Application of a Global Magnetospheric-Ionospheric Current Model for Dayside and Terminator Pi2 Pulsations

Application of a global magnetospheric-ionospheric current model for dayside and terminator Pi2 pulsations

S. Imajo1), A. Yoshikawa2),3), T. Uozumi3), Shin. Ohtani4), A. Nakamizo5), P. J. Chi6)

1) WDC for geomagnetism, Kyoto, Kyoto University, Japan 2) Department of Earth and Planetary Science, Kyushu University, Japan. 3) International Center for Space Weather Science and Education, Kyushu University, Japan. 4) Johns Hopkins University Applied Physics Laboratory, USA. 5) National Institute of Information and Communications Technology, Japan. 6) Institute of Geophysics and Planetary Physics, University of California, USA

The results are included in the published paper:

Imajo, S., A. Yoshikawa, T. Uozumi, S. Ohtani, A. Nakamizo, and P. J. Chi (2017), Application of a global magnetospheric-ionospheric current model for dayside and terminator Pi2 pulsations, J. Geophys. Res. Space Physics, 122, 8589‒8603, doi: 10.1002/2017JA024246. Key points

• The magnetic ﬁelds derived by a numerical M-I current model reproduce observed spatial characteristics of dayside and terminator Pi2s.

• The oscillating global ionospheric current driven by localized nightside FACs can be a main source of dayside Pi2s.

• The terminator effects on Pi2s can be explained by a change in the main contributing currents between FACs and ionospheric currents. Chapter 3. Solar Terminator Eﬀects on Pi2 Pulsations 29

(a) 2011/11/26 AL index (b) 2012/03/06 AL index (c) 2012/03/26 AL index 0 0 0 AEI AL AEI AL AEI AL −500 −500 −500 [nT] [nT] [nT] −1000 −1000 −1000 2100 2130 2200 2230 2030 2100 2130 2200 2030 2100 2130 2200 UT[hhmm] UT[hhmm] UT[hhmm] 2011/11/26 filt 040−150 data 2012/03/06 filt 040−150 data 2012/03/26 filt 040−150 data HVD H −0.5 −1 HVD H (ΔTsr=−1.8 h) −1 Δ HVD H θ =42.0, θ =8.1, ( Tsr=−2.3 h) −1 Δ −1.5 H H θ =8.8, ( Tsr=−2.5 h) C =0.99 −1.5 C =1.00 −1.5 H H ASB H H ASB H C =0.99 −2 −2 H ASB H (ΔTsr=1.4 h) (ΔTsr=1.3 h) −2 (ΔTsr=0.9 h) −2.5 −2.5 −2.5 HVD D [nT] HVD D [nT] HVD D [nT] −3 −3 −3 (ΔTsr=−1.8 h) θ (ΔTsr=−2.3 h) (ΔTsr=−2.5 h) θ =195.5, =183.2, θ =156.1, −3.5 D −3.5 D −3.5 D C =1.00 C =1.00 C =0.98 D D ASB D D ASB D ASB D −4 −4 −4 Δ (ΔTsr=1.3 h) (ΔTsr=0.9 h) ( Tsr=1.4 h) 2150 2155 2200 2205 2055 2100 2105 2110 2055 2100 2105 2110 UT[hhmm] UT[hhmm] UT[hhmm] (d) 2012/04/04 AL index (e) 2012/04/06 AL index (f) 2012/07/06 AL index 0 0 0 AEI AL AEI AL −500 −500 −500 AEI AL [nT] [nT] [nT] −1000 −1000 −1000 2130 2200 2230 2300 2130 2200 2230 2300 1830 1900 1930 2000 UT[hhmm] UT[hhmm] UT[hhmm] 2012/04/04 filt 040−150 data 2012/04/06 filt 040−150 data 2012/07/06 filt 040−150 data HVD H 0 HVD H −1 −1 Δ (ΔTsr=−0.2 h) θ =236.7, ( Tsr=−0.3 h) θ =−42.8, −1.5 H −1.5 H HVD H C =0.82 C =0.97 −1 Δ H ASB H H ASB H θ =18.1, ( Tsr=−1.7 h) −2 −2 H (ΔTsr=2.9 h) (ΔTsr=3.0 h) C =0.97 ASB H −2 H −2.5 −2.5 (ΔTsr=1.2 h) HVD D [nT] −3 [nT] HVD D [nT] HVD D (ΔTsr=−0.3 h) −3 θ =168.2, (ΔTsr=−0.2 h) −3 θ Δ D θ =157.6, =158.1, ( Tsr=−1.7 h) −3.5 C =0.95 −3.5 D D D ASB D C =0.96 C =1.00 ASB D −4 D ASB D −4 D (ΔTsr=2.9 h) −4 (ΔTsr=1.2 h) (ΔTsr=3.0 h) −4.5 2205 2210 2215 2220 2205 2210 2215 2220 1855 1900 1905 1910 UT[hhmm] UT[hhmm] UT[hhmm] (g)2012/08/10 AL index (h) 2012/08/17 AL index (i) 2012/08/19 AL index 0 AEI AL 0 0 AEI AL AEI AL −500 −500 −500 [nT] [nT] [nT] −1000 −1000 −1000 1900 1930 2000 2030 2000 2030 2100 2130 2100 2130 2200 2230 UT[hhmm] UT[hhmm] UT[hhmm] 2012/08/10 filt 040−150 data 2012/08/17 filt 040−150 data 2012/08/19 filt 040−150 data HVD H HVD H −1 Δ −1 HVD H Daysideθ and (terminatorTsr=−1.7 h) Pi2 pulsations(ΔTsr=−0.9 h) −1 =7.2, θ =70.2, θ =−75.4, (ΔTsr=−0.3 h) −1.5 H −1.5 H H C =0.97 C =0.99 H ASB H H ASB H C =0.94 ASB H Dayside−2 Pi2 pulsations are not a simple−2 extension of nightside Pi2s. −2 H (ΔTsr=1.4 h) (ΔTsr=2.2 h) (ΔTsr=2.8 h) SHINOHARA ET AL- GEOMAGNETIC PULSATIONS ACROSS THE DIP EQUATOR 11,749 −2.5 −2.5 HVD D −3 HVD D Jun. 20,1992HVD 13:14-13:22UTD We concludeθ =223.7,that the phase lag of Pi2 pulsationsis (ΔTsr=−0.3 h) Dayside[nT] −3 Pi2 [nT] −3 Δ equator most[nT] lagged D at the dip equator.With increasingof the Δ . θ ( Tsr=−1.7 h) θ =203.6, ( Tsr=−0.9 h) dip latitude,C =0.98 the phaselag is graduallydecreasing. ASB D • =204.0, D D EquatorialD enhancement [Yanagihara and Shimizu,−3.5 1969] SLZ −4 Δ −3.5 C =0.99 C =0.97 3.2. Equatorial Enhancement of Pi2 ( Tsr=2.8 h) ChapterD 3. Solar TerminatorASB D EﬀectsD on Pi2 PulsationsASB D Amplitudes 30 • Small phase delay at the equator [Shinohara −et4 al., 1997] TER −4 Δ (ΔTsr=2.2 h) −Sastry5 et al. [1983]and Sarma and Sastry [1995] ex- ( Tsr=1.4 h) amined the local time dependenceof amplitude en- −4.5 hancementof the pulsationsignal at the dip equator. In • Near zero m-number (H comp) [Kitamura et al., 1988] EUS 1950 1955 2000 2005 2045 2050 2055 2100 order to discuss2125the relationship2130between 2135amplitude en-2140 UT[hhmm] UT[hhmm] hancementand phaselag UT[hhmm] in the equatorialregion, the CPA amplituderatios between the dip stationand off-dip sta- tionswere plotted as a functionof localtime in Figure 7. Terminator(a)(j) 2012/08/242012/01/17 Pi2 (Pi2 ALAL nearindexindex the dawn/dusk(b) terminator)2012/08/242012/03/03 ALAL indexindex (m)(c) Figure7a shows2012/09/052012/03/23the ratio of Pi2 amplitudesAL AL index indexobserved (k) SMA 00 AEI AL 00 at the0 0Brazilian east coastarray at $LZ (dip latitude • Large D amplitude on the sunlitAEI morningAL [Saka et al., 1982] AEI AL is 0.3ø) to thoseobserved at TER (-2.5ø). The ampli- AEIAEI AL AL AEI ALoff equator tude ratio was distributedat ,.- I during the entire day. −−500500 −−500500 1315UT 1320 −Figure−500500 7b showsthe ratio of Pi2 amplitudesat SLZ to

[nT] • [nT] [nT]

[nT] D component phase reversals [Imajo et al., [nT] 2015] [nT] thoseat EUS (-3.8ø). The amplituderatio becomes Figure 5. Exp•ndedDayside amplitude-time recordsPi2 from the −1000 −1000 Brazilian east coast arrw SLZ, TER, EUS, CPA, and −1000,.- I duringlocal nighttime, whereas the averagedra- −•1000 −1000 SMA for the period from 1314 to 1322 UT. −1000tio reaches1.5 duringlocal d•ytime. Figure7c shows Dawn-dusk19300700 20000730 asymmetry20300800 2100of0830 terminator effects [Imajo et0800 2130al., 2016]08302200 09002230[Shinohara09302300 et al., 1998] the ratio2130 of Pi20830 amplitudes22000900at SLZ2230 and SMA0930 (-19.8ø).23001000 UT[hhmm]UT[hhmm] UT[hhmm]UT[hhmm] UT[hhmm]UT[hhmm]

120 2012/08/242012/01/17 filtfiltDawn 040040−−150150 side datadata 2012/08/242012/03/03 filtfiltDusk 0403.1.040 Phase−−150 150side Relation datadata of Pi2 at the Dip Equator 2012/09/052012/03/23 filt filt 040 040−150−150 data data −0.5 −0.5 In order to clarify the dependenceof phaselag of an HVD H equatorial Pi2 on localHVD HVDtime andH H dip latitude, we sta- −1 HVD H −0.5 HVD H −1 −1 (∆Tss=−3.9 h) −1 HVD H −1 tistically analyzed 107( Pi2Δ∆Tsr=0.1 events observed h)from June θ =28.2, (ΔTsr=−0.0 h) −1 (∆Tss=−3.7 h) θθ==6.0,−47.1, 1, 1992,to July 5, 1992,( atTss= the Brazilian−4.0east h) coast θ =39.9,H θθ =20.0,=21.6, (ΔTsr=−1.8 h) −−1.51.5 HH −−1.51.5H −1.5 HH CC=0.99=1.00 array. The diurnal changesin the phase differencebe- CC=0.98=0.99 −1.5 C =0.99 HH tweena pair of stationsASB(TER (dipH latitude = -2.50) - H ASB H C H=0.99 ASB H −2 H ASB H H ASBASB HH −−22 SLZ (0.3ø), EUS (-3.8ø)-SLZ, and SMA (-19.8ø) - −2 (∆Tss=−0.5 h) −−22 SLZ) were obtainedby ( using(Δ∆Tsr=3.2Tss=the cross-correlation−0.6 h) h)func- TER- SLZ (ΔTsr=3.2 h) ((Δ∆Tsr=1.4Tss=−0.5 h) h) i i I i i −2.5 tion. 6 12 −2.5 −2.5 −−2.52.5-120•) 18 LT 24 −2.5 The phaselags of Pi2 HVDpulsations D between TER-SLZ, 120 - [nT] [nT] [nT]

[nT] HVD D [nT] [nT] HVD D HVD D −3 EUS-SLZ, and SMA-SLZHVD are D shown as a function of HVD D −3 Δ −3 θ =146.7, local time in Figure 6. A( positive∆Tss=(negative) −4.0sign h) is as- −3−3 −3θ =184.1, ( Tsr=−1.8 h) D (ΔTsr=0.1 h) (Δ(Tsr=∆Tss=−0.0−3.9 h) h) −3.5 D (∆Tss=−3.7 h) −3.5θ =174.7, signedto the phaselag if the signalat the formerstation θθ=184.0,=156.1, Cθ =0.99=123.0, −3.5 CD =1.00 lags (leads) that at the ASBother station. D Figure 6a shows− −3.53.5D D −3.5 DD ASB D D CC=0.96=1.00 −4 C =0.95 −4C =1.00 the phase lags of Pi2 pulsations between dip equator D D D Δ D stationSLZ (dip latitudeASB( is∆ 0.3 Tss=Dø) and− near-equator0.6 h)sta- (b) ASBASB D D (ASBTsr=1.4 D h) −4−4 ß% , −4 tion TER (-2.5 ø) as a functionof localtime. The phase −4.5−4 −4.5 (ΔTsr=3.2 h) _ ß (Δ(Tsr=3.2∆Tss=−0.5 h) h) (∆Tss=−0.5 h) lagsof Pi2 pulsationsobserved near the dip equatorare small during the entire day. Significantphase lags ap- EUS-SLZ 0735 0740 0745 0750 0830 0835 0840 0845 0900, , 0905I • ,, I 0910, , I , 0915• I 2005 2010 2015 2020 2155 2200 2205pear between2210SLZ and EUS (-3.8ø), as shownin Fig- 2210 2215 2220 2225 -1200 6 12 18 LT 24 UT[hhmm]UT[hhmm] UT[hhmm]UT[hhmm]ure 6b. A local time dependenceof phase lags can be UT[hhmm]UT[hhmm] seen in this figure. The phase of Pi2 at SLZ lags that 120 - at EUS when the stations are on the dayside. The aver- deg agedphase lag duringlocal daytime (0800-1600 LT) is 60 -28 ø. On the other hand, the phase lag is small when Figure 3.8: the stations are on the nightside. The averagedphase ß ß **% (f) 0 AL index and (e)H and D componentlag duringlocal nighttime bandpass-ﬁltered (2000-0400LT) is -9 ø. Fig- (c) magnetic ﬁelds at (d) 2012/03/26 AL index 2012/03/27 ureAL 6c index shows the phase lag of Pi2 between SLZ and 2012/07/13ß AL. index ß ß •e e ß ß ß SMA. SMA (-19.8 ø) is the station farthest south, in -60 -- ß 0HVD and ASB near the dawn terminator0 forthis array. 12 Although events. the plots are more scattered,θH,D Fig- and0 CH,Dß. are phase. lag AEI AL SMA-SLZ AEI AL ure 6c showsthe same trend as Figure 6b. The averaged , , I _. , , I , , .I , , −500 −500 phase lag during the localAEI daytime AL is -44 ø, while that −500-120• 6 12 18 LT 24

[nT] and squared coherence, respectively,[nT] whereduring the subscriptslocal nighttime is -16 ø. Though show negative[nT] Figure a v6. ectorPhase difference component. between Pi2 pulsations deviations are also seen in the predawn sector, it will at dip station SLZ (dip latitude is 0.3ø ) and the −1000 −1000 be re-examinedin detail and presentedin the future −1000other Brazilian east coast stations TER (-2.5ø)• EUS 0930 1000 1030 1100 1000 1030 1100 1130 (-3.8ø)• and SMA1000 (-19.8 ø)1030 as a function1100of local time.1130 UT[hhmm] UT[hhmm]paper whether these deviationsare significantor not. UT[hhmm] 2012/03/26 filt 040−150 data 2012/03/27 filt 040−150 data 2012/07/13 filt 040−150 data 0 −0.5 0 HVD H HVD H −1 −1 HVD H θ =5.5, (∆Tss=−3.2 h) θ =14.3, (∆Tss=−2.7 h) −1 H −1.5 H θ =−0.9, (∆Tss=−4.4 h) C =1.00 C =1.00 H H ASB H H ASB H C =1.00 ASB H −2 −2 −2 H (∆Tss=0.3 h) (∆Tss=0.8 h) (∆Tss=−0.6 h) HVD D −2.5 HVD D [nT] −3 [nT] HVD D [nT] −3 θ =141.7, θ =175.1, (∆Tss=−3.2 h) −3 D (∆Tss=−4.4 h) D θ =178.7, (∆Tss=−2.7 h) ASB D D C =0.99 C =0.99 ASB D −3.5 −4 D ∆ −4 D C =0.97 ASB D ( Tss=−0.6 h) (∆Tss=0.3 h) −4 D (∆Tss=0.8 h) −5 −4.5 −5 0955 1000 1005 1010 1025 1030 1035 1040 1035 1040 1045 1050 UT[hhmm] UT[hhmm] UT[hhmm]

(g)2012/07/25 AL index (h) 2012/10/25 AL index 0 0 AEI AL AEI AL −500 −500 [nT] [nT] −1000 −1000 0900 0930 1000 1030 0830 0900 0930 1000 UT[hhmm] UT[hhmm] 2012/07/25 filt 040−150 data 2012/10/25 filt 040−150 data −0.5 HVD H −1 HVD H (∆Tss=−5.0 h) −1 θ =10.6, (∆Tss=−2.5 h) −1.5 H θ =7.9, C =1.00 −1.5 H H ASB H C =1.00 −2 H ASB H (∆Tss=−1.3 h) −2 (∆Tss=0.8 h) −2.5 −2.5 [nT] HVD D [nT] −3 HVD D (∆Tss=−5.0 h) −3 θ =174.0, (∆Tss=−2.5 h) −3.5 D θ =169.5, C =0.99 −3.5 D D ASB D C =0.99 −4 D ASB D (∆Tss=−1.3 h) −4 (∆Tss=0.8 h) 0940 0945 0950 0955 0905 0910 0915 0920 UT[hhmm] UT[hhmm]

Figure 3.9: AL index and H and D component bandpass-ﬁltered magnetic ﬁelds at HVD and ASB near the dusk terminator for 8 events in the same format as Figure 3.8

Figure 3.12 presents the LT and ∆Tsr dependences of the phase lag of the H component between HVD and the ﬁve examined stations. Positive values indicate that the phase of reference data (HVD H)isdelayedwithrespecttotheexamineddata.Redand cyan vertical lines show sunrise times at the summer solsticeandthewintersolstice, ◦ respectively. It is clear that most phase lags are near 0 for all LT and ∆Tsr except for PTK. The phase lag of PTK H is more scattered, but the phase of HVD tends to be delayed from that of PTK.

Figure 3.13 shows the LT and ∆Tsr dependences of the phase lag of the D component between HVD and the ﬁve examined stations. The phase lags at ASB, KAK, and Purpose of this study

Observations suggest that ionosphericJournal currents of Geophysical may play an Research: important Space role. Physics 10.1002/2013JA019691

• The ionospheric current is considered compared with events on the dawn side because the amplitude of the D compo- to be driven by Pi2-associated electric nent is very small in the postnoon sector, and other dayside disturbances (e.g., Pc ﬁelds from the high-latitude region pulsations) easily mask Pi2 pulsations.

[Kikuchi and Araki, 1979; Shinohara et 4. Discussion al., 1998], but this idea has not been The D component of Pi2s at low and middle latitudes on the nightside has quantitatively and numerically tested. been investigated in previous studies, but few studies focused on the D component Pi2s on the dayside. Night- • side studies reported that the phase of The present study estimates the the D component oscillations changes by distribution of the ground magnetic 180◦ across the central meridian of the SCW and the magnetic equator [Lester field produced by the magnetospheric- et al., 1983; Yumoto et al., 1994; Li et al., 1998]. These phenomena have been ionospheric current system for Pi2. explained by the SCW oscillations [Lester et al., 1983] and/or the cavity-mode resonance [Allan et al., 1996]. In the • case of the SCW oscillations, since D Then we check whether the result component Pi2 pulsations are caused by a pair of oscillatory FACs, the FACs reproduces the observational features Figure 8. Schematic diagram of the current system explaining Expected dayside ionospheric alone do not cause the phase reversal D component magnetic perturbations. Green and red arrows indicate or not. magnetic andcurrent current perturbations, system [Imajo respectively. et Magnetic al., 2015] around the terminator. Cavity modes FAC perturbations produced by FACs are represented by !B , and with nonzero m numbers can have magnetic perturbations on the ground produced by ionospheric nodes resulting in longitudinal phase IC currents are represented by !B . reversals. The small phase difference of H oscillations over entire local times indicates that the dominant m number is nearly zero. While the cavity mode with m = 0 is decoupled from azimuthal oscillations (D oscillations), cavity modes with m ≥ 1 have both H and D oscillations and their nodes. The uniform phase structure of the cavity mode with m ∼ 0 can still be maintained if the amplitude of the m ∼ 0 mode is larger than the amplitude of m ≥ 1 modes. However, there is no reason a node of D oscillations should always be located near the dawn terminator. Also, the azimuthal polarization does not seem to support the plasmaspheric cavity resonance. The plasmaspheric cavity resonance consists of eigenmodes of fast waves in the plasmasphere, and the fast waves contribute less to the D component of magnetic variations than to the H component of magnetic variations on the ground. Fast waves can be converted to Alfvén waves if the radial component of polarization currents and the gradient of the Alfvén velocity are significant [Itonaga and Yoshikawa, 1996]. However, since the polarization current of the fast wave flows in the azimuthal direction in the inner plasmasphere, the mode conversion is not significant in the inner plasmasphere [Itonaga and Yumoto, 1998]. The D component phase reversals and the azimuthal polarization may be explained by considering the configuration of oscillatory FACs and ionospheric currents. We suggest that the meridional component of ionospheric currents is a possible source of the enhanced D component geomagnetic disturbances on the sunlit side. If a meridional current on the dark side flows in opposite direction to the meridional current on the sunlit side, an opposite magnetic perturbation can be produced on the dark side. However, this magnetic perturbation would not be significant because currents are weak in the dark low-latitude ionosphere, where the conductivity is low. Alternatively, we consider that the oscillatory FAC in the postmidnight sector generates azimuthal Pi2 oscillations in darkness. Possible mechanisms of the oscillatory FACs with Pi2 period include the transient response of the FAC (e.g., substorm current wedge) formation [e.g., Baumjohann and Glassmeier, 1984], the periodic bursty bulk flow (BBF) braking [e.g., Kepko and Kivelson, 1999; Kepko et al.,2001],andthereboundofbrakedBBFs[Panov et al., 2010]. The identification of the mechanism of the current oscillation is beyond the scope of this study.

FAC distribution in the magnetosphere perpendicular magnetospheric current in the equatorial plane

extending along the dipole ﬁeld line calculating total current and equatorial footprint of centers of FACs FAC distribution at ionospheric altitude initial input parameters ﬁeld-aligned current (FAC) ionospheric current (IC) conductivity distribution solving potential

Potential and Electric ﬁeld [e.g. Tsunomura et al., 1999; Nakamizo et al., 2012] Ohm’ s law

horizontal ionospheric current perpendicular magnetospheric current (PMC)

Total magnetic variation contribution contribution contribution

ionospheric current contribution magnetospheric current contribution The Biot-Savart law generalized in polar coordinates [Kisabeth and Rostoker, 1977] is used to calculate ground magnetic ﬁeld. Inputs (FAC, and conductivity tensor) log(Σ ) (a) FAC density x 10−7 (b) θθ 90 2 90 60 60 4 upward 1 downward ]

30 2 30 3 0 0 0 2 −30 −30 −1 [A/m −60 −60 1 [log(S)] −90 −2 −90 0 Latitude [deg] 0 3 6 9 12 15 18 21 24 Latitude [deg] 0 3 6 9 12 15 18 21 24 Local time [h] Local time [h]

Σ log(Σ ) (c) θφ (d) φφ 90 40 90 2.5 60 60 20 2 30 30 1.5 0 0 0 −30 [S] −30 1 −20 −60 −60 0.5 [log(S)] −90 −40 −90 0 Latitude [deg] 0 3 6 9 12 15 18 21 24 Latitude [deg] 0 3 6 9 12 15 18 21 24 Local time [h] Local time [h]

• We calculate the distribution of the height-integrated conductivity tensor, using the method developed by Nakamizo et al. [2012]. The method includes modiﬁcations by auroral precipitation [Hardy et al., 1987] and in the low-latitude region [Tsunomura et al., 1999]. • The conductivity tensor in the 0–12 h LT sector is mirrored in the 12–24 h LT sector for simplicity. Result: hight-integrated ionospheric current

• Around the noon meridian, the zonal current reaches a peak at the equator. • The meridional currents in the dayside region ﬂow equatorward in the prenoon sector and poleward in the postnoon sector, so as to connect with the equatorial current. Journal of Geophysical Research: Space Physics 10.1002/2017JA024246

Results: Equivalent current (just 90° rotation of magnetic ﬁeld) magnetospheric current contribution ionospheric current (IC) contribution

total equivalent current

Figure• 4. The distribution pattern ofof equivalent IC contribution current vectors on causedthe dayside by (a) the is magnetospheric similar to the currents ionospheric (FAC and PMC), (b) the ionosphericcurrent current, pattern and on (c) boththe currents.dayside. The color contours in Figures 4a and 4b show the absolute values of the magnetic field. The background color in Figure 4c shows the percentage of the IC contribution. • The ionospheric current mainly contributes to the dayside equivalent current. calculations of the SCW [e.g., Bonnevier et al., 1970; Kisabeth and Rostoker, 1977; Cramoysan et al., 1995]. The I ionospheric current contribution Jeq (Figure 4b) has a maximum amplitude in the high-latitude nightside M I region. Contrary to Jeq, Jeq has a significant value in the dayside region, and its amplitude is enhanced at I the equator. The pattern of Jeq on the dayside is similar to the ionospheric current pattern on the dayside (Figure 3). This means that the ionospheric current contributes mainly to the dayside equivalent current (or the magnetic field).

I I To clearly show the contribution of Jeq, we deﬁne the percentage of the IC contribution R :

I Jeq RI = × 100 (13) JM | + |JI eq| | eq | | Figure 4c shows the distribution of the total equivalent| | | current| (JM JI ) and RI. Except in the high-latitude | | | | eq + eq | | | | M region, the patterns of the equivalent current on the nightside and dayside are similar to the patterns of Jeq I I I and Jeq, respectively. R on the dayside is about 90%, while R on the nightside is only about 20%. In the nightside high-latitude region, RI is about 80% due to a strong auroral electrojet. The increase in RI on the dawnside is steeper than the decrease in RI on the duskside due to the skewed structure of the ionospheric current. A sign of the magnetic field produced by a stationary current corresponds to a phase relation of 0∘ or 180∘ for an oscillating current in a quasi-stationary state. Figure 5 shows the distributions of the sign of H and D com- ponents. The white area is positive, and the black area is negative. The red line shows the isoline of Σ!" = 0.8 as indicators of the sunrise/sunset terminator and the edge of the auroral region. The H component is posi- | | tive in most regions except the midnight auroral region and postmidnight middle latitudes. This means| | that | | the phase of the H component at low latitudes does not vary with local time, being consistent with previous studies [e.g., SutcliffeandYumoto, 1991; Nosé et al., 2006]. On the other hand, the D component shows a more complicated structure. The sign is antisymmetric with respect to the equator. The phase reversal at 0 h LT is reported by previous observations, and this is interpreted by the contribution change of upward and downward FACs [e.g., Lester et al., 1983]. The phase reversals are also shown in the dawn and dusk regions, as reported by Imajo et al. [2015]. The phase reversals occur at sunrise and 1.5 h before sunset, and this time difference between dawnside and duskside is consistent with the result of Imajo et al. [2016]. To determine the contribution from each current component in detail, we examined the LT dependence of magnetic fields at specific latitudes (0, 30, and 45∘) produced by each current component as shown in

IMAJO ET AL. CURRENT MODEL FOR DAYSIDE PI2 7 Results: Distribution of sign (phase) of the magnetic ﬁeld (a) (b) H H(north-south) component component sense DDD (east-west) component component sensesign 90 90 60 60 30 30 0 0 −30 −30 −60 −60 −90 −90

Latitude [deg] 0 3 6 9 12 15 18 21 24 Latitude [deg] 0 3 6 9 12 15 18 21 24 LT [h] LT [h] ※ The white area is positive and the black area is negative. ※ The red line shows the isoline of as indicators of the sunrise/sunset terminator and the edge of the auroral region.

• The H component is positive in most middle-to-low latitude regions. • The changes in sign of the D component appear at approximately 0, 5, 10, and 17 h LT. The result is consistent with observed phase relation of low-to-middle latitude Pi2s. H component (Lat.=0) H component (Lat.=30) H component (Lat.=45) 1.5 1.2 2 (a) FAC (b) (c) PRC 1 IC 1.5 1 Total 0.8

0.6 1 0.5 [nT] [nT] 0.4 [nT] 0.5 0.2 0 0 0

−0.5 −0.2 −0.5 0 3 6Explanation9 12 15 18 21 of24 D phase0 3 reversal6 9 12 15 near18 21 the24 terminator0 3 6 9 12 15 18 21 24 LT [h] LT [h] LT [h] FAC D component (Lat.=0) D componentD component (30° (Lat.=30) in latitude) D component (Lat.=45) 0.1 0.6 1.5 (d) ionosphericFAC current (e) FACFAC(f) contribution PRC 0.4 PRCMPC1 contribution IC 0.05 magnetic ICIC contribution Total 0.2 variation 0.5Totaltotal 0 0 0

[nT] [nT] −0.2 [nT] −0.5 −0.4 −0.05 −0.6 sunset −1 sunrise −0.1 −0.8 −1.5 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 LT [h] LT [h] LT [h] • (HThe2+D 2D)1/2 component (Lat.=0) produced by the (Hmeridional2+D2)1/2 (Lat.=30) ionospheric current in the(H prenoon2+D2)1/2 (Lat.=45) 1.5 sector is opposite to that produced1.4 by the postmidnight downward 2FAC. (Same (g) FAC (h) (i) applies to dusk side)PRC 1.2 IC • 1.5 The difference betweenTotal phase1 reversal meridians with respect to dawn and dusk 1 terminators is attributed to prenoon-postnoon asymmetry of the IC contribution. 0.8 1 [nT] D phase reversal near dawn[nT] 0.6 and dusk can be explained[nT] by a change 0.5 0.4 of a main contribution from the FAC to the IC, and, vice versa.0.5 0.2

0 0 0 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 LT [h] LT [h] LT [h]

x 10Conductivity4 (Lat.=0) Conductivity (Lat.=30) Conductivity (Lat.=45) 3.5 50 20 Σ (j) θθ (k) (l) |Σ | 3 θφ Σ 40 φφ 15 2.5

2 30 10 [S] [S] [S] 1.5 20 1 5 10 0.5

0 0 0 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 LT [h] LT [h] LT [h] Journal of Geophysical Research: Space Physics 10.1002/2017JA024246

Example of observed equivalent currents: 2052–2112 UT on 26 March 2012

Figure 8. (a) H component magnetic data high-pass ﬁltered at 300 s observed by nightside stations. (b) Horizontal amplitude, (c) H component, and (d) D component magnetic data that are band-pass ﬁltered with periods between 40 and 150 s at longitudinally separated stations for 2052–2112 UT on 26 March 2012. Vertical red lines in Figure 8b show four successive largest peaks at ASB. Vertical dotted lines in Figures 8c and 8d indicate times of peaks at HON and ASB, respectively. (e–h) Distributions of equivalent currents at four successive times on the map in IGRF geomagnetic coordinates. Red dots show station locations, and blue pointers show an equivalent current over each station. The grey and white regions show dark and sunlit regions at 100 km in altitude, respectively.

the representative of all stations since the time difference of local maxima among stations is small (This will be shown in the next paragraph). Finally, we derived the equivalent current vectors at each time of the local maxima of horizontal amplitude by rotating vectors by 90∘ clockwise (Figures 7d and 7e). These estimated equivalent current vectors are then drawn on the map in IGRF (International Geomagnetic Reference Field) geomagnetic coordinates. Figures 8 and 9 show filtered magnetic data from the three longitudinally separated dayside stations (ASB, HON, and TUC) and equivalent current distributions during two Pi2 events occurring at 2335 UT on 2 March 2012 and 2100 UT on 26 March 2012, respectively. The first event was related to a substorm since the AL index started to decrease in concurrence with Pi2 and reached −230 nT, while the second event may not be related to a substorm because of no clear AL decrease (not shown here). The typical Pi2 signatures, which are short-duration damping oscillations whose amplitude is larger than dayside counterpart, are shown in

IMAJO ET AL. CURRENT MODEL FOR DAYSIDE PI2 10 Journal of Geophysical Research: Space Physics 10.1002/2017JA024246

Example of observed equivalent currents: 2326–2346 UT on 2 March 2012

Figure 9. Filtered magnetic data for 2326–2346 UT on 2 March 2012 and the distributions of equivalent currents at four successive times in the same format as in Figure 8.

the high-pass-ﬁltered magnetic data at two nightside IMAGE stations (Figures 8a and 9a). Local maxima of ΔH2 + ΔD2 are nearly coincident among three latitudinally separated dayside stations (Figures 8b and 9b). √The D oscillation at the prenoon station ASB was in antiphase with the D oscillation at the postnoon station TUCasshowninthenumericalresult(Figures8c,8d,9c,and9d).The D amplitude at ASB was larger than the D amplitude at TUC for both the events. The equivalent current associated with the dayside Pi2 ﬂowed into the equator region from higher-latitude regions via meridional equivalent currents in the prenoon and postnoon sectors (Figures 8e–8h and 9e–9h). The equivalent current system nearly simultaneously oscillated with a Pi2 period and exhibited a prenoon-postnoon asymmetry that the meridional component was larger in the prenoon sector than in the postnoon sector. Thus, equivalent current distributions of both events support the numerical results.

IMAJO ET AL. CURRENT MODEL FOR DAYSIDE PI2 11 Limitation of the model 1. We neglected the inductive term of the ionospheric electric ﬁeld in the model. The present model could not reproduce the small phase delay at the magnetic equator.

2. Our model does not include any MHD-wave effects. Since the time of flight of fast wave from an expected Pi2 source is equivalent to, or even greater than Pi2 period range [Chi et al., 2009], as for the perpendicular magnetospheric current, far-field (wave) effects are probably dominant. So, it is not certain that the near- fast wave field (static) assumption is appropriate for the nightside H component. Source 3. The wave effects may need to be taken into account to better interpret observations in dawn and dusk regions, which are transition regions between nightside and Waves can reach dayside natures. Some previous studies observed Pi2 dawn and dusk oscillations in the dawn and dusk magnetospheres [Nose et al., 2003; Kim et al, 2010; Kwon et al., 2012]. Summary The present study numerically tested the interpretation by the magnetospheric-ionospheric current system for dayside and terminator Pi2s. ionospheric current region Results Following features are reproduced; • Uniform H-component phase HON • The equatorial enhancement TUC auroral region • D-component phase reversals ASB

(sign changes) Dusk Dawn • More sunward shift of the meridian of the D-component phase premidnight FAC region reversal near the dusk terminator. postmidnight FAC region • Large D amplitude on the sunlit current perturbation magnetic perturbation morning. on the ground Oscillating FACs D component phase reversal meridian

Conclusion: Oscillating current source • The oscillation of the magnetospheric-ionospheric current system is a plausible explanation of Pi2s on the dayside and near the terminator. • The terminator effects on Pi2s can be explained by a change in the main contributing currents between FACs and ionospheric currents. Thank you for your attention

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Acknowledgement: This work was supported in part by the JSPS Core-to-Core Program, B. Asia-Africa Science Platforms, by grant- in-aid for JSPS Fellows (15J02300 and 17J00472) and by JSPS KAKENHI (15H05815). Work at JHU/APL was supported by NASA grant NNX16AG74G and NSF grant AGS-1502700. MAGDAS/CPMN magnetic data were provided by the principal investigator of MAGDAS/CPMN project (http://magdas.serc.kyushu-u.ac.jp/). The magnetic data from the U.S. Geological Survey magnetometers are provided by the USGS Geomagnetism Program (http://geomag.usgs.gov). The McMAC project is sponsored by the Magnetospheric Physics Program of the National Science Foundation. We thank the national institutes that support INTERMAGNET for promoting high standards of magnetic observatory practice (www.intermagnet.org). We thank the institutes who maintain the IMAGE Magnetometer Array. The magnetic ﬁeld data at Kakioka, Chichijima, Memanbestu, and Kanoya were provided by the Kakioka Geomagnetic Observatory (http://www.kakioka-jma.go.jp). AL index was provided by the Kyoto WDC (http://wdc.kugi.kyoto-u.ac.jp). We acknowledge the Inter-University Upper Atmosphere Global Observation Network (IUGONET) project funded by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.