2 sec sr MeV/nuc) particle /(m

Acceleration and Transport of Galactic Cosmic Rays

Vladimir Ptuskin

IZMIRAN, Moscow, Russia

“AMS days at CERN”, April 15-17, 2015

ultrafast pulsar

Sun

close binary

Galactic disk pulsar,

PWN

SNR stellar

wind

AGN GRB

interacting galaxies

N_cr = 10^-10 cm^-3 - total number density in the Galaxy w_cr = 1.5 eV/cm³ - energy density

E_max = 3x10²⁰ eV - max. detected energy

Q_cr = 10⁴¹ erg/s – power of Galactic CR sources A₁ ~ 10^-3 – dipole anisotropy at 1 – 100 TeV

r_g ~ 1×E/(Z×3×10¹⁵ eV) pc - Larmor radius at B=3x10^-6 G

Fermi bubble

GC

WMAP haze

cosmic ray halo, Galactic wind

cosmological shocks

10⁹ eV 10²⁰ eV

JxE² extragalactic

1/km²/century

E^-2.7

LHC

CR spectrum at Earth

direct measurements of interstellar CR spectra at low energies

Voyager 1 at the edge of interstellar space

after E. Stone 2013

energy, MeV/nuc

10⁰ 10¹ 10² 10³ 10⁴ 10⁵

particle /(m2 sec sr MeV/nuc)

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10² 10³

low energies:

Voyager 1

Stone et al. 2013

high energies:

BESSPamela

Sparvoli et al 2012

H He

launched in 1977, 70 kb, 22 w

M51

J

(E) = Q

(E)×T

(E)

source

power escape time of CR from the Galaxy;

~ 10⁸ yr at 1 GeV

~ 15% of SN kinetic energy transfer to cosmic rays

Ginzburg & Syrovatsky 1964 sn -1

ν = (30 yr)

cosmic ray intensity

traversed matter thickness (escape length) X_e = m<n_ism>T_e ~ 12 g/cm² at 1 GeV/nuc

(surface gas density of galactic disk ~ 2.5 10^-3 g/cm²)

E^-2.7 E^-2.2 E^-0.5

after Moskalenko





basic empirical diffusion model

Ginzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998(GALPROP),

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

28 2

~ 3 10 cm / s 1 GeV/nat

1 pc

_e 2 D

l

X vH D







empirical diffusion coefficient

H = 4 kpc, R = 20 kpc

diffusion mean free path

NGC4631

escape length

diffusion-convection transport equation for cosmic rays

Ginzburg & Syrovatsky 1964, Skilling 1975, Berezinskii et al. 1990 (loaded in GALPROP code)

2 2

2 2

,

1 3

1 v .

i i i

i i i i

i

i i i i ij

i ion i j i

f f f

f f p p K

t p p p p

f

p dp f n f q S

p p dt 

 _

    

       

   

 

        

    



D u u

2

2 2

( , , ) - phase-space density (isotropic part);

( , ) 4 - total cosmic-ray number density;

( , , ) 4 ( ) / v - spectrum on kinetic energy;

( , , ) 4 ( ) - cosmic ray intensity.

cr

cr kin

f t p

N t dpp f

N t E p f p

J t E p f p















r r r r

spatial diffusion advection stochastic acceleration

ionization energy loss fragmentation radioactive

decay source contribution of fragmentations and decays

r_g = 1/k - resonance condition

2 2

v 3

g tot

res

r B D_   B

cosmic ray particles are strongly magnetized but large-scale random magnetic field (L_max ~ 100 pc) makes diffusion close to isotropic

mechanism of cosmic ray diffusion



2res

kres

B = w(k)dk

Jokipii 1966, …

spectrum of turbulence

interstellar turbulence

Armstrong et al 1995

w(k) ~ k^-5/3… k^-3/2 Kolmogorov

Kraichnan

10⁹eV 10¹⁷ eV

max

1/3

27 2 17

GV

1/ 2

Kolmogorov-type spectrum 100 pc, 3 G, ( / ) 1,

4 10 cm /s, 10 eV

Kraichnan type spectrum 0.3,

L L

L

L B

A B B

D p E Z

Z

A D p

Z











     

 

   

 

 





Lin et al. 2015

flat component of secondary nuclei produced by strong SNR shocks Wandel et al. 1987, Berezhko et al. 2003

Berezhko et al. 2003

production by primaries inside SNRs reacceleration in ISM by strong shocks 02

. 0

~

~

ISM SNR stand

, 2

flat , 2

X X N

N ~ _SNR ~ 0.2

SNR ISM stand

, 2

flat ,

2 f

X X N

N

volume filling factor of SNRs grammage gained in SNR

grammage gained in interstellar gas

standard plain diff.

reacceleration

plain diff.

reacceleration n_ism = 0.003…1 cm^-3 Bohm diffusion T_SNR = 10⁵yr

RUNJOB 2003 preliminary

regimes of cosmic ray diffusion

Kolmogorov spectrum: D ~ vR^1/3 + reacceleration

- may be valid up to 10¹⁷Z eV

- source spectrum R^-2.4 at high energies – too soft to be produced in SNRs ? (dispersion of SNR parameters may help); considerable flattening at < 3 GV - anisotropy – acceptable

- peak of B/C ratio at 1 GeV/n – explained by distributed reacceleration - underpredicts antiproton flux below few GeV

- in contradiction with theory of MHD turbulence (Alfven wave distribution in k-space)

Kraichnan spectrum: D ~ vR^1/2 + wave damping

- may be valid up to 10¹⁶Z eV only

- source spectrum R^-2.2 – consistent with shock acceleration in SNRs - anisotropy – too high

- peak of B/C ratio at 1 GeV/n – qualitatively explained by turbulence dissipation on CR - not in contradiction with theory of MHD turbulence (fast magnetosonic waves)

1 1.1

27 2

1 2 0.55

~ v 10 cm / ,

(3 1) / 2 2.7, at 2.1

~ ~ ~

s

s

cr p p

s s

ef

p

B p p

D s

q Zm c Zm c

H p p

X D Zm c Z







  



 

   

    

   

   

   

   

   

   

 

diffusion-convection model: galactic wind driven by CR

Zirakashvili et al. 1996, 2002, 2005, VP et al. 1997, 2000, Ipavich 1975, Breitschwerdt et al. 1991, 1993,

Everett et al.2008, 2010, Salem & Bryen 2014

+ cosmic ray streaming instability with nonlinear saturation

CR scale height is larger then the

scale height of thermal gas. CR pressure gradient drives the wind.

H_ef(p/Z) u_inf= 500km/s R_sh= 300 kpc

sh sh

u R > 10 D(p)

,

-γs

s

σ + 2

J ~ p γ = = 2

σ -1

   ^sh  

max sh

E 0.3 Ze u B R c

- D(р) should be anomalously small both upstream and downstream; CR streaming creates turbulence in shock precursor

Bell 1978; Lagage & Cesarsky 1983; McKenzie & Vőlk 1982 …

diffusive shock acceleration

Fermi 1949, Krymsky 1977, Bell 1978, …

“Bohm” limit D_B=vr_g/3:

E_max,ism = 10¹³…10¹⁴Z eV

SNR

u_sh

shock

compression ratio = 4

-condition of CR acceleration and confinement

for B_ism = 5 10^-6 G

for test particles !

~ B_sht^-1/5 at Sedov stage

more detailed investigation:

- streaming instability gives B >> B_ism in young SNR

Bell & Lucek 2000, Bell 2004, Pelletier et al 2006; Amato & Blasi 2006;

Zirakashvili & VP 2008; Vladimirov et al 2009; Gargate & Spitkovsky 2011, Bell 2013, Caprioli & Spitkovsky 2014

confirmed by X-ray observations

under extreme conditions (e.g. SN1998 bw):

E_max ~ 10¹⁷Z eV, B_max ~ 10^-3 G

-wave dissipation in shock precursor leads to rapid decrease

of E_max with time VP & VZ 2003

- finite V_a leads to

steeper CR spectrum ^{t = 103yr} Alfv. drift downstream Jxp²

1 ,1

2 ,2

a a

u V u V

  ^



B²/8π = 0.035 ρu² /2 Voelk et al. 2005

from Caprioly 2012

effect of cosmic ray pressure

 ² 

cr cr sh cr

P ξ ρu , ξ 0.5

- back reaction of cosmic-ray pressure modifies the shock and produces concave particle spectrum

Axford 1977, 1981; Eichler 1984; Berezhko et al. 1996, Malkov et al. 2000; Blasi 2005

sub 

σ 2.5

approximate modified spectrum

-2

cr kin kin

N (E ) E - Eichler spectrum

equations for numerical modeling

Zirakashvili & VP 2008- 2012,

particle acceleration and radiation in SNR

radio polarization in red(VLA), X-rays in green(CHANDRA), optical in blue(HST)

Cas A

Zirakashvili et al 2014 Zirakashvili & VP 2012 Berezhko et al. 1994-2006, Kang & Jones 2006

Zirakashvili & VP 2006-2012,

semianalytic models Blasi et al.(2005), Ellison et al. (2010) )

- Bohm diffusion in amplified magnetic field B²/8π = 0.035 ρu²/2

( Voelk et al. 2005empirical; Bell 2004, Zirakashvili & VP 2008theoretical) - account for Alfvenic drift w = u + V_a

upstream and downstream

- relative SNR rates: SN Ia : IIP : Ib/c : IIb

= 0.32 : 0.44 : 0.22 : 0.02 Chevalier 2004, Leaman 2008, Smart et al 2009

15 1/6 -2/ 3

knee sn,51 ej

15 • -1

knee sn,51 -5 w,6 ej

E Z = 1.1×10 W n M eV,

E Z = 8.4×10 W M u M eV

«knee» is formed at the beginning of Sedov stage

protons only

E^-3

VP, Zirakashvili, Seo 2010

cosmic ray spectrum injected in ISM during SNR life time

JxE²

calculated spectrum of Galactic cosmic rays

(normalized at 10³ GeV; ISM diffusion )

data from HEAO 3, AMS, BESS TeV, ATIC 2,

TRACER experiments data from ATIC 1/2, Sokol, JACEE, Tibet, HEGRA, Tunka, KASCADE, HiRes and Auger experiments

interstellar spectrum of all particles

solar modulation extragalactic

component

JxE^2.75

 

 pc ^0.54

D Ze VP, Zirakashvili, Seo 2010

spectra of p and He are different hardening above 200 GeV/nucleon

superposition of sources Vladimirov et al 2012

new source Zatsepin & Sokolskaya 2006

reacceleration in local bubble Erlykin & Wolfendale 2011

streeming instability below 200 GV Blasi et al. 2012

shock goes through material enriched in He:

- helium wind VP et al. 2010,

- bubble Ohira & Ioka 2011

effect of injection Malkov et al 2011

features to explain:

possible explanation of both features:

concave spectrum and contribution of reversed SNR shock

VP et al 2013

JxE^2.7

positrons in cosmic rays

collection of data Mitchell 2013

electrons positrons

AMS, 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

- e+ production and acceleration in shell SNRs Blasi 2009, Mertsch & Sarkar 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

electrons positrons

electrons + positrons positron fraction

Di Mauro et al 2014: SNR (electrons), PWN (electrons + positrons), secondary leptons from ISM

anti-matter factory

L_pairs =

20-30% L_psr

after Amato

p,He knee 2nd knee

structure above the knee

knee at 3 PeV (light primaries),

hardening at 20 PeV (medium component), 2^nd knee at 300 PeV

JxE³

Prosin et al 2013

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

TUNKA KASCADE-G

JxE^2.7

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 component or onset of a new high energy Galactic source population

other Galactic accelerators at ultra-high energies

• reacceleration by multiple shocks

SNR SNR

SNR

OB

association u=3×10³ km/s B=10^-5 G

R=30 pc

f ~ 1/p³

t_a ~ R/(F_shu) at D_i< uR

~ D/(F_shu²) at D_i > uR R

u

E_max ~ 10¹⁷Z eV

Bykov & Toptygin 1990, 2001, Klepach et al. 2000

• newly-born pulsars with ultrarelativistic wind E ~ 10¹⁹ Z B₁₃(Ω/3000 rad/s)² eV

Blasi et al. 2000, Arons 2003, Fang et al. 2013,

• Fermi bubbles

gamma-ray emission E_ph = 1 – 100 GeV, 4x10³⁷ erg/s

J_e ~ E^-2 Su et al 2010

gamma rays, X-rays, radio, WMAP Haze

•Galactic wind

u

R acceleration at termination shock Jokipii & Morfill 1985, 1991

Zirakashvili & Völk 2004

R = 300 kpc, u = 400 km/s E_max = 10¹⁸Z eV

galactic disk SNR

Kulikov & Kristiansen 1958

from Beatty et al 2013

GZK

suppression?

Conclusions

Cosmic ray origin scenario where supernova remnants serve as principle accelerators of cosmic rays in the Galaxy is strongly confirmed by numerical simulations. SNRs can provide cosmic ray acceleration up to 5x10¹⁸ eV. PWN may be responsible for observed flux of cosmic ray positrons.

Diffusion provides reasonably good description of cosmic ray

propagation in the Galaxy even under simple assumptions on cosmic ray transport coefficients and geometry of propagation region (e.g. as

loaded in GALPROP code).