On the importance of antiparallel reconnection when the dipole tilt and IMF B y are nonzero

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2004ja010972, 2006 On the importance of antiparallel reconnection when the dipole tilt and IMF B y are nonzero K. S. Park, 1 T. Ogino, 1 and R. J. Walker 2 Received 10 December 2004; revised 16 November 2005; accepted 4 January 2006; published 12 May [1] Several parameters may influence reconnection at the dayside magnetopause. They include the relative orientation of the magnetic fields in the magnetosheath and magnetosphere, the relative perpendicular velocities of field lines both before and after reconnection, and the location of the minimum geomagnetic field. We have used a threedimensional global MHD simulation of the magnetosphere to evaluate the relative importance of these parameters at the dayside magnetopause, when the interplanetary magnetic field (IMF) has a B y component and the dipole tilt is nonzero. For a purely southward IMF and finite tilt, reconnection occurs near the magnetic equator. The reconnection rate at the magnetic equator is smaller than the case with zero tilt because of increased magnetosheath plasma flow. For finite IMF B y the reconnection sites move away from the subsolar point. When we include a positive dipole tilt, the reconnection site in the summer hemisphere shifts sunward and equatorward while the one in the winter hemisphere moves tailward and away from the equator. Reconnection near the magnetic equator becomes less effective because IMF field lines move rapidly past the magnetic equator for the finite tilt. We have evaluated the importance of antiparallel reconnection by calculating the electric field at the magnetopause and found that antiparallel reconnection is more important than component reconnection for cases with finite dipole tilt and an IMF B y component. Citation: Park, K. S., T. Ogino, and R. J. Walker (2006), On the importance of antiparallel reconnection when the dipole tilt and IMF B y are nonzero, J. Geophys. Res., 111,, doi: /2004ja Introduction [2] Magnetospheric dynamics are controlled by magnetic reconnection between the geomagnetic field and the interplanetary magnetic field (IMF). Dungey [1961] first proposed magnetic reconnection at the dayside magnetopause for a purely southward IMF. Two different models are often invoked to describe dayside magnetic reconnection: antiparallel reconnection and subsolar reconnection. The former occurs preferentially where the magnetosheath magnetic field is antiparallel to the geomagnetic field [Sonnerup, 1974; Crooker, 1979; Luhmann et al., 1984]. Crooker [1979] and Luhmann et al. [1984] showed that the reconnection occurs at the equator for purely southward IMF and in asymmetrical regions at high latitudes in both hemispheres of the magnetopause for northward IMF orientation. They also estimated the reconnection sites for cases with finite IMF B y. Subsolar point reconnection, which is sometimes called component reconnection, occurs in the stagnation region where the IMF first encounters the geomagnetic field [Sonnerup, 1974; Gonzalez and Mozer, 1974]. 1 Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Japan. 2 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA. Copyright 2006 by the American Geophysical Union /06/2004JA010972$09.00 [3] It is a difficult problem to determine which of these two models better describes the reconnection process at the dayside magnetopause from observations. Observations of flux transfer events at the dayside magnetopause usually are explained by the subsolar reconnection model [Russell and Elphic, 1978; Gosling et al., 1990; Kawano and Russell, 1997a, 1997b], in which most reconnection occurs at low magnetic latitudes. On the other hand, observations of ionospheric convection [Iijima and Potemra, 1976; Coleman et al., 2001; Chisham et al., 2002; Maynard et al., 2003] and observations by satellites at high latitudes [Šafránková et al., 1998; Němeček et al., 2003, 2004] are often explained by antiparallel reconnection. [4] There have been many studies of dayside magnetopause reconnection by using global MHD simulations [Ogino et al., 1986, 1989; Berchem et al., 1995; Fedder et al., 2002; Siscoe et al., 2002]. Ogino et al. [1986] showed that if the IMF is rotated from northward to duskward to southward the reconnection occurs on the dayside magnetopause at progressively from high to low latitudes. They argued that this is consistent with antiparallel reconnection being dominant at the dayside magnetopause. Antiparallel reconnection can occur anytime when the magnetic field in the magnetosheath and the magnetosphere are oppositely directed but the reconnection rate is greatest near the subsolar point, as the magnetosheath flow is slower there. In the simulations the dayside reconnection leads to twisted magnetic flux tubes on the dayside magnetopause [Ogino et 1of12

2 al., 1989; Berchem et al., 1995; Fedder et al., 2002]. Siscoe et al. [2002] showed high-speed magnetosheath flow through a stationary reconnection site at high latitudes for northward IMF. They showed that the direction of the IMF more strongly influences antiparallel reconnection than subsolar reconnection, but they did not include the effects of the dipole tilt in their calculations. Recently, Maynard et al. [2002, 2003] used their MHD simulation results to suggest that the reconnection appears away from the equatorial latitudes when the IMF is strongly southward and the dipole tilt is finite. However, they did not systematically study the effects of the IMF B y component and dipole tilt. [5] The purpose of the present study is to determine which model better describes dayside reconnection and to determine its location on the dayside magnetopause. We have performed a high-resolution and time-dependent threedimensional MHD simulation of the interaction between the solar wind and the Earth s magnetosphere when the dipole tilt, and B y and B z components of the IMF are included simultaneously in the whole volume of the simulation box. We briefly describe the simulation model in section 2 and present our results in section 3. Given all the previous studies it is not surprising that we find that antiparallel reconnection is dominant. Including the effects of the dipole tilt in the calculation helps us to isolate the reasons why antiparallel reconnection dominates. This is discussed in section 4 and we present our conclusions in section Simulation Model [6] We have solved the normalized resistive MHD and Maxwell s equations as an initial value problem by using a modified version of the Leapfrog scheme. The basic MHD simulation model has been described in detail by Ogino [1986] and Ogino et al. [1992]. The only differences are that the simulation uses a full 3-D simulation box rather than the half box used in the early work and the spatial resolution is much higher in this case. The MHD equations are written @r ¼ r ð ÞþDr2 r; ð1þ ¼ V ð r ÞV 1 r rp þ 1 r J B þ g þ 1 r mr2 V; ¼ ð ÞP gprvþd pr 2 ¼rðVBÞþhr2 B; ð4þ J ¼rðB B d Þ; ð5þ where r is the plasma density, V is the plasma flow velocity, P is the plasma pressure, B is the magnetic field, B d is the dipole field of Earth, J is the current density, g = g 0 /x 3 (x 2 = x 2 + y 2 + z 2, g 0 = (9.8 m/s 2 )) is the force of gravity, mr 2 V is the viscosity, and g is the ratio of specific heats, g = 5/3. The resistivity, h = h 0 (T/T 0 ) 3/2, has a classical temperature dependency, where T = P/r is the temperature and T 0 is the ionospheric temperature. The model resistivity h 0 is set to and the diffusion coefficients are D = D p = m 0 = m/r sw = 0.001, where r sw is the solar wind plasma density. The magnetic Reynolds number is S = t h /t A = , where t h Dx 2 /h, and t A = Dx/n A. Dx is the mesh size. The numerical Reynolds number is larger than 5 times of the magnetic Reynolds number. The normalized quantities in the basic equations are the radius of the Earth, R E = m, the Alfvén transit time, t A = R E /v A = s, the density at the ionosphere, r s = mn s (n s =10 10 m 3 ), the magnetic field at one Earth radius at the equator, B s = T, and the Alfvén velocity at the surface of the Earth, v A = B s /(m 0 r s ) 1/2 = m/s. We used a full simulation box with dimensions of 120R E X 30 R E, 60 R E Y 60 R E, 60 R E Z 60 R E, in Cartesian solar magnetospheric coordinates. The number of grid points is (n X, n Y, n Z ) = (500, 400, 400) with a uniform grid spacing of 0.3 R E. A uniform solar wind with a density of n sw =5/cm 3,a temperature of T sw = 200,000 K, and velocity of V sw = 300 km/s, was maintained. The uniform IMF is initially given by B IMF = (0, B IMF cosq, B IMF sinq) nt, where q is a counterclockwise angle from the Y axis. 3. Simulation Results [7] We ran three simulations with different IMF and dipole tilt conditions for each case. A quasi-steady state configuration usually resulted after about 3 hours in real time Pure Southward IMF [8] Figure 1 shows simulation results for purely southward IMF and 30 dipole tilt. The magnetic field configuration in the noon-midnight meridian plane is shown in Figure 1a. Figure 1b shows the configuration of magnetic field lines in a view from the Sun. The Earth is located at the origin, closed field lines that connect to the Earth in both hemispheres are green, open field lines that connect to the ionosphere at one end and to the distant IMF at the other end are blue, and detached field lines (IMF) that do not connect to the Earth at all are red. The open field lines in the northern hemisphere are sharply bent forward, while those in the southern hemisphere are stretched tailward because of the positive tilt angle. From these figures, we find that the reconnection region is near the magnetic equator. Figure 1c shows a projection of the region of minimum magnetic field magnitude from the simulation in a view from the Sun. To determine the minimum values we included values for X > 15 R E at a fixed (Y, Z) point. The blue area in Figure 1c shows the location value jbj < 0.1B IMF. If we compare Figure 1b with Figure 1c, we see that the reconnection occurred near the magnetic equator well south of the subsolar point. The points smallest jbj along the magnetic field lines define the magnetic equator. In this case, the reconnection occurs preferentially where the IMF encounters the weakest field magnitude and where the magnetosheath magnetic field lines were antiparallel to the geomagnetic field. However, the region of minimum jbj does not always define the reconnection site. The recon- 2of12

3 Figure 1. Configuration of magnetic field lines in the (a) noon-midnight meridian plane and (b) dawndusk plane for a case where the interplanetary magnetic field (IMF) is purely southward and dipole tilt is 30. (c) Projection of magnetic field magnitude for X > 15 R E from the simulation. nection site should be confirmed by using other indications such as the kinked reconnected field lines shown in the Figure 1a Southward and Duskward IMF [9] Figure 2a shows the configuration of magnetic field lines in a view from the Sun for a simulation with 30 dipole tilt, IMF B z = 5 nt, and IMF B y = 5 nt. The reconnection sites lie between the regions with the highly kinked open field lines in Figure 2a. There are two reconnection sites: one in the northern dusk sector A and one in the southern dawn sector B. In Figure 2b, the regions of minimum magnetic field magnitude for all values of Y have been projected onto the XZ plane (Figure 2b, top left). Similarly, for all values of Z, minimum jbj has been projected onto the XY plane (Figure 2b, bottom left), and values for X > 15R E have been projected onto the YZ plane (Figure 2b, right). The two reconnection regions noted in Figure 2a can be seen as the regions marked A and B in Figure 2b. Regions A and B are not symmetric with respect to the Y and Z axes. Region A is sunward and closer to the equator than region B because of the effects of the positive dipole tilt. [10] We also have examined parameters mapped to the ionosphere for this case. The physical quantities were mapped onto the ionosphere along the magnetic field lines by using R f B dl/r 1 Bdl, where f stands for each of the physical quantities and B is the magnitude of magnetic field. This expression generally gives an averaged value along the magnetic flux tube. Figure 3a (left) shows the ionospheric convection and the energy flux (rv 3 th = P 3/2 pffiffi / r where Vth is the thermal velocity) to the ionosphere, and Figure 3a (right) shows the electric potential mapped in the polar region. The ionospheric potential is calculated by using the relationship, r 2 f = r( V? B). The velocity, V?, or electric field, E?, is mapped directly from the inner boundary of the magnetosphere to the ionosphere along the magnetic field 3of12

4 Figure 2. (a) Configuration of magnetic field lines viewed from the Sun and (b) projection of the minimum magnetic field strength (blue) in the XZ, XY, and YZ planes for a simulation with dipole tilt of 30, IMF B z = 5 nt, and IMF B y = 5 nt. lines. In this case, the potential does not exactly match that due to convection since incompressibility condition was not assumed. If we impose rv? = 0, the potential pattern exactly matches the convection pattern. [11] Figure 3a (top) corresponds to the summer or northern hemisphere, and Figure 3a (bottom) corresponds to the winter or southern hemisphere. In the northern hemisphere the reconnection maps to the region marked A. A double green line delimits the boundary between open and closed field lines. Note that the convective flow in the ionospheric throat region where the flow changes from sunward to tailward has a large dawnward component in the northern (summer) hemisphere, while it is more poleward in the southern (winter) hemisphere. Chisham et al. [2002] examined SuperDARN observations taken in December and found similar flows. Because the positive dipole tilt, the flow patterns are very different in the northern and southern ionospheres. The perpendicular velocity of the reconnected magnetic field, V?, flows dawnward over the dayside polar region and then duskward on the nightside in the northern 4of12

5 Figure 3. (a) (left) Ionospheric convection and energy flux and (right) electric potential mapped onto the polar region. (b) Zonal component of the electric field along the open-closed boundary. hemisphere (summer). The flow (V?) in the southern hemisphere is more tailward in the dayside polar region. The energy flux deposited in the ionosphere is enhanced in the midnight region of the winter hemisphere compared with the summer hemisphere. [12] In Figure 3a (right), blue and red contours indicate negative and positive potentials, respectively. The ionospheric potential peaks are on the dayside in the north and the nightside in the south. The peak value of the potential is higher in northern hemisphere than that in southern hemi- 5 of 12

6 Figure 4. (a) Configuration of magnetic field lines viewed from the Sun, (b) projection of minimum magnetic field strength, and (c) electric potential comparison between the summer (top) and winter (bottom) hemispheres from a simulation with IMF B z =0,B y > 0, and dipole tilt of 30. sphere. In Figure 3b we have plotted the absolute value of the zonal component of E (the gradient of the potential (E? = rf = V? B) along the open-closed boundary) in the throat region. The zonal component of E in the throat region is larger in the northern (summer) hemisphere than in the southern (winter) hemisphere. The asymmetry of the zonal electric field comes from the increase in the perpendicular velocity due to the reconnection. Moreover, the zonal component of E along the open-closed boundary has two peaks in the late morning and afternoon Duskward IMF [13] Figure 4 shows the simulation results for a case in which the IMF was purely duskward (B y = 5 nt and B z = 0 nt) with a positive dipole tilt. In Figure 4a we have plotted field lines as viewed from the Sun. The geomagnetic 6of12

7 Figure 5. (a) Electric field E c and resistive electric fields (b) jhjj, (c) jhj? j, and (d) jhj k j viewed from the Sun with IMF B z <0,B y > 0, and dipole tilt of 30. Antiparallel region E APN of the northern hemisphere, antiparallel region E APS of the southern hemisphere, subsolar region E SS, and magnetic equator E ME. (e) E? showing directions of the two components at the dayside magnetopause; dotted line indicates reconnected open field line. (f) Current separated into parallel and perpendicular components. field is less eroded by reconnection in this case than for the case with B z < 0 (Figure 2a). The reconnection sites move when we turn off IMF B z. However, the changes in location of the reconnection sites are subtle. In both cases the dusk sector reconnection site labeled A lies sunward of the dawn sector region B. In Figure 4 these regions are closer to the Z axis than those in Figure 2b in both hemispheres. However, there are significant differences in the polar cap potential patterns on the dayside (compare Figure 3a with Figure 4c). Also the electric field along the open-closed boundary (gradient in the potential) is smaller in Figure 4 than in Figure 3. As before the electric field for the B z =0 case is larger in the northern hemisphere than that in the southern hemisphere. The reconnection rate for zero B z is less than that for nonzero B z. Similarly, it is smaller for the two cases with finite B y than for the purely southward IMF case. [14] We have calculated the electric field and projected it onto the ZYplane in Figure 5 for case 2 with B z < 0 and B y >0. In Figure 5a, we have plotted the component of the convection electric field along the direction c. It was calculated from E c = je cj, where E = V B + hj, b = B/jBj, a = J B/jJ Bj, and c = a b. Figures 5b 5d show the resistive electric field, jhjj, in (Figure 5b), the perpendicular component, jhj? j, in (Figure 5c) and the parallel component, jhj k j = je k j = E b = je bj, in (Figure 5d). Figure 5e shows the directions of the two components of the 7of12

8 Table 1. Value of the Electric Fields (E c and jhjj) and Potential Caused by Reconnection a Region APN APS ME SS For IMF Angleq= 315 E c, mv/m jhjj, mv/m f, kv For IMF Angleq= 0 E c, mv/m jhjj, mv/m f, kv a APN delimits antiparallel region in the northern dusk sector, APS is the antiparallel region in the southern dawn sector, ME is the magnetic equator, and SS is the subsolar region. convective electric field, E c and E a (= je aj), and Figure 5f shows the directions of the parallel and perpendicular components of the current. The direction of the current is usually different from that of c because of J k. [15] In Figure 5, we have attempted to consider only the electric fields near the magnetopause. First, we included only values from X > 3 R E. Values from the inner magnetosphere were removed by requiring that jbj B c, where B c was chosen to be 86% of the magnetic field value at the magnetopause (27.6 nt). We made sure only values close to the magnetopause were included by requiring that jjj J c, where J c was taken to be 10% of the maximum magnetopause current density (2 na/m 2 ). Moreover, electric fields from the magnetosheath and solar wind were removed by requiring jvj V c, where V c is 50 km/s or 17% of the solar wind speed. The reconnection electric field values for this case and case 3 with B z = 0 and the positive dipole tilt have been summarized in Table 1. [16] In the northern and southern hemispheres both E c and jhjj are largest in the region where we would expect antiparallel reconnection to occur (Table 1). For instance from Table 1 and Figure 5a the convective electric field (E c ) in the northern reconnection region (1.2 mv/m) is larger than that at the magnetic equator (0.2 mv/m) as well as that at the subsolar point (0.1 mv/m). The convective electric field is larger than jhjj away from the diffusion region, because of solar wind acceleration of reconnected field lines. Reconnection in resistive MHD occurs because of the resistivity. Most importantly the resistive electric field in the antiparallel region also is 50% larger than those in the subsolar and magnetic equator regions (Figure 5b and Table 1) as expected if antiparallel reconnection is dominant. [17] Both jhj? j and jhj k j appear in the antiparallel region in northern and southern hemispheres (Figures 5c and 5d). In particular, jhj k j, which corresponds to the twist of magnetic field lines, splits in two parts with the large values on duskside and very weak values on dawnside. (Within the dashed circle the scale for J k is 0.1 times the scale elsewhere in Figure 5d.) The reasons for this large asymmetry in jhj k j are discussed in section 4. [18] Hesse and Schindler [1988] showed that magnetic reconnection in 3-D with a finite B depends on E k (= hj k ). The results in Figure 5d are consistent with reconnection occurring at high latitudes on the duskside and dawnside. However, in a simulation of a realistic magnetosphere with finite grid size it can be very difficult to isolate parallel currents associated with the reconnection from nearby currents associated with other sources. Field-aligned currents related to the twisting of magnetic field lines (i.e., where the field-aligned vorticity decreases) can be generated near the magnetic equator [see, e.g., Ogino, 1986]. These currents flow away from the equator (by symmetry they are zero right at the equator). Some of these equatorially generated currents can be seen in Figure 5d near the equator. They also flow to higher latitudes near the region which we have believe antiparallel reconnection is occurring complicating the problem of separating out the effects of high-latitude reconnection. [19] The electric potential was calculated by estimating the reconnection width from Figure 5 and is given in Table 1. The potential in the northern hemisphere (summer) is 26% larger than that in the southern hemisphere (winter) for case 2 (Table 1 and Figure 6a). We could not estimate the potential for case 3 (B z = 0) in magnetic equator and Figure 6. (a) Dependence of the polar electric potential in the summer and winter hemispheres on the IMF orientations, where the IMF angles are 270 for southward, 0 for duskward, and 90 for northward. (b) Positive dipole tilt creating different path lengths of reconnected open field lines between the dayside reconnection (Dr) and tail reconnection (Tr) regions. 8of12

9 subsolar point because the reconnection line was unclear. In Table 1, the electric fields at the northern reconnection site are larger than those at the equator and subsolar point. For both cases the electric field at the northern reconnection site is larger than that at the southern site. E c in the northern reconnection region is about 40 80% of the solar wind electric field (E sw = V sw B z = 1.5 mv/m). [20] We have plotted the electric potential in the summer and winter hemispheres as a function of IMF orientation in Figure 6, where f(+), f( ), and f(+) f( ) denote the maximum, the minimum, and the cross polar cap potential, respectively. The solid lines indicate the potentials in the summer hemisphere and the dotted lines indicate the potentials in the winter hemisphere when the dipole tilt is 30. The positive dipole tilt has created different path lengths of reconnected open field lines between the dayside reconnection (Dr) and tail reconnection (Tr) regions (Figure 6b). In Figure 6b, l N is the path length in the northern hemisphere, l S is the path length in the southern hemisphere from Dr to Tr and l is interval between the magnetic equator and Tr region. The positive dipole tilt affects the configuration of the magnetic field, such that the upper region bulges more than the lower region. Thus the upper velocity, V N, is higher than the lower velocity, V S, for the positive dipole tilt as shown in Figure 6b. The polar cap potentials can be different in northern and southern hemispheres for finite dipole tilt. The magnetic flux in the north and south must be equal; however, it does not always require the potential differences to be equal. [21] The cross polar cap potential in the summer is 6 26% larger than that in the winter. The cross polar cap potential decreases when the IMF changes from southward to northward as expected. The winter negative potential is almost 15% smaller than the summer negative potential for southward IMF and 50% smaller for northward IMF. These differences in the cross polar cap potential appear in the zonal component of the electric field in Figure 3b. The north-south asymmetry can be understood in terms of the perpendicular velocity, V?, of the reconnected magnetic field. This is explained in detail in section 4. Figure 7. Schematic diagram showing the factors that may be important for dayside magnetic reconnection in a view from the Sun. Here AP is the antiparallel region, SP is the stagnation point, SS is the subsolar region, MM is the magnetic equator, and FE is the first encounter region where IMF field lines first reach the magnetopause. 4. Discussion [22] It is not easy to determine the reconnection sites, and to understand fully reconnection processes from single point observations or simple superposition of the geomagnetic field lines and IMF field lines since the reconnection process and movement of the magnetized plasma dynamically change the magnetospheric configuration. In this study, we have used global MHD simulations to determine whether antiparallel reconnection or component reconnection better describes dayside reconnection and where it occurs on the dayside magnetopause. Several factors influence dayside reconnection: [23] 1. The angle between the IMF and the geomagnetic field. Reconnection occurs efficiently when the magnetic fields on both sides of the reconnection region are antiparallel [Sonnerup, 1974; Sato, 1985]. When evaluating the magnetic field configuration it is important to consider the draping of the IMF field lines over the magnetopause. [24] 2. The magnitude of the magnetic field. Reconnection occurs efficiently when the magnitude of the magnetic fields on both sides of the magnetopause are the same (jb IMF jjb g j [Sonnerup, 1974], where jb IMF j and jb g j are the magnitudes of the IMF and the geomagnetic field, respectively). [25] 3. The magnetosheath flow velocity. The solar wind decelerates in the magnetosheath and stagnates at the subsolar point. This tends to favor component reconnection. In addition, the flow away from the reconnection site must be considered [Ogino et al., 1986]. [26] In this study, we have carried out simulations that are representative of the interaction between the solar wind and the magnetosphere for cases with southward IMF, nonzero B y and dipole tilt. [27] Figure 7 is a schematic diagram showing where various factors may be important for dayside magnetic reconnection while Table 2 summarizes the relative importance of the various factors such as IMF direction and tilt angle. Here AP denotes the region where the magnetic field lines on either side of the magnetopause are antiparallel, SP denotes the location of the stagnation point of the magnetosheath flow, and SS refers to the subsolar region on the magnetopause. The magnetic equator (ME MM) is the region of the minimum magnitude along the geomagnetic field lines, and FE is the first encounter region where the IMF field lines first reach the magnetopause. [28] For all cases, we found that having antiparallel magnetic fields was the most important factor in determining where reconnection occurs. [29] 1. In case A, when the IMF is southward and the tilt angle is zero, the reconnection occurs in the subsolar region for both antiparallel reconnection and component reconnection. For this case all of the factors (AP, SS, SP, MM, and FE) that may influence the dayside reconnection are found at the same location. 9of12

10 Table 2. Relative Importance of the Characteristic Regions on Magnetic Reconnection at the Dayside Magnetopause for Cases With IMF Orientation and Tilt Angle a Region Tilt Angle 0 Tilt Angle 30 B y =0nT Equator Case A: AP(O), SS = SP(O), MM(O), FE(O) Magnetic equator Case B: AP(O), SS = SP(X), MM(O), *FE(X) Symmetric away from equator Asymmetric near equator away from equator B y >0nT Case C: AP(O), SS = SP(X), *MM(X), *FE(X) Case D: AP(O), SS = SP(X), *MM(X), *FE(X) a AP is the antiparallel region, SS is the subsolar region, SP is the stagnation point, MM is the magnetic equator, and FE is the first encounter region. O, satisfies condition; X, does not satisfy condition; asterisk, no necessary condition. [30] 2. In case B, when the IMF is southward and dipole tilt is positive, reconnection occurs near the magnetic equator (MM) not the subsolar point (SS). The FE condition becomes less important because the IMF lines drape over the magnetopause through the bow shock as shown in Figure 1 reaching the magnetopause away from the reconnection site. Moreover, reconnection occurred preferentially where the IMF encountered the weakest field along the geomagnetic field line, and the magnetosheath magnetic field line was antiparallel to the geomagnetic field (Figure 2). This simulation also shows that stagnation (SP) is not critical for reconnection. However, the reconnection rate was 0.84 times that in the case with no tilt because the magnetosheath flow at the reconnection site (MM) was larger than that at the subsolar point (SS = SP). [31] 3. In case C, when the IMF is southward, duskward, and has zero tilt, the reconnection site splits into two regions located away from the subsolar point [Ogino et al., 1986]. They are located on the northern dusk and southern dawn flanks at high magnetic latitudes. The regions at high latitudes only satisfy the AP condition. Reconnection could simultaneously occur at the subsolar point. However, even though the magnetosheath flow at the high magnetic latitude reconnection region is large, antiparallel reconnection dominates. The reconnection sites also are far from the point of first contact and the location of the magnetic minimum so the FE and MM conditions are not satisfied. Thus the SP, FE, and MM factors are less important than antiparallel magnetic fields for reconnection. [32] 4. In case D, when the IMF is southward, duskward, and has finite tilt, the reconnection also occurs at northern dusk and southern dawn sites. The splitting of the reconnection sites is purely an effect of IMF B y. The sites shift sunward (nearer the equator) in the summer hemisphere and tailward (away from the equator) in winter hemisphere because of the positive tilt angle. When the IMF approaches the minimum field region (MM) for positive tilt, the IMF field lines already have a dawnward and southward motion because of the magnetosheath flow. Moreover, the IMF lines and the geomagnetic field lines are not antiparallel at the subsolar point (SS). Therefore it is hard for dayside reconnection to occur in either the SS or MM regions for finite tilt and IMF B y. The AP condition is the most important at the reconnection sites for B y >0. [33] As was mentioned above, the inclusion of the dipole tilt and IMF B y component breaks all of the symmetry in the location of dayside reconnection. This occurs because the places, where the fields are antiparallel, are no longer symmetrically located. Figure 8 illustrates the reasons for this. Here magnetic field lines have been plotted in views from the Sun (Figure 8, top), dawn (Figure 8, bottom left), and dusk for the case with positive dipole tilt and southward and duskward IMF component (B z = 5nT,B y = 5 nt). In Figure 8 (top), the color shading in the background gives the magnetic field magnitude from Figure 2. The reconnection occurs in the dusk sector of the high-latitude magnetopause in the summer hemisphere and in dawn sector in the winter hemisphere. In the absence of dipole tilt the magnetic configurations in the northern dusk sector and southern dawn sector would be symmetric. Němeček et al. [2003, 2004] analyzed of the satellite data and showed similar schematic structure of field lines for southward IMF B z and without dipole tilt. However, dipole tilt has created asymmetry that strongly affects the direction of the plasma flow following reconnection. After the reconnection, open field lines convect from dusk to dawn in the dayside polar region in the summer N( ) hemisphere (V? in Figure 8 (top)). The transverse velocity, (V N( )? = 40 km/s), is fast and poleward on the duskside in the summer hemisphere while it is tailward and slower (V S(+)? = 29 km/s) in the winter hemisphere. [34] The characteristic features of the effect of the IMF B y and dipole tilt can be explained as follows: the tailward motion is interrupted by a ridge of magnetic field in the northern dusk region and as a result the plasma can move dawnward more easily than tailward (V N( )? ). On the other hand, the velocities in the southern hemisphere (V S(+)? and V S( )? ) are primarily tailward because magnetic field lines are stretched tailward in the southern region. As a result the magnetic field lines are twisted in the northern hemisphere while on the contrary there is little twisting in the southern hemisphere. This results in smaller parallel currents on the dawnside in Figure 5d. The tailward flow and the flat configuration of tail field lines cause the enhancement of the energy flux around midnight in the winter hemisphere (Figure 3, left). Furthermore, we found that the magnitude of the negative potential in the summer hemisphere is larger than that in the winter hemisphere (Figure 3, right). [35] The magnitude of the negative potential (49 kv) in the summer also is larger than the positive potential (44 kv) in the winter hemisphere. The reconnected open field lines are not connected to the both hemispheres. These lead to the different polar cap potential in the northern and southern hemispheres. The peak summer and winter electric fields (E N(+)? + E S(+)? = E N( )? + E S( )? = 14.9 mv/m) have the same value, but the duskward electric field (E N(+)? = 8.7 mv/m) in the summer hemisphere is larger than the dawnward electric field (E S(+)? = 6.4 mv/m) in the winter. The electric field is more broadly distributed in the winter hemisphere. N( ) Therefore in this antisymmetric reconnection case V? 10 of 12

11 Figure 8. Schematic view from the Sun and views from dawnward and duskward of magnetic field lines at the dayside magnetopause for finite IMF B y and dipole tilt. Background color in Figure 8 (top) shows the magnetic field magnitude (also see Figure 2). (= 40.4 km/s) is larger than V S( )? (= 29 km/s) in the dayside S(+) polar region, while V? tends to move toward the nightside. The reconnection rate in the dusk sector is higher than that in the dawn sector because of the positive tilt. [36] Generally, the dynamics of magnetic reconnection depend on the model of resistivity, h as well as the boundary conditions, which are self-consistently treated in the global model. In the present simulation a resistivity model with classical temperature dependency was adopted. It gives similar results to those with a constant resistivity in the local reconnection regions [Ogino, 1986]. The purpose of the present study is to determine which model better describes dayside reconnection and to determine reconnection sites at the dayside magnetopause. Therefore we selected a simple resistivity model rather than a more complex currentdependent resistivity model [e.g., Otto, 2001]. 5. Conclusion [37] We have studied dayside magnetic reconnection by using a full 3-D global MHD simulation of the solar wind and magnetosphere interaction as a function of dipole tilt, IMF B y and B z components. When all three are nonzero the magnetosphere is asymmetric and we must model the entire three-dimensional magnetosphere. [38] We have considered three factors that are thought to be important for understanding dayside reconnection: The antiparallel field condition, the relative perpendicular velocities into and from the reconnection site and the magnitude of the magnetic field at the reconnection site. For a purely southward IMF and finite tilt of 30, reconnection occurs near the magnetic equator (MM and AP region). This is because the reconnection occurs preferentially where the draped magnetosheath magnetic field is antiparallel to the geomagnetic field (AP region). It also occurs where the IMF encounters the weakest field magnitude along the geomagnetic field line (MM region), jb IMF jjb g j where jb g j is the actual field of the magnetosphere at the reconnection site. At that point the IMF should disappear for the antiparallel field case. Furthermore, the reconnection rate for this case with finite tilt is 0.84 times that with no tilt because of increased magnetosheath plasma flow at the reconnection 11 of 12

12 site. This tendency is consistent with the analysis that the polar cap potential is on the average smaller at solstice than at equinox [Cliver et al., 2000]. [39] When the IMF B y is finite, reconnection site moves from the subsolar point to the high-latitude flanks to satisfy the antiparallel field condition. For IMF B y > 0 and a positive dipole tilt, we find that the reconnection site shifts sunward and equatorward in the summer hemisphere, and moves tailward and away from equator in the winter hemisphere. The dipole tilt has created asymmetry that strongly affects the direction of the plasma flow following reconnection. The transverse velocity from the reconnection in the dusk sector is faster and moves from dusk to dawn in the summer hemisphere while it is slower and moves tailward in the winter hemisphere. Reconnection tends to occur efficiently at locations where the magnitude of the IMF approaches the minimum value along the geomagnetic field line, (jb IMF jjb g j). However, other factors, namely the relative angle between the IMF and the geomagnetic field are often more important. For instance at the dayside magnetosphere, reconnection near the magnetic equator (MM region) becomes less effective because IMF field lines move rapidly past the magnetic equator. However, subsolar (component) reconnection becomes less effective for finite tilt because the subsolar region does not satisfied either the antiparallel field (AP) nor the minimum magnitude (MM) conditions. Finally, we examined the electric field in the direction of convection, E c, and the parallel electric field from the simulation. While it is not possible to completely separate hj due to reconnection from that due to other causes, that both hj and E c peak near the location expected for antiparallel reconnection is consistent with antiparallel reconnection being dominant. These results also are consistent with a higher reconnection rate on the duskside than the dawnside (Figure 5d). Thus we conclude that antiparallel reconnection is dominant over component reconnection at the dayside magnetopause for cases with finite dipole tilt and IMF B y component. [40] Acknowledgments. We would like to thank Hiroyoki Shinagawa for a critical reading of the manuscripts. Computing support was provided by the Information Technology Center of Nagoya University. Support was provided by Grants-in-Aid from the Japan Society for Promotion of Science (JSPS) and a grant from the Ministry of Education, Culture, Sports, Science and Technology, Japan (Dynamics of the Sun-Earth-Life Interactive System, G-4, 21st Century COE Program). The work at UCLA was funded by NASA grant NAG [41] Arthur Richmond thanks J. Safrankova and another reviewer for their assistance in evaluating this paper. References Berchem, J., J. Raeder, and M. Ashour-Abdalla (1995), Magnetic flux ropes at the high-latitude magnetopause, Geophys. Res. Lett., 22, Chisham, G., I. J. Coleman, M. P. Freeman, M. Pinnock, and M. Lester (2002), Ionospheric signatures of split reconnection X-lines during conditions of IMF B z < 0 and jb y jjb z j: Evidence for the antiparallel merging hypothesis, J. Geophys. Res., 107(A10), 1323, doi: / 2001JA Cliver, E. W., Y. Kamide, and A. G. Ling (2000), Mountains versus valleys: Semiannual variation of geomagnetic activity, J. Geophys. Res., 105, Coleman, I. J., G. Chisham, M. Pinnock, and M. P. Freeman (2001), An ionospheric convection signature of antiparallel reconnection, J. Geophys. Res., 106, 28,995 29,007. Crooker, N. U. (1979), Dayside merging and cusp geometry, J. Geophys. Res., 84, Dungey, J. W. (1961), Interplanetary magnetic field and the auroral zones, Phys. Rev. Lett., 6, Fedder, J. A., S. P. Slinker, J. G. Lyon, and C. T. Russell (2002), Flux transfer events in global numerical simulations of the magnetosphere, J. Geophys. Res., 107(A5), 1048, doi: /2001ja Gonzalez, W. D., and F. S. 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Stahara (1984), Patterns of potential magnetic field merging sites on the dayside magnetopause, J. Geophys. Res., 89, Maynard, N. C., et al. (2002), Predictions of magnetosheath merging between IMF field lines of opposite polarity, J. Geophys. Res., 107(A12), 1456, doi: /2002ja Maynard, N. C., et al. (2003), Polar, Cluster and SuperDARN evidence for high-latitude merging during southward IMF: Temporal/spatial evolution, Ann. Geophys., 21, Němeček, Z., et al. (2003), Structure of the outer cusp and sources of the cusp precipitation during intervals of a horizontal IMF, J. Geophys. Res., 108(A12), 1420, doi: /2003ja Němeček, Z., J. Šimunek, J. Šafránková, and L. Přech (2004), Spatial and temporal variations of the high-altitude cusp precipitation, Ann. Geophys., 22, Ogino, T. (1986), A three-dimensional MHD simulation of the interaction of the solar wind with the Earth s magnetosphere: The generation of fieldaligned currents, J. Geophys. Res., 91, Ogino, T., R. J. Walker, M. 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Rev., 22, Šafránková, J., Z. Němeček, D. G. Sibeck, L. Pøech, J. Merka, and O. Santolík (1998), Two point observation of high-latitude reconnection, Geophys. Res. Lett., 25, Sato, T. (1985), Three-dimensional reconnection between two colliding magnetized plasmas, Phys. Rev. Lett., 54, Siscoe, G. L., G. M. Erickson, B. U. Ö Sonnerup, N. C. Maynard, J. A. Schoendorf, K. D. Siebert, D. R. Weimer, W. W. White, and G. R. Wilson (2002), Flow-through magnetic reconnection, Geophys. Res. Lett., 29(13), 1626, doi: /2001gl Sonnerup, B. U. Ö (1974), Magnetopause reconnection rate, J. Geophys. Res., 79, T. Ogino and K. S. Park, Solar-Terrestrial Environment Laboratory, Nagoya University, Honohara 313, Toyokawa, Aichi , Japan. (ogino@stelab.nagoya-u.ac.jp; sun@stelab.nagoya-u.ac.jp) R. J. Walker, Institute of Geophysics and Planetary Physics, Slichter Hall, University of California, Los Angeles, CA , USA. (rwalker@ igpp.ucla.edu) 12 of 12