Arcs in Jovian Spectra
Arcs in Jovian decametric dynamic spectra are a remarkable feature.
I have not seen any during the current 2008 observing season, but here
are examples from 2002, with many thanks to the Nancay Radio
Observatory Archive :
http://www.obs-nancay.fr/a_index.htm
020110 vertex leading RHP and LHP
020101 vertex following RHP and LHP
I have been reading some of the papers that analyze and propose models for the arcs.
In 1981 Goldstein and Thieman, after studying the data from the Voyagers
1 and 2 planetary radio astronomy experiment, wrote this interesting
paper :
From the abstract (in part):
L=6 means that the magnetic field lines of the
flux tube intersect the magnetic equator at 6 Rj (Jovian radii). This
is Io's orbital radius. In other words, these are field lines along
which Io injects energetic electrons.
In this model, the emission cone half angle varies between 45-65 deg at the low
and high ends of the spectrum and is closer to 80 deg in between.
After searching for the best model parameters, they obtain arcs that
nicely represent the main features of the observations, as shown in
their Fig. 6 :
There are A LOT OF COMPUTATIONS behind this overlay !!!
For many points along the flux tube, they compute the angle between the
magnetic field and the direction to the terrestrial observer. The
difference between that angle and the radiation cone half angle, at
that point along the flux tube, should be zero for the radiation to be
observable.
These computations need to be done for many Central Meridian Longitudes
before a theoretical arc can be drawn. The computations had to be
repeated for a variety of model parameters and compared to the
observations.
I understand that the Voyager spacecraft
discovered the arcs. After nearly 25 years of Jovian radio observations
from the Earth, they had not been noticed. They are best observed below
15 Mhz.
In the same issue of the Journal of Geophysical Research :
Boischot and collaborators published spectra from
the Voyagers, showing many arcs such as these of the vertex leading
type (from their Fig. 2) :
The arcs are vertex leading or following depending on the side from which the emission cones are being observed.
There are many other interesting aspects to Goldstein and Thieman's 1981 paper, hard to summarize in this brief review. Please read the full publication.
A great deal more has been written about arcs since their discovery.
More to follow !
Victor Herrero
2008 August 23
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Following are comments posted on the Radio Jove Technical Group, with many thanks to the authors :
Hi Victor,
it seems that above a certain frequency, the photons lag in time.
Since they contain more and more energy at greater and greater
frequencies, perhaps they take a longer time to reach the "burst" stage.
Perhaps these photons (or their precursor processes) are simply taking
more time to fill up with "juice". Assuming a constant rate of energy
supply to the precursor processes. An interesting subject for a math model.
Steve
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Hi Steve,
Those not interested in models of Jovian radiation please press delete. This is going to be very boring.
Yes, I agree with you, this is an interesting subject for those who do like mathematical modeling. You and me, for example.
It is not a simple problem, but we could set up a spread sheet and do
some simplified computations of the angle between the magnetic field
and the line of sight to the observer. Even if we are unable to do a
full analysis, we will learn a lot about the geometry of the field and
the emission cones.
We do not need to model the emission mechanism, the "burst" stage, as
you say. That is understood to be cyclotron emission. In cyclotron
radiation the electrons radiate forward, along the direction of motion,
in a narrow beam. The helical motion along the magnetic field sweeps
the beam in a radiation cone.
The emission is very bright because there is Maser action. The
electrons move towards Jupiter and get reflected in a magnetic mirror
that occurs as the field lines converge towards the magnetic poles. The
reflected electrons have a suitable energy distribution for Maser
action.
The question is: what is the angle of the cone ? how does it vary along the energized flux tube ?
In 1981 Goldstein and Thieman investigated that question very nicely.
By the way, where is the PDF of your interesting Smoothing Study ?
I have drafted one, would you like to see it ?
I put the small shovel, the one you attached to an earlier message, to very good use in digging for this paper. Thank you !
Victor
==========================================
Hi Victor,
delighted to hear that the shovel has been of use. Gardening is a
wonderful activity, I will be interested to see what grows.
Currently my primary interest is the data that we have as a
consequence of storms over the past few months. In view of the fact that
I am new to it, I am interested to study all it's contours and curves.
Whether they be "features", and of interest to the list, or not. There
is a great deal going on at Jupiter. The burst has my interest at the
moment - as it ought in these matters. It appears to show some
indication of being multi-part. I think there may be plateaus - for want
of a better description. Or perhaps it is Richard's gear, bedeviled by
Transfer Function deep in the bowels of the Jove rx. No matter - the
thing to do is to see what the data says, in it's own way.
Steve
The arcs are interesting - but I don't care to compare notes at this point,
apologies to Jim,
complements to the Cone.
==============================
Hello Victor,
I'm not challenging the type of radiation emitted from Jupiter, but your statement,
"In cyclotron radiation the electrons radiate forward, along the direction of motion, in a narrow beam"
is incorrect. You are describing synchrontron radiation. In cyclotron
radiation, where the particles are moving sub-relativisitically, the
emitted radiation is dipolar. The beam is perpendicular to the gyrating
orbit. But because of the retarded potentials, when the particles
gyrate at relativistic speeds, the dipole pattern is seen to fold
into narrow beam in the direction of motion. The effect is
pronounced. If y memory serves me rightly, the beamed power goes as the
fourth power of the Lorentz factor, gamma, tha one sees in special
& general relativity.
John
====================================
John,
You may be right, but I think that the linearly-polarized cyclotron
radiation beam is emitted in (parallel to) the plane of the orbiting
particle, with the (electric) polarization vector also lying in the
plane. Also that the circularly-polarized beam component is
radiated (in two directions) perpendicular to the plane of the orbit.
We amateur Jove astronomers usually choose a frequency and sit there
waiting, and we watch the nice waterfall displays of the spectrum. The
frequency distribution that we see is just the distribution of plasma
frequencies but fourier analysis should show harmonics related to field
variability and turbulence. Analysis of circular polarization (RHC vs
LHC) would show maser activity and turbulence. Spectral analysis and
searching for variations in polarization would appear to hold a lot of
potential.
Cheers,
David
======================================
David,
You say, "You may be right, but..."
I am right and there should be no "but" after the statement. What you
say after the "but" is simply consistent with what I had said. My
comment was strictly on the emitted radiation pattern of an accelerated
charge and nothing else what Victor might have been saying.
John
======================================
Hi John,
Unless I misunderstand, you were saying that cyclotron radiation is
emitted perpendicular to the orbital plane, although you coined the
phrase "gyrating orbit" instead of saying "orbital plane". I agreed
regarding the circularly polarized component, but disagreed regarding
the linearly-polarized component. The latter would be emitted with the
E-vector lying in the orbital plane, and the power peak would lie in
this plane.
I'll change my "may be" to a "sometimes" if you like :-)
Anyway, you can summarize, but I won't belabor this more. The Jupiter
emission has a lot of information hidden within. What do you think are
the most productive research avenues that include analysis of the
Jovian emissions?
Cheers,
David
==================================
Hi John, David, Steve,
I am slow in responding, at times, because I am traveling and camping.
First of all, let me agree with Dave that "...Jupiter emission has a lot of information hidden within..."
More detail about the beaming of synchrotron radiation:
I refer to John Kraus "Radio Astronomy" textbook. I have the 1966 first
edition, which I have been using for 40 years now ! One of the very few
Astronomy books that I carry while traveling.
Section 8-4b is a very compact 5 page summary of the Synchrotron Mechanism.
Expression 8-22 gives the beam width as a function of rest mass and energy of the particle.
For an electron at 1 Gev the beam is 3.4 arcminutes wide.
The width is inversely proportional to the energy, for high energies, so for 1 Mev the width is about 57 deg.
For 100 Kev, the radiation follows a distorted dipole
pattern, stronger in the forward direction. The axis of the
dipole is parallel to the acceleration. This situation is called
gyrosynchrotron radiation.
In synchrotron or cyclotron radiation the acceleration is perpendicular
to the velocity, in the plane of the orbit, for circular motion in a
plane perpendicular to the magnetic field.
At lower energies the pattern gets closer and closer to a dipole pattern and pure cyclotron radiation.
I do not think that I agree with John that "...The beam is
perpendicular to the gyrating orbit...". I may misunderstand his
description. We may need to sketch some diagrams. I think there is
radiation perpendicular to the orbital plane, but not a beam.
I do not have a detailed understanding of how the cones of Jovian
radiation, with their thin walls, get generated. I have several papers
that propose models and I am studying them slowly. An important paper
is Schwinger 1949, Phys Rev 75, 1912-1925 "On the classical radiation
from accelerated electrons". I studied it many years ago and I have
forgotten most of it. I do not have it with me.
I agree with David that from an Observer's viewpoint "...Spectral
analysis and searching for variations in polarization would appear to
hold a lot of potential..."
Victor
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