Physics at the End of the Cosmic-Ray Spectrum

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Physics at the End of the Cosmic-Ray Spectrum
Theory Summary Talk
J. R. Jokipii and Frank Jones
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• First, look at the general background physics

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basic empirical diffusion model
Ginzburg Ptuskin 1976, Berezinskii et al. 1990,
Strong Moskalenko 1998 (GALPROP code)
surface gas density 2.4 mg/cm2
cosmic-ray halo
Sun
escape length
SNR
2H
galactic disk
r 20 kpc
- plain diffusion break of D at 5 GV
- diffusion reacceleration
Va 30 km/s
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energy balance Ginzburg Syrovatskii 1964

• required source power 31038 erg/(s
  kpc2)
• SN kinetic energy 21039 erg/(s
  kpc2)
• (Wsn1051 erg, ?Gal 0.03 yr-1
• local SN rate 50 Myr-1kpc-2)

15 - efficiency of CR acceleration in SNRs
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 dt gt 105yr Leske 1993)
other Galactic accelerators pulsars
21050 (10 ms/t)2 erg, stellar winds 21038
erg/s kpc2, Galactic GRBs 1051 erg/105
yr, micro quasars, Galactic Center
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• Basic Theoretical Themes or Issues
• 1. Acceleration Mechanisms
• 2. Sources and Knees
• 3. The Sharpness of the Knee (s)

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• Acceleration Mechanisms
• Diffusive Shock Acceleration

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maximum energy
condition of acceleration, critical Pecklet
number (parameter of modulation)
SNR Wsn1051erg

• maximum value

-typical in interstellar medium
ism n01cm-3
diffusion should be anomalously slow near the
shock (upstream and downstream) cosmic ray
streaming instability in shock precursor
Bell 1978, Lagage Cesarsky 1983, McKenzie
Volk 1982, Achterberg 1983, Volk et al. 1988,
Fedorenko 1990, Bell Lucek 2000, 2001
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MHD simulations demonstratemagnetic field
amplification
Development of previous modelling, Lucek Bell
(2000)
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Filamentation self-focussing
B
E0
R
proton beam j velocity vbeam
E-uxB
E0
Magnetic field growth
Focuses CR, evacuates cavity
Ideal for focussing CR into beam
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Non-spherical aspects of SNRs
Ion injection only for instantane-ously
quasi-parallel shocks ?nBp/2
?
Stochastic self-limitation of injection rate
through nonlinear wave pro duction from ??
10-2 to ?eff 10-4
?
Plus systematic reduction of ion injection.
Strong wave production only locally in polar
regions
Confirmation by Rothenflug et al. 2004using XMM
on SN 1006
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Hadronic ?-ray emission dipolar for uniform
external B1Renormalization of spherically
symmetric flux
?
Synchrotron emission also overall dipolar for
uniform external B1
Völk et al.(2003)
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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

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SN 1006

• Accreting White Dwarf (Type Ia) Mej 1.4 M?
• Age 999 yr
• Angular diameter 0.5 degrees

Koyama et al. (1995)
ASCA
Extended source for ?-ray instruments H.E.S.S.
upper limit lt 0.02 Crab From other
measurements NH 0.3 0.05 cm-3
Distance 1.8 2.2 kpc
Winkler et al. (2003)
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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

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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

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• 2. Different Sources

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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 (lt 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
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Two Component CR Spectrum
1
0
Flux X E2.7
-1
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Log E (eV)
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CR flux evolution from a local GRB simple
power-low D(E)
(conservs the number of particles in rdif3)
Injected CR energy 1052 ergs at 1 kpc Emax1021
erg, ? 2.2 D(1 PeV) 1029 cm2 s-1, ?
0.6 Galactic halo size 10 kpc
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flat component of secondary nuclei produced by
strong SNR shocks Wandel et al. 1987, Berezhko
et al. 2003
production by primaries inside SNRs
reacceleration in ISM by strong shocks
grammage gained in SNR
volume filling factor of SNRs
grammage gained in interstellar gas
Berezhko et al. 2003
RUNJOB 2003 preliminary
plain diff. reacceleration nism 0.0031
cm-3 Bohm diffusion TSNR 105 yr
standard plain diff. reacceleration
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microscopic theory of cosmic-ray diffusion
resonant interaction rg 1 / k
p
Larmor radius
resonant wave number
parallel diffusion Jokipii 1966 anomalous perpend
icular diffusion Jokipii Parker 1970 Chuvilgin
Ptuskin 1993 Giacolone Jokipii 1999 Casse et
al 2001 Hall diffusion
lt B gt dB
109 eV
1017 eV
Armstrong et al 1995
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
Kolmogorov
Kraichnan
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All-particle spectrumKnee 3 PeV
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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 11018 eV.This energy is
universal for all propagation modes (rectilinear
or diffusive) and it is determined by transition
from adiabatic to ee- -energy losses .
g
diffusive propagationLemoine 2004, Aloisio, V.B.
2004
rectilinear propagation
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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)

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knee as effect of propagation
Candia et al 2003
Galactic disk
ltBgt
Hall diffusion in average Galactic magnetic
field Ptuskin et al.1993 Kalmykov Pavlov
1999 Candia et al. 2003
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• 3. How Sharp is a Knee ?

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Conclusions Theory is in good shape, but there
are too many alternatives.
Need more observations, chosen specifically to
distinguish between theories!