Morphology of magnetic merging at the magnetopause

N. U. CROOKER*

University of California, Los Angeles, CA 90024, U.S.A.

(Recei~edin,/inulfisrnl 30 Jz& 1990)

Abstract---To illustrate the basic features of magnetospheric topology. the development of a global model is traced from the superposition of dipole and uniform fields to the effects of adding, in turn. diffusion regions, surface currents, and a magnetic field component normal to the magnetopause. The subsolar, antiparallel. tearing, and patchy merging geometries proposed in the past all emerge under various conditions. but models that deduce merging geometry from global boundary conditions are lacking. An exception is a model in which the external field merges wherever it falls tangent to the magnetopause. The result is a subsolar merging line that has all the characteristics of early sketches based on local arguments. Magnetosheath plasma beta affects magnetospheric topology and, consequently, merging geometry. Low, high, and variable beta favor subsolar. tearing, and patchy merging, respectively. Proposed flux transfer event models of bursty reconnection from a single merging line, flux ropes from multiple merging lines, and flux tube elbows from patches can also be categorized by plasma beta in the same respective order. The topological modeling reviewed here may prove to be most useful for interpreting merging results from MHD simulations.

1. INTRODUCTION

Scientists are trained to test competing models with

the goal of proving which is correct and rejecting the

others. But space physics models, for the most part, are based directly on observations ; consequently,

there is usually some measure of truth in all of them.

A goal of this review is to bring together those truths from global models of magnetic merging at the mag-

netopause, and begin to synthesize them into a com-

prehensive model. The problem of the global configuration of mag-

netic merging at the magnetopause began with the

attempt to extend DUNGEY’S (1961) two-dimensional picture of merging in the noon-midnight meridian plane into the third dimension. Dungey introduced

the concept of magnetic merging as a means of energy

transfer from the solar wind by having a southward interplanetary magnetic field (IMF) merge with the northward-directed magnetospheric field at a null

point at the nose. Adding an east-west component to the IMF immediately raises the question of relocation of the merging site, since the null is now removed from

the nose. Does merging continue at the nose as long as some component of the IMF is antiparallel to the Earth’s field there? Does it continue because the flow stagnates at the nose? Or does the merging site remove

*On leave at the Geophysics LaboratoryiPHG, Hanscom Air Force Base, MA 01731. U.S.A.

itself to the new location of the null? The problem

arises because no-one knows what controls the merg- ing rate. Nevertheless, progress has been made in

understanding the available options and their conse-

quences. Both local and global approaches have been taken

toward solving the problem of merging site location, and the results from each approach have produced

widely differing patterns in the past. Figure 1 shows the pattern deduced from the earliest local argument

(NISHIDA and MAEZAWA, 1971) that the properties of two-dimensional merging at the null point at the nose

remain unchanged in the presence of a magnetic field

component perpendicular to the plane of the merging configuration (PETSCHEK, 1964). The result is the subsolar or component merging line, tilted from

the Equator by an angle that depends upon the field

strength and orientation on either side of the mag- netopause (e.g. SONNERUP, 1974). Figure 1 assumes equal field strength with the result that the merging line bisects the angle between the IMF and the north- ward-pointing geomagnetic field. Features that dis-

tinguish Fig. 1 from global models are the lack of null points and the field connection directly through the boundary. This review shows how recent advances in global modeling bring the results of the local and

global approaches together again. The review is tutorial rather than reporting. It con-

centrates on global models that begin with the basic components of superposed magnetic fields and then add in appropriate ways the effects of more realistic

II23

1124 N. U. CRWKEH

Fig. 1. A sketch of straight IMF lines merging with curved geomagnetic field lines at the dayside magnetopause. viewed from the Sun, from NISHIUA and MAEZAWA (1971). The heavy curve is the merging line, which passes through the subsolar point; it is tilted from the Equator so that it bisects the angle between the merging fields. The global con- figuration results from extending longitudinally a pattern

derived from local arguments.

features. These models are not dynamic but, because they are analytical, they can aid in our understanding of the result of magnetohydrodynamic models. The topics covered are: (I) the role of null points and of parallel electric fields in the diffusion region, (2) the effects of surface currents on the magnetopause, (3) the role of the magnetic field component normal to the magnetopause, and (4) the variation in mag- netic field topology with plasma beta. In the course of covering these topics, the merging sites that have been proposed in the past will be placed in the context of the giobal models ; these sites are merging patches and the subsolar, antiparailel, and multiple merging lines.

2. NULL POINTS AND PARALLEL ELECTRIC FIELDS

The two-dimensional magnetic topology of the magnetosphere proposed by DUNCEY (1961) can be produced in three dimensions by superposing a dipole and a uniform field (DUNGEY, 1963). In the special case of an exactly southward uniform field, a merging line that is a null line encircles the magnetosphere in the equatorial plane. Otherwise, the magnetosphere is encircled by a separator line containing two null points [see the diagrams of COWLEY (1973), STERN (1973) and SISCOE (1988)]. If the uniform field lies in the plane perpendicular to the Sun-Earth line, as will be assumed throughout this paper, then the nulls are on the flanks and the separator line passes through the subsolar point. The separator line is treated as a

subsolar merging line, but doing so introduces com- plications.

As reviewed by SISCOE (1988), using the static pic- ture of superposed dipole and uniform fields as a time sequence of magnetic field lines passing from the solar wind into the magnetosphere leads to two related problems, illustrated in Fig. 2a. The figure shows field lines on the separatrix surfaces encompassing the open and closed field line volumes formed by superposing a dipole field and a uniform field with southward and duskward components. The resulting magnetosphere has cylindrical tail lobes that extend upward and downward in the direction of the uniform field (instead of being blown back, realistically, by the solar wind). The separator line near the Equator joins null points on either side and marks the intersection of the two lobes with the closed field line volume. The solar wind bIows toward the figure, as indicated, and carries the IMF with it. The first problem arises as a result of the IMF being frozen to the solar wind plasma. A single IMF line is illustrated approaching the mag- netosphere. As it nears the separator line, it must distort greatly to align itself with the separator line, since the latter is also a field line. To pass into the magnetosphere, it must become the separator line and break at the null points [see illust~dtions by COWLEY (1973) and STERN (1973)]. This picture differs con- siderably from the sketch in Fig. 1, where fields con- nect directly across the magnetopause. The distortion required by the model poses a dilemma; it cannot occur on field lines imbedded in a plasma following independent hydrodynamic flow requirements.

The second problem results from the attempt to map the solar wind electric field down to the iono- sphere along the field lines on the separatrix surfaces. All of the field lines on the north tail lobe converge to the duskside null point at 0 kV and then map down to the duskside ionosphere along a single field line on the polar cap boundary, and all of the field lines on the northern half of the closed field line volume ema- nate from the dawnside null point at 60 kV and dis- tribute themselves around the circumference of the polar cap boundary save for the singular dusk point. The result is an infinitely large electric field in the ionosphere at dusk, where the potential changes from 60 to 0 kV and back to 60 kV across a single point.

Both problems can be resolved with the addition of a magnetic field diffusion region, as illustrated in Fig. 2b. Usually diffusion is introduced along the entire length of the separator line (e.g. COWLEY, 1973 ; VASY- LIUNAS. 1984). but SISCOE (1988) demonstrates that a limited region is sufficient to solve the two problems. In a diffusion region, the magnetic field no longer is frozen to the flow. Thus the first problem is resolved

Magnetopause magnetic merging 1125

by allowing convecting field lines outside the diffusion

region to ‘change partners’ with those within

(COWLEY, 1973). The partner-changing is from inter-

planetary-to-interplanetary field line until a separatrix surface is reached. At this time, the fields are con- nected to one of the two nulls, as Fig. 2 illustrates for all field lines in the separatrix surfaces, but the nulls

play no active role in the merging process. Merging occurs as the field lines pass through the portion of the separatrix surfaces that intersect the diffusion region and change their connection from inter-

planetary to geomagnetic partners ; but since partner- changing is confined to the diffusion region, merging

can be remote from the nulls, as in Fig. 2b. The addition of a diffusion region solves the infinite

electric field problem by allowing electric fields par- allel to the magnetic field within the region. The cen-

tral role of these parallel electric fields in the recon-

nection process in general has been discussed recently by SCHINDLER et al. (1988). Here we continue with

the specific argument given by SISCOE (1988). Consider the field line in Fig. 2b that emanates from the dawn

null at 60 kV and passes along the surface of the closed

field line volume just above the separator lint. When it emerges from the diffusion region, its potential has

dropped to 20 kV, and this is the potential that sub-

sequently maps down to the polar cap boundary in

the ionosphere. The neighboring field line that passes

further from the separator line and through a smaller volume of the diffusion region emerges at 40 kV. Thus the potential becomes distributed along a finite scg- ment of the polar cap boundary rather than being concentrated at a point. The longer the diffusion region is along the separator line, the longer the polar

cap boundary segment over which the potential becomes distributed. A uniform diffusion region encompassing the entire length of the separator line

between the nulls results in a potential drop dis- tributed evenly completely around the polar cap

boundary from dawn to dusk.

3. SURFACE CURRENT EFFECTS

Although the dipole-plus-uniform-field superposi-

tion model provides separator boundaries between magnetospheric and interplanetary field lines, it has

no magnetopause boundary with currents to shield the dipole field from the solar wind plasma. The

effects of shielding currents can be added to the model on a plane surface, following CHAPMAN and

Fig. 2a

1126 N. U. CROOKER

Fig. 2b.

Fig. 2. Magnetic field lines on separatrices formed by superposing dipole and uniform fields, from SISCOE (1988). The uniform field lies in a plane perpendicular to the solar wind flow vector. The cylinders directed upward and downward contain open field lines representing magnetospheric tail lobes, and the enclosed torus contains closed field lines. The separatrices intersect along the singular separator field line that encircles the volume and joins null points at either side. Field lines just outside the volume are not connected to the dipole but are highly distorted, as illustrated by the IMF line in (a). Numbers indicate solar wind electric potential that maps down along field lines to the ionosphere. (a) Since all field lines on the separatrices converge at the null points, the potential drop that they transmit to the ionosphere concentrates at a singular point, resulting in an infinite electric field there, with the rest of the polar cap boundary between open and closed field lines being an equipotential (upper right). (b) The problem of the infinite electric field is resolved by adding a diffusion region around some portion of the separator line, in which electric fields can be parallel to the magnetic field. The solar wind potential drop is then distributed across the shaded area of field lines leaving the diffusion region on the tail lobe surface and, also, across field lines mapping from the diffusion region down to the ionosphere along the torus surface. The ionospheric equipotential pattern (upper right) assumes that a symmetric diffusion region exists on the nightside of the

separator.

FERRARO (193l), by placing an image dipole field of magnitude equal to the Earth’s dipole field in the

vicinity of the solar wind arrow in Fig. 2. The resulting

magnetosphere appears flattened on the sunward side. as if a knife, with a vertical stroke, had sliced off the face of the cylindrical volume in Fig. 2 [see SISCOE’S (1988) fig. 51. The two nulls move forward to the plane current surface, and the separator line joining them bifurcates. A qualitative sketch with the tail lobes blown back and the plane magnetopause draped over the usual bullet-shaped magnetosphere is shown in Fig. 3. All field lines on the magnetopause surface

converge at the two cusps, as in the original Chap- man-Ferraro picture, but the presence of the uniform field adds to that picture the two null points on the

flanks joined to the cusps by the split separator line. The latter forms the clefts that separate the open lobe field from the closed, dipolar field. Thus the model has both a cleft and a cusp. This is possible because the magnetic field is aligned with the cleft rather than perpendicular to it, as first conceived [see, for example, fig. 1 in WALTERS (1966)].

The position of the clefts in the model depends upon the magnitude and orientation of the superposed

Magnetopause magnetic merging I221

Fig. 3. The Fig. 2 model with surface current effects added. The model is sketched in the realistic bullet shape, with the tail lobes blown antisunward by the solar wind. The currents split the separator line on the magnetopause surface into clefts, exposing closed field lines between them, and configure the surface field to converge at the cusps. The model has open tail lobes but is closed in the sense that there is no magnetic held component normal to the boundary

(CROOKER. 1990b).

uniform field. The hemispherically symmetric sketch in Fig. 3 represents the model with a southward uni-

form field. (Note that split separators form even in this special case, where, without surface current effects, a

neutral line rather than a separator line crosses the dayside.) Figure 4a illustrates how increasing the mag-

nitude of the uniform field brings the clefts together. The view is from the Sun, and the clefts are the cal-

culated split separator lines on a plane magnetopause (CROOKER, 1985). The encircled dots are the positions

of the Chapman-Ferraro cusps without the addition of a uniform field. Adding a weak field yields the

outermost contour; it passes through cusps slightly displaced equatorward and joins equatorial null

points at a distance of 20 R, from the subsolar point (scaled to a distance of 10 RE between the Earth and the magnetopause plane). When draped over a bullet- shaped magnetosphere, the outer contour would

resemble the clefts in Fig. 3, with null points on the flanks. Increasing the uniform field causes further

equatorward displacement of the cusps and displace- ment of the nulls toward the subsolar point, with con- sequent shrinking of the area enclosed by the separ- ator lines joining the cusps and nulls. The limiting case occurs when the uniform field strength reaches

the magnitude of the Chapman-Ferraro field strength at the subsolar point. which is twice the dipole strength there. The cusps and nulls then converge to the subsolar point, and the clefts disappear. [See CROOKBR and SISCOE (1986) for consequences of this limit.]

Figure 4b was constructed in the same manner as

Fig. 4a except that the uniform field was given a dusk- ward component equal to the southward component.

(a)

(b) ’ 1 I I I

-20 0 20RE

Fig. 4. Families of clefts or split separator lines, calculated for a range of uniform field strengths superposed upon dipole and image fields on a plane magnetopause. The dots marking the cusps and nulls where each pair of separators meet trace out the antiparallel merging lines (after CROOKER, 1986a). The dashed portions of the separators extend beyond the clefts and separate IMF lines from open lobe field lines. Each separator pair may be considered as the configuration in a single layer of a finite-thickness magnetopause. (a) South- ward uniform field -B_ forms symmetric tail lobes, as in Fig. 3. (b) Uniform field with equal southward and duskward components, -B_ and + B,, respectively, skews separators

and lobes.

The results differ in several respects. First, the nulls

locate off the Equator, at higher latitudes, and the cusps displace more sideways than equatorward. Consequently, the contours that connect the cusps and nulls to form the clefts are skewed. Second, the

limiting case occurs when the uniform field strength reaches a value less than the subsolar value, a value equal to the maximum in the ChapmanFerraro field

along the loci formed by the cusps and nulls in each hemisphere. The innermost contour connects these points. which mark the coalescence of cusp and null points.

The most important feature of Fig. 4 is that the cusps and nulls trace out the antiparallel merging lines, defined as the loci where the IMF (uniform field) and magnetopause magnetic field are antiparallel. These were proposed as merging sites by CROOKER (1979) as an alternative to the subsolar merging line, but their relation to the topological features of cusps and nulls was not realized until later (CROOKER, 1986a). Here we see their significance in the context

112x N. U. CROOKER

of building a global, topological model of the mag- netosphere. They arise as a consequence of adding surface currents to a dipole-plus-uniform-field mag- netosphere model, and they constrain the location of the clefts.

In the model considered so far, only one of the cleft contours connecting one pair of nulls appears in any version, depending upon the strength of the uniform ticld relative to the dipole fields. However, one can imagine adding to the model a finite-thickness mag- nctopause in which the uniform field increases from a weak value inside to a strong value outside (CKOOKER and Srscnt-l. 1984). Altllough this con~guration remains to bc tested quant~t~itively. it seems reason- able to assume that alf of the clefts in Fig. 4 would form a surface within the magnctopause layer, and the chains of nulls would form neutral lines along the antiparallel merging lines for any IMF orientation (CROOKER, 1986a).

A complication arises, however, in converting the two-dinlensional patterns in Fig. 4 to a three-dimen- sional, thick magnetopause (VASYLI~N~S, publiccom- munication. 1987). Consider a model in which the ChapmanFerraro field is formed by superposing a dipole field with a series of small image dipoles slightly displaced from each other along the x-axis. Except for the symmetric case of southward IMF, these fields introduce a small field component normal to the mag- netopausc at the sites of all but the outermost two nulls, where the Chapman-Fer~ro field falls to zero. The result is chat the antiparallel merging lines are no longer true neutral lines; however, they remain sites of weak magnetic field.

Whether a magnetopause surface, as in Fig. 3, or the more complicated finite-thickness magnetopause is considered, it is clear that adding surface currents to the superposed field model dispfaces the separators and nulls associated with merging lines away from the subsofar region. The next section shows how adding a magnetic field that penetrates the magnetopause can return the merging site to the subsolar region.

4. NORMAL FIELD COMPONENT

Up to this point. our model magnetosphere is open in the sense that the tail lobes are connected to the IMF but closed in the sense that there is no magnetic field component normal to the magnetopause sur- face that connects the internal and external fields (CR~OKCR, 1990b). It is the normal component that plays a major role in merging theories. since its mag- nitude is proportional to the merging rate (e.g. LEVY PI QI., 1964). A normal component must be present

during periods of active merging. Models with this feature have been classified by Srsco~ (1988) as ‘cur- rent penetration models’, since the normal component penetrates the magnetopause current layer. Most of the following treats current penetration over the entire magnetopause surface; but, first. we consider pen- etration in patches.

The concept of ‘patchy reconnection’ was explored by SCHINDLER (1979). partly in response to LEMAIRE'S (1977) suggestion that solar wind plasma crosses the magnetopause by impulsive penetration of’ localized plasma parcels with excess momentum. More recent models of patchy rcconnect~on and implications for the nlagnetospheric boundary layers and convection have been considered by a number of authors (e.g. KAN. 198X; NISHIDA. 1989: CRooRea. 1990a.b: HESS~ et (I/., 1990). The models begin with a closed magnetopause surface and then add patches through which the IMF and geomagnetic fields connect by a normal field component. The models assume that the

patches are diffusive. in order for the fields to ‘change partners’.

In the global model in Fig. 3. diffusive patches can bc added in the closed magnetopause region between the clefts. (Such a region occurs even in the case of a finite-thickness magnetopause. for example, the cen- tral region in Fig. 4b. For southward IMF. in Fig. 4a, a closed region is present if the uniform field has less than its limiting strength.) There is a curious fcaturc about the field topology with the addition of merging across these patches: the separator lines and null points play absolutely no role in the reconnection process. That this is possible was first recognized by SCHINDLER et 01. (1988) and later developed by HESSE. et al. (1990) : they label the process ‘generalized recon- nection’. to contrast with the specialized null-sep- arator reconnection discussed in the literature up to that time. Recall that the diffusion region in Fig. 2b contains a segment of the separator line. It plays a central role in merging there because, without surface currents on the boundary, it is the only place where closed field lines lie adjacent to IMF lines and, thus, can interconnect. And, although the nulls are remote from the merging site in Fig. 2b, they play at least a passive role by connecting to the merging fields. In contrast, in the region between the clefts in Fig. 3, no field line connects to the nulls on the Ranks. Merging in patches allows newly connected field lines to pass locally through the boundary independent of nulls and separators.

Observed signatures that support the concept of patchy reconnection, for example, flux transfer events (FTEs). suggest that the patchiness may be super- posed upon quasi-steady-state merging, at least dur-

CONFINED DIPOLE

~agn~topaus~ magnetic merging

Fig. 5. Superposing a uniform field on a dipole confined to a spherical magnetosphere adds a magnetic field component normal to the magnetopause everywhere except along the great circle where the uniform field lies tangent to the sphere. This circle, marked T,-TV in the lower diagram, forms a subsolar merging line (ALEKSEYEV and BELEN’KAYA, 1983).

called a tangent merging line (CKOOKER cl ~1.. 1990).

ing periods of south~rd IMF (e.g. &UDDER, 1989).

Models of steady-state merging usually require a mag-

netic field component normal to the magnetopause

everywhere. Adding a global normal component to our superposed field model with surface currents in

Fig. 3 changes the magnetic field topology in a major way: it restores the subsolar merging line that was lost with the addition of surface currents and changes

its appearance from the separator geometry in Fig. 2 to the sketched geometry based on local arguments in

Fig. 1. Thus, the addition of a global normal com-

ponent is the turning point that begins to bring the local and global models back together again.

The characteristics of the merging line for a global

current penetration model were first demonstrated by ALEKSEYEV and BELEN’KAYA (1983). Their method and results are illustrated in Fig. 5. To obtain a mag- netic field component normal to the magnetopause

current layer everywhere, they chose to superpose a uniform field with a dipole field confined to a sphere rather than behind a Chapman-Ferraro plane. The curvature of the sphericai current surface auto- matically allows penetration of a uniform field. [Sur- face curvature could also be obtained by increasing the strength of the image dipole in the Chapman- Ferraro configuration, as is commonly done in other

Fig. 6. If the Fig. 5 dipole partially leaks through the mag- netopause, and if only a fraction of the uniform field pen- etrates the magnetosphere, then the resulting superposition yields a tangent merging line that tilts more toward the Equator. bisecting the uniform field clock angle, as in Fig, 1

(CROOKEK L’/ c/l., 1990).

applications (e.g. TAYLOR and HONES, 196.5).] It is

clear from the figure that the uniform field provides a normal component everywhere except along the great circle where it lies tangent to the sphere. It follows, then, that this circle must be the merging line, where the normal field reverses. CROOKER et al. (1990) call

it a ‘tangent merging line’. Following concepts of current penetration models

developed by VOIGT (e.g. 1981), CROAKER et ul. (1990)

extend the work of Alekseyev and Belen’kaya by allowing the dipole field to leak and only a fraction of the uniform field to penetrate, as illustrated in Fig. 6. The resulting superposition tilts the tangent

merging line so that it lies closer to the equatorial plane. Setting the leaking flux equal to the penetrating flux, as expected for magnetic merging, tilts the line so that it bisects the IMF clock angle.

At this point we have succeeded in creating an ana- lytical. global model with a merging line that has all the characteristics of the schematic merging line in Fig. 1. including its tilt angle, which was based on local arguments. Figure 7 gives a three-dimensional view of the Fig. 6 model in the Fig. I format, with field lines connecting along the merging line. That the field lines in Fig. 7 are calculated, not sketched. makes

1 IXI N. U. CROOKER

Fig. 7. .+‘+ three-dimensional view of the Fig. 6 tangent merg- ing lint model, showing field lines connected along the merg- ing line, to emphasize the similarity with Fig. 1. Whife Fig. 1 is a sketch based on local arguments. Fig. 7 gives results

of a global calculation.

the similarity with Fig. 1 remarkable. Neither figure has null points or separator lines, in contrast with the models in Figs 2 and 3. (The tangent merging line has some but not all properties of a separator line ; it lacks the property of being a magnetic field line.) In both Figs 1 and 7, field lines connect directly across the magnetopause rather than divert to null points. As noted by ALEKSEYEV and BELEN’KAYA (1983), this feature maps directly down to the polar cap boundary and allows the electric potential to be distributed rather than concentrated at points, without invoking diffusion (yet), as was required for the Fig. 2 model.

The tangent merging line model also raises the ques- tion ‘What happened to the null points? As dem- onstrated by GREENE (1%X8), nub are very stable aspects of magnetic topology. The answer is that they lie within the magnetopause and reappear when the boundary is given finite thickness, a calculation that remains to be done. Their location will he at the sides of the sphere where the dipolar and uniform fields are antiparallel. These points are marked TzV and T, in Fig. 5. It is easy to understand that nulls will form there in a finite-thickness magnetopause, since within the layer, from outside in, the external field decreases and the internal field increases. At some depth they will be of equal strength and cancel each other out.

With the formation of nulls in a finite-thickness ma~etopause comes the separator line topology and the infinite electric field problem illustrated in Fig. 2a. Thus one cannot avoid invoking parallel electric fields in a diffusion region in the tangent merging line model, as in Fig. Zb, nor can one avoid at teast a passive role

for nulls and separator line. Although in the limit of an infinitely thin magnetopause the merging fields connect directly across the boundary, and this limit is appropriate for practical appli~a~jon in view of observed scale sizes, in a realistic, finite-thickness magnetopause the fields become magnetically con- nected to the remote null points at the moment of merging, as described for Fig. 2. Only in patchy recon- nectinn can nulls be dissociated from merging. The difference between the Fig. 2 modd and the tangent merging line model is the presence of the magncto- pause current Iayer, which controls the location of the merging line.

The relationship between the magnetic topology of the tangent merging line model and the loci where the merging fieids are antiparallel has not been addressed. Unlike the Fig. 3 model, from which the antiparallel loci in Fig. 4 were developed, the spherical model in Figs 5-7 has no tail lobes and, thus, no cleft or split separator line topology. To address this question, one would need to impose a normal component on a finitc- thickness magnetopause version (e.g. Fig. 4a) of a model with pre-existing tail lobes (e.g. Fig. 3), a com- ponent in addition to the normal Chapman-Ferraro component within the layer, and map out the topalogy in the weak field regions of the antiparallel loci.

On the other hand, taking the tangent merging line model as given, the concept of antiparallel merging C;in be incorporated by postulating that the merging rate along the line increases with the degree of shear between the merging fields. Figure 8 shows solid anti- parallel merging hnes and dashed tangent merging lines for various IMF orientations as viewed from the Sun. It is clear that they differ greatly in the subsolar region but, at the periphery, they nearly coincide. As noted by CKU~KEK et ab. (1990), if the merging rate along a tangent merging line is highest where it nearly overlies the corresponding antiparallel merging lines,

the result is a simple synthesis of the two models. Finally, the distribution of the normal component

on the magnetopause may not be determined by global, external conditions as in the tangent merging liae model, wher-e the merging line lies where the draped IMF naturally falls tangent to the mag- netopausc, hut by some other criterion. For example, TOFFCUTTO and HKIL (1989) constructed a quan- titative model with the features of Fig. 3 and then specified the location of the merging line and a normal component distribution consistent with assumed merging outflow velocities. They began with the sub- solar merging line in Fig. 1 and then modeled anti- parallel merging lines by placing a merging gap in the middle of d subsolar line. It is interesting to note that even though their normal component was not

Magnetopause magnetic merging 1131

predict for high beta, and single subsolar merging

lines into the topology for low beta.

Fig. 8. A comparison between antiparallel (solid) and com- ponent (dashed) merging lines on the dayside magnetopause, viewed from the Sun, for a range of five IMF orientations. For southward IMF, both lines lie on the Equator. As the IMF rotates toward northward, the antiparallel lines with- draw from the subsolar region while the component lines continue to pass through it. However, away from the sub- solar region. the two kinds of lines remain coincident as they move to higher latitudes. If the merging rate along a component merging line is proportional to the degree of shear between the merging fields, then it essentially becomes

As reviewed earlier (CROOKER, 1986b), PODGORNY

et al. (1978) first demonstrated magnetic topology

changes at the dayside magnetopause in a laboratory terella experiment simulating the solar wind inter- action with the magnetosphere for southward IMF.

They showed that the topology is considerably differ- ent for high and low values of the simulated solar wind Alfven Mach number M,, which is proportional

to plasma beta. For low M,, the noonmidnight mer-

idian cross-section appears identical to the standard merging picture first presented by DUNGEY (1961). with connecting fields at the subsolar point. But for

high M.,, which is normal for measured values, a large, closed loop between two, .x-type nulls at high latitudes

covers the dayside. Further. PODGORNY et (11. (1980)

showed evidence that the loop disintegrates into tcar-

ing islands.

an antiparallel merging line.

determined by global. external conditions, their merg- ing geometry is nearly identical to the tangent merging

line with variable merging rate based on field shear,

as described above.

5. VARIATION WITH PLASMA BETA

PASCHMANN et al. (1986) found that accelerated

boundary layer flows at the dayside magnetopause, a signature of merging, increase in speed with decreas-

ing plasma beta (the ratio of thermal energy density to magnetic energy density) in the adjacent mag- netosheath. This result is consistent with models which indicate that plasma beta may play a significant role in merging topology. In general, merging rates

should increase with decreasing beta, as magnetic forces become significant (e.g. SONNERUP, 1984) and Paschmann et al. specifically suggest that increased tearing may be responsible for their result. However, as pointed out by SIsco~ (1988), accelerated flows from multiple merging lines between tearing islands would oppose each other and tend to cancel. Detec- tion of accelerated flows from a single merging line should be clearer. Furthermore, tearing islands fit nat- urally into the magnetospheric topology that models

The results of PoDCoRNY et a/. (1978) can be placed

in the context of the Fig. 3 model with its Fig. 4a cleft position dependence on the magnitude of the superposed uniform field. Weak uniform field rep-

resents high plasma beta and gives clefts joining cusps at high latitudes. In noon-midnight meridian cross- section, the cusps are y-type nulls but can easily con- vert to -u-type to accommodate a closed loop between

them (CROOKER, 1985 ; SISCOE, 1988), reproducing the

Podgorny et al. high M, result. On the other hand, strong uniform field represents low plasma beta. In

the limiting case where the uniform strength is equal to the shielded dipole strength at the subsolar point, the clefts and cusps converge to the subsolar point; the resulting noon-midnight meridian cross-section then becomes the Dungey merging picture, in agree- ment with the Podgorny et al. low A4,, result. For a finite-thickness magnetopause version of the Fig. 3- 4a model with strong uniform field, the single null at the subsolar point extends into an equatorial merging line in the third dimension (CROOKER, 1986a).

Tearing, then, fits into the high beta field topology, although at this stage there is no global model that produces multiple separator or merging lines between the split separators that form the clefts. Simulations of local tearing at the dayside magnetopause also are consistent with the global result. LEE (1988) shows that a tearing configuration can convert to a single .Y- type, null topology by varying a number of parameters in his simulation box. One of these parameters is Alfven speed V,,. which is inversely proportional to plasma beta. Low V,4 and, therefore, high beta, favor tearing.

PODGORNY et al. (1980) and, later, LEE and Fu (1985) recognized that tearing islands. extended in the

FLUX TRANSFER EVENT MODELS Variation with Plasma Beta

VARIABLE Flux rope elbow

HIGH Tearing

Multiple X-lines

LOW Bursty Reconnection

Single X-line

Fig. 9. The variation of flux transfer event models with plasma beta. Variable beta may yield the flux tube elbows of RUSSELL and ELPHI~ (1979), as suggested by CKOLEY rt al. (1986) [ftg. from CKMXE~ (1990a)l. High beta may lead to the transverse flux ropes of PODGOKNY et uf. (1980) and LEE and Fu (1985) from tearing between multiple merging lines [fig. from BAUM (1984)]. Low beta may result in the longitudi~ily elongated plasmoids of SOUTHW~O~ et al. (1988) and SCHOLER (1988) from bursts of quasi-steady-state

reconnection at a subsolar merging line [fig. from SCHOLER (1988)].

third dimension to form coils, make a viable model for flux transfer events. According to the global topology results, these FTEs should occur under high beta con- ditions. Two other FTE models are illustrated in Fig. 9 along with the tearing model. On the right are the longitudinally elongated plasmoids formed by bursts of reconnection at a single merging line, proposed by SOIJTHW~OD et al. (1988) and SCHOI,ER (1988), and on the left is the original model of isolated flux tube elbows formed as a result of patchy reconnection, proposed by RUSSELL and ELPHIC (1979). GIobal topology indicates that the former should occur under low beta conditions ; the latter may occur under vari- able beta, generated, for example, by drift mirror waves in the magnetosheath, as suggested by CROLEY et al. (1986). Thus, magnetosheath plasma beta may be used either to test between FTE models or, in the spirit of synthesis, to distinguish between different types of FTEs that may occur at different times, as Fig. 9 illustrates. The right two sketches in Fig. 9 also illustrate the difference in noon-midnight meridian topology For high and low beta, as discussed above,

On the other hand, the ordering in Fig. 9 may be complicated by other factors. For example, KAN (1988) suggests that, in three dimensions, tearing may occur in patches rather than in elongated coils. This kind of pattern develops naturally in laboratory

experiments (GEKELMAN and PFISTER, 1988) and is discussed in the context of dayside merging by GEKEL-

MAN er al. (1990). The resulting FTE topology would be Aux tube elbows formed under high beta conditions, without the Fig. 9 requirement that beta be variable.

Another complication arises with regard to the cause of the accelerated flow-beta correlation of Paschmann etal., cited at the beginning of this section. SIXOE (private communication, 1988) has pointed out that magnetosheath beta is a function of the angle between the IMF and the Earth--Sun line (cone angle). Maximum field compression and, consequently. mini- mum beta occur when the cone angle approaches 90”. Since southward IMF has a cone angle of 90’, it follows that the increased accelerated flow speed for low beta may be a consequence of enhanced south- ward field in the magnetosheath rather than the low beta itself. Large cone angle also decreases beta at the magnetopaLlse owing to increased plasma depletion (MIDGLEY and DAVIS, 1963; LEW. 1964; ZWAPU’ and WOLF, 1976), which, in turn, leads to the development of drift mirror waves (CR~OKER and SISCOE, 1977) and variable beta. Small cone angle produces mag- netosheath fluctuations and upstream pressure vari- ations (e.g. FAIRFIELD it ul., 1990) which may induce patchy reconnection. All of these factors should be

taken into account when sorting according to plasma beta.

FTE observations

I . Null points and parailei electric &Ids

(a) Nulls organize magnetospheric topology, but reconnection can occur at sites remote from nulls.

(b) Diffusion regions dismiss the need for distortion of merging field lines along a separator lint and create field-aligned potential drops that alleviate the problem of infinile electric fields at nulls.

(a) The addition of magnetopause currents to superposed di~le-plus-uiliform-field models of the magnetosphere splits the dayside separator line and brings the nulls to the surhce.

(b) The split separators pass through the cusps and form clefts that meet on the flanks at the nulls.

(c) The position of the nulls depends upon the strength of the uniform field superposed to form the tail lobes.

(dj The locus of nulls for varying uniform field strength traces the antiparallel merging lines.

(a) Global penetration of the IMF and leakage of the Earth’s field form 3 field component normal to the magnetopausc.

(bj Addition of a normal field component destroys the two-dimensional nulls that form the antiparallel merging lines in a finite-thickness magnetopause ver- sion of the superposed field model.

(c) Addition of a global normal field component to a model with currents confined to an infinitely thin surface yields a subsolar merging line identical to early merging line models extrapolated from local argu- ments.

(d) This subsolar merging line locates where the external iield lies tangent to the magnetopause.

(ej Tha tangent and antiparallel merging lines nearly coincide away from the subsolar region, where the mergmg rate may be highest.

4. C’oriucion M?th plasma heta

(a) Laboratory experiments and superposition models indicate that magnetospheric topology varies with maenetoshcath plasma beta.

(b) High beta favors tearing between split scp- arators that form clefts.

(c) Low beta favors a subsolar merging line. (d) Variable beta favors patchy reconnection. (e) Flux transiir event models can be sorted into

the above three beta categories.

7. CX~NCLCISION

CJlohal models of the magnetic topology of the mag-

netosphere can serve as tools for organizing obser- vations but, because they lack dynamical features. perhaps their most useful role will be the intermediary one of interpreting topological ‘data’ from dynamical computer simulation models. For example, in an

MHD simulation of the magnetosphere for high IM t (proportional to beta) (FEDDER and LYOY. 1990, private communication), merging occurs at neutral lines that appear to track the antiparallel loci, and reverse draping of the freshly connected field lines mimics the hend in the dashed separators that cxtcnd tailward of the clefts III Fig. 4. Thus. the merging topology in the MHD simulation closely resembles the Fig. 3 model with a finite-thickness magnctopausc laycrcd with the Fig. 4 separators-an antiparallel merging model. 1 Iowcvcr. as discussed in detail above, the Fig. 34 model has no field component normal to the ~n~~gnetopause, wh~clt must certainly exist in the MHD simulation: yet imposing a globally determined normal component on the Fig. 3 4 model t,which has yet to bc quantified) will destroy the nulls that fom

the antiparallel merging lines and replace them with a subsolar. tangent merging line, which is not appar- cnt in the simulation. This dilemma has yet to be resolved (possibly by lowering 2U t in the Fcddcr-- Lyon stmulatlon, although a time-dependent scheme that is independent of :I+‘, seems more promising: F~IXXX. pri~atecommuttication. lY90]. Nevertheless.

even at this stage it 1s clear that the topological and dynamical models share common features and that

pursuing studies of both will hasten our tmder- standing of lhe cnmpiicatcd morphology of magnetic

merging at the magnetopause.

Acknouicduemmr-This reciew was nresented at the 1988 IAGA Sy&osium on Global Ma&etosphenc Dynamics and WAS supported by the National Science Foundation under grant ATM87-22962 and by the Air I‘orce Unwer~~ty Resident Research Prqram.

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