The Polar Cap Magnetic Activity (PC Index) as a Tool of Monitoring and Nowcasting the Magnetospheric Disturbances

Abstract

PC index was originally introduced as a characteristic of the polar cap magnetic activity generated by geoeffective solar wind coupling with the magnetosphere. Subsequent researches showed that the PC index follows changes of the solar wind electric field EKL through the field-aligned current system (R1 FAC) responding to variations of the solar wind parameters. Appearance of magnetospheric disturbances is specified by the PC index value (with a typical threshold level ~ 1.5 ± 0.5 mV/m) and by the PC index growth rate. The disturbance progression strongly follows the PC index variations, the intensity of substorms (AL) and magnetic storms (Dst) being linearly related to the PC magnitude. In view of these statistically justified relationships, the PC index is regarded at present as a proxy of the solar wind energy input into the magnetosphere. A great advantage of the PC index application over other methods, based on the satellite measurements, is a permanent on-line availability of information on the magnetic activity in both northern (PCN) and southern (PCS) polar caps, providing a means for monitoring the magnetosphere state and for nowcasting the magnetic disturbances development.

1. Introduction

The term “solar wind” is referred to flows of low-energy solar plasma including the magnetic field, which is ejected continuously by the Sun’s surface. The Earth’s magnetosphere is a result of the solar wind impact on the dipole-like geomagnetic field, the form and size of the magnetosphere being determined by the solar wind parameters such as the solar wind velocity Vsw and the solar magnetic field |B| named usually as an interplanetary magnetic field (IMF). It is totally accepted that the solar wind energy incomes into the magnetosphere, the accumulated energy being realized in form of magnetospheric substorms and magnetic storms. Geomagnetic storms are associated with formation of powerful currents flowing around the Earth at the distance of ~3–7 R_E and displayed as a planetary depression of the geomagnetic field (Dst variation) revealing the most power at low- and mid-latitudes [1, 2]. Magnetospheric (or magnetic) substorms [3, 4] are characterized by even stronger magnetic disturbances up to 2000 nT, but they are typical of limited auroral zone, where they are displayed as aurora and are accompanied by a variety of phenomena and processes in the auroral ionosphere.

The polar cap magnetic activity is one of the specific manifestations of the solar wind influence on the magnetosphere, which is displayed in the high-latitude region disposed of poleward of the auroral zone. As it was shown in [5], the polar cap magnetic disturbances correlate the best with the solar wind electric field determined by formula of [6] E_KL = Vsw*(By² + Bz²)^1/2sin²θ/2, where By and Bz are the azimuthal and vertical IMF components and θ is the clock angle between geomagnetic dipole and IMF tangentional component BT = (By² + Bz²)^1/2. The corresponding PC index was put forward [7] as a measure of the solar wind electric field E_KL coupling with the magnetosphere. The numerous subsequent studies (see [8, 9]) showed that the PC index growth determines the development of magnetospheric disturbances, the intensity of the magnetic storm and substorms being related to the PC index value. Thus, the PC index proved to be strongly responding to the solar wind E_KL field changes, and regulating, afterwards, the development and intensity of the magnetospheric disturbance. Based on these experimental results, the International Association of Geomagnetism and Aeronomy (IAGA) approved the PC index as “a proxy for energy that enters into the magnetosphere during solar wind-magnetosphere coupling” [10]. The 1-min PC index is calculated on-line by magnetic data from near-pole stations Qaanaaq (Thule) in the Northern hemisphere (PCN) and Vostok in the Southern hemisphere (PCS) beginning in 1997. The unified method for derivation of the PCN and PCS indices was put forward in [11].

In this chapter the following topics, revealing the PC index significance, are examined: mechanisms of the solar wind influence on the polar cap magnetic activity, relationship between the PC index and the solar wind electric field E_KL, relationship between the PC index and magnetospheric disturbances, the PC index use for checking the actual state of magnetosphere.

2. Mechanism of the solar wind influence on magnetic activity in the polar caps

Magnetic alterations typical of the polar caps in periods free of magnetic disturbances in the auroral zone (substorms) were found by Nagata and Kokubun [12]. They were named DP2 magnetic disturbances [13] to distinguish them from magnetic substorms (DP1). Current systems of DP2 disturbances consist of two vortices with currents flowing sunward in the near-pole region without any peculiarities in the auroral zone, the current intensity is correlated with the southward IMF [14, 15]. As it was shown later [16, 17], the two-vortex DP2 current system is terminated by the geomagnetic latitudes Ф = 50–60° with the focuses located at the morning and evening poleward boundaries of the auroral oval, and the DP2 disturbances can be observed in the polar cap in absence of the southward IMF.

Other types of magnetic disturbances typical of the sunlight summer polar cap are the “near-pole DP variation”, named as DP3 disturbances, which are observed under conditions of northward IMF [16, 18], and magnetic disturbances related to azimuthal IMF [19, 20, 21], named as DP4 disturbance [16]. The DP3 system consists of two vortices with opposite anti-sunward directed currents in the very limited near-pole area. The DP4 system includes currents flowing along geomagnetic latitudes with maximal intensity in the daytime cusp region (Ф ~ 80°), the current direction being determined by sign of the IMF azimuthal component.

Figure 1 shows current systems of DP2, DP3, and DP4 magnetic disturbances, generated under action of the southward B_ZS (a) and (b), northward B_ZN (c), and azimuthal B_Y (d) IMF components [16]. The multi-functional analysis of relationships between the IMF and geomagnetic variations has been fulfilled by Troshichev and Tsyganenko [17] to separate effects of the IMF Bx, By, Bz components in case of their combined influence. Results of the analysis have also demonstrated availability of the DP2, DP3, and DP4 current systems associated with action of the southward, northward, and azimuthal IMF components, respectively. The electric field structure and intensity derived from magnetic DP2 and DP3 disturbances [16] turned out to be in total agreement with results of direct measurements of electric fields at satellite OGO-6 [22] and in balloon experiments [23].

Figure 1.

Current systems of DP2, DP3, and DP4 disturbances related to variations of IMF components: (a) southward B_ZS = -1nT, (b) southward B_ZS = -0.25nT, (c) northward B_ZN, (d) azimuthal B_Y [17].

Mechanism of generation of the polar cap magnetic disturbances became clear when the field-aligned magnetospheric currents were detected onboard the OGO 4 spacecraft [24] and Triad spacecraft [25, 26]. These experiments have fixed a layer of the field-aligned currents on the poleward boundary of the auroral oval (Region 1 FAC system), with currents flowing into the magnetosphere in the morning sector and flowing out of the ionosphere in the evening sector, and layer of the field-aligned currents on the equatorward boundary of the auroral oval (Region 2 FAC system), with opposite directed field-aligned currents. The currents in Region 1 are observed permanently, even during the quiet conditions, whereas Region 2 currents are detected only in periods of magnetic disturbances (Iijima and [27]). The intensity of the field-aligned currents demonstrates the strong dependence on the IMF BY and BZ components and the solar wind electric field [28, 29]. During substorm events, the average latitude width of Regions 1 and 2 increases by 20–30% and complicated small-scale structures are superimposed upon the large-scale field-aligned currents, especially in the nighttime sector (Figure 2).

Figure 2.

Pattern of field-aligned currents derived from Triad data [25].

The field-aligned currents of reverse polarity were found [30] in the near-pole area, at latitudes of Ф > 75°, under conditions of the IMF northward component (not shown in Figure 2). Later these currents were named as NBZ FAC system [31, 32]. The specific BY FAC system, controlled by the azimuthal B_Y IMF component, was separated in the daytime cusp region [33, 34, 35]. This FAC system consists of two current sheets located on the equatorward and poleward boundaries of the cusp, the current directions and intensity being determined by the IMF B_Y sign [34, 36]. Influence of the BY FAC system strongly distorts the effects of the regular R1 and NBZ FAC patterns.

It should be noted that R1 and R2 FAC systems presented in [24, 25, 26] were outlined by the poleward and equatorward auroral oval boundaries. The same result was obtained by [37] by measurements onboard the Viking and DMSP-F7 satellites and by [38] by measurements onboard the ISEE 1 and 2 satellites. It implies that generators of R1/R2 FAC systems are positioned within the closed magnetosphere, not on the dayside magnetopause. Results of the R1/R2 FAC mapping to the equatorial plane [27, 39] have also demonstrated that R1 and R2 field-aligned current systems are located within the closed magnetosphere. Availability of the appropriate plasma pressure gradients in the closed equatorial magnetosphere has been displayed in [40, 41].

The numerical simulations of ionospheric electric field and currents generated by field-aligned currents were fulfilled in [42, 43] with use of satellite data [25, 26] on the FAC intensity and structure and data on ionospheric conductivity in the polar caps. The results of numerical simulations have clearly demonstrated that DP2, DP3, and DP4 magnetic disturbances in the polar caps are generated by the corresponding R1, NBZ, and BY FAC systems, the R1 FAC system being presented constantly irrespective of the IMF B_Z polarity. As this takes place, magnetic effect of the ionospheric Pedersen currents in the summer polar cap with high-conductive ionosphere is roughly compensated by the distant magnetic effect of the field-aligned currents, as a result, the magnetic disturbances distribution is determined by ionospheric Hall currents, in full agreement with the theorem of Fukushima [44]. On contrary, in the winter polar cap with the low-conductive ionosphere, effect of the ionospheric Hall and Pedersen currents is insignificant, and the polar cap magnetic disturbances are determined by the distant effect of the field-aligned currents. The conclusion was made [45] that the field-aligned currents are responsible for generation of magnetic activity in the polar cap.

Relationship between the PC index and really observed field-aligned currents under concrete conditions was examined in [46] based on measurements onboard the SWARM satellites. The analysis, carried out for growth phase of isolated substorms started against the background of magnetic quiescence, showed that increase of the R1 FAC intensity in dawn and dusk sectors of the auroral oval was always accompanied by the PC index growth. On contrary, correlation between the PC index and field-aligned currents in the noon and the midnight sectors of the oval during the substorm growth phase was absent. In paper [47] relationship between the R1 field-aligned currents and PC index was examined for different types of magnetospheric disturbances. The high correlation between the PC index and FAC was found, with zero time lag, for all examined events. Thus, the experimental results are indicative of the magnetospheric field-aligned currents as a driver of the polar cap magnetic activity.

3. Response of PC index to the E_KL field changes

Comprehensive analysis of relationships between the E_KL field and PC index in course of isolated and expanded substorms (see Section 3) observed in 1998–2001 was fulfilled by Troshichev and Sormakov [48] with use of the 1-min E_KL and PC values. To exclude the possible effect of inconsistency between the “estimated” E_KL field (that calculated by solar wind parameters fixed far upstream of the magnetosphere) and actual E_KL field affecting the magnetosphere, in reality, the specific “coordinated” substorms (N = 261) were also examined, when the PC index and E_KL field demonstrated the obviously corresponding variations on the 2-hour interval preceding the substorm onset (SO). The E_KL field raise commencement was taken as a key date (T₀) and correlation between the E_KL and PC quantities over the time period T₀ ± 30 minutes was analyzed. Figure 3 shows distribution of the number of substorms with different coefficients of correlation (R) between the E_KL field and PC index for various types of substorm events. For coordinated substorms, the correlation was so high as R > 0.7 in 98% of events, the delay time in response of PC to E_KL field alterations being extended in the range from 0 to 40 minutes with the pronounced peak at ∆T = 10–20 minutes.

Figure 3.

Histograms of the substorm occurrence over the level of correlation between E_KL and PC for isolated (a), expanded (b) and coordinated substorm events (c) [48].

To ascertain possible influence of the solar wind parameters on the value of ΔT, the relationships between ΔT and such solar wind parameters as the IMF vertical (B_Z), azimuthal (B_Y) and horizontal (B_T) components, the solar wind speed (Vsw) and solar wind dynamic pressure(Pd) were examined, the solar wind parameters being averaged for the interval T₀ ± 30 min. Contrary to the expectations, any single solar wind parameter demonstrated a minor importance in the ΔΤ value setting. In case of the solar wind speed (R = -0.32), only a slight tendency for the decrease of ΔT value with the growth of Vsw was seen. Other solar wind parameters, such as the vertical, azimuthal, and tangential IMF components, did not show any relation to the ΔT value at all.

To reveal the solar wind parameter actually controlling the ΔΤ value, the 1-min values of V_X, B_Z, E_KL and PC fixed in course of coordinated events were smoothed with the use of the boxcar average of the 15-min width, and then they were separated into different groups according to delay value ΔT. The smoothed values of V_X, B_Z, E_KL, and PC were put afterwards through the superposed epoch analysis, the moment of the sudden jump of the 15-min smoothed E_KL being taken as a zero time T₀. The behavior of the smoothed values of V_X, B_Z, E_KL, and PC in course of coordinated events is shown in Figure 4 for the most statistically justified groups with ΔT = 10–12 min (N = 33), ΔT = 13–15 min (N = 53), ΔT = 16–18 min (N = 60) and ΔT = 19–21 min (N = 38). Thin red lines represent the time evolution of V_X, B_Z, E_KL, and PC in course of individual events. Solid black lines show the behavior of the mean V_X, B_Z, E_KL, and PC quantities for each ΔT group. Vertical lines mark the delay time interval boundaries T₀ and T₀ + ΔT, the latter corresponds to the moment when the PC index starts to increase.

Figure 4.

Time evolution of the 15-min smoothed values V_X, B_Z, E_KL and PC observed in case of coordinated events with delay times ΔT = 10–12, 13–15, 16–18 and 19–21 min. [48].

As Figure 4 demonstrates, the solar wind speed by itself is not a decisive factor in the ΔT setting (1st panel): the speeds values, as large as V_X = -800 km/s and as small as Vx = −300 km/s, are common for any ΔΤ group and the time evolution of V_X is not responsive to the moment T₀. The IMF vertical B_Z component (2nd panel) starts to turn down (southward) just at the moment T₀; however, the larger ΔB_Z values are built up at the expense of positive (northward) B_Z IMF preceding the moment T₀, as a result, the delay times ΔT turn out to be shorter under conditions of the northward IMF (averaged for the 1-hour interval). At the same time, the correlation between ΔΤ and the E_KL field (3rd panel) turns out to be quite explicit: the higher the E_KL raise (ΔE_KL) during the ΔT interval is, the shorter the delay time ΔT is. It means that the actual delay time in response of PC index to changes of E_KL field is determined by the E_KL growth rate, not by such solar wind parameters, as the IMF Bz component or the solar wind speed Vsw, contrary to the concept of Dungey [49].

4. PC index as an indicator of the magnetospheric substorms development

Energy and dynamics of magnetic substorms are commonly estimated by AL index, which characterizes intensity of the negative magnetic deviations produced by westward ionospheric currents (auroral electrojets) in the auroral zone [3, 50]. In study [51], the 1-min PCN and PCS indices, calculated by the unified method [11], were used in analysis of substorms observed in 1998–2001 (N = 1798), the substorm sudden onset (SO) being identified as the AL increase by the value more than −100 nT within 15 minutes. It has been demonstrated that the development of magnetic substorms is always preceded by the PC index growth. If the PC index increases gradually and slightly for a long time, the AL index also slowly increases but without SO signatures. The substorm sudden onsets were related to a sharp increase of the PC growth occurring within the 10 min interval proceeding the SO moment. Usually, the PC index continues to grow after the substorm’s sudden onset, the PC growth rate being unaffected by SO. The substorm occurrence sharply increases when the PC index exceeds the threshold level ~ 1 mV/m and reaches the maximum when PC ~ 1.5 mV/m, irrespective of the substorm growth phase duration and type of substorm. Fall of PC value below the threshold level leads to substorm completion.

The following classes of magnetic substorms were selected in [8, 51]: isolated substorms (N = 194) – disturbances, which arise out of the background of quiet conditions (AL ≤ 200nT) lasting as a minimum during three hours prior to substorm sudden onset; expanded substorms (N = 1418) – disturbances which occurred against the background of noticeable magnetic activity in both the auroral zone and the polar cap; delayed substorms (N = 154) – disturbances with sudden onset occurring against the background of invariable, over a long time, magnetic activity substorms. Examples of isolated, expanded and delayed substorms are presented in Figure 5.

Figure 5.

Examples of isolated, expanded and delayed substorms for different levels of PC index in moment of substorm sudden onset PC₀ marked by vertical line [51].

The results [8, 51] demonstrated that substorms commonly start when the PC index exceeds a certain threshold value, i.e. when the energy input into the magnetosphere exceeds a certain crucial level (“energy storage threshold”). It is very essential that this crucial level, dependent on the PC growth rate and the magnetospheric activity grade is not the constant value. If the PC index (i.e. solar wind energy input) grows gradually and slowly, the magnetic activity also steadily increases, but without substorm onset. It implies that the magnetosphere adapts to new conditions in case of slight energy input. It can occur at the expense of the higher energy dissipation (for example, in the absence of magnetic substorm the Joule heating in the auroral ionosphere is much higher in the periods of enhanced magnetospheric convection than in the periods of ordinary convection). Under these conditions, the balance between the incoming and dissipating energies is retained, but level of energy that is necessary and sufficient for substorm beginning is gradually raised. The substorm is generated by “jump of energy input” when the solar wind energy incoming into the magnetosphere suddenly exceeds the existing level of storage energy. It means that substorm can start with any level of magnetospheric activity and irrespective of how long the solar wind energy was entering into the magnetosphere, in contrast to “directly driven” and “loading-unloading” concepts of the substorm development [3, 52, 53, 54, 55]

In case of minor dissipation, when the threshold level is low, the required excess of the energy input over the “storage” energy is insignificant and intensity of the corresponding magnetic substorm will be weak (isolated “magnetic bays” starting against the background of full magnetic quiescence). In case of major dissipation, when the energy crucial level is high, the required excess of the energy input should be significant and the intensity of magnetic disturbance will be, correspondingly, largest (powerful “sawtooth substorms”). In case, when the PC index remains unchangeable for tens of minutes after reaching the threshold level and then sharply raises, the “delayed substorm” are observed. Application of the PC index as a proxy of the solar wind energy that entered into the magnetosphere gives grounds for verification of the “threshold-dependent driven mode” in different manifestations of magnetospheric substorms.

Figure 6 shows relationships between the PC mean and AL values in course of isolated, expanded, and delayed substorms obtained for time intervals before the substorm sudden onset SO (T₀, T₀-5min and T₀-20min) and after sudden onset (T₀ + 5 min, T₀ + 10 min, and T₀ + 20 min) [51]. One can see that the slope coefficient after SO turned out to be twice as much as before SO, as an evident consequence of the aurora particle precipitation leading to the rise of conductivity of the auroral zone ionosphere and formation of powerful westward auroral electrojet during the substorm expansion phase. The isolated, delayed, and expanded substorms demonstrate a similar linear dependency of AL on PC during the substorm expansive phase, with coefficients of correlations changing in range from 0.85 to 0.94.

Figure 6.

Relationships between the mean PC and AL values in course of isolated, expanded, and delayed substorms [51].

5. PC index as a precursor of the magnetic storms progression

Term geomagnetic storm is designated for the geomagnetic field depression produced by ring currents flowing in the inner magnetosphere [1]. Intensity of magnetic storms is estimated by 1-hour Dst index [56] or its 1-min analog - SymHindex. Relationship between the PC index and the magnetic storms progression was examined in [57] with the use of the PC mean and SymH values. The running window of 30-min width was used in the analysis for smoothing the 1-min PC and SymH indices and E_KL field to reveal a link between the processes occurring with quite different time scales (the time scale typical of the E_KL field variations and polar cap magnetic activity is ~1 minute, whereas the ring currents are formed in the inner magnetosphere with a time scale of tens of minutes). Results [9] have demonstrated that exceeding the threshold level PC ~ 1.5 mV/m is a necessary condition for beginning the magnetic storms like to substorms, but duration of the threshold exceeding should be longer than 1 hour to ensure the storm development. Progression of geomagnetic storms generally follows the time evolution of the 30-min smoothed PC index, irrespective of the type and intensity of magnetic storms. Correspondingly, the magnetic storm beginning can be identified as a moment when the PC index steadily exceeds the threshold level. Such identification of the storm beginning turns out to be very fruitful in case of storms with positive DCF effect at the initial storm phase, which is provided by the magnetopause currents responded to the solar wind dynamic pressure.

Three types of magnetic storms were separated in [9, 57] based on peculiarities of the PC index behavior, as follows: “classic storms”, related to ICME impact, with clearly expressed maximum of depression, “pulsed storms”, related to SIR impact, with periodically repeating oscillations in PC and SymH indices, and “combined storms”, which are regarded as the effect of simultaneous ICME and SIR action. Figure 7 shows, as an example, the relationship between the PC time evolution (upper panel) and the storm progression of SymH (lower panel) for different lengths of the storm growth phase in case of classic storms of different intensity (the scale diminution in Figure 7c and d should be taken into account). Thin red lines show the run of the PC and SymH indices in course of individual events, thick black solid lines show the behavior of the PC and SymH values averaged for each storm category and group, the threshold level of PC = 1.5 mV/m being marked by the solid horizontal line on upper panels of each figure. The vertical solid lines indicate the moment of the key date T₀when the PC value steadily (in lapse >1 hour) exceeded the threshold level of PC = 1.5 mV/m.

Figure 7.

Relationships between the PC evolution (upper panel) and the SymH progression (lower panel) for 5 categories of classic storms: (a) Dst = −(30-60nT), (b) Dst = −(60-90nT), (c) Dst = −(90-120nT), (d) Dst = −(120-200nT) and (e) Dst = −(200-400nT) with different PC growth durations [57].

Figure 8 shows relationships between the PC and SymH values for pulsed storms in category of Dst = −(30–60) nT with roughly constant (a) and decayed (b) amplitudes of PC fluctuations, in category of Dst = −(60–90) nT with roughly constant amplitude of PC fluctuations (c), and in category of Dst = −(90–120)nT with varying amplitude of PC fluctuations (d). The beginning of the pulsed storms is determined, like classic storms, by exceeding the PC index above the threshold level PC = 1.5 mV/m. However, the further development of storms turns out to be quite different: instead of steady PC growth, the pulsed magnetic storms demonstrate the repeated irregular PC fluctuations with different periods and different magnitudes (roughly constant, either decayed or alternating) extended over ten hours. The appropriate response in the geomagnetic field depression presents the SymH fluctuations of modified periods and smoothed amplitudes, which implies the different processes’ actions in the magnetosphere. In order to derive the generalized relationship between the PC and SymH indices for pulsed storms, the PC and SymH characteristics, averaged over the main phase duration, were used.

Figure 8.

Relationships between the PC and SymH indices in case of pulsed storms for category SymH = −(30–60) nT with roughly permanent (a) and decayed (b) amplitudes of PC fluctuations, for category SymH = −(60–90) nT with permanent amplitude of PC fluctuations (c), and for category SymH = −(90–120) nT with alternating PC amplitude (d) [57].

The mean values of PCmax and SymHmin derived for different categories of storm intensity and growth phase duration (see black solid lines in Figures 7 and 8) were used in [57] to derive a relationship between the appropriate SymH_MIN and PC_MAX quantities for classic and composite storms. Results of the analysis are presented in Figure 9 for 26 categories of classic storms (a) and 22 categories of composite storms (b), and for their total (c) with inclusion of the mean data for 4 categories of pulsed storms (olive circles), the standard deviation for each category being marked by vertical bars. The relationships between the storm intensity (SymH_MIN) and the foregoing PC_MAXvalue are described best by the linear dependences shown in Figure with corresponding correlation coefficients R.

Figure 9.

Relationship between the associated mean values of SymH_MIN and PC_MAX for classic (a) and composite (b) storms. Panel (c) presents integrated dependence of SymH_MIN on PC_MAX, with inclusion of data for pulsed storms (large squares) [57].

Delay times ΔT in response of SymH_MIN to the PC_MAX occurrence lie in the range from half-hour to some hours, being dependent on dynamics of the PC index alterations. The shortest delay times (ΔT ~ 30–45 min) are observed in case of strong but short PC increases when the ring current is quickly formed at a large distance from the Earth and then quickly deceases. The longer delay times are observed in case of the prolonged and irregular PC index dynamics, which initiates the ring currents formation (and subsequent decay) at various distances from the Earth, with the correspondingly different DR current lifetimes. As a result, the longer and unsteady the PC growth period is, the larger is delay time.

Thus, the intensity of magnetic storms (SymH_MIN) is predetermined by value of the PC_MAXindex, like magnetic substorms. However, it is well to bear in mind that this correspondence was obtained with the use of mean, averaged for 30 minutes, indices for different categories of storms (see Figure 7). The actual value of SymH_MIN (and delay time ∆T) in each concrete storm event will be depended on the PC index dynamics, i.e. on the PC index growth (and decay) rates and duration. It implies that formulas (5)–(7) provide reliable estimations of the storm intensity (SymH_MIN) for low (< 8 mV/m) PC values, the discrepancy between the estimated and actual results being increased while raising the PC index value and duration of action.

6. PC index as a verifier of the solar wind geoefficiency

In spite of statistically justified agreement in response of E_KL field and PC index to action of the solar wind, the correspondence between E_KL and PC can be essentially distorted in the concrete events. The typical examples of consistency and inconsistency between E_KL field and PC index are presented in Figure 10, where the upper panel shows the courses of E_KL (green) and PCmean = (PCN + PCS)/2 (violet), the middle panel is for PCN and PCS indices (blue and red lines), the lower panel shows the AL/AU indices of magnetic activity (which indicate intensity of negative and positive disturbances in the auroral zone), the substorm onsets being marked by vertical dotted line.

Figure 10.

Examples of consistency and inconsistency in behavior of E_KL field and PCN, PCS, PCmean index [58].

Figure 10a demonstrates concerted changes of E_KL, PC, and AL in course of an isolated magnetic substorm on October 2, 2000, when the disturbance started against the background of quiet magnetic field in response to the PC growth related to the E_KL field increase. Figure 10b demonstrates a specific event on August 17, 2001, when the substorm started in response to the PC index jump, but this jump in the ground-based PC index was registered ~10 min ahead of the appropriate increase of the estimated E_KL field. Figure 10c gives example (February 20, 1998), when the electric field E_KL was unchanged and quiet (E_KL ~ 1 mV/m), whereas the PCN and PCS indices demonstrated jump above 2 mV/m, which was accompanied, as usual, by the development of substorm with intensity of AL ~ -400nT. In contrast, on 21 October 1999 (Figure 10d) the E_KL field demonstrated a sharp increase above 2 mV/m for long, but this increase was not followed by the PC index growth. It is worthy to note that validity of the PC index behavior in all cases was certified by reaction of AL index, as a substorm indicator.

It should be reminded that E_KL field is estimated by data on the solar wind parameters, such as the solar wind speed Vsw and interplanetary magnetic field (IMF) components, available at the OMNI database (https://omniweb.gsfc.nasa.gov/). These parameters are fixed onboard the spacecraft located far upstream of the magnetosphere, usually at the Lagrange point L1, far upstream of the magnetosphere (at the distance of ~1.5 million km from the Earth). Thereupon they are reduced to the Earth’s magnetopause, under the silent presumptions that the solar wind observed in the Lagrange point always encounters the magnetosphere, the Vsw and IMF characteristics is not altered on the way from the L1 point to the magnetopause. That is why the inconsistency between the “estimated” E_KL field and PC index should be considered as evidence that the solar wind measured by distant monitors did not contact with magnetosphere at all (case of Figure 10c), either touched sideways to magnetosphere (Figure 10d) or traveled in space with acceleration, as in case of August 17, 2001 (Figure 10b), when the real contact of solar wind with magnetosphere (and jump of PC index) occurred ahead of the “estimated” contact. As results [58, 59] showed, the solar wind, fixed by distant monitors, did not contact with the Earth’s magnetosphere in about 20% of time history and extended in space with acceleration in ~1.5% of examined substorm events. Under these circumstances, the PC index takes on great significance as a filter of the OMNI data applicability for analyses of the solar-terrestrial relationship.

7. Relationships between E_KL field and PC, AL, Dst indices in 23/24th cycles of solar activity

Invariability of relationships between the E_KL, PC and AL, Dst parameters were checked [60] with the use of the daily quantities of these parameters in course of 23/24 solar cycles. Figure 11 shows, as an example, courses of the E_KL, and PCN, PCS daily values in years of solar maximum (2000, 2015) and solar minimum (2008, 2019). One can see that daily values of E_KL and PC on average were higher the threshold level 1.5 mV/m in years of solar maximum and lower the level in years of solar minimum, the PCN, PCS (and PCmean) indices being strongly responded to alterations of the E_KL field irrespective of the solar activity phase.

Figure 11.

Coordinated variations of the daily values of E_KL field and PCN, PCS indices in epochs of solar maximum (2000, 2015) and solar minimum (2008, 2019) [60].

To display relationships between the PC and AL, Dst indices, which are quite different in scales of values and changes, the relative values of PC, AL and Dst (i.e. the running quantities related to their average value for period under examination) were taken in [60]. Figure 12 shows the courses of the relative daily quantities PCmean, AL, Dst in 2000, 2015 and 2008, 2019 years, the PC mean, AL and Dsttraces being marked, correspondingly, by black, red, and green colors. It should be reminded in this connection that correlation between the two quantities remains the same irrespective of the kind, absolute or relative, of quantity. One can see that red traces of AL index in Figure 12 practically hide the traces of PCmean index. It means that the daily values of PC and AL indices alter in almost one-to-one correspondence, irrespective of solar activity, which was maximal in 2000, 2015 and minimal in 2008, 2019. The perfect correspondence in courses of the daily PCmean and AL quantities is consistent with excellent correspondence in variations of the 1-min PCN, PCS, and AL indices in course of substorm events, noticed in [8, 9].

Figure 12.

Coordinated variations of daily values of the PCmean and AL, Dst indices in epochs of solar maximum (2000, 2015) and solar minimum (2008, 2019) [60].

The daily Dst index demonstrates much worse correspondance with PCmean than with AL index in agreement with reduction of correlation between the corresponding 1-min values while passing from AL index to SymH index [9]. Indeed, the AL index reacts to PC index changes in a few minutes, whereas the storm progression responses to the maximal PC value with longer and different delay times (from 30 minutes to some hours), as a result, the storm return phase can last for some hours without evident counterparts in the PC index (see for example green traces in Figure 11, which extended beyond black and red traces). The reason is that the PC index dynamics (i.e. by changes in value, duration and rate of the PC jumps and drops), determines the different disposition of the DR currents within the magnetosphere and, therefore, the different times of their growth and decay.

As Table 1 shows, the correlation between E_KL field and PCN, PCS indices is higher in years of solar minimum (2008, 2019) and worse in years of solar activity maximum (2008, 2015). According to [60] reduction of correlation is related to solar protons (SPE), which intrusion in polar caps extremely increased ionospheric conductivity in the polar caps and violated the regular relationship between the E_KL and PC values. The daily AL index demonstrates the perfect correlation with PC irrespective of the solar activity phase.

Year	a	b	R	Year	a	b	R
	PCN = a + b * EKL				PCS = a + b * EKL
2000	−0.19	1.01	0.85	2000	−0.096	1.04	0.87
2008	−0.08	1.34	0.89	2008	−0.098	1.29	0.91
2015	−0.07	1.02	0.81	2015	−0.16	1.16	0.88
2019	−0.20	1.26	0.87	2019	−0.21	1.33	0.91
1998–2020	0.098	1.106	0.85	1998–2020	0.167	1.161	0.85
	AL = a + b * PCmean				Dst = a + b * PCmean
2000	−37.9	−86.7	−0.94	2000	−1.6	−14.8	−0.69
2008	9.4	−111.1	−0.93	2008	−1.6	−11.9	−0.72
2015	−18.0	−104.8	−0.93	2015	2.4	−15.1	−0.74
2019	−0.4	−114.5	−0.91	2019	2.6	−11.0	−0.73
1998–2020	−12.35	−100.99	−0.93	1998–2020	1.7	−13.8	−0.72

Table 1.

Relationships between the daily values of E_KL field and PCN, PCS indices and between the PCmean and AL, Dst indices described by linear functions (Y = a + b*X) and corresponding coefficients of correlation (R) for years of solar maximum (2000, 2015) and solar minimum (2008, 2019) and for entire period (1997–2020).

Correlation between the yearly values of E_KL, PC and AE, Dst indices in course of 23/24 solar activity cycles was examined [61]. The analysis has demonstrated the remarkable consistency in their variations in 1998–2019, the parameters being perfectly correlated with the yearly values of solar wind velocity Vsw and interplanetary magnetic field, as well as with their product electric field E_KL. As this takes place, the best correlation of the yearly values E_KL, PC, AE, Dst was observed with the total IMF field |B| (R = 0.96, 0.84, 0.88, 0.86 correspondingly), not with the IMF Bz component (R = 0.81, 0.72, 0.69, 0.74), in evident contradiction with the Dungey’s concept.

Results of analyses [60, 61] indicate that calibration coefficients determining relationship between the E_KL field and PC, AL, Dst indices remain unchanged during 23 and 24 cycles of solar activity. It means that mechanisms ensuring the solar wind influence on magnetosphere are valid irrespective of solar activity.

8. Discussion

The PC index has been affirmed as a proxy of the solar wind energy input into the magnetosphere (Resolution No. 3, IAGA 2013; Resolution No. 2, IAGA 2021). What are the physical implications of this certification? There are three well-known concepts explaining the solar wind’s influence on the magnetosphere.

According to the first concept, put forward by [49], the IMF carried by the solar wind contacts with the terrestrial magnetic field at the dayside magnetopause, where the geomagnetic field is northward. When the IMF is southward, the terrestrial field lines will interconnect with the interplanetary field lines, and the electric potential ΔV = l_effE(where E is the interplanetary electric field and l_eff is the effective extent of reconnection zone at the dayside magnetopause) will be mapped along infinitely conducting magnetic field lines into the polar ionosphere ensuring the cross-polar cap potential. As a result, the antisunward plasma convection is generated in polar caps, where the ionospheric plasma attached to interplanetary field lines moves together with the solar wind. The merged field lines will reconnect again in the tail neutral sheet, giving rise to the return magnetic flow, which ensures the dayside magnetosphere balance. The Dungey’s hypothesis provided the big impulse for the researches of the IMF influence on processes in the magnetospheric. Nevertheless, the hypothesis was criticized from the outset with reference to such theoretical problems as validity of the frozen-in condition in the real magnetosphere, ignoring the turbulence in the real magnetosheath and plasma sheet, necessity to make distinction between the physical laws in passive and active plasma regions and so on.

It should be noted that the original Dungey hypothesis does not even mention the field-aligned currents owing to absence of any information about their existence in those times. At present, the FAC systems registered in the satellite experiments are commonly regarded as favoring the Dungey concept. Indeed, the NBZ FAC system fixed in the near-pole area and BY FAC system fixed in the day-time cusp area [30, 32, 34, 35] can be regarded as a result of interconnection of the interplanetary and terrestrial fields under influence of the IMF northward B_Z and azimuthal B_Y components. However, it is well to bear in mind that these FAC systems are always observed against the background of the permanent R1 FAC system, which continues to exist even under condition of the northward IMF. Moreover, the R1 FACs are positioned far inside the magnetosphere, within the plasma sheet boundaries [39, 62]. The permanent availability of the R1 FAC system (affected by EKL field) in presence of independent NBZ (or BY) FAC systems, responding to influence of the northward (or azimuthal) IMF influence, seems to be inconsistent with the interconnection as a reason of the permanent availability of the R1 FAC system. It is possible, that mechanism of interconnection generates, under condition of southward IMF, a specific “SBZ” FAC system (in a similar manner to NBZ and BY systems), but product of this “SBZ” system is added to the effect of permanent R1 FAC system.

The second concept, known as a “viscous-like interaction”, was put forward by Axford and Hines [63], who suggested that the antisunward plasma convection on closed field lines along the boundary layer of magnetosphere can be ensured via the transfer of the solar wind momentum to the magnetospheric plasma across the magnetopause. At present the viscous-like interaction is regarded as a little effective mechanism, it may be responsible for not more than 15% of the polar cap voltage under the normal solar wind conditions. In addition, it was shown [64] that the particles that originated in the magnetospheric low-latitude boundary layer (LLBL) are positioned in the 09–15 MLT time sector equatorward of day-time cusp, whereas the mantle particles are positioned in the same sector poleward of cusp region. The regularity has been confirmed later by Wing et al. [40]. It implies that the whole boundary layer between the solar wind and magnetosphere plasmas is mapped into the narrow daytime sector, not into the dawn and dusk sectors of the auroral oval, where the R1 FAC system is positioned.

The third concept, formulated ten years later by [65], was elaborated in [66, 67]. According to this concept, the solar wind impact on magnetosphere violates the magnetostatic equilibrium in the outer magnetosphere resulting in the formation of the plasma pressure gradients within the magnetosphere. Redistribution of the plasma pressure leads to generation of large-scale dawn-dusk electric field and initiates the magnetospheric field-aligned currents responsible for cross-polar cap electric potential. The concept of the field-aligned currents generated in the equatorial magnetosphere due to formation of the plasma pressure gradients was supported later by statistically justified data on the plasma gradients distribution in the plasma sheet [40, 41]. Thus, Tverskoy’s concept predicted, in fact, the existence of the magnetospheric field-aligned currents discovered by [24, 25, 26]. Concept of [65] declared that plasma gradients in the magnetosphere are determined by the solar wind impact on the magnetosphere, however, the mechanisms ensuring the link between the solar wind parameters (Vsw and IMF B_Y, B_Z components) and the magnetospheric plasma redistribution have not been defined. As for solar wind dynamic pressure (Psw) influence, it should be reminded that the Psw impulses compressing the magnetosphere lead to magnetic disturbances (polar cap magnetic activity and substorms) only if they are accompanied by the corresponding changes in the E_KL field [68].

Thus, the experimental results unambiguously testify that the geoeffective solar wind generates, through the field-aligned currents, magnetic activity in the polar caps. The PC index, characterizing the polar cap activity, demonstrates the best relation to the electric field E_KL = Vsw*(By² + Bz²)^1/2sin²θ/2, which is termed as the solar wind electric field. It should be kept in mind that E_KL field is displayed only in the Earth’s coordinate system (i.e. in the magnetosphere) which is stationary relative to the moved solar wind. Nevertheless, neither of the three above concepts does explain the link between the PC index and EKL field. What is the PC index significance in such a case?

The PC index serves as an indicator of capacity of the solar wind influence on the magnetosphere resulting in generation of the electric fields and field-aligned currents responsible for the magnetospheric convection and polar cap magnetic activity and for development of magnetic disturbances. It is very significant that the value and behavior of the PC index are related to the solar wind parameters being independent of the intensity and duration of the magnetospheric disturbances. Indeed, features of the PC index growth define the onset and intensity of the disturbance, the PC index behavior being independent on the disturbance development; to the contrary, the PC index decline below the threshold level (~ 1.5 mV/m) is followed by prompt decay of disturbances. This specific feature of the index makes it possible to use the PC index not only for monitoring the magnetosphere state but also for nowcasting the disturbance progression.

9. Conclusions

The PC index uniquely responds to variations of the interplanetary electric field E_KL coupling with the magnetosphere, the E_KL effect being transported in the polar caps by means of the field-aligned currents generated in the equatorial magnetosphere due to the plasma pressure gradients. On the other hand, the PC index growth predetermines the development of magnetospheric disturbances (substorms and magnetic storms). These experimental results convincingly testify that PC index serves as an indicator of the solar wind energy that enters into the magnetosphere during the solar wind-magnetosphere coupling. Advantage of the PC index application over other methods, based on the ground-based or satellite data, is permanent on-line availability of information on the magnetic activity in both northern and southern polar caps and, correspondingly, accessibility of information on the solar wind energy input into the magnetosphere. The PC index in this charge might be useful for monitoring the space weather, nowcasting the actual state of the magnetosphere, fitting the solar wind-magnetosphere coupling functions, and validating the utility of the solar wind data presented on OMNI website.

A special procedure agreed in 2011 by the Arctic and Antarctic Research Institute (responsible for the production of PCS index) and Space Institute of the Danish Technical University (responsible for the production of PCN index), ensures the calculation of the 1-min PC indices in quasi-real-time based on data of magnetic observations at the polar cap stations Vostok and Qaanaak (Thule). The PCN/PCS indices are freely available at the website http://pcindex.org.