JOURNAL OF GEOPHYSICAL i•ESEAI•CH
VOL. 72, NO. 23
DECEMBER 1, 1957
Some Remarks on the Position and Shape of the Neutral Sheet
CHRISTOPHER T. RUSSELL AND KENNETH
I. BRODY
Institute o• Geophysicsand Planetary Physics
University o• California, Los Angeles, California 90024
Recent measurements have delineated some of
the major featuresof the structureof the earth's
geomagnetic
tail [Ness, 1965; Speiserand Ness,
1967]. The so-calledneutral sheet is an important feature of the tail dividing it into two
main regionswith the largest flux components
directed, respectively,parallel and antiparallel
to the solar wind. The existingmeasurements
suggesta relatively simple empirical formula
for the locationof the neutral sheetin the geocenttic solar magnetosphericcoordinatesystem,
in which many researchersorder their data
taken in the tail [see for example,Speiserand
Ness, 1967; Murayama, 1966; Bame et al.,
1967].
In this coordinatesystem the X axis points
toward the sun; the Z axis, coplanar with the
X axis and the earth's magnetic dipole axis,
points abovethe ecliptic plane; and the Y axis,
which completesthe right-handedCartesianset,
points to the dusk meridian. The X-Y plane
rocks with respect to inertial spacewith a 24hour period so that the geomagneticequator
always cuts the solar magnetosphericequator
along the Y axis. The orderingof data in this
coordinatesystem acknowledgesthe dual control of the geomagneticdipole and the solar
wind on the direction of the field lines in the
tail. Ideally, we would like our X axis to be
antiparallel to the solar wind flow vector, corrected for the aberration of the solar wind by
coordinatesystempointedtoward the sun.However, again, the nonradial flow of the solar wind
introducesa differencebetweenthesetwo ar•gles.
Thus we will alwayshave somescatter when we
attemptto ordertheneutralsheetpositions
in
the nonidealcoordinatesystem.
The
neutral
sheet serves to divide
the tail
into two regionswith substantiallyequal magnetic fluxes acrossany Y-Z plane, oppositely
directed above and below the neutral
sheet.
The magneticequator servesa similar function
within the magnetosphere.
There is a component of the field toward the dipole axis in the
northern hemispherean'daway in the southern.
Thus a simple rational model of the neutral
sheet would place its closestapproach to the
earth on the geomagneticequator just outside
of the particletrappingregionon the night side
of the earth.As the neutralsheetextendsaway
from the geomagnetic
equator,it may be assumedto quickly take a positionso that lines
of constantY coordinateare nearly parallel to
the solar wind and perhapsasymptoticallyapproach the X-Y plane at a great distancefrom
the earth.
Assumingthat the neutral sheet starts out
from the geomagneticequator and that there
is no dependenceon the distance behind the
earth, it is easyto showthat we expectto fin'd
the neutral sheet at a distance Z• above the
solar magnetosphericequator where
the earth's orbital .motion. This is not neces-
sarily the solar direction [Wolfe e• al., 1966],
and the fluctuationsin velocity and direction
observedwill produce a scatter in the measurements of a feature that is well defined and fixed
Z• -- F•(Y•) sink
(1)
Here Y•. is the Y coordinateat the point of
observation,X is the angle betweenthe dipole
axis and Z axis. We defineX as positive when the
in the ideal coordinate system. Another useful north magnetic pole is pointed toward the sun
parameter in addition to the spatial coordinates and negativewhen the north magneticpole is
of a feature is the angle between the dipole pointedaway from the sun.
axis and the Z axis at the time of the measureSuch a formula has already been used by
ment. This would be the same as the geomag- Speiser and Ness [1967] and by Murayama
netic latitude of the subsolarpoint if the ideal [-1966]. Speiserand Ness [1967] assumedno Y
6104
LETTERS
dependenceand found F•(Y•)
to be equal •o
6105
I
I
I
I
i IMPI
OGO I
10 Rs -+- 3 Rs for ]Y•] _< 6 Rs. Murayama
[1966]setF•(Y•) -- 8 Rs for [Y•] _<8 Rs and
zero otherwise,in order to estimatethe distance
from the neutral sheet at the times IMP
I was
within the geomagnetictail. However we have
no a priori reasonto excludeeither a Y dependenceor X dependence.
If we wanted to take accountof the tendency
for the neutral sheet to approach the magnetospheric equator, we would multiply the righthand side of equation I by a function of the
distanceof the point of observationbehindthe
earth. Then (1) becomes
Zj•r= Fi( YN)F2(XN) sin X
(2)
if the X 'dependence
is independentof Y.
Two sets of data on the positionsof.the neutral sheet have been reported up to this date.
These are the IMP 1 measurements[Speiser
and Ness, 1967] and the OGO 1 results [Brody
et al., 1967]
Table 1 lists the crossingswhen X was equal
to or greater than 5ø. This arbitrary cutoff in
X was chosen since the errors inv'olved are
io
5
o
Y DISTANCE
-5
(EARTH
-IO
RADII)
Fig. 1. The distanceabove the magnetospheric
equator normalized by dividing by the sine•)f the
magnetic latitude of the subsolar point plotted
versusthe magnetosphericY coordinatefor neutral
sheet crossingsobserved by IMP I and OGO 1.
Distances
are in earth radii.
foun'd in the OGO 1 data have been omitted
becauseof insufiSeientdata coverageeither before or after the erossing.Figure 1 is a plot of
Z•/sin X versus Y. The error bars indicate the
change that would occur in g•/sin X with a
changein X of --+3ø. This plot is equivalent to
possibly greater than 3ø and the plotting of normalizing'the positionof the observedcrossthese points in Figures 1 and 2 requires a
ings to the equivalent position if the dipole
division by sin X. In addition severalcrossings axiswere alignedwith the solarwind. If equation
1 holds,i.e. there is no X dependence,and the
TABLE
1.
neutral sheetstarts from a circle in the geomagnetic equator,then within the errors mentioned
Satellite
Orbit
X
Y
Z
X
above we expect the points to fall on a circle.
If the neutral sheet started from an ellipsein
--12 7
.1
8
30
--65
IMP 1
the geomagneticequator, the points would fall
--11 0
- .2
-9
31
--65
on an ellipsein this plot. Within the scatter of
33
--53
--81
- .2
-5
the data shownhere a circle fits just as well as
--13 7
-.1
6
34
--18 5
OGO
-1
35
40
41
42
43
43
44
44
45
45
45
46
47
47
--17
--18
--14
--14
--27.8
--25.2
--27.5
--19.3
--16
--25
--26
--27
--25
-23
142
--14.5
--11.6
--13.3
143
145
5
2
8
0
8
4
5
5
0
8
--11 8
--62
--53
-- 4.5
-.1
--
.4
+
1.3
--
.3
+
.2
+ 2.3
+2.5
+ 5.9
+5.2
+4.5
9.5
6.2
11.1
.7
.5
1.8
2 1
1 6
24
2 5
3 7
4 0
3 5
3 4
2 5
4.6
4.9
7
11
9
16
10
9
16
25
,12
18
32
30
25
.3
-1.2
-1.3
8
-11
-11
25
an ellipse.Althougha strictly circularshape
would not be expectedphysically,the spreadin
the data doesnot justify a more complicated
approximationthan a circle. If there were a
strongdependence
of g• on X, then the points
wouldfill the circlerather than lie near its edge,
provi'ded,of course,therewasenoughvariability
of the X coordinatesin the sampling.The lack
of a strongX dependencesuggested
by Figure
1 is verified by Figure 2. There those points
with Y coordinate between -+1.5 RB have been
plotted versusX. There is no obviousdecrease
of Z/sin X with X, but the statisticsare poor,
and there are no data at geocentricdistances
greaterthan 28 Rs.
6106
LETTERS
I
I
i
20--
_
-•
I0--
o
i
i
-10
i
-20
X DIST.•,NCE
(E.•,RTH
-30
-, 0
R.•,DII)
to lie closeto the magnetospheric
equator (the
Z = 0 plane). Other more reasonablefunctional forms for F• (Y,), giving an asymptotic
approachof the neutral sheetto the magnetospheric equator with increasingdistancefrom
the center of the tail, would require fitting two
arbitrary parameters,e.g., for a Maxwelltan.
We feel that the above formula shouldprove
usefulin studyingphenomenain the magnetotail whenevera knowledgeof the distancefrom
the neutral sheet is an important parameter.
abovethe magnetospheric Acknowledgments. We wish to thank ProfesFig. 2. The distance
equator normalized as in Figure 1 plotted versus sor R. E. Holzer and Dr. E. J. Smith for helpful
the distance behind the earth for those neutral
discussionsand advice during the preparation of
sheet crossingsof •igure 1 with a Y coordinate this note.
between ñ 1.5 R•.
This work representsthe results of one phase of
researchperformed for the Jet PropulsionLaboraWe concludefrom the abovethat in properly tory, California Institute of Technology,sponsored
ordering data taken in the tail it is necessary by the NASA contract NAS7-100.
to know the direction and velocity of the solar
REFERENCES
wind outside the tail at the same time as the
observations within the tail are being made.
This is of courseobvious.However, even if the
coordinatesystemused to order the 'data were
Bame, S. J., J. Asbridge, H. E. Felthauser, E. W.
Hones, and I. B. Strong, Characteristicsof the
plasma sheet in the earth's magnetotail, J. Geo-
rotated
Brody, K. I., R. E. Holzer, and E. J. Smith, OGO
1 search coil magnetometer measurements in
the geomagnetic tail (abstract), Trans. Am.
Geophys. Union, J8, 168, 1967.
Murayama, T., Spatial distribution of energetic
electrons in the geomagnetic tail, J. Geophys.
Res., 71, 5547-5557, 1966.
Ness,N. F., The earth's magnetictail, J. Geophys.
with
the
X
axis
of the
coordinate
systempointingin a directioncorrectedfor the
nonradial
solar wind
flow and the associated
aberration angle, the neutral sheet does not
coincidewith the X-Y plane (whenever the
dipole is not perpendicularto the solar win'd),
but rather it is a curved surface touching the
X-Y plane at the edgesof the tail and furthest
from the X-Y plane in the center of the tail.
For regionswithin about 11 R• on either side of
the center of the tail
and less than 30 R•
behind the earth, the data presentedhere suggestthat a reasonableempiricalfit is given by
phys.Res.,.72,113-129,1967.
Res., 70, 2989-3005, 1965.
Speiser,T. W., and N. F. Ness, The neutral sheet
in the geomagnetictail: Its motion, equivalent
currents, and field line connnection through it,
J. Geophys. Res., 72, 131-141, 1967.
Wolfe, J. H., R. W. Silva, I). I). McKibbin, and
R. H. Mason, The compositional, anisotropic
and nonradial
flow characteristics
of the solar
wind, J. Geophys.Res., 71, 3329-3335,1966.
=
-
x
with Ro equal to 11 R•. Between Y• -- 11 and
the ee•geof the tail we expectthe neutral sheet
(Received July 10, 1967;
presentation revised August 18, 1967.)