Search for ULF Waves in the Jovian Magnetosphere with Galileo

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1 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 1/11, 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. B r (nt) B φ (nt) Voyager 2 Jupiter fly by Day of July 1979 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 1 at 1.1 R J and had then reached 72.7 R J outbound by the 15 th July. B θ (nt) B mag (nt) Analysis of Voyager 2 data by Khurana and Kivelson in 1989 showed evidence for 1 to 2 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 Page 53

2 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, 2].) 3.2 Introduction Fly-By Missions Jupiter is the largest of all the Solar planets with a radius of 71492km or 1 R J. 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 1 & 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 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 2 R J from the planet's centre out to between 7 to 11 R J, depending on solar wind conditions which can be very dynamic and change rapidly. (See Chapter 1 for further details). Page 54

3 Figure 3.2: Plot of fly-by trajectories of Pioneer 1, 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. Page 55

4 z (R J ) y (R J ) x (R J ) 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 1 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 4 minutes (i.e. one sixth of a planetary rotation). Page 56

5 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 1 to 2 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 8 and 4 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 1-2 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 1 minutes in period. Thus one model suggests radially propagating or standing waves, the other azimuthally propagating waves 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 1 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 2 R J 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. Page 57

6 4 2 2 y (R J ) x (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 3 R J from the planet, which is firmly in the middle magnetosphere region. One might expect that with Galileo s large excursions to beyond 1 R J downtail one may explore beyond the middle magnetosphere and reach the outer region. However, for all Galileo data from the first 1 orbits, even though the spacecraft reaches 14 R J 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. 5 z (R J ) x (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 R J in z but 17 R J in x, which explains why Jupiter is represented as an ellipse shape at (,). 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 Page 58

7 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 C1. 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 R J ), 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, B r, and azimuthal, B φ, components appear to be the most significant while the poloidal/theta component, B θ, remains small and appears unstructured on the small scale. Numerous current sheet crossings (CSC's) have fluctuations superposed on the general form that appear Page 59

8 to be similar to that of a few wavelengths of a 1 to 15 minute period wave. Figure 3.7 shows an example CSC observed during the G8 orbit. 5 Magnetic Field components B r (nt) 5 B φ (nt) B θ (nt) 2: 2:15 2:3 2:45 3: 3:15 3:3 3:45 4: Time 31 st May 1997 (PDT) 5 B mag (nt) 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 1: 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 1 to 15 minute periods, while a wave of 12 minute period can be visually seen in B φ. 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 1 to 2 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 (1 hours) worth of data would be used, resulting in a fine resolution in frequency. However, in each 1-hour segment two CSC's occur, totalling around 18 minutes, with the other 42 minutes worth of data being relatively featureless. On performing Fourier analysis over a 1 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. Page 6

9 The compromise employed was to analyse sections of 12 minute duration to search for 1 to 2 minute waves, thus placing the regions of interest between the 7 th and 13 th 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 R J down-tail at 1:8 local time. The dynamic spectra are produced by sliding a 12 minute window over the 6-second averaged data in steps of 1 minutes. A Hanning filter is subsequently applied to the data before Fourier analysis, from which the first 3 ordinates are plotted, thus producing a range in frequencies from 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 B r field component where it can be seen that the large-scale field oscillates twice with a period of 1 hours. The region around 3: hours represents the power spectra of the data previously shown in figure 3.7. B r Orbit G8, 3 May 97 6: to 31 May 97 4:9 B θ B φ F (mhz) F (mhz) F (mhz) B mag F (mhz) : 1: 12: 14: 16: 18: 2: 22: : 2: 8: 1: 12: 14: 16: 18: 2: 22: : 2: 8: 1: 12: 14: 16: 18: 2: 22: : 2: 8: 1: 12: 14: 16: 18: 2: 22: : 2: Time in hours since 3 May 97 : T/min T/min T/min T/min Wave Power 2 db db 2 db Figure 3.8: A dynamic spectra of the magnetometer data taken from orbit G8, centred at 1:8 local time (from to R J ). 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 Page 61

10 sheet, the power spectra are very quiet and uneventful. A prime example of this can be observed in figure 3.8 at 21: hours. In general for all dynamic spectra, the B θ component is also much quieter than that of B r and B φ, 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 B θ 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:, 14: and at 3: (UT) on the following day. The B φ 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 3: in figure 3.8, and it is clearly seen in B φ that there is an enhancement at 12 minutes, yet B θ 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. 12 minutes of data centred on the CSC was then Fourier analysed after applying the usual Hanning filter. Finally a peaksearching 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 1-2 minutes, along with the total number of CSC's identified. Orbit Table 3.1: A preliminary statistical study of the abundance of 1-2 minute period waves during current sheet crossings (CSC's). Total number of CSC's examined Number of CSC's with wave signatures B r B θ B φ B mag Orbit Summary * G % G % E % E % G % G % C % C % Percentage by component 41.77% % 41.88% 43.98% * Orbit Summary: The average percentage that any B-field component will have a wave signature during any CSC on that orbit. Page 62

11 3.5 Abundance of Wave Signatures Location of Waves It became clear whilst searching for 1 to 2 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 C1 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 1-2 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 B r & B φ components are the strongest and most significant, while the B θ 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. B r B θ B φ B mag Average Peak Power 2.1dB -1.99dB 1.79 db.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 1-2 minute period waves) resulting in sixteen permutations. Each current sheet crossing from orbits G1 through to C1 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 1-2 minute period regime. Page 63

12 Table 3.3: Investigating the configurations that 1-2 min wave signatures are seen in. Case B r B θ B φ B mag Number of occurrences: 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 1-2 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 1 to 2 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 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. Page 64

13 1 Likelihood (%) ( & //) + ( ) & // // none Radial Distance (R ) J Energy (db) & // // Radial Distance (R J ) Figure 3.9a (top panel) shows the likelihood of finding a 1-2 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 C1 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 4% 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 8% over all distances in the middle magnetosphere. It appears that if the perpendicular curve increases, Page 65

14 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 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 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 3.1a 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 1% region. The dotted black line in figure 3.1a 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: to 23: it resides in percentages of the high eighties, while from 3: to 6: it resides in the high seventies, possibly indicating that there is more ULF wave activity on the premidnight sector of local-time. The corresponding average energy versus local-time plot (figure 3.1b) showed a minimum in all cases near midnight. Nevertheless, the trajectory of Galileo during G1 to C1 had apojove near midnight localtimes (see figure 3.5, where the midnight line lies along y = for x < ) so this is simply the same result as before, which is that energy decreases as distance increases. Page 66

15 1 Likelihood (%) ( & //) + ( ) & // 2 none // 21: 22: 23: : 1: 2: 3: 4: 5: 6: Local Time 2 Energy (db) & // // 5 21: 22: 23: : 1: 2: 3: 4: 5: 6: Local Time Figure 3.1a (top panel) shows the likelihood of finding a 1-2 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 C1 were used to compile these results. Figure 3.1b (bottom panel) shows the average energy of each data point from 3.1a 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 8 R J 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 Page 67

16 deviation of the B // curve (blue) is far more variable and jumps to a very low value of under 1 db at just under 8 R J, 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 3 for each point, however the parallel case tends to have a sample size below 1. At the anomalous feature in the parallel case there are in fact only 5 current sheet crossings in the sample (compared to over 2 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. Page 68

17 1 Standard Deviation (db) // & // Radial Distance (R J ) Number of crossings per bin & // // Radial Distance (R J ) 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 B r, B θ & B φ ) with Field Aligned Co-ordinates (of B 1, B 2 & B // ) a new feature was observed. A clearly visible ULF wave in, say B r, 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 Page 69

18 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. z ρ Figure 3.12: The alignment of B // and B during a current sheet crossing. The plot is in the northsouth 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). Page 7

19 3.7 Conclusions The first new result was that the 1 to 2 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 8 R J, however this is due to poor statistics for that data point rather than a physical trend. A similar anomaly may be seen in figure 3.1b just before 2:, 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. Page 71

20 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 4 & 8 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 4 minute waves with MeV ions). Irrespective of the waves mechanism, Khurana and Kivelson [1989] and Lachin [1997] had found evidence for these 1 to 2 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. Page 72