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