Longitudinal structure of low-latitude Pi2 ... - Semantic Scholar

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, A12206, doi:10.1029/2004JA010580, 2004

Longitudinal structure of low-latitude Pi2 pulsations and its dependence on aurora Kazue Takahashi and Kan Liou Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA Received 10 May 2004; revised 13 August 2004; accepted 15 October 2004; published 10 December 2004.

[1] The relationship between the spatial and temporal properties of auroral power and

low-latitude magnetic Pi2 pulsations is statistically studied using auroral images obtained with the Ultraviolet Imager on the Polar spacecraft and magnetic fields measured at the Kakioka Observatory (L = 1.3). We select auroral intensification events from spatially integrated auroral power at time steps of 180 s and for each event determine various properties of associated Pi2 pulsations in a 300-s time window. Since our auroral events are simply defined to be a power increase of 30% or greater, some events are well-defined substorm expansion phase onsets reaching 50 GW, but some are weak events reaching only 1 GW. Nevertheless, the Pi2 pulsations show very similar local time patterns of amplitude and polarization regardless of the magnitude of the increase in auroral power. This implies that a single mechanism excites Pi2-band oscillations over a wide range of auroral activity. A likely source of the low-latitude pulsations is a plasmaspheric cavity mode, and our local time patterns of Pi2 parameters show features consistent with theoretical models of the cavity mode excited by longitudinally localized INDEX TERMS: 2752 Magnetospheric Physics: MHD waves and instabilities; 2704 disturbances. Magnetospheric Physics: Auroral phenomena (2407); 2788 Magnetospheric Physics: Storms and substorms; 2768 Magnetospheric Physics: Plasmasphere; 2736 Magnetospheric Physics: Magnetosphere/ionosphere interactions; KEYWORDS: Pi2 pulsations, auroral emission, longitudinal structure, intensity correlation, POLAR UVI, Kakioka Citation: Takahashi, K., and K. Liou (2004), Longitudinal structure of low-latitude Pi2 pulsations and its dependence on aurora, J. Geophys. Res., 109, A12206, doi:10.1029/2004JA010580.

1. Introduction [2] This paper investigates the local time variation of low-latitude (L < 2) Pi2 pulsations and its relationship to the intensity and location of auroral brightening. Pi2 pulsations usually occur at the onset of magnetospheric substorms [Saito et al., 1976], which makes the phenomenon useful in identifying and time-ordering the sequence of events occurring during substorms [Liou et al., 1999]. However, the definition of a Pi2 onset is often a controversial subject [Kepko and McPherron, 2001; Liou et al., 2001a; Higuchi et al., 2002] and it is necessary to find general, quantitative relationships between auroral activities and Pi2 pulsations in order to make better use of Pi2 pulsations in studying magnetospheric substorms and space weather. The spatial properties of Pi2 pulsations, which are less frequently studied than the timing properties, also deserve attention because they have significant implication for substorm dynamics and the generation mechanism of the pulsations. The goal of the present study is to quantify the relationship between aurora and low-latitude Pi2 pulsations and to discuss the result in relation to possible Pi2 generation mechanisms. We use global auroral images obtained by Copyright 2004 by the American Geophysical Union. 0148-0227/04/2004JA010580$09.00

the Ultraviolet Imager (UVI) on the Polar spacecraft. Global images are essential in this study because we are interested in capturing all auroral activations that might trigger a Pi2 pulsation detectable at low latitudes. [3] This study is in part motivated by previous studies of the longitudinal structure of midlatitude Pi2 pulsations and its relationship to aurora. Using a midlatitude array (55 magnetic latitude, L 3) Lester et al. [1983, 1984] and Gelpi et al. [1987] found that the polarization of Pi2 pulsations varies systematically relative to the center of the substorm current wedge (SCW) and location of the auroral surge. Figure 1 is a schematic summary of their results. The top diagram shows an upward field-aligned current (FAC), which is collocated with the head of the auroral surge, and a downward FAC, which is located several hours west of the upward FAC. The FAC pair is an element of the SCW proposed by McPherron et al. [1973]. The middle portion of Figure 1 illustrates the magnetic field perturbations DH (northward) and DD (eastward) produced by the SCW. At the center of the current wedge, which is placed at 0000 magnetic local time (MLT), DD is zero, while DH is a maximum. Here we use DH and DD to represent the baseline part of field variations, which should be distinguished from pulsation components denoted bH and bD. The bottom portion of the figure illustrates the longitudinal variation of the polarization ellipse of Pi2. The ellipse is

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TAKAHASHI AND LIOU: LOW-LATITUDE Pi2 PULSATIONS

Figure 1. A schematic illustrating the relationship between the longitudinal polarization patterns of midlatitude Pi2 pulsations and the location of auroral surge and associated field aligned currents (adapted from Figure 16 of Gelpi et al. [1987]). MLTa is magnetic local time relative to the head of auroral surge. stretched (i.e., ellipticity is close to zero), and the orientation (‘‘azimuth’’) of the major axis of polarization systematically changes with longitude. In the western portion of the current wedge the major axis lies in the northeast quadrant (positive azimuth). At the center of the current wedge the azimuth is zero. The ellipticity is negative (counterclockwise sense of rotation) at all longitudes. In the eastern portion of the current wedge the azimuth is negative. Li et al. [1998] reported a similar local time pattern of polarization on Pi2 pulsations observed at low latitudes (L 1.6), but they did not make a direct comparison of the pulsations with auroral images. [4] Qualitative and numerical models have been presented to explain the spatial pattern of Pi2 pulsations. Lester et al. [1983] attributed the longitudinal pattern of the azimuth to an oscillating current flowing on a circuit similar to the SCW. Southwood and Hughes [1985] explained the negative ellipticity by a superposition of eastward and westward propagating waves whose amplitudes are not equal. In these studies, however, the mechanism to generate the oscillating current was not fully addressed. Standing shear Alfveń waves [Rostoker, 1967], plasmapause surface waves [Fukunishi, 1975], cavity mode waves [Saito and Matsushita, 1968], and periodic forcing by plasma flow in the near-Earth magnetotail [Kepko and Kivelson, 1999] are among the possible origins of Pi2 pulsations. [5] Studies conducted more recently favor the cavity mode for Pi2 pulsations observed at middle to low latitudes (L < 4). Numerical simulations employing a realistic mag-

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netic field model and a plasmapause density gradient indicated that fast mode waves are indeed trapped within the plasmapause density gradient [Allan et al., 1986; Lee, 1998]. Observations from both ground [Yeoman and Orr, 1989] and space [Takahashi et al., 1995, 2003] showed that the L dependence of the amplitude and phase of Pi2 pulsations is consistent with the theoretical model of the plasmaspheric cavity mode. More realistic simulations have been conducted to explain the longitudinal variation of Pi2 properties, incorporating the longitudinally localized energy source, energy escape into the magnetotail, and energy loss at the ionosphere [Allan et al., 1996; Pekrides et al., 1997; Lee and Lysak, 1999; Fujita et al., 2002; Fujita and Itonaga, 2003]. [6] Figure 2 shows the result of a theoretical study by Allan et al. [1996], which is a useful reference in interpreting our observations. The amplitude and phase plots were obtained by mapping the numerically simulated magnetic field component of the cavity mode oscillations directly to the ground. Kivelson and Southwood [1988] provided justification for this mapping. The horizontal axis of this diagram is longitude js relative to the center of the Pi2 source region. Figure 2a shows the amplitude of the bH (horizontal, magnetically northward) and bD (horizontal, magnetically eastward) components. The bH component has a peak (antinode) at js = 0, whereas the bD component has a zero (node) at this longitude. Figure 2b shows the phase of these components. The phase of bH does not change with longitude and it is taken to be 0. The phase of bD is 0 for js < 0 and 180 for js > 0. Since the original figure by Allan et al. [1996] was made for the Southern Hemisphere, we flipped the phase of bD to accommodate the present observations made in the Northern Hemisphere. Figure 2c shows the azimuth of the major axis of polarization calculated from the amplitude and phase. It is positive for js < 0 and negative for js > 0. The ellipticity, shown in Figure 2d, is zero (purely linear polarization) at all longitudes since bH and bD are exactly in phase or 180 out of phase. [7] It is clear that in order to better understand the mechanisms for Pi2 generation and propagation, it is necessary to observe the spatial and temporal structure of both the Pi2 pulsations and the energy source for the pulsations. Since in situ observations of the spatial properties of Pi2 and substorm generation region are extremely difficult, the global auroral images are the best resource currently available for investigating the relationship between Pi2 pulsations and the spatial properties of the onset of auroral substorms. Until now, however, no observational study of low-latitude Pi2 pulsations specifically addressed the relationship between the Pi2 longitudinal structure and the location of auroral activation. [8] We build the present study upon a detailed study of a 3-hour episode of auroral intensifications and Pi2 pulsations reported by Takahashi et al. [2002]. In that study, the timing, amplitude, and polarization of the low-latitude Pi2 pulsations were compared with the temporal and spatial characteristics of auroral emission detected by the Polar UVI instrument. It was found that the temporal variations of the auroral power and the Pi2 amplitude are highly correlated even when the variation of the auroral power is small. It was also found that the major axis of polarization is a

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useful parameter in distinguishing wave sources located on the dayside and nightside. We use the time series analysis technique presented by Takahashi et al. [2002] to characterize the spectral properties of low-latitude Pi2 pulsation. In addition, we develop an automated selection procedure for auroral intensification events and the associated Pi2 wave packets. This methodology allows us to define events objectively and to analyze large amounts of data efficiently. [9] The remainder of this paper is organized as follows. Section 2 describes the UVI experiments and ground magnetometer at Kakioka. Section 3 presents a statistical analysis of the aurora – Pi2 relationship for a 3-month period from December 1996 to February 1997. Section 4 presents a summary and conclusions.

2. Experiments [10] The Polar spacecraft was launched in February 1996, and the UVI experiment [Torr et al., 1995] on board the spacecraft has been in operation since March 1996. The spacecraft has an elliptical 1.8 9 RE orbit with an inclination of 86 that decreases slowly with time and an orbit period of 18 hours. The UVI experiment covers some major O (130.4 and 135.6 nm) and N2 Lyman-BirgeHopfield emission (160– 180 nm) bands, allowing diagnosis of atmospheric content and precipitating electron energy flux and characteristic energy. The instrument has a nominal cadence of 37 s and a spatial resolution of 40 km at apogee. Longitudinal resolution can be greatly compromised at local times where the wobble of the direction of the despun platform is along the oval, but this does not affect the present study since we are not seeking local time resolution higher than 1 hour. [11] Magnetic field measurements from the Kakioka Observatory are used to detect low-latitude Pi2 pulsations. Kakioka is located at a geographic longitude of 140.1E and on a magnetic L shell of 1.30 according to the Altitude Adjusted Corrected Geomagnetic (AACGM) system [Baker and Wing, 1989]. The magnetic field experiment at this station consists of a fluxgate magnetometer, which acquires vector samples every 1 s at 0.01 nT resolution for scientific use, and four Overhouser magnetometers, which are used for baseline calibration [Tsunomura et al., 1994]. We have reduced the time resolution of the data to 5 s by taking fivepoint running averages of the 1-s data.

3. Data Figure 2. Longitudinal variation of the amplitude and phase of horizontal magnetic field components for lowlatitude Pi2, as produced in a simulation assuming source strength that varies with longitude (adapted from Figure 2 of Allan et al. [1996]). The horizontal axis is longitude relative to the center of the Pi2 source region, which would correspond to the 0000 MLT of Figure 1. (a) Amplitude of the northward (bH) and eastward (bD) components. (b) Phase of bH and bD. (c) Azimuth angle of the polarization axis relative to the H axis, taken positive eastward. (d) Ellipticity.

[12] In this section we first use exemplary events to show how we processed the data and then present an in-depth discussion of the statistical results. 3.1. Exemplary Events [13] We determine the properties of Pi2 pulsations on the ground by two-dimensional spectral analysis. An example of this technique is shown in Figure 3. Figure 3a shows the horizontal magnetic field perturbations bH and bD at Kakioka for a 300-s segment starting at 1348:30 universal time (UT). These field components are deviations about the trend, which is defined as the 150-s running averages of the original data. Throughout this paper we adopt a time window of 300 s to obtain a set of Pi2 parameters. This

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Figure 3. Example of a time series analysis of Pi2 pulsation. (a) Detrended time series. (b) Hodograph of the same data. (c) Power spectra. (d) Polarization spectrum. (e) Orientation (‘‘azimuth’’) of the major axis of polarization. (f ) Ellipticity. The heavy dots indicate the location, 8.4 mHz, of the peak in the bH power.

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time window corresponds to two to eight cycles of Pi2 oscillations (period = 40– 150 s by definition), which is long enough for determining the frequency. The time series shown in Figure 3a exhibits approximately two cycles of oscillation, with the bH and bD components varying nearly in phase. The oscillation produces a hodograph (Figure 3b), which is elongated in the northeast quadrant with an angle (azimuth) of 30 from the bH axis. [14] Figures 3c through 3f show the power density, polarization, azimuth of the major axis of polarization, and ellipticity, respectively, as a function of frequency. These parameters were derived from a spectral matrix obtained by fitting an autoregressive (AR) model to the bH and bD time series as described by Ioannidis [1975]. We have fixed the order of the AR model at 6. The AR method provides a convenient way of extracting spectral information from a relatively short time series. The spectra (Figure 3c) exhibit a clear peak at 8.4 mHz. The bandwidth, defined at the 75% level from the peak, is 1.2 mHz. At the peak frequency (marked by a large dot), the polarization is 0.99, the azimuth of the major axis of polarization is 34, and the ellipticity is 0.13. Note that following Lester et al. [1983], and to be consistent with Figure 2, we define the azimuth to be positive if the major axis lies in the northeast (positive bH –positive bD) quadrant. Similarly, the ellipticity is defined to be positive if the magnetic perturbation rotates clockwise in the bH – bD plane. As will be seen in Figure 5b, the auroral intensification associated with this Pi2 event occurred in the 2300– 2400 MLT bin, and Kakioka (MLT = 23.1 hours) was virtually at the same longitude. In this case, according to Figure 1, Kakioka was likely located 1 hour west of the center of the substorm current wedge. We find that the observed positive azimuth and negative ellipticity at the Kakioka local time are qualitatively consistent with the schematic polarization plots of Figure 1. [15] As individual frame-by-frame UVI images are too voluminous and difficult to compare with Pi2 events quantitatively, we use a local time auroral keogram [Meng and Liou, 2002] constructed from UVI energy fluxes that are integrated over an hourly MLT sector and from 55 to 90 magnetic latitude. Figure 4a displays data processed in this manner for a 6-hour span, 1100 – 1700 UT, on day 33 (2 February), 1997. This interval is chosen because Kakioka was near midnight, where the Pi2 signal is expected to be strong. The width of the pixels along the time axis is usually 184 s but varies somewhat depending on the instrument’s mode of data acquisition. The gray pixels represent areas outside the view of the UVI instrument. The darkest pixels are areas that were within the field of view of the instrument but did not give any photon counts. A display in this format is used to check the quality and spatial and temporal coverage of the data as well as to find the auroral activity. Several intensifications of auroral power are seen. They begin near midnight and then spread longitudinally [Newell et al., 2001]. [16] Figure 4b presents the overview of ULF activity at Kakioka for the same 6-hour period. Pi2 oscillations in the Pi2 band (7 – 25 mHz) are present in both the H and D components with the peak power appearing near 10 mHz. Note that the removal of 150-s running averages from the original time series causes a greater than 50% reduction in power spectral density at frequencies below 6 mHz. Major

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Figure 4. (a) Latitude-integrated auroral power as a function of universal time (UT) and magnetic local time (MLT) for a 6-hour interval on 2 February 1997. (b) Dynamic power spectra of the H and D components of the magnetic field at Kakioka for the same interval. Moving averages with a 150-s boxcar have been removed from the magnetic field data prior to computation of the spectra by Fourier transform.

enhancements of ULF power occur nearly simultaneous with the onset of auroral activity, for example, at 1331 UT and 1617 UT. On average, the Pi2 power is higher in the H component than the D component. [17] Figure 5 shows parameters extracted from the Polar UVI and Kakioka magnetometer data for the interval shown in Figure 4. The upper trace in Figure 5a is the total auroral power P in gigawatts accumulated within the 2000 – 0200 MLT sector. The lower trace in Figure 5a is the root-mean-square amplitude, APi2, of magnetic field variations in the Pi2 band at Kakioka. The amplitude is obtained by calculating the AR spectra of the bH and bD components as shown in Figure 3, integrating the trace power of these components over the Pi2 band (7– 25 mHz), and taking the square root of the integrated power. The calculation was done continuously by moving a 300-s data window in 60-s steps. The open and solid circles on the P trace indicate the value Pstart at the start time tstart and the value Pend at the end time tend, respectively, of an auroral intensification event. We selected auroral intensification events using an automated procedure that required a power increase higher than 30%, that is, Pend/Pstart > 1.3. The open squares on the APi2 trace indicate the maximum value occurring between tstart and tend (the time of maximum Pi2 power is denoted tPi2). The arrows at 1351 UT point to the example shown in Figure 3. Figure 5b shows the local time of the maximum auroral power at tstart (open circles) and tend (solid circles). [18] Figures 5c through 5d show the Pi2 frequency, azimuth, and ellipticity, respectively, computed in the same 300-s time window. These parameters are plotted only when

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the bandwidth, Df, of the Pi2 spectral peak is smaller than 3 mHz. The Pi2 frequency is the frequency at the peak, searched between 5 and 30 mHz, of the bH and bD trace power. The azimuth and ellipticity were calculated using the spectral matrix integrated over the spectral width, which is defined at the 75% level of the peak intensity. When there were multiple spectral peaks for a given time segment, the one with the highest peak was chosen. No Pi2 parameters were calculated when the spectral width exceeded the whole Pi2 band. The occurrence distribution of the bandwidth peaks at 2.5 mHz. [19] The moving time window analysis indicates that oscillations in the Pi2 band are present even when there is no obvious sudden increase in the auroral power. Take, for example, the data around 1430 UT. The auroral power is steadily decreasing and the Pi2 amplitude is at the overall minimum of 0.02 nT. However, this amplitude is still well above the amplitude, 0.0006 nT, of the Kakioka magnetometer digitization noise contained in the Pi2 band. This leads us to believe that this oscillation is of natural origin. From spectral analysis of the 1427 – 1432 UT interval, we find a frequency of 10 mHz, an azimuth of 49, and an ellipticity of 0.1, which are not very far from those of the example shown in Figure 3. This is not a coincidence since during 1330 – 1700 UT both the azimuth and ellipticity, shown with gray dots in Figures 5d and 5e, exhibit small deviations about a general trend. The implication of these findings is that the nightside magnetosphere continuously sustains oscillations in the Pi2 band and that these oscillations originate from a single magnetospheric eigenmode. Whether the oscillations are identified as Pi2 events largely depends on the amplitude threshold or other criteria imposed. We point out that multiharmonic standing shear Alfveń waves are continuously present in the inner magnetosphere [Takahashi and McPherron, 1982] and are recognized as a natural mode of the magnetosphere. 3.2. Statistical Results [20] We processed all UVI and Kakioka data from December 1996 to February 1997 into several parameters, including those illustrated in Figure 5. From the parameters we generated a file containing the onset time and other properties of the auroral intensification events and the associated Pi2 parameters. To minimize the influence of pulsations of dayside origin (i.e., Pc4 pulsations) [Nose´ et al., 1998], we limited the analysis of Pi2 pulsations to those observed when Kakioka was on the nightside, that is, from 1800 to 0600 MLT. In this data set we found a generally good correspondence between a sudden rise of auroral power and an occurrence of a peak in Pi2 amplitude. However, the local time dependence of the intensity is different between aurora and Pi2, and we address this next. [21] The MLT dependencies of auroral power and Pi2 amplitude are compared in Figure 6. Figure 6a shows the occurrence histogram of the MLT of peak auroral power at t = tend. For this figure we scanned MLT-binned UVI data in the 1900 – 0300 MLT sector, so the peak local time was defined only within the 2000 – 0200 MLT sector. The chances of having peak power outside this sector are very low according to Liou et al. [2001b], who visually examined individual frames of auroral images. Figure 6a

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Figure 5. Comparison of properties of auroral power and Pi2 pulsations. (a) The upper trace is the total intensity of the aurora. The circles define auroral intensification events, with the solid circles marking the beginning and the open circles marking the ending of the events. The lower trace is the band-integrated Pi2 power at Kakioka. The open squares on this trace mean the maximum value in between the start and stop times of an auroral intensification event. The arrow indicates the Pi2 event shown in Figure 3. (b) Local time of maximum auroral intensity. Only values at tstart and tend are shown. (c) Frequency of the peak in the spectrum of Kakioka magnetometer data. (d) Ellipticity of Pi2 pulsations. (e) Azimuth of the major axis of polarization. In Figures 5c, 5d, and 5e, only samples with Df < 3.0 mHz are plotted. shows that the occurrence has a peak at the 2300 – 0000 MLT bin and quickly tapers off toward east and west, consistent with the result of Liou et al. [2001b]. [22] Figure 6b shows the MLT variation of the peak auroral power. The thin horizontal bars are individual events and the large dots are the hourly medians. The local time dependence here is quite different from that in

Figure 6a. Following the median values, we find that Pend is highest when the auroral power peaks in the 2100– 2200 MLT bin, 2 hours west of the MLT of most frequent occurrence of auroral intensification. There is a sharp increase in Pend from 2000– 2100 MLT to 2100 – 2200 MLT and a gradual decrease from 2100– 2200 MLT to 0100– 0200 MLT.

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Figure 6. MLT dependence of the auroral power and Pi2 amplitude. (a) Occurrence histogram of the MLT of the peak auroral intensity. The horizontal variable is the center of the MLT bin that shows the maximum auroral power at the end (t = tend) of an auroral intensification event. The vertical lines indicate the limits of the local time domain used for the statistics. (b) Intensity of the total auroral power Pend versus the same MLT used in Figure 6a. (c) Pi2 amplitude at Kakioka versus the MLT of that station. The heavy dots connected by a line are the hourly medians. The vertical error bars connect the lower and upper quartile values. This figure uses only those Pi2 pulsations that have a bandwidth narrower than 3 mHz, in order to be consistent with Figure 5. [23] In Figure 6c the Pi2 amplitude shows yet another type of local time dependence. The amplitude peaks in the 2300 – 0000 MLT sector, 2 hours east of the longitude of the highest auroral power. This implies, in accordance with Figure 1, that the Pi2 source region is located east of the head of the auroral surge. Note also that the Pi2 amplitude

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does not fall off quickly outside the longitude of strong auroral activity. In particular it does not change very much around 2100 MLT, unlike the auroral intensity. This confirms the well-known longitudinal spread of low-latitude Pi2 pulsations [Sutcliffe and Yumoto, 1989]. [24] Both auroral power and Pi2 amplitude show a significant degree of variability, but there is a positive correlation between them. Figure 7 compares correlations among the variables that characterize the temporal variations of Pi2 and auroral power: the Pi2 amplitude APi2, the change of the auroral power Pend – Pstart, the rise time of the tstart, and the rate of auroral power auroral power tend tstart). The number shown increase (Pend – Pstart)/(tend near the top of each figure is the linear correlation coefficient computed for the logarithms of the two variables used in the scatterplot. Figures 7a and 7b demonstrate that the rise time is not correlated with either the Pi2 amplitude or the change in auroral power. Figure 7c shows, by contrast, that APi2 is strongly correlated with the change in auroral power. Figure 7d shows a similarly strong correlation between APi2 and the rate of auroral power increase. The similarity between Figures 7c and 7d results from the fact that the dynamic range of auroral power increase (2 decades) is much larger than that (1 decade) of the rise time. [25] It is difficult, simply based on Figures 7c and 7d, to determine which of Pend – Pstart and its time derivative is more essential in controlling the Pi2 amplitude. Takahashi et al. [2002], who obtained a correlation similar to that of Figure 7c for events occurring in a short (3-hour) span, explained the correlation by excitation of plasmaspheric cavity mode by a sudden change in the cross-tail current system that also produces FAC connected the ionosphere. The FAC is connected to the auroral bulge and is carried by precipitating electrons. Therefore the strength of the current should be proportional to the number of electrons precipitating per second, which in turn is proportional to the auroral power. The change in the cross-tail current, on the other hand, should be proportional to the amplitude of the cavity mode. However, it is also possible that the Pi2 amplitude is proportional to the sharpness of the impulse that excites the cavity mode. In that case the time derivative of the auroral power would be a more physically meaningful parameter to compare with the Pi2 amplitude. [26] It is important to note that the present data set includes weak (Pend 1 GW, APi2 0.05 nT) as well as strong (Pend 50 GW, APi2 0.5 nT) events, which as a whole produce a general positive correlation. This implies that Pi2 pulsations are excited under a wide range of auroral intensities, consistent with previous studies reporting that pseudobreakups and poleward boundary intensifications accompany Pi2 pulsations [Takahashi et al., 1997; Sutcliffe and Lyons, 2002]. Pi2 pulsations may occur even without any obvious geomagnetic disturbances, that is, when the magnetosphere is in the ‘‘ground state’’ [Sutcliffe, 1998]. In addition, since the scatterplots do not exhibit any distinctive groups of data points, there is no need to invoke separate wave excitation mechanisms for weak and strong Pi2 pulsations. We will come back to this point regarding the longitudinal structure of low-latitude Pi2 pulsations. [27] Figure 8 summarizes the local time variation of Pi2 pulsations at Kakioka. In each panel the small dots are individual Pi2 samples and the large dots are hourly

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Figure 7. Relationship among parameters characterizing auroral power and Pi2 pulsations. The MLT range is 2000 – 0200 for both peak auroral power and Kakioka. The number of samples is 182 in each panel. The value of rlog-log indicates the linear correlation coefficient between the logarithms of the horizontal and vertical variable.

medians. The horizontal axis, labeled MLTa, is the MLT of Kakioka relative to the MLT of peak auroral intensity as illustrated in Figure 1. In Figure 8 we use all auroral events occurring when Kakioka was located between 1800 and 0600 MLT. We do not impose any condition of the magnitude of Pend or APi2. [28] Figure 8a shows that the frequency changes with MLTa. It is about 7 mHz at 4.5 hours MLTa and increases to about 10 mHz at 5.5 hours MLTa. Longitudinal variation of Pi2 frequency is not new. Kosaka et al. [2002] reported similar local time dependence in Kakioka data for 1984 and 1985, which correspond to a solar minimum (our samples are also taken from around a solar minimum in 1996 and 1997). A follow-up study using simultaneous observations at five longitudinally separated low-latitude stations [Han et al., 2004] confirmed this MLT dependence for individual events. [29] It is possible to explain the frequency behavior in terms of magnetohydrodynamic modes associated with the plasmasphere. Initially, the frequency behavior was attributed to surface waves on the plasmapause [Kosaka et al., 2002]. The waves are by definition radially localized in the vicinity of the plasmapause and have short azimuthal wavelengths. The frequency of the waves is determined by the Alfveń velocities just inside and outside the plasmapause and can be local time dependent if the plasma density varies. This is not the only possibility, however. Fujita

and Itonaga [2003] demonstrated by numerical simulation that cavity modes (or virtual resonances according to Lee [1996]) in the plasmasphere also produce frequencies that vary with MLT. In an azimuthally inhomogeneous plasmasphere a localized perturbation excites an ensemble of cavity eigenmodes that have different azimuthal structures and eigenfrequencies. For each mode the frequency is determined by the configuration of the plasmasphere and the fast mode speed. At a given longitude the frequency spectrum is dominated by the mode that happens to have an antinode at or near that longitude. In view of large longitudinal extent [Sutcliffe and Yumoto, 1989] and small azimuthal wave numbers of low-latitude Pi2 waves [Li et al., 1998], we favor the cavity mode interpretation. [30] Figures 8b through 8e display several properties of bH and bD in a format that allows straightforward comparison with Figure 2. In Figures 8b and 8c the amplitudes are normalized to the peak auroral power (Pend) in order to reduce the vertical scatter of data points that arises from the intrinsically wide dynamic range of the two quantities (see Figure 7). The two components clearly exhibit different MLTa dependencies. The normalized bH amplitude, labeled AH/Pend, is nearly flat with a minor peak at 0.5 hours MLTa and an enhancement at 5.5 hours MLTa. The normalized bD amplitude, labeled AH/Pend, is also flat at MLTa < 0 but shows a strong minimum at 2.5 hours MLTa. As a consequence, the ratio AD/AH also shows a minimum at 2.5 hours MLTa. The

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minimum is indicative of the azimuthal node of bD expected for a cavity mode excited by an azimuthally localized energy source, as illustrated in Figure 2. The occurrence of the AD minimum to the west of the maximum auroral power (see Figure 6) is qualitatively consistent with the morphology of

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auroral surge and the substorm current wedge shown in Figure 1. However, our amplitude minimum occurs farther east (2.5 hours) of the peak auroral power (head of the surge) than illustrated (1 hour) in Figure 1. The bH – bD phase (Figure 8e) stays in a narrow range centered on 0 – 30 at MLTa < 0, nearly consistent with the westward half of the theoretical model in Figure 2. At MLTa > 0, the phase shows a very large variability. [31] Figures 8f and 8g display polarization properties of bH and bD in a format appropriate for comparison with Figure 2. The azimuth is 40 at 4.5 hours MLTa, decreases monotonically to 0 at 4.5 hours MLTa, and then increases to 15 at 5.5 hours MLTa. Comparing this result with the midlatitude observations [Gelpi et al., 1987] summarized in Figure 1, we find consistency for MLTa < 0, where the azimuth is positive and decreases toward 0 MLTa. For MLTa > 0, however, our data points do not turn negative, unlike the result of Gelpi et al. The ellipticity is mostly within the 0.5 to 0.3 range, corresponding to strongly elliptical polarization, with median values around 0.1, which means a counterclockwise sense of rotation. The dominance of negative ellipticity at nearly all MLTa is consistent with the observations of Gelpi et al. [32] We can make our results more consistent with the results of Gelpi et al. [1987] if we redefine the coordinates for the Kakioka magnetic field vector by tilting the northward axis 10 to the east. Although we have not done the data analysis using the new coordinates, it is obvious from geometrical consideration that the rotation will have the following consequences: (1) the baseline of the azimuth will be 10 higher, which means that the azimuth crosses zero at 1 hour MLTa. (2) The minimum of the bD amplitude will also move closer to 1 hour MLTa. The bD component is smaller than the bH component to begin with, which means the bD amplitude is sensitive to how we define the northward axis. (3) The ellipticity does not vary with the rotation of the coordinate axes so its MLTa profile will be the same. Although we cannot offer a good physical reason why we should introduce such coordinate rotation, the above discussion does demonstrate that the discrepancies between the present and previous studies found for some Pi2 parameters are not as large as they appear. [33] As the midlatitude and low-latitude Pi2 pulsations share some common properties, it is possible that the same wave mode contributes to both latitudes. We argue that the midlatitude array (L 3) on which Figure 1 is based was mostly within the plasmasphere. On average, the plasmapause is located near L = 4, so it is not unreasonable to assume that the Pi2 pulsations observed on the ground at L 3 propagated from the plasmasphere. Satellite obser-

Figure 8. Average longitudinal profile of Pi2 pulsation as a function of MLTa. The small dots are individual samples, the heavy dots are medians in hourly MLT bins, and the vertical error bars connect the upper and lower quartiles. The number of samples in the hourly MLTa bins ranges from 16 to 43. (a) Frequency. (b) Amplitude of bH. (c) Amplitude of bD. (d) The bD to bH amplitude ratio. (e) Phase of bD relative to bH. (f ) Azimuth of the major axis of polarization. (g) Ellipticity. 9 of 12

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Figure 9. Longitudinal profile of Pi2 pulsation as a function of MLT of Kakioka relative to the MLT of the peak auroral intensity, plotted separately for low and high values of Pend. The vertical bars indicate the difference between the lower and upper quartiles. The number of samples per MLTa bin ranges from 4 to 21. Data gaps indicate samples fewer than 8.

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vation demonstrated that cavity mode-type oscillations exist throughout the plasmasphere [Takahashi et al., 2003], which gives justification for the argument that low-latitude and midlatitude Pi2 pulsations originate from the same mechanism. [34] Having summarized the overall longitudinal structure of Pi2, we now turn to the dependence of the structure on the intensity and location of aurora. Figure 9 compares median values of Pi2 parameters for low (Pend < 5 GW) and high (Pend 5 GW) auroral power. The overall patterns are similar between the intensity classes, basically following what we have seen in Figure 8. The fact that Pi2 pulsations maintain consistent properties at all levels of auroral power implies that the plasmasphere sustains Pi2 pulsations regardless of the level of auroral activity. However, some interesting differences occur. [35] We take the frequency as an example. In Figure 9a the frequency in the postmidnight sector is higher when the auroral power is higher. By contrast, there is no Pend dependence in the premidnight sector. This could be explained by the cavity mode mechanism. As discussed above in reference to the work by Fujita and Itonaga [2003], cavity mode frequency can vary with local time. In a simplest approach the mode period would scale as the plasmapause radius divided by the mean fast mode speed. If the geomagnetic activity dependence of the plasmapause radius varies with local time, the activity dependence of the cavity mode frequency will also vary with local time. Using CRRES electron density measurements, Moldwin et al. [2002] reported that the Kp dependence of the plasmapause distance varies with local time. It is much stronger in the 0300 – 0900 LT sector than in the 1500– 2100 LT sector. With this type of local time plasmapause variation, the cavity mode frequency will more strongly depend on the geomagnetic activity in the postmidnight sector than in the premidnight sector. Although the Kp index used in the study by Moldwin et al. and the Pend parameter used in our study are not equivalent, the observations of Moldwin et al. give the type of plasmapause location that provides support to our cavity mode mechanism. [36] The effect of the local time of peak auroral power is weak but appears clearly in some Pi2 parameters. Figure 10a shows the comparison of the median azimuth of the major axis of polarization for two sets of MLT of peak auroral power: 2000 – 2300 MLT (class 1) and 2300 – 0200 MLT (class 2). Figure 10b shows the same data but with the data points for class 2 shifted to the left by 2 hours. The fact that Figure 10a shows a 20 difference at 2300 MLT between the classes but that it disappears in Figure 10b means that the azimuth has a tendency to tilt toward the location of peak auroral power around this local time. To be precise, the azimuth does not point to the aurora. Rather, it points toward the east of the auroral activation, regardless of the local time of the peak auroral power. This implies that the center of the Pi2 energy source is located east of the auroral surge and probably close to the center of the substorm current wedge, as illustrated in Figure 1. We also note that the azimuth increases in the morning sector MLT > 0300, which is probably outside the longitudinal range of the models illustrated in Figures 1 and 2. To summarize, the morphological relationship between aurora and Pi2 azimuth derived

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[39] 2. The frequency, amplitude, and polarization of the pulsations depend on MLT in a manner consistent with previous observations. [40] 3. The frequency depends on the auroral power, but the longitudinal pattern of amplitude and polarization does not vary between low and high auroral power. [41] 4. The longitudinal pattern of the azimuth of the major axis of polarization is organized by the local time of the location of peak auroral power in a manner consistent with case studies reported for midlatitude Pi2 pulsations. [42] We conclude that these observations are consistent with the cavity mode mechanism for Pi2 pulsations. Recent numerical studies indicate that cavity mode waves in the plasmasphere can exhibit longitudinal variation in frequency and amplitude. Other mechanisms, such as plasmaspheric surface waves, encounter serious inconsistencies with observations, including large azimuthal extent of the wave fields and filling of the entire plasmasphere with the pulsation electric field, as reported from satellite observations. [43] Acknowledgments. The ground magnetometer data used in this study were provided by Kakioka Magnetic Observatory, Japan Meteorological Agency. The work of K. Takahashi was supported by NSF grants ATM-9901102 and ATM-0001687 and NASA grant NAG5-13119 to the JHU/APL. The work of K. Liou was supported by AFOSR through the NSF grant ATM-0001665 to the JHU/APL. [44] Lou-Chuang Lee thanks Shigeru Fujita and Larry Kepko for their assistance in evaluating this paper.

References Figure 10. Comparison of the Pi2 azimuth for two ranges of the local time of peak auroral power: 2000 – 2300 MLT (solid circles) and 2300 – 0200 MLT (open circles). (a) Original. (b) The data points for 2300 – 0200 MLT power peak are shifted to the left by 2 hours. The number of samples per MLTa bin ranges from 5 to 24. Data gaps indicate samples fewer than 8. from midlatitude observations (Figure 1) is confirmed for the MLT < 0300 region from our low-latitude observations.

4. Summary and Conclusions [37] We combined global ultraviolet auroral images from the Polar spacecraft and Pi2 pulsations from the Kakioka ground station to investigate the longitudinal structure of the pulsations and its dependence on aurora. Use of the Polar images enabled us to determine the local time of auroral onset. The location of peak auroral intensity was examined in the range from 2100 to 0200 MLT. In addition, we included all auroral intensifications satisfying a simple criterion but did not classify them into pseudobreakup or expansion phase onset. The auroral power in our event list, integrated in the 2000– 0200 MLT sector, ranged from 1 to 50 GW. This approach allowed us to obtain a general view of the aurora-Pi2 relationship. Our results include the following: [38] 1. There is a positive correlation between auroral power and Pi2 amplitude. The amplitude is typically 0.05 nT for auroral power of 1 GW and 0.5 nT for auroral power of 50 GW when the peak auroral power occurs in the 2200 – 0100 MLT sector and Pi2 pulsations are observed in the same MLT sector.

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K. Liou and K. Takahashi, Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA. ([email protected])

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