THE RESPONSE OF THE MAGNETOSPHERE TO THE SOLAR WIND

CHRISTOPHER T. RUSSELL

Originally Published in:
The Magnetospheres of The Earth and Jupiter
edited by V. Formisano, pp. 39-53, D. Reidel Publishing Co., Dordrecht-Holland, 1975

 

1. Introduction

          Almost seventeen years have elapsed since the first probes were sent into the Earth's magnetosphere. Since that time, our understanding of the magnetosphere has gradually evolved to the point that now we have a clear, although at times qualitative, understanding of the dominant physical mechanisms at work in the terrestrial magnetosphere. Many of these processes undoubtedly occur in the magnetosphere of Jupiter also. While their relative importance will be altered by the different scales of the parameters in the Jovian magnetosphere, our understanding of Jupiter will be hastened by our experience in studying the Earth.

          To set the stage for the Pioneer 10 results, we will first review the terrestrial magnetosphere, its topology, morphology dynamics and how the solar wind transfers energy to the magnetosphere. Next we review attempts to predict magnetospheric response to interplanetary conditions, and finally discuss the possibility of inferring interplanetary parameters from geomagnetic records.

 

2. Magnetospheric Topology and Morphology

          The principal controversy of magnetospheric physics in the 1960's concerned the topology of the terrestrial magnetosphere, whether it was open or closed. In the open magnetosphere field lines from the polar cap, which are blown back behind the earth and form the geomagnetic tail, do not return to Earth. Rather, they enter the solar wind. In the closed magnetosphere, all field lines cross the surface of the Earth twice.

          It is now commonly accepted that the magnetosphere is indeed open. The evidence for the open magnetosphere comes from many sources, the strongest of which is the control of the magnetospheric dynamics by the direction of the interplanetary magnetic field, and the nature of energetic particle access to the polar caps. The former evidence has been reviewed by Russell and McPherron (1973a) and the latter by Morfill and Scholer (1973) and will not be repeated here. However, because we have every reason to believe the Jovian magnetosphere is also open, we will discuss the topology of the magnetosphere at some length.

          The principal architect of the open magnetosphere was J. W. Dungey (1961, 1963). Figure 1 shows Dungey's open magnetospheric model for a southward directed interplanetary magnetic field in the top panel and for northward directed fields in the bottom panel In the top panel the southward directed interplanetary magnetic field is carried by the highly electrically conducting solar wind towards the magnetopause, the boundary of the terrestrial magnetic field. If the magnetopause were a perfect superconductor, currents would be set up to cancel this field inside the magnetopause and the interplanetary field would be shielded from the interior. However, the magnetopause is not perfectly conducting and the two fields merge, or, reconnect. At one point on the nose there is a neutral point where the field strength goes to zero. This should not be mistaken for the merging region which is much bigger and which occurs along a line across the nose of the magnetosphere.

Fig. 1. Schematic illustration of the open magnetosphere, for southward, top panel and northward bottom panel, interplanetary fields (Dungey, 1963). These sketches do not attempt to show the correct length of the tail nor the magnitude of the magnetic field normal to the magnetopause. Arrows illustrate plasma flow directions.

          The interplanetary magnetic field lines are carried along by the solar wind exerting a stress on the magnetospheric field lines which were connected in the merging process, and these lines become draped behind the Earth forming a tail The flux in the tail cannot build up forever, so that eventually merging or reconnection must occur here too. Again, there is a neutral point and a merging line which is a continuation of the day side line. We note that this topological discussion should also hold for Jupiter. Since Jupiter's dipole moment is opposite the Earth's, it interacts with northward fields. The relative importance of merging in the Jovian magnetosphere may be quite different. For example, the rapid rotation of Jupiter distorts the Jovian magnetosphere into a tail-like configuration at all local times. Thus, the magnetosphere of Jupiter might be responsive to changes in the stress of the solar wind in ways not found on Earth.

          Returning to Figure 1, the lower panel shows merging for a northward field. This mechanism adds flux to the day side of the magnetosphere and removes it from the tail. There is only weak evidence for the existence of this mechanism.

          Figure 2 shows the morphology of the magnetosphere. First, there is the bow shock which deflects the solar wind, slows it and heats it so it can flow around the Earth. The bow shock is a complex and poorly understood region requiring of much more detailed study. The region of diverted and heated solar wind is called the magnetosheath. Magnetosheath p1asma is also found in the polar cusps which at times appear to be extensions of the magnetosheath into the ionosphere. This region falls between the region of open and closed field lines. The tail consists of two bundles of flux, or lobes, with field towards the Earth in the north lobe and away from the Earth in the south lobe. These two lobes are separated by the plasma sheet. The plane that separates field away from the Earth from that towards the Earth has been termed the neutral sheet even though it is far from neutral.

          In the interior of the magnetosphere is a field aligned 'doughnut' of cold plasma called the plasmasphere. This is the region of corotating cold plasma The cold plasma in the magnetosphere moves along equipotential lines of the electric fields due to corotation al forces and convective forces. Corotational forces are due to the drag of the neutral particles on the ionospheric particles causing them to rotate with the Earth. Convective forces are ultimately due to the tangential stresses of the solar wind on the boundary and in the open magnetosphere cause a flow that intersects the boundary. When these field lines encounter the boundary and merge with the interplanetary field, they open up and lose their cold plasma. Thus, the field lines in the convection dominated region are depleted in cold plasma by this periodic emptying, while the corotation zone can fill up to saturation. On Jupiter the corotation zone is thought to dominate the magnetosphere.

Fig.2. A schematic noon-midnight meridian cross-section of the terresrial magnetosphere (Russell, 1972).

          The same physical processes should act in the Jovian magnetosphere as in the terrestrial magnetosphere. There should be radial diffusion caused by electric and magnetic fluctuations at the particle drift period. There should also be pitch angle diffusion caused by a variety of wave-particle interactions and plasma instabilities. One important process that is presently receiving a lot of attention in magnetospheric physics is field-aligned currents. These currents transmit stresses from the outer magnetosphere to the ionosphere. If the current density becomes too large, these currents develop instabilities and become resistive. Figure 3 shows an example of field-aligned currents in the polar cusp accompanied by a VLF emission (Fredricks et al., 1973). If such wave amplitudes accompanied this current all the way down to the ionosphere a potential drop of 2 kV would have been present on this occasion.

 

3. Magnetospheric Dynamics

Fig.3. VLF elecric field amplitude (top panel) seen in conjunction with field-aligned currents (bottom panel) during a traversal of OGO 5 through the polar cusp (Fredricks et al., 1973).

          While the solar wind dynamic pressure determines the overall size and shape of the magnetosphere, tangential stresses play an essential role in the dynamics of the magnetosphere, particularly of the magnetospheric tail. Since we have recently reviewed the evidence for the role of tangential stress on the magnetosphere and the sequence of events which ensue upon a sudden increase in this stress (Russell and McPherron, 1973a; Russell, 1974a), we will not repeat the detailed evidence here. However, we will briefly review the sequence of events associated with what has been called an isolated magnetospheric substorm.

          Figure 4 summarizes the phenomena observed when the interplanetary magnetic field suddenly changes from north-pointing to south-pointing. This has been called the growth phase. At the nose of the magnetosphere, the magnetopause moves inward. In the tail the boundary increases its flare angle, and the resulting increase in pressure on the boundary results in an increased field strength in the lobes. The plasma sheet thins, tail currents strengthen and the midnight magnetosphere becomes tail-like deep into the magnetosphere.

          Figure 5 illustrates what is commonly thought to occur at the onset of the expansion phase, when auroral breakup occurs. First, the plasma sheet begins to thin fastest close to the Earth so that the neutral points forms or moves to a position close to the Earth. Once the neutral point is formed, reconnection takes place at a rapid rate and the midnight magnetosphere returns to a more dipolar configuration. Eventually, when the 'demand' for merged flux by the magnetosphere is satiated, the neutral point moves tailward. This behavior explains the appearance of southward magnetic fields in the plasma sheet, the thickening of the plasma sheet with variable delays after substorm onsets, the reduction in the tail lobe field strength at the time of substorm onset and the inward moving field compression seen at substorm onsets.

Fig.4. Summary of the magnetospheric changes observed during the growth phase of substorms (Russell, 1974a).

Fig.5. Model of the expansion phase in the tail (after Russell, 1972). Dotted area represents plasma sheet and length of arrows roughly proportional to convective velocity. The X marks the position of OGO 5 during a substorm on August 15, 1968 studied by many authors (see McPherron et al., 1973 and accomanying papers). The asterisk marks the position of Vela during a typical event.

 

4. Predicting Magnetospheric Response

          While much has been learned about the details of magnetospheric processes, the magnetosphere is too complex to use our present knowledge to predict quantitatively the entire sequence of cause and effect within the magnetosphere, given a change in the magnetospheric boundary conditions. Yet it is important for many purposes to be able to predict the magnetospheric response. Thus, several workers have treated the magnetosphere as a 'black-box' whose transfer function is to be determined. The inputs to this black-box are the solar wind parameters: number density and velocity, field strength and direction. The output is usually taken to be one of the geomagnetic indices.

          One of the first successful predictions of magnetospheric response was that of Arnoldy (1971) who used hourly integrals of the north-south component of the interplanetary field to predict the AE index (auroral electrojet index) In his integrations he assumed that northward fields were non-interacting and gave them zero weight. In this way, he achieved an 80% correlation between the integrated southward component and the hourly AE index one hour later. Several important points noted by Arnoldy in this study are:

          A similar approach has been followed by Garrett et al., (1974), who have attempted to model the Kp index and the A index. When they use the same integrated southward component as Arnoldy, they obtain an 80% correlation coefficient. When they use the rectified interplanetary electric field, the coefficient increases to 84%, and when a second term is added such as the variance of the interplanetary magnetic field the correlation coefficient increases to 90%. However, they also show that other functional forms involving the southward field, e.g., V B dt can correlate just as well or even better and that the addition of dynamic pressure terms also improve the correlation.

          The prediction of the Dst index has been undertaken by Burton et al. (1974). First, they divide the index into two parts: that due to the magnetopause surface currents and that due to the ring current. The former currents are taken to be proportional simply to the square root of the solar wind dynamic pressure. The latter currents are considered to be a balance between a source whose strength is a function of the interplanetary electric field and a sink whose strength is proportional to the strength of the ring current. In this model, if the source is turned off, the ring current decays exponentially with a time constant of 8 hours, and if the Y-solar magnetospheric component of the interplanetary electric field suddenly increases to positive values the ring current will strengthen until a saturation level is reached at which the loss rate balances the new source rate.

Fig.6. Comparison of predicted (dashed line) and measured (solid line)
Dst using equations given in text. Upper two panels give the square root of the dynamic pressure and the Y-solar magnetospheric component of the interplanetary electric field.

Figure 6 shows an example of the actual and the predicted Dst , index using this technique. The prescription used here was:

where
with

P is the solar wind dynamic pressure and E is the Y-solar magnetospheric component of the interplanetary electric field. We note that the usual rectification found in such models is centered on 0.5 mV-m here and not on 0.

          The fact that the magnetosphere acts as a rectifier and seemingly does not interact with northward magnetic field (or equivalently negative Y-solar magnetospheric electric fields) has been used to explain the observed semiannual variation of geomagnetic activity (Russell and McPherron, 1973b) and to predict many of the properties of this variation, some of which were known but unexplained at the time of the conception of the model and some of which were discovered later. Most importantly it predicted the separation of the semiannual variation of geomagnetic activity into two annual waves one for each polarity of the interplanetary field. This neatly explains the occasional observations of a 12 month wave in geomagnetic activity (Meyer, 1972). It also explains the 22-yr variation discovered by Chernosky (1966) and predicted the separation of the diurnal variation of activity according to interplanetary polarity (Mishin et al., 1973). However, the magnetic field alone cannot account for all the properties of the semiannual variation and Murayama (1974) has demonstrated that the velocity must play a role. This will be discussed in more detail in the following section.

          Finally, we note that the fact that it is the interplanetary electric field which is the important driving function for geomagnetic activity, rather than simply the southward component, explains quite well the correlation observed between the solar wind velocity and the K index by Snyder et al. (1963). The principal feature of this correlation was an average increase in K with increasing solar wind velocity, but with such scatter in the correlation that almost every possible K value could be found at any solar wind velocity.

 

5. Inferring Interplanetary Conditions from Geomagnetic Records

          The inverse to the problem discussed in the previous section is also of some interest. Geomagnetic records have been kept for over 100 years. If we can infer interplanetary conditions from these records, we can determine, for example, whether the properties of the solar wind measured during the present solar cycle are indeed typical. We may even be able to infer some properties of the solar magnetic field in the extended period in which good optical measurements were taken, but before the solar magnetograph was invented.

          The first step in this direction was taken by Friis-Christensen et al., (1971, 1972) who showed that terrestrial polar cap magnetic variations are sensitive indicators of the interplanetary magnetic field This effect has, in turn, been used to infer the interplanetary magnetic polarity from 1926-1969 (Svalgaard, 1972). However, this technique has its limitations. First, the measurement responds to the Y-solar magnetospheric component of the interplanetary magnetic field not the projection of the field along the expected Archimedean spiral direction which defines the interplanetary polarity and which is ordered in solar equatorial coordinates. (For a discussion of coordinate systems and the transformations from one to another see Russell, (1972). In a test using actual interplanetary data, the sign of the Y-solar magnetospheric component agreed with the spiral polarity of the field only about 85% of the time (Russell and Rosenberg, 1974).

          In applications of the technique to ground-based data, Campbell and Matshusita (1973) found that this upper limit to the accuracy was approached only in the sunlit polar cap, northern summer in the data they used, and only when the signature was large. Overall they found an accuracy of only 60% in predicting interplanetary polarity. Svalgaard (1972) nevertheless, has published an index of interplanetary polarity from 1926-1969. While the above discussion indicates that this index should not be used for the identification of the polarity of specific days or times of sector boundary passages, the index might be useful for statistical purposes if the errors were random. Unfortunately this is not true.

Fig.7. Average A index for C and A days (top panel); yearly average A index and number of C days per year (middle panel) and phase of the annual wave in C days (bottom panel).(Russell and Rosenberg, 1974).

          The top panel of Figure 7 shows the A index for C days, which are days of inferred towards polarity, and A days which are days of inferred away polarity, from 1932 to 1969. Up to about 1962 when in situ measurements of the interplanetary field began, A and C days are quite different geomagnetically. However, after 1962 the traces join and the C/A designation no longer orders geomagnetic activity. This correlation is also shown in the middle panel in a different way. This shows the average Ap index and the yearly number of C days. We note the strong correlation until 1962. This correlation with geomagnetic activity has been found independently both by Fougere (1974) and Russell et al. (1974).

          The bottom panel shows the phase of the annual wave in the C days. A heliographic latitude dependence in the interplanetary polarity has been found by Rosenberg and Coleman (1969). If it were present in the index the phase of the C days should be either - 115 degrees or 65 degrees and should change every solar cycle at the time of the dashed vertical line. It does, indeed, show up for the last two solar cycles but it is not present from 1932 to 1949. For reasons discussed later we interpret this as a decrease in the amplitude of the heliographic dependence of the sector structure rather than a further decay of the index prior to 1949. In light of the correlation of the index with geomagnetic activity, and its poor predictive ability even in the satellite era, we urge extreme caution in the use of this index and suggest that it be reworked, perhaps under the auspices of IAGA.

          Another method of deducing the average solar wind properties in the past is to use the average properties of geomagnetic activity. For example, the discussion of the driving function of geomagnetic activity in the previous section indicates that geomagnetic activity is proportional to the product of the solar wind velocity and the rectified southward interplanetary magnetic field, or some similar function. Thus, we could interpret the decrease in the solar cycle average aa index (Mayaud, 1973) from 1868 to 1907, its subsequent rise to a peak during the IGY solar cycle and then its recent decline as a long term, perhaps periodic, variation in the solar wind velocity, or the strength or variance of the interplanetary field. Examination of high latitude polar cap magnetograms could provide the answer as to whether the interplanetary strength had changed since the signature of Y-solar magnetospheric effect is proportional to the strength of the component (Friis-Christensen et al., 1972).

          The amplitude and phase of the semiannual variation of geomagnetic activity can also be used in this regard. Figure 8 shows predictions of the semiannual variation according to various idealized models. The top model shows the variation expected assuming a fixed 5 nT field along the Archimedean spiral direction, (Russell and McPherron, 1973b). This curve maximizes about April 5 and October 5. If there is a modulation of the dominant polarity of the interplanetary magnetic field as a function of heliographic latitude then this will either enhance or diminish the interaction as sketched in the second panel. The phase will also change. Such a modulation is seen in the interplanetary magnetic field and it switches about 2 years after solar maximum (Rosenberg and Coleman, 1969). This can also be seen in Figure 7, bottom panel. We can remove this effect in the data by averaging data from two successive sunspot cycles.

          The next panel shows the semiannual variation when the variability of the field is added (Murayama, 1974). Here an amplitude of 2.3 nT in B has been assumed. The phase of the maxima are not altered by the introduction of the variability of the field. To alter the phase we must modulate the solar wind velocity, the magnetic field strength or the variability of the field with heliographic latitude. In the bottom panel we show the semiannual variation of the rectified interplanetary electric field from a 5 nT magnetic field with 2.3 nT variability and a 25% velocity gradient from 0-degrees to + or - 7.25 degrees heliographic latitude. Both the phase and amplitude are altered by the addition of the latitudinal variation.

Fig.8. The semiannual variation of the effective component of the interplanetary magnetic field, i.e., the strength of the solar wind-magnetospheric interaction, for several models. The numbers on the abscissa are days of the year.

          Murayama (1974) has shown that the phase and amplitude of the semiannual variation varies with sunspot number. A harmonic dial of these results is shown in the lower right-hand corner of Figure 9. Roughly as sunspot number decreases the amplitude of the semiannual variation increases and the variation maximizes earlier. By modulating the solar wind velocity and introducing differing amounts of variability we can attempt to model this behavior. The upper left dial shows the results when the variability is set equal to zero. This obviously disagrees with observations. The other two dials do mimic the observations quite well. However, a quantitative comparison should await analyses of linear measures of activity such as A.

Fig.9. Harmonic dials of the semiannual variation of geomagnetic activity. The lower right-hand dial shows the observations of Murayama (1974). The other three dials show several model variations.

          Finally, the 22-yr variation of geomagnetic activity (Chernosky, 1966) can be used to measure the amplitude of the heliographic latitude dependence of the dominant polarity of the magnetic field (Russell, 1974b). As discussed above this effect either diminishes or enhances the interaction. Thus, alternate solar cycles, starting two years after solar maximum, should be alternately more active and less active. The bottom panel in Figure 10 shows this effect in the C index. The middle panel shows the amplitude of this cycle to cycle oscillation formed by taking the ratio of each value to the average amplitude of its neighbours and inverting every second ratio. This then should reflect the amount of heliographic latitude dependence of the polarity of the interplanetary field It has been suggested that this variation is in fact due to the overall dipole moment of the Sun (Rosenberg and Coleman, 1969) and thus it appears that the solar polar field strength has changed with time reaching a minimum early this century. In the top panel, we show a smoothed C index for this period It also shows a long term trend As discussed above this could be due to changes in the solar wind velocity, or the magnetic field strength or its variability. We should add a warning here that C is a subjective index which may itself have varied somewhat with time.

Fig.10. The 22-yr cycle as seen in the geomagnetic C index. The bottom panel shows the solar cycle average C index starting 2 years after sunspot maximum. The middle panel shows the ratio of the C index for each cycle to that of its neighbours inverting every second ratio. The top panel shows the average C index with the 22-yr ripple removed.

 

6. Summary and Conclusions

          Nearly two decades of magnetospheric research has revealed the terrestrial magnetosphere to be a complex and dynamic region. The processes occurring therein are in many cases quantitatively and most cases at least qualitatively understood. Merging of the terrestrial magnetic field with the interplanetary magnetic field is a key element in the dynamics of the magnetosphere and ultimately provides the driving force for most magnetospheric processes. Presently, the interaction is understood well enough to predict geomagnetic indices rather accurately, and this understanding can be turned around to infer interplanetary conditions.

          The Jovian magnetosphere should topologically resemble that of the Earth, and the same physical processes should act there as in the terrestial magnetosphere. However, the relative importance of the various processes will be different on Jupiter primarily because its corotation electric field is stronger relative to the merging electric field than in the terrestrial case. Another important difference between Jupiter studies and terrestrial studies, is that we expect a much more rapid advance in our understanding of the Jovian magnetosphere because of our terrestrial experience. Of course this will transpire only if we use this experience. The most important area to which this experience should be used is the proper selection of magnetosphenc instrumentation for future Jupiter missions.

 

Acknowledgement

This work was supported by the National Science Foundation under NSF grant GA 34148-X.

 

References

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