¹Institute of Geophysics and Planetary Physics, University of California, Los Angeles
²Lockheed Martin, Palo Alto, CA
³University of Iowa, Iowa City, IA

Abstract. The POLAR mission is ideally suited to explore the high-altitude polar cusp. POLAR magnetometer data, together with electron and ion measurements from the HYDRA and TIMAS instruments from March 1996 to December 1997, have been used to identify 459 polar cusp crossings. These crossings are used to study the statistical behavior of the cusp location and its dependence on the solar wind conditions. We find that the invariant latitude of the center of the cusp varies from 70 to 86 degrees as solar wind conditions change and the magnetic local time of the footprints of the cusp magnetic field lines extends from 0800-1600 MLT, the cusp extending slightly further in local time for increasing solar wind dynamic pressure. The average latitude of the center of the cusp is at 80.3^o invariant latitude at noon and decreases to 78.7^o at 0800 and 1600 MLT. The cusp also appears to thicken slightly in invariant latitude with increasing dynamic pressure. The center of the cusp moves equatorward with increasingly southward IMF to 73^o invariant latitude for a 10 nT southward IMF. The cusp moves only slightly for northward IMF. This motion is consistent with erosion of dayside magnetic flux for southward IMF but little or no erosion for northward IMF. The cusp is also somewhat wider in invariant latitude with increasingly northward IMF. Consistent with low altitude observations, we find that there is a clear MLT shift due to the IMF By for strongly southward IMF. We interpret the motion of the local time of the cusp for southward IMF as a shift of the reconnection site away from the noon meridian when the IMF is not due southward.

Introduction

The polar cusp has been studied extensively at low altitudes using observations from the Defense Meteorological Satellite Program (DMSP). With about 5,609 crossings, Newell and Meng [1988] studied the local time dependence of the cusp, showing that it is observed most frequently near magnetic local noon. The effects of dipole tilt angle and the orientation of the interplanetary magnetic field (IMF) on the location of the polar cusp were studied by Newell and Meng [1989] and Newell et al. [1989]. They found that when the IMF is southward, the polar cusp moves equatorward with more negative Bz and when it is northward, the magnetic latitude of the cusp changes very little. When the IMF By component is negative (positive), the cusp shifts dawnward (duskward), while the IMF Bx component has no effect on the cusp position. At high-altitudes our understanding of the cusp behavior is derived mainly from HEOS 2 and Hawkeye observations. Using Hawkeye data in a survey of the polar cusp crossings, Farrell and Van Allen [1990] reported that the latitudinal extent of the cusp region is enlarged when the solar wind dynamic pressure is greater. While these authors reported the same IMF Bz effect on the position of the cusp (see also Zhou and Russell, 1997) as that observed at low altitudes [Newell et al., 1989], a later report by Fung et al. [1997] did not find any significant IMF By effect at high altitudes. Fung et al. [1997] also reported that when solar wind dynamic pressure is greater, the extent in magnetic local time of the polar cusp at high altitudes is smaller.

The POLAR spacecraft provides us an excellent opportunity to study the polar cusp at high altitudes. We identify entries into the polar cusp along the POLAR trajectories with the POLAR magnetic field data [Russell et al., 1995] together with HYDRA [Scudder et al, 1995] and TIMAS [Shelley et al, 1995] key parameter data. The cusp entries occur at altitudes of 4.8 to 8.8 R_E in the northern hemisphere. We have reported the location of the cusp and its dependence on the dipole tilt angle in an earlier paper [Zhou et al., 1999]. In this paper we discuss how the local time and invariant latitude of the cusp depends on solar wind dynamic pressure, and IMF By and Bz.

Examples of Cusp Crossings

In the cusp region, we expect to see magnetosheath-like (high density and low energy) plasma. Further at high altitudes, the plasma causes a diamagnetic depression and fluctuations in the magnetic strength, because the plasma in the polar cusp region has an energy density that is significant relative to background magnetic field in contrast to low altitudes where the magnetic energy density is far greater than that of the plasma. As described in our previous paper [Zhou et al., 1999] the criteria used to identify the cusp crossings are: fluctuations in the magnetic field; a greater than 1 nT depression of the magnetic field strength below the neighboring background level; a sudden increase in the low-energy ion and electron density that is greater than 5 cm^-3; electron thermal energy less than 100 eV; and the presence of significant He⁺⁺, which indicates solar wind origin for the plasma.

The four panels of Figure 1 show examples of polar cusp crossings for northward, southward, eastward and westward IMF. The upper trace in each panel shows the residual of the magnitude of POLAR MFE data with the Tsyganenko 96 model [Tsyganenko and Stern, 1996]. The second and third traces show the Hydra electron density and energy. The fourth and fifth traces show the Timas low energy range H⁺ density and temperature. Not shown is the He⁺⁺ density. The vertical dashed lines indicate the polar cusp entry and exit.

In the upper left panel of Figure 1, the polar cusp is found from 0457-0532 UT, corresponding to a magnetic local time of the footprint on the surface of the Earth 1214-1250 MLT. During this period POLAR moves from (3.05, -0.09, 5.91) R_E to (2.70, 0.30, 6.64) R_E in SM coordinates. The residual between the MFE data and Tsyganenko 96 model is about 20 nT, the highest electron density is 28 cm^-3, the electron energy is about 40 eV. The data from the Timas low energy range H⁺ shows that the density is 13 cm^-3, and the energy is 90 eV. These are all consistent with the criteria discussed above. In this case, the solar wind dynamic pressure is 2.3 nPa, IMF By=-0.6 nT, Bz=2.3 nT. The solar wind conditions are derived from the WIND key parameters and are time-shifted according to the distance along the Earth-sun line from the WIND spacecraft to 10 R_E and the solar wind velocity Vx component in GSM. The invariant latitude ranges from 79.7°-81.9°. The invariant latitude, here and throughout the paper, was determined by field-line tracing the Tsyganenko 96 model for a dynamic pressure of 2 nPa. The results of this study are not sensitive to this choice of pressure.

The upper right panel shows an example of southward IMF conditions. The solar wind has a dynamic pressure of 2.8 nPa; an IMF By of -5.5, and Bz of -9.7 nT. The POLAR spacecraft is in the cusp from 1740-1750 UT at a magnetic local time from 1116 to 1114 MLT. The magnetic local time was obtained from the difference in magnetic longitude of the northern cusp foot point and that of the subsolar point. As it transverses the cusp plasma POLAR moves from (3.42, -0.39, 3.87) R_E to (3.37,-0.41, 4.19) R_E. This case has one of the largest southward Bz values in our entire data set. The invariant latitude ranges from 73.0-74.2^o. This is also a low invariant latitude for the cusp, but it is not the lowest in the data set.

The lower left panel shows a case for eastward IMF. The solar wind conditions are: a dynamic pressure of 3 nPa; an IMF By component of 4 nT, and a Bz component close to 0 nT. The position ranges from (2.81, 0.24, 5.77) R_E to (2.40, 0.79, 6.61) R_E in SM. The magnetic local time is 1317-1410 MLT, so that the entire pass took place postnoon.

The lower right panel is an example of westward IMF. The solar wind conditions are: dynamic pressure 1.6 nPa; IMF By=-4.2, and Bz= -0.1 nT. The position ranges from (2.33, -0.53, 6.33) R_E to (2.71, -0.44, 5.41) R_E in SM. The magnetic local time ranges from 1018 to 1056 MLT.

Figure 1. Examples of polar cusp crossings for (top left) northward, (top right) southward, (lower left) eastward and (lower right) westward IMF respectively. The upper trace shows the residual of the magnitude of POLAR MFE data with Tsyganenko 96 model. The second and third traces show the Hydra electron density and energy. The fourth and fifth traces show the Timas H+ density and temperature in the energy range 15 eV to 370 eV. The vertical dashed lines indicate the polar cusp crossings.

The Polar Cusp Location

Figure 2 shows the local time and invariant latitude distribution of the footprints of the cusp boundaries, calculated using the Tsyganenko 96 model to trace the magnetic field lines down to the surface of the Earth. The left panel shows the equatorward boundary of the cusp, while the right panel shows the poleward boundary. We remove the dipole tilt-angle effect from these plots based on the observation that the invariant latitude of the cusp increases 1 degree for every 14 degrees increase in the tilt angle [Zhou et al., 1999]. We also restrict these plots in which the solar wind dynamics pressure was less than 4 nPa, to avoid the mantle region and broad cusp observed near the magnetopause. The polar cusp is located from 69° to 87° invariant latitude and the magnetic local time of these crossing ranges from about 0700-1700 MLT. The large scatter is due principally to the motion of the cusp caused by the variations in the IMF that we discuss below.

The central horizontal bars in the figures show the median values. At noon the median upper border of the cusp is 81.5^o and the lower border is 78.8^o invariant latitude. The smooth curves show the least square fit to the median positions as a function of local time. We use the following function to fit the data. The parameters (₀ and A) are shown in Table 1.

=0+A* (MLT - 12)2

(1)

where is the invariant latitude, MLT is the magnetic local time in hours. Also shown in the table are the standard deviation of the residuals of the fit to the 8 median values, and the correlation coefficient.

Table 1. The Least Square Fit to the Polar Cusp Position

	0	A	2	R
Equatorward Boundary	78.8°	0.11	0.73	0.83
Poleward Boundary	81.8°	0.095	0.04	0.94

Figure 2. The invariant latitude-magnetic local time distribution of the polar cusp boundaries: (left) the equatorward boundary; (right) the poleward boundary. The central horizontal bars in the figures show the medians every hour of magnetic local time.

The Solar Wind Control

There is much scatter in Figure 2. Since dipole tilt effects [Zhou et al., 1998] have been removed in this study, the scatter here is due to the solar wind conditions. The cusp changes with solar wind dynamic pressure, IMF Bz and IMF By. Figure 3 shows the invariant latitude of the center of cusp crossings versus IMF Bz again restricted to solar wind dynamic pressures of less than 4 nPa. The cusp center is taken as the average of the entry and exit locations in latitude and longitude. We note that the cusp at the altitude of Polar is long (in local time) and narrow (in latitude) and does not appear to thin with distance from noon. This geometry together with the near vertical line of upsides of the Polar spacecraft means that there are no grazing encounters with the cusp. The spacecraft generally penetrated the cusp cleanly. The horizontal bars indicate the median invariant latitudes within different IMF Bz ranges. For IMF Bz<0, when IMF is more negative, the cusp moves more equatorward, but when IMF Bz>0 the cusp latitude is approximately constant.

Figure 3. The invariant latitude of the center of cusp versus IMF Bz. The horizontal bars indicate the median invariant latitudes every 2 nT of IMF BZ GSM.

In Table 2, we show the parameters of the least square fit to the medians shown in Figure 3 to the equation:

= 0 + m*IMF Bz

(2)

For southward IMF, the invariant latitude of the center of the cusp in degrees becomes just under 1° further equatorward for every 1 nT of southward IMF. The correlation coefficient of the fit is 98%. For northward IMF, the slope is slightly negative (-0.027), i.e., the cusp moves slightly equatorward for increasingly northward IMF. According to the standard t-test, the correlation coefficient of 53% indicates that the slope is inconsistent with the null hypothesis at the 86% level.

The variations of the equatorward and the poleward boundaries with IMF Bz are shown in Figure 4. The fits to the medians are also given in Table 2 for both cases. The two boundaries behave the same way as the center of the cusp. The boundaries move equatorward for southward IMF but remain nearly fixed for northward IMF. The equatorward boundary moves 0.86° equatorward for each nT of southward IMF and 0.07° equatorward for each nT of northward field. The latter variation has a correlation coefficient of 0.76 and is inconsistent with the null hypothesis at the 98% level. The poleward edge moves equatorward 1.08° for every 1 nT of southward field and moves 0.02° for every 1 nT of northward IMF. This latter variation is inconsistent with the null hypothesis at the 74% level.

We have used our best estimate for the instantaneous magnetic field in the solar wind near the Earth using WIND data time-shifted by the solar wind convection time in the x direction. This is consistent with the near immediate response of the location of the cusp to IMF By changes found by Moen et al. [1999]. However, the cusp lies roughly at the boundary between the dayside magnetic field lines and those that are swept into the tail and this interface moves as magnetic flux is carried from the dayside into the tail. Since the location of the cusp should be related both to the history of the IMF and of reconnection in the tail, we do not expect the polar cusp to immediately move to its new equilibrium position in response to a change in the IMF direction and there will be some scatter in this result. To take the effect into account in the motion of the cusp would require both a study of the time history of the IMF and the time since the last substorm in the tail. Since this would be a daunting task in a statistical study of this size, we defer it at this time.

As in our study of the invariant latitude of the cusp with local time, we find from the coefficients in Table 2 that the cusp is about 3^o wide in the latitudinal direction, varying slightly with the north-south component of the IMF.

Figure 4. The invariant latitude of (left) the equatorward boundary, (right) the poleward boundary of the cusp versus IMF Bz. The horizontal bars indicate the median invariant latitudes every 2nT of Bz.

We show explicitly the latitudinal width of the cusp as a function of IMF Bz observed on individual passes in Figure 5. The least squares fit to the medians given in Table 2 indicates that the cusp increases in width with increasingly northward IMF Bz. The cusp is about 2^o wide for an IMF Bz of -10 nT and 4^o wide for an IMF Bz of 10 nT.

Figure 5. The width of the cusp in invariant latitude versus IMF Bz. Horizontal bars show the median values of the width every 2 nT in Bz.

We now consider the effect of IMF By on the cusp position. Figure 6 shows the local time of the encounter with the center of the cusp versus the IMF By for each of three ranges of IMF Bz, northward, horizontal and southward. The northward fields are defined as those more than 15^o above the horizontal direction in GSM coordinates and the southward fields are defined as those more than 15^o below the horizontal. Periods of dynamic pressure greater than 4 nPa have been omitted from these panels. The short vertical bars indicate the medians of the magnetic local time within each 2 nT increment of IMF By. For positive IMF By and northward IMF, there is one bar in the prenoon sector, and three in the postnoon sector. For negative IMF By, there are one in the prenoon and two in the postnoon sector. This is not a significant variation with By.

Figure 6. The local time of the center of the cusp crossings versus the IMF By: (upper) for northward IMF;(center) for horizontal and (lower) for southward IMF. Vertical bars show median values of the magnetic local time every 2 nT of By.

For horizontal IMF, there are one prenoon and three postnoon for positive By and one prenoon and three postnoon for negative By. Again this is not a significant variation althougth there is a tendency to change local time with changing By in the direction found by Newell et al [1989]. For southward IMF, there is clearly a duskward (dawnward) shift for positive (negative) IMF By. Only one point, and one with poor statistics, seems to not follow this trend. This shift is in the same direction as seen at low altitudes in the northern hemisphere. We recall that all the data studied here were obtained in the northern hemisphere, while the low altitude data were obtained in both hemispheres.

In Table 3 we show the parameters of the least square fit to the medians shown in Figure 7 to the equation: