PC INDEX AS A PROXY OF THE SOLAR WIND ENERGY THAT ENTERED INTO THE MAGNETOSPHERE

The paper includes a short review of advantages of the PC index which is a characteristic of the magnetic activity in the polar caps in the northern ( PCN ) and southern ( PCS ) hemispheres. It is demonstrated that the PC index properly responds to variations of the geoeffective interplanetary electric field E KL coupling with the magnetosphere, on the one side, and predetermined the development of magnetospheric disturbances (magnetic storms and substorms), on the other side. These experimental results formed the physical backgrounds for concept that the ground-based PC index characterizes the solar wind energy input into the magnetosphere. It is shown that problem of random discordances in behavior and value of the PCN and PCS indices during the summer/winter seasons is easily solved by choosing the PC index in the winter polar cap ( PCwinter ) as the best characteristic of the polar cap magnetic activity. At present the PC index is successfully applied to


Summary
The paper includes a short review of advantages of the PC index which is a characteristic of the magnetic activity in the polar caps in the northern (PCN) and southern (PCS) hemispheres. It is demonstrated that the PC index properly responds to variations of the geoeffective interplanetary electric field E KL coupling with the magnetosphere, on the one side, and predetermined the development of magnetospheric disturbances (magnetic storms and substorms), on the other side. These experimental results formed the physical backgrounds for concept that the ground-based PC index characterizes the solar wind energy input into the magnetosphere. It is shown that problem of random discordances in behavior and value of the PCN and PCS indices during the summer/winter seasons is easily solved by choosing the PC index in the winter polar cap (PCwinter) as the best characteristic of the polar cap magnetic activity. At present the PC index is successfully applied to Citation: Troshichev O.A., Sormakov D.A. PC index as a proxy of the solar wind energy that entered into the magnetosphere (summary). Problemy Arktiki i Antarktiki. Arctic and Antarctic Research. 2019, 65, 3: 275-299. doi: 10.30758/0555-2648-2019 validate the utility of SW data presented at OMNI website (i.e. to verify whether or not the solar wind, measured in the Lagrange point, encountered the magnetosphere in reality). A special procedure agreed by the Arctic and Antarctic Research Institute (responsible for production of PCS index) and DTU Space (responsible for 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 (Antarctic) and Qaanaaq (Greenland).

INTRODUCTION
At all times the Sun radiates in space a fully ionized, electrically neutral plasma, which was named as solar wind (SW). The solar wind carries a magnetic field B of solar origin named as Interplanetary Magnetic Field (IMF). Under action of solar wind and IMF the Earth's magnetic field is confined to "magnetosphere", the limited region in space, where the plasma processes are guided by geomagnetic field. The state of magnetosphere is strongly controlled by the solar wind energy incoming into the magnetosphere in course of the solar wind -magnetosphere coupling. Different combinations of the solar wind parameters, mainly the solar wind velocity (Vsw) and the vertical (B ZS ) or tangential (B T ) IMF components, were repeatedly examined to reveal the "coupling function" -the optimal combination providing the best correlation between the solar wind changes and the magnetosphere disturbances development. The comprehensive analyses [1, 2] revealed that (1) different coupling functions demonstrate the best correlation with different variables characterizing the magnetosphere state, and (2) the unique coupling function, if it exists, must involve the solar wind velocity Vsw to the first (or a little higher) power, transverse IMF component B T to the first (or a little lower) power, and sine θc to the second (or more) power (θc is clock angle between B T and the geomagnetic dipole).
The solar wind parameters determining the coupling functions are fixed on board ACE spacecraft in the point of Lagrange L1, at distance of 1.5 million km far upstream of the Earth. This circumstance defines the most serious imperfection of all coupling functions because the "estimated" characteristics of solar wind can be quite distinguished from characteristics of real solar wind coming into contact with the magnetosphere. Knowledge of the real solar wind impacting magnetosphere is necessary to monitor the magnetosphere state and to forecast the magnetospheric disturbances, which strongly affect many aspect of human activity. The PC index is intended to estimate the solar wind energy input into the Earth's magnetosphere in actuality.
The PC index has been introduced [3, 4] to characterize the polar cap DP2 disturbances [5] produced in polar caps by southward IMF [6-9]. As results [9] showed, DP2 disturbances are generated by the magnetospheric field-aligned currents (FAC) in Region 1. As measurements at satellites demonstrated [10][11][12][13], the R1 FAC system with currents strongly dependent on IMF, which flow into ionosphere in the dawn sector and flow out of the ionosphere in the dusk sector, is permanently presented on poleward boundary of the auroral oval, the R2 FAC system with opposite directed currents is located on the equatorward boundary of the oval.
Statistical analysis of the relationships between the DP2 disturbances and various coupling functions showed [3] that the polar cap magnetic activity correlates the best with interplanetary electric field E KL determined according to formula of Kan and Lee [14] E KL = Vsw . (By 2 + Bz 2 ) 1/2 sin 2 θ/2 (1) where By and Bz are the azimuthal and vertical IMF components and θ is clock angle between the geomagnetic dipole and the IMF tangentional component B T = (By 2 + Bz 2 ) 1/2 . Based on this result, the PC index, characterizing the polar cap magnetic activity generated by the EKL field, has been elaborated in the Arctic and Antarctic Research Institute This paper summarizes the results of long-standing researches of relationships between the PC index and such solar wind characteristics as interplanetary electric field and dynamic pressure impulses, on the one side, and between the PC index and magnetospheric disturbances (magnetic storms and substorms), on the other side. The aim of the paper is to demonstrate that the PC index can serve as reliable indicator of the solar wind energy, incoming into the Earth's magnetosphere, and can be used in this charge to monitor the current state of magnetosphere and to verify whether or not the solar wind, whose parameters were measured in the Lagrange point, encounters the magnetosphere in reality.

PC INDEX: METHOD OF DERIVATION
The unified technique for derivation of the PCN and PCS indices [15] consists of two separate procedures. In course of the first procedure the statistically justified regression coefficients α (slope), β (intersection) and angle φ, defining relationship between the interplanetary electric field E KL and the DP2 magnetic disturbance vector δF, have been determined for each UT moment of each day of the year, basing on 1-min data of geomagnetic measurements at stations Thule and Vostok and E KL data. Analysis carried out separately for epoch of the maximum solar activity (1998)(1999)(2000)(2001), epoch of the minimum activity (1997,(2007)(2008)(2009) and for the complete solar cycle (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009) has demonstrated [16] a close consistency of parameters α, β and φ for these different epochs of solar activity, if the proper choice of the quiet daily variation (QDC), as a level of reference for estimation of the polar cap magnetic activity, is made. The statistically justified coefficients α, β and φ, ensuring allowance for the diurnal and seasonal changes of δF response to E KL variations, are used in everyday practice for calculation of PCinst index for any instant moment UT РСinst = ξ (δFinst -β)/α (2) where δFinst is value of the DP2 magnetic disturbance in this moment, ξ is the scale coefficient taken equal to 1 for convenience of comparison of the PC index with E KL field (mV/m). Being calibrated for interplanetary electric field E KL the PCN and PCS indices vary in conformity with E KL and consistent, in general, one with another in their value and behavior irrespective of UT time and point of observation. Thorough description of method of the PC index derivation is given in [15,16].

PC index and substorm development
The name "magnetic substorm" was given to magnetic disturbances occurring in the auroral zone [17]. Their distinctive feature is formation of the westward and eastward ionospheric currents (electrojets) and development of corresponding strong negative and positive magnetic disturbances, which intensity is described by the 1-min AL and AU indices [18]. The "substorm" includes a lot of accompanying phenomena in the auroral zone, such as sudden auroral brightening (produced by the auroral particle precipitation), its poleward expansion, simultaneous sudden increase of westward electrojet intensity and others. Рис. 1. Временной ход РС и AL индексов во время развития магнитной суббури. Суббури разделены на три группы в соответствии с величиной РС в момент внезапного начала суббури [19] Relationship between the PC behavior and magnetic disturbances was examined in detail for different types of substorms in [16,19]. Figure 1 shows, as example, time evolution of PC and AL indices in course of isolated substorms observed in epoch of the solar maximum (1998)(1999)(2000)(2001), the value of PC in the winter hemisphere (PCN or PCS) being chosen for the analysis [19]. Substorms were divided into groups according to value of PC at moment of substorm sudden onset (SO) taken as a reference date (T = 0). Thin red lines represent a run of PC and AL in course of individual events. Thick black line represents variation of mean PC and AL values for each group. The following consequences were made: -Development of magnetospheric substorms is always preceded by growth of the PC index.
-The substorm sudden onset (SO) is associated, as a rule, with the distinct PC value growth occurring in range of 0-10 min ahead of SO.
-If PC remains unchanged, the substorm does not begin till moment of the PC sharp growth.
-Occurrence of substorms SO reaches maximum (> 75 %) under values of PC = 1-2 mV/m, irrespective of the substorm growth phase duration and type of substorm.
-The PC growth rate is not affected by the substorm sudden onset. The summarizing conclusion was that development and intensity of magnetic disturbances in the auroral zone is controlled by the PC index level [19] .

Relation of PC index to magnetospheric field-aligned currents
Relationship between the field-aligned currents and the PC index was examined [20] basing on data of SWARM satellites. The Swarm mission includes three satellites, two of them, Swarm A and Swarm C, being flown side by side separated by 1.4° in longitude, at an altitude of about 460 km. Owing to orbital configurations three Swarm satellites covered all sectors of the auroral zone through 2014 year and provided information on field-aligned currents features in different FAC patterns. Method of estimation of the FAC density by data of Swarm measurements is described in [21,22]. The R1 and R2 currents observed by SWARM satellites in dawn (06 MLT ± 4h), dusk (18 MLT ± 4h), noon (12 MLT ± 2h) and midnight (00 MLT ± 2h) sectors of the auroral zone were examined. The downwards currents (flowing into ionosphere) and upwards currents (flowing out of the ionosphere) were regarded, as positive and negative currents, correspondingly.
With aim to reveal a regular relationship between the R1 and R2 FAC intensities and the PC index in course of substorm development, the examination was restricted to growth phase of isolated substorms started against the background of magnetic quiescence. The data of Swarm satellites showed that the field-aligned currents in the morning sector of the auroral zone are always downwards (flowing into the ionosphere) in Region 1 and always upwards (flowing out of the ionosphere) in Region 2. The field-aligned currents in the evening sector of the zone are always upwards in Region 1 and downwards in Region 2. The field-aligned currents in the noon and midnight sectors in both R1 and R2 FAC systems can be positive as well as negative, the downwards currents in Region 2 being related to upward currents in Region 1, and vice versa.
Results of the analysis showed ( Figure 2) that intensity of the field-aligned currents in Region 1 and Region 2 are well correlated (R ~ 0.75), the R1 FAC intensity being nearly