Geomagnetic Field Response along the Polar Orbit to Rapid Changes in the Solar Wind Dynamic Pressure

G. J. Fowler and C. T. Russell

Department of Earth and Space Sciences and
Institute of Geophysics and Planetary Physics
University of California, Los Angeles

Originally Published In: J. Geophys. Res, 106, 18,943-18,956, 2001.

 

Abstract. Magnetometer observations on board the Polar spacecraft have been used to measure the magnetospheric response to rapid changes in the dynamic pressure of the solar wind. Over much of the magnetosphere the magnetic field increases when the solar wind dynamic pressure increases, roughly in proportion to the square root of the change of the solar wind dynamic pressure with a proportionality similar to that seen in ground-based data. Nevertheless dynamic pressure increases can lead to reductions in the magnitude of the magnetic field. These reductions occur on the dayside polar field lines where the magnetospheric field points southward while the perturbation field due to the magnetopause current is northward. Throughout most of the magnetosphere these changes occur slowly over approximately 5-10 minutes as the interplanetary shock envelopes the dayside magnetosphere and near tail. Compressions of the magnetosphere generally lead to increases in the intensity of the ULF waves along the field lines, but in one case the wave intensity decreased upon compression of the field. This decrease occurred in the predawn sector while the increases occurred in the noon to post dusk sector.

1. Introduction

Sudden Impulses (SIs) are caused by sudden increases in the dynamic pressure of the solar wind, generally associated with interplanetary shock waves that at 1 AU are most often caused by the passage of an Interplanetary Coronal Mass Ejection (ICME) [Lindsay et al., 1994]. These pressure pulses compress the magnetosphere and increase the magnetopause tail currents and possibly other magnetospheric current systems as well. The thin interplanetary shock that crosses an interplanetary spacecraft in seconds produces a lengthy response in the magnetosphere because the shock requires many minutes to pass by the magnetosphere and the near tail region [Wilken et al., 1982]. Compressional waves within most of the magnetosphere can communicate the effect of the shock on the magnetopause faster than the disturbance can travel down the tail. Thus the magnetospheric field increases slowly and gradually over about a two to ten minute period. In the limited regions where the shock-induced disturbance moves faster than the local fast mode speed, the compression inside the magnetosphere is shock like. The rise times of these disturbances in the magnetosphere are important because suddenly compressing the magnetosphere can enhance the radial diffusion of energized particles and the energy range of the acceleration depends on the sharpness of the compression. Compressions can also lead to ULF and VLF wave growth, as the pitch angle distributions become flatter due to the conservation of the first adiabatic invariant. It is the purpose of this paper to examine the rise times and the sizes of the compressions throughout the volume of the magnetosphere to aid in our understanding of this source of particle acceleration.

Most previous studies of the magnetospheric response to solar wind pressure changes have used ground-based records, including those of the compression of the magnetic field, and the enhancement of ULF and VLF waves. No statistical in situ study throughout the volume of the magnetosphere has been undertaken. Present literature consists mainly of studies in synchronous orbit and in the tail [Kokubun, 1983; Nagano and Araki, 1986; Patel, 1972; Collier et al., 1998], and a few case studies in the magnetosphere proper such as those of Wilken et al. [1982].

The ground-based studies have attempted to isolate factors affecting this relationship such as local time, altitude, solar activity, tilt angle of the dipole and the IMF direction. Some of the earliest studies were conducted by Siscoe et al. [1968], Ogilvie et al. [1968], Verzariu et al. [1972], Su and Konradi [1975], Burton et al. [1975], Russell et al. [1992], and Russell et al. [1994a,b]. These authors found that the ground level magnetic field (nT) increased proportionately as the change in the square root of the dynamic pressure (nPa½) with a coefficient that ranges from 13 nT/nPa½ [Siscoe et al., 1968] to 34 nT/nPa½ [Su and Konradi 1975]. However, in these early studies of the influence of the solar wind dynamic pressure the authors did not consider the direction of the IMF and its possible effect on the magnetospheric response.

Russell et al. [1994a, b] investigated the ground-based response to dynamic pressure changes with an analysis that separated the SI events into occurrences during either a northward or southward IMF. Russell et al. [1994a] showed from high resolution records that after the initial transient had subsided, the mid-latitude responses for a northward IMF was 18.4 nT/(nPa)½. Equatorial and high latitude responses were more complex because of ionospheric currents induced by the changes in the magnetosphere. In the case of southward IMF Russell et al. [1994b] found that the dayside responses were reduced by 25%, an effect attributed to an increase in the Region 1 Birkeland currents as a consequence of dayside reconnection. Russell et al. [1994a] also found a day-night asymmetry in the response of the magnetosphere. They attributed this to the enhancement of the tail current system by the sudden impulse. In this paper we use the results of these two studies as a qualitative indicator of the relative responses in the magnetosphere and on the ground. Although the sizes of the ground responses to SIs are fairly well understood, the magnetospheric responses are not nearly as well understood.

Finally we note that the effect of magnetospheric compression on the wave populations of the magnetosphere has also been studied using ground-based records [Anderson et al., 1996; Arnoldy et al., 1996, and Dyrud et al.,1997]. These authors determined that Pc 1 bursts were generated on the dayside of the magnetosphere near the magnetic equator and were the result of magnetospheric compressions [Anderson et al. 1996, and Arnoldy et al. 1996].

2. Solar Wind Observations

Five minute and 64-second average solar wind measurements were respectively examined from both the Wind [Ogilvie et al., 1995; Lepping et al., 1995] and ACE spacecraft [McComas et al., 1998; Smith et al., 1998]. Pressure increases that might lead to SIs were identified with the solar wind data by considering significant and abrupt changes in the following components: dynamic pressure, particle density, solar wind velocity in the x-component (GSM) of the solar wind, and magnetic field magnitude. Once a potential SI was identified with Wind data, the arrival time of the pressure change at Earth was estimated based on the XGSE location of the Wind satellite relative to Earth. Figure 1 illustrates solar wind data from the Wind spacecraft for the interplanetary shock on February 18, 1999. The VX component of the solar wind, the number density NP, and dynamic pressure all indicate the passage of the shock beginning at 0240 UT and rapidly increasing at 0245 UT for a total 10-minute interval before settling into a steady state. The apparently lengthy duration of the shock encounter is due to the use of 5-minute averages. Figure 2 is the complementary magnetic field data from Wind for the same event. These data indicate that the IMF has a northward orientation, before and after the shock passage. In this event the magnetic field magnitude continues to increase for an additional 5 minutes beyond the original 10-minute interval of the SI. The expected delay time here is -5 minutes, i.e. the impulse should have arrived at earth before being detected by Wind, because on this occasion Wind was downstream of the subsolar magnetopause.

Figure 1. Solar wind data from WIND spacecraft for pressure increase on February 18, 1999. The signatures in the VX component of the solar wind, the number density NP, and dynamic pressure all indicate the passage of an interplanetary shock at 0240 UT. WIND data shown is 5-minute averages.

Figure 2. Magnetic field data from WIND spacecraft the shock on February 18, 1999. The onset of the shock is at 0240 UT. It is a northward IMF orientation for this event before and after the passage of the shock.

The Solar Wind Electron, Proton and Alpha Monitor (SWEPAM) onboard the ACE spacecraft was used to provide detailed information about solar wind conditions, when they became available (beginning February 4, 1998) since they included the fraction of helium in the solar wind, which could potentially double the solar wind dynamic pressure for high helium abundance intervals. The Wind dynamic pressures have been increased by 16% assuming an average helium content of 4% by number.

Figure 3 provides an example of the ACE data for the same February 18, 1999 shock passage. The dynamic pressure change has occurred because of an interplanetary shock passage as evidenced by the sharp increase in the number density, solar wind speed and the temperature.

Figure 3. SWEPAM data recorded by ACE spacecraft for the February 18, 1999 shock. The shock crossed ACE at 0205 UT.

3. Magnetospheric Observations

Our sample of magnetospheric responses covered 25 SI events in different regions of the magnetosphere. Several events in the sample were excluded in our analysis since the Polar spacecraft was at perigee where spatial gradients are large when the shock arrived at 1 AU. Also, some responses were not analyzed because the Polar spacecraft crossed the magnetopause boundary due to the compression of the magnetosphere and recorded data in regions of magnetic turbulence. Both of these situations affected our ability to measure the response and the data were not analyzed further. Figures 4 and 5 show projections of Polar’s location in the Solar Magnetospheric (GSM) X-Y and Y-Z planes at the time of the SI. As seen in these two projections Polar has sampled the magnetosphere well at the time of sudden compressions of the magnetosphere.

Figure 4. Location of POLAR spacecraft as viewed from north in solar magnetospheric (GSM) equatorial plane. Distances are in earth radii (RE). The symbols denote specific occurrences after the passage of the SI: (o) Events with a decrease in magnetic field magnitude, (+) events with wave amplification, and (-) events with wave attenuation.

Figure 5. Location of POLAR spacecraft as viewed in the antisunward direction in the YZ solar magnetospheric plane. See caption of Figure 4.

The magnetometer on the Polar spacecraft was used to record the magnetospheric response to the dynamic pressure changes in the solar wind. The Magnetic Field Experiment (MFE) as the Polar magnetometer has been named was designed to measure the vector magnetic field in three ranges: ± 700 nanoTesla (nT), 5700 nT, and 47000 nT. Polar was originally placed in a 90o inclination, elliptical orbit with a 9 RE apogee and a 1.8 RE perigee. The orbit began with a southward tilt of less than 10 degrees. Gravitational torques caused the orbital line of apsides to swing over the north pole and continue southward at a precession rate of ~10o/year. This precession will cause future dayside observations at apogee to cross more frequently into the magnetosheath whenever the magnetosphere is compressed.

The magnetic field plots presented in this paper were examined in the field-aligned (FA) coordinate system at full resolution (8 samples/sec). In the FA coordinate system the z direction is always oriented along the magnetic field line determined from the Tsyganenko 96 model for 2 nPa solar wind dynamic pressure, and Dst=By=Bz=0 nT, and records the changes in the magnitude of the geomagnetic field. The y direction is eastward perpendicular to the model magnetic field in the direction that is the cross product of the direction of the magnetic field and the radius vector to the spacecraft. The x direction is along the cross product of the y direction and the model magnetic field. This particular coordinate system was chosen to simplify the analysis of Figures 6-9 which are samples of SI events presented with 3 field components (DBx, D By, DBtotal) rather than the GSM coordinate system that requires the presentation of 4 components not aligned with the localized field. Moreover it separates affects due to the normal stresses that should appear in the x and z directions from those due to field-aligned currents that should appear in the y component. The model used to subtract from the observations to get the residual fields in Figures 6-9 was also 1996 Tsyganenko magnetic field.

3.1 Examples of Magnetic Field Response

When an interplanetary shock compresses the magnetosphere the magnetic field is expected to generally increase throughout the magnetosphere. Compression of the magnetic field should amplify cyclotron waves and in head-on resonance with energetic charged particles if the particles are near marginal stability because any pitch angle anisotropy will be increased by the compression. These "loss cone" instabilities are thought to generate both VLF chorus and Pc1 waves [Brice, 1964]. In this section we examine the quasi-steady-state response of the magnetic field to the pressure change. Section 3.3 compares the observations to the 1989 Tsyganenko vacuum model. Section 4 discusses the wave response. For the purposes of the survey reported below we divide the IMF conditions into northward, horizontal and southward directions if the angle between the field and the GSM equator of the magnetic field is above 15° , between ±15°, and less than -15° respectively.

Figure 6 illustrates the SI that occurred on October 6, 1998 at 1631 UT. From the data recorded by ACE, the passage of this shock changed the steady state solar wind bulk speed from 343 km/sec to 367 km/sec and the number densities of hydrogen and helium jumped from 6 and 0.13 cm-3 to 13 and 0.39 cm-3 respectively, which corresponds to a change in dynamic pressure from 1.29 nPa to 3.27 nPa. The IMF was oriented northward before and after the passage of this shock. During this SI event Polar was at a GSM location of (-6.08, -0.85, 5.38)RE. In this event the field-aligned component of the magnetic field increased in magnitude by 6 nT which was slightly less than the 8 nT expected from the 12.3 nT/nPa½ proportionality found on surface magnetic records by Russell et al. [1994a] for a nightside event in a northward IMF as this event was. This event occurred closer to the tail region (XGSM = -6.08 RE) than any other event in this study and the muted response could be attributed to the tail current counteracting the compression of the tail lobes.

Figure 6. Magnetospheric response recorded by Polar spacecraft for the passage of a shock on October 6, 1998 at 1631 UT plotted in FA (nT). The z direction is along the magnetic field and y is eastward.

Figure 7 shows the event on February 18, 1998 at 0843 UT. ACE recorded increases in solar wind speed from 380 km s-1 to 420 km s-1, number density for hydrogen from 21.5 cm-3 to 32.5 cm-3, and number density for helium from 0.23 cm-3 to 0.41 cm-3 with the passage of the shock, corresponding to a change in dynamic pressure from 5.6 nPa to 10.0 nPa. The IMF had a horizontal orientation throughout the passage of the shock. Polar was at a GSM location of (2.47, 3.00, 0.40)RE. Here the FA component increased quickly at its initial onset and then more slowly reached a steady state after approximately five minutes. Events with sharp onsets, as seen in Figure 7, were not as common in our sample although sharp increases are seen in the near tail and near synchronous orbit as shown for the September 24, 1998 event studied herein and by data observed by Geos 10 [Russell et al., 1999]. Typically, in our sample such rapid field increases were associated with dayside events at lower altitudes, but we have no observations near the equator in our present sample. The sharp increases in the dayside equatorial region are associated with the relatively slow speed of compressional waves here compared to the speed with which the magnetopause is compressed. Although no study has been undertaken of ground magnetograms to determine the proportionality between the field increases and the change of the square root of the dynamic pressure for strictly horizontal IMF conditions, the observed 15 nT increase is similar to the value expected from ground-based studies for northward IMF.

Figure 7. Magnetospheric response recorded by Polar spacecraft for the passage of a shock on February 18, 1998 at 0843 UT plotted in field-aligned coordinates (FA) with z along the magnetic field and y along the direction of rotation of the Earth perpendicular to the magnetic field. Notice the rapid response at the beginning of the rise in contrast to the other much more gradual onsets.

Figure 8, another example of a slow onset, also illustrates the occurrence of transverse oscillations that begin at 0246:30 UT on February 18, 1999 and damp out over several minutes. This event coincides with the dynamic pressure increase shown in Figures 1, 2, and 3. The solar wind speed as recorded by ACE increased from 430 km s-1 to 600 km s-1, the number density of hydrogen increased from 4.6 cm-3 to 10.8 cm-3, and the number density of helium increased from 0.14 cm-3 to 0.86 cm-3. These changes in solar wind conditions led to an increase in dynamic pressure from 1.6 nPa to 8.6 nPa. The IMF had a northward orientation throughout the passage of this shock. Polar was at a GSM location of (-2.39, -1.84, 1.74)RE. The oscillations in the transverse components of the magnetic field had little or no compressional counterpart but clearly appear to be caused by the impact of the shock on the magnetosphere. The magnitude of the magnetic field increase of 5.2 nT was significantly less than the 21 nT expected from the 12.3 nT/nPa½ proportionality constant obtained from ground-based records on the nightside with a northward IMF. The low magnetic response might be a result of Polar being located in a region in which the local magnetic field direction was at a large angle to the field perturbation caused by the increase in magnetopause current. Furthermore, the magnetic field begins to decrease after about 5 minutes. We attribute this decrease to the motion of the shock down the tail enhancing currents that weaken the magnetic field and countering the dayside compression at this location.

Figure 8. Magnetospheric response recorded by Polar spacecraft for the passage of a shock on February 18, 1999 at 0247 UT plotted in FA. This response can be associated with the pressure pulse seen in Figures 1, 2, and 3. Notice the oscillations in the orthogonal components.

In most cases of magnetospheric compression the magnetic field increased in magnitude. However, Figure 9 shows the event on November 7, 1998 at 0815 UT in which the magnitude of the field decreased significantly by 18 nT over an interval of approximately 5 minutes. With the passage of this shock Wind recorded increases in solar wind speed from 425 km s-1 to 465 km s-1 and hydrogen number densities from 6 cm-3 to 11 cm-3, which corresponds to a change in dynamic pressure from 2.48 nPa to 5.48 nPa. The IMF changed orientation from northward to horizontal after the passage of the shock. For this event Polar was at a GSM location of (0.23, -0.32, 5.42)RE. This event was not the only negative response to a magnetospheric compression. In Figures 4 and 5, events with these remarkable reactions are distinguished with open circles. An examination of this figure suggests that magnetospheric responses with decreasing magnitudes are concentrated on the dayside in the noon sector. Figure 5 shows these negative responses occur over the polar cap regions.

Figure 9. Magnetospheric response recorded by Polar spacecraft for the passage of a shock on November 7, 1998 at 0815 UT plotted in FA. The most prominent aspect here is the 18 nT decrease in magnetic field over a five minute interval.

3.2 Overview of the Compressional Response

Table 1 summarizes the magnetospheric steady state responses. Listed in the table are the values obtained from the Wind and ACE spacecraft that quantify the change in the square root of the dynamic pressure after the passage of the shocks. Also listed are the magnitudes of the magnetic field changes related to each event as recorded by the Polar spacecraft. The proportionality constant is the ratio of the change in magnetic field magnitude to the change in the square root of the dynamic pressure. The ratios for each event were used in turn in Figures 10, 11 and 12 which subdivide the events into three categories: low, mid and high altitudes. Based on the z-component in GSM coordinates of the positions plotted in Figure 5 the events were split into three regional categories: low altitude (± 3 RE), mid altitude (3-6 RE), and high altitude (³ 6 RE). These divisions were made to analyze the response on a regional basis within the magnetosphere. Also associated with each event is the orientation of the IMF, which was determined by examining the components of the magnetic fields at Wind and dividing the results into three groups consisting of northward, southward, and horizontal IMF.

Figure 10. Plot of constants of proportionality at low altitudes with events categorized by dayside or nightside occurrence and distinguished by orientation of IMF. ACE data was used in lieu of Wind data when available. The overlying slopes correspond to the ground-based constants of proportionality determined by Russell et al. [1994a,b]: (1) 18.4 nT/nPa½ for dayside responses in a northward IMF; (2) 13.8 nT/nPa½ for dayside responses in a southward IMF; and (3) 12.3 nT/nPa½ for nightside responses in a northward IMF.

Figure 11. Mid altitude constants of proportionality with events categorized by dayside or nightside occurrence and distinguished by orientation of IMF. Comments of Figure 10 apply.

Figure 12. High altitude constants of proportionality with events categorized by dayside or nightside occurrence and distinguished by orientation of IMF. Comments of Figure 10 apply.

Table 1. Changes in the solar wind, dynamic pressure, magnetic field magnitude at Polar, and proportionality between the changes in the field and the change in the square root of the dynamic pressure.

      Change Sq. Rt. Dyn. Press (nPa)½

Change B-Field

(nT)

Response Ratio

nT/(nPa)½

Event Date Event Time (UT) IMF Orientation WIND ACE POLAR WIND ACE

4/2/96

1025

H

0.466

-

4

8.58

-

11/11/96

1527

S

0.641

-

-7

-10.91

-

3/5/97

1345

N

0.845

-

13

15.39

-

3/20/97

2045

N

0.701

-

7

9.99

-

5/1/97

1245

H

0.823

-

23

27.95

-

5/15/97

0159

H

1.865

-

18

9.65

-

5/20/97

0600

H

0.888

-

8.5

9.57

-

9/2/97

2300

N

0.825

-

8

9.70

-

11/1/97

0636

N

0.794

-

5

6.30

-

11/22/97

0950

S

1.454

-

18

12.38

-

2/1/898

0843

H

0.796

0.796

15

18.86

18.85

4/23/98

1825

N

1.343

1.487

23

17.13

15.47

4/30/98

0930

N

1.617

2.251

9

5.57

4.00

8/6/98

0736

S

1.043

1.337

15

14.38

11.22

8/10/98

0047

H

0.725

-

-8

-11.03

N/A

8/19/98

1846

S

0.797

0.804

-17.5

-21.96

-21.78

9/24/98

2345

N

2.164

1.882

57

26.34

30.29

10/2/98

0726

H

1.523

1.435

19

12.48

13.24

10/6/98

1633

N

0.591

0.673

5.8

9.81

8.62

10/18/98

1951

S

0.935

1.083

13.5

14.44

12.46

11/7/98

0815

H

0.835

-

-17.5

-20.96

N/A

11/30/98

0508

S

0.762

0.875

8

10.50

9.14

1/13/99

1054

S

1.003

0.788

-17

-16.95

-21.57

2/17/99

0710

H

0.923

0.808

1.5

1.63

1.86

2/18/99

0247

N

1.873

1.668

5.5

2.94

3.30

               

Since ground-based responses to sudden pressure increases in the solar wind depend on latitude and local time and exhibit overshoots of varying duration, we defer comparison on an event by event basis to future studies and use the statistical results of earlier studies for referencing our in situ magnetospheric compression. Russell et al. [1994a,b] determined the following proportionality constants for the ground based data: 18.4 nT/(nPa)½ for dayside responses in a northward IMF; 12.3 nT/(nPa)½ for nightside responses in a northward IMF; and 13.8 nT/(nPa)½ (25% weaker response) for dayside responses in a southward IMF. A comparison of these proportionality constants to our data is displayed on Figures 10, 11 and 12. The data on these figures are labeled according to the orientation of the IMF, to show how the data compares to the constants of proportionality found by Russell et al. for northward and southward IMF. Generally, most constants of proportionality were consistent with the responses found by Russell et al. [1994a,b] as can be seen on the plots, but with the ground based responses tending more to bracket the in situ magnetospheric responses. We note that the ground-based data were all taken at mid to low latitude whereas the space-based data were generally at high latitudes. Also these ground-based studies investigated changes in the horizontal component of the magnetic field (DH), whereas in space our observations detect changes in magnetic field strength.

3.2.1 Low Altitude

Two events in the low altitude region were significantly less than elsewhere (4/30/98 and 2/18/99). Both of these events were on the nightside of the earth and within close radial proximity to the earth (2.13 RE and 3.48 RE respectively). We attribute the weakness of these events to the enhancement of the tail currents that oppose the magnetopause current enhancement.

3.2.2 Mid Altitude

The February 17, 1999 event at (-2.32, 0.11, 5.56)RE GSM is of particular interest in this altitude region. There was almost no observable response to the passage of the shock at this location over the polar cap at about 6 RE. It appears that the tail currents and the magnetopause current enhancement nearly completely cancelled at this point. Kokubun [1983] observed such behavior for events on the nightside in the equatorial region. A larger sample of SIs is needed to establish a trend in the data for this particular region. The majority of the observations seen in the mid-altitude region were due to weak pressure changes unlike in the other two regions.

3.2.3 High Altitude

Probably the largest event in the high altitude region was due to the interplanetary shock on September 24, 1998 when Polar was at (-2.38, -2.72, 8.13)RE GSM. The details of this event have been presented elsewhere [see Russell et al., 1999]. It is clear from Figure 12 that there is a rough linear relationship among the majority of the points but the existence of regions of low and negative response suggest that a least square fit to the data would not be useful at this stage. From the observations we have not yet been able to constrain the geometry of the negative response region. The ground-based proportionality constants found by Russell et al. are similar in magnitude to these negative and positive space-based values. Part of the weak response appears to be due to the proximity of the tail currents. Such a weak response at synchronous orbit in the night sector near midnight was also found by Kokubun [1983].

3.3 Comparison to T89 Model

Table 2 summarizes the changes in magnetic field magnitudes for the 25 SI events recorded by Polar giving the spacecraft location and the field change in GSM. These in situ observations were subsequently compared to the 1989 Tsyganenko (T89) vacuum model [Tsyganenko, 1989] using the dynamic pressure change upstream and downstream of the interplanetary shock as recorded by the WIND spacecraft. This model was selected because it isolates the effects of the magnetospheric currents and contains no field-aligned currents or diamagnetic plasma. A strong correlation with the predictions of the T89 model would indicate that the response in the magnetosphere is principally due to the increase in the (dayside and nightside) magnetopause currents.

Table 2. Comparison of in situ (GSM coordinates) observation of magnetic field changes for SI event by Polar versus magnetic field changes predicted by the 1989 Tsyganengko vacuum model. The model predictions are based solely on dynamic pressure changes in the solar wind as observed by WIND spacecraft.

    GSM Coordinate (Re) Dynamic Pressure (nPa) Residual B-field components in GSM GSM T89
Event
Date
Event Time (UT) X Y Z Upstream Downstream dBx dBy dBz dBT dBT
4/2/96 1025 -4.17 0.56 7.23 2.668 4.408 3.8 -0.8 -1.2 4.0 2.01
11/11/96 1527 0.87 -1.44 7.98 2.784 5.336 20.5 2.0 10.8 -7.0 5.49
3/5/97 1345 -3.00 -2.07 0.73 1.856 4.872 5.5 5.5 10.0 13.0 7.36
3/20/97 2045 -3.66 -2.06 5.75 3.248 6.264 7.0 1.5 -1.3 7.0 8.51
5/1/97 1245 3.42 1.60 7.92 2.900 6.380 30.0 -3.0 -18.0 23.0 16.50
5/15/97 0159 -1.60 1.52 5.83 3.480 13.920 37.0 3.0 10.0 18.0 16.19
5/20/97 0600 -1.41 2.84 5.14 1.740 4.872 21.0 -1.5 6.5 8.5 14.54
9/2/97 2300 -2.16 -3.99 5.54 2.204 5.336 10.5 -6.5 5.0 8.0 27.39
11/1/97 0636 -1.58 0.17 8.36 6.380 11.020 23.0 3.5 12.0 5.0 3.81
11/22/97 0950 -5.19 3.14 2.21 3.480 11.020 24.0 4.0 -2.0 18.0 13.62
2/18/98 0843 2.47 3.00 0.40 4.640 8.700 -3.5 3.0 14.0 15.0 15.26
4/23/98 1825 2.50 -0.54 -1.62 2.900 9.280 7.0 2.0 23.0 23.0 -1.56
4/30/98 0930 -2.00 0.46 -0.56 2.320 9.860 -9.0 -2.0 16.0 9.0 13.02
8/6/98 0736 2.86 1.11 6.90 2.900 7.540 38.0 3.5 -14.0 15.0 -7.01
8/10/98 0047 2.77 -0.88 6.91 1.160 3.248 24.0 5.0 -3.0 -8.0 -11.92
8/19/98 1846 2.87 1.13 4.54 1.276 3.712 28.5 1.5 2.5 -17.5 -11.34
9/24/98 2345 -2.38 -2.72 8.13 3.480 16.240 68.0 20.0 -15.0 57.0 90.98
10/2/98 0726 -4.98 -0.28 7.39 2.320 9.280 24.5 -8.0 4.0 19.0 7.30
10/6/98 1633 -6.08 -0.85 5.38 1.160 2.784 5.8 0.3 -1.3 5.8 2.68
10/18/98 1951 -3.20 -1.49 7.83 4.060 8.700 23.0 3.5 5.0 13.5 13.49
11/7/98 0815 0.23 -0.32 5.42 1.740 4.640 19.0 3.5 14.0 -17.5 -9.84
11/30/98 0508 -5.25 2.04 6.89 2.320 5.220 13.0 4.0 -1.5 8.0 9.43
1/13/99 1054 0.90 0.04 -1.76 2.320 6.380 -30.0 22.0 2.0 -17.0 -13.96
2/17/99 0710 -2.32 0.11 5.56 2.036 5.510 9.5 0.8 5.0 1.5 -1.33
2/18/99 0247 -2.39 -1.84 1.74 1.160 8.700 1.0 7.0 18.0 5.5 13.33

The data presented in the last two columns of Table 2 are compared in Figure 13. The 1east square fit has a slope close to 0.9 with a correlation of coefficient 0.815. We note that the T89 model predicts decreases in the field consistent with our hypothesis that these decreases occur where the field due to the magnetopause currents is opposite to the magnetospheric field. This effect occurs in a small local time sector centered near noon at high latitudes in both the data and the model.

Figure 13. Change in magnetic field, DBT, observed by Polar versus the D BT predicted by the T89 vacuum model based on the dynamic pressure change upstream to downstream of the interplanetary shock as recorded by the WIND spacecraft. Data from Table 2. Least square fit line is shown.

Figure 13 includes several outliers that lie further from the best fit curve than the others. One set of these, occurring on 11/11/96, 4/23/98 and 8/6/98, were in the region of the magnetosphere in which there was a transition from the external perturbation being parallel to anti-parallel to the internal field. These differences, thus, occurred because the model does not precisely replicate the volume in which the anti-parallel external perturbations occur. Another pair of observations on 9/2/97 and 9/24/98 were obtained well away from the central portion of the magnetosphere, closer to the magnetopause where the local field strength depends more sensitively on the precise shape of the magnetopause that in the real world changes with the interplanetary magnetic field direction unlike the T89 model. Overall the comparison supports our hypothesis that magnetopause current increases are principally responsible for the observed increases and decreases in the field strength. It also suggests that the T89 analytical model imperfectly represents the magnetospheric field confinement.

4. ULF Wave Response

Another interesting phenomenon observed in conjunction with the compression of the magnetic field lines is the occurrence of transverse waves. After applying a high pass filter with a corner frequency at 0.1 Hz to the high-resolution data, four-minute samples of the transverse power before and after the SI at Polar were compared. If a magnetospheric compression takes a marginally unstable loss cone distribution and increases the temperature anisotropy, then transverse waves should be generated and the wave power will increase from before the compression to after it. Ground based studies of Pc 1 waves by Anderson et al. [1996], Arnoldy et al. [1996], and Dyrud et al. [1997] determined that Pc 1 waves are generally generated in the dayside equatorial region when the magnetosphere is compressed.

Figure 14 is an illustration of wave amplification in the frequency range from 0.1 Hz to 0.3 Hz for the event on November 22, 1997. This example shows that dynamic pressure changes in the solar wind are capable of amplifying Pc-2 pulsations. Ground studies also illustrate this behavior. At some frequencies the power density (nT2/Hz) increased by nearly a factor of 10.

Figure 14. Power spectrum of transverse fluctuations for November 22, 1997 comparing the power spectral density before and after the passage of the shock over a frequency range 0.1 Hz - 10 Hz.

Magnetospheric compressions are also capable of generating higher frequency, Pc1, waves as seen in Figure 15 on August 6, 1998, which includes an amplification centered around 1.5 Hz. However, the intensity of the wave amplification at lower frequencies was not as significant for this event compared to the November 22, 1997 compression although the changes in the square root of the dynamic pressure (1.34 nPa1/2 and 1.35 nPa1/2 for 8/6/98 and 11/22/97 respectively) were very similar.

Figure 15. Power spectrum of transverse fluctuations for August 6, 1998 comparing the power spectral density before and after the passage of the shock over a frequency range 0.1 Hz - 10 Hz. Notice the additional wave amplification centered around 1.5 Hz.

Figure 16 illustrates the event of November 7, 1998 in which the wave was amplified over a broad range of frequencies, 0.1 Hz to 1 Hz. The broad range of frequency amplification covers both the Pc-1 and Pc-2 band. Not only is this event interesting because of the broadband wave amplification but also because this amplification occurred when the magnetic field strength was locally decreasing. We do not know if the field strength in the wave generation region was increasing or decreasing at this time.

Figure 16. Power spectrum of transverse fluctuations for November 7, 1998 comparing the power spectral density before and after the passage of the shock over a frequency range 0.1 Hz - 10 Hz. Notice that the wave amplification occurred over a broader band of frequencies and also that this event was previously noted for having a negative magnetospheric response to the shock.

Of all the events studied only five displayed significant changes in the transverse waves, and of those five occurrences only one event, that of March 20, 1997 recorded a decrease in the wave activity as seen in Figure 17. For this event the wave attenuation spanned a frequency range of 0.1 Hz - 0.5 Hz and the spectral density decreased by a factor of 10. The activity in waves for this event indicates that pressure pulses are capable of amplifying waves as well as attenuating them.

Figure 17. Power spectrum of transverse fluctuations for March 20, 1997 comparing the power spectral density before and after the passage of the shock over a frequency range 0.1 Hz - 10 Hz. Notice that in this case there was a decrease in the average power as a result of the compression.

On the power spectra shown in Figures 14-17 are shown the changes in the square root of dynamic pressure for each event, which range from 0.65 nPa½ to 1.35 nPa½. Clearly, wave effects can be generated by only modest changes in the dynamic pressure and a large pressure change is not necessary to cause waves to grow. Several larger pressure changes did not show any significant indication of a change in transverse wave activity. We attribute this to the need for the particle distribution to be near the threshold for instability when the compression occurs.

Indicated on Figures 4 and 5 are the events that had wave amplification (+) or attenuation (-). Wave activity appeared to only occur at higher altitudes. No events were found at a radial distance of less than 5 RE.

The only event with wave attenuation was located on the dawnside. We note that ion cyclotron resonance could generate Pc 1-2 waves with a head-on encounter or an overtaking encounter. A compression of the magnetic field would increase the particles’ pitch angles. This would stimulate further wave amplification by a loss cone instability via the head-on (anomalous) Doppler shifting resonance. However, for a distribution with T||> T^, the direct overtaking resonance would be quenched by the increase in pitch angle.

5. Discussion and Conclusions

Our study of the magnetospheric response to sudden increases in solar wind pressures examined how the response of the magnetospheric magnetic field varied with position within the magnetosphere. Previous ground-based studies have shown that the position of the observer, latitude, and local time are important. In space the third dimension, along the field line, is also important. The decrease in the magnetic field strength is more likely to occur on the dayside rather than the nightside. Wave amplification occurs on the afternoon and duskside and our one event of wave attenuation occurred on the dawnside. The magnitude of the space-based positive and negative constants of proportionality were of similar magnitude to the ground-based constants found by Russell et al. [1994a,b] at low and mid latitudes. However, the Polar values are position dependent because of the varying relative orientation of the external and internal fields so that the ground-based proportionality constants tend to bracket the space-based responses rather than precisely equal them.

Despite the large number of events compared to previous studies a larger sample would still be beneficial to isolate the regional variations. Fortunately Polar continues to operate. Although we attempted to determine whether the response of the magnetosphere to compressions varied with the IMF direction, the variation of the response with location masked any such variation in our data set. It is clear in our study that it is the increase in the magnetopause currents that is responsible for the observed changes. The comparison with the T89 model confirms this association. The rather slow response of the magnetospheric field compared to the sharpness of the causative interplanetary shock is somewhat surprising but can be easily reconciled with the time for the shock to move across the dayside and near-tail magnetosphere. The occasional increase in wave activity is consistent with previous studies but the one example in the dawn magnetosphere of a decrease in wave activity was unexpected.

Acknowledgments

WIND data were provided by K. W. Ogilvie and R. P. Lepping through the CDAWeb. ACE data were provided by D. J. McComas at Los Alamos National Laboratory, C. W. Smith and the CDAWeb. This work was supported by the National Aeronautics and Space Administration under research grant NAG5-7721.

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