Over 500 days of low frequency (less than 5 MHz) radio observations from the IMP-6 spacecraft were accumulated to produce a two dimensional map (frequency versus elongation) of solar type III burst occurrences. This map indicates that most solar bursts are emitted at the second harmonic of the plasma frequency rather than the fundamental. The map also shows that the solar wind electron density varies

Kaiser, M. L.

English

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THE SOLAR ELONGATION DISTRIBUTION
OF LOW FREQUENCY RADIO BURSTS
by
M.L. Kaiser
Radio Astronomy Branch
Laboratory for Extraterrestrial Physics
Goddard Space Flight Center
Greenbelt, Maryland USA
ABSTRACT
Over 500 days of low frequency (<5 MHz) radio observations
from the IMP-6 spacecraft have been accumulated to produce a
two dimensional map (frequency versus elongation) of solar type III
burst occurrences. This map indicates that most solar bursts are
emitted at the second harmonic of the plasma frequency rather
than the fundamental. The map also shows that the solar wind
electron density varies as R-Y where 2 - y s 3.
The question of whethersolar fast-drift radio bursts (type III)
emit their radiation at the fundamental or the second harmonic (= 2fo)
of the solar wind plasma frequency is important in assessing the
viability of the several current theories on type III mechanisms.
For the past several years, spacecraft observations of these bursts
at low frequency ( <5 MHz) have given indirect evidence that emission
occurs at the second harmonic (see Fainberg and Stone, 1974). In
this paper, data from the Goddard Space Flight Center's radio
astronomy experiment on board the IMP-6 spacecraft have been
analyzed to search for a predicted geometrical effect which could
provide additional evidence on this problem.
If the angular distances from the Sun of type III solar bursts
at a given frequency are collected over a long period of time, there
will be an elongation angle beyond which bursts are rarely seen. This
maximum angle corresponds to a viewing direction tangent to the
relevant plasma level; the solar limb for that frequency. A simplified
version of this geometry is shown in Figure la. The plane of the
figure is the ecliptic and a plasma level corresponding to a particular
plasma frequency is shown as a heliocentric circle of radius P. A
burst occurring at this plasma level and a central meridian longitude
angle e will be measured at Earth as occurring at elongation 0. When
1
the sum of and e are 900, the elongationo reaches maximum and
additional increases in 8 are either observed at lower elongation
angles, or, more likely, not observed at all due to propagation
difficulties'.
If the observed occurrence rate of bursts as a function of elonga-
tion were measured, there would not only be a maximum elongation,
but also an bnhancement in the distribution near this maximum. This
enhancement is due to foreshortening and can be. seen numerically in
Figure lb. Here, the rate of change of longitude as a function of
elongation is plotted against elongation for several plasma levels.
For example., at a plasma level of 0.5 AU (corresponding to a very
low plasma frequency) the maximum elongation is 300, which occurs
at a longitude of 600. However, when the elongation angle is 250,
bursts are produced at a longitude of 32? 7, so that the outermost 50
of the distribution integrates over 27?3 in longitude. If we assume
bursts are produced uniformly in longitude this effect will cause a
large enhancement in the distribution at the limb.
In principle, observations of these limb enhancements as a
function of observing frequency could be used to decide if solar
bursts are generated at the fundamental or the second harmonic of
the plasma frequency, and possibly to determine the average solar
wind electron density as a function of radial distance. However,
2
there are a number of complications which must be considered before
conclusions can be drawn from actual observations.
The first problem is the expansion of the simple geometry of
Figure 1 to three dimensions, where the plasma levels become spheres.
A burst occurring on a particular sphere has both a longitude and
latitude component, each of which will also have maximum values
analogous to the two-dimensional case. The total number of bursts
at a given elongation is then a double integral over some range of
solar latitude and longitude. The general effect will be to enhance
the center of the elongation distribution relative to the limbs. This
will be particularly important close to the Sun because the maximum
latitude dictated by the line-of-sight tangent to the plasma level
sphere is large.
A second consideration is the effect of varying distance from
the point of emission to the observer. The observed flux varies
inversely with the square of distance, but the variation of the number
distribution is more subtle. The observations discussed in this
paper and similar observations discussed by Fitzenreiter et al. (1975)
show that solar bursts are distributed in a form
n(F) . F-$
where n is the number of bursts of a given flux, F, and 0 varies
between 1.25 a very low frequencies (00 kHz) to perhaps 1.75 at
3
5 MHz. If each point on the plasma sphere shows a similar flux
distribution, then the contribution to the elongation distribution is
No , F- dF,
t
where t is the detection threshold. At a distance R this contribution
would be changed by
At a plasma level of 0.5 AU, the ratio NR/No is never less than 0..80,
thus at higher frequencies, with plasma levels closer to the Sun, the
distance effect is negligible. However, at lower frequencies, the
distance differential becomes more important. This effect also
tends to reduce the limb-to-center ratio in the elongation distribution.
A general smearing or broadening of the distribution will result
from variations in the solar wind electron density. Montgomery et al.
(1972) indicates that in situ observations show a scatter of 50% around
the mean electron density at 1 AU. This is equivalent to approximately
20% variation in the position of plasma levels.
An attempt to depict the elongation distribution resulting from
these considerations is shown in Figure 2. The left panel (2a).shows
the predicted elongation distribution for three plasma levels, taking
into account a three-dimensional plasma sphere, an R-1 and R-1/2
( = 1. 5 and 1.25) source-to-observer distance correction, and a
4
+ 20% plasma level variation (one sigma level of a normal distribution).
The expected limb-to-center de-emphasis, caused mostly by the
inclusion of three dimensions, can be easily seen at the 36R e level
and the broadening is evident at all levels. The differential distance
correction is noticeable only at 191R.
Several assumptions are implicit in Figure 2, the most important
of which is the presumption that solar bursts occur at a uniform rate
at all points on the plasma level sphere. Inclusion of arbitrary cutoffs
in solar latitude produce central holes in the distribution, particularly
at plasma levels close to the Sun. However, at lower frequencies
(plasma levels 2 0.75 AU) where the emphasis of this study lies,
the latitude at the line-of-sight tangent is less than 400, so no
latitude cutoff was used in the numerical simulation. Also, no
attempt was made to include the effects of scattering or any intrinsic
beaming of emission.
Figure 2b shows the numerical prediction of solar burst distribu-
tion for plasma levels from the Sun to very near the Earth. The distribu-
tion peak at each plasma level is normalized to 100%, and the contours
are drawn relative to the peaks. A very broad limb enhancement can
be seen from 2 0 0 Re until it merges into a central peak at around 30Ro .
The point of this study is to try to observe this limb enhancement and
to relate the plasma levels to observing frequency.
5
The Goddard Space Flight Center radio astronomy experiment
onboard the IMP-6 spacecraft was used in an effort to make these
observations. The experiment, described in detail by Brown (1973),
consisted of two 32-channel radiometers connected to a 90-m dipole
and operated between 30 kHz and 9.9 MHz. The IMP-6 was spin
stabilized, with the dipole antenna lying in the spin plane, which was
parallel to the ecliptic. plane. Even at these very long wavelengths,
the direction of emission was accurately measured by cross-correlation
between the dipole antenna pattern and the imposed spin modulation
pattern. This has proved to be a powerful technique for low-frequency
solar work as shown by Fainberg et al. (1973).
The data prqcessing approach used to study the limb enhancements
was to stack all data from IMP-6 in Sun-centered elongation coordinates.
It was reasoned that over a long period of time non-solar events would
scatter when stacked in this way and the repeatable solar scans would'
be enhanced. A major exception to this philosophy was an extensive
effort to eliminate obvious terrestrial emissions (see Kaiser and Stone,
1975) by excluding: all data taken when the spacecraft was inside the
Earth's magnetosphere as well as any emission originating within 7.5
Earth radii of the gEarth. This Earth filtering eliminated typically 90%
of the IMP-6 data. However, even with this extreme reduction about
106 five-second data samples spread over 500 days (May 1971-Oct 1972)
6
remained for use in this study.
Specifically, the data were accumulated in two-degree solar-
elongation bins determined by the emission direction (as deduced from
spin-modulation measurements over three-minute processing windows).
This resulted in a histogram for each observing frequency of some
arbitrary "number of events" versus elongation. As a check on the
validity of this overall data processing method, these histograms
were compared to histograms of selected solar type III events culled
from the same IMP-6 data base by Fitzenreiter et al. (1975). The
two methods appeared to produce nearly identical histograms, thereby
justifying the data-processing method used in this paper.
Figure 3 is the result of this 500-day accumulation displayed
in a manner similar to Figure 2b with contours again relative to the
peaks. Both eastern and western elongations are shown, whereas,
in Figure 2b, symmetry is implied.
Note that Figures 2b and 3 can be aligned only if we set 1 AU
(=215R.) approximately equal to 50 kHz. In situ solar wind measurements
at 1 AU (Montgomery, et al. 1972) indicate a plasma frequency of approx-
imately 25 kHz; thus, Figure 3 strongly suggests that most low-frequency
solar emission occurs at the second harmonic of the plasma frequency as
suggested by earlier measurements (see Fainberg and Stone, 1974).
7
The shaded curves marked A and B illustrate this point even better.
Curve A was made by assuming that emission occurs at the plasma
frequency, which is fixed at 25 kHz near the Earth. Curve B results
if emission occars at the second harmonic. The boundaries of
curves A and B are formed by solar-wind density functions proportional
to R- 2 (inner edge) and R-2 63 (outer edge). The second harmonic
interpretation is strongly favored over curve A particularly at western
elongations.
The other"goal of this research was to determine the solar wind
electron density as a function of distance. Fainberg and. Stone (1971)
have determined an electron density scale proportional to R-2 .63 for
a particular radio storm in August 1968. The lower boundaries of the
shaded areas represent this type of function and it does appear for
curve B to follow the contours. However, the upper boundary of B,
which is an Ne C R-2 function, also follows the contours. It therefore
appears, not too surprisingly, that averaged over 500 days, the
electron density scale varies considerably. There is evidence that
this data processing method can be used to determine electron density
scales for particular active regions and this type of investigation will
be pursued.
Figure 3 indicates a small but systematic asymmetry between
the eastern and western halves of the distribution. The "limb" in
8
the east seems to be at a slightly smaller elongation (relative to 0O)
than the west. Also, at higher frequencies, the center of the distribu-
tion is marginally displaced toward the west.
The cause of the western excess is not known. It is possible
that, over the sample time period, more bursts were produced in the
west than the east. However, 500 days seems rather long for an
effect of this type to persist. In fact, the only known solar feature
which shows an east-west asymmetry over long time periods is
the magnetic field. Our line of sight intersects the Archimedean
spiral differently in the west than in the east. Thus, any type of
emission beaming (intrinsic or imposed by propagation) related to
the magnetic field could cause the distribution shown in figure 3.
The low-frequency central peak that is observed, but was
not predicted, can be numerically accounted for with more smearing.
Two likely candidates for this smearing are the finite receiver
bandwidth (10 kHz) which becomes, at low frequencies, a sizeable
fraction of the observing frequency, and scattering, which becomes
more important as observing frequencies approach the local plasma
frequency.
In summary, a rather simple data-processing technique has been
employed to study the distribution in elongation of type III solar bursts.
This study indicates that, at low frequencies, most bursts occur at the
9
second harmonic of the plasma frequency, rather than at the fundamental.
Also, the solar wind electron density scale appears to be within
boundaries of I/R 2 to I/R 3 .
10
REFERENCES
Brown, L.W.: 1973, Astrophys. J. 180, 359.
Fainberg, I., and Stone, R.G.: 1971, Solar Physics 17, 392.
Fainberg, I., Evans, L.G., and Stone, R.G.: 1972, Science 178,
743.
Fainberg, J., and Stone, R.G.: 1974, Spa. Sci. Rev. 16, 145.
Fitzenreiter, R.J., Fainberg, J., and Malitson, H.H.: 1975,
in preparation.
Kaiser, M.L., and Stone, R.G.: 1975, Science, in press.
Montgomery, M.D , Bame, S.J., and Hundhausen, A.J.: 1972,
J. of Geophys. Res., 77, 5432.
Figure Captions
Fig. la. A type III burst occurring at a distance P from the Sun
will have an elongation angle 4 as seen from the Earth
and longitude 0 as seen from the Sun.
Fig. lb. The rate of change of longitude as a function of elongation
for various distances from the Sun.
Fig. 2a. The predicted distribution of solar bursts at three levels
taking into account three dimensions, varying source-
observer distance and local electron density fluctuations.
Fig. 2b. Contours of equal distribution relative to the peak at
each plasma level between the Earth and Sun.
Fig. 3. The result of accumulation. of 500 days of IMP-6 data
in solar elongation coordinates. Contours are analogous
to those of figure 2b.
TWO - DIMENSIONAL SOLAR LIMB ENHANCEMENT
20
10
PLASMA LEVEL
RADIUS P 0.
Q6
de
LONGITUD T d 0.1
TYPE IrI
LOCATION 1.0 0.8
PO.9 AU
ELONGATION
ANGLE
0.1
EARTH 0 20 40 60
ELONGATION (0)
(a) (b)
ELONGATION (DEGREES)
0 10 20 30 40 50 60 70
10200 /
36 R DISTANCE CORRECTION 150 90 90 60
S36- 1 
5
IPLASMA LEVEL 2
R-%
= ,- 191 R2
' 10
S 10 20 30 40 50 60
ELONGATION (DEGREES)
(a) -I)
ELONGATION
E W
-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90
30
5050 75 90 90 40 30
50 -
100 -... i......N
W 200 -
-00
z
'. 300
Ili
400
500-
750 -
Iff#


The solar elogation distribution of low frequency radio bursts

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