The response of the magnetotail to changes in the IMF orientation: The magnetotail's long memory

Phps. Chem. Earth (C), Vol. 24, No. l-3, pp. 221-227, 1999 0 1998 Elsevier Science Ltd

Pergamon

All rights reserved 1464- 19 17/99/$-see front matter

PII: S1464-1917(98)00032-4

The response of the Magnetotail to Changes in the IMF Orientation: The Magnetotail’s Long Memory R. J. Walker’,

R. L. Richard’,

T. 0gino2

and M. Ashour-Ahdalla1y3

‘Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, U.S.A. 2Solar Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Aichi, 442, Japan ‘Department of Physics, University of California, Los Angeles, CA 900951567, U.S.A. Received

26 September

1997; accepted

30 March 1998

Abstract. We have used a three dimensional global simulation of the interaction magnetohydrodynamic between the solar wind and the magnetosphere to investigate the changes which occur in the magnetotail when the interplanetary magnetic field (IMF) changes orientation. For IMF R,, # 0 the entire magnetotail twists when the IMF changes from southward to northward. The twisting at a given location on the tail magnetopause occurs shortly after the IMF change reaches that location. Inside the magnetosphere the response time is much longer. New field lines with open ends formed by the reconnection of tail lobe field at a near-Earth neutral line also twist as the field lines convect tailward. Initially formed with a southward R, they end up with a northward R, The response of the tail to a change in the IMF is controlled by the penetration of the solar wind electric field into the magnetosphere. 0 1998 Elsevier Science Ltd. All rights reserved.

magnetopause and a neutral line in the tail largely control the magnetospheric configuration (see Usadi et ul., [1993]; VuZker et al., [1993]; and Slinker et al., 119951 for recent simulation studies). The models and theory predict that in the presence of a more realistic IMF with B, f 0 and B,, ?e 0 the magnetotail becomes much more complex. For instance CowZey [1981] used theoretical arguments and Brecht et al., [ 19811 used a simulation to point out that the north-south symmetry breaks down when BY f 0 and the entire tail becomes twisted. This twisting has been confirmed in more recent simulation studies [Ogino et al., 1985; 1986; Fedder et al., 1995; Kuymuz et al., 1995; Khurunu et ub, 19961. Khuruna et uZ., [1996] point out that for southward IMF, B,, enters the magnetosphere in regions where newly opened magnetic flux tubes are being added to the magnetotail. Kuymaz et al., [1995] carried out a statistical study in which they examined the effect of IMF BY on the field configuration at X=-30R, and found good agreement between the observations and MHD simulations. They note that the tail configuration is different than that expected from a superposition of the IMF and magnetospheric fields. The International Solar Terrestrial Physics program has provided modelers with the opportunity to test the response of their models and simulations to IMF changes by comparing their results with observations. The first study to try to calculate the changes in the magnetosphere that result from a changing solar wind and to compare the results with in situ observations within the magnetosphere was by Frank et al., [1995]. Observations from the plasma and magnetic field experiments on the Geotail spacecraft SlR, from the Earth in the magnetotail indicated that the spacecraft had moved from the magnetosheath to the tail lobes in response to rotations in the IMF. Solar wind and IMF observations from IMP-8 were used as input to a global magnetohydrodynamic (MHD) simulation that was used to predict the time series of observations at Geotail as the entire magnetotail twisted in response to the changing IMF. More recently Berchem et al., [1998] have successfully modeled a similar event when Geotail was over 2OOR,tailward of the Earth. The success in modeling the motion of the distant tail has lead simulators to try several other intervals during which Geotail was located nearer the Earth. So far most of the

1 Introduction It has long been recognized that the interplanetary magnetic field (IMF) orientation controls the contiguration of the magnetotail. For over two decades modelers have been building more and more realistic models of the interaction of the magnetosphere with the solar wind and IMF (see Walker and Ashour-Abdulla, [1995] and Birn et al., [1996] for recent reviews). When IMF B, = 0 and BY = 0 the magnetotail in models and simulations of the magnetosphere has north-south and east-west symmetry. For northward IMF the magnetotail contiguration is controlled by magnetic reconnection between the IMF and tail lobe field just tailward of the polar cusp (see Usudi et aZ., [1993]; Ogino et al., [1994]; Raeder et al., [1995] and Fedder and Lyon [I9951 for recent simulation studies). When the IMF is southward the reconnection between the IMF and closed terrestrial field lines at the subsolar

Correspondence

to: R.J. Walker 221

222

R. J. Walker et al.: Response of the Magnetotail to Changes in the IMF Orientation

published studies have concentrated on intervals when the RviF was northward. As before the MHD models were driven by input from solar wind and IMF observations and the time series of plasma moments and the magnetic field vector at the positions of Geotail were compared with observations. In general the agreement was good but not exact. Several factors influence how well the model results and data agree. Simplifying assumptions concerning the solar wind input (e.g. constant IMF B, and neglecting solar wind aberation) can affect the simulation results. In addition differences occur when Geotail is located near regions with steep gradients in the plasma and field parameters [Raeder et al. 1997; Ashour-Abdalla et al., 19981. Ashour-Abdalla et al., [I9981 have found that displacing the spacecraft by a few (l-3) grid points can greatly improve the fit. These studies support the picture that the magnetospheric structure becomes very complex when IMF B, z 0 and B, + 0. In addition they show that the response of the magnetosphere to IMF changes is not simple. Raeder et aZ., [1998] have argued that the magnetosphere retains a memory of past IMF orientations. The recent studies comparing MHD models with Geotail observations indicate that the MHD models reproduce the major features of the magnetotail contiguration and its dependence on IMF orientation. In this study we present a simulation study in which we investigated how these changes occur and try to quantity the response of the tail. We have examined the response of the magnetotail to a northward turning of the IMF following an extended interval when the IIvIF was southward. In section 2 we describe how the simulation study was carried out. In section 3 we examine the changes in the magnetotail during the simulation experiment and in section 4 we discuss the factors that control these changes.

2 Approach For this study we used a high-resolution global MHD code developed by Ogino et al., [1992; 19941. Since the details of this code have been published we will describe it only briefly. We solve the resistive MI-ID equations and Maxwell’s equations as an initial value problem on a rectangular (322 x 82 x 162) points grid with a uniform mesh size of OSR,. We solve the differential equations by using a modified version of the Leapfrog scheme that is a combination of the Leapfrog scheme and the two-step LaxWe&off scheme. The simulation parameters are fmed to solar wind values at the upstream edge of the simulation box with free boundary conditions at the sides and back. Since the simulation includes only the dawn half of the magnetosphere, symmetry boundary conditions are used to construct the dusk half of the magnetosphere given the values of the parameters on the dawn half. The ionospheric boundary is at 3.5RB The solar wind velocity was 300 km/s, the density was 5 cm’ and the temperature was 2 x 10%.

N (98, T= 750 min.)

min.) ‘Dawn (04 T= 660 min.)

vS(27Cf.T=570

min.)

Fig. 1. The directionof the IMF duringthe simulation. The mows point in the direction of the IMF while the rotation angle and time are in parentheses.

Initially the simulation was run for 90 min in real time without an IMF in order to form a “quiet” magnetosphere. Then the simulation was run for an additional 300 min with a northward IMF. Starting at 390 min the IMF was rotated in the YZ plane in 15” steps every 15 minutes. The direction of the rotation and the time at the start of the 15 min period at each IMF orientation are given in Figure 1. The actual rotation lasted approximately 1s (1 IviHD time step). This is short compared with most rotations of the IMF and compared to the time it takes the solar wind to convect across the dayside magnetosphere (-10 minutes). As we will see in section 3 the response time of the magnetosphere is much longer than the time for the rotation. The fast rotation makes it easy to follow the effects of the rotations as they move through the system. Since the rotation is essentially a step function this approach gives the minimum time for the magnetosphere to respond to a given IMF change. In the results that follow the IMF orientation is given by a clock angle (Figure 1) which is 0” when the IMF points toward dusk, 9O’when the IMF is northward, 180” when the IMF is dawnward and 270” when the IMF is southward. In our numerical experiment the rotation was counterclockwise (i.e. from north to dawn to south to dusk and back to north). We have chosen to study the interval during which the IMF was rotated 90’ between duskward and northward in greatest detail. By then the IMF had had a southward component for 3 hours and a duskward component for 90 minutes. The simulation results are voluminous (approximately 275 Mbytes/ time step) so we only saved one time step every 15 minutes for analysis. The response of the magnetotail to the rotations (section 3) was sufficiently slow that these results are adequate for investigating the controlling mechanisms.

R. J. Walker et al.: Response of the Magnetotail to Changes in the IMF Orientation

223

Pressure in the YZ Plane x=-20Re T = 570 min.

T = 615 min.

T = 660 min.

9= 270°

e=3150

e-00

-4ORe

4YORe

T = 750 min. e=900

T = 705 min. cl=450

X=-100& T = 660 min. e=on

T = 615 min. 8=315”

T = 570 min. 6 = 270”

-4ORe

T = 705 min. 0=450

T = 750 min. \8=90”

Fig. 2. Contours of plasma pressure in the X=-2Ohbplane (top) and in the X=-I OORe plane (bottom). The time and the IMF clock an&a (0) are givenat the top of each panel. order of increasing time. Both the time and the IMF clock 3 Response of the magnetotail to changing IMF angle are given for each panel. The entire tail cross section twists as the direction of the Ih4F changes. For Ih4F B,, > 0 (duskward) the magnetopause normal and the plasma sheet In Figure 2 we have plotted snapshots of pressure contours normal twist toward dawn. The twisting is more in the YZ plane at X=-20& (top) and X=-100& (bottom). pronounced at X=- 1OOR,than at X=-20RP At each distance from the Earth the plots are arranged in

224

R. J. Walker et al.: Response of the Magnetotail to Changes in the IMF Orientation

The twisting can most easily be studied by examining the magnetopause and plasma sheet. When the IMF is either purely northward or purely southward the magnetotail cross section should be symmetric with respect to both the equator and the noon-midnight meridian. This is not the case when the IMF was either southward (f=570 min) or northward (t-750 min) in the simulation. The magnetosphere lags behind the IMF and the tail at X=lOOR, lags behind the tail at X=2OR,. We can use the simulation results to calculate the response time for the magnetotail. For instance at X=2OR, the magnetopause, identified by the pressure gradient between the magnetosheath and the tail lobes, became roughly symmetric between 15 min (f=585 min) and 30 min (~600 min) after the IMF became southward. It takes the solar wind about 17 min to convect the IMF from the upstream edge of the simulation box to X=-2OR,. Similarly at X=lOOR, the tail magnetopause became approximately symmetric between 45 min (t=615 min) and 60 min (t=630 min) afier the southward turning of the IMF. The solar wind took about 44 minutes to reach X=lOOR,. Thus the tail magnetopause responds to the changes in the IMF on a time scale which is only slightly longer than the time required for the solar wind to convect to a given position.

turning of the IMF while at X=lOOR, it took about 105 minutes (r-675 min). Thus at a given distance down the tail the plasma sheet response lags that of the magnetopause. In Figure 3 we have plotted B, and V, along the X-axis for four times when the IMF was between duskward (0”) and northward (90”). The flow reverses direction from earthward (Vpl) for a-2OR, to tailward (V,
-40

Velocity and Magnetic Field Along the Noon-Midnight Meridian

Fig. 4. Magnetic field lines calculated at r=690 min. The short dashes show closed field lines, black solid field lines are open and black dashed field lines are formed by reconnection of lobe field lines. The view is from the magnetotail on the dawn side.

Magnetic Field Lines (t=735 minutes, El=79) Z(b)

Fig. 3. The Z-component of the magnetic field (&) and the X-component of the velocity (V,) versus the distance along the X-axis at four times in the simulation. The four times are ~690 min (upper left), f=705 min (lower left), r=720 min (upper right) and r=735 min (lower right). The IMF clock angle is given in the label.

We also can study the twisting of the magnetotail in response to the changes in the IMF by examining the orientation of the plasma sheet identified by the pressure peak near Z=O. At t = 660 min in Figure 2 the tail magnetopause has twisted toward dawn in response to an IMF with a duskward component (BY > 0) at X=-lOOR, while the plasma sheet is still twisted towards dusk, an orietitation reflecting a prior interval with dawnward IMF (BY< 0). We can use the time at which the plasma sheet became symmetric to estimate the response time much as we did with the magnetopause. At X=-2OR, it takes between 45 min (%=615 min) and 60 min (~630 min) for the plasma sheet to rotate in response to the southward

Fig. 5. The same as Figure 4 at f=735 min.

In Figure 4 we have plotted magnetic field lines giving a snapshot of the magnetosphere at N90 min (8=30’). The view is from the tail on dawn side. In this figure closed

R. J. Walker er nl.: Response of the Magnetotail to Changes in the IMF Orientation field lines with both ends at the Earth have been plotted with short dashes and are found near the Earth. Open field lines with one end on the Earth and one end in the IMF are solid and field lines that cross the equator once and are not attached to the Earth are dashed. The dashed field lines were formed by reconnection of tail lobe field lines at the near-Ear& neutral line, a process that is ongoing at this time. The dashed field lines cross the equator at X=-40, -60 and -8OR,. Virtually the entire length of the tail is filled with these newly formed &IF field lines. The plane of the dashed newly formed IMF field lines is nearly parallel to the equator because of the extended interval with IMF B, f 0. Arrows show the direction of the field. The dashed field lines start in the northern dawn magnetotail and pass through the equator into the southern dusk magnetotail.

-10 -40

0

4040

0

40

w#) Fig. 6. IMF field lines formed by reconnection of tail lobe field lines. The tield lines are plotted in the YZ plane for all X values. The times and IMF clock angles are given at the top of each panel. Note that the scale on the Z-axis ( f IOR,) is different than that on the Y-axis ( f 4ORs).

Selected field lines from the simulation at t=735 min (0=75O) are plotted in Figure 5. The view is the same as in Figure 4. The region of dashed IMF field lines and the region of closed field lines have moved tailward. This reconfiguration of the tail began following the cessation of tail reconnection at t=705 min. Now the dashed field lines start in the southern dawn quadrant, pass through the equator and emerge into the northern dusk quadrant. The B, component of the reconnected field lines has changed from southward to northward. The time changes in the IMF field lines threading the tail can be seen in Figure 6 where we have plotted the reconnected field lines in the YZ plane (for all X values) at t=690 min, 705 min, 720 min, and 735 min. Most of these field lines exit the simulation box through the downstream boundary. Those that exit near midnight appear short in this projection. l’he reconnected tield lines are southward as long as reconnection continues at the

225

Electric Field in the X=-2ORJ3Piane 30

(T=wJmin.) f304

0

Fig. 7. The Y-component of the electric field (f&Jin the YZ plane at X=ZOR,. The values are plotted for three times (?=69Omin, t=72Omin, and f=75Omin). ‘I&ecolar bar gives the values of Ey in mV/m.

near-Earth neutral line. However, after reconnection stops at t=705 min and the reconnected field lines begin moving out of the simulation box they twist northward. As we will see in the next section this is how the part of the tail near the equator adjusts to the northward turning of the IMF while By f 0. 4 Discussion Under the infhtence of IMF B,, the entire magnetotail twists as the IMF rotates from southward to northward. In the tail the twisting occurs fust at the magnetopause, which responds on the time scale of magnetosheath convection. The motion of the magnetopause in this study is similar to that seen in the Geotail event studies [Frank et al., 1995; Berchem et d., 19981. Inside the magnetosphere the response time is much longer, in our examples it took the plasma sheet at least twice as long as the magnetopause to respond. Thus the magnetotail retains information about previous states of the solar wind and IMF well after they change but that information is coded in the structure of the tail in a complex way.

R. J. Walker et al.: Response of the Magnetotail to Changes in the IMF Orientation

226

Electric Field in the X=-6ORs Plane 30

IT&al-Im;n 1

0

-30 rr=720 min.) 30

(600)

’ 0.5

-30

30

-0.5 (T=7JO min.) (904

0

-30

Fig. 8. The same as Figure 7 at X=-60%.

The response of the tail to changes in the IMF can produce surprises. When tail lobe field lines reconnect in the near Earth tail the magnetic field tailward of the neutral line is expected to have a southward component (R, < 0) and to have tailward flow (Vx< 0). Observers have long used this signature as evidence-for tail reconnection. The tail lobe reconnection at the near-Earth neutral line forms new IMF field lines, which convect tailward. When the reconnection stops these IMF field lines eventually move out of the simulation box. In our simulation as the field lines moved tailward the R, component rotated from southward to northward. The configuration changes result from MHD convection within the magnetosphere as suggested by Kaymaz et al. [ 19951 and Khuruna et al. [ 19961. In Figure 7 we have plotted the E,, component of the electric field in the YZ plane at X=-2OR, at three times during the simulation. Ey=(VxB+qJ), where -VxB is the convective term and qJ is the resistive term. A uniform resistivity n=O.OOl in normalized units [see Ogino et al, 19941 was used. For R, > 0 we have E,,
At ti90 min (top) most of the tail cross section has Rp (i.e. a dawn to dusk electric field). Near midnight in the plasma sheet the electric field in the closed field region near the equator is R,H.SmV/m. The electric field is directed dusk to dawn (E,,
References Ashow-Abdalla, M., J. Raeder, M. El-Alaoui and V. Pemomian, Magnetotail sbuctwe and its internal particle dynamics for northward IMF, Geophys. Mongr., (in press), 1998. Berchem, J., J. Ftaeder, M. Ashour-Abdalla, L. A. Frank, W. R Paterson, K. L., Ackerson, S. Kokubun, T. Yamamoto, and R P. Lepping, The

distant tail at 2oORE:Comparison between Geotail observations and the results tium a global magnetohydrodynamic I&s., (in press), 1998.

simulation,

J. Geophys.

R. J. Walker Bim, J., M. Hesse, and K. Schindler,

er al.: Response MHD simulations

of the Magnetotail

of magnetotail

dynamics, J. Geophys. Res., 101, A6, 12,939, 1996. Geophys. Res., Lett., 8,

397,198l.

Fedder, J. A., and J. G. Lyon, The Earth’s magnetosphere is 165 RE long: Self-consistent

currents,

convection,

magnetospheric

structure

and

processes for northward interplanetary magnetic field, J. Geophys. Res., 100, A3,3623,1995. Fedder, J. A., J. G., Lyon, S. P. Slinker and C. M. Mobany, Topological stmcture of the magnetotail

as function of interplanebuy

direction, J. Geophys. Res., 100, A3,3613, Frank, L. A., M. Ashour-Abdalla, T. Yamamoto,

Fairfield, and K. L., Ackerson, J.Geophys.

magnetic field

1995.

R. P. Lepping,

F. V. Comniti,

D. H.

Observations of plasmas and magnetic Comparison

with a global

Res., lOO,AlO, 19,177, 1995.

J.

Walker,

and

M.

Interplanetary

magnetic field control of magnetotail

field: IMP 8 data

and MHD model compared, J. Geophys. Res., 100, 17,172, 1995. Khumna, K., K., R. J. Walker, and T. Ogino, Magnetospheric and simulations,

J. Geophys. Res., 101, A3,4907, M.

convection

of

when the interplanetary

1996.

Ashour-Abdalla, the

global

simulation

of By dependent

and J. M. Dawson, An MHD

magnetospheric

convection

and field

aligned currents during northward IMF, J. Geophys. Res., 90, 10,835, 1985. Raeder, I., R. J. Walker, and M. Ashour-Abdalla, distant

geomagnetic

tail

during

Geopbys. Res., Lett., 22,4,349,

long periods

The structure of the of northward

IMF,

1995.

Raeder, J., J. Berchem, M. Ashour-Abdalla,

L. A. Frank, W. R Paterson,

K. L. Ackerson, S. Kokubun, T. Yamamoto, and J. A. Slavin, Boundary formation

comparisons

in

the

magnetotail:

Geotail

with a global MHD simulation,

observations

and

Geophys. Res. Lett., (in

press), 1998. Slinker, S. P., I. A. Fedder, and J. G. Lyon, Plasmoid evolution

in a numerical

simulation

formation and

of a substorm, Geophys.,

Res.,

1995.

Usadi, A., A. Kageyama, K. Watanabe, and T. Sate, A global simulation of the magnetosphere

with a long tail: Southward

and northward

Walker,

R. J., and M. Ashour-Abdalla,

1993.

The magnetosphere

in the

machine: Large scale theoretical models of the magnetosphere, Reviews of Geophys., Supplement, 639,1995.

A

global

magnetosheath and magnetic field is northward,

IEEE Trans. Plasma Sci., 20, 6, 817, 1992.

A

interplanetary magnetic field, J. Geophys. Res., 98, A5,7503,

in the presence of interplanetary magnetic field By: A conceptual model Ggino, T., R. J. Walker, and magnetohydrodynamic simulation

Ashour-Abdalla,

simulation of the response of the magnetosphere

Res., 99,11,027, 1994.

Lett., 22,7,859,

Kaymaz, Z., G. Siscoe, J. G. Luhmann, J. A. Fedder, and I. G. Lyon,

magnetosphere

R

to a northward turning of the interplanetary magnetic field, I. Geophys.

layer

J. Berchem, J. Raeder, W. R. Paterson,

fields in the Earth’s distant magnetotail: MHDmodel,

T.,

Ogino, T., R J. Walker, M. Ashour-Abdalla,

Cowley, S. W. H., Magnetospheric asymmetries associated with the ycomponent of the IMF, Planet. Space Sci., 29,79,1981.

S. Kokubun,

Ogino,

227

in the IMF Orientation

magnetohydrodynamic

Brecht, S. H., J. G. Lyon, J. A. Fedder, and K. Hain, A simulation study of east-west IMF effects on the magnetosphere,

to Changes

Walker, R. J., T. Ogino, J. Raeder, and M. Ashour-Abdalla, magnetohydrodynamic interplanetary

simulation

of the magnetosphere

A global when the

magnetic field is southward: The onset of magnetotail

reconnection, J. Geophys., Res., 98,17,235,1993.