A storm in the magnetospheric magnetic field

Yu. P. Maltsev and A. A. Ostapenko

Polar Geophysical Institute, Apatity, Murmansk Region, Russia

Contents

Abstract

Introduction

The magnetospheric magnetic field is

(1)

where B^int is the field due to currents inside the Earth and B^ext is the field produced by magnetospheric currents. The internal field B^int is rather stable; the external field B^ext exhibits a strong variability. In particular, magnetic storms are accompanied by considerable variations in the magnetospheric magnetic field. The main characteristic of a magnetic storm is the hourly Dst index defined as the H component of the magnetic disturbance averaged over magnetograms of several low-latitude observatories located at different longitudes. The Dst index anticorrelates with the AE, AL, and Kp indexes which serve mainly to measure the substorm activity.

It is impossible to build a detailed distribution of the external magnetospric field during a particular storm because of an insufficient number of spacecraft, and, therefore, we are limited to statistical studies. In previous works the external field was studied in relation with the other than Dst indexes or with the Dst index, but in separate limited magnetospheric regions. For instance, Sugiura and Poros [1973] considered the field at 3-23  R_E for quiet ( Kp = 0-1 ) and slightly disturbed ( Kp = 2-3 ) conditions. In the inner magnetosphere ( r < 5 R_E at noon and r < 10 R_E at midnight) the external field was found to be directed preferentially in the negative z direction (in the SM coordinate system). A similar result was obtained by Mead and Fairfield [1975] who approximated the external field at the distances from 4 R_E to 17 R_E by second-degree polynomials in the geocentric distance.

The dependence of the field on the Dst index was analyzed in the equatorial plane at 2.3-3.6  R_E only. For these distances the empirical relation for the field averaged over longitude was obtained [Sugiura, 1973]

(2)

The external field at 4-8.8  R_E near the equatorial plane was plotted by Iijima et al. [1990] for long disturbed periods ( 2 Kp 6, -70 Dst -20 nT). A strong azimuthal field inhomogeneity which is likely to be due to the fact that the current in the nightside magnetosphere is by a factor of two or three stronger than in the dayside magnetosphere was discovered.

Ostapenko and Maltsev [1997] approximated the fields at 3-10  R_E by the forth-degree polynomial in the geocentric distance. The polynomial coefficients were sought for as a linear combination of Dst and Kp indexes, dynamic solar wind pressure, and vertical IMF component. The dependence on Dst proved to be similar to that described by (2). With increasing distance from the Earth the dependence on Dst becomes weaker and at r = 10 R_E it is negligibly weak. Earlier a similar result was obtained by Fairfield et al. [1987] for dependence of the external field on the Kp value.

So far the statistical dependence of the tail lobe field on the Dst index has not been studied. It was found that the tail lobe field grows with the AE index [Baumjohann et al., 1990]; the AL index [Nakai et al., 1991]; the southward IMF component [Fairfield and Jones, 1996; Nakai et al., 1991]; and dynamic solar wind pressure [Fairfield and Jones, 1996; Nakai et al., 1991; Ostapenko and Maltsev, 1998].

Up until now the field variations caused by a storm have not been studied for the entire magnetosphere. The goal of this work was to investigate the response of the magnetic field at distances -30 R_E < x < 10 R_E ; -15 R_E < y < 15 R_E ; and -15 R_E < z < 15 R_E to changes in the Dst index.

Treatment of the Data

The database described by Fairfield et al. [1994] was used. It includes more than 70,000 three-component magnetic field measurements carried out by 11 satellites in the region from 3 to 60  R_E during 20 years. All the magnetic field measurements are supplemented by hourly Dst indexes and three-hour values of the Kp index. 67% of the data are complemented by hourly averages of the dynamic solar wind pressure p and three IMF components. For 47% of the data in the database, an hourly AE index is also given.

We used the data for the region -30 R_E < x < 10 R_E, y < 15 R_E, and z < 15 R_E. Depending on the Dst value, the initial data set was divided into three subsets. Table 1 shows the number of data points N in each subset and average values of Dst, Kp, AE, p, and IMF B_z. For each subset the external magnetic field was averaged over a three-dimensional mesh with the side length of 4  R_E.

In averaging, the dawn-dusk and north-south symmetries were taken into account. For distances x > -10 R_E, the SM coordinate system with the z axis antiparallel to the Earth dipole axis was used. For distances x < -10 R_E, in the magnetotail, the GSM coordinate system with the x axis pointed toward the Sun was employed. To improve spatial resolution in the vicinity of the neutral sheet which experiences considerable variations due to changes in the Earth dipole tilt, we introduced the coordinate z = z_GSM - z_ns, where z_GSM is the solar-magnetospheric coordinate and z_ns is the coordinate of the neutral sheet determined from expression [Peredo et al., 1993].

where y is the Earth dipole tilt angle, H₀ = 9 R_E, D = 7 R_E, and y₀ = 13.5 R_E.

Results

Figure 1 shows the magnetic field B^ext due to external sources in the noon-midnight meridian plane for three magnetic activity levels: Dst > 0 ; 0 > Dst > -50 nT; and Dst < -50 nT. In the tail lobes the field is nearly horizontal. It is evident that this field is produced by the electric current in the plasma sheet flowing from east to west. The current grows with increasing storm activity. On the front side of the magnetosphere (at x > -10 R_E) the field has a more complicated structure.

Figure 2 shows isolines B_z^ext = const in the equatorial plane (z = 0). It can be seen that magnetic depression spreads over the major part of the magnetosphere. As the storm intensity grows, the depression deepens and expands.

Figures 3, 4, and 5 present isolines B_x^ext = const and B_y^ext = const in the x = -20 R_E, x = -10 R_E, and x = 0 planes, respectively. B_x^ext is seen to grow with increasing storm intensity. The B_y^ext component depends on the Dst index in the x = -10 R_E and x = 0 planes. The greatest increase in both components with storm enhancement is observed in the x = 0 plane.

To find the magnetospheric response to variations in the Dst index, we subtracted the left panel of Figure 1, which corresponds to quiet conditions (Dst > 0), from the right panel (Dst < -50 nT) plotted for the storm conditions. The result is shown in Figure 6.

Discussion

The external field B^ext is typically presented as a sum of the fields of four magnetospheric currents

(3)

The right-hand side of (3) includes the fields of the currents at the magnetopause, ring current, tail current, and field-aligned currents. The fields due to each of these currents in the noon-midnight meridian plane are shown schematically in Figure 7.

Comparison of Figures 1 and 7 reveals that the effect of the tail currents B_ct dominates at all levels of magnetic activity. Only near the dayside magnetopause the field of the currents at the magnetopause B_mp dominates. The effect of the ring current B_rc is rather weak. Most likely, it manifests itself in the increase in depression with approaching the Earth (Figure 2). The effect of field-aligned currents B_fa is even weaker.

It can be seen from Figures 3 and 4 that the magnetic field in the tail lobes grows with increasing depression during a storm. This points to intensification of tail currents.

Figure 5 demonstrates that the greatest growth in B_x during a storm takes place in the near-Earth tail lobes, at x = 0. This means that the near-Earth region of the tail current increases. Note that according to Figure 7 the ring current gives (  B_rc)_x =0 in the x = 0 plane. It can be expected that during a storm the region 1 fieldaligned currents inflowing into the ionosphere in the morning and outflowing in the evening will also become more intense. Above the Earth poles the x components of the fields due to the field-aligned and tail currents have the same sign (see Figure 7). At the magnetic shells located lower than the field-aligned current, the B_x component produced by the field-aligned current changes the sign, thereby weakening the field in the low-latitude regions of the near tail lobe. Thus the field-aligned current gives rise to irregularities in the magnetic field in the near-Earth tail lobe. This irregularity is seen at the top of Figure 5, but it is not very pronounced. This suggests that the tail currents give rise to a stronger magnetic effect in the x= 0 plane than field-aligned currents.

The B_y component of the external field is nearly independent of Dst at distances x = -20 R_E (Figure 3). A slight dependence on Dst appears at x = -10 R_E (Figure 4). In the x = 0 plane passing through the Earth center the B_y component exhibits a very strong dependence on storm intensity (Figure 5).

Magnetic depression is observed in the major part of the equatorial plane of the magnetosphere at all activity levels (Figure 2). As the storm activity grows, depression increases and expands to more distant regions. The epicenter of depression is shifted relative to the Earth center by approximately 3  R_E toward the night side. Note that measurements for distances less that 3  R_E are not available, and so isolines in this region in Figure 2 are the result of interpolation. Sugiura [1973] studied the field in the equatorial plane at 2.3-3.6  R_E. For the field averaged over longitude the empirical relation (2) was obtained. Iijima et al. [1990] plotted the field distribution near the equatorial plane at 4-8.8  R_E for -70 Dst -20 nT with the average value of Dst of -34 nT. The field distribution in Figure 2 is similar to that obtained by these authors, but it is more smooth. This is caused probably by the fact that we used larger meshes for field averaging. Otherwise we would not have had enough data to plot the field dependence on the Dst index for the entire magnetosphere volume.

The differential field shown in Figure 6 resembles most of all the field B_ct in Figure 7. This implies that mainly the tail current increases as the storm becomes more intense.

Conclusions

Variations in the external magnetic field at distances up to 30  R_E have been studied as a function of storm intensity. It has been shown that for all storm activity levels the effect of magnetotail currents dominates. As the storm enhances, the tail current effect becomes stronger. The field due to magnetopause currents prevails in the distant region of the dayside magnetosphere.

Acknowledgment

References

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