Particle distributions in large scale radio jets

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Particle distributions in large scale radio jets
This work is largely based on the Ph.D. thesis of
Andrew Young (the MN incarnation), using
techniques developed over the years with Debora
Katz.

• Lawrence Rudnick
• University of Minnesota

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conclusion
Heres the bottom line. If it doesnt look
interesting, you can stop here!
CONCLUSIONS (without context)
FRI (low luminosity, non-classical double source)
jets have a narrow distribution of low
frequency spectral (energy) indices around
-0.55 ( -2.1), not the test particle strong
shock limit of -0.50 ( -2.0).
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Particle acceleration in kpc jets
Radio galaxies have (at least) several sites
where relativistic particles are accelerated in
the nucleus, giving rise to pc-scale structures,
in hot spots, where optical and sometimes X-ray
emission can be seen, and along kpc jets, where
energy arguments and sometimes the presence
of optical and/or X-ray emission provide evidence
for in-situ acceleration.

• Why look in the radio?
• How do you look in the radio?
• What do we find about particle distributions?

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WHY look in the radio?
In the optical and X-ray, the evidence for in
situ article acceleration is pretty clear, since
the particle lifetimes are shorter than the light
travel time from the nucleus. However, the
optical and X-ray spectra are then modified by
radiative (complicated further by adiabatic)
losses, whereas the low frequency radio emission
preserves the low energy power law signature of
the acceleration process.

• Low frequencies can see injection power law
• averages over
  long timescales

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HOW do you measure low frequency (injection)
slope?
Its remarkable that after 30 years of radio
source mapping, we have not (until this work),
managed to address what appears to be a quite
simple question what is the low frequency power
law slope of radio emission from jets? However,
for practical reasons, this has been a quite
challenging prospect. The eyes of non-observers
may now begin to blur over.

• 1. Need clear indication of low frequency power
  law
• 2. Must measure homogeneous population
• - resolve spatial variations in spectra
• - separate out background (lobe)
  confusion

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These are the questions that need to be answered
in the affirmative before A measure of the low
frequency power law can be made. In general, the
answer to these questions is negative, and
specific techniques must be used to get
around the problems.
Has the low frequency power law been seen?
Has jet/lobe emission been separated?
Are spectral variations adequately resolved?
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Multi- resolution filtering
Heres one simple technique for separating out
jet emission. The top shows the decomposition of
the map on the left into two components. At
bottom are the spectral indices that result from
doing this at two frequencies. (See Rudnick,
2002, PASP 114, 427).
3C438
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Spectral Tomography
On the question of separating jet emission from
the background lobe information, another powerful
but simple techniques we use is spectral
tomography (see Katz-Stone Rudnick, 1997, ApJ
488, 146).

• Make series of images, St by varying at
• St S(n2) (n2/n1)a S(n1)

t
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This is from the 1997 paper, showing successive
tomography slices for 3C449. When the jet
disappears in the subtracted image (either in
grayscale or in slices across the jet) then the
jet spectral index has been identified between
the pair of frequencies used.
Jet spectra from tomography
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Both multi-resolution filtering and spectral
tomography have idiosyn- cracies. Here is
a comparison that they give consistent results
for spectral indices. (see Treichel et al.
2001, ApJ 561, 691)
x original map filtered
filtered tomography
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Here I turn to the question of whether the low
frequency emission actually has a power law. The
data at the top left are from Cygnus A, (Carilli
et al.) with data at five frequencies (and,
through a little magic, additional points see
Katz-Stone, Rudnick and Anderson, 1993).
Although many authors have assumed a lower
frequency power law for Cygnus A (see earlier
slide with the low frequency data cut off) , it
is clear that no power law has been observed in
this classic source.
Has the low frequency power law been seen?
Has jet/lobe emission been separated?
Are spectral variations adequately resolved?
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So, in the absence of multifrequency observations
at sufficiently low frequency, with sufficiently
high and matched resolution, we have two
techniques that still allow us to find the low
frequency index.

• Determining the low frequency index
• Asymptotic behavior ? nucleus
• Color-color diagrams

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Evolving electron population spectral changes
First, lets look at what is observed if there is
a single electron population in a source, which
is then seen under conditions Of different
magnetic fields, or after different amounts of
radiative losses. At different locations in the
source, we will then observe different spectral
indices (from the same electron population)
Log Intensity
Log Frequency
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Here are a few examples of jet spectral indices,
isolated through tomography and filtering, as a
function of distance from the nucleus. For 3C401
South (on the left), but not the other two jets,
the spectral index near the nucleus stays
constant, even though there is a major change in
brightness (and likely in magnetic field). Under
these conditions, a constant Spectral index
suggests that we are in the power law regime,
where shifts in field will change intensity, but
not slope.
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Heres another example where the jets asymptote
to a constant spectral index as one approaches
the nucleus. The original data, shown in green,
did not show an asymptote, because there was
confusion between the jet and its surrounding
sheath. After separation, the power law
asymptote becomes clear. WAT 1231674
Tomography separation Original spectrum Jet
( sheath)
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COLOR-COLORDiagrams
Heres the second method for determining the low
frequency power law. see Katz-Stone, Rudnick
and Anderson 1993, ApJ 407 549

• reconstructing full spectral shapes from three
  frequency observations

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Evolving electron population mapping spectral
shape
Now we look at three frequency data (two spectral
indices), as we move from one location in a
source to another, seeing variations in particle
energy (scaling, e.g., adiabatic) or B field, or
age.
The diagram at bottom shows how the color-color
diagram uniquely maps out the spectral shape,
and points back to the initial power law.
Log Intensity
Log Frequency
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Standard radiative loss models (such as the
Kardashev-Pacholcyzk or Jaffe Perola) predict a
very specific shape in the color-color diagram.
The intersection of these lines with the
alpha1alpha2 line indicates the low
frequency index.
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Color-color problem diagnosis
The use of color-color diagrams to determine the
low frequency index depends on the assumption
that there is a single Homogeneous electron
population in the source, possibly scaled in
energy, or through radiative losses, but
maintaining Its shape. However, the C-C diagram
has its own built-in diagnostic. Here you can
see the data from radio observations Of 3C273 -
there is clearly more than one (unresolved)
component within the observing beam.
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Heres 3C449 again, With tomography at Three
frequencies. The low frequency power law is
obvious both north and south.
North
South
3C449
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a -0.55
Heres three more examples of color-color
diagrams. To the right is 3C98, without a clear
jet, a classical double in appearance On the
bottom are two FRIs, a WAT (111628) and a
relaxed Double (3C386). In all cases, the
Jaffe-Perola model with a low frequency index of
-0.55 is shown. The two black lines are for
-0.50 and -0.60.
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Summary of spectra
Heres a summary of all the data we could find in
the literature, combined with our own work. In
general, FRII jets like those shown earlier, do
not yield a well-defined low frequency index
using our techniques, but the FRI jet results are
pretty clear there is a typical value of -0.55.
a -0.55
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Summary of spectra
This compares the results of our low frequency
index determinations and the distribution of
integrated spectral Indices from the B2.3 survey
(grey). The moral of the story is, integrated
spectral indices do not tell you anything at all
about the low frequency index (although youll
find a lot of literature assuming that to be
true).
a -0.55
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Regulating -0.55 -- where?
So where does this -0.55 index get set up? The
nucleus doesnt look very promising. Hydra A is
one pretty clear example where the spectra are
steeper at pc scales, so the acceleration
happened later. We really like the
flaring region in FRI jets --- theres other
pretty compelling arguments that they must be
acceleration sites.
Initial acceleration at nucleus?
e.g.,Hydra A pc
scale, optically thin regions -0.7,
kpc scale, -0.59 Flaring
region? jet flaring/ brightening regions post
gap
NGC315
155324
3C449
Multifrequency. Spectra needed
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Regulating -0.55 how?
First-order Fermi doesnt seem very promising as
a -0.55 regulator. We have to have moderate Mach
numbers (approx 5-10), but very carefully not go
below 4.5, where the spectra would steepen
rapidly. Speculation welcome!
First-order regulation?
Other regulation? 2nd order, shock-drift in
turbulence/shear at flare? Ultra-relavistic (but
? -2.25?) Shock modification
self-regulation?
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Crab Nebula
This is just for fun. Its a picture of the Crab
nebula - infrared spectral index on the left.
On the right, a tomography image showing that the
spectral gradients are partially due to a
superposition of the jet and torus (which has
been made to disappear from the image on the
right), and the energy losses as electrons
diffuse out into the nebula. Spitzer IRAC data
see Temim et al. astro-ph/0606321 . Bottom
diagrams too complicated to explain here see
the paper.
pileup from high energy losses
a -0.3
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caveat - NGC315
OK, back to FRI jets. Heres a caveat.
Although there is a substantial -0.55 region in
NGC315, its clearly not the whole story. So
while -0.55 is something to be reckoned with,
there is more going on in particle acceleration
in FRIs.
Multifrequency observations of the jets in the
radio galaxy NGC315, 2006MNRAS.368...48L
Laing, R. A. Canvin, J. R. Cotton, W. D.
Bridle, A. H.
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So, were back where we started.

• FRI (low luminosity, non-classical double source)
  jets have a narrow distribution of low frequency
• spectral (energy) indices around -0.55 ( -2.1),
  
• not the test particle strong shock limit of -0.50
  ( -2.0).
• We need a characteristic acceleration mechanism
• It may happen in the flaring region of FRI jets
• ? And, its not the whole acceleration story.