Dependence of the amplitude of Pc5-band magnetic field variations on the solar wind and solar activity

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011ja017120, 2012 Dependence of the amplitude of Pc5-band magnetic field variations on the solar wind and solar activity Kazue Takahashi, 1 Kiyohumi Yumoto, 2 Seth G. Claudepierre, 3 Ennio R. Sanchez, 4 Oleg A. Troshichev, 5 and Alexander S. Janzhura 5 Received 31 August 2011; revised 17 February 2012; accepted 20 February 2012; published 10 April [1] We have studied the dependence of the amplitude of magnetic field variations in the Pc5 band ( mhz) on the solar wind and solar activity. Solar wind parameters considered are the bulk velocity V sw and the variation of the solar wind dynamic pressure dp sw. The solar activity dependence is examined by contrasting observations made in 2001 (solar activity maximum) and 2006 (solar activity declining phase). We calculated hourly Pc5 amplitude using data from geostationary satellites at L = 6.8 and ground stations covering 1 < L < 9. The amplitude is positively correlated with both V sw and dp sw, but the degree of correlation varies with L and magnetic local time. As measured by the correlation coefficient, the amplitude dependence on both V sw and dp sw is stronger on the dayside than on the nightside, and the dependence on V sw (dp sw ) tends to be stronger at higher (lower) L, with the relative importance of the two solar wind parameters switching at L 5. We attribute the V sw control to the Kelvin-Helmholtz instability on the magnetopause, occurring both at high and low latitudes, and the dp sw control to buffeting of the magnetosphere by variation of solar wind dynamic pressure. The GOES amplitude is higher at the solar maximum at all local times and the same feature is seen on the ground in the dawn sector at L > 6. A radial shift of the fast mode wave turning point, associated with the solar cycle variation of magnetosphere mass density, is a possible cause of this solar activity dependence. Citation: Takahashi, K., K. Yumoto, S. G. Claudepierre, E. R. Sanchez, O. A. Troshichev, and A. S. Janzhura (2012), Dependence of the amplitude of Pc5-band magnetic field variations on the solar wind and solar activity, J. Geophys. Res., 117,, doi: /2011ja Introduction [2] A consequence of solar wind interaction with the terrestrial magnetosphere is excitation of ultra-low-frequency (ULF) waves in the magnetosphere. The waves interact with trapped particles [Fälthammar, 1965], and currently there is much interest in understanding, both theoretically and empirically, the interaction of the waves with energetic electrons in the outer radiation belt. It is hoped that by finding factors that control magnetospheric ULF waves we can better understand not only how the waves are excited but also how the solar wind affects the behavior of magnetospheric particles. 1 Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. 2 Space Environment Research Center, Graduate School of Sciences, Kyushu University, Fukuoka, Japan. 3 The Aerospace Corporation, Los Angeles, California, USA. 4 Center for Geospace Studies, SRI International, Menlo Park, California, USA. 5 Arctic and Antarctic Research Institute, St. Petersburg, Russia. Copyright 2012 by the American Geophysical Union /12/2011JA [3] In this paper, we report a statistical investigation of solar wind control of ULF waves in the Pc5 band ( mhz) and how the control depends on the solar activity. Our analysis focuses on the relative importance of the solar wind velocity, V sw, and dynamic pressure variations, dp sw. This work is an extension of our analysis of Pc5 pulsations at geosynchronous orbit [Takahashi and Ukhorskiy, 2007, 2008] to Pc5 pulsations on the ground in order to extend the L-range of Pc5 measurements. Using data covering a wide range of L, we gain insight into how different source mechanisms contribute to Pc5 pulsations at different locations. Ground observations cover multiple locations at any given time, and along with techniques to map the magnetic field to the electric field in the magnetosphere [e.g., Ozeke et al., 2009], the observations potentially provide valuable information to evaluate particle transport in the magnetosphere that cannot be obtained by satellite observations. Pulsations with periods of 30 min (frequency 0.5 mhz) or longer [e.g., Lyons et al., 2002; Lessard et al., 2003] show significant power. However, such pulsations are not included the present study because they likely have different source mechanisms than pulsations in the Pc5 band. [4] The motivation for our study is as follows. First, a study by Rostoker et al. [1998] reported that strong 1of18

2 correlation exists between the amplitude of Pc5 pulsations on the ground and the flux of energetic electrons (MeV) at geosynchronous orbit. Rostoker et al. [1998] discussed the possibility that the Pc5 waves are excited by high-speed solar wind flow through the Kelvin Helmholtz instability (KHI) on the magnetopause [e.g., Southwood, 1968] and that the waves interact with the electrons. This scenario gained support from subsequent statistical analyses of ULF waves observed on the ground [Green and Kivelson, 2001; O Brien et al., 2003; Mann et al., 2004] and prompted numerical studies of electron response to Pc5 pulsations [Elkington et al., 1999]. Note that there have been numerous studies reporting V sw control of the amplitude or occurrence probability of magnetospheric ULF waves [Greenstadt et al., 1979; Wolfe et al., 1980; Junginger and Baumjohann, 1988; Mathie and Mann, 2001; Baker et al., 2003; Posch et al., 2003; Pahud et al., 2009; Liu et al., 2010]. [5] Second, there are studies reporting that a significant portion of ULF pulsations in the Pc5 band is directly driven by solar wind dynamic pressure variations. Density structures with various spatial scales are imbedded in the solar wind, leading to temporal variations, dp sw, of the solar wind dynamic pressure, P sw, as seen in the magnetosphere frame of reference. When a series of P sw pulses impacts the magnetosphere, the resulting fast mode pulses launched into the magnetosphere produce global compressional pulsations with a waveform nearly identical to that of dp sw. Rostoker and Sullivan [1987] suggested a possible link between ground Pc5 pulsations and changes in solar wind dynamic pressure. The link became convincing in studies that compared variations of the solar wind dynamic pressure and ULF pulsations [Matsuoka et al., 1995; Kepko et al., 2002; Takahashi and Ukhorskiy, 2007, 2008; Kessel, 2008; Huang et al., 2010a; Liu et al., 2010]. Since the KHI-driven waves are evanescent with respect to distance from the magnetopause, radially propagating dp sw -driven ULF waves could be the dominant wave type away from the magnetopause when both types of waves are present at the magnetopause. For instance, Claudepierre et al. [2008] reported localization of KHI-driven waves to the vicinity of the magnetopause based on a global magnetohydrodynamic (MHD) simulation. Claudepierre et al. [2010] reported on a set of similar simulations where both KHI waves and dp sw -driven waves were present at the magnetopause. The authors found that the KHI did not penetrate Earthward beyond 2 3 R E from the dawn/dusk magnetopause (i.e., L > 6), whereas the dp sw -driven waves resonated throughout the majority of the dayside magnetosphere (i.e., globally). dp sw -driven ULF waves have been incorporated in numerical analysis of the acceleration and radial transport of energetic electrons in the outer radiation belt [Ukhorskiy et al., 2005, 2006]. dp sw - driven compressional pulsations can also resonantly couple to toroidal standing Alfvén waves [Baumjohann et al., 1984; Kivelson and Southwood, 1988; Araki, 1994; Kim et al., 2002; Takahashi and Ukhorskiy, 2007; Sarris et al., 2010], which may accelerate electrons [Elkington et al., 1999]. Given observational evidence for the two competing pulsation source mechanisms, it is important to evaluate their relative strength as a function of position in order to relate the waves to particle transport phenomena. [6] Finally, in conducting statistical analyses of solar wind and magnetosphere interactions, it is in general important to recognize that both the solar wind parameters and solar extreme ultraviolet (EUV) radiation change over a solar cycle. Previous studies have already noted that the degree of solar wind control of Pc5 power varies over a solar cycle [e. g., Mathie and Mann, 2001], yet its origin has not fully been addressed. The solar wind directly affects ULF wave intensity, and the EUV radiation controls the ion composition and mass density and thus the magnetospheric response to applied external ULF disturbances. Takahashi et al. [2010] reported that over a solar cycle, the mass density varies by a factor of 5, which translates to a variation of magnetospheric MHD wave velocities by a factor of 2. The solar cycle variations in ULF waves will be most evident when observations are compared between the solar maximum and the solar minimum [e.g., Murphy et al., 2011]. Therefore, we contrast data from different phases of solar activity. [7] The remainder of this paper is organized as follows. The data are described in section 2, the data analysis method is presented in section 3, the data analysis results are presented in section 4, the discussion is presented in section 5, and the conclusions are presented in section Data [8] The data set for the present analysis comes in three types, which are all given in 1 min time resolution: solar wind ion bulk parameters that are time shifted to the bow shock nose (OMNI data, provided by the Space Physics Data Facility of NASA Goddard Space Flight Center); magnetic field data from the Geostationary Operational Environmental Satellites (GOES)-8 and -12 ( goes.html) [Singer et al., 1996]; and ground magnetic field data from a total of 7 stations available through the World Data Center (WDC), Kyoto University ( and the Circum-pan Pacific Magnetometer (CPMN) project ( [Yumoto and the CPMN Group, 2001]. Table 1 lists the sources of ground magnetic field data. The corrected geomagnetic (CGM) coordinates (epoch = 2004) listed in the table were obtained by using the online utility provided by the Virtual Ionosphere, Thermosphere, Mesosphere Observatory ( nasa.gov/vitmo/cgm_vitmo.html). [9] We have chosen years 2001 and 2006 for analysis. Year 2001 was close to the sunspot maximum (July 2000) in solar cycle 23 and will be referred to as solar maximum. Year 2006 will be referred to as declining phase, because the sunspot number was decreasing toward the minimum in We selected 2001 and 2006 in part because we have already studied solar wind control of Pc5 pulsations at geostationary orbit for these periods [Takahashi and Ukhorskiy, 2007, 2008]. GOES-8 (2001) and GOES-12 (2006) were chosen from several similarly instrumented GOES satellites because they were both located at geographic west longitude of 75 corresponding to dipole magnetic latitude of 10. Having common magnetic latitude allows us to ignore the latitude dependence of ULF wave amplitudes. 3. Method of Data Analysis 3.1. Definition of Hourly Parameters [10] Our data analysis follows the approach used in our previous studies of solar wind control of Pc5 pulsations at 2of18

3 Table 1. List of Ground Magnetic Field Data a Location Code Source Geographic Latitude ( ) Geographic Longitude ( ) CGM Latitude ( ) CGM Longitude ( ) Barrow BRW WDC Fort Churchill FCC WDC Tixie TIK CPMN Chokurdakh CHD CPMN Zyryanka ZYK CPMN Magadan MGD CPMN Kakioka KAK WDC a The corrected geomagnetic (CGM) coordinates are for the epoch of 2004 evaluated at the altitude of 100 km. L the GOES geostationary satellites [Takahashi and Ukhorskiy, 2007, 2008]. All parameters derived from the 1 min time series data are defined in non-overlapping hourly universal time (UT) windows beginning at 0000 UT of 1 January 1 and ending at 2400 UT of 31 December. The hourly solar wind velocity V sw is the simple arithmetic mean of the 1 min samples. Other variables are the amplitude of various parameters contained in ULF bands defined in two ways as follows. [11] First, to evaluate the overall variations of variable X in the entire Pc5 band we defined the total amplitude, dx T,as dx T ¼ 2 N k¼k1 XT k¼k0 T j~x k j 2! 1=2 where ~X k is the Fourier transform of the discrete time series X j (j =1,N) in the 1-h UT windows, given as [e.g., Bendat and Piersol, 1971], ~X k ¼ XN 1 X n exp i 2pkn ð2þ N n¼0 The upper and lower limits of the summation in equation (1) correspond to the lower (1.7 mhz) and upper (6.7 mhz) frequency boundaries of the Pc5 band, respectively. dx T is the root-mean square amplitude of all variations contained in the Pc5 band. Note that we remove the best fit second-order polynomial from the original time series X n. The total amplitude was calculated for P sw, the ground magnetic field H (horizontal northward) and E (horizontal eastward) components, and the magnetic field compressional (B z ) and azimuthal (B y ) components at GOES. These are expressed as dp swt, dh T, de T, db zt, and db yt, respectively. Our definition of the dynamic pressure is P sw ¼ N sw M p V 2 sw where N sw is the solar wind proton number density and M p is the proton mass. Using dx T as the definition of Pc5 intensity is appropriate in evaluating the overall level of ULF wave activity regardless of its origin; it is also convenient for comparison with many previous studies that used parameters equivalent to dx T, its square (= power), or its square divided by the pulsation bandwidth (= power spectral density) [e.g., Wolfe et al., 1980; Mathie and Mann, 2001; Pahud et al., 2009; Huang et al., 2010a]. [12] Second, noting that narrowband oscillations sometimes dominate the spectrum of ULF oscillations [e.g., Baker et al., 2003], we adopted a method used by Takahashi and Ukhorskiy [2007] to capture hourly segments containing ð1þ ð3þ narrowband oscillations. Briefly, this method searches for spectral peaks for which we can define the full width at half maximum (FWHM) within the Pc5 band. Field line resonance is the main candidate for narrowband oscillations. Since field line resonance on the ground appears most strongly in the H component [e.g., Walker et al., 1979], we defined the FWHM using the H component data and computed the amplitude of narrowband oscillations, dx N,as dx N ¼ 2 N k¼k1 XN k¼k0 N j~x k j 2! 1=2 Here the summation of the Fourier components is taken from k0_n, corresponding to the lower boundary of the FWHM, to k1_n, corresponding to the upper boundary of the FWHM. The frequency boundaries vary from one 1-h segment to another. [13] The L and MLT dependence of the occurrence rate of narrowband oscillations is shown in Figure 1 using a dial plot format. For this figure we define L and MLT by using the CGM coordinates of the ground stations listed in Table 1. For plotting purposes we sort the UT hourly values into MLT hourly bins according to the MLT at the center of the UT data window, and we define L bins such that their boundaries are located at the midpoint of neighboring stations. White circles are drawn at L = 5 and L = 10. [14] At high-latitudes (L > 6) the occurrence probability approaches 50% at around 0900 MLT. This high-latitude feature is very similar to that reported by Baker et al. [2003], who used a technique different than ours to identify Pc5 events. Based on the analysis of Baker et al. [2003], we believe that many of our high-latitude narrowband pulsations resulted from field line resonance. [15] At low latitudes (L < 3), the occurrence rate of narrowband oscillations is about 20 30%. Since the fundamental field line resonance frequency in this region is higher than the upper limit of the Pc5 band [e.g., Takahashi and Anderson, 1992], we would argue that relatively monochromatic solar wind dynamic pressure variations are a main source of low-latitude narrowband events Regression Analysis [16] To quantify the relationship between the solar wind condition and Pc5 amplitudes, we use the standard linear regression analysis technique [e.g., Draper and Smith, 1966; Wolfe et al., 1980]. In our analysis the independent variables are the logarithm of hourly V sw and dp swt, and the dependent variable is the logarithm of the hourly total amplitude in the Pc5 band: dh T, de T, db zt,ordb yt. Our task is to use the ð4þ 3of18

4 Figure 1. L-MLT dial plots of the occurrence rate of narrowband oscillations in the H component. The rate is defined to be the number of 1-h intervals with a sharp spectral peak as described in section 3.1 of the text divided by the number of 1-h intervals for which we have ground magnetic field data. (a) Occurrence rate for (b) Occurrence rate for least squares method to determine the parameters, c (intercept), S V (slope with respect to V sw ), and S P (slope with respect to dp swt ) for the assumed log linear relationship log 10 dx T ¼ c þ S V log 10 V sw þ S P log 10 dp swt In the regression analysis we obtain other statistical parameters including the correlation coefficients (R s) and confidence intervals of the parameters in equations (5). When a single independent variable x and a single dependent variable y are considered, the slope S is related to linear correlation coefficient R by the equation S ¼ s y =s x R ð6þ where s y is the standard deviation of y, and s x is the standard deviation of x [Draper and Smith, 1966]. [17] We use the notation R V (dx T ), R P (dx T ), and R VP (dx T ) for the correlation of dx T with V sw, dp sw, and V sw and dp sw both, respectively. Note that we graphically show results mainly for the total amplitude dx T, because the overall number of samples is small for dx N. 4. Statistical Analysis 4.1. Joint V sw and dp swt Distribution [18] Solar wind parameters cover different regimes in the parameter space at different solar activity phases, which may ð5þ result in changes in the behavior of the magnetosphere over a solar cycle timescale. Some solar wind parameters can be mutually correlated, which results in apparent control of magnetospheric phenomena by one parameter when another is physically connecting the solar wind and the magnetosphere. Therefore, it is a good practice to examine the distribution of the solar wind parameters before starting correlation analysis of solar wind control of magnetospheric phenomena [Takahashi et al., 1981]. [19] Figure 2 shows an overview of the solar activity and solar wind parameters relevant to our statistics. Figures 2a 2c show that 2001 was near the peak of the sunspot number in solar cycle 23 and that 2006 was in the late declining phase of the solar cycle; the 27-day averages of V sw was 400 km/s in both 2001 and 2006; and the 27-day average of P sw was also similar, 2 npa, in the two selected periods. [20] Because solar wind parameters vary significantly in 27-day periods, it is necessary to find the variability of these parameters in a finer time scale. This is examined in Figures 2d and 2e using hourly V sw and dp swt defined in section 3.1. For each year V sw and dp swt data points exhibit a large 2-dimensional spread, indicating that they are only weakly (but positively) correlated. This is confirmed by correlation analysis of log 10 V sw and log 10 dp swt. We obtain a correlation coefficient of 0.25 for 2001 with the 95% confidence interval of (0.23, 0.27), and 0.28 for 2006 with the 95% confidence interval of (0.26, 0.30). Because P swt has V sw in its definition (see equation (3)) and dp swt is highly correlated with P sw [Takahashi and Ukhorskiy, 2007], it is somewhat surprising that the values of the correlation coefficient are low. This apparent contradiction is easily resolved by noting that it is the variation of N sw that contributes most to the variation of P sw [Kepko et al., 2002] and that N sw and V sw are weakly correlated. In addition, we note important differences between the two periods. For example, in 2001, there is a single population in the joint V sw -dp swt distribution, which is peaked at (400 km/s, 0.05 npa); in 2006, there is a second population peaked at (600 km/s, 0.08 npa), which results from recurrent highspeed streams L-MLT Dial Plots of Median Pulsation Amplitude [21] Figure 3 shows the L-MLT dial plots of the median values of the ground pulsation amplitude computed according to equation (1) or (4): from left to right, dh T, de T, dh N, and de N. The plots are compared between 2001 (upper row) and 2006 (lower row). Several features are evident in the plots: [22] 1. The spatial pattern is similar between the total (T) and narrow (N) bands. However, the former shows higher values, because the FWHM is a fraction of the total Pc5 band. Also, the amplitude exhibits a more pronounced early morning minimum at L > 6 in the N band than in the T band. [23] 2. The H component exhibits higher amplitude than the E component in both the T and N bands. [24] 3. The amplitude is an increasing function of L except in 2001 when de T and de N show a peak at L 7.5 (FCC), most prominently near midnight. Larger amplitude at higher L, when observed on the dayside, implies that the source of the magnetic field variations is external to the magnetosphere. [25] 4. In the dawn sector there is a high latitude (L >7) enhancement of dh T and dh N in 2001 (dh N exhibits a similar but weaker feature in 2006). This feature has been 4of18

5 Figure 2. Solar wind condition for the periods studied. (a) Twenty-seven day averages of the sunspot number. The two shaded areas indicate the 2 one-year periods covered in the present study. (b) Twentyseven day averages of solar wind velocity V sw. (c) Twenty-seven day averages of solar wind dynamic pressure P sw (not to be confused with its variations in the Pc5 band, dp swt ) for solar cycle 23. (d) Joint distribution of hourly V sw and dp swt for The color key shows the number of hourly samples in parameter bins uniformly spaced in logarithmic scale. (e) Same as Figure 2d but for reported previously [e.g., Vennerstrøm, 1999], and we believe that it is caused by field line resonance [i.e., Baker et al., 2003]. Strong appearance of the resonance at the solar maximum, when high speed solar wind streams are infrequent (Figure 2d), would appear contradictory to the notion that high solar wind velocity is favorable to drive the resonance on the magnetopause through the KHI [Rostoker et al., 1998].We provide an explanation for the observation in sections 5.2 and 5.3. Figure 3. L-MLT dial plots of the median value of the amplitude of ground magnetic field oscillations. The inner and outer white circles indicate L = 5 and L = 10, respectively. The amplitude is computed for the H and E components both in the fixed Pc5 band (dh T, de T ) and in a narrow data adaptive band defined using the H component (dh N, de N ). The upper row is for 2001 and the lower row is for of18

6 Figure 4. Hourly solar wind and amplitude of magnetic field variations in the total Pc5 band at geosynchronous orbit and on the ground for a 50-day period each in (left) 2001 and (right) [26] 5. In the midnight sector there is a high latitude (L > 5) enhancement of dh T, dh N, de T, and de N, with a peak at 2200 MLT. This feature was noted previously [e.g., Vennerstrøm, 1999; Baker et al., 2003] and has been attributed to disturbances associated with substorms. Both large-amplitude fluctuations in substorm current systems as well as high-latitude Pi2-type pulsations [Kepko and Kivelson, 1999] would contribute to this feature. Other high-latitude phenomena such as poleward boundary intensifications [Lyons et al., 1999] and auroral streamers [Nakamura et al., 2001] may also contribute to the enhancement. Although these field variations are not necessarily MHD waves, they well could affect energetic particles in the magnetosphere. [27] 6. In addition to these localized features, the high-l regions exhibit appreciable amplitude at all local times. Such background pulsations cannot be ignored. For example, pulsations near noon could be attributed to buffeting of the magnetopause by solar wind dynamic pressure variations, which cause strong compressional magnetospheric magnetic oscillations near the subsolar magnetopause [Ukhorskiy et al., 2006; Huang et al., 2010b] Solar Wind Dependence of Pulsation Amplitude: Examples [28] We now examine the relationship between the solar wind condition and ground pulsation amplitude. First, we examine sample time series from 2001 and The two columns of Figure 4 show hourly parameters for a 50-day period in 2001 (left) and 2006 (right), respectively. In both periods, V sw and dp swt are highly variable and are correlated with the Pc5 amplitudes in space (db yt and db zt ) and on the ground (dh T and de T ). For example, a sudden rise in V sw occurring on day 118, 2001 is accompanied by a similar rise in all amplitude values. The same happens with a dp swt spike on day 111, 2001 (most evident at KAK). The objective of the analyses presented below is to provide a more quantitative description of such a relationship between the solar wind and pulsation amplitude. [29] To find independent contributions from V sw and dp swt to pulsation amplitude, we devised a data display technique shown in Figure 5. In this example, each panel in the top row covers data from one ground station for year 2001 and for MLT. The color-coded quantity is 6of18

7 Figure 5. (a) Dependence of dh T at MGD (L = 2.9) on V sw and dp swt at MLT for The color of the pixels represents the median value of dh T in bins which are evenly spaced in log 10 (V sw ) and log 10 (dp swt ). (b) Same as Figure 5a but for (c) Ratio between Figures 5a and 5b. The red (blue) portion of the ratio plots indicates that the amplitude is higher for 2001 (2006). (d f) Same as Figures 5a 5c but at CHD (L = 5.6). (g j) Same as Figures 5a 5c but at BRW (L = 8.7). the median value of dh T computed in the V sw -dp swt bins. The bin boundaries are evenly spaced in logarithmic scale. The second row is the same as the first row except for The third row shows the 2001 to 2006 ratio of the median dh T. The three columns represent low latitude (left, MGD, L = 2.9), intermediate latitude (middle, CHD, L = 5.6), and high latitude (right, BRW, L = 8.7), respectively. [30] There are a few notable features in Figure 5. First, dh T increases as L increases as was already seen in Figure 3. Second, in all panels in the first and second rows, dh T is positively correlated with both V sw and dp swt (i.e., the color becomes brighter as either V sw or dp swt increases). Third, dh T is higher for 2001 than 2006 at all 3 stations (in the third row, the color is mostly white to red). We will use other display formats in the following sections to qualitatively evaluate the L and MLT dependence of various statistical parameters Solar Wind Dependence of Pc5 Amplitude: Regression Coefficients [31] Figure 6 summarizes the results of regression analysis of the relationship between the solar wind condition and the pulsation amplitude on the ground. Each panel shows the color-coded value of the regression coefficient (the slope), S V or S P, as defined in equation (5), as a function of L and MLT. The dependent variable for the regression is ground pulsation amplitude dh T or de T. The L-MLT binning scheme is the same as in Figure 3. There are many interesting features in the dial plots. We point to a few obvious ones. [32] First, for a given year, there is a high degree of similarity in the spatial pattern between S V (dh T )ands V (de T )and between S P (dh T )ands P (de T ). This implies that oscillations in H and E are strongly coupled at all local times and are related to the solar wind condition in basically the same manner. 7of18

8 Figure 6. L-MLT dial plots of regression coefficients S V and S P, defined in equation (5) for the relationship between solar wind parameters and ground pulsation amplitude. The dependent variable is dh T or de T. Comparison is made between 2001 (top row) and 2006 (bottom row). [33] Second, the spatial pattern of the coefficients differs between 2001 and Both S V (dh T ) and S V (de T ) are generally higher in 2006 than in 2001(Figures 6a 6d). For 2006, there are regions of particularly high S V, the high-l region in the evening sector and the high-l region in the prenoon and dawn sectors (Figures 6b and 6d). The evening sector enhancement suggests magnetic field variations associated with substorms. The dawn sector enhancement suggests the KHI. The value of S P (dh T ) and S P (de T ), in contrast, is higher in 2001, especially in the low-l region of the postmidnight sector (Figures 6e 6h). [34] We also examined the slopes for narrowband pulsations, S V (dh N ), S V (de N ), S P (dh N ), S P (de N ), plotted in the same format as Figure 6 (not shown). The plots are significantly noisier than Figure 6 because of the smaller number of samples. Nonetheless, we find the L and MLT dependence of the slopes to be generally similar between the total and narrow bands. One notable difference is that S V (dh N ) Figure 7. L slices of regression coefficients S V (dh T ) and S P (dh T ) in 4 MLT bins. The results are compared between 2001 (solid circles) and 2006 (open circles). The vertical bars indicate the standard errors. 8of18

9 Figure 8. (a f) L-MLT dial plots of the correlation coefficients R V, R P, and R VP for dh T and (g l) de T. The coefficients are shown separately for 2001 and and S V (de N ) are higher than S V (dh T ) and S V (de T ), respectively, in the region where narrowband pulsations occur frequently, that is, the high latitude (L > 6) region on the morning side (see Figure 1). If the narrowband pulsations are mainly caused by field line resonance, then the above result implies that field line resonance is more strongly dependent on solar wind velocity than Pc5 pulsations generated by other mechanisms. [35] To examine the features seen in Figure 6 more quantitatively we show in Figure 7 the L profiles of S V (dh T )and S P (dh T ) in 4 evenly spaced MLT bins: (midnight), (dawn), (noon), and (dusk). Each data point shown here was computed from approximately 250 hourly samples. The first to be noted in these plots is that all S V and S P values are positive, which means that increase in V sw or dp swt increases the pulsation amplitude on the ground. However, there are important differences between the two 1-year periods examined, and between S V and S P, as was already noted in Figure 6. We find, from the panels in the upper row (Figures 7a 7d), that S V (dh T ) for 2006 tends to increase with L except near midnight, whereas S V (dh T ) for 2001 tends to increase with L only up to L 5 and decreases or remains flat thereafter. As a consequence, S V (dh T )atl > 6 is higher for 2006 than for The large value of S V (dh T ) for 2006 means that V sw is increasingly effective in driving Pc5 pulsations as L increases. We also find, from the four panels in the lower row (Figures 7e 7h), that in contrast to S V (dh T ), S P (dh T ) tends to decrease with L except for a minor peak at L 6. At L < 5 and in all MLT bins, S P (dh T ) is higher for 2001 than for of18

10 Figure 9. L profile of the linear correlation coefficients R V (dh T ), R P (dh T ), and R VP (dh T ) in 4 MLT bins. In each panel the results for 2001 (solid circles) and 2006 (open circles) are plotted separately. The vertical bars in the top and middle rows indicate the 95% confidence intervals Solar Wind Dependence of Pc5 Amplitude: Correlation Coefficients [36] In the same mathematical procedure that we use to determine the relation (5), we obtain the correlation coefficient R (not to be confused with its square R 2 ) as a measure of the degree of solar wind control of pulsation amplitude. Figure 8 shows the dial plots of the coefficients, labeled using the notation defined in section 3.2. A major feature seen in the spatial pattern is the similarity between the results for dh T (Figures 8a 8f) and de T (Figures 8g 8l). This was noted also in the dial plots of the regression coefficients (Figure 6). Therefore, we focus below on the dh T results in describing the differences among R V, R P, and R VP, and the dependence of these coefficients on the solar activity level. [37] At the solar maximum (2001), R V (dh T ) shows a moderate value all over the dayside with a pattern more or less symmetric about the noon meridian (Figure 8a), whereas R P (dh T ) is highest in the low-l region on the morning side (Figure 8b). The combined effect of these is that a region of high R VP (dh T ) is present on the dayside in the low-l region with a skew toward the morning side (Figure 8c), and also in regions of moderate L (the auroral zone). [38] During the declining phase (2006), R V (dh T ) exhibits higher values than at the solar maximum with the maximum occurring around noon at the highest L surveyed (Figure 8d). Meanwhile, R P (dh T ) is more uniform in L and MLT (Figure 8e) and exhibits lower values in the dawn sector compared to the solar maximum. As a result, R VP (dh T ) exhibits enhanced values in the high-l region on the dayside (Figure 8f) compared to the solar maximum. [39] Figure 9 shows the L profiles of R V (dh T ), R P (dh T ), and R VP (dh T ) in 4 MLT bins generated from a subset of correlation coefficients shown in Figure 8. In the top row (Figures 9a 9d) we find that R V (dh T ) for 2001 remains low at a value of 0.5 or lower whereas R V (dh T ) for 2006 is higher than 0.5 and reaches 0.7 at large L except at midnight. In the middle row (Figures 9e 9h) we find that R P (dh T ) is generally a decreasing function of L and exhibits a relatively small difference between 2001 and 2006 as compared to R V (dh T ). In the bottom row (Figures 9i 9l) we find that R VP (dh T ) is in the range of 0.6 to 0.8 on the dayside, which means that about 40 60% (R 2 ) of the variance of the observed magnetic field variations can be explained by the combined effect of V sw and dp swt Solar Activity Dependence of Pc5 Amplitude [40] In the introduction we pointed out the possibility that the solar activity dependence of the magnetospheric mass density affects the magnetospheric response to ULF disturbances from the solar wind. One way of detecting the effect is to examine the spatial distribution of the pulsation amplitude for fixed values of solar wind parameters. This was already attempted in Figure 3, which compared the 10 of 18

11 Figure 10. L-MLT dial plots of dh T and de T evaluated at V sw = 400 km/s and dp swt = 0.05 npa using the equation, log 10 dx T = c + S V log 10 V sw + S P log 10 dp swt, where the slopes S V and S P are determined from the observational data using linear multiple regression analysis. median pulsation amplitudes between 2001 and We make this comparison more rigorous by substituting the median amplitudes with the amplitudes estimated using our model, equation (5), for a fixed point in the V sw -dp swt parameter space. Figure 10 shows an example of this approach. We have chosen the set V sw = 400 km/s and dp swt = 0.05 npa, which is near the center of distribution of V sw and dp swt for both 2001 and 2006 and can be considered to be a typical solar wind condition. Not surprisingly, Figure 10 is very similar to the left hand portion of Figure 3 (dh T and de T dial plots) and all of our comments made to Figure 3 hold. [41] Figure 11 shows the L profile of dh T values generated from a subset of the data shown in Figure 10. The vertical error bar attached to each data point gives the 95% confidence limit [Draper and Smith, 1966] of the dh T values obtained using equation (5). At all local times the amplitude is an increasing function of L, similar to previous reports [e.g., Mathie and Mann, 2001], except for a small dip at L 6 seen at MLT and MLT. The difference between 2001 and 2006 is small except at MLT where the 2001 (solar maximum) values are higher by a factor of 1.5 at L > 5 (the margin is greater than the error bars) Comparison of Ground and GOES Satellite Observations [42] Magnetic pulsations observed on the ground are an indirect manifestation of ULF waves in the magnetosphere because the ionosphere modifies the waves. Therefore, we compare the ground observations with spacecraft observations. [43] Figure 12 compares our statistical parameters at geosynchronous orbit (GOES-8 for 2001 and GOES-12 for 2006, L = 6.8) and on the ground at TIK (L = 6.1) and FCC (L = 7.5). The two ground stations are chosen because they are close to GOES in L. The Pc5 parameter considered is the total amplitude in the GOES B z and B y and ground H components. In each column the top panel shows the total amplitude evaluated at V sw = 400 km/s and dp swt = 0.05 npa, using the regression coefficients S V and S P defined in each MLT bin. Other parameters plotted are S V, S P, R V, R P,andR VP. [44] At GOES, some features are commonly seen at both solar activity phases. First, db zt is peaked at noon, exhibits a minimum near 0400 and 2000 MLT, and increases toward midnight. db yt also exhibits a midnight maximum but lacks a peak at noon. These features can be attributed to strong magnetic field compression near noon and strong field line azimuthal bending away from noon [Matsuoka et al., 1995; Takahashi and Ukhorskiy, 2007]. Second, S V and S P are not much different between 2001 and 2006 except for the higher 2001 value of S V (db zt ) and S P (db zt ) in the postnoon sector. Third, for both db zt and db yt, R P (0.7 on the dayside) is higher than R V (0.5 on the dayside) at most local times. [45] At GOES, a notable difference is also found between 2001 and Both db yt and db zt are higher in 2001 at all local times. The difference is more obvious in db yt, with the Figure 11. L profile of dh T evaluated at V sw = 400 km/s and dp swt = 0.05 nt using the relationship log 10 dh T = c + S V log 10 V sw + S P log 10 dp swt and compared between 2001 (solar maximum) and 2006 (solar minimum), where S V and S P are defined at each L and MLT grid point. The error bars give 95% confidence limits. Results are shown in 4 MLT bins: (a) , (b) , (c) , and (d) of 18

12 Figure 12. MLT dependence of Pc5 statistical parameters at geosynchronous orbit (L = 6.8) and on the ground at stations close to GOES in L: TIK (L = 6.1) and FCC (L = 7.7). The total Pc5 amplitude for the GOES B z, GOES B y, and ground H components is shown at the top row and its relation to solar wind condition is shown in the lower panels in terms of the regression coefficients S V and S P and the correlation coefficients R V, R P, and R VP. The vertical bars indicate the 95% confidence intervals for the total Pc5 amplitude, R V, and R P ; they are the standard errors for S V and S P. The amplitude is evaluated at V sw = 400 km/s and dp swt = 0.05 npa. The R V, R P, and R VP values at GOES are the same as those shown by Takahashi and Ukhorskiy [2008, Figure 8]. 12 of 18

13 2001 to 2006 ratio of 2. This translates to a power difference of 4, which is substantial when considering radial diffusion via ULF waves. [46] Ground dh T and the associated statistical parameters on the ground exhibit both similarities and differences compared to the GOES results. First, dh T is highest near midnight, similar to db yt at GOES. Also, dh T in the dawn sector is higher in 2001 by a factor of 1.5 (TIK, L = 6.1) to 2 at (FCC, L = 7.5), similar to db yt. However, this feature on the ground diminishes away from the dawn sector. A feature most pronounced at FCC is the high S V value in the morning sector, which reaches 3.5 in At this station the R V value is also high in Finally, the MLT profile of R V, R P, and R VP is similar between space and ground, with most of them exhibiting a broad maximum around noon Summary of Data Analysis [47] Although we have chosen only 2 solar wind parameters, V sw and dp swt, these are found to account for a substantial fraction of magnetic field variations in the Pc5 band observed on the ground and at geosynchronous orbit. On the dayside the correlation coefficient R PV for the combined V sw and dp swt effects exhibits values in the range of , which means that 40 60% of the magnetic field variations in the Pc5 band are accounted for by mechanisms related to V sw and dp swt. The degree of dependence of the Pc5 amplitude on these parameters varies with the location of observation as well as with the solar activity phase. [48] Figure 13 shows a schematic representation of the L-MLT domains of Pc5 pulsations regarding their amplitude and dependence on the solar wind and solar activity. The L and MLT boundaries are only for illustrative purposes: the transition in the actual magnetosphere is not as abrupt as in this figure and actual observations contain much more complex finer features that we do not attempt to capture in the figure. Below we present major features of each domain and offer a brief description of processes that can explain our statistical results. Additional specific discussions are presented in Section 5. [49] In domain A (L > 5, dawn sector), dh T is higher in 2001 than in 2006 for typical values of V sw and dp swt. This is related to the observation at GOES, which shows that both db zt and db yt are higher in 2001 at all local times. An explanation is given in Section 5 as to why the amplitude is higher in Also in this domain, dh T in 2006 is more strongly dependent on V sw than in 2001, in terms of both S V (Figure 7) and R V (Figure 9). This suggests that the highspeed solar wind flows characteristic during the declining phase are effective in driving the pulsations. Narrowband power is also prominent in this domain, which is attributed to field line resonance. [50] Domain B (L > 5, noon and dusk sectors) is similar to Domain A except for the lack of solar activity phase dependence of the amplitude. Although dh T in this domain is lower than in domain A or C, the correlation coefficient R V here is high even at noon. [51] In domain C (L > 5, midnight sector), the amplitude is the highest, exceeding that in Domain A. This domain exhibits much lower dependence on V sw or dp swt, however, which can be explained by the magnetic field variations here being caused by substorms and associated phenomena. Substorms are highly dependent on the solar wind condition, but one major controlling factor is the southward component of IMF, which is not included in our investigation. Also, substorms occur with an intrinsic time delay with respect to changes in the solar wind parameters. The delay would lower correlation of pulsation amplitudes with instantaneous values of the solar wind parameters. [52] In domain D (L < 5), the pulsation amplitude is much lower than in the other domains and it depends more strongly on dp swt than on V sw. This can be explained by penetration of dp swt -driven ULF waves into the inner magnetosphere. 5. Discussion [53] In this section, we provide explanations for some features found in our analysis Comparison of V sw and dp sw Effects [54] In relation to the flux variations of radiation belt electrons, previous studies strongly emphasized the role of high-speed solar wind streams in driving Pc5-band pulsations [e.g., Mathie and Mann, 2001; Mann et al., 2004]. In accordance with these studies, we find that the total Pc5 amplitude on the dayside is strongly controlled by V sw in the high-l (>6) region in the morning sector. The V sw control is particularly evident during the declining phase when highspeed streams develop, which was also noted previously [e.g., Mathie and Mann, 2001]. [55] However, during the solar maximum, the V sw control is subdued, and the dp sw control becomes comparable to or even stronger than the V sw control. This is particularly clear in the low L (<5) region where the dp sw dependence is stronger even during the declining phase (see Figures 7, 8, and 9). A strong dp sw dependence of both db zt and db yt was already noted at geostationary orbit [Takahashi and Ukhorskiy, 2008] and the present study confirms that qualitatively the same dependence appears on the ground. Since field line resonance in the Pc5 band is unlikely in the low-l region (see Figure 14), the dp sw dependence can be attributed to penetration of compressional (fast mode) waves that are generated by buffeting of the magnetosphere by the variations of the solar wind dynamic pressure [Matsuoka et al., 1995; Kepko et al., 2002; Huang et al., 2010a; Liu et al., 2010]. Therefore, it is quite possible that the compressional ULF waves play an important role in changing the energy and the orbit of energetic electrons in the radiation belt, as has already been discussed in numerical studies [Ukhorskiy et al., 2006; Huang et al., 2010b] Mass Density Effect [56] We have shown that both db z and db y at GOES exhibit the same solar activity dependence, at all MLT (Figure 12). Also we have shown that dh T on the morning side is higher at the solar maximum than during the declining phase (Figures 5, 10, 11, and 12). Since the pulsation amplitude was evaluated for a common value of V sw and dp swt close to their respective median, these findings lead us to suggest that the solar cycle variation of the mass density, which is strongly related to the solar EUV radiation, plays an important role in controlling the response of the magnetosphere to Pc5-band disturbances originating from the solar wind. 13 of 18

14 At the late declining phase (Figure 14b), this contour is located a few Earth radii outward. The actual turning points need not match the contours illustrated here because they depend on k f, which is a quantity that we cannot determine in the present study. Nonetheless, the resulting location of the contours emphasizes the property that Pc5 waves can penetrate deeper into the magnetosphere during solar Figure 13. Schematics of L-MLT domains for Pc5 amplitude characteristics on the ground. [57] Between the solar maximum and the solar minimum, there is a large difference in the amount of ionospheric O + ions that are transported to the magnetosphere [Young et al., 1982; Nosé et al., 2009; Denton et al., 2011]. At solar maximum, the EUV intensity (usually expressed by the F10.7 index) is high, which increases the scale height and the temperature of ionospheric ions. This leads to a magnetosphere that is heavily loaded with ionospheric O + ions. This, in turn, results in a pronounced solar cycle variation of magnetospheric mass density and the MHD wave speeds [Denton et al., 2011]. According to statistical studies using the frequency of standing Alfvén waves as an indicator of the mass density, the density increases from the solar minimum to the solar maximum by a factor of 2 at L 1.7 (plasmasphere) [Vellante et al., 1996] and by a factor of 5 atl 6.8 (plasma trough) [Takahashi et al., 2010]. [58] In the inhomogeneous magnetosphere, fast mode MHD waves propagating inward from the magnetopause encounter a turning point earthward of which they become evanescent [e.g., Yumoto and Saito, 1983]. The turning point is the location where w = k f V A is satisfied, where w is the wave frequency, k f is the azimuthal wave number and V A is the Alfvén velocity [Lee and Lysak, 1990]. Because V A is a function of the plasma mass density r and the magnetic field intensity B and only the former varies significantly over a solar cycle, r is the major controlling factor of the location of the turning point for a given value of k f V A. [59] We can get a semiquantitative evaluation of the location of the turning point based on the knowledge that we have of the frequency of standing Alfvén waves in the magnetosphere. Figure 14 shows a schematic illustration of the equatorial contour of the fundamental standing Alfvén wave frequency, f T1, drawn at 6.7 mhz (the upper limit of the Pc5 band). Satellite observations leading to this schematic are found by Takahashi et al. [2002, Figure 5]. At the solar maximum (Figure 14a), the contour is located closer to the Earth, crossing the geostationary orbit on the dayside. Figure 14. Schematics of the contour of the fundamental toroidal wave frequency at 6.7 mhz, the upper boundary of the Pc5 band, viewed in the magnetic equatorial plane. The location of the GOES satellites along with model bow shock and magnetopause [Fairfield, 1971] are drawn. (a) Solar maximum. (b) Declining phase. 14 of 18

15 maximum than during solar minimum. This scenario qualitatively explains why the Pc5 amplitude (db yt ) is higher in 2001 than in 2006 at geosynchronous orbit (Figure 12g). [60] Similar solar activity dependence is seen on the ground, but not at all local times. In Figure 11 we found that dh T is significantly higher in 2001 than in 2006 in the MLT bin but not at other local times examined. In Figure 12s, we confirmed this local time dependence at L = 7.5. This feature in the dawn sector can be attributed to the same mass loading effect as discussed above for GOES observations, but that does not explain why this happens only in the dawn sector on the ground Dawnside Amplitude Enhancement During Solar Maximum [61] The dawn-dusk asymmetry noted above only in 2001 is reminiscent of those reported previously in space for the fundamental-mode field line resonance [Yumoto et al., 1983; Anderson et al., 1990] and on the ground for narrowband Pc5 waves [Glassmeier and Stellmacher, 2000; Baker et al., 2003]. Glassmeier and Stellmacher [2000] noted that the asymmetry did not exist at geostationary orbit, in agreement with our analysis shown in Figure 12, and explained the asymmetry on the ground by the local time dependence of ionospheric screening of magnetospheric ULF waves. [62] The absence of the dawnside enhancement during the declining phase (2006), on the other hand, could be explained by using once again the model illustrated in Figure 14. At the solar maximum, dawnside field line resonance in the Pc5 band ( mhz) occurs outside of L 8 (Figure 14a), while during the declining phase, the resonance region moves to outside of L 12 (Figure 14b). Therefore, during the declining phase, the ground stations used in the present study were on average located on L shells lower than the L shells that participate in field line resonance in the Pc5 band. This means that in 2006, amplification of fast mode waves coming from the solar wind or the magnetopause by field line resonance did not contribute to the Pc5-band magnetic field variations observed on the ground at L <9. [63] Another possible factor for the solar activity dependence of pulsation amplitude on the ground is the ionospheric conductivity. Magnetic pulsations observed on the ground are affected by currents driven by the electric field of ULF waves that are incident from the magnetosphere. As a consequence, the amplitude of the pulsations should depend on the ionospheric conductivity [e.g., Yumoto et al., 1996; Motoba et al., 2002]. According to Nishida [1978], the ionospheric transmission coefficient for Alfvén waves has a factor S H /S P, where S H and S P are the height-integrated Hall and Pederson conductivities, respectively. For fast mode waves the coefficient does not depend on the conductivity, meaning only Alfvén waves are affected. [64] The solar illumination in the EUV wavelength range, which is relevant to the conductivities, varies significantly over a solar cycle. According to Rasmussen et al. [1988], this illumination variation results in a factor of 1.6 variation of S P over a solar cycle, but the ratio S H /S P remains nearly constant at Therefore, we would expect the solar activity dependence of the conductivities to play a relatively minor role in controlling ground Pc5 amplitude V SW Dependence of Pc5 Amplitude at Noon [65] A puzzling finding is that R V exhibits a broad peak around noon as shown in Figures 8 and 12, both at GOES and on the ground. Traditionally, the V sw dependence of the amplitude of magnetospheric ULF waves has been attributed to the magnetopause KHI [e.g., Greenstadt et al., 1979], but it is difficult to explain the peak correlation occurring near noon with this instability. The instability would excite waves away from noon because the instability requires the velocity shear across the magnetopause to exceed a threshold value [e.g., Southwood, 1968]. The shear is zero at the nose of the magnetopause and gradually increases toward the tail. The global numerical simulation of the instability reported by Claudepierre et al. [2008] clearly shows that the instability is absent at the nose and grows on the flanks of the magnetopause. [66] However, we argue that KHI is still relevant to the Pc5 pulsations around noon. In the above discussion of the local time dependence of wave excitation, we considered KHI on the equatorial magnetopause, ignoring KHI on the high-latitude magnetopause. In a theoretical study, Yumoto [1984] showed that KHI can generate Pc4 5 waves in the plasma mantle and that the waves can propagate to the dayside because the plasma flow speed is lower than the Alfvén wave speed in the wave-generation region and in its vicinity. [67] This possibility of high-latitude KHI prompted us to reexamine the results of the numerical simulation of magnetopause KHI reported by Claudepierre et al. [2008]. The simulation was done using the 3-dimensional Lyon Fedder Mobarry (LFM) code [Lyon et al., 2004], so it covered the high-latitude region. However, the authors did not discuss high-latitude KHI. From a run for a constant solar wind velocity of 600 km/s, we generated Figure 15, which shows simulation results in the noon midnight meridian in the geocentric solar magnetospheric (GSM) coordinates. The results stated here regarding the high-latitude KHI are also true in the 400 km/s and 800 km/s runs done by Claudepierre et al. [2008]. [68] Figure 15a shows the amplitude of the azimuthal component of the electric field, de f, for the mhz band, defined in the same manner as dx T in equation (1) but computed over the duration (4 h) of the simulation. The arrows indicate plasma flow vectors. Figure 15b shows de f and a snapshot of the last closed field lines at the start of the simulation. We note enhanced wave power at the dayside high-latitude magnetopause. In a few movies of electric and magnetic field components, we confirmed that there are indeed waves propagating in this region (an example movie is available in Animation S1). 1 These waves have several features in common with the KH waves that Claudepierre et al. [2008] studied at the dawn and dusk flank magnetopause. They propagate in the direction of the magnetosheath flow and anti-sunward. This is consistent with what should be expected for KHI. They have wave characteristics similar to those seen for the dawn/dusk KHI, with frequencies in the 5 10 mhz range, phase speed of 175 km/s, and wavelengths of 3 4 R E. We do note that the waves are more broadbanded in nature and are not as monochromatic as the 1 Auxiliary materials are available in the HTML. doi: / 2011JA of 18

16 Figure 15. Figures generated from a simulation run in the study reported by Claudepierre et al. [2008]. (a) The amplitude of the azimuthal component of the electric field for the mhz band, expressed as de f, along with the bulk velocity vector. (b) de f and the last closed field lines at the end of the simulation. dawn/dusk KH waves. The constant solar wind driving likely plays some role in the monochromatic nature of the KHI because the KHI in LFM runs driven by solar wind parameters derived from satellite measurements is less monochromatic and has a more broadband character. We also found that the wave amplitudes of the high-latitude KH waves are not as strong as the dawn and dusk KH waves. The high-latitude waves have peak amplitude (RMS) of 1 mv/m, whereas the dawn/dusk KH waves are 2 mv/m in this simulation (in general in the LFM, we find that the KH wave amplitudes and frequencies increase with increasing V sw ). Based on these simulation results we propose high-latitude KHI as a possible source of Pc5-band pulsations observed near noon. [69] In relation to the simulation result we note that Posch et al. [1999] discussed broadband ULF noise (including but not limited to the Pc5 band) observed across local noon at high (near-cusp) latitudes. Their observations, and in particular the absence of simultaneous power in opposite hemispheres in many cases, can perhaps provide observational support or confirmation for the Claudepierre et al. [2008] results near local noon. Posch et al. [1999] also noted a clear and strong dependence on V sw, although they did not stress the KHI as being the relevant source mechanism. This study may also provide information on the longitudinal width of the broadband source Amplitude Enhancement on the Nightside [70] We have discussed Pc5-band pulsations primarily in relation to dayside wave sources. However, amplitude enhancements do occur on the night side, with median amplitude comparable to or exceeding that of pulsations detected in the dawn sector, according to the amplitude dial plots shown in Figures 3 and 10. This nightside feature was also evident in the statistical study of GOES magnetic field power spectral density (PSD) in the mhz band reported by Huang et al. [2010a]. Huang et al. sorted the PSD by the level of AE index and found a positive correlation between the two, which is not surprising because during substorms the magnetic field variations have strong power in a near-dc to the Pi2 band (7 25 mhz). [71] It is important to note that the amplitude of Pc5-band pulsations near midnight is comparable to those in the dawn sector, at all L, according to Figures 3 and 10. Observations from elliptically orbiting equatorial satellites [e.g., Nosé et al., 2010] indicate that magnetic field dipolarization and associated ULF oscillations penetrate as deep as L = 3.5 during geomagnetic storms. Assume for now that the magnetic field amplitude on the ground represents the amplitude of the azimuthal component of the electric field or the compressional component of the magnetic field in the magnetosphere. Then electrons drifting through the wavefield will experience modulation in energy and guiding center location when they pass the midnight sector. Of course electron interaction with the waves depends not only on the electromagnetic field amplitude but also on the azimuthal wave number, on which we do not have direct information. Nonetheless, the fact that we detect magnetic field variations on the ground means that the variations have relatively small azimuthal wave numbers (little ionospheric screening [Nishida, 1978]), which would mean that drift resonance will occur at high energy. Thus it is possible that magnetic field variations near midnight contribute significantly to the radial diffusion of electrons at least in the region outside of L = Summary and Conclusions [72] We have presented a statistical study of the dependence of the amplitude of magnetospheric Pc5 pulsations on V sw and dp sw, known to be major controlling factors of the amplitude from previous studies. We derived statistical Pc5 parameters using data from 7 ground stations and two GOES spacecraft and compared the results between 2001 (solar maximum) and 2006 (declining phase). Our findings and interpretations are summarized as follows: [73] 1. The pulsation amplitude is positively correlated with both V sw and dp sw, but the degree of correlation depends on the location of L and MLT of the position where 16 of 18