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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:. basic empirical diffusion model. Ginzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998 ( GALPROP code ). - PowerPoint PPT Presentation
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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!