JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 103, NO. A3, PAGES 4723-4737, MARCH 1, 1998
Magnetic field near Venus:
A comparison between Pioneer Venus Orbiter magnetic
field
observations
and
an MHD
simulation
E. Kallio • and J. G. Luhmann
Space SciencesLaboratory, University of California, Berkeley
J. G. Lyon
Department of Physicsand Astronomy, Dartmouth Collage, Hanover, New Hampshire
Abstract. PioneerVenusOrbiter (PVO) measurements
revealedthe shapeand the
changinglocation of the Venus bow shockwith solar cycle and provided a detailed
picture of the magneticfield pileup in the daysidemagnetosheath.Nevertheless,the
reasonfor the increaseof the terminator shockposition to the observeddistances
has evadedour understanding,and the "magnetic barrier" region has been studied
primarily by comparisonswith gasdynamicmodels due to the difficulty of using
more sophisticated treatments. In this study we investigate the extent to which
a three-dimensional
magnetohydrodynamic
(MHD) modelof the Venus-solar
wind
interaction, with and without "mass loading" by photoionizationof the atomic
oxygenupper atmosphere,can reproducesomeof the basic featuresof the dayside
magnetic field observedon PVO. The ideal MHD model usesa conductingsphere
to representthe basic Venusionosphericobstacleto the solar wind flow. We adopt
the viewpoint that during solar maximum, a conductingobstaclewith oxygenmass
loading is appropriate, while a no-massloading caseis a good first approximation
to the solar minimum situation. The MHD simulationsare found to give a realistic
picture of both the shapeof the bow shockand its observedelliptical crosssection
at the terminator. The introductionof the oxygenmassloadingmovesthe shock
position to that observedat solar maximum. The magnetic field strength on the
daysidehas a dependenceon solar zenith angle similar to that found in statistical
analysesof the PVO data, although the field is strongerthan that measured.
The mass loading creates a layer near the planet where the magnetic pressureis
replaced with the thermal pressuremuch like observed. Our studies also raise
the questionof the role of nightsideflow vorticesin the formation of the effective
obstacleboundary. Overall, our results illustrate that many features seen in the
MHD model are consistentwith the previouslyreported observationsof the Pioneer
Venus Orbiter.
1.
Introduction
sellet al., 1988]andthe subsolarregionwherethe magneticpressure
playsan importantrole [see,e.g., Zhang
Improved computational capabilities have recently
et al., 1991]. Comparisons
of the modelresultswith
made it possibleto simulate the global features of the
Venus-solarwind interaction processusing global mag-
observationscan lead to better insightsof the physics
underlying
global behavior than is possiblewith any
netohydrodynamic
(MHD) models. Becausethe magother
approach.
netic field is taken into accountself-consistently,
these
There are several basic features of the solar wind
modelsare expectedto be a good approachto studying
observed
featureslike the asymmetric
bowshock[Rus- interactionobservedby PioneerVenusOrbiter (PVO)
that a realistic global model must reproduce. First,
•Now at Finnish MeteorologicalInstitute, Geophysical the shape and location of the bow shock are quite well
known[see,e.g.,Russellet al., 1988;Zhanget al., 1990,
and references
therein]. The bow shockis closestto
Research, Helsinki.
Copyright 1998 by the American GeophysicalUnion.
Paper number 97JA02862.
Venus during solar minimum and movesoutward with
increasingEUV flux. This behavior may be a result
0148-0227/98/97JA-02862509.00
of massloadingby VenusJan
oxygen(O+) ionsadded
4723
4724
KALLIO
ET AL.: MAGNETIC
FIELD
NEAR VENUS
to the solar wind flow becausethe photoionization rate
increaseswith the increasingEUV flux. Moreover, the
crosssection of the bow shock is known to be asymmetric with respect to the direction of the cross-flow
depletionthat occursin the innermostbarrier (magnetosheath)wherethe magneticfield is strong. The
componentof the interplanetarymagneticfield (IMF).
1994; Murawski and Steinolfson,1996a; de Zeeuw et
At the terminator the bow shockis closerto the planet
at the magnetic "equator," i.e., on the plane of the IMF
containingthe Venus-Sunline than on the planeperpendicular to it, i.e., at the magnetic"poles." This may be
a consequenceof the fact that the magnetosonicspeed
is different along the magnetic field than perpendicular to it. Second,the magnetic field is piled up on the
dayside of Venus forming a region know as the mag-
al., 1996],but 2-D modelscan only offera limitedapproximationof the full 3-D problem.Several3-D MHD
modelshavebeenappliedto Venus[Wu, 1992;Tanaka,
1993; Cableand Steinolfson,1995] and a 3-D MHD
modelwas most recentlyusedto study mass-loading
ef-
magneticfield effectsare taken into accountin the two-
dimensional
(2-D) MHD models[McGaryandPontius,
fects[Murawskiand'Steinolfson,
1996b].Of course,
the
3-D MHD
models also have their
limitations
because
all usea singlefluid description.Moreover,they do not
netic barrier [see,e.g., Braceand Kliore, 1991;Zhang include finite ion Larmor radius effects which are taken
et al., 1991,andreferences
therein].The solarwinddy- into accountin hybridmodels[Brecht,1990;Brechtand
namic pressureturns to magneticpressureat the obsta- Ferrante,1991;Mooreet al., 1991]. Nevertheless,
they
cle boundary and is then replacedwith thermal pressure have the potential to contribute to our understanding
of planetary ions near the ionopause.In the magnetic providedthat we keep these limitations in mind.
barrier the magnetic pressuredecreaseswith increasAnother cautionary note concerningthe globalmoding solarzenith angle(SZA) in roughaccordance
with els is that they may give somewhatdifferentresultsbecause of the different numerical schemes used. The sosimple Newtonian pressurebalance equation.
These features have previouslybeen studied using
lutions of various models can thus differ although the
variety of global models. The location and shapeof the modelsare basedon the sameequations. In our work we
bow shock have been studied with gasdynamicmodels usea 3-D MHD schemethat has beenusedto study the
[Belotserkovskii
et al., 1987;SpreiterandStahara,1992] interactionbetweenEarth and the solarwind [Fedder
and MHD models[Wu, 1992; Tanaka,1993; McGary andLyon,1987,1995].In the model,asin all previous
and Pontius, 1994; Murawski and Steinolfson, 1996a,
3-D MHD models of the Venus-solar wind interaction,
b; Cableand $teinolfson,1995;de Zeeuwet al., 1996] the surface of the obstacle is an infinitely conduction
aswell as hybridmodels[Brecht,1990;BrechtandFer- sphere.We have simulatedboth the casewith no mass
rante,1991;Mooreet al., 1991].The generalconclusion loading and when the ionization of upper atmosphere
of the mass-loading studies is that the mass loading
movesthe bow shock farther from the planet but that
the ionization rate has to be larger than the photoion-
oxygen atoms is taken into account. Our model uses
a nonuniform spider-web-like mesh which differs from
the onesusedin previousmodelsfor Venus. This mesh
ization rate in order to move the bow shock as far as ob-
providesespeciallyfine grid spacingnear the subsolar
served[Spreiterand Stahara,1992;Mooreet al., 1991; region.
McGary and Pontius, 1994; Murawski and Steinolfson,
In this study we use our 3-D MHD model with and
1996b].The physicsof the subsolar
regionhasbeen
withoutmassloadingto makea detailedcomparison
be-
other focusof these models. The modelshave generally
succeededin producing a region where the magnetic
field is piled up near the planet in a manner at least
qualitatively consistentwith the observations. However, a detailed study of this region is difficult with
tween the model and PVO magneticfield observations
global modelsbecausethe computationalgrid is often
too largeto resolvethe near-boundaryregion.Another
difficultyconcernshowthe collisionalionosphere
should
be taken into account as an obstacle.
The models are
also expectedto be somewhatlimited near the planet
becausethey usean ideal Ohm'slaw everywherearound
Venus.
The accuracyof a global model is evaluatedprimary
on its ability to reproduceobservations. Various approximations used in the global models restrict their
realism. The gasdynamicmodel doesnot include the
magneticfield self-consistently.The solutionis axially
symmetric,and thus, for example,the crosssectionof
the bow shock is a circle. Its ability to describethe
obtained near Venus at solar minimum and solar max-
imum. In particular,we studythe location,shape,and
asymmetryof the bow shockand their dependence
on
massloading.We thenexaminein detailthe magnetic
barrier, its dependenceon SZA, and behaviorof the
regionjust abovethe conductingsphereand the possible roleof vorticeson the nightsidenearthe terminator
producedby the massloading. Finally,we compare
our resultswith the previousglobalsimulations,
especially previousMHD simulations,and point out some
similaritiesand differences.Overall, the modelseems
to reproducemany of the featuresobservednear Venus
and leadsto further insightsas to their causes.
2. MHD
Model Description
Our simulationsare carriedout by numericallysolvphysicsof the magneticbarrier is alsolimited [Zhang
et al., 1993a]becauseit doesnot describethe plasma ing the standard ideal MHD equations
KALLIO
ET AL.'
MAGNETIC
FIELD
NEAR
VENUS
4725
i.
i.
a)
+ v. [pv]= s
ß
0(pV)
t-V.pVV
+I(p
+•--•o)
- =0(2)
Ot
ß
-0 (3)
[pV
2 ffp)V+Bx(VxB)]
--+V.
(•+
oqt
7-
I
ß
ß
ß
2.5
ß
ß
ß
ß
po
ß
ß
ß
ß
ß
ß
ß
ß
ß
c•B
oqt
V.[VxB]=0.
(4)
ß
ß
ß
ß
where p is the mass density,V is the fluid velocity,p
ß
ß
ß
ß
ß
ß
ß
ß
ß
,
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
ß
is thermal pressure(assumedisotropic),J is current
density, mo is permeability, B is magnetic field, E is
electricfield,and e is the energydensity(= pV2/2 +
B2/21•o+ p/(-- 1) with- equalto theratioof specific
heats). The mass-loading
term "S" on the right-hand
side of the continuity equation accommodatesatmospheric sourceswithin the single fluid approximation.
0.5
Equations(1)-(4) both with and without the massloadingterm have beenusedin severalearlier MHD simulations, although the numericalalgorithmsand grids
usedvary from study to study. In our model the solutions are obtained usingessentiallythe samemeshand
algorithm as used in the global simulationsof the solar wind-magnetosphere
interactionby Fedderand Lyon
1.5
I
0.5
b)'ø•
0
-0.5
-1
-1.5
•
[1987]. The major differenceis the introductionof a
central conductingsphereas the obstaclein place of a
dipole field.
The mesh point locations used in the simulation are
shownin Figure la.
The 24x32x40 (=30,720) grid
pointsare within the region-6.3 < X < 1.6 Rv, 0.07 <
R(= x/Y•' + Z2) < 4.2 Rv (Rv is radiusof Venus).
Grid points are on 24 planes,and Figure la showsone
of these planes. The angle betweenthe planes is 15ø
and the grid points on these planes can be obtained
by rotating the grid points in Figure l a around the X
axis. As seen in Figure la, there are 32 grid "lines"
on a grid plane. Each grid line contains40 grid points,
_01
10
0
101
102
103
104
IZXrl(km)
Figure 1. (a) The grid pointsusedin the MHD model.
(b) The distanceof the grid pointson the three "grid"
lines shown in Figure la: lines 1, 7, and 13. Each line
includes40 grid points.
perature" is specifiedin terms of a soundspeedof 50
and the grid line closestto the X axis (markedby 1 in km s-• whichcorresponds
to the sonicMach number
Figure l a) is almostradial in contrastto the lineson Ms = 8. At the surface of the conductingspherethe
higher SZA. Note also that becausethe length of the normal componentsof the velocity and magnetic field
grid line near the subsolarpoint is smallest,the resolu- vectors are assumed to vanish. This condition is ention is highest there. Figure lb showsmore clearly the
forced by making the interior boundary of the spider-
grid resolutionalongthreegrid lines(lines1, 7, and 13 web-like mesh coincide with that surface. The surface of
in Figure l a) whichstart at SZA •-. 3ø,40ø, and 80ø on the conductingspherein the simulationwas assumedto
the surfaceof the obstacle, respectively. In Figure lb be located at 300 km altitude, the averageheight of the
the horizontalaxis showsthe distanceof the grid points subsolarionopauseobservedduring the Pioneer Venus
on thesethreelines.Near the subsolarline (line 1) this Orbiter primary mission[see,e.g., Brace and Kliore,
distanceis generally,0<100km, the minimumbeing-060 1991].
km (-00.01Rv). Note that line 13 crosses
the terminaSimulationswere run for both no atmosphericsource
tor plane at R .• 2.2 Rv so that the resolutionnear the (S=0) in the continuityequation(1) andwith a source
bow shock at the terminator is -00.1 Rv.
representingionization of a combinedoxygen corona
For the present case the following boundary condi- ("hot" component)
andthermalexosphere
("cold"comtions were adopted. The solar wind parameters are ponent).The photoionization
sourceSpnwasdescribed
magnetosonicMach number MM$ ----4.5, solar wind by the sum of two exponentialsin altitude, giving the
density
n = 18cm-a, bulkvelocity
Usw
= (-400,0,0)km s-•, andinterplanetary
fieldB•m•-
photoionizationion productionrate qpn,which is the
oxygendensityn(O+) multipliedby the photoioniza(B•, B•, B•) = (0,14,0)nT. Theupstream
plasma"tern- tion frequencyv for atomic oxygenat Venus, and the
4726
KALLIO
ET
AL.'
MAGNETIC
FIELD
NEAR
VENUS
oxygen mass; a cosinefactor was used to approximate
et al., 1987;$preiterandStahara,1992]anda 2-D MHD
the decrease in ionization
model[McGaryandPontius,1994]'n(O+) = 3 x 10a
cm-3 s-1 exp(-(h- 400)/400),whereh is the distance
rate as a function of solar
zenith angle(SZA)'
from the Venus surface in kilometers.
$pn= qpnmo= n(O+)
I
mo=
.,300
h-h--300
1co(SZA)
Equation (5) givesthe mass-loading
rate due to the
mo.
(5)
In (5), at = 3.3 x 10• cm-3 andae = 8.3 x 104cm-3
are the oxygen densities at 300 km altitude for the
thermosphereand exosphere,respectively;Ht = 15 km
and He = 450 km are the approximatescaleheightsof
each contribution, and h is the altitude in kilometers.
The oxygen photoionizationrate at solar maximum is
photoionization. However,the total ion production rate
at Venus may be about 3 times larger than photoionization rate alone, if one takes also into account electron
impact ionization and the chargeexchangeprocessbe-
tweensolarwindprotonsandoxygenions[Zhanget al.,
1993b].In this studywe havethusmultipliedthe nom-
inalphotoproduction
rate(1.35x 10-6 s-1) bya factor
of 3 to mimic
the additional
ionization
due to electron
impact ionization and charge exchange. Therefore in
y • 1.35x 10-6 s-1 [Zhanget al., 1993b],
andmoisthe our simulationwe usedin (1) a sourceterm
atomic oxygen mass of 16 amu.
The density of the assumedoxygen atmosphereat
SZA angles0ø,30ø, and 60ø are shownin Figure 2a.
The dots in Figure 2a showthe oxygendensitybasedon
PVO UV measurements
on one orbit at solar maximum
5' = 3 x
The value of the total
= (3 x qp/) mo
ionization
(6)
rate $ in three SZA
angles(0ø,30ø,60ø) are shownin Figure 2b.
It is important to be recall that the valuesin Figure
from SZA 30ø- 53ø (data pointsadoptedfrom Nagy et 2b determine the strength of the mass loading effect
al. [1981]).For a comparison,
the dottedlinein Figure in our MHD model becausethe mass loading depends
2a illustrates the approximationfor the oxygendensity on the total ion production rate S. It has been found
usedin mass-loaded
gasdynamic
(GD) [Belotserkovskiiin several earlier mass-loadingstudies concerningthe
location of the Venusian bow shock that the production rate based on observedoxygen density profiles is
a)
too small to move the bow shock as far from Venus as
observedduring solar maximum. For example, when
lOOO
Spreiterand $tahara[1992]useda oxygendensityprofile shownin Figure 2a (the dotted line), they had to
80O
multiply the obtained photoionizationproduction rate
\\
km
?
6O0
qphby a factorof 10 to movethe shockfartherfromthe
planetnotable.Whenthis 10x qphtotal productionrate
profile(Figure2b, dottedline) wasusedin a 2-D mass-
sz,=o.
sz,=6oo
400
Figure 2. The density and the ion production rate
profilesof oxygenusedto study the massloadingeffects
20O
in this and in somepreviousstudies.(a) The threesolid
103
104
105
106
107
Thedensityofoxygen(cm-3)
b)
108
linesshowsthe oxygendensityusedin the presentstudy
for SZA = 0ø, 30ø, and 60ø. The dots showsthe PVO
oxygen measurementsbased on UV data. The dotted
line shows the oxygen density used in a gasdynamic
(GD) model [$preiterand $tahara, 1992,Figure 17],
andin a 2-D MHD model[McGaryandPontius,1994].
The shaded region is below the obstacleboundary in
our MHD model (h = 300 km) and is not a sourceof
O+ ions.(b) The production
rate of O+ ionsat various
\
400
/sz,--o.
••SZA
- =60
ø
2oo
lo3
.................
lo4
lo5
lo6
The ionproduction
rateq (m-3
heights. The solid lines are obtained by multiplying the
densitiesshown by the three solid lines in Figure 2b by
the nominalphotoionization
frequency
of 1.35x 10-6
s-1 times3. The dottedlineshowsthe production
rate
when the mass-loadingeffectsare found to be important
accordingto the mass-loaded
GD simulation[Spreiter
and$tahara,1992,Figure18, caseno - 3 x 105cm-3,
Hno = 400 km], and MHD simulations[McGary and
Pontius,1994].This productionrate is 10 timeshigher
thanthe photoionization
production
rate (qph)obtained
from the dotted line in Figure 2b and the photoioniza-
tion frequency
of 10-6 s-1.
KALLIO
ET AL.: MAGNETIC
FIELD
NEAR VENUS
4727
loadedMHD model, it was found to be strongenough although the total magnetic field in the X Z plane is
to producea boundarylayerabovethe planet[McGary qualitatively much like the field in the XY plane, the
and Pontius,1994]. Later, a hybridsimulationusinga solution is asymmetric.
productionrate consistentwith the observedoxygenion
outflowrate in the Venustail alsohad to multiply the 3.2. Shape of the Bow Shock
coronaldensity by a factor of 5 to movethe bow shock
Plate 2 showsthe total magnetic field at the termiappreciably[Mooreet al., 1991]. However,whenthe nator plane as seen from the sun in our MHD model.
observeddensity profile was usedin a mass-loadedGD
The bow shockis located farther from the planet in the
modelby Belotserkovskii
et al. [1987],the bow shock loadedmodel. In that respectthe solar maximum looks
in the mass-loadedcase was found to be considerably like the mass-loaded MHD case and the solar minimum
farther from the planet than the bow shock in their like the unloaded MHD case. Note that in Plate 2 the
unloadedmodel, although this mass loaded result was
magnetic field is stronger on the magnetic polar plane
questionedby Spreiterand Stahara[1992]. It should
than on the magnetic equatorial plane in the magne-
finally be notedthat Spreiterand Stahara's10 x qph tosheath near the bow shock because the former is a
total productionrate profile(Figure2b, dottedline) is
region of a perpendicular shockand the latter a quasimuchlike our valuesat SZA •0<30ø suggesting
that our
adoptedmassloading rate are expectedto affect to the
flow notable.
3.
PVO
Measurements
and
MHD
Model: A Comparison
3.1.
Overview
Plates la and lb showcontoursof the averagetotal
magneticfield measuredby PVO duringsolarminimum
parallel shock. Moreover, the crosssection of the bow
shockis asymmetric,the bow shockbeing farther from
the planet in the XZ plane than in the XY plane, i.e.,
at the magnetic poles than at the magnetic equator.
The asymmetry is seen clearly when the bow shock is
comparedwith the two circleswhich representthe average distanceof the bow shockbasedon PVO measurements.
Figures 3 and 4 give a quantitative comparisonof the
bow shock in the MHD
model and PVO
data shown in
(1985-1987)and solarmaximum(1979-1981)periods. Plates I and 2. Figure 3 showsa comparisonof the avThe PVO displayswere obtainedfrom I min magnetometer data by assumingaxial symmetry around the
X axis. The dark blue colorshowsthe regionwherewe
do not have PVO measurementsdue to spacecraftorbital sampling.Note that we do not havethe samespa-
erage location of the bow shock. In all casesthe shape
of the bow shock is modeled by a conic section r --
R•-(1 +e cos(SZA)),whichgivesthe planetocentric
distance of the shockr at a given solar zenith angle, SZA
(R•-is the distanceof the bowshockat the terminator
tial coveragefor solar minimum and maximum because planeand e is the eccentricity).The PVO resultsused
of the evolution of the PVO orbit. In particular, for here are for high coneangles(> 60ø), e.g., when the
solar minimum the periapsiswas higher, and therefore anglebetweenthe IMF and the solarwind velocity was
we do not havemeasurements
in the daysidemagnetic larger than 60ø, becausethe cone angle in the MHD
barrier. For solar maximum, in contrast, we have data model was 90ø. Accordingto PVO measurements,the
near the planet from the magneticbarrier and the iono- averagevaluesare (Figure 3) (R•- = 2.15 Rv for sosphere. The bow shockis visible in both Plates la and lar minimumand (RT) = 2.45 Rv for solarmaximum
lb as an region of increasingmagneticfield. Note that
from
rgur a]). At
the measurementsare a sum of a long time period in- Venus,e is typically•0.66 [Zhanget al., 1990]which
cludingdifferent solarwind dynamicpressureand IMF givesthe nosealtitude RN: (RN) = 1.30 Rv for solar
values, and therefore the bow shock is a rather wide minimumand (R•) = 1.48 Rv for solarmaximum.
transition region in Plates la and lb.
Figure 3 illustrates that the MHD model reproduces
Plates lc and ld show the total magnetic field in the shape of the bow shock quite well for both solar
the (ecliptic)XY planeaccording
to the unloadedand minimum and solar maximum. In the MHD model the
loadedMHD models,respectively.This plane is ideal location of the bow shockwas obtained by determining
for studying the magneticbarrier near the planet be- the position of the bow shock on the grid lines on the
causePVO had a nearly polar orbit with a periapsis XY and XZ planes(seeFigure la). The positionof
near the ecliptic plane. The bow shockand the mag- the bow shock was taken to be at the midpoint of the
netic field compressionnear the subsolarpoint can be
seen in both Plates lc and ld. The compressionof
the magneticfield is a result of the magneticfield line
geometryin the model which is much like the geom-
bow shock gradient. The values obtained for the unloaded case are Rs = 1.37 Rv, RT x¾ = 2.03 Rv and
the magneticfield in the (polar) XZ plane. Note that
to be the averageof R•, x¾ and R•, xz in the unloaded
RT xz -- 2.18 Rv and in the loaded case RN -- 1.47
Rv, RTX¾ -- 2.27 Rv andRTxZ2.42Rv. Here
etry obtainedin a 3-D MHD modelby Tanaka[1993] RT x¾ and RT x z are the distancesof the bow shock
where the magneticfield lines pile up on the dayside at the terminator on the XY and XZ planes, respecand then slip around the planet. Plates le and If show tively. If the averageterminator distanceR•, is taken
4728
a)
.
b)
PVO' solar minimum
PVO' solar maximum
,
2.5
25
nT
80
½(Rv)
1,5
60
40
0.5
0.5
2
1.5
1
0.5
0
-0,5
2O
2
c) unloaded
MHD,XV-plane
1.$
1
o.$
o
-o.5
loadedMHD,XV-plane
2.5
nT
2
Y (Rv)
1.5
60
40
0.5
0.5
20
BIMF
o2
1.5
I
0.5
0
-0.5
BIMF
I
-1
e) unloaded
MHD,XZ-plane
-
o
2
3
2.5
2,5
2
2
Z (Rv) ,.•
,
f)
,
1.5
1
0,5
0
0
-0.5
loadedMHD,XZ-plane
nT
,.,;
60
I
1
40
o.$
o.s
20
0
•)BIMF •
'
2
1.5
I
0.5
0
-0.5
-1
(•BIMF
0
2
1.5
1
X(RV)
0.5
0
-0.5
-1
X(Rv)
Plate 1. The total magneticfieldnearVenusat (a) solarminimumand (b) solarmaximum
basedon PVO measurements.
The total magneticfieldaccording
to MHD model(c) without
mass
loading
and(d) withmass
loading
ontheXY plane,and(e)withoutmass
loading
and(f)
with massloadingon the XZ plane.In the MHD modelthe IMF hasonly a y component.
MHD model RT = 2.11 Rv and in loaded MHD model
RT = 2.34 Rv. The massloading thus movesthe bow
shockby approximatelythe observedamount,although
it movesthe bow shockslightly lessthan observedat
the terminator.
In the unloaded case the nose altitude
is greater,while the terminator positionis againslightly
less than observed.
It should be noted that the conic
sectionmatchesthe shapeof the model bow shockquite
KALLIO
ET AL.' MAGNETIC
FIELD
NEAR VENUS
4729
i
3 i
2-
1
40
33
26
20
-3
3
•
13
i
Plate 2. The total magneticfield at the terminatorplanein (a) the unloadedand (b) loaded
MHD model. The solidlineson the unloaded(loaded)MHD modelshowa circleof the radius
of 2.15 Rv (2.45 Rv) whichrepresents
the averagedistanceof the bow shockat the terminator
on solarminimum(maximum)basedon PVO observations
[Zhanget al., 1990].
well in both XY and X Z planesboth in the loaded and
the unloaded
MHD
models.
0.39, and in the loaded caseit is 0.32, 0.35, and 0.39 at
X - 0.5, 0 and -0.5 Rv planes, respectively.
Figure 4 showsthat the shape of the crosssection of
the bow shockis muchlike observed.It alsorepresentsa
more correct comparisonof the terminator values with
the measurementsthan shown in Figure 3 because it
displaysthe location of the averagepositionof the bow
shock, and we know that the shock shape is not circular. The curves are planetocentricellipses,and they
are determined by the distanceof the bow shockon the
XY plane, RT xY, and on the X Z plane, RT x z. The
crosssection of the bow shockis shownat three planes
at X - - 0.5, 0, and 0.5 Rv in the unloaded and loaded
Figure 5 shows a quantitative comparisonbetween
the PVO data and the MHD model in the dayside
magnetic barrier by comparing the normalized magnetic pressureas a function of altitude. The normalized
magnetic pressureis defined as the magnetic pressure,
tively. They show an ellipse where R7 xY - 2.14 Rv,
In these profiles, K = 0.86 was assumed,and the dy-
3.3. Magnetic Barrier
B2/21•o,dividedby the dynamicpressure
of KpV•'.
Here p is the mass density of the solar wind, V is the
velocityof solarwind, and K is a constant[see,e.g.,
cases.
Zhanget al., 1991]. In Figure 5a the valueof K was
ThePVObowShock
results
fortheterminator
plane about 0.844-0.881 and p includes5% of helium. The
seenin Figure4 arefromRussellet al. [1988].The PVO normalizedheight hnorm,is equalto (h - h•p)/(h•p +
results are oriented so that the component of the IMF
Rv), whereh•p is the heightof the ionopauseand Rv
perpendicularto solar wind velocity vector is along the the radiusof Venus. The PVO measurements
(Figure
Y axis and the data were collectedfor high coneangles 5a) werecollectedfor three SZA ranges,at SZA = 0ø(78ø - 90ø). Figures4a and 4b illustratethe observed 30ø,30ø -60 ø, and 60ø - 90ø (the profilesare adopted
bow shock cross sectionsfor high and low EUV con- from Zhanget al. [1991]).Figures5b and 5c showthe
ditions (solar maximum and solar minimum), respec- correspondingprofiles derived from the MHD model.
and Ra-x z - 2.33 Rv (Figure4a) and an ellipsewhere namic pressure is the dynamic pressurein the undis-
Ra-xY - 2.22 Rv, andRa-xz - 2.43Rv (Figure4b) turbed model solar wind. The height of the ionopause,
andapproximate
the observed
values(the distances
are which was observedto increasewith increasingSZA,
adoptedfromRussellet al. [1988,Figures10 and 12]). wastaken from the analyticalexpressiongivenby Zhang
In the MHD model the distances at the terminator in
et al. [1991]. Note that becausethe ionopause
in the
the unloadedcasewere Ra- xr = 2.03 Rv, and Ra- x z
- 2.18 Rv. The modelbow shockshapeis realistic,but
the shockis slightly closerto the planet than observed.
In the loaded case, R• xY - 2.27 Rv, and R• x z 2.42 Rv, muchas observed.Note that the eccentricity
of the ellipseincreases
slightlywith increasingX values
in the model: in the unloadedcaseit is 0.33, 0.36, and
MHD simulation is modeled simply by a sphereof 300
km above the surfaceof Venus, the normalized height
may have negative values. The magnetic pressuresare
obtained by calculating the average magnetic field on
the grid lines 1-4, lines 7-9, and lines 11-13, which
approximatesthe SZA ranges0ø - 30ø, 30ø -60 ø, and
60ø- 90ø, respectively(seeFigure la).
4730
KALLIO ET AL.' MAGNETIC FIELD NEAR VENUS
loadedcasethe maximummagneticpressureis located
PVO: solar min.
at higheraltitudesthan observed.A notabledifference
PVO: solar max.
between the model and the data is that the magnetic
2.5
MHD:
fieldis piledup onthe daysidemorethan observed
both
o
MHD: unloaded
in the loaded and in the unloaded case.
loatled
Figure6 showsanotherillustrationof howthe loaded
2
and the unloaded models differ from one another on the
daysideandhowthe decrease
of the magneticfieldseen
+1.5
1
in the loadedcaseis causedby the increasingmassden-
sity nearthe planet.The top panelsshowthe bulkvelocity,thetotalmagnetic
field,andthevalueofpimp(total massdensity/proton
mass)alongthefirstgridline
at SZA= 3ø (seeFigurela). Notethat in theunloaded
o
0.5
casepimpshows
theprotondensity,
whilein theloaded
cases
p includes
oxygenionsaswell. The bottompanels
02
1.5
1
0.5
0
-0.5
showthe pressures:
thebulkpressure
(Pbulk
= PV2),
themagnetic
pressure
(PB= B2/2•o),andthethermal
pressure
(Pr,T = PVs2ound/7,
whereVsound
is thesound
-1
X(RV)
Figure 3. Venusianbow shockmodeledby conicsec- speedand7 = 5/3). The dotsshowthe total pressure,
tions. A comparisonof the averagepositionsof the bow the sum of PB and P-,T, at the grid points.
shockin the unloaded(dashedline) and loaded(solid
The parametersin Figure6 vary in a similarway in
line) MHD modelwith the PVO measurements
during the loaded and the unloaded MHD model at the bow
solarminimum(circles)andmaximum(stars).
shockand in the magnetosheath.The absolutevalues
at a givendistance,however,changebecause
the mass
loading
moves
the
bow
shock
farther
away
from
the
A comparisonbetweenthe observedvaluesat solar
planet
producing
a
thicker
magnetosheath
in
the
loaded
maximum(Figure5a) with the loadedmodelagainsuggestssimilaritiesbetweenthesecases:in both casesthe than in the unloaded case. The main difference between
normalizedmagneticpressuredecreaseswith increas- Figures6a and 6b occursnearthe obstacleboundary
ing SZA, the absolutemaximumbeingnearthe subso- at r m 1.1 Rv, i.e., •300 km abovethe obstaclesurlar point, with the maximumvaluealonga givenSZA face. In the loadedmodel the magneticfield starts to
line located above the nominal ionopause. In the un-
decreaseat r m 1.1 Rv where the total mass density
loadedmodelthe magneticpressureis alsohighestnear increases.This is oppositeto what happensin the unthe subsolarpoint but its maximumis on the obstacle loaded case where the magnetic pressurecontinuesto
with decreassurface. Note also that the existenceof the magnetic increaseand the massdensityto decrease
thevelocitydecreases
nearthe
peak is moreconsistent
with the observations
than is ingheight.In bothcases
the unloadedcaseprofilewith no peak, althoughin the planet,its valuebeingsmallerin the loadedthanin the
MHD[
a) s --Unioaded
MHD i
b) --Loaded
0
oPVO(mi_n.)
o•
=-0.5'
=0
2
-3
----
-2
0
v'
X = -0.5'
PVO(m•)••'••x•X- 0
,
2
v' (%)
Figure 4. Crosssections
of the bowshockat X = constant
planes.(a) Thecross
section
of
the bowshockat X = -0.5, 0,0.5 Rw planesin the unloaded
MHD model(solidlines).The
circlesrepresent
the bowshockat.the terminatorplanefor low EUV conditions
according'
to
PVO measurements.
(b) The bowshockcross
section
at the samethreeplanesin the loaded
MHD model(solidlines).Thecircles
represent
theobserved
shapeat theterminator
planefor
highEUV (solarmaximum)conditions.
The IMF pointsto the left.
KALLIO
ET AL.'
MAGNETIC
a) PVO (sol. max.)
\
FIELD
NEAR
VENUS
4731
c) unloadedMIID
b)loaded
MIID
SZA
0.4
0 - 30 ø
30 - 60 ø
.......... 60- 90 ø
0.3
0.2
0.1
0
ß
-0.1
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
normalizedmagneticpressure:
0.2
0.4
0.6
0.8
B2/2•t
v 2sw
KPsw
Figure 5. Magnetic pressurein the Venusianmagneticbarrier. The normalizedmagneticpressuresat the normalizedheightsfor threeSZA regionsaccording
to (a) PVO measurements
from
solarmaximum,(b) the loadedMHD model,and (c) unloadedMHD model.The solid,dashed,
and dotted linesshowthe valuescollectedin the SZA ranges0ø - 30ø, 30ø -60 ø, and 60ø - 90ø,
respectively.The normalizedheight is zero at the observedionopause.
unloaded
case.Similarchanges
nearthe planetcanbe a)
seenin the pressuresas well: in the loadedcasethe magnetic pressuredecreasesnear the planet while the ther-
i
i
km/s
•oo-I
100
L
in the unloaded
Plane
ture exists above the nightsideobstaclesurface. The
reasonfor the differencecan be seenby comparingthe
velocity vectors for these two cases.The magneticfield
maximum
is associated with the formation
of a vortex
in the flowwakebehindthe planet (Figure7b), which
has a counterpart in the other half-plane. In the unloaded case,these twin vorticesare smaller and are lo-
I
I
I
i
i
/
o
....
,
nPa 3
case no similar fea-
I
•
,
,
,
,
•/ .............
'
,
lOO
•,
......
• .........................................
,
The above analysisof the bow shockand the properties of the magnetic barrier on the dayside suggest
b)
that the loaded MHD model resemblesthe magnetic
field near Venus at solar maximum. Figure 7 presents km]s
another comparisonthat reinforcesthis view. Figures
7a, 7b, and 7c show details from the contour plots of
the total magnetic field seen in Plates lc, ld, and lb,
respectively.Velocity vectorshave been superimposed
for reasonsof interpretation, as will became apparent.
Figure 7b illustrates that there is a local magnetic
field maximum near the planet on the nightsidein the
XY plane in the loaded model that appearsto be the
extensionof the magneticfield of the daysidemagnetic
Note that
I
F?"---'-•
i
1.5
barrier.
Ir
/
\
/
in contrast, does not change markedly inside r • 1.1
Rv. In the unloaded casesthe magnetic pressureinstead increasesand the thermal pressuredecreaseswith
decreasingheight. The total pressureincreasesdown to
3.4. Magnetic Field Near the Terminator
I
/ loaded MHD
"\V
mal pressure
increases.
The total pressure
(PB + PAT),
1.1 Rv much like in the loaded case. '
•
i
i
1.4
,
,
[/mp
,
,
---•
,
i ..... i........ i ..... , '
1.3
1.2
i
1.1
Irl (Rv)
500 i
i
i
i
i
/ unloaded
MHD
3oo
i
i
i
i
"\
i
-
B
\
3OO
I
so
cm'3
60
0
,
,
,
,
,
,
,
,
,
6
i
i
i
i
i
i
i
i
i
nT
..........
i
s-•
.........
.P...b.•!.k..
...................
PB
+PnT '.'""
4-•
\ ..........
'",
:
01 - . ,- - -,- . .,.J'
1.5
1.4
,
,
PB
...........................
PnT-"'
1.3
,
.............................
,
,"
,,, . ,
1.2
1.1
1
Irl (Rv)
Figure 6. Propertiesof the MHD modelnear the X
axis(SZA- 3ø). Theparameters
(a) in theloaded,and
(b) in the unloaded
model.(top) The valueof the bulk
velocity(V, in km s-1) is shown
ontheleft-hand
side,
and the total magneticfield (B, in nT) and the value
ofpimp(- totalmass
density/proton
mass,
in cm-3)
on the right-handside.(bottom)The bulk (Pbulk),the
thermal(PAT),the magnetic
(PB),andthetotal (PaT+
cated near midnight (not clearlyseenin Figure 7a). Ps) pressures
(all valuesin nanopascals).
4732
KALLIO
ET AL.' MAGNETIC
FIELD
NEAR VENUS
The mass loading increasesthe size of the vorticesso
that they affect the terminator flows and fields. The
vorticeseffectivelyincreasethe size of the obstaclebecausethey preventthe flow from convergingbehindthe
planet. They are evidently associatedwith the shear
layer at the wake boundary that is enhancedby the
massloading. Wake vorticeswere alsoobtainedin the
>-
unloadedmodelsof Tanaka[1993]and de Zeeuwet al.
[19961
.
0.8 .• / ,, ..
0.6
0.4
4. Discussion and Comparison
With
0.2
0
1
b)
0.5
0
0.5
-1
Other
Models
In this paper we have presentedthe resultsof a massloaded 3-D MHD
model of the Venus-solar wind interac-
tion and showedthat it reproducessomebasic features
observedon PVO. Our comparisonfocusedon the shape
and locationof the bow shockand the daysidemagnetic
barrier. Investigationsof mass loading effectsusing3-
1.6
1.4
D MHD modelshave only recentlybegun[Murawski
and Steinolfson,
1996b]so that there are few compar-
1.2
isonsthat can be made between models. However, our
unloaded MHD model can be comparedboth with sev>.
eral 2-D models[McGaryand Pontius,1994;Murawski
and Steinolfson,1996a; de Zeeuwet al., 1996],and a
few other 3-D models[Wu, 1992; Tanaka,1993; Ca-
0.8
0.6
0.4
ble and Steinolfson, 1995; Murawski and Steinolfson,
0.2
1996b].Hybrid models[Brecht,1990;Brechtand Ferrante, 1991;Mooreet al., 1991]includefiniteion Lar-
Loaded MHD
0
1
0.5
0
i
I
0.5
I
-1
I
mor radius effectswhich are not in the singlefluid MHD
models and henceprovide a basisfor evaluatingthese
effects, but most of these efforts have concentrated on
Mars and so we considermainly the other MHD work
here.
4.1.
Bow
Shock
Table I gives a summary of the distanceof the bow
shockaccordingto measurements,in our study, and in
earlier
MHD
simulations.
It should be noted that the
distances of the bow shocks obtained
from the models
can be subject to somechangeif we regardthe obstacle
boundary used in the simulation as the surfaceof the
planet or the surfaceof the (cOnducting)
ionosphere.
The typically largegrid spacingnear the terminator and
the criteria
0.2
0
'
1
0.5
'
0
0.5
-1
x (RVenus)
used to determine
the location
of the bow
shockaffectthe distancesgiven by other studiesas well.
The upstream values also differs somewhatfrom study
to study.
Table I shows that our unloaded
similar
to the measured
values.
distances are rather
Our values are also
Figure ?. The total magneticfield nearthe terminator. quite similar to distancesderived earlier from a general
The four plots show the total magnetic field contours 3-D MHD magnetosheath
modelby Wu [1992]andthe
15, 20, 25, and 30 nT, in (a) the unloadedand (b)
the loadedMHD model in the XY plane and (c) the
3-D MHD modelby Tanaka[1993]. A recentaxially
symmetric
(2-D) MHD modelby de Zeeuwet al. [1996]
observedfield at solarmaximum. The vectorsin Figures
7a and 7b show the plasma velocity from the models. gave very realistic distances for the bow shock, while
The shaded region in Figure 7c showswhere the PVO the 3-D MHD modelby Cableand $teinolfson[1995]
data were collected.
values are somewhat
smaller than observed.
The cross
KALLIO
ET AL'
MAGNETIC
FIELD
NEAR
VENUS
4733
Table 1. Distancesof the Bow ShockAccordingto PVO Observations
and MHD Models.
Study
UnloadedModels/Observations(sol.
min.)
Model/Data
R•v
Zhang et al. and
PVO
data
R•,
R•, xr
LoadedModels/Observations(sol.max.)
R•v
R•, xz
R•.
R•. xr
R•. xz
1.30
2.15
• 2.14
• 2.33
1.48
2.45
• 2.22
• 2.43
1.37
2.11
2.03
2.18
1.47
2.34
2.27
2.42
Russell et ed. •
3-D MHD
this study
with
mass loading
Wu b
Tanaka c
Cable and
Steinolfson
Steinolfson e
Murawsky and
Steinolfsonf
McGary and
g
•
1.35
2.25
1.26
1.95
2.2-2.5
2.20
....
2.31
RTxz
....
>
....
c
de Zeeuwet ed.•
Murawsky and
Pontius
1.32
3-D MHD
3-D MHD
3-D MHD
2-D MHD
1.28
3-DMHDwith
•1.17
2.13
-
• 1.6
RTxz >•
R•,x•,
mass loading
2-D MHD
with
•
1.23
-
• 1.8
1.15
'
2
mass loading
2-D MHD
with
1.2-
1.2
1.3
mass loading
The nosealtitudeis shownby J•N and J•T is the averagedistanceat the terminator.J•TXY and RT x z showthe
distanceof the bow shockat the terminatoralongthe magneticmagneticequatorand poles,respectively.The PVO
measurements
fromsolarminimum(maximum)
areshowntogether
with the unloaded
(loaded)MHD model.All values
are in Venusian radii if not otherwise mentioned. See text for details.
a Rs andRT arefromZhanget al. [1990],
andRT x•' andRT xz fromRussell
et al. [1988].
5 The unit of the valuesis the radiusof the obstacleusedin the model. BIMF perpendicularto the Vsw. Valuesadopted
fromWu[1992,Figures
I and2]. RN represents
theapproximate
position
ofthehalfpointof thebowshock.
c BIMF is perpendicular to the Vsw
d BIMF is parallel to the Vsw
e Thevalues
represent
theapproximate
positions
ofthehalfpointofthebowshock
in Murawsky
and$teinolfson
[1996b,
Figure6]. Thepositions
areobtained
byredefining
theirshock
position
asa halfpointofthebowshock
pressure
gradient.
Values are for the caseBIMF perpendicular to the Vsw.
f BIMFisparallelto theVsw. Values
areaverage
values
forcases
wheretheplasma
betawas0.1,0.5,and10[Murawsky
andSteinolfson,
1996a].
g BiM• is perpendicular
to theVsw. Venusa cylinder.The distance
depends
onthe differentmass-loading
ratemodels
used.
section of our bow shock in the unloaded model was
whetherthe coneangleis large(greateror orderof 45ø)
foundto be asymmetriccorresponding
to a 7% equator- or small. These simulations are similar to our unloaded
to-poleasymmetrywhichis closeto the 10%asymmetry case. For the Much numbers relevant for this paper,
observed
on PVO [Russellet al., 1988].Our asymmetry the high coneangleshockcan be morethan 1.5 times
is a little closer to that observedthan the asymmetry farther from the obstaclethan for zero coneangle. Al-• 5% obtainedearlierby Tanaka[1993]and Cableand though Venusdiffersfrom the Earth becauseit does
Steinolfson
[1995]. However,our terminatordistances not have an intrinsic magneticfield, the Venusianbow
are smaller than the values observed for low EUV fluxes
shockwas found to move farther from the planet with
increasingconeanglesaccordingto PVO observations
and high coneangles.
upstream
solarwind
It important to note how the adopted approxima- [Zhanget al., 1990].Furthermore,
tions are expectedto affect to the distanceof the bow parametersand Muchnumbersare somewhatdifferent
shock in our model. First, the distancesin our un- at solar minimum than at solar maximum. However,
loaded model would have been somewhat larger if we variationsof MM$ and Ms [see,e.g., Luhmannet al.,
to PVO observations
and a
had not used a completelyunloadedmodel. In nature, 1993]are, both according
et al. 1988],toosmallto explainthe
the massloadingis not exactlyzeroevenwhenthe EUV GD model[Russell
flux is low. Moreover, the subsolaraltitude of the bow observedchangesof the bowshocklocation.Variations
shockin our model is expectedto be somewhatcloserif of the Parker spiral angle can neither be an important
the spiralangleis ratherindependent
of
we use a more realistic IMF than in our present model factor,because
(the Parkerspiral anglefor Venusis -•36ø). In 3-D
the solarcyclephase[Luhmann
et al., 1993].Finally,in
MHD simulations of the position of the Earth's bow
our modelwe disregardedpossibleasymmetriesof the
ionopause.
However,thisapproximation
isnot excepted
to affectmarkedlyto the locationto the bow shockin
shock[Cairnsand Lyon, 1996],the distancefromthe
obstacleto the nose bow shockcan vary dependingon
4734
KALLIO
ET AL.' MAGNETIC
FIELD
NEAR VENUS
our model becausethe positionof the bow shockis quite
insensitiveto the positionof the ionopauseaccordingto
The observedequator-to-pole asymmetry is believed
to be a consequence
of the differentmagnetosonic
speeds
a GD model[see,e.g,SpreiterandStahara,1992,Figure along the magnetic field and perpendicularto it althoughmassloadingmay alsohavesomeintrinsicequaMany studieshave addressedthe questionof whether tor-poleasymmetry[Russellet al., 1988].However,in
the massloading of oxygenions can movethe Venusian addition to the equator-to-pole asymmetry PVO obserbow shock away from the planet as much as observed vationsshoweda north-to-south asymmetryin the bow
during solar maximum. As noted before,a massloaded shockcrosssection, the bow shockbeing 5% farther
GD model [Spreiterand Stahara,1992],a 3-D MHD from the planet in the hemispherewhere the cross-flow
model[MurawskiandSteinolfson,
1996b],and a hybrid component of the convectiveelectric field in the solar
model[Mooreet al., 1991]whichusedthe oxygenprofile wind,E (- -Vsw x BIMF) pointsawayfromthe planet
based on the PVO UV measurements did not succeed
[Russellet al., 1988]. Note that there is no physical
in movingthe bow shockfar enoughwithout artificially
increasing
the productionrate (seeFigure2a). In a GD
model, for instance, the production rate has to be increased a factor of 10 to move the subsolar altitude
from
Rs ..• 1.22 Rv to RS • 1.28 Rv and the terminator
altitude from /i•T • 1.86 RV to /r/T • 2.00 /i•V, which
b•is for reproducingan additional observednorth-tosouth asymmetry in the MHD modelswith equatorial
field. The elliptical crosssectionof the bow shockgives
thus an oversimplifiedview. The observednorth-tosouth asymmetry is suggestedto be a consequence
of
the finiteLarmorradiusof the O+ ionswhicharepicked
up by the convectiveelectricfield in the Venusianmag-
according
to Table 1 arestill lessthan observed
(the valuesare adoptedfrom Spreiterand Stahara[1992,Fig- netosheath
[Russellet al., 1988]. Moreover,the cross
ure 18]). In our mass-loaded
MHD modelwe adopted section of the shock dependson the cone angle while
a strategy where we roughly approximatethe effect of we studiedthe crosssectionfor a oneconeangle(90ø)
the three ionizationprocesses
(electronimpact ioniza- only. The crosssectionis expectedto becamemore cirtion, chargeexchange,
andphotoionization)
by increas- cularwith smallerconeangles[Russellet al., 1988]and
to have dawn-duskasymmetry for a Parker spiral field.
As a summary of our mass-loadinganalysis,our reIn our mass-loadedmodelthe massloadingwasfound sultssuggestthat the massloadingcan producea realisto substantially move the bow shock away from the tic bow shockif we take into accountthe additional proplanet (Table 1). The nosedistanceis closeto the ob- duction from electron impact ionization and chargeexserveddistanceduring solar maximum, althoughthe changeprocesson top of photoionization.The adopted
strategy seemsjustified becausethe spatial distribution
terminator distance is somewhat less than observed. In
the only other mass-loaded
3-D MHD modelpublished of the production rates for electron impact ionization
so far by Murawskiand Steinolfson[1996b]the bow and the chargeexchangeprocesslookmuchlike the proing the photoionization production rate by a factor of
3, consistent
with the analysisof Zhanget al. [1993b].
(compareFigures2b,
shockwas closerthan observedbut the displacement ductionrate fromphotoionization
of nosealtitudewasmuchlikein ourmodel(.• 0.1 Rv)
4b, and 8b of Zhanget al. [1993b]).Ionsproducedby
for a similar production rate. A shock at too small photoionizationor electron impact at relatively low energiesare includedrelatively accuratelyby the scheme
a distance was also obtained from 2-D MHD simulationswherethe IMF was perpendicular[McGaryand used in this paper. Charge exchange, however, does
Pontius,1994]and parallel[MurawskiandSteinolfson,not changethe number of ions but doeschangetheir
1996a]to the flow. The crosssectionof the bowshock mass(in O chargeexchange)and doesaffectmomen-
tum and energy conservation. The gradient in mean
tion, with asymmetry•07%. In the mass-loaded3-D atomicweight is anotherfactor not includedin the curmodelby Murawskiand Steinolfson[1996b],instead, rent simulations. However, future simulationswhere all
they pointed out that the asymmetryis smallerthan three ionization processesare taken into accountselfobserved.Unfortunately,comparisonof our study with consistentlymust be made to study this question in
detail.
the Murawski and Steinolfson's
work is complicatedbecauseit is somewhatunclearwhat productionrate they
really used. They state that their value is basedon Belotserkovskii
et al. [1987],whousedn(O+) = 3 x 104 4.2. Magnetic Barrier
cm-3 at h = 400 km and ionization rate 10-6 s- • i.e.
in our loaded model is close to the observed cross sec-
Anotherinterestingaspectconcerning
the solarwind
the production
rate of 3 x 104m-3 s-1 at h = 400km, interactionwith Venusis how the planet formsan obbut on the other hand, they alsowrote that they used stacle to the solar wind flow. The PVO observations
a productionrate of 3 x 105cm-3 s-• at h = 400 km.
If they had useda productionrate of 3 x 105m-3 s-•
at 400 km, the production rate profile in their MHD
simulationsis the one shownin Figure 2b by the dotted
line, that is, closeto our values.
showed
the characteristic
featuresof the magneticbarrier at solar maximum. Our model comparisons
illustratedthat the magneticbarrier obtainedfrom our
loaded MHD model has characteristics much like those
observedat solarmaximum:the magneticpressureis
KALLIO
ET AL.: MAGNETIC
highestat the subsolarpoint and decreaseswith increasing SZA, with its maximumvalue at a givenSZA above
the surfaceof the planet. The modeledmagneticpressureswere foundto be higherthan observed,indicating
that in our MHD model more pileup occursthan in na-
FIELD
NEAR VENUS
4735
analysiscomparedto previousworks becausein our sim-
ulation the radial grid spacingAr near the planet was
m 0.01Rv, whilein Tanaka's[1993]modelArm 0.1 Rv
and in Cableand $teinolfson's
[1995]MHD modelAr
• 0.017 Rv.
ture.
In our loaded MHD model the thermal pressurewas
found
to increaseand the magnetic pressurewas found
It is worthwhileto noteseveralaspectsconcerning
the
to
decrease
near the planet, in contrast to the our unmagneticbarrier regionin our model. The excessive
pilloaded
model.
This feature, where the plasma beta
ing up of fieldin our modelcanpartly resultfromusing
dividedby magneticpressure)
bethe idealOhm'slaw (E+VxB = 0), whilein naturethe (thethermalpressure
comes
less
than
unity
close
Venus,
has
been
found
in
the
diffusionaroundVenusis not exactly zero everywhere.
[see,e.g.,BraceandKliore,
On the numericalpoint of viewthe strengthof magnetic solarmaximumobservations
1991].
In
the
model
the
mass
loadingwasfoundto profield piling up on the daysideand the "slipping"of the
duce
a
layer
-0
300
km
thick
at
the subsolarpoint where
field linesto the nightsideand thereforethe strengthof
the
magnetic
field
decreases
rapidly.
It is interestingto
the magneticbarrier, the width of the magnetosheath,
note that while the magnetic field starts to decreaseat
r • 1.09 Rv, the mass density starts to gradually inthat while in our loadedmodelthe heightof the mag- creaseat much higher altitudes, about r • 1.15 Rv, i.e.,
netic pressurewas found to be at higher altitudes than within the magneticbarrier (seeFigure6a). Of course,
observed,the peak value would have been almost at the our 3-D MHD model is a single fluid model, and we
observedheights if we had regardedthe surfaceof the cannot separate the oxygen ions from the solar wind
obstacleas the surfaceof the planet (rather than the protons in our model in order to study how much the
ionopause).By interpretingthe model surfaceas the increasedmassdensity in the magneticbarrier is caused
surface of the planet in our loaded model, our model by the increasingdensity of oxygenions. For the same
would also have automatically created an ionospheric- reasonwe do not know how much the particle density
of the
like layer abovethe surfaceof the planet wherethe mag- and/or the plasmatemperatureaffectthe increase
netic pressureis replaced with the thermal pressure. plasma pressurenear the planet in our loaded model.
However, this interpretation would have not been real- However, PVO particle measurementshave shownthat
istic for our unloaded model because in that model the
the Venusianmagnetic barrier is a regionoccupiedby
magneticfield increasesmonotonicallynear the obstacle substantialfluxesof superthermal(15 - 90 eV) oxygen
et al., 1993].
boundary. In the presentstudy we used,for consistency, ions[Grebowsky
the sameinterpretation for the obstacleboundaryboth
Our mass-loadedmodel differs from the previously
in our unloaded and loaded model.
published mass-loaded3-D MHD simulation becausein
The subsolar region was found to be quite different that simulation the thermal pressurewas found to decreaseand the magnetic pressurewas found to increase
in our unloaded and loaded MHD models. In the unloaded casethe magnetic pressurewas found to increase near the surface both in the loaded and the unloaded
and the thermal pressuredecreasecloseto the planet. case[seeMurawskiand $teinolfson,1996b,Figures6a
and the location of the bow shock are related to the
numerical diffusion of the code. It should also be noted
,
A similar
kind of behavior
has obtained
in the earlier
and 7]. In addition,the massloadingwas foundto in-
3-D MHD simulations[Wu, 1992; Tanaka,1993;Cable creaseonly slightly near the obstacle,while in our simand $teinolfson,1995]. The monotonicincreaseof the ulation it increasesmarkedly for a quite similar productotal magnetic field closethe planet can also be seenin
tion rate. In a 2-D MHD model the magnetic field has
with decreasing
altitudes[seeMcan unloadedGD model [see,e.g., Zhanget al., 1993a]. alsofoundto decrease
Cary
and
Pontius,
1994,
Figure
9].
However,
their field
However, although there is qualitative agreementwith
the unloaded MHD models there are quantitative differences. For example, a notable differencebetween our
subsolarregion and the subsolarregion analyzedearlier
in detailby Cableand$teinolfson[1995]is that in their
MHD model the bow shockis -0 0.1 Rv thick layer centered at r • 1.2 Rv. The bow shock was thus much
closer to the planet than in our simulation, and the
magnetosheathconsequentlywas much thinner than in
our rnodel.
an unloaded
Our unloaded
GD
model
MHD
model differs also from
because in a GD
model
both
decreasesonly slightly and the magnetic field maximum
on the X axis is in the middle of the magnetosheath.
Nevertheless,in this 2-D simulation, the mass loading
was alsofound to decreasethe flow speednear the obstacle producinga thin boundary layer abovethe obstacle.
Like the simulations
of Tanaka[1993]and de Zeeuw
et al. [1996],our simulationproduces
vorticeson the
nightside. Near the terminator on the XY plane is a
region of increasedmagnetic field produced by these
vortices.
This
feature
looks like the extension
of the
plasmadensityand temperature[$preiteret al., 1966] dayside the magnetic barrier. It is tempting to specand thus the plasma pressureincreaseclosethe planet
along the X axis. It should finally be noted that the
subsolarregion could be studied in more detail in our
ulate that this magnetic field structure increasesthe
effective
size of the obstacle
and could also affect the
position of the bow shockin the mass-loadedcase.
4736
KALLIO
ET AL.:
MAGNETIC
FIELD
NEAR
VENUS
Cable, S., and R. S. Steinolfson, Three-dimensionalMHD
5. Summary
simulation of the interaction
between Venus and the solar
In conclusion,our 3-D MHD model of the Venus-solar
wind, J. Geophys.Res., 100, 21,645-21,658,1995.
wind interaction seemsto reproducesomeglobal fea- Cairns, I. H., and J. G. Lyon, Magnetic field orientation
effectson the standoffdistanceof Earth's bowshock,Geotures observedduringthe PVO mission.The comparphys. Res. Lett., 23, 2883-2886, 1996.
isonof the model resultswith massloadingand with- de Zeeuw, D. L., T. I. Gombosi,A. F. Nagy, K. G. Powell,
out massloadingwith the PVO magneticfield measureand J. G. Luhmann, A new axisymmetricMHD model of
the interactionof the solarwind with Venus, J. Geophys.
ments from solar minimum and maximum suggestthe
Res., 101, 4547-4556, 1996.
following:
Fedder,
J. A., and J. G. Lyon,The solarwind-magnetosphere1. The MHD model can produce a quite accurate
ionospherecurrent-voltagerelationship,Geophys.Res. Left.,
approximation to the Venusianbow shockposition and
14{,880-883, 1987.
shape. The unloaded model representssolar minimum, Fedder, J. A., and J. G. Lyon, The Earth's magnetosphere
and the loaded model representssolar maximum condiis 165 Rs long: Self-consistentcurrents,convection,magnetosphericstructure, and processesfor northward intertions. Our resultssuggestthat the massloading can be
planetary magnetic field, J. Geophys.Res., 100, 3623strong enough to move the bow shockto the observed
3635, 1995.
distancesif we take into accountall ionization processes: Grebowsky,J. M., W. T. Kasprzak, R. E. Hartle, K. K. Maimpact ionization, charge exchange,and photoionizahajan, and T. C. G. Wagner, Superthermalions detected
tion.
2. The MHD model produced a magnetic barrier
much like that detected by PVO at solar maximum:
the total magnetic field decreaseswith increasingSZA
and the magnetic field maximum is located above the
effective obstacle. In addition, the mass loaded model
was foundto give a realisticpicture of the daysideinteraction region where the magneticpressureis replaced
with thermal pressurenear the planet. However, the
model was found to pile up the magnetic field on the
dayside more than observed. Wake vortices, enhanced
when massloading is at a maximum, may increasethe
effectivesize of the obstacleduring solar maximum.
In general, the 3-D MHD model givesa relatively realistic picture of the solar wind-Venusinteraction. Such
modelsprovide a powerful tool for the study of global
interaction features at weakly magnetizedbodieswhen
usedtogether with the observations,as well as a framework for analyzing other matters such as pick up ion
behavior. While the caseof Mars may be complicated
by ion gyroradiuseffects,there may be many grossfeatures at that planet that can also be understood with
the application of models like that describedabove to
future data sets.
Acknowledgments.
This work was partially supported
by NASA grant NAGW-4600 and by the Academy of Finland.
The
Editor
thanks
T. Tanaka
and S. H. Brecht
for their
assistancein evaluating this paper.
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FIELD
NEAR
VENUS
4737
J. G. Luhmann, Space Sciences Laboratory, Univer-
sity of California, Berkeley, CA 94720. (e-mail: [email protected].
edu)
J. G.
Lyon,
Department
of Physics and Astron-
omy, Dartmouth Collage, Hanover, NH 03755. (e-mail:
[email protected])
E. Kallio, Finnish Meteorological Institute, Geophysical
Research,P.O. Box 503, FIN-00101, Helsinki,Finland. (email: [email protected])
(ReceivedMay 30, 1997; revisedOctober3, 1997;
acceptedOctober7; 1997.)