Conjugacy of Pc 3-4 waves in the high latitude magnetosphere

Pc 3-4 pulsations observed at high latitudes have been examined for evidence of magnetic field line resonances. Previous studies have suggested that these pulsations are due to harmonics of the lower frequency Pc 5 pulsations. We investigated near-conjugate properties of high latitude Pc 3-4 pulsations using magnetometers of the IMAGE array in northern Scandinavia and the fluxgate magnetometer at Davis station. Analysis included comparison of time series, dynamic power spectra, and cross-phase, cross-power and coherence properties between the conjugate points. Our analysis of 11 events from March, 1996 suggests that the Pc 3-4 pulsations are not standing field line oscillations or harmonics of field line resonances. We discuss two possible mechanisms for their generation; the forced oscillation of field lines and propagation direct to the ionosphere. In both cases the pulsation source is the upstream ion-cyclotron resonance mechanism.

This paper will focus on low frequency Pc 3-4 (f ~ 10–50 mHz) waves in the high latitude regions. At low latitudes (L ~ 2–3), Pc 3-4 pulsations are attributed to the standing oscillation of magnetic field lines at their eigenfrequency, called field line resonance or FLR (Ansari and Fraser 1986, Menk et al. 1994). However, at higher latitudes (L ³ 6) the field lines are longer, and the resonant frequency moves into the lower frequency (1 – 10 mHz) Pc 5 range (Samson and Rostoker 1972, Waters et al. 1995). Throughout local daytime, there is a largely continuous Pc 5 band observed in the high latitude regions which is attributed to field line resonances (Waters et al. 1995, Ziesolleck and McDiarmid 1995). Pc 3-4 signals are also often observed in the dayside magnetosphere.

Previous workers have identified high latitude Pc 3-4 as higher harmonics of Pc 5 (Fukunishi and Lanzerotti 1974a, Tonegawa and Fukunishi 1984, Ziessolleck et al. 1997). They proposed that energy from an external source couples with Pc 5 waves, which are nearly always present in the dayside magnetosphere to drive higher harmonics of Pc 5 FLRs with frequencies in the Pc 3-4 range. Signals of this nature would be expected to possess characteristics of a FLR. Such characteristics include a phase reversal in phase-latitude profiles and an amplitude peak in amplitude-latitude profiles (Waters et al. 1991b, Howard and Menk 1999), in addition to the conjugate point properties discussed later. Another possible Pc 3-4 generation mechanism is that of modulated electron precipitation (Olson and Szuberla 1997).

Figure 1: The symmetry relations at magnetically conjugate points for the oscillation of the lines of magnetic force (Sugiura and Wilson 1964). H and D represent the horizontal and easterly components respectively and the arrow indicates the direction of the magnetic perturbation.

The use of conjugate point measurement to determine various properties of waves has been known for many decades, since Alfvén (1950) developed the stretched string analogy of magnetic field lines. A magnetic field line has its "fixed" ends at conjugate ionospheres in opposite hemispheres. At low latitudes the field lines are approximately dipolar and conjugate points are thus calculated using a dipole model. However, at high latitudes the field becomes distorted and models such as the corrected geomagnetic (CGM, Gustafsson 1992) or the Tsyganenko (1989) model must be used to determine conjugate point locations. The conjugate stations used in this study are the Longyearbyen-Davis pair. These, as shown in figure 2, are not exact conjugates of each other. Other examples include the Mawson-Jan Mayen and Syowa-Husafell (Kato et al. 1994) pairs.

Figure 2: The IMAGE array with the Davis conjugate point. The conjugate point was determined using the Tsyganenko (T89c) model.
Figure 3: Time series for the event on March 23, 1996. The time series is shown for Longyearbyen (LYR: Latitude = 78.2º CGM), Hornsund (HOR: 77.0º CGM), Bear Island (BJN: 74.5º CGM), Sørøya (SOR: 70.5º CGM) and Davis (DAV: -68.6º CGM). The signal is bandpass filtered at 20-35 mHz.

The first mathematical analysis of conjugate points was made by Sugiura and Wilson (1964). They showed that if standing field line oscillations are present, then at conjugate points one would detect H components which are in phase and D components which are out of phase for an odd mode (Figure 1) and vice versa for an even mode. Other wave features such as polarization can also be determined by studying magnetic footprints at conjugate sites. Experimental studies by Lanzerotti et al. (1972) and Fukunishi and Lanzerotti (1974b) found that Pc 3-4 activity around L = 4 is predominantly odd mode suggesting that the pulsations are caused by field line oscillations, possibly resonances.

This paper will focus on the conjugate point properties of Pc 3-4 waves at L ³ 10 in order to investigate whether the pulsations are higher harmonics of Pc 5. A previous study has examined the phase and coherence of high latitude Pc 3-4 and suggested the pulsations are not FLR harmonics (Howard and Menk 1999). Further investigation is clearly required.

Data were obtained using the IMAGE magnetometer array (CGM latitudes = 60° - 79° ) in northern Scandinavia and the magnetometer at Davis station (CGM latitude = - 69° ). IMAGE consists of 19 triaxial fluxgate magnetometers which sample in units of nT at 0.1 Hz with a resolution of 0.1 nT. Details on IMAGE can be obtained from http://www.geo.fmi.fi/image/index.html. Southern hemisphere data were from the fluxgate at Davis (details at http://www.antdiv.gov.au). For the time interval chosen, the Davis magnetometer also sampled at 0.1 Hz. Figure 2 shows the IMAGE array along with the location of the Davis conjugate point calculated with the Tsyganenko T89c model. This is a semi-empirical model which takes the time of day, season and K_p value into account. The CGM model is basically a distorted dipole field model. Any CGM value in this paper is for an altitude of 100 km above sea level and epoch 1996. The Davis conjugate footprints for both models essentially map to the same location and are about 400 km south west of Longyearbyen.

Data were obtained from the IMAGE and Antarctic Division webpages. At all stations, data are recorded in geographic (X,Y,Z) coordinates and a coordinate rotation into geomagnetic (H,D,Z) coordinates was performed. For this, an accurate determination (in geographic latitude and longitude) of the geomagnetic pole was needed. This can be determined experimentally, such as the alignment with the compass needle; theoretically, such as from models such as CGM; or semi-empirically, such as with the Tsyganenko model. For the purposes of this study, the experimentally determined value was used (geographic latitude –64.7° , longitude 138.6° ; http://www.ngdc.noaa.gov/seg/potfld/faqgeom.shtml). From here, spherical geometry was used to determine the bearing of this pole from geographic north, which is compared with the value of D (declination angle of the magnetic field), obtained from http://nssdc.gsfc.nasa.gov/space/cgm/cgm.html. The coordinates were then rotated by the value of D (~78° for Davis). As the Z component always points "downward" this component and the X component were rotated by a further 180° to accommodate for opposite hemispheres. All data were recorded in UT, where LT ~ UT+1 for IMAGE and LT ~ UT+2 for Davis.

Eleven events were selected from two weeks of data from March 1996, embracing one week of quiet and the other of disturbed magnetic activity. An event was selected if a Pc 3-4 was seen across most of the IMAGE array and was clearly resolved from noise using whole-day dynamic cross-phase and power spectra. For each event the time series were compared for each IMAGE station and at Davis. Next, dynamic power spectra were examined for the Longyearbyen-Davis pair. Finally, the cross-phase, cross-power and coherence for this pair were determined. Both H and D components were considered for each measurement. The dynamic power, cross-power and cross-phase spectra were computed with a 256-point (43 min long) FFT stepping every 35 points and were used for event selection. Interstation phase was measured from individual 20 minute long cross-phase spectra (Howard and Menk 1999). The dynamic spectra were weighted by f^1.5 to enhance the higher frequency features; spectral resolution was 0.83 mHz. For the dynamic power spectra, windowing was performed in the frequency domain using a truncated exponential taper stepping every five points, and a Hanning window of the same dimension as the FFT length was used for the cross-phase measurements.

A list of the events is shown in Table 1. Also included is the coherence length as determined by Howard and Menk (1999). Coherence length is the ground distance covered by a signal before its coherence relative to a central reference station falls below 0.65. Figure 3 shows time series data for several IMAGE stations and Davis for a typical event on March 23. The event had a frequency of 27 mHz and occurred around 07:30 UT. Filter bandwidth was 20–35 mHz. For this example the H component results are shown. In all cases the H component was considerably larger than the D component but a signal could still be seen at the IMAGE stations for both components. Notice the packet structure of the wave in the top four plots from around 07:35 to 07:48. The packet structure for the signal at Davis does not resemble the structure at the other stations.

Figure 4 shows whole-day dynamic power spectra from Longyearbyen and Davis for the event shown in figure 3. Note the almost continuous band of low frequency Pc 5 activity at both stations up until ~11:00 UT. The event appears as a dark patch around 07:30 UT and 27 mHz in the LYR spectrum. However, it has lower power in the DAV spectrum, where instead a later event is more prominent. Note the broadband bursts at both stations commencing at 01:05, 18:00 and 21:55 UT. These are substorm events which are simultaneous everywhere. The other vertical features in the DAV spectrum beginning at 11:15 and 15:45 UT are due to local noise.

Figure 5: Panel 1: Unfiltered time series for the LYR-DAV pair; Panel 2: Normalised relative cross-power spectra; Panel 3: Relative coherence values; Panel 4: Cross-phase values for the event on March 23. The H component only is shown.

Figure 5 illustrates how determinations of cross-phase and coherence are made and includes the cross-power to assist in signal identification. The H component only are shown, high pass filtered at 5 mHz. The top panel is the unfiltered time series for each station. Note the peak in cross-power around 27 mHz in panel 2. This identifies the same frequency signal in both hemispheres. Note also the low coherence at this frequency (panel 3), ~ 0.1, far too low to be considered reliable. This suggests the same Pc 3 wavepacket is not seen at DAV and LYR.

Figure 6: Low frequency time series for H (top traces) and D (bottom traces) components for the same March 23 event. This has a filter bandwidth of 1-4 mHz revealing the Pc 5 band at each station. Scaling of this Davis record is approximate.

Figure 6 shows the same event presented in figures 4 and 5 over a different time scale and with a filter bandwidth of 1–4 mHz to show the Pc 5 band present here. It is clear that similar Pc 5 pulsations were present at both locations, and analysis of this signal reveal a peak in coherence and cross-power around 2.5 mHz.

Of the eleven events examined here, none of the IMAGE data revealed any high values for coherence, or displayed similar time series, when compared with Davis data. For 3 events, interhemispheric peaks in cross-power were detected for one component, and for 4 others values of coherence reached 0.5, but never was this the case for both H and D components.

For each Pc 3-4 event the continuous Pc 5 band was observed at the near conjugate points as shown in figures 4 and 6. This indicates the presence of a Pc 5 field line resonance (fundamental standing odd mode field line oscillation) at these latitudes and can also be used as an indication of closed field lines (Ables et al. 1998). Pc 3-4 pulsations were clearly visible across each station in the IMAGE array and at the conjugate point, but the packet structure was dissimilar and coherence was very low, at the conjugate station. Even in the cases where the coherence reached the threshold of acceptability (0.65), in no cases was this achieved in both H and D components.

The same Pc 3-4 events exhibit high coherence over extended distances (³ 10³ km) as determined using the IMAGE stations (Howard and Menk 1999). The distance between the actual conjugate point of Davis and Longyearbyen is ~ 400 km and falls well within the coherence length of each signal at IMAGE.

Summarizing, the results of this study have shown that:

1. Pc 3-4 pulsations are observed simultaneously at near-conjugate high latitude locations although the waveforms and spectral structure are different and the interhemispheric coherence is low.
2. The Pc 3-4 pulsation events exhibit similar waveforms and spectral structure in the same hemisphere, measured using the IMAGE array. They maintain high coherence over ground distances typically exceeding 1 ´ 10³ km.
3. These results and the amplitude-latitude and phase-latitude results reported by Howard and Menk (1999) indicate that the Pc 3-4 pulsations are not standing oscillations of field lines and do not exhibit properties of harmonics of field line resonances.
4. At the same time, sustained low frequency Pc 5 pulsations are seen in both hemispheres. Their conjugate characteristics are consistent with standing fundamental field line resonance oscillations.

It is generally believed that the energy source for Pc 3-4 signals is the ion-cyclotron instability involving backstreaming protons upstream of the solar wind (Greenstadt et al. 1983). The resultant fast mode waves may penetrate the magnetosheath and enter the outer magnetosphere. Olson and Szuberla (1997) found short coherence lengths (£ 200 km) for burst-like Pc 3-4 signals at high latitudes and these are most likely connected with electron precipitation which is modulated by the Pc 3-4 waves near the last closed field lines. This perturbs local ionospheric current systems, resulting in a broadband spectrum (extending into the Pc 3 range) at the ground. This mechanism cannot account for the long-range coherent signals investigated in this study.

We consider two possiblities to explain the observations. We have previously shown (Howard and Menk 1999) that the Pc 3-4 events examined are most likely closely connected with properties of the solar wind. Accordingly, we believe that the pulsations’ source mechanism is the upstream ion-cyclotron instability. Incoming fast mode waves may couple to field lines forcing them to oscillate with the same frequency as the incoming wave. As the wave propagates inward it forces further field lines to oscillate until all of its energy is transferred into the field. As the travel time for waves along field lines to the ground is longer for the outer field lines the waves would arrive at the lower latitudes first, thus creating the appearance of poleward propagation as found by Howard and Menk (1999). The amplitude of the signal detected on the ground would also appear to decrease with decreasing latitude which also agrees with the findings of Howard and Menk, and with Bol’shakova and Troitskaya (1984). The lack of conjugacy found in this paper puts some constraints on this model.

Alternatively, the fast mode waves may propagate directly to the ionosphere, undergoing refraction though the magnetosphere as they did so. This model also predicts the direction of propagation determined by Howard and Menk (1999) and can account for the lack of conjugacy found here.

Figure 6 displays Pc 5 properties between Longyearbyen and Davis. In this figure we have assumed a typical azimuthal wavenumber of m = - 3 (Ziessolleck et al. 1997, Mathie et al. 1999) and adjusted the signal phase at Davis accordingly to account for the ~ 400 km separation between the Davis conjugate and Longyearbyen. The conjugate signals are seen to be in phase, while the D component is variable but generally around 90° - 180° out of phase, as expected for odd mode Pc 5 resonances. The exact phase relationship depends on the difference in latitude and longitude between the conjugate locations. Future work will also examine data from the Jan Mayen-Mawson pair, which are more nearly conjugate than Longyearbyen-Davis. Nevertheless, it is clear that the Pc 5 pulsations are being observed on closed field lines, and that the Pc 3-4 pulsations are not coherent at the conjugate locations.

We thank all members of the IMAGE team and those at ANARE responsible for operating the magnetometers and providing the data. TAH was supported by an Australian Research Council fellowship, and this work was supported by the Australian Research Council, Antarctic Science Advisory Committee, the University of Newcastle and the Cooperative Research Centre for Satellite Systems.

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