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Cosmic Ray Propagation
Vladimir Ptuskin
IZMIRAN, Russia
Cosmic Ray Propagation
Vladimir Ptuskin
IZMIRAN, Russia
SPSAS-HighAstro, May 2017
Outline
• Transport equation for cosmic rays. Elementary theory of
diffusion.
• Basic galactic model of cosmic ray origin.
Primary and secondary nuclei. Electrons and positrons. Anisotropy. Fluctuations.
• Nature of the knee.
• Cosmic rays of extragalactic origin.GZK cutoff. Data interpretation.
• Collective effects of cosmic rays.Streaming instability. Parker instability. Galactic wind model.
Outline
• Transport equation for cosmic rays. Elementary theory of
diffusion.
• Basic galactic model of cosmic ray origin.
Primary and secondary nuclei. Electrons and positrons. Anisotropy. Fluctuations.
• Nature of the knee.
• Cosmic rays of extragalactic origin.GZK cutoff. Data interpretation.
• Collective effects of cosmic rays.Streaming instability. Parker instability. Galactic wind model.
2
Voyager 1Stone et al. 2013BESSPamelaSparvoli et al 2012
extragalactic
knee
p
He
e
B/C
“golden age” of new cosmic ray measurements
Spacecrafts: Voyagers, ACE, Pamela, Fermi/LAT, AMS
Balloons: BESS, ATIC, CREAM, TRACER
Cherenkov telescopes: HESS, MAGIC, VERITAS
EAS detectors: KASCADE/KASCADE-Grande, MILAGRO, ARGO-YBJ,TUNKA, EAS-TOP, IceCube/IceTop,Auger, Telescope Array
4
“golden age” of new cosmic ray measurements
Spacecrafts: Voyagers, ACE, Pamela, Fermi/LAT, AMS
Balloons: BESS, ATIC, CREAM, TRACER
Cherenkov telescopes: HESS, MAGIC, VERITAS
EAS detectors: KASCADE/KASCADE-Grande, MILAGRO, ARGO-YBJ,TUNKA, EAS-TOP, IceCube/IceTop,Auger, Telescope Array
ultrafast pulsar
Sun
close binary
Galactic disk
pulsar, PWN
SNR stellar wind
AGN GRB
interacting galaxies
WMAPhaze
cosmic ray halo,Galactic wind
cosmologicalshocks
Fermibubble
5
ultrafast pulsar
Sun
close binary
Galactic disk
pulsar, PWN
SNR stellar wind
AGN GRB
interacting galaxies
Ncr ~ 10-10 cm-3 - number density in the Galaxywcr ~ 1.5 eV/cm3 - energy densityLcr ~ 1041 erg/s - total power of galactic sources Emax ~ 3x1020 eV - max. detected energyA1 ~ 10-3 – dipole anisotropy at 1 – 100 TeVrg ~ 1×E/(Z×3×1015 eV) pc - Larmor radius at B=3x10-6 G
GC
8.5 kpc
Transport equation for cosmic rays.Elementary theory of diffusion.
6
M51
7
energy balance: ~ 15% of SN kinetic energy go to cosmic rays to maintain observed cosmic ray density Ginzburg & Syrovatskii 1964
M51
Jcr(E)= Qcr(E)×T(E)
source
steady state:(without energylosses andfragmentation)
escape time from the Galaxy
E-2.7 E-2.1…-2.4 E-0.6…-0.3
- two power laws!
secondary nuclei and escape lengthsecondary species:
Li, Be, B, d, 3He, p …
cosmic ray escape length:
X = ma <nism> vT
221 1>vism
J n JT
8
cosmic ray escape length:
X = ma <nism> vT~ 10 g/cm2 at 1 GeV/nucleon
surface gas mass density of galacticdisk ~ 2.4 mg/cm2
- good confinement and intermixingof cosmic rays in the Galaxy
Jones et al 2001
basic empirical diffusion modelGinzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998 (GALPROP: http://galprop.stanford.edu),Donato et al 2002, Ptuskin et al. 2006, Strong et al. 2007, Vladimirov et al. 2010, Bernardo et al. 2010,Maurin et al 2010, Putze et al 2010, Trotta et al 2011, Johannesson et al. 2016
9
28 2 at~ 3 10 cm / s 3 GeV/n1 pc1/g
Dlr k
empirical diffusion coefficient
H = 4 kpc, R = 20 kpc
diffusion mean free path
diffusion is due to resonant scattering by random magnetic field wave number
2
2loss cat3
( , , ) is the cosmic ray number density per unit of total particle momentum,total number density ( , ) ( , , ),
pp
F dp F FF F F pF p D Qt p dt p p p p
F p tN t dpF p t
Fdp
uD u
rr r
24 in terms of phase-space density ( , , ),
2intensity ( ) ( ) / 4 ( ).
1 12 2 .2 23 loss
p fdp f p t
J E F p p f p
f u f dp ff u f p p D f p f qppt p p p p dtp p cat
r
D
transport equation for cosmic rays
diffusion convection adiabaticchange ofmomentum
stochasticacceleration
energyloss, <0 catastrophic
losses(fragmentation,
decay …)
sourceterm
3p p
u
2
2loss cat3
( , , ) is the cosmic ray number density per unit of total particle momentum,total number density ( , ) ( , , ),
pp
F dp F FF F F pF p D Qt p dt p p p p
F p tN t dpF p t
Fdp
uD u
rr r
24 in terms of phase-space density ( , , ),
2intensity ( ) ( ) / 4 ( ).
1 12 2 .2 23 loss
p fdp f p t
J E F p p f p
f u f dp ff u f p p D f p f qppt p p p p dtp p cat
r
D10
microscopic theory of diffusion
p
B0
B1L
θaveragefield
random field(MHD turbulence)
Larmor radius
cm /103.3 12
0GGV
tg BP
ZeBcpr
effect of random field:
11
effect of random field:2a) large-scale field: 1 - adiabatic motion, sin /
( 2 / - wave number)
b) small-scale field: 1 scattering,
cyclotron resonance v , 0, 1, 2,...
v, 1,
g
g
z z B
a
kr B const
k
kr
k n n
kV k n
-1 ( cos )z gk r rg = 1/kresonancecondition
B1L
p
B1
1
1
2 21, 0
with estimates
particle scattering by weak magneticfield perturbations, :
/
diffusion on pitch-angle:
/ (v / ) ( / ) , at 1 /
( , / v)
scatte
g
g
g res res g
g g
r L
L r
D t r B B k r
L r t r
2
0 1,2
0 1,
20
1,
ring back 1 at 1 / ( / v) ( / )
mean free path v ( / )
vdiffusion coefficient
3
Bohm diffusion v / 3
g res
g res
g
res
Bohm g
D r B B
l r B B
r BDB
D r
elementary theory
12
B0
1
1
2 21, 0
with estimates
particle scattering by weak magneticfield perturbations, :
/
diffusion on pitch-angle:
/ (v / ) ( / ) , at 1 /
( , / v)
scatte
g
g
g res res g
g g
r L
L r
D t r B B k r
L r t r
2
0 1,2
0 1,
20
1,
ring back 1 at 1 / ( / v) ( / )
mean free path v ( / )
vdiffusion coefficient
3
Bohm diffusion v / 3
g res
g res
g
res
Bohm g
D r B B
l r B B
r BDB
D r
perpendicular diffusion
D
┴ ~ rg2/ ~ vrg(B1,res/B0)2
Hall diffusiongrad Ncr
flux
B0rg
scattering, 1
13
grad Ncr
DA ~ vrg B0
diffusion tensor
grad Ncr
B0
jllj
┴
jA – Hall component
Ares = B1,res/B0<<1ll
2g
ll 2
s
00 , z
0 0
v v vr, ,
3 33
0,
A
A
g g resA
res
s sm m sm m
D DD D
D
r r AD D D
AJ D J j D Jt
0D B
Kres=1/rg
14
ll2
gll 2
s
00 , z
0 0
v v vr, ,
3 33
0,
A
A
g g resA
res
s sm m sm m
D DD D
D
r r AD D D
AJ D J j D Jt
0D B
Kres=1/rg
spectrum of random field
W(k)dk ~ k-2+adk, Dll ~ vrga
a = 1/3 Kolmogorov spectrum
a = 1/2 Kraichnan spectrum
a = 0 random discontinuities
a = 1 white noise (leads to Bohm
diffusion scaling DB = vrg/3)
2 ( )reskres
B W k dk
15
spectrum of random field
W(k)dk ~ k-2+adk, Dll ~ vrga
a = 1/3 Kolmogorov spectrum
a = 1/2 Kraichnan spectrum
a = 0 random discontinuities
a = 1 white noise (leads to Bohm
diffusion scaling DB = vrg/3)
k
W(k)
kmin~1/Lmax
1/k2-a
interstellar turbulence
Armstrong et al 1995
109 eV1017 eV
max
1/327 2
GV17
observations:Kolmogorov-type spectrum
100 pc, 3 G,( / ) 1,
2 5 / 3 1 / 3
estimate of diffusion coefficient:
4 10 cm /s
up to 10 eV
alternative: Kraichnan t
L L
L BA B Ba
pDZ
E Z
1/2
ype spectrum2 - 3 / 2 1 / 2
0.3, L
a
pA DZ
16
w(k) ~ k-5/3… k-3/2
KolmogorovKraichnan
max
1/327 2
GV17
observations:Kolmogorov-type spectrum
100 pc, 3 G,( / ) 1,
2 5 / 3 1 / 3
estimate of diffusion coefficient:
4 10 cm /s
up to 10 eV
alternative: Kraichnan t
L L
L BA B Ba
pDZ
E Z
1/2
ype spectrum2 - 3 / 2 1 / 2
0.3, L
a
pA DZ
problem: structure of interstellar mhd turbulence- anisotropic quasi-Alfvenic Kolmogorov turbulencewhere Alfvenic eddies are stretched along magneticfield, , can not provide required diffusioncoefficient since a particle traverses many uncorrelated during one gyro-rotation Shebalin et al. 1983,Higdon 1984, Montgomery & Matthaeus 1995, Goldreich & Shridhar 1995, Chandran 2000, Yan & Lazarian et al. 2002, Bereznyak et al 2010, Yan 2013
- fast magnetosonic waves can be isotropic (via independent acoustic-type cascade Cho & Lazarian 2003)and effectively scatter cosmic rays but they maynot provide needed diffusion coefficient in galactic disk because of strong dissipation in warm plasma via Landau damping
2/3 1/3k k L
: , 0,
: , , , 0.
z a
y y
x y x
k Vu B
kVu u B
A
MS
17
- fast magnetosonic waves can be isotropic (via independent acoustic-type cascade Cho & Lazarian 2003)and effectively scatter cosmic rays but they maynot provide needed diffusion coefficient in galactic disk because of strong dissipation in warm plasma via Landau damping Barnes & Scargle 1967, … Spanier & Schlickeiser 2005
“sandwich” model
halogas disk
, 0
,
h
g h g
D
D D
2h2H ◦
random shocks Bykov & Toptygin 1987
magnetosonic waves
: , 0,
: , , , 0.
z a
y y
x y x
k Vu B
kVu u B
A
MS
spreading of magnetic field lines and cosmic ray diffusion
literature: “Handbook of Plasma Physics”, ed. R.N. Sudan, A.A. Galeev, 1981, North-Holland; M. B. Isichenko 1992, Rev. Mod. Phys. 64, 961; L. Chuvilgin, V. Ptuskin 1993, Astron. Astrophys. 279, 278 ; R. Balescu 1995, Phys. Rev. E, 51, 4807,Casse et al 2002
Basic galactic model of cosmic ray propagation.
Primary and secondary nuclei. Electrons and positrons. Anisotropy. Fluctuations.
24
Basic galactic model of cosmic ray propagation.
Primary and secondary nuclei. Electrons and positrons. Anisotropy. Fluctuations.
leaky box approximationfor 1D diffusion modelwith galactic disk ofinfinitesimal thickness
22
2 2
0
( , ) v 1( ) ( ) ( , ) ( , ) ( ) ( ) (*)
/ ( ) ( ) / 0
solution of (
ion
ion
f p z dpD p z f p z p f p z s p zz m p p dt
dp dt b p z m
0 0
20 00 02
*) at 0 : 1 , where ( )= ( , 0) (**)
integration of (*) lim ... at 0 gives the boundary condition at 0 :
v 12 ( ) (***)
calculating
zz f f f p f p z
H
dz z
f bD f p f s pz m p p m
00
220
0 0
2 from (**) and substituting it in (***) gives eq. for ( ) :
( ) v, - escape length; in g/cm .v 2
ion
fD J Ez
J d dE s p p HJ J XX dE dx m D
2H
disk of sources and matter
cosmic-ray halo
z
D(p)
0absorbing boundaries
surface source densitysurface gas density 22.4 mg/cm
Stable nuclei
25
22
2 2
0
( , ) v 1( ) ( ) ( , ) ( , ) ( ) ( ) (*)
/ ( ) ( ) / 0
solution of (
ion
ion
f p z dpD p z f p z p f p z s p zz m p p dt
dp dt b p z m
0 0
20 00 02
*) at 0 : 1 , where ( )= ( , 0) (**)
integration of (*) lim ... at 0 gives the boundary condition at 0 :
v 12 ( ) (***)
calculating
zz f f f p f p z
H
dz z
f bD f p f s pz m p p m
00
220
0 0
2 from (**) and substituting it in (***) gives eq. for ( ) :
( ) v, - escape length; in g/cm .v 2
ion
fD J Ez
J d dE s p p HJ J XX dE dx m D
leaky boxEq.
physical explanations of peak in sec./prim. ratio:
sources spectrum q ~ R-2.4
(more flat at R < 3 GV)
steep sourcespectrum
E = 30 GeV/nsources spectrum q ~ R-2.4
(more flat at R < 3 GV)
sources spectrum q ~ R-2.2
(more steep at R < 40 GV) Eres = 1GeV/n
diffusion models
27
Voyager 1LIS2013
cosmic ray energy spectra below the knee
low-energy spectra and composition; Voyager 1 space probe, (Cummings et al 2016)
deviations from the plain power laws at 10 to105 Gev/n:ATIC-2 , Advanced Thin Ionization Calorimeter, balloon-borne instrument (Panov et al. 2009), CREAM, Cosmic Ray Energetics and Mass, ionization calorimeter, balloon instrument (Yoon et al 2011),PAMELA, Payload for Antimeater Matter Exploration and Light-nuclei Astrophysics, magneicspectrometer, satellite-based experiment (Adriani et al. 2011), AMS-02, Alpha Magnetic Spectrometer, International Space Station (Aguilar et al 2015), …
cosmic ray energy spectra below the knee
low-energy spectra and composition; Voyager 1 space probe, (Cummings et al 2016)
deviations from the plain power laws at 10 to105 Gev/n:ATIC-2 , Advanced Thin Ionization Calorimeter, balloon-borne instrument (Panov et al. 2009), CREAM, Cosmic Ray Energetics and Mass, ionization calorimeter, balloon instrument (Yoon et al 2011),PAMELA, Payload for Antimeater Matter Exploration and Light-nuclei Astrophysics, magneicspectrometer, satellite-based experiment (Adriani et al. 2011), AMS-02, Alpha Magnetic Spectrometer, International Space Station (Aguilar et al 2015), …
Voyager 1 in the interstellar space
after E. Stone 2013
d = 138 AU at present
Cummings et al 2013Galactic cosmic ray nuclei from H to Ni down to 3 MeV/n; electrons to 2.7 MeV
secondary nuclei
D ~ vR0.41D ~ vR0.4
AMS-02
Kappl et al 2015_p/ p
Ting 2016
flat component of secondary nuclei produced by strong SNR shocks Wandel et al. 1987, Berezhko et al. 2003, Aloisio et al. 2015
Berezhko et al. 2003
production by primaries inside SNRs reacceleration in ISM by strong shocks
02.0~~ISMSNR
stand,2
flat,2XX
NN
2.0~~ SNRSNRISM
stand,2
flat,2 fXX
NN
volume fillingfactor of SNRs
grammage gained in SNR
grammage gainedin interstellar gas
RUNJOB 2003preliminary
Berezhko et al. 2003
volume fillingfactor of SNRs
grammage gainedin interstellar gas
standardplain diff.reacceleration
plain diff.reaccelerationnism = 0.003…1 cm-3
Bohm diffusionTSNR = 105 yr
RUNJOB 2003preliminary
hardening of H & He spectra above ~ 300 GV
p
He
spectra of p and He are different
hardening above 300 GeV/nucleon
shock goes through material enriched in He:bubble Ohira & Ioka 2011 or variable (ionized) He/p concentration Drury 2011;p,He injection for varying MA Malkov et al 2012.
some suggested explanations of features in H & He spectra:
spectrum produced by superposition of sources Vladimirov et al 2012, Zatsepin & Sokolskaya 2006;reacceleration by SNR shocks VP, Zirakashvili, Seo 2011, Thoundam & Hoerandal 2015;effect of local sources Erlykin & Wolfendale 2011, Bernard et al 2013, Liu et al 2015;streaming instability below 300 GV Blasi, Amato. 2012;different turbulence in halo and disk Tomassetti 2012.
possible explanation of both features:concave spectrum and contribution of reversed SNR shock VP, Zirakashvili, Seol 2013
JxE2.7
I
II
overall spectrum of accelerated CR
forward
reverse
direct measurements at higher energiesdirect measurements at higher energies
protons helium
in all models three different cosmic-rayinjection spectra are used for protons, He, and heavier elements Z > 2; breaksin source spectra and diffusion coefficient
Cummings et al 2016
Model of cosmic ray propagation at 3 MeV/n to 100 GeV/n
in te rs te lla r e n e rg yE , G e V /n
1 1 0
survi
ving f
ractio
n
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 0 B e
VA
UH
le a k y b o x
s ta t ic d if fu s io n
d if fu s io n + re a c c e le ra t io n
w in d
radioactive secondaries10Be (2.3 Myr) 26Al (1.3 Myr) 36Cl (0.43 Myr) 54Mn (0.9 Myr) 14C (0.0082 Myr)
decay timeat rest
d
( )( )J
J
37
in te rs te lla r e n e rg yE , G e V /n
1 1 0
survi
ving f
ractio
n
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 0 B e
VA
UH
le a k y b o x
s ta t ic d if fu s io n
d if fu s io n + re a c c e le ra t io n
w in d
28
22 12 1
2 222
2 212 1
180 pc
- D ... ( )v
( )elementary model at 4 : ( )
leaky box approximation + =<n>v gives ... does not work!
d DJJ n r J
JH DJ H
DJ J JT T
D = (2 … 5)×1028 cm2/sat 0.5 GeV/n
H ~ 4 kpc, Tesc =H2/2D ~ 7.107 yr
VP & Soutoul 1998
radioactive secondary Be
Ting 2016
60Fe nucleosynthesis-clock isotope in Galactic cosmic raysBinns et al 2016
ACE – CRIS instrument(Si solid-state detectors)
17 yr of data collection at 195 – 500 MeV/n
3.55 105 Fe nuclei 15 60Fe nuclei
average source ratio 60Fe/56Fe = (7.5+-2.9) 10-5
ratio ejected by massive star ~ 4 10-4
time between nucleosynthesis and acceleration: 105 yr < T < 2 106 yr
distance to the source (SNR) < 600 pc
beta-decay t1/2 = 2.6 106 yrprimary cosmic-ray clock
17 yr of data collection at 195 – 500 MeV/n
3.55 105 Fe nuclei 15 60Fe nuclei
average source ratio 60Fe/56Fe = (7.5+-2.9) 10-5
ratio ejected by massive star ~ 4 10-4
time between nucleosynthesis and acceleration: 105 yr < T < 2 106 yr
distance to the source (SNR) < 600 pc 59Ni 60Fe
electrons and positrons in cosmic rays
2 -16 -1 28 2max max GeV
5max
inverse Compton and synchrotron losses diffusion distance
, (1.2-1.6) 10 (GeV s) , = 6 , 3 10 cm /s
(1 TeV) 2 10 yr
adE bE b r Dt D Edt
t
max (1 )/2
GeV
10 kpcarE
solution for point instant source in infinite medium Syrovatsky 1959
0
2 202 2
2 10 0 1 2
0 1
2
2
( ) 1( ) ( ) ( ) ( ); (...)= (...)4
( )1 1introduce new function and new variables and ( , )= .
exp( ) 4 ( ) ( )
4
E
E
G rD E G bE G E E t rt E r r r
D EbE G y t t E E dEbE bE bE
rr y Gr
10
3/2 0 0
0 0
, = for .1 ( ) (1 )4
aa
a
D EEE D D Eb t t E a bE
40
0
2 202 2
2 10 0 1 2
0 1
2
2
( ) 1( ) ( ) ( ) ( ); (...)= (...)4
( )1 1introduce new function and new variables and ( , )= .
exp( ) 4 ( ) ( )
4
E
E
G rD E G bE G E E t rt E r r r
D EbE G y t t E E dEbE bE bE
rr y Gr
10
3/2 0 0
0 0
, = for .1 ( ) (1 )4
aa
a
D EEE D D Eb t t E a bE
2
22
( ) ( )
JD E bE J s zEz
( )
2
( ) ( ) 2 ( )
at ( ) 1 (1 ) , low energies ( 3 GeV);
s ae
s E HJ E ED E
H D E a bE
12
2
2 ( ) ( )(1 ) ( )
at ( ) 1 (1 ) , high energies
sa
es EJ E Ea bED E
H D E a bE
( 1)
(3 ... 100 GeV).
NB: if source region has finite thickness 2 then ( ) at hseh J E E
2 /D 1/((1-a)bE)
1 0.7...0.8 above few GeV expected primary electron spectrum , 32
ee e
a J E
e+ expected secondary positron spectrum , 3.5eeJ E
sources
solution for homoginious source distribution in Galactic disk
41
2
22
( ) ( )
JD E bE J s zEz
( )
2
( ) ( ) 2 ( )
at ( ) 1 (1 ) , low energies ( 3 GeV);
s ae
s E HJ E ED E
H D E a bE
12
2
2 ( ) ( )(1 ) ( )
at ( ) 1 (1 ) , high energies
sa
es EJ E Ea bED E
H D E a bE
( 1)
(3 ... 100 GeV).
NB: if source region has finite thickness 2 then ( ) at hseh J E E
2 /D 1/((1-a)bE)
1 0.7...0.8 above few GeV expected primary electron spectrum , 32
ee e
a J E
e+ expected secondary positron spectrum , 3.5eeJ E
Kobayashi et al 2004
data on positronscollection of data Mitchell 2013 anti-matter factory
Lpairs = 20-30% Lpsr
AMS 02
Gaggero et al 2014
- pulasar/PWN origin Harding, Ramaty 1987, Aharonian et al. 1995, Hooper et al. 2008,Malyshev et al. 2009, Blasi, Amato 2011, Di Mauro et al. 2014
- reverse shock in radioactive ejecta Ellison et al 1990, Zirakashvili, Aharonian 2011- annihilation and decay of dark matter Tylka 1989, Fan et al 2011
after Amato
contribution of nearby pulsars and SNRs
01
0 0
3 .v
zzz
ff DAf f z
Cosmic ray anisotropyassuming z axis is in direction of maximum intensity.
particle flux
diffusion approximation
degree of anisotropy(first angular harmonic)
0 1 0 1 0
1cos , , ,4
f f f f d f f f
2
1 1
4cos sin .3zj J d d J
0 0
1
3 .vzz
z zz
f fDj D fz z
Compton-Getting effect: cosmic rays are isotropic in a flow with velocity u
0
00 0
30
( ) ( ) ( ( )) - Lorentz - invariance
: , ,v v
( ) ( ) ( ) ,v v
( )( ) ( ) - Compton-Getting flux, ,4 3CG CG cr
f f f p
u c p p p
ff f p f pp
f pd pp f p d p Np
p pu upp p
up upp
uj v j u
Compton-Getting effect: cosmic rays are isotropic in a flow with velocity u
f(p)
f’(p’)=f0(p’)
lab ref frame
CR are isotropic
u
0
0vCG
fpf p
uAanisotropy
leakage from the Galaxy
hz
Xhz
HDAz 2
3c
3
anisotropy perpendicular to galactic disk:
2H
2h
halo
source disk
distance from themidplane~ 20 pc
N=0
Ad = 1.1×10-3ETeV0.54
Aa = 6.2×10-4ETeV0.3
h = 100 pcH = 4 kpc
too large at ~ 100 TeV
radial anisotropy:
drdN
NcDAr
13
1/Lr
Lr = 19 kpc
Ad = 1.5×10-3ETeV0.54
Aa = 8.2×10-4ETeV0.3
wrong phase !
h = 100 pcH = 4 kpc
too large at ~ 100 TeV
SNRSun2H
cosmic-ray halo
galactic disk
z
“statistical mechanics of supernovae”Jones 1969, Lee 1979, Berezinskii et al. 1990, Lagutin & Nikulin 1995, Taillet et al. 2004, Büsching et al. 2005, Ptuskin et al. 2005, Sveshnikova et al. Blasi & Amato 2012, Sveshnikova et al 2013, Mertsch & Funk 2015
)()()()()( iii
i ttzyyxxESNdtdE
END
tN
R
energy loss term,< 0(for electrons)
number of particles accelerated in one burst
proton densityfluctuation
electron densityfluctuations
fluctuation anisotropyof protons
“typical” fluctuations:
a
a
sne
e
a
sn
EcHED
EEDbEa
NN
EEDHN
N
4)(23
.)(2
)1(
,)(2
1
fluct
42
4/1
2/1
4
4/1
4/3
(~ Az !)
a
a
sne
e
a
sn
EcHED
EEDbEa
NN
EEDHN
N
4)(23
.)(2
)1(
,)(2
1
fluct
42
4/1
2/1
4
4/1
4/3
electrons
Strong & Moskalenko 2001
data:
Lallerment et al 2003
direction of magnetic field based on: l = 185°, b = -38°observed direction of CR anisotropy
Nature of the knee
48
Berezhnev et al. 2012structure above the knee
different types of nuclei, Eknee ~ Zdifferent types of SNtransition to extragalactic component
knee and beyond
p,He knee 2nd knee
JxE3
p
49
p
He
Fe
composition at 1PeV: H 17%, He 46%, CNO 8%, Fe 16%+ EG component H 75%, He 25% as in Kotera & Lemoine 2008
Sveshnikova et al 2014:
p,He
CNO,Si,Fe
JxE2.7
Iron knee at 8*1016 eV = 26*3*1015 eV
light ankle at 1.2*1017 eV- transition to EG componentor onset of a new high energyGalactic source population
TUNKAKASCADE-G
p,He
CNO,Si,Fe
Iron knee at 8*1016 eV = 26*3*1015 eV
light ankle at 1.2*1017 eV- transition to EG componentor onset of a new high energyGalactic source population
Syrovatsky 1971, Berezinsky et al. 1991, Gorchakov et al 1991, VP et al 1993, Lampard et al 1997, Zirakashviliet al 1998, Candia et al. 2003, Hörandel et al. 2005
extension of propagation model to higher energies:trajectory calculations
regular halo field Tdisk
protonsdiffusionworks here ~ 1/E
51
regular disk field
Galacticdisk <B>
alternative explanation of the knee:
knee as effect of Hall diffusion
protons
Hörandel et al. 2005
52
D
┴ ~ R0.2, DA ~ R
additional change of source spectrum is needed
trajectories
diffusion
cosmic ray anisotropy, equatorial dipole amplitude
p, Gal
Fe, Gal
E, eV
Giacinti et al 2012VP et al 2006
Cosmic rays of extragalactic origin.
GZK cutoff. Data interpretation.
54
Cosmic rays of extragalactic origin.
GZK cutoff. Data interpretation.
ankle 4-5 1018eV
suppression
knee
TA
Auger
Extragalactic cosmicrays
2nd knee
Auger data on dispersion of <Xmax> are also available
extragalactic sources of cosmic rays
needed in CR SN AGN jets GRB newly born accretion on at Е > 1019.5 eV fast pulsars galaxy clusters
(< 5ms)3 10-4 (Auger) 3 10-1 3 3 10- 4 10-3 10
kin. & 6 10-2 for X/gamma rotation strong shocks
8 10-3 for E>109 eV Lkin > 1044 erg/s
energy release in units 1040 erg/(s Mpc3)
AGN jets
1/220 1/2 45max jet
219 4max
E 10 × Z×β × L / 10 erg / s eV
E 10 × Z× Ω / 10 sec eVfast new bornpulsarsB = 1012…1013 G
Lovelace 1976, Biermann & Strittmatter 1987, Norman et al 1995, Lemoine & Waxman 2009
Gunn & Ostriker 1969, Berezinsky et al. 1990, Arons 2003, Blasi et al 2000, Fang et al. 2013
energy loss of ultra-high energy cosmic rays in extragalactic space
expansion
Greisen 1966; Zatsepin & Kuzmin 1966
• pair production pγ
→ pe+e-
• pion production pγ
→ Nπ
GZK cutoff at EGZK ~ 6×1019 eV pairs
photodis-integration
EGZKmicrowave & EBL photons
Greisen 1966; Zatsepin & Kuzmin 1966
energy loss length
z = 0
• photodisintegration of nuclei
Stecker 1969
• Universe expansion
- (1/E) (dE/dt)adiabatic = H
H0=100h km/(s Mpc), h=0.71
pairs pions
photodis-integration
cosmic ray nuclei in expanding Universe
33
1,2...
( , , ) ( ) 1( )(1 ) ( , , )(1 ) ( , , )1
+ ( , , ) ( , , ) ( , , ) ( , , ) ( , ) (1 )mi
F A z H zH z z F A zz z A zz
A z F A z A i A z F A i z q A z
0
( , , ) - cosmic ray distribution function, Z = 1 ... 26,/ - energy per nucleon,
z 1 , is the cosmic scale factor,
, (1 ) ( ), at ; =1
-
00 km/
redshi t,
(
f now
then
az aa
dr dz dErH z H z HE E pc Hdt dt dt
F A zE A
30
3 1
0
s Mpc), =0.7,
Hubble scale = 3 10 ( ) (1 ) - Hubble parameter (at 0.3 0.7 1),
( , ) - source term at 0, describes source evolution,( , , )
Mpc,
- e
nergy loss time on e
m m
mg
H z H z
q A z
h
A
h
z
R
m
cH
+ - 0e and photoproduction,( , , ) - photodisintegration rate,A z
for homogeneous source distribution and arbitrary regime of cosmic-ray propagation:
Ptuskin et al 1999
0
( , , ) - cosmic ray distribution function, Z = 1 ... 26,/ - energy per nucleon,
z 1 , is the cosmic scale factor,
, (1 ) ( ), at ; =1
-
00 km/
redshi t,
(
f now
then
az aa
dr dz dErH z H z HE E pc Hdt dt dt
F A zE A
30
3 1
0
s Mpc), =0.7,
Hubble scale = 3 10 ( ) (1 ) - Hubble parameter (at 0.3 0.7 1),
( , ) - source term at 0, describes source evolution,( , , )
Mpc,
- e
nergy loss time on e
m m
mg
H z H z
q A z
h
A
h
z
R
m
cH
+ - 0e and photoproduction,( , , ) - photodisintegration rate,A z
Aab et al 2016
at the source:E-0.96, Emax = 5 1018 Z eV H=0%, He=67%, N=28%, Si=5%, Fe=0%
EG
G Si
NHeH
TA data (pure protons?) Auger dataBerezinsky 2014
dip
sources of Galactic cosmic rays: E-2.2, H=92% , He=7.7% , C=0.27% , O=0.38%, Mg=0.067%, Si=0.07% , Fe=0.073%
sources of extragalactic cosmic rays:
at the source:E-0.96, Emax = 5 1018 Z eV H=0%, He=67%, N=28%, Si=5%, Fe=0%
• source composition is highly enriched in medium and heavy nuclei;• source spectrum is more hard than E-1, Emax ~ 5 1018Z eV• disappointing model for UHE neutrino production• shape of the all-particle spectrum is likely due to concurrenceof two effects: maximum energy reached at the sources and energy losses during propagation
source spectrumE-2.5, Emax ~ 1022 eV
* GZK suppression ofproton spectrum* ankle structure is due
to e+e-production
Collective effects of cosmic rays.
Streaming instability. Parker instability. Galactic wind model.
60
cosmic-ray streaming instability
2 2
4 1 , at 1/
cr cr a Bcr
a
cr cr acr res g
cr
w u V wc V
eu N V k rc u
growth rate of waves amplitude
motion of cosmic rays through background plasma with bulk velocity ucr > Va generates Alfven waves
CR energy density
wave energy density δB2/4π
resonantscattering
Ginzburg 1965, Lerche 1971, Wentzel 1969, Kulsrud & Pearce 1969, Kulsrud & Cesarsky 1971, Skilling 1975, Holmes 1975, Bell 1978, Farmer & Goldreich 2004
after Wentzel; Blasi2 2
4 1 , at 1/
cr cr a Bcr
a
cr cr acr res g
cr
w u V wc V
eu N V k rc u
2
20
v res
g
BBr
rate of momentumloss by particles
rate of momentumgain by waves
resonantscattering
2 416 v( )3 ( )
acr res
res res
V p fkk W k x
in diffusionapproximation
Bell 2004
strong instability wcr(ucr/c) > B02/4π
almost purely growing non-resonant mode
weak turbulence δB << B0 and Γcr << ω
(k)
→ wcr(ucr/c) << B02/4π
z ak V
4 cr crcr
eu Nc
2
4cr
cruB wc
non-linear saturation at
max 20
4at cr crres res
u wk k kcB
(not always reached because of finite shock age/size !)
nonlinear diffusion in the Galaxy
cosmic ray leakage from the Galaxy is regulated by streaming instability which is substitutedby diffusion on background interstellar Kolmogorov - type turbulence above ~300 GeV/n
Aloisio et al 2015
absorbing haloboundary, Ncr=0
63XSNR=0.17 g/cm2 (TSNR=2 104 yr) added
B/C
protons
cosmic ray halo
Galactic wind
non-linear evolution of cosmic ray “cloud” injected from SNR
VP et al 2007, Nava et al 2016
SunSNR
Galactic disk
injected “cloud” of CR particles,N(p) ~ p-2.1, Wcr = 1050 erg
flux tube
constG5B const,
total
SB
300 pc
,0
xfD
xtf
,3/2
xf
D
3/83/73/13/5
3/43/1
32)v(
pCBr
K
g
where
3 2
2
( )(2 ) , 3.6dis K a K
kW kC kV CB
the nonlinear wave dissipation is assumed
1/26 3 2 4 3 4
2 4 8 2 3 2 4 3
1 4 9( , , )4 9 ( ) 2
S p t xf p x tp S N p S p t
solution
3 2
2
( )(2 ) , 3.6dis K a K
kW kC kV CB
the nonlinear wave dissipation is assumed
3-
kpc*0.7
GV
50cr11
*cr
3/2Myr*
0.2GV
50cr*
cm erg10
107
pc erg10 79
xPW
n
tPWx
,
100.3 erg10107.1
cm10
),,(4
3Myr
4kpcGV
123Myr
8.1GV
4cr
503
3-10
3cr
txPtPW
txpfpn
0.707
0.032
f t( )
50.1 t
f(t) x = x*
t3/2
3-
kpc*0.7
GV
50cr11
*cr
3/2Myr*
0.2GV
50cr*
cm erg10
107
pc erg10 79
xPW
n
tPWx
0.707
0.032
f t( )
50.1 t tt*
t-3/2
t3/2
Application: gamma-rays from nearby dense gas material of W28, IC443 … Aharonian & Atoyan 1996, Gabici et al 2009, Ohira et al 2010
compare to testparticle diffusion
2
1/2
exp( / 4 )2( )x DtfDt
Parker instability
galactic mid-plane
gravity
Parker 1966, 1992et, Kuznetsov & Ptuskin 1983, Hanasz & Lesch 2000, Kuwabara & Ko 2006, Lo et al. 2006, Rodrigues et al. 2015
2 20 ( ) ( ),
8 24rand
gas cr
gas
B BP P z g zzP
equilibrium:
height scale of equilibrium distribution~ few kpc with non-exponential tail
galactic mid-plane
( )crcr cr cr cr
w D w w w P St
u u
Eq. for cosmic ray energy density:
unstable if the polytropic index * , 00
*
0 ,
0.51
1.5gas m crm
gas g m m rand cr
P P PPP P P P P
instability develops during 107 to 108 yr
height scale of equilibrium distribution~ few kpc with non-exponential tail
Galactic wind driven by cosmic rays
Zirakashvili et al 1996Cosmic rays are produced in the galactic disk. Thermal gas is confined by gravity and cosmic rays are not. Cosmic ray scale height is larger then the scale height of thermal gas and cosmic ray pressure gradient drives the wind flow.
Ipavich 1975, Breitschwerdt et al. 1991, 1993, …
68more on wind model Recchia et al 2017, Uhlig et al 2012, Everett et al 2008, Girichidis et al 2916, Ruszkowski et al 2016
diffusion – convection transport in galactic halo
u
z
u = wzD(p)~v(p/Z)a
zc
diffusiondominates
convectiondominates stable nuclei
2
/21/2
0.5
( , ) ( )( ) ( , ) ( )
( )( ) if
vz ( ) v v 2 ( ) 2 ( )
requiers
c c cc
c c c
c
ac
z z D p zz pu z D p z u z
D pz p u wzw
pX p ZD p wD p
X p D p
69
z0 zc
effect of boundary layer
2
/21/2
0.5
( , ) ( )( ) ( , ) ( )
( )( ) if
vz ( ) v v 2 ( ) 2 ( )
requiers
c c cc
c c c
c
ac
z z D p zz pu z D p z u z
D pz p u wzw
pX p ZD p wD p
X p D p
cosmic ray streaming instability with nonlinear saturation
energies. lowat
/
1GeV/n,Eat
1.2,7.22/)13(
,/cm 10
0.55-
2/)1(
21.1
271222/1
a
ss
ppcrBith
Vc
R
RX
scZm
pcZm
pBcCD
s
s
CR emissivity of Galactic disk per unit area
uinf = 500km/sRsh = 300 kpc
Zirakashvili et al. 1996, 2002 Ptuskin et al. 1997
energies. lowat
/
1GeV/n,Eat
1.2,7.22/)13(
,/cm 10
0.55-
2/)1(
21.1
271222/1
a
ss
ppcrBith
Vc
R
RX
scZm
pcZm
pBcCD
s
s
uinf = 500km/sRsh = 300 kpc
effective halosize H(p/Z)
stable secondaries: radioactive secondaries:
s*(1TeV)=15 kpcs*(1 PeV)= 150 kpc
ultrafast pulsar
Sun
close binary
Galactic disk
pulsar, PWN
SNR stellar wind
AGN GRB
interacting galaxies
WMAPhaze
cosmic ray halo,Galactic wind
cosmologicalshocks
Fermibubble
71
ultrafast pulsar
Sun
close binary
Galactic disk
pulsar, PWN
SNR stellar wind
AGN GRB
interacting galaxies
Ncr ~ 10-10 cm-3 - number density in the Galaxywcr ~ 1.5 eV/cm3 - energy densityLcr ~ 1041 erg/s - total power of galactic sources Emax ~ 3x1020 eV - max. detected energyA1 ~ 10-3 – dipole anisotropy at 1 – 100 TeVrg ~ 1×E/(Z×3×1015 eV) pc - Larmor radius at B=3x10-6 G
GC
8.5 kpc