Chapter 3 Search for ULF Waves in the Jovian Magnetosphere with Galileo Page 53 Chapter 3: Search for ULF Waves in the Jovian Magnetosphere with Galileo "And this whole thing with the yearbook - it's like, everybody's in this big hurry to make this book... to supposedly remember what happened, but it's not even what really happened. It's what everybody thinks was *supposed* to happen. Because if you made a book of what *really* happened, it'd be a really upsetting book. You know, in my humble opinion." – Angela Chase My So-Called Life: Pilot episode (Production number 1, 25 th August 1994) 3.1 Motivation All five of the fly-by spacecraft that have visited Jupiter (Pioneer 10/11, Voyager 1/2 and Ulysses) were able to measure the magnetic field strength and direction in the middle magnetosphere using the magnetometer instruments on board. Figure 1 shows the measured field from one such fly-by. 5 6 7 8 9 10 11 12 13 14 15 0 100 200 300 400 B mag (nT) Day of July 1979 -100 0 100 B φ (nT) 0 100 200 300 B θ (nT) -300 -200 -100 0 100 B r (nT) Voyager 2 Jupiter fly-by Figure 3.1: Plot of B-field over entire fly-by encounter of Voyager 2, with the data in Jovian System III co-ordinates. On 5 th July 1979 Voyager 2 was 71.3 R J away from the planet, passed closest approach just before July 10 at 10.1 R J and had then reached 72.7 R J outbound by the 15 th July. Analysis of Voyager 2 data by Khurana and Kivelson in 1989 showed evidence for 10 to 20 minute period waves observed throughout the magnetometer data as the spacecraft traversed the middle magnetosphere on the dayside of Jupiter. Approximately ten years later, Lachin described in his Ph.D. thesis work carried out on Ulysses magnetometer data taken from the dayside middle magnetosphere. This encounter was recorded as Ulysses used Jupiter for a gravity assist manoeuvre to send it out of the
Transcript
Chapter 3 Search for ULF Waves in the Jovian Magnetosphere with Galileo
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Chapter 3: Search for ULF Waves in the Jovian
Magnetosphere with Galileo
"And this whole thing with the yearbook - it's like, everybody's in this big hurry to make this book... to supposedly remember what happened, but it's not even what really happened. It's what everybody thinks was *supposed* to happen. Because if you made a book of what *really* happened, it'd be a really upsetting book. You know, in my humble opinion." – Angela Chase
My So-Called Life: Pilot episode (Production number 1, 25th August 1994)
3.1 Motivation
All five of the fly-by spacecraft that have visited Jupiter (Pioneer 10/11, Voyager 1/2 and Ulysses) were
able to measure the magnetic field strength and direction in the middle magnetosphere using the
magnetometer instruments on board. Figure 1 shows the measured field from one such fly-by.
5 6 7 8 9 10 11 12 13 14 150
100
200
300
400
Bm
ag (
nT)
Day of July 1979
−100
0
100
Bφ (
nT)
0
100
200
300
Bθ (
nT)
−300
−200
−100
0
100
Br (
nT)
Voyager 2 Jupiter fly−by
Figure 3.1: Plot of B-field over entire fly-by encounter of Voyager 2, with the data in Jovian System III co-ordinates. On 5th July 1979 Voyager 2 was 71.3 RJ away from the planet, passed closest approach just before July 10 at 10.1 RJ and had then reached 72.7 RJ outbound by the 15th July.
Analysis of Voyager 2 data by Khurana and Kivelson in 1989 showed evidence for 10 to 20 minute
period waves observed throughout the magnetometer data as the spacecraft traversed the middle
magnetosphere on the dayside of Jupiter. Approximately ten years later, Lachin described in his Ph.D.
thesis work carried out on Ulysses magnetometer data taken from the dayside middle magnetosphere.
This encounter was recorded as Ulysses used Jupiter for a gravity assist manoeuvre to send it out of the
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ecliptic plane and into a Solar Polar orbit. Lachin found indications of waves of approximately 15
minute period in the same region, supporting the Voyager 2 result.
The Galileo orbiter arrived in orbit around Jupiter in 1995 and since then has extensively explored the
nightside magnetosphere of Jupiter. The question addressed in this work is whether similar Ultra Low
Frequency waves ( less than 2 milli-Hertz) would be observed?
(This chapter is an extension of a paper published in Geophysical Research Letters [Wilson &
Dougherty, 2000].)
3.2 Introduction
3.2.1 Fly-By Missions
Jupiter is the largest of all the Solar planets with a radius of 71492km or 1 RJ. Although it has been
observed for centuries from the Earth, only six spacecraft missions have visited it. Five of these were
fly-by missions, consisting of probes Pioneer 10 & 11, Voyager 1 & 2 and Ulysses in chronological order
(see figure 3.2). The sixth spacecraft to visit Jupiter is Galileo, but it is the first orbiter mission to the
planet. So far it has completed over twenty-five orbits in the five years since it’s arrival in December
1995.
Jupiter has an enormous magnetosphere, which encompasses a current sheet that enables the Jovian
Magnetosphere to be readily described as having three distinct regions; the inner, the middle and the outer
region. The current sheet lies in the middle magnetosphere, which resides roughly from around 20 RJ
from the planet's centre out to between 70 to 110 RJ, depending on solar wind conditions which can be
very dynamic and change rapidly. (See Chapter 1 for further details).
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Figure 3.2: Plot of fly-by trajectories of Pioneer 10, Pioneer 11, Voyager 1, Voyager 2 and Ulysses. (Adapted from Simpson et al., 1992.) All five spacecraft entered the Jovian system from the bottom right corner of the plot. Previous shown as figure 1.5 but repeated here for clarity within this chapter.
The current sheet is essentially a collection of charged ions orbiting Jupiter, as such these charged moving
ions create their own magnetic field that perturbs the local (approximately dipolar) planetary magnetic
field, resulting in a cumulative magnetic field that is measured by instruments as being primarily radial in
nature.
When a spacecraft is above the current sheet, that is to say in the northern magnetic hemisphere of
Jupiter, the measured field points approximately radially outwards. When a spacecraft is below the
current sheet, i.e. the magnetic southern hemisphere, the measured field approximately points towards the
planet. Figure 3.3 shows this utilising the idea of magnetic field lines from Jupiter.
As a spacecraft moves through the current sheet from one side to the other, the magnitude of the radial
component of the magnetic field decreases to zero at the centre of the sheet. Moving through the centre,
the direction of the field reverses (i.e. outward to inward or vice versa) before increasing in magnitude
until the edge of the current sheet is reached.
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0 5 10 15 20 25 302468
101214
−4
−2
0
2
4
6
x (RJ)
z (R
J)
y (RJ)
Figure 3.3: Magnetic field lines in the middle magnetosphere. Field lines of the inner and outer regions are not shown. The x-y plane is that of the ecliptic and the magnetic dipole tilt is responsible for skewing the lines away from that plane.
Similar such trends are also seen, although to a lesser magnitude, in both the poloidal and toroidal
components of the magnetic field too. This is due to Jupiter’s magnetic dipole tilt of 9.6 degrees to that
of the planet’s own rotational axis. This results in the current sheet appearing to flap up and down with a
period of one Jovian day to a stationary observer in space (see figure 3.4). Therefore, if that stationary
observer were in the middle magnetosphere, the current sheet would pass over him twice every 10 hours.
Figure 3.4: Schematic of the flapping Jovian current sheet. Due to the offset of the magnetic and rotational equators, the current sheet flaps up and down as the planet rotates. The figure covers one Jovian day, where each panel represents the view a stationary observer would have, taken at intervals of 1 hour 40 minutes (i.e. one sixth of a planetary rotation).
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3.2.2 Past Work on Fly-by Data
Work by Khurana and Kivelson [1989] on Voyager 2 data taken from the dayside middle magnetosphere
observed evidence of 10 to 20 minute period waves by utilising dynamic spectra of the data after
removing the local background of the field. Lachin [1997] examined data from Ulysses' swing-by of
Jupiter and found evidence of approximately 15 minute wave periods in the same region, as well as
indications of 80 and 40 minute period waves.
Russell et al.[1999] suggest that these waves could be due to the oscillating position of the current sheet,
possibly caused by standing Alfvén waves. Other models have been discussed in papers by both Khurana
and Kivelson & Lachin. Lachin explained the 10 - 20 minute period wave as being an acoustic wave
either standing or propagating radially. Khurana and Kivelson suggested a standing wave in the
corotating plasma that had a period of ~65 minutes. However, when this is Doppler shifted to the frame
of the spacecraft (Voyager 2) it would be measured as a wave of 10 minutes in period. Thus one model
suggests radially propagating or standing waves, the other azimuthally propagating waves.
3.2.3 The Galileo Orbiter
Galileo is the first orbiter around Jupiter and the first spacecraft to spend significant time in the nightside
regions. Figure 3.5 shows the trajectories of the first 10 orbits of Jupiter that Galileo completed.
For the vast majority of its trajectory, Galileo is deep in the nightside magnetosphere. Apojove is around
midnight local-time while perijove is near midday. As a result, if one considers just the dayside
magnetosphere, Galileo never explores more than around 20 RJ from the planet. Thus it remains in the
inner magnetosphere for essentially all of its dayside exploration. As such there is no data from the
dayside middle magnetosphere that could allow comparisons with previous work on the Voyager 2 and
Ulysses data sets.
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−140 −120 −100 −80 −60 −40 −20 0 20−120
−100
−80
−60
−40
−20
0
20
40
x (RJ)
y (R
J)
Figure 3.5: A plot of Galileo’s trajectory about Jupiter for the first ten orbits, as viewed from above looking down on the ecliptic plane (with positive x pointing towards the Sun). The gaps on the trajectory curve correspond to regions where there is no magnetometer data.
On the nightside of Jupiter, Galileo is always over 30 RJ from the planet, which is firmly in the middle
magnetosphere region. One might expect that with Galileo’s large excursions to beyond 100 RJ downtail
one may explore beyond the middle magnetosphere and reach the outer region. However, for all Galileo
data from the first 10 orbits, even though the spacecraft reaches 140 RJ downstream, the signature of a
current sheet is ever present twice a Jovian day. Thus one is able to conclude that the outer
magnetosphere is never reached and the spacecraft always remain in the middle region on the nightside.
−140 −120 −100 −80 −60 −40 −20 0 20−10
−5
0
5
x (RJ)
z (R
J)
Figure 3.6: A plot of Galileo’s trajectory about Jupiter for the first ten orbits, as viewed from the side. That is to say that z is aligned with Jupiter’s rotational axis while positive x points towards the Sun. Notice the range of the axes of the plot, only 15 RJ in z but 170 RJ in x, which explains why Jupiter is represented as an ellipse shape at (0,0).
Figure 3.6 shows the same trajectory data as before, but in this instance from a meridional view of the
North-South plane. Galileo remains closely aligned with the equatorial plane, never straying more than a
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few Jovian radii from it. The exception is part of orbit G1, which does stray further away, however this
was actually part of the Jupiter insertion manoeuvre.
Galileo’s orbits are each named using a letter and a number. The first ten orbits are called G1, G2, C3,
E4, J5, E6, G7, G8, C9 and C10. The number simply refers to which orbit it represents, number 1 being
the first after the main orbital insertion burn of the spacecraft. The letter corresponds to the Galilean
moon of closest approach on that particular orbit, such that G, C and E represent Ganymede, Callisto and
Europa respectively. Thus E4 corresponds to the fourth orbit of Galileo at Jupiter, and the Galilean moon
that the spacecraft has the closest approach to is Europa. Each orbit is of a different orbital period,
ranging from one to three months.
The exception to this rule is orbit J5. The fifth orbit occurred around Jupiter when the Sun was directly
between Jupiter and the Earth, which is known as a conjunction. This made radio communication with
Galileo impossible. The only other option was to record data on-board for playback later. However due
to having to rely on the low gain antenna after the high gain antenna failed, the downtime for a whole
orbit or data could never be spared. As such Galileo was put in a safe orbit about Jupiter with no close
encounters to any moons and simply left until Jupiter moved out from behind the Sun and communication
could be re-established. All science objectives were suspended and started again afresh on orbit E6.
Thus there is no science data at all for orbit J5.
The main question the rest of this chapter will address is whether ULF waves similar to those found from
Voyager 2 and Ulysses data on the dayside middle magnetosphere would also occur in the magnetic field
data sampled from the Jovian magnetotail on the nightside.
3.3 Initial Observations of Galileo Data
The Galileo magnetometer data was kindly provided by the Magnetometer Team at UCLA [Kivelson et
al., 1992] and arrived as data tabulated in three columns representing components of Jovian System III
co-ordinates (see chapter 2 for further details) with a fourth column for the field magnitude. Also
included in these files were columns giving each row in the file a time stamp, as well as a position from
Jupiter in terms of Radial distance (in RJ), Latitude (degrees), Longitude (degrees) and also Local-Time
of the spacecraft (hours).
Examining this magnetic field data in detail reveals that most wave activity occurs while Galileo traverses
through the current sheet. The radial, Br, and azimuthal, Bφ, components appear to be the most significant
while the poloidal/theta component, Bθ, remains small and appears unstructured on the small scale.
Numerous current sheet crossings (CSC's) have fluctuations superposed on the general form that appear
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to be similar to that of a few wavelengths of a 10 to 15 minute period wave. Figure 3.7 shows an example
Figure 3.7: A plot of the three components of the magnetic field and the magnitude over a 2 hour period, centred on a current sheet crossing during orbit G8 at 99.6 RJ and 01:00 local time. The Br and Bφ components show the greatest fluctuations, and are clearly out of phase. Fourier analysis over this region shows enhanced energies at 10 to 15 minute periods, while a wave of ≈12 minute period can be visually seen in Bφ.
Unfortunately however, Galileo tends to traverse the current sheet in one to two hours (although the
situation may be more aptly described as the current sheet traversing Galileo). Assuming that there is 10
to 20 minute wave activity during such a crossing one can thus only observe a few wavelengths during
each crossing.
3.4 Analysis
A fundamental property of Fourier Analysis is that in order to examine low frequency waves, the data
needs to be analysed over a long time duration. Ideally a single Jovian day's (10 hours) worth of data
would be used, resulting in a fine resolution in frequency. However, in each 10-hour segment two CSC's
occur, totalling around 180 minutes, with the other 420 minutes worth of data being relatively featureless.
On performing Fourier analysis over a 10 hour period, any interesting signals during the CSC's tend to be
averaged out by the large regions of relatively constant field. As such, a compromise must be made
between the resolution of the frequency ordinates in the Fourier analysis and the amount of data sampled.
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The compromise employed was to analyse sections of 120 minute duration to search for 10 to 20 minute
waves, thus placing the regions of interest between the 7th and 13th ordinate of the Fourier frequency for
any given spectra. Dynamic spectra were then calculated for each component of the field and examined
for signatures of strong wave activity. Figure 3.8 shows one such dynamic spectrum, taken from orbit G8
and centred 99.3 RJ down-tail at 01:08 local time. The dynamic spectra are produced by sliding a 120
minute window over the 60-second averaged data in steps of 10 minutes. A Hanning filter is
subsequently applied to the data before Fourier analysis, from which the first 30 ordinates are plotted,
thus producing a range in frequencies from 0 to 4 mHz.
Twenty-two hours worth of data are shown in figure 3.8, corresponding to just over two Jovian days.
This is clearly evident from the Br field component where it can be seen that the large-scale field
oscillates twice with a period of 10 hours. The region around 03:00 hours represents the power spectra of
Time in hours since 30−May−97 00:0008:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 02:00
0
2
4
Wave Power
−20 dB
0 dB
20 dB
Figure 3.8: A dynamic spectra of the magnetometer data taken from orbit G8, centred at 01:08 local time (from 99.075 to 99.632 RJ). The spectra are overlain with the magnetic field (in white, and on an arbitrary vertical scale) which was used to calculate the spectra. The dotted white line indicates the zero line for the field. The scale on the axis on the right-hand side is of period in minutes, with black horizontal lines being overlaid to aid identification of features.
From the figure, it can clearly be seen that all frequencies have enhanced energies during CSC's, with far
less wave activity observable in the regions in between. Other dynamic spectra calculated using data
from other sections of the trajectory show the same pattern, that when Galileo is outside of the current
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sheet, the power spectra are very quiet and uneventful. A prime example of this can be observed in figure
3.8 at 21:00 hours.
In general for all dynamic spectra, the Bθ component is also much quieter than that of Br and Bφ, but this
is unsurprising when the field components are compared. The magnetic field used to calculate the
dynamic spectra are overlain on the spectra as white curves. The scale used is arbitrary, but is identical
for all four panels (see figure 3.8). Clearly there are less oscillations and with lower amplitude in Bθ than
any other component, which is reflected in the dynamic spectra.
The predominant peaks of the dynamic spectra shown in figure 3.8 are at 11:00, 14:00 and at 03:00 (UT)
on the following day. The Bφ component is the most intriguing with a 4 hour long signature at 17
minutes, with other periods appearing in the other components simultaneously. The region covered in
figure 3.7 appears at 03:00 in figure 3.8, and it is clearly seen in Bφ that there is an enhancement at 12
minutes, yet Bθ is featureless over the same region.
This technique provided a quick way to examine a small section of data in detail, but was impractical for
examining entire orbits of data. Software was compiled to detect current sheet crossings where the data
rate was of a consistent resolution at 24 seconds. A local background was removed from the field data,
calculated from a running best fit second order polynomial of an hour duration. 120 minutes of data
centred on the CSC was then Fourier analysed after applying the usual Hanning filter. Finally a peak-
searching algorithm inspects the power spectra for any ordinates that peak above 5dB compared to its
neighbours within three Fourier ordinates.
Table 3.1 summarises how common the peaks were, simply listing the number of CSC's found with any
wave peak of a period between 10 - 20 minutes, along with the total number of CSC's identified.
Table 3.1: A preliminary statistical study of the abundance of 10 - 20 minute period waves during current sheet crossings (CSC's).
* Orbit Summary: The average percentage that any B-field component will have a wave signature during any CSC on that orbit.
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3.5 Abundance of Wave Signatures
3.5.1 Location of Waves
It became clear whilst searching for 10 to 20 minute waves by using dynamic spectra that there were most
often signatures during current sheet crossings. The field outside the sheet was predominantly featureless
at these frequencies, whereas almost all the signatures found were directly aligned with CSC's.
The spectrogram shown in figure 3.8 is just one example, but it shows that there are often enhancements
in power at the designated periods about CSC's, and that the periods of these peaks are often slightly
different even on neighbouring crossings. We assume that this is related to variations in plasma density,
but have been unable to retrieve plasma data to analyse for this.
The work above carried out a study over orbits G1 to C10 in the middle Jovian magnetosphere. Table 3.1
summarises our findings per orbit, and examining the table by component over all orbits shows that they
are all very similar, with 43.98% ± 2.77% of all current sheet crossings in any one component having
wave signatures. However it must be remembered that these figures are completely independent of the
other components and of the power of the waves.
Table 3.2 shows the average power of a 10 - 20 minute period wave in each component (taken from
CSC's in table 3.1). This clearly reinforces the observations from the dynamic spectra that the Br & Bφ
components are the strongest and most significant, while the Bθ component is weaker with less than half
their power on average.
Table 3.2: The average strength of the waves found from table 3.1.
Br Bθ Bφ Bmag Average Peak Power 2.10dB -1.99dB 1.79 dB 0.57 dB
A separate analysis examined the correlation between signatures found in each component on a given
current sheet crossing. Sixteen configurations were possible, that is four field components either with or
without a wave signature (of 10 - 20 minute period waves) resulting in sixteen permutations. Each
current sheet crossing from orbits G1 through to C10 was then re-investigated and classified in one of the
scenarios. The results (shown in table 3.3) did not show that any one combination was more likely than
another, although the case of no signatures in any field component occurs twice as often as most of the
other fifteen scenarios. Of over nine hundred crossings examined, only ~15% were signature free. Thus
in the majority of cases there are some signatures of a wave in the 10 - 20 minute period regime.
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Table 3.3: Investigating the configurations that 10-20 min wave signatures are seen in.
Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Br Bθ Bφ Bmag
× × × ×
√ × × ×
× √ × ×
√ √ × ×
× × √ ×
√ × √ ×
× √ √ ×
√ √ √ ×
× × × √
√ × × √
× √ × √
√ √ × √
× × √ √
√ × √ √
× √ √ √
√ √ √ √
Number of occurrences: 135 48 69 54 85 55 61 54 56 41 45 61 64 50 47 78
The software was subsequently refined to transform the data from Jovian System III into Field Aligned
Co-ordinates, FAC. The field-aligned direction was calculated from the local background as described in
Chapter 2. The data was then analysed to find signatures in parallel, //, and perpendicular, ⊥, components
to the field (B// and B⊥ respectively). Subsequently, the sixteen permutations of table 3.3 reduce to just
four permutations, the results of which are displayed in table 3.4.
Table 3.4: Investigating the configurations that 10-20 min wave signatures are seen in data that is in Field Aligned Co-ordinates.
Case Neither in B// or B⊥
Only in B//
Only in B⊥
Both in B// & B⊥
Percentage of occurrences 12% 9% 34% 45%
It is now interesting to note that the chance of seeing a 10 to 20 minute wave signature in B// but not in B⊥
is comparable to the case of seeing nothing in either component. The occurrence of a wave in B⊥ during a
CSC is nearly fourfold that of just being observed in B//, at a frequency of once in every three crossings.
Finally the most frequent case for observing waves is when they are observed in both components. From
this table it can be inferred that the direction perpendicular to the local field direction is significantly
richer in wave activity than the parallel direction.
The above results were obtained by utilising all of the data irrespective of the position of Galileo in radial
distance from Jupiter or in local time. The following sections will examine the data under these
parameters.
3.5.2 Wave Signature Dependence on Radial Distance
Figure 3.9a was compiled using the Field Aligned Co-ordinate data to examine the results of the
correlation at different radial distances from Jupiter. The data from all CSCs were ordered in terms of
increasing radial distance of the CSC from Jupiter before this new list was divided into fifteen equal (by
number of CSCs) consecutive bins. Thus the data from 55 CSCs in each of these bins were then averaged
to provide the information to produce the final plot.
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30 40 50 60 70 80 90 100 110 120 130 140 0
20
40
60
80
100
Radial Distance (RJ)
Like
lihoo
d (%
)
(⊥ ⊥ & //) + ( )
⊥ & //
⊥
none
//
30 40 50 60 70 80 90 100 110 120 130 140−5
0
5
10
15
20
Radial Distance (RJ)
Ene
rgy
(dB
)
⊥ & //
⊥
//
Figure 3.9a (top panel) shows the likelihood of finding a 10 - 20 minute period wave in various field component configurations as a function of radial distance from the planet. Each data point plotted represents the average over a bin of data containing information on 55 neighbouring CSCs. There is no overlap of data between bins & 24-sec resolution data from Galileo orbits G1 to C10 were used to compile these results.
Figure 3.9b (bottom panel) shows the average energy of each data point from 3.9a. Notice that although the likelihood of any wave is remarkably stable over all distances, the actual energy decreases as they get further away from Jupiter.
The likelihood of finding no signatures at all within a CSC is fairly constant over all ranges at about 12%
(red curve). The case of a signature being found in the parallel component to the field, but not in the
perpendicular, also remains fairly constant (the blue curve in the figure), typically being less likely that
the no signature scenario at 9%.
Signatures only in the perpendicular component (the green curve) and the case of waves in both the
parallel and perpendicular components (the black solid curve) appear to be out of phase with each other
and both lie close to 40% at all times. The black dotted curve represents any CSC with a signature in the
perpendicular component irrespective of anything in the parallel one, and this remains very constant near
80% over all distances in the middle magnetosphere. It appears that if the perpendicular curve increases,
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it is at the expense of the curve representing both the parallel and perpendicular signature case, and vice
versa.
Figure 3.9b is similar to figure 3.9a except that the average energy of a wave per bin is plotted against
radial distance. The average energy falls almost linearly as radial distance increases. The parallel case is
far more variable than the others, probably due to having a smaller sample size than the other two cases.
This will be investigated further in section 3.5.4.
Clearly radial distance from Jupiter appears to have no effect on the likelihood of these waves, and these
waves are predominantly found in the perpendicular field component. However, the energy of the waves
decreases as the distance increases.
3.5.3 Wave Signature Dependence on Local Time
A similar study was carried out investigating the dependence of wave signatures versus local time. In this
instance the results from all current sheet crossings were ordered in terms of increasing local time before
being split in to fifteen bins and averaged as before. For convenience, the hours of midnight to dawn
were ordered above dusk to midnight to provide a plot that better represented the orbits. This wrapped
around scale is visually more useful and appealing, rather than having a single plot with two sections of
interest at either end of the axis.
The results were similar to that of likelihood versus radial distance. As figure 3.10a shows, the
perpendicular curve (green) and the ‘perpendicular & parallel’ curve (solid black) are often reacting out
of phase with each other, just as before. Similarly, the case of a wave signature in just the parallel
component or the case of nothing in either component both hover near the 10% region.
The dotted black line in figure 3.10a represents the likelihood that a wave signature is seen in the
perpendicular component irrespective of the parallel component. Whereas this plot was near constant
when plotted against radial distance, it could now be argued that it has a slightly negative gradient.
Between local times of 21:00 to 23:00 it resides in percentages of the high eighties, while from 03:00 to
06:00 it resides in the high seventies, possibly indicating that there is more ULF wave activity on the pre-
midnight sector of local-time.
The corresponding average energy versus local-time plot (figure 3.10b) showed a minimum in all cases
near midnight. Nevertheless, the trajectory of Galileo during G1 to C10 had apojove near midnight local-
times (see figure 3.5, where the midnight line lies along y = 0 for x < 0) so this is simply the same result
as before, which is that energy decreases as distance increases.
Chapter 3 Search for ULF Waves in the Jovian Magnetosphere with Galileo
Figure 3.10a (top panel) shows the likelihood of finding a 10 - 20 minute period wave in various field component configurations as a function of local time about Jupiter. Each data point plotted represents the average over a bin of data containing information on 55 neighbouring CSCs. There is no overlap of data between bins & 24-sec resolution data from Galileo orbits G1 to C10 were used to compile these results.
Figure 3.10b (bottom panel) shows the average energy of each data point from 3.10a.
3.5.4 The Anomaly in Energy of a Purely Parallel Wave Signature
Figure 3.9b showed a general trend of wave energy decreasing as radial distance increased in both the
‘just ⊥’ and ‘⊥ & //’ scenarios. However the wave signature in the B// component appears to be have a
feature at about 80 RJ where the energy suddenly increases before returning to its general decreasing
from. What could cause this saw-tooth feature?
I believe this event is due to the statistical analysis used. Figure 3.11a shows the standard deviation of
each of the data points plotted in figure 3.9b. For the B⊥ and ‘B⊥ & B//’ curves (green and black curves
respectively), the standard deviations do not vary greatly from point to point. However the standard
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deviation of the B// curve (blue) is far more variable and jumps to a very low value of under 1 dB at just
under 80 RJ, just where the feature is located. Why would it be so low here?
Figure 3.11b plots the number of samples used in each bin from each scenario (i.e., just parallel, etc.).
Both the perpendicular and ‘perpendicular & parallel’ curve have sample sizes of 15 to 30 for each point,
however the parallel case tends to have a sample size below 10. At the anomalous feature in the parallel
case there are in fact only 5 current sheet crossings in the sample (compared to over 20 in each of the
other two cases). By coincidence these few samples must have had very similar energies resulting in an
unusually small standard deviation.
The small standard deviation (in decibels) of the anomalous result may also be attributed to the low
energies of the corresponding wave signatures and the way that the means were calculated, of which there
are two. The first is to produce the mean from a sample of energies that are in units of decibels. The
second is to have a sample of energies in units of (nT)2/Hz, compile the mean of this sample (still in those
units) and then transform the mean into units of decibels. Due to the logarithmic nature of the decibel
scale, a spread of low energy samples in units of decibels will have a smaller standard deviation than an
equivalent spread of samples at a higher energy. Hence the anomalous result appears as a more
pronounced feature than it really is.
Thus it is believed that the small sample sizes for the parallel case combined with their low energies will
throw up spurious results that do not follow expected trends.
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30 40 50 60 70 80 90 100 110 120 130 1400
2
4
6
8
10
Radial Distance (RJ)
Sta
ndar
d D
evia
tion
(dB
)
⊥
//
⊥ & //
30 40 50 60 70 80 90 100 110 120 130 1400
10
20
30
40
50
60
Radial Distance (RJ)
Num
ber
of c
ross
ings
per
bin
⊥ & //
⊥
//
Figure 3.11a (top panel) shows the standard deviation of the data points used in figure 3.9a. Crosses mark the actual data points while the coloured line guide link all those of the same scenario.
Figure 3.11b (bottom panel) shows the number of samples (current sheet crossings) used to create the average represented by each data point from figure 3.9a.
3.6 Implications of Field Direction
While comparing plots of magnetic field data in Jovian System III co-ordinates (of Br, Bθ & Bφ) with
Field Aligned Co-ordinates (of B⊥1, B⊥2 & B//) a new feature was observed. A clearly visible ULF wave
in, say Br, would also be visible in the FAC system, however it would switch between being visible in the
B// component to that of B⊥ as Galileo passed through the centre of the sheet. It would then switch back
to the B// component as Galileo completed its passage through the sheet.
This is logical if the wave is not propagating along field lines but rather through the plasma. For a FAC
system, B// is always aligned along the local background field. However during a current sheet crossing,
the field direction changes substantially (see figure 3.3 and the nose-like configuration of the field lines),
hence on assuming Galileo is in the magnetic Northern Hemisphere, it will measure the field pointing
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approximately radially outwards. As it passes through the sheet the B// direction rotates from radial
through to approximately vertical at the current sheet centre, and that continues rotating until it is pointing
approximately radially inwards in the magnetic southern hemisphere (see figure 3.12). Thus it is now
obvious that if a wave is perturbing the current sheet plasma radially (for instance), as Galileo begins to
pass through the current sheet this perturbation will be seen first in B//. As the spacecraft passes through
the centre of the sheet it will be seen in B⊥ and then as the spacecraft leaves the sheet it will be seen in B//
again. The power spectra analysis on the FAC data would then identify waves in both components, even
though it only appeared in one component of Jovian System III co-ordinates.
ρ
z
Figure 3.12: The alignment of B// and B⊥ during a current sheet crossing. The plot is in the north-south plane (c.f. cylindrical polar co-ordinates) and a modelled field line (red) within a current sheet is shown. At three points there is a cross, where the B// and B⊥ unit vectors of that point are shown as a thick blue and slim green line respectively. As one moves along the field line it can be seen that B// and B⊥ change dramatically. If a wave were propagating along ρ (represented by the black arrows), one would see this wave in different components depending where on the field line one is.
This could explain why the proportion of waves seen in the ‘⊥ & //’ scenario is so high. Although one
interpretation is that two waves are observed, it could equally be the result of just one wave propagating
in a non-field aligned direction. Under this latter assumption, the four scenarios described in table 3.4
decrease to only two; the existence of a ULF wave (present 88 % of the time) or no ULF wave (present
12 % of the time).
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3.7 Conclusions
The first new result was that the 10 to 20 minute waves were only observed when Galileo was passing
through the current sheet. Earlier Jovian ULF work had not identified this, although Khurana and
Kivelson [1989] had hinted at a link with the current sheet. Lachin had failed to notice this since he was
analysing a Jovian day’s worth of data at a time rather than shorter sections of the data. It is also seen that
the radial and azimuthal components have the strongest wave signatures, with the poloidal component
being significantly weaker than the others.
It appears the likelihood of finding these waves is independent of the radial distance from Jupiter. It was
postulated that the waves could be due to Field Line Resonances but one would expect the likelihood of a
wave to peak at a specific distance for this to be the case. This is not observed, hence Field Line
Resonances are not the mechanism, confirming Khurana and Kivelson’s [1989] earlier work.
The occurrence of these ULF waves also seems to be independent of the Local Time of Galileo. However
in the two years of Galileo data investigated, the orbit of Galileo with respect to the Jupiter-Sun line has
not precessed significantly (since only one sixth of a Jovian year has passed). Therefore of the ten orbits
of Galileo used there is a strong correlation between radial distance and Local Time; thus this is
essentially the same result (i.e. at midnight Local Time the spacecraft is always near apogee). The energy
of the ULF waves is seen to be smaller at larger radial distance, probably due to the fact that plasma
density is smaller and the magnetic field weaker the further away from Jupiter they are.
Whereas the energy versus radial distance curves of figure 3.9b for the B⊥ and ‘B⊥ & B//’ cases drop fairly
smoothly, there appears to be an anomaly in the B// curve just before 80 RJ, however this is due to poor
statistics for that data point rather than a physical trend. A similar anomaly may be seen in figure 3.10b
just before 02:00, again when the sample size drops and thus produces poor statistics.
The likelihood of a wave being observed in both B⊥ and B// is high but leads to doubts whether field
aligned co-ordinates are the best system in which to analyse the data during a current sheet crossing. If
the wave was Alfvénic and just travelled along field lines, then it would be suitable. However if the wave
is in the current sheet and propagating radially then it would appear in both components of the field
aligned co-ordinates (see figure 3.12). Khurana and Kivelson [1989] noted that transverse perturbations
fell off quickly moving away from the centre of the current sheet. This is not surprising since in the field
geometry of this region, transverse at the centre of the current sheet is essentially radial. As a field line is
traced away from the centre, the transverse component very rapidly turns to be dominant in the poloidal
direction. Thus a radially propagating wave in the current sheet that crosses magnetic field lines would fit
with both Khurana and Kivelson’s work and that presented here.
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It should be noted that the values in the tables and graphs for non-null results (i.e. every case except the
‘nothing in any component’ case) should be considered as lower limits. This is because it is likely there
are waves in individual components which are not strong enough to reach the critical limit the software
was searching for, nevertheless they may still be there. A more thorough statistical analysis needs to be
carried out which would utilise the new data that Galileo has returned whilst this work on the first ten
orbits has been in progress. More specific characteristics should be used to establish when there is a
wave present and to evaluate the period it has, but the present evidence is encouraging. The next stage
should take account of the plasma density alongside a polarisation analysis in a bid to understand the
nature and origin of these waves. Also, it may provide an insight into searching for wave periods of 40 &
80 minutes which were discussed by Lachin [1997] and also found in Ulysses ion data (McKibben et al.
[1993], MacDowall et al. [1993], the latter associated the 40 minute waves with MeV ions).
Irrespective of the waves’ mechanism, Khurana and Kivelson [1989] and Lachin [1997] had found
evidence for these 10 to 20 minute waves in the dayside magnetosphere. Galileo has now revealed their
presence in the nightside magnetosphere too. They are present in at least 88 % of current sheet crossings,
covering all radial distances and local times that Galileo has explored so far. Hence these ultra low
frequency waves appear to be a global phenomenon within the Jovian middle magnetosphere.
