Discussion

Two years of the AFGL wave power data set and the solar wind data constitute a good test-bed to examine the statistical relationships between pulsations and solar wind parameters. In particular, the wide frequency range of the wave power data set provides us with an opportunity to compare the features between the pulsations with different frequencies. We find that the low-frequency P₂ (4-8 mHz) events and the high-frequency P₅ (32-64 mHz) events appear to be caused by very different IMF conditions. The P₅ events occur overwhelmingly at low IMF cone angles, but the P₂ events behave oppositely (Figures 6 and 7). The two events also differ in the locations of occurrence: P₅ has a higher normalized occurrence rate near local noon, while P₂ is more likely to occur at dawn and dusk. The P₃ and P₄ events do not reveal themselves as different classes of waves in terms of the IMF dependence and the local time dependence, and their characteristics present a mixture of those of the P₂ and P₅ events. For example, Figure 6 shows that the P₄ events have a slight preference for low IMF cone angles, and Figure 5 shows that the P₃ events have a similar diurnal variation as that of the P₅ events.

The results for the P₅ events are consistent with the existing model that the source energy is the upstream waves in the foreshock region. The same model can also explain the occurrence of P₄ events. First, the P₄ and P₅ events mainly occurred during low IMF cone angles (Figures 6 and 7), which is the necessary condition for the upstream wave energy to propagate toward the dayside magnetosphere. Second, the expected frequencies of upstream waves matches well with the pulsation frequencies. Figure 8 shows that the normalized occurrence rate of the P₅ events is larger than 1 as $0.7 \leq \log B_t \leq 1$ (or 5 nT $\leq B_t \leq$ 10 nT). According to the empirical formula f (mHz) = 6 B_t (nT) [Gul'elmi, 1974], this range of B_t agrees well with the frequencies of P₅, 32-64 mHz. The same argument can be applied to the P₄ events (16-32 mHz), which have the corresponding IMF magnitude 2.7-5.3 nT (or $\log B_t$ = 0.4-0.7) that is also consistent with Figure 8. The frequencies of the P₂ and P₃ events are too low to be associated with the upstream waves, and, indeed, the P₂ events rarely occur at low IMF cone angles (Figures 6 and 7). It is clear that the P₂ events have a different source of energy. Third, the normalized occurrence rate for the P₅ events maximizes just slightly prenoon (Figure 5) This result is consistent with early work on this subject. It has been known for a long time that Pc3-4 waves are dayside phenomena and have a maximum occurrence rate roughly in the morning [e.g., Saito, 1969; Nishida, 1978]. Recently, Cao et al. [1994] performed an extensive investigation of the pulsations recorded by the ISEE 1 spacecraft and showed that the maximum occurrence rate of Pc3 and Pc4 waves is located approximately near local noon.

Engebretson et al. [1991] suggest that the cusp region might be important for the upstream wave energy entering the magnetosphere and generating Pc3-4 waves. This possibility was also conjectured earlier by Lanzerotti et al. [1981]. We may test this hypothesis by examining the observed wave power for different foreshock geometries. Russell et al. [1983] depicted the foreshock geometry and the streamlines in the magnetosheath under different IMF cone angles ($\theta_{BX}$). Their pictures clearly present that most of the upstream wave energy may propagate to only one side of the dayside magnetosheath if the IMF is not exactly radial ($\theta_{BX} \neq 0\deg$). We extend their argument by including the consideration of the IMF clock angle ($\phi$) to discuss the tentative location of the wave energy in the magnetosheath with respect to the cusps. It should be mentioned here that the sign of B_x, in addition to $\theta_{BX}$ and $\phi$, is also a variable that determines the foreshock location. For example, if we consider $\phi = 0\deg$ (B_y = 0 and B_z > 0), most of the foreshock region is located in the northern (southern) hemisphere when B_x > 0 (B_x < 0). However, if we confine our discussion to the difference between an equator-aligned foreshock ($\phi = \pm 90\deg$) and a meridian-aligned foreshock ($\phi = 0\deg$ or $\pm 180\deg$), the sign of B_x may be ignored. Having these considerations, we may envisage two different IMF conditions according to the cusp entry hypothesis. If $\phi$ is $0\deg$ or $180\deg$, the foreshock geometry results in a condition that one of the two cusps is bathed in the magnetosheath that contains strong wave activity caused by the upstream waves. Therefore more wave energy is expected to enter the magnetosphere. However, if $\phi = \pm 90\deg$, the wave energy is mainly aligned with the equatorial plane, and the cusps are expected to receive less wave energy from the foreshock region.

Our observations indicate a different result. From Figure 11, we see that the average P₅ wave power is not a strong function of $\phi$ when $\theta_{BX} \gt 30\deg$. The low-cone-angle ($0\deg \leq \theta_{BX} \leq 30\deg$) condition allows the upstream waves to propagate in the subsolar magnetosheath; however, the P₅ events are stronger when the IMF roughly aligns with the equatorial plane ($\phi \approx \pm 90\deg$). In addition, for the northern hemisphere, the location of our ground observations, cusp entry would suggest that when $\theta_{BX}$ is large and $\phi \simeq 0\deg$ (if B_x > 0) or $\phi \simeq \pm 180\deg$ (if B_x < 0), there should be a large occurrence of wave activity in the P₅ band. However, this is not the case, as seen in the P₅ plot in Figure 7. Therefore the cusp entry hypothesis does not appear to be important for the low-latitude Pc3 power observed in this study. Instead, our observations are more consistent with the scenario depicted by Yumoto et al. [1985] that the propagating compressional waves may enter the magnetosphere at low-latitude regions. The mechanisms related to the propagation of Pc3 waves from the upstream region to low latitudes are also discussed by Wolfe et al. [1985, 1989] and Venkatesan et al. [1986].

For Pc5 waves, the sources of wave energy have been studied by using both spacecraft and ground station data. For the high-latitude regions, Pc5 can roughly be categorized as the toroidal Pc5 and the compressional Pc5 [Anderson, 1994]. The toroidal Pc5 waves occur mainly in the morning sector, and they are the fundamental mode of field line resonances, possibly driven by the Kelvin-Helmholtz (K-H) instability [Anderson et al., 1990]. The compressional Pc5 waves are most probably drift mirror waves driven by plasma pressure anisotropy [e.g., Hasegawa and Chen, 1989]. Their primary occurrence regions are on the nightside toward the flanks of the magnetosphere at L typically greater than 7 or 8 [Anderson et al., 1990]. The correlation of compressional Pc5 and the substorm onset was demonstrated by Kokubun [1985]. The Pc5 has an overall local time distribution that peaks at dawn and dusk [Cao et al., 1994].

The Pc5 at low-latitude regions is relatively less explored, partially because the low-latitude magnetosphere is the region where spacecraft can hardly make proper measurements of long-period waves. In addition, the fundamental mode frequencies of the field lines at these latitudes well exceed the frequency range of P₂ (4-8 mHz) [Menk et al., 1994, Table 1], and therefore the low-latitude Pc5 may not simply be considered as the consequence of its high-latitude counterpart. Ziesolleck and Chamalaun [1993] suggested that these waves might be the global compressional mode of a large-scale cavity resonance.

The local time dependence of Pc5 occurrence may not be a definite indication of the energy sources. Anderson et al. [1990] and Nosé et al. [1995] showed a strong bias of Pc5 occurrence toward the dawnside, whereas Zhu and Kivelson [1991] and Cao et al. [1994] presented a roughly equal occurrence rate of Pc5 at both flanks of the magnetosphere. The dissimilarity between the two results may come from the difference of spacecraft orbits. In this study, the local time dependence of P₂ (4-8 mHz) is a weak function of local time, which is expected since the distinction at different local times may be smeared as the waves propagate toward low latitudes in various directions.

Our results for the P₂ events reveal an interesting relationship between the IMF and low-latitude Pc5 activity. It is clear from Figures 6 and 7hat the P₂ events mainly occurred when the IMF cone angle was large. Although the normalized occurrence rate is above the average level as $0\deg < \phi < 90\deg$, the opposite sector ($-180\deg < \phi < -90\deg$) when the IMF is southward is the dominant occurrence region. Figure 11 also shows that the wave power of P₂ is at its maximum when the IMF is southward. The P₄ events (8-16 mHz) also occur more during southward IMF (Figures 6 and 7). These results are consistent with the scenario of substorm-related Pc5. The magnetosphere is open and acquiring energy from the solar wind when the IMF is southward [Dungey, 1961]. The energy is released by reconnection in the magnetotail and the associated ion injection traveling westward and causing compressional Pc5 waves in the afternoon sector [Kokubun, 1985].

Some of the generation mechanisms of Pc5 mentioned earlier do not show their significance in our results. For example, the preference of southward IMF is not in agreement with the field line resonance model driven by the K-H instability since it would raise the instability threshold [Nosé et al., 1995]. It is not indicative of the cavity resonance model, which has no preference of IMF orientation, as a generation mechanism either. Nevertheless, the cavity mode, if it exists, may act as a modification of wave characteristics at the low-latitude region.

Our results suggest that the flux transfer events (FTEs) on the dayside magnetopause are also a possible energy source of Pc5 activity we observed. It is known that the reconnection is expected to occur on the dayside magnetopause during the southward IMF condition. The associated phenomenon, FTEs, statistically has a recurrence rate of approximately once per 8 min [e.g., Kuo et al., 1995]. In addition, Lee et al. [1988] also proposed that the sporadic multiple X line reconnection process at the dayside magnetopause could be a source of energy to produce low-frequency ULF waves ($f \sim$ 1-10 mHz). The perturbations related to reconnection have been observed both on the ground and in space. For example, the FTE-like magnetic spikes followed by damped-type Pc5 pulsations are observed by the ground stations near the cusp region, and those magnetic spikes are always accompanied by a sporadic appearance of discrete auroras [e.g., Fukunishi and Lanzerotti, 1989]. The reconnected flux tube of an FTE may compress the surrounding plasma and result in a magnetic-field enhancement that has been observed by spacecraft [Russell and Elphic, 1979]. Song et al. [1988] studied the oscillations of the magnetopause observed by the ISEE 1 and 2 satellites and found that the amplitude of magnetopause oscillations increases with local time away from the subsolar point for southward IMF, but it decreases for northward IMF. They concluded that the magnetopause oscillations during southward IMF are most likely due to the reconnection-related phenomena. Russell et al. [1997] further found that although the foreshock might contribute oscillations at the magnetopause, the FTEs did not occur more frequently behind the foreshock. Therefore, considering that the P₂ events are stronger when the IMF is southward, we suggest that the dayside reconnection process is also an important energy source of Pc5.

Ground-based observations have shown that the low-latitude Pc5 exhibits a peculiar polarization asymmetry across local noon [Ziesolleck and Chamalaun, 1993; Bloom and Singer, 1995]. Chisham et al. [1995] examined the low-latitude Pc5 in the morning sector in detail and suggested that the special polarization pattern was a consequence of ionospheric conductivity gradients that occurred at dawn. We have examined the IMF dependence for both X and Y components of P₂ (4-8 mHz) but cannot find distinguishable difference between them. Therefore the asymmetry of polarization should be caused internally in the magnetosphere rather than by the upstream sources. The explanation of this polarization asymmetry requires further investigation.

Figure 10 shows a clear correlation between the wave power and the solar wind velocity. Similar results are found by Singer et al. [1977], Greenstadt et al. [1979], and Wolfe [1980]. This correlation was used to support the argument that the K-H instability is an important energy source of pulsations, since the K-H instability is more likely to occur at a higher-velocity shear. However, according to the observations the K-H instability does not seem to be the major energy source for either the low-frequency P₂ events or the high-frequency P₅ events. Some other processes may also explain the correlation in Figure 10. First, the size of the magnetosphere is controlled by the solar wind dynamic pressure. Although the dynamic pressure is a function of the velocity and the density, we find that in our data higher solar wind velocity is statistically correlated with higher dynamic pressure, which results in a smaller magnetosphere and a shorter distance between the magnetopause and the observation site. Higher-velocity solar wind will generally also be associated with a stronger (higher Mach number) shock and a stronger foreshock interaction. Reconnection is also proportional to the velocity of the solar wind. These effects may combine to cause the increase of approximately 10 times of wave power when the solar wind speed doubles (Figure 10).

Although the correlation shown in Figure 10 is clear, the scatter of data points is so large that a prediction of the upstream solar wind parameters from the ground observations may not be practical. In this study, each data point represents the average wave power for a 20-min time interval. The time resolution of other similar studies [e.g., Greenstadt et al., 1979; Wolfe, 1980] might be even lower. Some attempts have been made before to improve the correlation, such as choosing the minimum of the IMF cone angle and the maximum of the wave power during each time interval. However, the scatter might come from the complications due to the resonances or during wave propagation rather than the procedures of data processing. For example, Chi et al. [1994] have shown a clear example of large variations of Pc3-4 wave power when the IMF conditions were relatively steady. Therefore caution needs to be used when attempting to predict the upstream conditions by using pulsation signals.