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High-energy limit of Galactic cosmic rays
Vladimir Ptuskin
IZMIRAN
CR Large Scale Experiments, 2011


JXE3

knee Galactic extragalactic

rg = 1в

EEeV Kpc Z в BG

black body suppression


Cosmic rays of Galactic origin: acceleration in supernova remnants and propagation in interstellar magnetic fields

VERITAS, MILAGRO


basic diffusion model
Ginzburg & Syrovatskii 1964, Berezinskii et al 1990, Strong & Moskalenko 1998 (GALPROP)

M51 ~ 15% of SN kinetic energy transfer to cosmic rays,

H = 4 kpc, R = 20 kpc

sn = (30 yr)-1

H2 Te 2D D 3 в1028 cm2 /s at 1 GeV D p / Z , a = 0.3...0.6
a

Jcr(E) = Qcr(E) Te(E)
source confinement time of CR in the Galaxy; ~ 108 yr at 1 GeV

s = 2.1...2.4
source spectrum


ush

diffusive shock acceleration
shock
Fermi 1949, Krymsky 1977, Bell 1978, ...

SNR

+2 J ~ p , s = =2 -1
-
s

compression ratio = 4

ush Rsh > 10 D(p)

-condition of CR acceleration

Cas A

- D() should be anomalously small both upstream and downstream; CR streaming creates turbulence in shock precursor
Bell 1978; Lagage & Cesarsky 1983; McKenzie & Vlk 1982 ...

Bohm limit DB=vrg/3:

Emax
Emax

ush 0.3 Ze B Rsh c 1014(B/Bism) Z eV B

Hillas criterion !
ism

= 5 10-6 G

B/Bi s m ~ 102

in young SNR from synchrotron X-rays obs.

Koyama et al 1995 ... & theory of CR streaming instability Bell & Lucek 2000, Bell 2004 ...


numerical simulation of cosmic-ray acceleration in SNR
VP, Zirakashvili & Seo 2010 ApJ 718, 31
- spherically symmetric hydrodynamic eqs. including CR pressure + diffusion-convection eq. for cosmic ray distribution function (compare to Berezhko et al. 1996, Berezhko & Voelk 2000; Kang & Jones 2006) - Bohm diffusion in amplified magnetic field B2/8 = 0.035 u2/2 ( Voelk et al. 2005 empirical; Bell 2004, Zirakashvili & VP 2008 theoretical)

- account for Alfvenic drift w = u + Va 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

sn

4 F( p) p4c /

sn

protons only

«knee» is formed at the beginning of Sedov stage

pkneec Z = 1.1в1015 sn,51n1/ 6Me2/ 3 eV, j

pkneec Z = 8.4 в10 sn,

15

51

M-5 u

·

w,6

Me1 eV j


calculated interstellar spectra produced by Type Ia, IIP, Ib/c, IIb SNRs (normalized at 103 GeV)
D pc
0.54

Ze

spectrum of all particles

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

composition

based on
max

>; data from Hoerandel 2007


another accelerator

Emax = 1017 Z eV


Cosmic rays of extragalactic origin: acceleration in AGN jets and propagation through background radiation in the expanding Universe

Hillas (1984) diagram updated by Kotera & Olinto 2011


ZGK cutoff
pair and pion production on microwave & EBL photons
Greisen 1966; Zatsepin & Kuzmin 1966

photodisintegration of nuclei
Stecker 1969

energy scales are multiplied by 1.2, 1.0, 0.75, 0.625 for Auger, HiRes, AGASA, & Yakutsk

Aloisio et al 2007


Auger ­ heavy composition; anisotropy (69 events at >57 EeV) Abreu et al 2010, Matthiae 2010,
PAO 2010

HiRes ­ proton composition; no significant anisotropy (13 events) Abbasi et al 2009, Sokolsky et first results of Telescope Array on spectrum, composition, anisotropy (13 events at >57 EeV) support HiRes Thomson 2010
al 2010

E rg = 100 1020 Z eV

10-9 G Mpc B

magnetic field effects are important everywhere: around sources, on the route to our Galaxy, in the Galaxy
Pierre Auger Observatory, 69 events at E > 5.5 1019 eV (with Swift-BAT AGN density map) Abreu et al 2010 Dolag et al 2004, Sigl et al. 2004, Berezinsky et al 2006 Das et al. 2008, Lemoine & Waxman 2009

heavy composition: easy to accelerate but difficult to identify sources; production of neutrinos is suppressed


extragalactic sources
energy release in units
needed in CR at > 1019.5 eV SN AGN jets

1040 erg/(s Mpc3)
newly born fast magnetars
-4

GRB

accretion on galaxy clusters

3 10

-4 -3

(Auger)
9

3 10 kin.

-1

&

3 6 10

3 10
-2 for

10

-3

10
strong shocks

X/gamma

rotation

8 10 for E>10 eV

Lkin > 1044 erg/s

low-luminosity AGN

FR II + RLQ

Koerding et al 2007


maximum energy of accelerated particles
Lovelace 1976, Biermann & Strittmatter 1987, Blandford 1993, Norman et al 1995, Waxman 1995, Farrar & Gruzinov 2009, Lemoine & Waxman 2009

Emax = Ze в в B в l
general electrodynamic estimate
Ljet B c 6
2

- Hillas criterion

shock acceleration
L
jet

R

2

- power of magnetized flow

0.5 u3 R
cr

2

proton-electron jet

jet velocity

jet radius
1/ 2

wcr B (4

u

2 2 cr

wcr )1/ Ze

Bell 2004
1/ 2

Emax

6 Ze Ljet c

Emax

8

c

L

jet

2.7 в1020 Z1/ 2L1/ 2,45 eV jet
- optimistic estimates of E
max

20 Z cr 1в10 L1/ 2,45 eV 0.1 jet
for not ultrarelativistic jets


Allard et al 2005, Berezinsky et al. 2006

VP et al 2010

empirical dip model

account for dmin(Ljet)

Galactic

empirical ankle transition model

heavy composition
Auger data

Allard 2009

30% of Fe

Galactic


Conclusions
Cosmic ray origin scenario where supernova remnants serve as principle accelerators of cosmic rays in the Galaxy is strongly confirmed by recent numerical simulations. SNRs can provide cosmic ray acceleration up to 5x1018 eV. More data on spectrum, composition, and anisotropy are needed in the energy range 1017 to 1019 eV, where transition from Galactic to extragalactic component occurs. Understanding discrepancy between Auger and HiRes results on composition and anisotropy is necessary for understanding of cosmic ray origin at the highest energies.