –γobs ~ Js/τesc
observed CR spectrum
γobs = 2.7
Τesc ~ ε-μ ( μ = 0.5 - 0.7)
JS ~ε-γS
γS = γobs – μ = 2 – 2.2
CR residence time inside the Galaxy
source CR spectrum
Supernova explosions
Supernova explosions supply enough energy to replenish
GCRs against their escape from the Galaxy
If there is acceleration mechanism which convert ~10% of
the explosion energy into CRS
Cosmic Ray Flux
Possible GCR sources:
SNRs
knee
SNRs (?)
Reacceleration (?)
ankle
Extragalactic (?)
GZK cutoff (?)
Cosmic Ray diffusive acceleration in Supernova Remnants
ESN ~ 1051erg
 2

 1
for strong shock
Krymsky 1977
Bell 1978

shock compression ratio
  4  2
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 expected
nonthermal emissions Fγ(εγ)
Nonlinear kinetic model: basic equations
Berezhko, Yelshin, Ksenofontov (1994)


    w   0,

t

w
 Hydrodynamic

   w  w    Pc  Pg  ,
 equations
t

Pg

  w  Pg   g  w  Pg   a 1   g  ca Pc , 
t

f
w f
 f  wf 
p
Q
t
3
p
ρ(r, t) – gas density
w(r, t) – gas velocity
Pg(r, t) – gas pressure
f (p, r, t) – CR distribution
function
CR transport equations (Krymsky, 1964)
fe
w fe 1   p  for protons and electrons
 fe  wfe 
p  2  fe 
t
3 p p p  1 
3
4 c 
Pc 
dp
3 0
pc
 ( p) 
3eB
p4 f
p 2  m2c 2
CR pressure
CR diffusion
coefficient
Q 
1u1
 ( p  pinj ) (r  Rs )
2
4 mpinj
source term
9me2 c 2
1  2 2
4r0 B p Synchrotron loss time
u = Vs - w
Particle spectrum in/near acceleration region
  N inj / N
η > 10-5
→
injection rate (parameter)
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 SNR
lg N
p
N

p
 2

 2
p 2
mpc
ppmax ~ RSVSB
test particle limit
p
pmax
lg p
maximum CR momentum
due to geometrical factors (Berezhko 1996)
Main nonthermal emission produced by Cosmic Rays
(how one can “see” CR sources)
• Synchrotron radiation
 e  0.1 10GeV
 e  1 100TeV
radio
B
X-ray
e
• Inverse Compton scattering

gamma-rays
 e  1 100TeV

e

• Nuclear collisions
N
0

gamma-rays
p
 p  1010 1015 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 and
gamma-ray production;
deduced from thermal X-rays
magnetic field B
influences CR acceleration &
synchrotron losses;
deduced from fit of
observed synchrotron spectrum;
expected to be strongly amplified
B >> BISM
injection rate η
(fraction of gas particles,
involved in acceleration)
influences accelerated CR number,
shock modification,
CR spectral shape;
deduced from observed shape
of radio emission
CR spectrum inside SNR
N

p
 2
lg N
p

 2
e
B
p
10G
radio
m p c pl
e  4
 /1GHz
GeV
B /10  G
α = (γ – 1)/2
e
pmax
 Vs B 1/ 2
3
test particle limit
X-ray
B  10 G
pl  t 1 B 2
p 2
p
e
max
p
pmax
lg p
due to synchrotron losses
Steep radio-synchrotron spectrum Sν ~ν -α
(>0.5,  >2) is indirect evidence of
i) efficient proton acceleration and
ii) high magnetic field B>>10G
Cassiopeia A
Type
Ib
Distance 3.4 kpc
Age
Radius
345 yr
2 pc
Circumstellar medium:
free WR wind +
swept up RSG wind +
free RSG wind
Tuffs (1986), VLA
Circumstellar medium
MS → RSG → BSG → SN
Ng, cm-3
Borkowski et al. (1996)
CSM number density
current SN shock
position
10
shell
1
BSG wind
1
d = 3.4 kpc
RSG wind
2
Mej = 2 MSun
r, pc
ESN = 0.4×1051 erg
Berezhko et al. (2003)
Synchrotron Emission from Cassiopeia A
Experiment: 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)
Proton injection rate η = 3×10--3
Interior magnetic
field Bd ≈ 0.5 mG
Strong SN shock modification
α ≈ 0.8
Steep concave spectrum
at ν < 1012 Hz
Smooth connection with
X-ray region (ν > 1018 Hz)
Magnetic field inside SNRs
Emission (X-ray, γ-ray)
due to high energy electrons
Line of sight
Rs
ρ
J Low field
Bd  BISM  5G
L  0.1RS
L
ρ
Bd
BISM
J High (amplified)
field
L
0.1RS
L  Bd 3 / 2
Unique possibility
of magnetic field determination!
-Rs
0
Rs
ρ
Filamentary structure of X-ray emission
of young SNRs
-consequence of strongly amplified magnetic field,
leading to strong synchrotron losses
Chandra
Cassiopeia A
Chandra
SN 1006
Projected X-ray brightness of Cassiopeia A
direct evidence for magnetic field amplification
Theory: Berezhko & Völk (2004)
Bd = 10 μG
Bd = 500 μG
Experiment (Vink & Laming 2003)
confirms high internal magnetic
field Bd  0.5mG
extracted from the fit of volume
Integrated synchrotron flux
(Berezhko, Pühlhofer & Völk 2003)
For strong losses
L
( acc
 10 cm 
Bd  0.5 

l


16
l  L / 7  103 Rs
2/3
mG
emissivity scale
brightness scale
angular distance
 loss )
Integral gamma-ray energy spectrum of Cas A
Components:
Hadronic (π0)
Inverse Compton (IC)
Nonthermal
bremsstrahlung (NB)
Confirmation of HEGRA measurement is very much needed
Already done by Magic (ICRC, Merida 2007)!
SNR RX J1713.7-3946
X-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)
Gamma-ray image (HESS)
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)
Aharonian et al. (2005)
Spatially integrated spectral energy distribution
of RX J1713.7-3946
Experiment: Aharonian et al. (2006)
Theory: Berezhko & Völk (2006)
required interior
magnetic field
Bd = 126 μG
Magnetic field amplification
ρISM
Beff
Results of modeling (Lucek & Bell, 2000) +
Spectral properties of SNR synchrotron
emission +
VS
BISM
Fine structure of nonthermal X-ray emission
SNR magnetic field is considerably
amplified
L
Beff2/8π ≈ 10-2ρISMVS2
Bd = Beff >> BISM
SNR magnetic field
• Influences synchrotron emission
• Determines CR diffusion mobility:
Κ ~ p/(ZBd)
CR diffusion coefficient (Bohm limit)
• Influences CR maximum momentum pmax:
pmax ~ Z e Bd RS VS
nuclear charge number
Energy spectrum of CRs, produced in SNRs
Berezhko & Völk (2007)
Amplified magnetic field
Bd2/(8π) ≈ 10-2ρ0VS2
Bd >> BISM
Cosmic Ray Flux
CR sources:
Supernova remnants
knee 1
Supernova remnants
knee 2
Extragalactic (?)
GZK cutoff (?)
Energy spectrum of CRs
Dip scenario
Dip
p + γ → p + e+ + e-
GZK cutoff
p+γ→N+π
Experiment:
Akeno-AGASA
(Takeda et al. 2003)
HiRes
(Abbasi et al. 2005)
Yakutsk
(Egorova et al. 2004)
CR spectrum,
produced in SNRs
CR spectrum from JEG~ε -2.7
extragalactic sources
(Berezinsky et al.2006)
Energy spectrum of CRs
Ankle scenario
Extragalactic
(AGNs, GRBs…)
SNRs
JEG~ε -2
Berezinsky
et al.(2006)
SNRs + reacceleration
Mean logarithm of CR atomic number
Ankle scenario
Dip scenario
Precise measurements of CR composition is needed
to discriminate two scenarios
Experiment:
KASKADE
(Hörandel 2005)
Yakutsk
(Ivanov et al.2003)
HiRes
(Hörandel 2003)
Fireball model of Gamma-ray bursts
Rees & Meszaros (1992)
R
Energy release (supernova ?)
Forward Shock
E
ISM
dΩ ~ 10-2 π
E ≈ 1051 erg
ESS ≈ 3×1053 erg
Fireball Γ ≈ 100
Lorentz factor
(?)
spherically symmetric analog
Γ ~ (ESS/NISM)1/2 R-3/2
R ~ t1/4
CR acceleration in GRBs
relativistic shock (Γ >> 1)
Achterberg et al. (2001)
assumption: isotropic CR diffusion in downstream region
εmax ≈ e BuΓ R c
unamplified magnetic field
Bu = BISM = 10 μG
maximum proton energy
εmax ≈ 5 × 107mpc2
amplified magnetic field
Bu2/8π = 0.1Γ2 ρISMc2
NCR(ε)~ ε-γ
εmax ≈ 5 × 1013mpc2
γ ≈ 2.2
GRBs are powerful extragalactic sources of CRs (?)
Problem
Bd ~ Γ2 Bu >> Bu
& Bdll >> Bd
┴
strongly anisotropic CR diffusion
low chance for CRs to recross shock
from downstream to upstream
inefficient CR production
downstream
upstream
VS
Bd
Bu
shock
(e.g. Ostrowski & Niemiec, 2006)
CR acceleration at late evolutionary stage
(nonrelativistic shock)
εmax ≈ e Bu R c
R(Γ = 1) =(ESS/3ρISMc2)1/3
ρISM = NISMmp
Bu2/8π = 0.1ρISMc2
For
InterStellar Medium density
amplified magnetic field
ESS= 3× 1053 erg, NISM = 1 cm-3
However assumption
Realistic numbers:
then
εmax = 3 × 1010 mpc2
Lγ = Qe , Pe ~ Γ2ρISM c2
Pp ~ Γ2ρISM c2
ESS≈1055 erg
seems to be unrealistic
Pe = 10-2Pp
εmax ≈ 1011 mpc2
Active Galactic Nuclei Jets
Powerful source of nonthermal emission
Powerful source of Cosmic Rays
Γ ≈ 10 Lorentz factor
Shear flow
Effective frictional acceleration
(e.g. Ostrowski, 2004)
Shock
Diffusive 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
= star explosions
lg( Luminosity)
0
-4
SN I
H lines
SN II
H lines
-8
0
100
200
t, day
300
SN Ia
MCO<1.4MSun
( 15 % )
No central objects
SNR in uniform ISM
thermonuclear
explosion
SN II/Ib
MCO>1.4MSun
( 85 %)
pulsar / black hole
SNR in CSM, modified
by progenitor star wind
core collapse
ν
detected from SN1987 A
Cosmic Ray Flux
CR sources:
Supernova remnants
knee 1
Supernova remnants (?)
Reacceleration (?)
knee 2
Extragalactic (?)
GZK cutoff (?)
Structure of the shock modified due to CR
backreaction
Flow speed
u
downstream
upstream
precursor
Pc
u0
CR pressure
u1
u2
subshock
shock front
Acceleration
sites
classical (unmodified)
shock σ = u0/u2 =
modified
shock σ
> 4, σS < 4
x
p < mpc
p >> mpc
σS = u1/u2 =4
γ>2
γ<2
Cutoff of CR spectrum due to CR interaction with CMB
Zatcepin, Kuzmin (1966)
Greisen (1966)
Cosmic microwave
background (CMB) radiation
CR source
π±
E = 1030 eV
π0
E=6×1019 eV
Galaxy
Projected radial profile of TeV-emission
(normalized to a peak values)
Smoothed with Gaussian
PSF of width
Δψ = 0.1o
Jγmax/Jγmin ≈ 2.3
consistent with
HESS value
L
L = 0.07 RS
Jγmax/Jγmin ≈ 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 PSF
of XMM-Newton
(Δψ = 15’’)
Experiment: L=1.2×1018 cm
(Hiraga et al. 2005)
L
Theory: L=1.15×1018 cm
(Bd = 126 μG)
test-particle limit
Bd = 20 μG
inconsistent
with experiment
CSM structure
wind
shell
bubble
Interstellar medium
SN
σshNISM
lg Ng
NISM
CSM number density
current SN shock position
Nb << NISM
Rsh
lg r