Acta Geod. Geoph. Hung., Vol. 32{1-2), pp. 193-202 (1997)

ARE PULSATIONS WITHIN THE MAGNETOSPHERE AFFECTED BY THE ORIENTATION

AND MAGNITUDE OF IMF?

T A PLYASOVA-BAKOUNINA 1

[Manuscript received April 23, 1997]

The paper discusses observational and theoretical characteristics of geomagnetic pulsation having a source in the solar wind (Pcsw) and in the magnetosphere (Pcm,). respectively. Possible pathways of propagation ere also shown.

Keywords: geomagnetic pulsations; interplanetary magnetic field; solar wind; upstream waves

Introduction

At the present time, the pathways of penetration of the upstream wave en­ergy from the solar wind, as well as their input into pulsation activity within the magnetosphere and at the ground surface, are still unclear. In clarification of this persisting uncertainty, it is very important that we deal only with trustworthy ex­perimental results as such data will provide the bases for selection of the correct model of energy transfer. In this connection, it is critical to determine whether the pulsations recorded on board stationary satellites within the magnetosphere do or do not display the following dependencies: a) is the frequency of occurrence of the pulsations inside the magnetosphere controlled by the orientation of Interplanetary Magnetic Field (IMF) as it is for upstream waves (Russell and Hoppe 1983) and pulsations on the ground (Bolshakova and Troitskaya 1968, Plyasova-Bakounina 1972, 1993, Webb and Orr 1976, Greenstadt and Olson 1977), and b) are the fre­quencies (F) of pulsations within the magnetosphere controlled by the magnitude B of IMF in the same manner as exists for upstream waves (F = 6B) in the solar wind (Fairfield 1969, Plyasova-Bakounina et al. 1978, Russell and Hoppe 1983) and on the ground (Troitskaya et al. 1971, Plyasova-Bakounina 1972, 1993, Gul'elmi et al. 1973, Vero 1986).

Arthur and McPherron (1977) and Takahashi et al. (1981, 1984), when analyzing pulsation data of ATS-6, found clear negative correlation between the angle of the IMF measured from the sun-earth line and the amplitude of pulsations. The frequency of occurrence and the amplitude of both compressional Pc3 and torroidal pulsations Pc3-4, measured at geostationary satellites GEOS-2 and AMPTE, has been associated with low IMF cone angle (Yumoto et al. 1985, Engebretson et al. 1986, Anderson et al. 1991).

1 Institute of Physics of the Earth, Moscow, Russia

1217-8977/97/$ 5.00 ©1997 Akademiai Kiado, Budaput

194 PLYASOVA-BAKOUNINA T A

On the ground, the amplitude and frequency of occurrence of the Pc2-4 pul­sations increases with decreasing cone angle of IMF, a fact demonstrated by Bol­shakova and Troitskaya (1968), Plyasova-Bakounina (1972), Webb and Orr (1976), Greenstadt and Olson (1977), Wolf et a1. (1980, 1987), Yumoto et a1. (1985) and Engebretson et a1. (1986). Analyzing this "angle effect" separately for PCsw (the solar wind-controlled pulsations, which display F = 6B correlation) and for PCmg

(the magnetosphere-controlled pulsations, i.e. standing resonance oscillations on the local field lines, the frequency of which is controlled by magnetosphere struc­ture and plasma parameters), Plyasova-Bakounina (1993) demonstrated that the frequency of occurrence of PCaw increases when the azimuthal angle of IMF is close to 1400 and close to 1800 for PCmg pulsations. Both pulsations are strongly dissi­pated when the azimuthal angle of IMF is 900 • Another unambiguous indication of the two types of pulsations was made by Miletits et a1. (1988).

Several contradictory results have been published relative to the dependence of the periods of the pulsations (T) observed within the magnetosphere on the IMF magnitude (B). Kovner et a1. (1976), Plyasova-Bakounina et a1. (1982), Plyasova-Bakounina (1993) investigated the T(B) dependence of monochromatic pulsations in the period band 20-150 sec which were recorded simultaneously by ATS-1 in geosynchronous orbit and on the ground at two ground stations. Analysis showed that that portion of the monochromatic pulsations recorded within the magnetosphere with periods coinciding with the periods of ground-based Pc activity displays a strong T(B) correlation (T = 160/B, or F = 6B). That portion of the monochromatic pulsations with periods that do not coincide with those of ground pulsation activity did not display any dependence of T on B.

When analizing data of ATS-6, Arthur and McPherron (1977) found no pulsation activity which displayed an F(B) correlation. Takahashi et a1. (1984) demonstrated that the high-harmonic standing waves within the magnetosphere display weak neg­ative correlation of frequency F on B. When analyzing data from the synchronous satellite AMPTE CCM, Engebretson et a1. (1989) found that the central frequency of the envelope of Pc3 power correlates with B.

In contrast to the work cited above, Yumoto et a1. (1984) attempted an anal­ysis of compressional waves recorded at geosynchronous orbit by GEOS-2. They reported a dependence of the frequency of the compressional waves on B as F = 6B (see Fig. 1 of their paper). They have reported also that, in contrast with com­pressional waves, the transverse waves do not display such dependence. Also, they analyzed simultaneously recorded ground pulsation data, concluding that such data display an F = 6B correlation. Yumoto et al. came to the conclusion that F vs. B correlation is good inside the magnetosphere and worse on the ground.

The main purpose of this paper is to reanalize data of Yumoto et al. and to illustrate the error of their conclusion.

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PULSATIONS AND IMF 195

Analysis and discussion

Statistical analysis free of imposed restraint on the solution shows clearly that the data points of Fig. 1 of Yumoto's paper do not fit the relationship F = 6B (see Fig. 1 of this paper). Yumoto et al. forced their solution to go through the point (F = 0, BO = 0). If this restraint is removed, the regression equation is F = 13 + 4B with standart deviation of the slope of 0.4. The center of mass of the point distribution (CM) is located in point (6.67, 39.81). Clearly, the correlation between F and B is weak.

Though Yumoto et al. affirm that the compressional waves within the mag­netosphere exhibit F - B dependence, it is our view that the roundish mass of points with no specifiable structure in Fig. 1 of Yumoto et al. demonstrates it to be most probably composed of both types of pulsations, F - B dependent PCaw and no F - B dependent Pcmg • We believe the fact of lack of F = 6B correlation within the magnetosphere for the compressional waves means that an additional criterion for selection of the F - B dependent pulsations inside the magnetosphere is required. We propose for such a criterion the coincidence of the periods of pulsations recorded

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196 PLYASOVA-BAKOUNINA T A

both in the magnetosphere and on the ground, as was done in Plyasova-Bakounina et al. (1982). Cases of coincidence between the periods of the compressional wave events inside the magnetosphere and pulsations recorded at the several ground sta­tions - which also correspond to the predicted periods of the upstream waves in the solar wind according to the formula T = 160/ B - were demonstrated in the studies of Odera et al. (1994) and Takahashi et al. (1994). These studies support the result of statistical study of Plyasova-Bakounina et al. (1982) and our con­clusion that simple selection of compressional waves is an inadequate criterion for defining the F - B dependent PCsw pulsations inside the magnetosphere.

Supposing that PCsw are present in the inner magnetosphere, we believe that only one point is important: what percentage of the day-time monochromatic pulsation events occurring within the magnetosphere are PCsw ? According to the estimation of Plyasova-Bakounina (1993), the PCsw population within the magnetosphere at geosynchronous orbit consists of only 5% of all day-time monochromatic pulsation events, which implies that the majority of pulsation events inside the magnetosphere are composed of the magnetosphere-controlled pulsations Pcmg •

At the ground surface, the situation is quite the opposite. More than 50% of all day-time monochromatic pulsation events recorded at the middle-latitude station Borok in the Pc2-4 frequency range were composed of Pcsw pulsations, the remainder being PCmg (Plyasova-Bakounina et al. 1986). At the sub auroral and high-latitude stations, PCsw pulsations (range of periods is 5-100 sec) are dominant (Plyasova-Bakounina 1993).

Yumoto et al. also conclude that F vs. B correlation is better inside the mag­netosphere than on the ground. By comparing the results of processing two sets of data which cannot be compared they reached this incorrect conclusion. While selecting only compressional waves (from their point of view F - B dependent pul­sations) when processing data of geochronous satellite, Yumoto et al. made no selection as regards wave type when processing ground pulsation data but used all pulsation events which were recorded whether PC.w or Pcmg • The fact that Yumoto et al. did not restrict analysis to pulsations simultaneously recorded at GEOS and at ground stations is shown by the different numbers of points presented on Fig. 1 of their paper: for GEOS N = 110, for SGC and OWN stations N = 201 and N = 173, respectively.

If they had performed their statistical analysis of pulsation data inside the mag­netosphere for both transverse waves (Pcmg) and compressional waves (partly PCsw ) as they did for pulsations on the ground, they would not have achieved even a poor F vs. B correlation. As a result of mixture of both types of pulsations Yumoto et al. calculated a poor correlation of T with B for ground-based data. The result is as expected, because only by use of the special method of selection of PCsw on the ground surface Plysova-Bakounina et al. (1982) were able to demonstrate that PCsw periods display a very high correlation with B.

Although Alfven resonances in the magnetosphere play the major role in forming the spectrum of PCmg pulsations, we can draw three conclusions about the necessary character of the initial source of the pulsations observed inside the magnetosphere:

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PULSATIONS AND IMF 197

1. their source is located in the solar wind (as their dependence on IMF orien­tation requires);

2. their source has no F-B dependence;

3. their source is multichromatic (broad-band) in nature because inside the mag­netosphere the resonance pulsations are driven at several L-shells simultane­ously (Glassmeier et al. 1984).

A source with such characteristics exists in the vicinity of the bow shock -it is the highly-compressional upstream waves of irregular wave form which are generated by reflected "diffuse" protons (Russel and Hoppe 1983, Yumoto 1988). They are multi chromatic (broad-band) waves. They do not display any F - B dependence. Their appearance depends upon the orientation of IMF as they are generated by reflected protons, the appearance of which in the solar wind strictly connects with the crossing of the IMF field lines of the bow shock. The reflected protons together with upstream waves disappear before the bow shock when the azimuthal orientation of IMF is 900 •

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198 PLYASOVA-BAKOUNINA T A

The dispersion curves of spectra of the excited MHD-waves in the proton plasma of the solar wind show (Fig. 2) that L-waves (Alfven type) are most effectively excited near the gyrofrequency of proton, WB (Stix 1968). The phase velocity Vph = c/n (c = speed oflight, n = refractive index) takes its minimum value in the vicinity of the gY,rofrequency of the protons. Because WB = 0.1 s-1 for typical conditions in the solar wind, Alfven waves are primarily generated in the frequency band of interest to us (low frequeny Pc2-4) although, of course, the compressional waves also are excited.

Upstream waves in the vicinity of the bow shock display a great number of monochromatic waves with frequencies following the formula F = 6B (or W = O.4wB), these waves being generated by the mechanism of the two-beams cyclotron instability (solar wind and reflected protons with "intermediate" function of the velocity distribution) (Russell and Hoppe 1983). Their appearance strongly depends on the orientation of IMF. They are mainly transverse waves, but sometimes they display a strong compressional component.

Given their presence within the solar wind, we require an explanation of how these waves enter the magnetosphere. This issue, which is very complicated, cannot be detailed here but some of the mechanisms supporting our hypothesis will be outlined.

The compressional upstream waves

The compressional upstream waves responsible for PCrng can penetrate into the magnetosphere due to their provoking motion of the boun'dary of the magneto­sphere. The penetration of normally incident compressional waves into the sub so­lar magnetopause (tangential discontinuity) has been considered both theoretically (Verzariu 1973, McKenzie 1970, Yumoto et al. 1984, Yumoto et al. 1985, South­wood and Kivelson 1990) and experimentally (Wolf and Kaufman 1975, Greenstadt et al. 1983, Song et al. 1993, Engebretson et al. 1991). In contrast with Versariu (1973) and Greenstadt et al. (1983), who reported a transition coefficient of incident power of compressional waves of 1-2%, Song et al. (1993) obtained an observed co­efficient of 18%. Inside the magnetosphere, these broad-band, highly-compressional upstream waves couple with Alfven and cavity resonance oscillations at different L­shells, forming PCrng pulsations. The theory of such coupling is developed by Chen and Hasegava (1974), Southwood (1974), Southwood and Kivelson (1990), Fedorov (1992). Because sometimes the monochromatic F - B dependent upstream waves display a strong compressional component, it must explain the existence of only a small portion of such F - B dependent compressional waves inside the magneto­sphere, which penetrate from the solar wind through the subsolar magnetopause.

Considering the magnetopause as a rotational discontinuity and under the as­

sumption that the reconnection of field lines takes place, Kwok and Lee (1984) considered the propagation of ULF waves of all polarizations across the magne­topause. They demonstrate that in this case (in contrast with Versariu's model) their wave power even can be amplified.

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PULSATIONS AND IMF 199

The transversal upstream waves

"High latitude" entry has been suggested for penetration to the ground of the F - B dependent mainly transverse upstream waves (Plyasova-Bakounina et al. 1984, Engebretson et al. 1989,1991). We believe two possible modes of penetration of the energy of the monochromatic transverse waves: one might be a non-linear mechanism of the exchange of energy with the surface waves on the magnetopause, as the PCaw pulsations appear when the condition for development of a Kelvin­Helmholz (K-H) instability on the magnetopause is fulfilled (Golikov et al. 1980). We believe that the corresponding frequencies in the wide spectrum of surface waves being driven by the K-H instability on the flanks of the magnetosphere amplified by interaction with the monochromatic upstream waves (which display F = 6B) by some as yet unknown mechanism. Such waves can observed at the ground surface as PCsw • Another possibile mode for penetration of the energy of transverse waves is reconnection of the field lines (model of Kwok and Lee 1984). The fact demonstrated by Plyasova-Bakounina et al. (1978) that PCsw pulsations are recorded on the ground when the radial component of IMF (B:/:) is directed away from the sun implies that the reconnection of B:/: with magnetospheric field lines takes place in the point which is projected into the cusp/cleft region. The transverse waves are guided along cusp field lines to the ground surface. Such a process explains very nicely that:

1. PCsw display their maximum of intensity in the cusp region (Plyasova­-Bakounina et al. 1984, 1986, Bolshakova and Troitskaya 1984, Engebretson et al. 1986, Morris and Cole 1987);

2. PCsw on the ground displays a pronounced F = 6B dependence.

3. The amplitudes of PCsw pulsations depend on the orientation of IMF.

The other possibility of "indirect" entry of wave energy into the magnetosphere is discussed by Southwood and Kivelson (1991) and Kivelson and Southwood (1991), who developed the mechanism of the non-linear transport into the cusp latitudes of the magnetosheath pressure impulses impinging on the magnetopause. We believe that this model qualitatively fits better for explanation of excitation of pulsations connected with sub-storms (Pil, Pi2) than for monochromatic PCsw pulsations, which do not display any correlation with the Bz component (Plyasova-Bakounina 1993). Finally, we note that Russell and Elphic (1978) proposed a much different model of penetration of the energy of transverse waves by creating on the mag­netopause mini-flux transfer events (FTE's). Though their mechanism may quite possibly be correct for upstream wave penetration into the magnetosphere, presently available data cannot determine the relationships between "FTE events" and "Pcsw pulsations" .

It is still a question how the Pcsw energy reaches the middle and low latitudes. Supposedly, the energy of these waves can be transferred through the ionosphere current system, which is created due to the modulation of the ionosphere conduc­tivity. The modulation can be affected by electron precipitation accompanied by

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pulsation events (Chernous et al. 1986). This idea was developed by Engebret­son et al. who suggested the creation of the 3-dimensional current system, which transfers the energy of the waves not only to low latitudes but also to the inner magnetosphere.

We believe the lack of PCsw inside the magnetosphere testifies that the PCsw

current system is located only at ionospheric heights. A similar situation exists for the DP2 current system which is a response to the southward component of IMF (Nishida 1978). The observation of the magnetic field at satellites at the inner magnetosphere demonstrates the absence of variations which are synchronous with IMF (9) variations.

Conclusion

The fundamental difference between our scenario of penetration of the wave energy and that of others (Yumoto et al. 1984, 1985 and Engebretson et al. 1989, 1991) is that these authors believe that inside the magnetosphere the pulsations display the F - B correlation exactly as upstream waves in the solar wind and PCsw on the ground. Hence, they must construct scenarios which explain such a phenomenon, which actually is a secondary phenomenon, as we have demonstrated in this paper.

Yumoto suggested "direct entry" of the monochromatic F - B dependent up­stream waves into the magnetosphere through the subsolar point of the magne­topause. Then, because "direct entry" is preferable for compressional waves, Yu­moto declares that the monochromatic F - B dependent upstream waves are of com­pressional mode. However, such a conclusion is contradicted both by the theoretical estimation of the exitation of the waves in the proton plasma and by the experimen­tal observations of the monochromatic upstream waves which have demonstrated that such waves are primarily transverse waves. Also, there are difficulties for such a model in explanation of the location of the maximum of the intensity of the F - B dependent pulsations at the cusp area.

In order to explain his observation of the maximum of F - B dependent pul­sations in the cusp region, Engebretson et al. (1989) have suggested penetration of monochromatic F - B dependent upstream waves through the cusp ("high lat­itude entry"). (They did not specify whether the waves were of compressional or transverse type.) But believing Yumoto's statement of the presence within the mag­netosphere of F - B dependent pulsations, Engebretson must try to explain this supposed fact. He hypothesizes a scenario involving the creation of a 3-dimensional field-aligned current system (cusp ionosphere - magnetosphere). The problem of all this development is that Yumoto's conclusion is not correct and Engebretson hypothesis is striving to explain a secondary phenomenon.

Our model of the penetration of the upstream wave energy into the magneto­sphere and to the ground has a merit not found in other models in that we explain the two observed types of pulsations observed on the ground (the F - B dependent solar wind-controlled PC.w and the no F - B dependent magnetosphere-controlled Pcmg) via the two main types of upstream waves known to exist in the vicinity of

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PULSATIONS AND IMF 201

the bow shock. Each type of upstream waves has its own preferred mode of en­try into the magnetosphere. The broad-band highly-compressional upstream waves penetrate through the subsolar point of the magnetopause coupling into Alfven and cavity resonances of the magnetosphere resonator, while the F - B dependent transverse upstream waves penetrate through the cusp forming the F - B dependent PCaw pulsations o~ the ground with maximum intensity in this area.

The energy of PCaw pulsations transfers to low latitudes through the pulsating current system. The lack of PC.w in the magnetosphere testifies that currents do not spread into the magnetosphere. A similar situation exists for the DP2 current system.

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