Polarization of Impulsive Signals at Venus - Section 3
J. Geophys. Res., 96, 22, 741-22, 752, 1991
(Received: June 11, 1991; accepted: October 1, 1991)
Copyright 1991 by the American Geophysical Union.
Paper Number 91JE02506.
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In order to carry out statistical analyses of the wave electric field polarization we reduce data such as those presented in Figures 2 and 4 to several parameters for inclusion in a data base. For each 30-s interval we determine the average direction of the magnetic field in the spin plane and the maximum variance direction for the wave power. These two angles allow us to estimate the average wave polarization in a 30-s interval. We can also calculate the maximum variance direction of the wave power using the instantaneous phase of the antenna with respect to the magnetic field direction in the spin plane. The latter method is less likely to be aliased because of fluctuations in the magnetic field. On the other hand, interference signals do not usually depend on magnetic field orientation but rather on spin phase. Since spin phase information is lost if we use the instantaneous magnetic field phase, we use both methods to determine the wave polarization.
In order to assess the reliability of the polarization determination with respect to the ambient magnetic field we also include in the data base the fraction of the magnetic field in the spin plane and the variability of the magnetic field in the averaging interval. In addition, the variance ratio (Smax /Smin in Figures 2 and 4) and the ratio of the maximum to minimum wave power are included as measures of the quality of the maximum variance determination. Lastly, in order to determine whether or not the waves lie within the whistler mode resonance cone, we include the spacecraft position.
We have elected to use data from the third season of nightside periapses to generate the data base in this initial statistical study. Most of the data acquired in the third season had 0.25-s resolution and periapsis altitude was usually below 170 km. Periapsis altitude was higher for later seasons, while data from earlier seasons tended to be of lower temporal resolution. However, we should be able to incorporate data from other seasons in subsequent studies using the insight gained from the analysis presented here. Only the data acquired in darkness on each orbit are included since the data suffer from interference due to photoelectron emission and solar cell interference when the spacecraft is in sunlight.
3.1 Effect on Interference
In the previous section we pointed out that the 100-Hz wave data often have interference signals present. Moreover, these signals are spin modulated and will consequently also result in a polarized signal as determined by the maximum variance method. As we shall show here, these interference signals will contaminate the polarization statistics. In Figure 5 the maximum variance phase angle in the spin plane is plotted as a function of orbit number for season III. The scatterplot shows a clear clustering of the maximum variance direction, which varies by about 1.4° per orbit, as indicated by the diagonal lines in the figure. These lines have been drawn by eye to bound the main cluster of points, using the parameters given at the bottom of the figure. In subsequent analyses we will refer to the interference reference angle = 18.5° - 1.4° (n - 522.5), where n is the orbit number. Maximum variance phase angles which fall in the range 20° are within the interference filter.
Fig. 5. Scatterplot of the maximum variance direction as a function of orbit number for all the 30-s intervals in the season III nightside periapsis passes. There is a noticeable clustering of the phase angle as a function of orbit. Using a visual fit to the data, we have defined a phase angle filter as shown by the diagonal lines in the plot. The filter parameters are given at the bottom of the figure.
We assume that the clustering of points in Figure 5 is due to interference since we would not expect any naturally occurring signal to depend in a systematic way on orbit number. However, it is not clear why an interference signal should show such a dependence. For example, impact ionization is known to generate wave signals due to the spacecraft motion through the dense ionospheric plasma at periapsis [Curtis et al., 1985], but the impact ionization signal shows no spin modulation. Moreover, photo-electron emission or solar cell interference are not probable causes since the data were acquired in darkness. At present we have not determined the cause of the interference signal, although the filter parameters may provide a clue. The interference signal precesses at 1.4° per orbit, while the Pioneer Venus Orbit precesses at 1.6°. This suggests that the interference signal is ordered roughly by the radius vector from the center of the planet to the spacecraft. Perhaps radial outflow of ionospheric plasma is responsible for the signal. However, this is highly speculative and further study is necessary to determine the cause of the interference.
In order to show that the interference signal biases the data we have plotted the polarization statistics for all of season III in Figure 6. Since there is a lot of information in the figure and other figures have a similar format, we will describe the figure in some detail here before discussing the results. At the left of the figure there are three panels. The largest of these shows a histogram of the percent occurrence of the relative phase between the maximum variance direction and the average magnetic field, plotted in 10° bins. Because of the 180° ambiguity in the maximum variance direction the phase angle is determined modulo 180, and the angles are restricted to the range 0°- 180°. The solid curve in the plot shows a sinusoidal fit to the histogram, with the solid circle giving the phase angle of the peak in the sinusoid. The error bar gives the 95% confidence limit, as discussed in th appendix.
Fig. 6. Phase angle histograms for all the season III data. The large histogram to the left shows the percent occurrence of different relative phases, while the two smaller histograms show the phase of the magnetic field and maximum variance directions. Auxiliary diagnostics are given at the right of the figure. The figure is described more fully in the text. The relative phase appears to be more perpendicular than parallel, although this is probably due to contamination by interference signals.
The upper panel near the center of the figure gives the percent occurrence for the orientation of the magnetic field with respect to the interference signal, where the interference reference angle is given by the filter parameters in Figure 5. The panel below the magnetic field phase shows the maximum variance phase with respect to the interference. Below this panel the phase angles and 95% confidence limits are given for the relative phase (R), magnetic field phase (B), and maximum variance phase (V). In addition, we include the probability (P) that the sinusoid fit is not random, as also discussed in the appendix.
To the right of Figure 6, we plot percent occurrence histograms for the diagnostic parameters. In descending order these are the maximum to minimum variance ratio, labeled "anisotropy," the log10 of the maximum over minimum wave power, the fraction of the average magnetic field in the spin plane, and the variability of the magnetic field, labelled "DeltaB/B", where DeltaB = (2x + 2y + 2z)1/2, with x, y, and z, being the standard deviations of the x, y and z components of magnetic field, respectively. These diagnostics show that about 50% of the data intervals are weakly anisotropic, < 2, but 25% are highly anisotropic, > 5. The weakly anisotropic signals are less likely to be due to real signals and may be the result of random fluctuations in the wave power, while the highly anisotropic signals may be interference. The second diagnostic shows that over 50% of the signals have a maximum power that is less than an order of magnitude more intense than the minimum, indicating that many of the signals included in the data base may not be significant in determining the polarization, which is also implied by the weak anisotropy.With regard to the magnetic field orientation, at least 60% of the intervals have over 90% of the average field in the spin plane, but only 50% of the intervals have the variation in the field less than the field magnitude.
At first sight the histogram of the relative phase in Figure 6 appears to support the interpretation that the average orientation of the wave electric fields tends to be more perpendicular than parallel to the magnetic field. The peak in the histogram is near 123°, and the sinusoidal fit is statistically significant. However, the peak is not centered on 90% which raises some doubt that the waves are perpendicularly polarized. Furthermore, the histogram of the maximum variance phase shows a large peak at 0° with respect to the interference signal phase angle determined in Figure 5. Obviously, since the same data are used in Figures 5 and 6, we would expect strong clustering of the maximum variance phase, but in addition, the magnetic field orientation also shows a peak around 74°. We might consequently expect a peak in the relative phase distribution around 107°, taking the difference of the peaks of the two distributions.
Since interference signals bias the determination of the wave polarization when we use the whole data set for season III, we have also considered a reduced data set. In this data set we only include the intervals for which a burst event occurs as defined by Russell, von Dornum, and Scarf [Russell et al., 1988] (hereinafter referred to as RvD&S). In this data set, each 30-s interval is classified as to whether or not any bursts occur in that interval. The RvD&S data set consists of 818 active intervals in season III, compared with the total of 3173 samples. With this data set we obtain a relative phase of 123° 23° (99.7% probability). This is very similar to the phase- obtained with the full season III data set and suggests that the polarization statistics are also contaminated by interference for the RvD&S data set. We must emphasize here that only the polarization data are compromised by the interference, the burst occurrence statistics published using the RvD&S data set are unaffected.
3.2 Removal of Interference
Given that the polarization data are probably contaminated by interference, we must derive some method for removing the interference signal from the data set. We could simply filter the data using the interference filter defined in Figure 5. However, not all the samples which fall within the interference filter are necessarily interference, and we find that removing those naturally occurring signals also biases the data. We consequently have cleaned the data primarily through visual inspection, using the interference filter parameters as a guide in the selection of the data. We have only applied this test to the RvD&S data set, rather than all of season III, since the former already excludes intervals of weak signal, and intervals containing only interference, such as the interval after 0930:30 in Figure 1, or after 1057:00 in Figure 3.
As a first pass through the data we rejected intervals that appeared to be strongly contaminated with interference, solely by scanning the time series. For example, the interval 1056:30 - 1057:00 in Figure 3 does contain a weak burst, but since the interference signal is likely to dominate the polarization determination, the interval is removed from the "cleaned" data set. Following this first pass through the data, 574/818 samples in the RvD&S date set were retained.
On the second pass through the data we determined if a datum fell within the interference filter, or if the signal was weak, with peak power less than an order of magnitude greater than the minimum wave power in each interval. Using this numerical filter as a guide, we again decided if a sample should be retained in the data set. For example, the interval from 0925:30 to 0926:00 in Figure 1 resulted in a maximum variance angle which fell within the filter range, but was retained in the data set. Similarly, the intervals from 1052:00 to 1053:30 in Figure 3 would be rejected by the phase angle filter but were retained in the cleaned data set. After the second pass, 99/202 samples which fell within the numerical filter were removed, while an additional 14/372 events which lay outside the filter were also removed. Consequently, 113 additional samples were deleted from the data base, giving a total of 461 samples in the cleaned data set.
The results of the phase angle analysis for the cleaned data set are shown in Table 1. The first row (average phase) shows the relative phase using the method employed in Figures 2, 4, and 6, where the electric field phase is determined from the difference of maximum variance phase and the average magnetic field direction in each 30-s interval. The second row (instantaneous phase) shows the relative phase using the instantaneous difference between the antenna direction and the magnetic field. The last two rows give the average magnetic field direction in the spin plane and the best fit maximum variance direction with respect to the interference reference angle. For each entry we give the best fit phase angle, 95% confidence limits, and the probability that the fit is not random. The low probability in the table shows that the "cleaned" data have no clear polarization of the 100-Hz signals, even though the magnetic field and maximum variance direction are both orientated near 70° to the interference reference angle. In the absence of any assumptions concerning the mode of propagation we would conclude that the 100-Hz data do not show clear parallel or perpendicular polarization.
3.3 Polarization Inside the Resonance Cone
Recent work [Sonwalkar et al., 1991; C.-M. Ho et al., 1991] has shown that the 100-Hz emissions in the nightside ionosphere of Venus fall into two classes. These classes are separated by whether or not the 100-Hz waves can propagate in the whistler mode. Since the refractive index for whistler mode waves in the Venus nightside ionosphere is large [Strangeway, 1991; Sonwalkar et al.,1991], the wave vector of any signal propagating through the ionosphere from below must be aligned along the plasma density gradient, which we assume is vertical. If the magnetic field is sufficiently far from vertical then the wave vector will lie outside of the resonance cone, and the waves cannot propagate as whistler mode waves, assuming a subionospheric source. Under the assumption of vertical propagation the requirement that the waves can propagate as whistler mode waves is Br cos-1f/fce where Br is the angle between the magnetic field and the radius vector in the range 0° - 90°. Using the average direction of the magnetic field in each 30-s interval, we calculate the resonance cone angle for 100-Hz waves and the orientation of the field with respect to the radius vector. The data can then be filtered for propergation inside and outside of the resonance cone.
The results for the cleaned data set are shown in Figure 7. On comparison with the diagnostic parameters shown in Figure 6, most of the extremely high anisotropy signals have been removed, and the peak wave power is usually at least an order of magnitude above background. The magnetic field is predominantly in the spin plane and well ordered. Both the histogram and sinusoidal fit show that the magnetic field phase is parallel to the interference reference angle, while the maximum variance phase is perpendicular. The histogram and fit show that the relative phase is perpendicular. The data in Figure 7 indicate that the wave electric field is polarized mainly perpendicular to the ambient magnetic field for waves inside the whistler mode resonance cone. This result also holds if we use the instantaneous phase, where we obtain a best fit relative phase angle of 82° 44° (87.8% probability).
Fig. 7. Phase statistics for the "cleaned" subset of the RvD&S data. The data are further restricted to those intervals for which the average magnetic field is sufficiently vertical to allow whistler mode propagation inside the resonance cone, assuming a subionospheric source. The 100-Hz waves that fall into this category are on the average polarized perpendicular to the ambient field as expected for whistler mode waves.
However, as already pointed out when discussing the results for the data not selected using the resonance cone condition, some care must be given to the effect of filtering out the interference signals. Figure 7 shows that the magnetic field is mainly aligned parallel to the interference reference angle. This is a consequence of the resonance cone criterion, which selects field directions that are mainly parallel to the radius vector. The maximum variance direction is near 90° for the cleaned data set. We might consequently expect the cleaned to be perpendicularly polarized, but it is not clear if this is solely a consequence of the filtering applied to the data.
To demonstrate that the cleaned data set is not biased by the filtering method employed, Table 2 shows the best fit phase angles for those data which have maximum variance phase angles within the interference filter. Only 35 of the 218 samples in the cleaned data set for which vertical whistler mode propagation is allowed fall into this category. Since the interference filter restricts the maximum variance phase angle, while the resonance cone condition might be expected to bias the magnetic field orientation toward radial, we would expect the relative phase to be biased toward parallel polarization. However, Table 2 shows this is not the case, and the magnetic field is orientated perpendicular to the interference reference angle, although with low probability. As a consequence, the relative phase is also weakly perpendicular with the probability being somewhat higher using the instantaneous phase. From Table 2 we conclude that the phase determination shown in Figure 7 is not biased by the filtering, method and those 100-Hz emissions which can propagate vertically within the whistler mode resonance cone are on the average polarized perpendicular to the ambient magnetic field.
Table 2. Best fit phase angles for cleaned data inside the resonance cone and inside the interference filter.
3.4 Polarization Outside the Resonance Cone
At Venus the electron gyrofrequency is usually only a few hundred hertz, and the waves observed at higher frequencies by the OEFD are presumably not whistler mode waves. It has been argued [Russell, 1991; C.-M. Ho et al., 1991] that the waves which are not whistler mode waves are analogous to the anomalous signals observed in the terrestrial ionosphere [Kelley et al., 1985] in association with lightning. In the terrestrial case the signals are field aligned. The polarization for the higher frequencies are given in Table 3. For completeness we also include the 100-Hz data, selected for inside and outside the resonance cone. Since the 100-Hz data are contaminated by interference signals, we have used the cleaned data set. We use the RvD&S data set for the higher frequencies.
In general, the nonwhistler mode waves are polarized parallel to the ambient field. Interestingly, the probability is low when the polarization is determined using the average phase but is quite high using the instantaneous phase. Phase angle histograms for the 30-kHz channel are shown in Figure 8, using the instantaneous phase. We assume the impulsiveness of the signals results in the poor phase determination using the average phase. The mode of propagation for the nonwhistler mode waves is not known, but the data in Table 3 do suggest that the waves are polarized along the magnetic field. This is consistent with the terrestrial observations of Kelley et al. . However, it should be noted that parallel polarization might also be expected for in situ plasma instabilities.
Fig. 8. Phase statistics for the 30-kHz burst intervals in the RvD&S data set. In this case the relative phase is calculated using the instantaneous angle between the OEFD and antenna and the magnetic field direction in the spacecraft spin plane. Although there are relatively few intervals and the statistics are poor, the waves are mainly polarized parallel to the average field.
Table 3 also shows that for the cleaned data set roughly half of the 100-Hz intervals are associated with horizontal magnetic fields. The fraction is slightly higher for the full RvD&S data set, 510/818 (62%) of the intervals in the RvD&S data set have 100-Hz events outside of the resonance cone. In terms of percent occurrence the RvD&S data set is not affected by interference and the distribution of events for this data set should be compared with the distribution of magnetic field orientation. We find that 2386/3173 (75%) of the intervals in the full season III data set have magnetic field orientation which does not allow vertical whistler mode propagation. Hence the percent occurrence rate is much higher for 100-Hz events inside the resonance cone (39%) than outside (21%). A similar result was found by C.-M. Ho et al., 1991 using burst rate statistics.
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