Particle acceleration in jets and lobes

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Particle acceleration in jets and lobes

• Michal Ostrowski

Astronomical Observatory Jagiellonian University
A shock, but what the role it plays ?
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Cygnus A in X rays

• Hot spots are the jet terminal mildly (?)
  relativistic shocks

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(No Transcript)
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Let us remind a few "generally accepted" facts
about the shock acceleration processes

• nonrelativistic (NR) shocks Ush ltlt 1
• relativistic (R) shocks Ush 1

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Diffusive shock acceleration (NR)
u2
u1
R u1/u2
in the shock rest frame

• Compressive discontinuity of the plasma flow
  leads to acceleration of particles reflecting at
  both sides of the discontinuity diffusive shock
  acceleration (I-st order Fermi)

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Acceleration at non-relativistic (NR)shock waves

• Cosmic rays with v gtgt u1 are nearly ISOTROPIC at
  the shock. This fact and particle diffusive
  propagation are the main factors responsible for
  relative independence of the accelerated particle
  spectrum on the background conditions.
• In the test particle approach
• and the only parameter defining the spectral
  index is
• the shock compression R u1/u2.

Below we use often ? ? ???
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1. Spectral index ? does not depend on, e.g.,
For NR shock acceleration

• turbulence character
• mean value and inclination of B
• shock velocity

2. From non-linear models we know, that
acceleration efficiency can be very high
a substantial fraction of the shock bulk
kinetic energy is transferred into energetic
particles.
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Relativistic shock waves

• u1 c
• or the shock velocity projection on
• the mean magnetic field is
• uB c

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Does there exist an universal spectral index for
relativistic shocks ?

• The same value of ? ? 2.2 2.3 derived for
  ultra-relativistic shocks by Bednarz, Gallant,
  Achterberg, Kirk, Guthmann, Vietri, Pelletier, et
  al.
• One can widely meet the opinion that acceleration
  processes acting at relativistic shocks produce
  spectra with this universal inclination,
• -gt equivalent to the synchrotron index s 0.6

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Most studies of energetic particles
(electrons) present in jets and hot spots
postulate the shock (I-order Fermi) acceleration
mechanism as its main source. Application of
the mentioned above theoretical results often
leads to a theoretical picture compatible with
the observational data. II-order Fermi
acceleration is believed to play some role in
radio lobes and extended structures.
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Is life so simple ?Do we really know so much
about the basic physics of energetic particles
in jet related phenomena ?
No, everything I've presented above is an unfair
selection of theoretical results and popular
opinions, sometimes applying contradictory or
even wrong pieces of the knowledge in this field
!
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NR shocks
Test particle spectrum requires small
acceleration efficiency and "simple" boundary
conditions. Efficient acceleration requires
non-linear models resulting in complex spectra.
Such models are not developed to the level
enabling modelling of real shocks, and never
produce a single-power-law spectra.
II order Fermi process can modify the shock
acceleration for VA gt 0.1 Ush
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Relativistic shock waves

• Particle anisotropy in the shock ??
  ?-1

Significant influence of the background
conditions near the shock at the resulting
spectrum !
The mentioned "universal spectral index 2.2" is
derived only in the models involving an effective
parallel mean field configuration and the pitch
angle diffusion model for particle transport.
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Sub- and super-luminal shocks
B2
ush,1
?1
uB,1
uB,1 lt c - subluminal particle
reflections possible
uB,1 gt c - superluminal only
transmissions 1?2
B1
shock
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Summary of results for mildly relativistic
shocks
Acceleration time scale
superluminal
???2
Bednarz Ostrowski 1996
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Cosmic ray density across an oblique subluminal
shock
log (turbulence amplitude ?B/B)
?B?B
?B?B
upstream
downstream
Distance to the shock in units of Xmax
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Niemiec MO (in preparation) short wave
turbulence only downstream
Niemiec MO 2004
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Oblique shocks with uB 0.7
Flat spectrum
Kolmogorov spectrum
?
?B?B
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Weakly turbulent superluminal shock
UB,1 1,93
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Spectrum variations (!) at parallel shock
Reflection probability !
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Spectral index for particles accelerated at
ultrarelativistic shocks (Bednarz Ostrowski
1998)
?
in this simulations dB/B grows with G
2.2
?
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High ? superluminal shocks ? 5 , UB 1,4
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ultrarelativistic shock with ? 10
short wave turbulence
? 4.2
Niemiec MO, in preparation
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It is not clear if, and at what amplitude of
dB, of the high amplitude turbulence
generated downstream of the shock (e.g. Medvedev,
et al.) generation of the universal index 2.2 is
possible. In our studies usually a steeper
spectrum appears followed by a cut-off .
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Final warning Observed radio and IC X-rays are
from ??103 (E ? 1 GeV) electrons. At
relativistic shocks propagating in ordinary (e,
nuclei) plasma such electrons are below the
energy limit required for the I order Fermi
acceleration rg,e ? shock thickness
? rg,nuclei
requires PIC modelling of the shock
structure, like the one described by Troels
Haugb?lle
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Summary of shocks

• cosmic ray spectra generated at relativistic
  shock waves strongly depend on physical
  conditions at the shock
• ? theory of cosmic ray acceleration at
  relativistic shocks
• is in its infancy yet. We know very little,
  if anything, for sure about such processes.
• existing theoretical models explain some features
  
• of the observed cosmic rays, but do not allow
  for reliable modelling of the studied objects
• the above applies at least partly to
  NR shocks

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Particle acceleration in the interstellar medium

• Inhomogeneities of the magnetized plasma flow
  lead to energy changes of energetic charged
  particles due to electric fields
• ?E ?u/c ? B
• compressive discontinuities shock wave
• tangential discontinuities and velocity shear
  layers
• - MHD turbulence

B B0 ?B
u
B
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Jet, and in particular knot morphology
inconsistent with the internal shock model
Stawarz talk
Physics of the medium with relativistic sound
(and Alfvén) velocity
if
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A significant role of MHD
turbulence and the related II
order acceleration at shocks and boundary shear
layers
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Acceleration time scale
in the jet rest frame, for ? rg
scattering centre velocity VA
"CR viscosity" acceleration
CR shear acceleration important only for high
energy nuclei
Efficiency
?
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Possible testing of this scenario Stawarz
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A role of the magnetic field reconnection
A myth the acceleration process takes place in
an extremely thin current layer with vanishing
(small) B and E ? (VA/c) B
where ? lt 1 and provides approximately
monoenergetic particles with energies L E .
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In real conditions the electric fields due to
advected magnetic field exist in vicinity of
null point. Due to compressive flow ( slow
shocks) in this region these electric fields
lead to particle acceleration until it escapes
from the turbulent vicinity of the reconnection
site.
V
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The resulting CR spectrum is relatively flat -
until particle escape starts to dominate and can
extend to energies much above the scale e
(VA/c) B L .
My speculation for radio lobes Possible
self-regulating mechanism to keep the magnetic
field and energetic particles pressures comparable
for Pcr gt PB particle diffusive/radiative
losses dominate until
Pcr PB for Pcr lt PB acceleration in
reconnection processes
increase Pcr until again Pcr PB
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Instead of conclusions With the present poor
theoretical knowledge of the acceleration
processes one is advised to use different
approaches to modelling the observed phenomena.
Only verification of the obtained results with
observational data can put theorists on the right
way to produce a usable theory.
My presented view at the situation is more
critical than views of many other colleagues !