Physics at the End of the Cosmic-Ray Spectrum

Theory Summary Talk

J. R. Jokipii and Frank Jones

First, look at the general background physics:

SNRSun

cosmic-ray halo

galactic disk

r =20 kpc

2H

basic empirical diffusion model

D

HX

2

v

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

surface gas density 2.4 mg/cm2

GV5 s,/2

cm54.0

528

102 RRHD

s,/2

cm3.0

528

109.5 RHD

GV rigidity, magnetickpc,5 5 Ze

cpRHH

- plain diffusion break of D at 5 GV

- diffusion + reacceleration Va = 30 km/s

escape length:

GV 5 ,6.0 RRD

energy balance Ginzburg & Syrovatskii 1964

•required source power 3×1038 erg/(s kpc2)•SN kinetic energy 2×1039 erg/(s kpc2)(Wsn=1051 erg, νGal = 0.03 yr-1

local SN rate 50 Myr-1kpc-2)

~ 15% - efficiency of CR acceleration in SNRs

other Galactic accelerators: pulsars [2×1050 (10 ms/τ)2 erg], stellar winds [2×1038 erg/s kpc2], Galactic GRBs [1051 erg/105 yr], micro quasars, Galactic Center …

acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility) b) delay between nuclear synthesis and acceleration (Soutoul test: 59Ni 59Co, high obs. 59Co/56Fe gives δt > 105yr Leske 1993)

Basic Theoretical Themes or Issues:

1. Acceleration Mechanisms

2. Sources and Knees

3. The Sharpness of the Knee (s)

1. Acceleration Mechanisms:

Diffusive Shock Acceleration

maximum energy

10)(

pD

Ru shshcondition of acceleration,critical Pecklet number(parameter of modulation)

SNRWsn=1051erg

ismn0=1cm-3

scmPD

scmnWRu

GVism

shsh

/106

/10

23.028

25/2

05128

-maximum value

-typical in interstellar medium

diffusion should be anomalously slow near the shock

(upstream and downstream)

cosmic ray streaming instability in shock precursorBell 1978, Lagage & Cesarsky 1983, McKenzie & Vőlk 1982, Achterberg 1983,Vőlk et al. 1988, Fedorenko 1990, Bell & Lucek 2000, 2001

MHD simulations demonstrate

magnetic field amplification

BjBBpt

ucr

||0

)(1

Development of previous modelling, Lucek & Bell (2000)

Filamentation & self-focussing

proton beam jvelocity vbeam

E=-uxB

B

R

Magnetic field growtht

U

jRR

E

t

B turb

1

~~

Ideal for focussing CR into beam

Focuses CR, evacuates cavity

E=0

E=0

Stochastic self-limitation of injection rate through nonlinear wave pro –

duction: from η 10-2 ≈ װ to ηeff ≈ 10-4

Plus systematic reduction of ion injection. Strong wave production only locally in “polar” regions

Synchrotron emission also overall dipolar for uniform external B1

Hadronic -ray emission dipolar for uniform external B1

Renormalization of spherically

symmetric flux

Völk et al.(2003)

Non-spherical aspects of SNRs

Confirmation by Rothenflug et al. 2004using XMM on SN 1006

Ion injection only for instantane-ously quasi-parallel shocks nB«π/2

Magnetic field amplification by accelerating particles in shocks

Accelerated particles tend to stream ahead upstream Instability (A.R. Bell 1978)

Nonlinear evolution Bohm limit of scattering

Mean field amplification (Bell & Lucek 2001; Bell 2004, 2005)

High field Beff Depression of IC emission

Faster scattering Increase of pmax for nuclei

Instabilities driven by dominant nuclear component

SN 1006

• Accreting White Dwarf (Type Ia): Mej ≈ 1.4 M

• Age = 999 yr

• Angular diameter ≈ 0.5 degrees

Extended source for -ray instruments:

H.E.S.S. upper limit < 0.02 Crab From other measurements:

NH = 0.3 – 0.05 cm-3

Distance = 1.8 – 2.2 kpc

ASCA Koyama et al. (1995)

Winkler et al. (2003)

The Importance of the Magnetic-Field Angle

• Acceleration to high energies:– Parallel Shocks

• Very slow• Efficient

– Perpendicular Shocks • Much faster• Also efficient (we point out in this talk

that there is no injection problem)

• New numerical simulations– Hybrid simulations (self consistent)

show efficient acceleration of thermal ions by a perpendicular shock

What about Injection and the limit of diffusive shock acceleration?

• An often-invoked injection criterion is

• This assumes, for no good reason, that there is NO motion normal the average magnetic field– In general, particles move normal to the field, and this

is important for the injection problem

2. Different Sources:

Lessons from the heliosphere

• ACE energetic particle fluences:• Smooth spectrum

– composed of several distinct components:

• Most shock accelerated

• Many events with different shapes contribute at low energy (< 1 MeV)

• Few events produce ~10 MeV

– Knee ~ Emax of a few events– Ankle at transition from

heliospheric to galactic cosmic rays

R.A. Mewaldt et al., A.I.P. Conf. Proc. 598 (2001) 165

Two Component CR Spectrum

Log E (eV)

10 11 12 13 14 15 16 17 18 19 20 21

Flu

x X

E2.

7

-1

0

1

2nd Tooth Fairy

1st Tooth Fairy

CR flux evolution from a local GRB: simple power-low D(E)

Injected CR energy: 1052 ergs at 1 kpcEmax=1021 erg, = 2.2

D(1 PeV)= 1029 cm2 s-1, =0.6Galactic halo size: 10 kpc

knee2nd knee ankle

tEDtEr

r

rrtrEN

dif

difdif

)(2),(

)exp(),,(2

23

(conservs the numberof particles in rdif

3)

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 SNRsreacceleration in ISM by strong shocks

02.0~~ISM

SNR

stand,2

flat,2

X

X

N

N2.0~~ SNR

SNR

ISM

stand,2

flat,2 fX

X

N

N

volume fillingfactor of SNRs

grammage gained in SNR

grammage gainedin interstellar gas

standardplain diff.reacceleration

plain diff.reaccelerationnism = 0.003…1 cm-3

Bohm diffusionTSNR = 105 yr

RUNJOB 2003preliminary

“microscopic” theory of cosmic-ray diffusion

p

< B > + δB

resonant interaction

rg ~ 1 / k Larmorradius

resonantwave number

parallel diffusionJokipii 1966

anomalousperpendiculardiffusionJokipii & Parker 1970Chuvilgin & Ptuskin 1993Giacolone & Jokipii 1999Casse et al 2001

Hall diffusion

2/13/1

res2

20

ll

...~

)(3

gg

g

vrvr

kB

BvrD

ll40

4tot~ D

B

BD

Armstrong et al 1995

3Hgvr

D

W(k) ~ k-5/3… k-3/2

hot topic: anisotropic Alfvenic turbulence Shebalin et al. 1983, Higdon 1984, Bieber et al. 1994, Montgomery & Matthaeus 1995, Goldrreich & Shridhar 1995, Lazarian et al. 2003

KolmogorovKraichnan

109 eV1017 eV

cm 103.3 1μGGV

12 BRrg

All-particle spectrum:Knee ~3 PeV

Tibet EE/1.23

x 0.1

x 0.01

SECOND KNEE and EXTRAGALACTIC PROTONS

Second knee automatically appears in the total spectrum (galactic +extragalactic) due to low-energy flattening of extragalactic spectrum, which appears at Ec~ 1×1018 eV.This energy is universal for all propagation modes (rectilinear or diffusive) and it is determined by transition from adiabatic to e+e- -energy losses .

rectilinear propagation diffusive propagationLemoine 2004, Aloisio, V.B. 2004

Unusually High Maximum p Energies at Sgr A East

• With 4mG field Sgr A East shock can accelerate particles to 1019 (R/10pc) Z eV in a perpendicular shock configuration (Jokipii 1982 & ApJ 1987)

• p-p cooling-limited p energy is ~1021 eV

• Time-limited p energy is ~1020 eV (given 10 000 year age)

<ln(A)>

Energy (GeV)

104 105 106 107 108

<ln

(A)>

0

1

2

3

4

CASA - BLANCAFly's EyeDICEBLANCAKASCADE max

knee as effect of propagation

Hall diffusion in average Galactic magnetic field

Ptuskin et al.1993Kalmykov & Pavlov 1999Candia et al. 2003

Galacticdisk <B>

Candia et al 2003

3. How Sharp is a Knee ?

Conclusions: Theory is in good shape, but there are too many alternatives.

Need more observations, chosen specifically to distinguish between theories!