JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. All, PAGES 26,833-26,849,NOVEMBER 1, 1998
Interplanetary Lyman observationsfrom Pioneer Venus
over a solar cycle from 1978 to 1992
WayneR. Pryor,1ScottJ.Lasica,
1A. IanF. Stewart,
1DoyleT. Hall,1
SeanLineaweaver,
l WilliamB. Colwell,l Joseph
M. Ajello,2OranR. White,3
and W. Kent Tobiska 4
Abstract. The PioneerVenus Orbiter ultravioletspectrometer(PVOUVS) routinelyobtainedinter-
planetaryhydrogenLyman ot datawhile viewingeclipticlatitudesnear30øSfrom 1978to 1992 (during solarcycles21 and22). We describe"hot"modelsfor this interplanetary
Lymanotdatathat include
the solarcyclevariationof (1) the solarflux, as a functionof latitudeand longitude;(2) the radiation
pressure
on hydrogenatoms;(3) the solarwind flux; (4) the solarEUV flux; and(5) the multiplescattering correctionto an opticallythin radiativetransfermodel. Thesemodelsmakeuseof solarradiation
flux parameters
(solarwind, solarEUV, andsolarLymanor)from spacecraft
andground-based
solar
proxyobservations.Comparison
of the upwinddataandmodelindicatesthatthe ratio of the solarLyman ot line centerflux (responsiblefor the interplanetary
signal)to the observedsolarLyman ot inte-
gratedflux is constant
to within-•20%,withaneffective
linewidthnear1.1A. Averaging
thesolarradiationpressureand hydrogenatomlifetimeover 1 year beforethe observation
reproduces
the upwind
intensitytime variationbut not the downwind. A betterfit to the downwindtime seriesis foundusing
the 1 year averageappropriatefor the time thatthe atomspassedclosestto the sun. SolarLymanot
measurements
from two satellitesare usedin our models. UpperAtmosphereResearchSatellite(UARS)
solarLymanot measurements
are systematically
higherthan SolarMesosphere
Explorer(SME) values
andhavea largersolarmaximumto solarminimumratio. UARS-basedmodelsworkbetterthanSMEbasedmodelsin fitting the PVOUVS downwindtime seriesLyman ct data.
1.
Introduction
drogenatoms are also ionized by solar EUV radiation. Solar
Lyman otresonancescatteringfrom the surviving slow hydrogen atomscreatesthe observedglow.
Modeling the interplanetary Lyman ot brightness pattern
of the processeslisted above.
from the Sun, well inside the solar wind termination shock, requiresdetailedunderstanding
thesehydrogenatomsare currentlydescribedby a temperature The Pioneer Venus Orbiter ultraviolet spectrometer
T=8000 K, a velocity v--20 km s-1 with respectto the Sun (PVOUVS) interplanetary Lyman ot observations provide a
[Bertauxet al., 1985] and,in our models,by a density n--0.17 particularly good test of our understandingof the solar proc-
The interplanetary
Lymanotglow comesfrom solarLymanot
that hasbeenscatteredby hydrogenatomsin the very local interstellarmedium. At a distanceof perhaps30 AU upwind
cm-3[Ajello et al., 1994]. A recenttabulation of the rather
wide rangeof hydrogendensity values in the literature is
givenby Puyoo,et al. [1997]. Theirwork finds a neutraldensityat largedistances
of n=0.25+0.08cm-3. Solargravity acts
to focusthe hydrogen atomsas they pass the Sun, but is
largelycanceledby solarLymanotradiationpressurethat repelstheatoms.Theratioof the radiationpressureto the solar
gravity is called g. Solar cycle variationsin g can makethe
Suneitherrepelthe atomsor slightly focusthemdownstream.
esses and their variations, since the data were obtained over
more than a full solar cycle (December29, 1978, to April 18,
1992) at a nearly constantdistance of 0.72 AU fromthe Sun.
Other spacecraft(Pioneer 10 and Voyagers 1 and 2) have obtained a long time seriesof interplanetaryLyman ct observations, but thesedata samplea range of distancesfromthe Sun,
complicatingthe interpretation becauseof the possible presenceof outerheliosphericeffects [e.g., Hall, 1992; Hall et al.,
1993; Quemeraiset al., 1995, 1996]. Successfulmodeling of
Fastmovingsolarwind protonschargeexchange
with the thePVOUVSinnerheliosphere
datasetis a firststeptoward
slower
interstellar
neutral
hydrogen
atoms,
creating
apopula-understanding
theouter
heliospheric
data.
The modeling describedhere builds on our earlier efforts.
the solarLyman ot line and leaving behind a cavity depleted Ajello et al. [1987] examinedthe PVOUVS interplanetary Lyin the slow neutralsthat scattersolar Lyman ot photons. Hy- man ot data set (1979-1985) and used the parallax shift over
the Venus year of the brightest emission region to determine
•Laboratoryfor Atmospheric
and SpacePhysics,Universityof the hydrogenatom lifetime. Ajello 1990 analyzeda unique set
Colorado, Boulder.
of PVOUVS Lyman ot observations from 1986 covering high
2JetPropulsion
Laboratory,
Pasadena,
California.
3High Altitude Observatory/National
Centerfor Astmospheric ecliptic latitudes during observations of Comet Halley. Improvementsin the model reflect subsequenteffortsat modeling
Research, Boulder, Colorado.
4FederalData Corporation/Jet
Propulsion
Laboratory,Pasadena, Galileo and Voyager data describedelsewhere[Pryor et al.,
tion of fastmovinghydrogenatomsDoI3pler-shifted
outside
California.
Copyright1998by theAmericanGeophysical
Union.
Papernumber98JA01918.
0148-0227/98/98JA-01918509.00
1992, 1996; Hall, 1992; Ajello et al., 1993, 1994]. This paper
applies our latest modelsto the full PVOUVS data set. These
modelsexplicitly computethe solar Lyman otflux at each latitude and longitudeas a functionof time by using He 1083 nm
imagesas a proxy for solarLyman ot [Pryor et al., 1996].
26,833
26,834
2.
PRYOR ET AL.: LYMAN ctOBSERVATIONS FROM PIONEER VENUS
Instrumentation
hydrogencoronawas necessary. We examinedthe brightness
of the coronaas a functionof the closestapproachdistanced of
The PVOUVS instrument [Stewart, 1980] was a compact the look vectorto the centerof the planet[Lasicaet al., 1993].
1/8-m Ebert-Fastiespectrometer
with a programmable
grating Data obtained with d greater than 5 Venus radii from the
drive and two photomultiplier tube detectors. The Pioneer planet center (30,255 km)had <5% contaminationand could
VenusOrbiter spin rate was typically 0.52 + 0.01 rad s-• be- safelybe included in the interplanetary data to be reduced.
foreMay 1981 and 0.48 + 0.01 rad s-• afterthat. The PV Or- The coronalcontaminationwas largestnearsolarmaximumand
biter spin axis was usually aligned within ---5ø of the south was unobservable past 5 Venus radii at solar minimum.The
ecliptic pole. The PVOUVS optical axis slanted60ø away Venus coronaand its variation over a solarcycle are discussed
fromthe spin axis. Thus the instrumentfield of view (1.4ø x by Colwell [1997]. A time-dependentinstrumental back0.14ø) observeda smallcircularstrip on the celestialsphere, ground of 7-12 R due to cosmicrays was subtractedfromthe
with a 1.4ø width, at an ecliptic latitude 30+_5øS. The data. This background was largest near solar minimum and
PVOUVS instrumentsensitivityat Lyman (z found in calibra- smallest near the two solar maxima.
tions was 130 counts s-• kR-•. Observed stellar brightnesses
Becauseof a minor problemin the grating drive system,difindicate that the Lyman (z sensitivity was nearly constant ferent fixed gratingpositionswere used to observethe Lyman
over the course of the mission.
3.
(z line during different parts of the mission. The reported intensities were correctedto reflectthe part of the instrumental
line profile being observed. No overall systematicoffsetsbe-
Observations
tween data and model were identified
that could be conclu-
The PioneerVenus Orbiter maintaineda polar orbit around sively attributed to the use of these differentgrating steps.
Venus with a 24-hour period. Typical distancesfrom planet However, residual differences between data and models in
centerwere •70,000 km for apoapsisand 6200-8000 km for early 1979 may be related to incompletelycorrectingfor the
periapsis. InterplanetaryLyman {x data were obtained at ir- transition from grating step 42 to step 41 on orbit 70 (1979
regular intervals when ground stations were available and day 43).
when Venus was not in conjunction with the Sun. The instrumentoperatedin fixed gratingpositionmode,typicallyusing a 32-ms integration. This integration period leads to a 5. Modeling
spinsmearingof about0.9ø. In orbits wheretwo setsof 240 ø
arcswere taken, the data were combinedfor a full 360ø coverage in longitude. Figure 1 illustratesthe spacecraft
orbit and
the PVOUVS observinggeometry.
Plate 1 includes a color display of the PVOUVS data selectedfor modeling,with time on the horizontalaxis and ecliptic longitude on the vertical axis. The data are brightest in
upwind longitudes near ecliptic longitude 250ø and dimmest
near the downwind direction, where slow neutrals have been
4.
Data
Reduction
BecausePV obtainedinterplanetary
Lyman c• data nearVenus, carefulexclusionof the Lyman c• signatureof the Venus
depleted by charge exchangeand photoionization. Data becamesparseras the missionprogresseddue to reducedground
station coverage. The brightest data are at the two ends of
Plate 1 during maximain the solar activity cycle. The data
PERIAPSlS
2 hr
SPACECRAFT
MOTION
30m
4 hr
PLANE OF ECLIPTIC
8 hr
30m
lhr
APOAPSIS
2hr
8hr
4hr
PVOUVS "VIEW CONE"
x = SUBSOLARPOINTAT VOl
SPACECRAFT
SPIN AXIS
Figure 1. Illustration of the Pioneer Venus Orbiter polar 24-hour orbit. The PVOUVS observedin longitude circlesat -30 ø
ecliptic latitude. InterplanetaryLyman (z datausedhere were obtainedwherethe distancefrom the instrumentlook vector to the
planetcenterexceeded5 Venusradii. Times from periapsisare indicated.VOI standsfor Venus Orbit Insertion.
PRYOR ET AL.: LYMAN o(OBSERVATIONS FROM PIONEER VENUS
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PRYOR ET AL.: LYMAN czOBSERVATIONS FROM PIONEER VENUS
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PRYOR ET AL.: LYMAN • OBSERVATIONS FROM PIONEER VENUS
MAXIMUM
•
\
EMISSION
• •
26,837
•
IONI•TION
CAVI•
Figure 2. An illustrationof the upwind-downwindviewing geometryat two spacecraftlocations. The ecliptic plane is viewed
edge-on. The interstellar wind (ISW) flows to the left. A cavity in the ISW hydrogen near the Sun is carved by solar wind
protons chargeexchangingwith the slow interstellar neutral hydrogen population, creatingfast neutrals which are Dopplershifted off the solar Lyman • line and are thereforeinvisible. The contour lines schematicallyillustrate the variations in the
Lyman a volumeemissionrate. It hasa local minimumcenteredon the Sun, and a local maximum(the maximumemissionregion)
upwind of the Sun, abouthalfway betweenthe Sun and the upwindcavity boundary. Waves visible in Plates 1 and 2 related to
the motionof Venus(andthe PV Orbiter) about the Sun are due to distancevariationsbetweenthe look vector in the upwind
direction and the maximumemissionregion. The PVOUVS views in longitude circles near-30 ø ecliptic latitude. These
instrumentlook directionsapproachthe maximumemissionregionmore closelywhen the spacecraftis upwind.
Throughoutthis paper, the PVOUVS values are scaledto the
Galileo-basedmodel values. The scalingfactorsare near 2 but
The bestfit SME-based"lagged"model is also presentedin vary somewhatdue to modeling variations and uncertainties.
Plate 1. Details of this model will be discussed below. Plate
Using the Galileo calibration [Hord et al., 1992], the current
2 presentsthe data and best fit SME-based lagged model for modelsrequire a high numberdensity of hydrogen inside the
the first 2 yearsof the mission. Apparentin the models(Plates termination shock, n=0.17 cm-3 [Ajello et al., 1994] as oplb and 2b), and somewhatlessapparentin the data, is a modu- posedto earlier modelsthat found n=0.07+0.01 cm-3[Ajello et
al., 1987], somewhatincreasing the importance of multiple
lation or waviness in the upwind intensity associatedwith
the 225-day orbital period of Venus. When the spacecraftis scattering.
We preferto use the more recent Galileo calibration for the
on the upwind side of the Sun (times marked with "U" in
Plates l a and 2a), it is closerto the upwind maximumemission following reasons. Becauseof launch delays, there was aderegion, increasingits angular extent (Figure 2). A parallax quatetime for extensivecharacterizationand calibration of the
shift in the direction to the maximumemissionregion due to Galileo UVS. The Galileo UVS laboratory absolute calibragreaterthan 1300 A, basedon National
the orbital motion of Venus makesthese waves appeardiago- tion at wavelengths
nal in Figure2. The brightnessmaximumon eachwave tends Institute of Standardsand Technology (NIST) standard photo passthrough the upwind directionwhen the spacecraftis todiodes, is estimated to be accurate to better than 20%. We
directlyupwind. In Plate 2 a diagonalvariation is also visi- also obtained Galileo UVS laboratory spectraof electron imble correlatedwith the -25-day sidereal rotation period (28 pact on H2 and N2 that providea high-quality relative calibradays as seenfromVenus) of Lyman ct bright solar active re- tion in the FUV, includingLyman {x [Ajello et al., 1988; Hord
gions. A detailed study of one suchwave was presentedby et al., 1992]. The estimatedadditionaluncertaintyat Lyman {x
with this technique is-20%.
Comparisonof Galileo UVS
Ajello et al. [1987].
The modeldevelopedfor fitting Galileo extremeultraviolet spectraof the star Sirius with rocket observationsshows ex(<20%) at wavelengths
greaterthan 1300 A
spectrometerdata [Pryor et al., 1996] was used here. This cellentagreement
modelis a versionof a "hot"density model describedby Tho- where sufficientstellar signal is present(W. McClintock, primas [1978]. The model has evolved to include latitudinal vate communication,1998]. Based on these considerations,
anisotropiesin the solarwind flux [Witt et al., 1979], as well the density derived from Galileo Lyman {x measurements,includingestimatederror barsfrom the calibrationonly, is -0.17
as latitudinal and longitudinal anisotropiesin the solar Lyman{xflux [Pryor et al., 1992, 1996]. One troubling, persis- -I-0.05 cm'3 .
The density used here should also be comparedto neutral
tent problemfound in our modelingeffortsis the differencein
absolutecalibrationsat Lyman {x betweendifferentspacecraft. hydrogendensity estimatesfrompickup ion studies. GloeckPVOUVS reportedLyman {x intensitiesare -•2.13 timeslower let et al. [1997] used Ulysses solar wind ion composition
than simultaneousmeasurements
by Galileo when it passed spectrometer(SWICS) pickup ion measurementsto derive a
Venus [Colwell 1997; also personal communication1998]. neutral hydrogendensity near the terminationshock of 0.115
takenfrom 1983 to 1987 are the least bright, correspondingto
solar minimum.
26,838
PRYOR ET AL.: LYMAN c•OBSERVATIONS FROM PIONEER VENUS
+ 0.025 cm-3. The SWICS estimate and the Galileo estimate
better calibrated than SME.
have overlappingerror bars. Another technique,measurement
of the solar wind slowdown due to massloading, has been
studied by Richardson et al. [1995]. From a measuredsolar
wind slowdownof •-30 km s-• between 1 and 40 AU, they es-
tion of time of SOLSTICE is closely monitoredby l:neasure-
the model as follows:
about0.9 A-1timestheSME-or UARS-derived
integrated
so-
The relative
calibration
as a func-
mentsof a suite of stars. The UARS Lyman ct fluxesare systematically higher than the SME measurements,
by •-30% or
more,and have a larger solar maximumto solar minimumratio
timatea low neutralhydrogen
densityof0.05crn
-3,basedon [Woods and Rottman, 1997; Tobiska et al., 1997; de Toma et
theory presentedby Lee [1997]. Another model for the slow- al., 1997]. Figure 3a shows the computedecliptic and polar
down presentedby Isenberg [1986, Figure 2] shows that a Lyman ct fluxesfor the SME model. As we have previously
slowdownof•-30kms'• at 40 AU corresponds
to a neutral suggested[Pryor et al., 1992; Ajello et al., 1994], the comhydrogen
density
of 0.1cm-3,closerto theGloeckler
et al. re- puted polar Lyman ct flux is substantially (---20%)below the
sults. Recentwork by Isenberg [1997] showsthat a neutral equatorialflux at solarmaxima.Figure 3b compares
the SMEhydrogen
densityof 0.125cm-3nearthetermination
shockis basedand UARS-basedeclipticLyman ct fluxes.
consistentwith an analysis of anomalouscosmicray spectra
A key assumptionin the modeling is that the unmeasured
by Stoneet al. [1996].
Lymanct linecenterflux (photons
cm-2s-1fl,-i) responsible
for
The solar cycle variationsof five quantities are included in resonancescatteringfrom interstellarneutral hydrogenequals
5.1. Solar Flux Variation
lar Lyman ct flux (photonscm-2s-i) throughoutthe solar cycle.
Ajello et al. [1987] usedPVOUVS data to show that this ratio
is fairly constant over the solar cycle. The rough validity of
this assumptionis testedhere by trying modelsthat assume
Our model uses solar He 1083-nm imagesto computethe
solar Lyman ct flux on a given day at any solar latitude and
the factor of 0.9 A-1 for all orbits. The 0.9 A-1 estimate comes
longitude[Pryor et al., 1996]. The He 1083-nm imageset obfrom recentmeasurements
of the disc-integratedsolar Lyman ct
tained at Kitt Peak provides a valuable indicator of the Sun's
line shapeobtainedat solar minimumby the Solar Ultraviolet
Lyman ct distribution. The disc-averagedequivalent width is
Measurementsof Emitted Radiation (SUMER) instrumenton
an excellentproxy for Lyman ct [Harvey, 1984; Tobiska 1991;
the Solar Heliospheric Observatory(SOHO) [Lemaire et al.,
Harvey and Livingston, 1994]. Harvey and colleagueshave
1998]. Our previousmodels[Ajello et al., 1987, 1994; Pryor
combinedthese imagesinto Carrington rotation maps,which
et
al., 1992,1996]assumed
a factorof 1.0.A'•. SUMERresults
provide the equivalent width as a function of latitude and
from closerto solarmaximummay shedlight on thisproblemin
longitudefor eachsolarrotation. TheseCarringtonmapsform
the basis for our calculation. First, holes and artifacts in these
imageswere correctedby using informationfromneighboring
Carrington rotations. This proceduremay introducesomeerrors in the record,particularly in the late 1970s when more
datagapswere present. Next, an integralwas performedwhich
finds the disc-averagedequivalent width that would be seen
above any solar latitude and longitude on any given day.
This procedurereproducesin considerabledetail the previously reporteddisc-integratedequivalentwidths in the ecliptic plane. It was then assumedthat the samelinear relationship that exists between the ecliptic plane disc-averaged
equivalent width of He 1083-nm and disc-integrated, lineintegrated Lyman ct flux [Tobiska, 1991] exists at all other
latitudes. Two different relationshipswere usedhere. The linear relationship between the He 1083-nm equivalent width
(EW) and the Solar Mesosphere Explorer (SME) line-
integrated
solar
Lyman
& measurements
is[Tobiska,
1991]
Lyman
c•SME
= 8.40x101ø
+ 3.78x109xEW
the future.
5.2.
Solar Radiation
Pressure
Variation
Estimatesof the radiationparameter
g alsorely on assuming
the numericalcorrespondence
between line centerand integratedsolarLyman ct emissions.The radiation pressurehas a
latitude dependencedirectly causedby the latitude dependenceof the solar flux [Ajello et al., 1994]. Atoms that pass
over the solar poles are exposedto a lower averageradiation
pressurethan those that passover more equatorial latitudes.
This effectis crudelyrepresented
by averagingthe 12-month
averageecliptic value of g, with the lower polar value. The
time averageis used to compensatefor the varying pressures
experiencedby a hydrogenatomas it approachesand then recedesfromthe Sun. During a 1-yearperiod a hydrogenatom
travels4.2 AU at a velocityof 20 km s-•. This is roughly comparableto the scalesize of the system:the maximumemission
region
isatdistances
rc/2from2.25to 3.35AU from
theSun,
dependingon the hydrogenatom lifetime [Ajello et al., 1987].
Hererc isthedistance
alongtheupwindaxisfromtheSunto
in units of photons cm-2s-1 at 1 AU fromthe Sun. Measured
valuesof EW rangefrom 39 to 97. The linear relationship between the He 1083 nm equivalent width and the Upper AtmosphereResearchSatellite(UARS) solarLyman cttime series
in the sameunits(throughthe end of 1995) is
the point where ionizationhas attenuatedthe original density
tral IrradianceMonitor (SUSIM)) reportsLyman ct values 10%
lower than SOLSTICE. The UARS instrumentswere probably
and1.0A-• timesthe line-integrated
flux. Theradiationpres-
by a factorof 1/e.
Both the ecliptic value and polar values of g are estimated
fromthe He 1083-nm solar images. The solar flux information
in Figures3a and3b is usedto computethe equatorialandpolar 1-year-average
ratio of radiationpressureto solargravity.
The
computed
polar
1-year-average
radiationpressureis lower
Lyman
ctUARS=0.95x(2.10x
101ø+7.07x
109x
EW).
than the equatorial value by 10-20% at solar maxima. For
The UARS data come from the Solar Stellar Intercomparison modelingpurposes
we usethe averageof the polarand equatoExperiment(SOLSTICE) measurements[Woods and Rottman, rial 1-year-averageradiation pressures,shown in Figure 3c.
1997] and have been scaled by the factor of 0.95 becausethe SME and UARS-based models of the radiation pressureare
other Lyman ct instrumenton UARS (Solar Ultraviolet Spec- bothshownfor caseswiththe line centerflux equalto 0.9
sureparameterg for the SME-basedLyman ct fluxesis gener-
PRYORET AL.: LYMAN c•OBSERVATIONSFROM PIONEERVENUS
5.0x10
26,839
11
7E 4.5x1011
I
I
c
o
-• 4.0x1011
i
c
o
3.5x10
11
E
__o
3.0x10
o
o
.o
2.5x10
11
11
........
South
i
North
2.0x10
Ecliptic
11
1980
1985
1990
199,5
Year
Figure3a. ThedailySME-based
solarLyman(xline-integrated
fluxfor theeclipticplaneandforthetwo solarpolesforthePV
period.ValuesaretakenfromtheHe 1083-nm
calculation
usingtheproxymodeldescribed
in thetext. Modelsin this paperuse
the line centerflux, assumedto be 0.9 timesthe valuesshown.
7.0xlO11l: '
7
m 6.0x10
?
E
u
•
5.0x10
I
....
I
....
I
....
I
'
11
11
o
o
.c
•- 4.0x10
11
i
c
o 3,0xt0
11
E
•
2.0x10
1.0x10
11
11
_-
UARS-bosed
-
_
-
_
:
SME-bosed
:
_
_
1980
1985
199o
1995
Year
Figure3b. TheSME-andUARS-based
solarLyman(xline-integrated
eclipticfluxcomputed
t•omthe He 1083-nmcalculation.
Modelsin thispaperusethelinecenterflux, assumed
to be 0.9 timesthevaluesshown.
26,840
PRYOR ET AL.: LYMAN •xOBSERVATIONS FROM PIONEER VENUS
o
........
0.5
I
...
UARS-based
SME-based
1980
1985
1990
1995
Year
Figure3c. Assuminga one-to-onecorrespondence
between
the numericalvaluesof line-integratedLyman(x solar flux (photons
-2
cm
-2s-])andlinecenter
Lyman
(xsolar
flux(photons
cm s'• A']) leads
to 1-year
average
(before
theindicated
date)radiation
pressureparameterp valuesfor SME andUARS fluxes. The averageof thenorthandsouthpolarp valueshasbeen averagedwith
the eclipticp valueto estimatethe "average"radiationpressure(solidlines). Modelsin this paperuseradiation pressurevalues
(dashedlines) equalto 0.9 timesthe solid lines. The horizontalline at p=l separatesp valuesthat leadto a net solarattractionof
hydrogenatomsby the sun(p<l) from valueswith net solarrepulsion(g> 1).
ally less than 1, so the net effectin passing the Sun is focusing. However, the UARS-based Lyman c• fluxes imply la generally >1, so the net effect is repulsion.
5.3.
Solar
Wind
Flux
Variation
Chargeexchangebetween slow (20 km s-l)interstellar hydrogenatomsand faster (---300-700km s-l) solar wind protons
createsa cavity near the Sun depletedin slow neutralsthat can
scatterthe solar Lyman c• line. The rate of this processin the
ecliptic is estimated l•om the National Space Science Data
Center (NSSDC) on-line databaseof solar wind proton density and velocity measurementsat 1 AU. These measurements
madeby the near-EarthspacecraftISEE 1, ISEE 3, IMP 7, and
IMP 8 are documentedby King [1977a, b, 1979, 1983]. Most
of the data used here comel•omthe IMP 8 spacecraft.Hydrogen atom-protonchargeexchangecrosssectionsare fi'omBarnett et al. [1990]. The rate of the chargeexchangeprocessat
other ecliptic latitudesis not well known; finding this rate is
one goal of our modeling efforts. If x(0) is defined to be the
time-averagedlifetime against solar wind charge exchangein
the ecliptic (ecliptic latitude 0 degrees),then the lifetime at
eclipticlatitude[• is assumed
to be of the form
•(1•)=•(0)/[1. - ,t sin2(13)l
Our initial model approximatesthe varying solar wind
fluxesencounteredby the interstellarneutralsby averaging
the solarwind flux overthe 12 monthsbeforea given observation. This is the sametimescaleusedfor the radiation pressure
calculation,for the samereasonsdiscussedabove. Figure 4
shows the monthly averagehydrogen lifetime against solar
wind chargeexchangeat 1 AU and the 12-month-averagelifetime. The averagevaluesrangefrom-1.2 to 1.9xl 06 s. The actual lifetime will be somewhatshorterdue to solar EUV photoionization of hydrogen.
5.4.
Solar EUV
Flux Variation
A secondaryloss processfor ground state (ls) interstellar
hydrogen is photoionization by photons with wavelengths
less than 91.2 nm. The solar EUV
flux variation
over a solar
cycle is not particularly well known. Ogawa et al., [1995]
evaluatedthe total photoionization rate [•, including a very
minor componentl•om loss of metastable(2s) hydrogen. Using Ogawa et al. 's, Table 3, we representthe total photoionizationrate at 1 AU, [•, in s-• as
[•=1.50x10-7+
(2.42x10'7-1.50x10
-7)
x ((F 10.7-62.7)/(214.0-62.7))
where F10.7 is the 10.7 cm radio flux l•om the Sun in units of
whereA is the solarwind asymmetryparameter.
10-22W m-2Hz-]. The photoionizationlifetime• is the recip-
PRYOR ET AL.: LYMAN ct OBSERVATIONS FROM PIONEER VENUS
5.5x106
'
5.0x106 -
'
t
....
I
....
I
,
•
....
26,841
I
'
monthly average H lifetime against charge exchange
...... 12-month average H lifetime against charge exchange
-12-month average H lifetime
'•' 2.5xl 06
'•'
• 2.0x106
:• 1.5x106
1.0x106
5.0x105
0
,
,
I
1980
,
,
,
,
,
1985
,
1990
1995
Yeor
Figure4. Thevariation
in themonthly
average
hydrogen
atomlifetimeagainstsolarwind chargeexchange.
Also shownis the
12-monthaverageof the monthlyaveragelifetimebeforea giventime,for chargeexchange
only; and for chargeexchange
combined
with photoionization.Valuesof solarwind densityandvelocityaretakenfi'omthe National SpaceScienceData
Center(NSSDC) database.
rocalof[3. A valueofF10.7=62.7is a very low solarminimum diationpressureandtwo valuesof the hydrogenatomlifetime
value, while F10.7=214.0 is moretypical of solar maximum at 1 AU. Linear interpolationbetweenthese six caseswas
conditions.
For a solar minimum value of F!0.7-62.7,
madeto derivethe multiple scatteringcorrectionsappropriate
•=l.50x10-7s-1andx=6.67x106s. For a solarmaximum
value for a givenday. Thesecorrectionswere computedfor a spaceof F10.7=214.0, [3=2.42x10-7s4 and x=4.13x106s. In both craft 1 AU downstreamfrom the Sun, with values for atomic H
casesthe photoionizationlifetimex is substantiallylonger outsidethe cavity but well inside the heliopause,of n=0.17
v=20.0km s-l, andT=8000K. Thedependence
on disthanthe hydrogenatom lifetimeagainstsolarwind chargeex- cm-3,
change. One-yearaveragesof the photoionizationlifetime tancefi'omthe sun and on spacecraftecliptic longitude is aswereusedin the modelshere. Combiningthe photoionization
lifetimeand the solar wind chargeexchangelifetimeyields a
surprisingly
constantlifetimefor slow neutralhydrogen(Figure 4). Photoionizationis largestnear solar maximum
when
the chargeexchangerate is smallest. The ecliptic lifetime
sumedto be minor. The corrections
to an optically thin model
brightness
/thin
arerepresented
as
I(0)--/thin(0)q(0)
found from solar wind and solar EUV flux measurements in
Theanglefi'omthe upwinddirection•isdenoted0. For 0=0,
Figure4 is generally
near-t.2xtO6s. Thiscompares
favorably upwind,the corrections
arenegligible
(<2%),whiledown'
with the lifetimeof 1.1x106sec derivedfromparallaxshifts of
stream,0=180,theybecomeimportant. The monotonicallyinthemaximumemissionregionin PioneerVenusinterplanetary
creasingfunctionq(0), where0 is in degrees,canbe well repdata [Ajello et al., 1987].
resentedas a polynomial:
5.5. Multiple Scattering Correction
q(O)=ao+a
• 0+a202+a
303
Next, the time dependence
of the multiple scatteringcorrection was includedin our optically thin model. (Currentcom- Table 1 showsthe six casesused. This multiple scatteringcorputationallimits favora hybrid approachbetweenfast opti- rection scheme was used for all models shown. A similar cal-3gavesimilarresults(within3%),incally thin modelsand slow multiple scatteringcodes.) The culationforn-0.10 cm
multiplescatteringmodelused [Hall, 1992; Ajello et al., dicatingthat the correctionfactorsare not a strong function of
between
0.10and0.17cm'3. An independent
calcula1994] assumescylindrical symmetry;no attemptis madeto density
deal with latitudinal variations in the solar wind flux or the
tion by Quemerais and Bertaux [1993, Table 3] found that q
solarLymanc• flux. Multiplescattering
correctionswere com- increases from 1.09 to 1.23 to 1.30 to 1.34 to 1.36 in the
putedfor six cases,involvingthreerealisticvaluesof the ra- downwind multiple scatteringcorrectionwhen the density
26,842
PRYOR ET AL.: LYMAN {xOBSERVATIONS FROM PIONEER VENUS
Table1. MultipleScattering
Corrections
%s
!.t
1.4x106
0.75
!.4x10•
1.10
1.4x10•
!.60
2.1x10•
0.75
2.1x10•
1.10
2.1x10•
1.60
(n=0.17 cm-3)
a0
0.99129
0.98381
0.97097
!.0005
0.99048
0.97638
a1
-2.1501x10-4
8.1145x10-5
6.0193x10-4
-3.1373x10-4
1.7690x10-5
4.8491x10-4
a2
q(180)
a3
6.0459x10-6
-2.6860x10-•
-1.873lx10-5
7.8907x10-6
-8.1105x10-7
-1.7107x10-5
2.6745x10-8
9.5069x10-8
2.1399x10-7
-4.1819x10-!0
7.06844xl 0-8
1.9652x10-7
1.301
1.462
1.716
!.195
1.377
1.651
increases
from0.01 to 0.05 to 0.1 to 0.15 to 0.20 cm'3,for an
observer1 AU fromthe Sun and 90ø fromthe upwind axis.
Theirresultssupport
the ideathatthe multiplescattering
correctionis not too sensitiveto densityvariationsin the range
genatomlifetimeat 1 AU of 1.4x10
6Sisfairlyrealistic;chang-
0.1-0.2 cm-3.
Querneraisand Bertaux [ 1993].
Increasingradiation pressuredepletesthe downwind density,leadingto a very anisotropicdensitydistribution. Multiple scatteringproducesa brightnessdistributionthat is less
ing to a 50% longerandlessrealisticlifetimeof2.1xl06 s has
only a modesteffecton the correction. An extensive discus-
sion of these radiativetransfereffectsis presented
by
6. Modeling Results
anisotropicthan would be obtainedin a single-scattering An initialattempt
wasmadeto fit thetimeseriesoftheupwind and downwinddatasets with an SME-based
model,
wherethe radiationpressure,
hydrogenatomlifetime,andmul-
model. The derived multiple scatteringcorrectionsare a
strongfunctionof the assumed
radiationpressure.A hydro-
i
....
i
,
UARS
o) t-- SME
Period
--I
1 500
Begin
700
600
'
500
•
' ....
OARSi
'b)I--SME
Period iBegin
i
_
:
400
1000
300
5OO
A=0.60
200
RMS Fit = 9.79%
Doto =
.
Foctor = 1.63
Model =-SME-bosed
Initiol
Model
,
i
,
i
i
,
i
,
,
,
,
i
,
•
100
1980
1985
A=0.60
RMS Fit = 18.1%
.
Dote =
Foctor
Model =--
=
1.53
0 SME-bosed
Inltio,
I Model
i
1990
i
i
1980
SME Period
I
,
,
,
1990
........
d) [--SME
Period
•
Begin
.
+
1.5
+
1.0
o10
C3
+
+
++
o
0A"S'
Begin:
+
+
+ +
+ +$
-½'
+**
+ •
+
•,
+
t+.%,
*+
+
ß
+
0.5
A=0.60
SME-bosed
0.0
,
Yeor
2.0
0.5
,
1985
Yeor
c)
•
ß
,
Initiol Model
I
I
1980
1985
+
-A=0.60
SME-bosed
,
i
1990
Yeor
0.0
•
Initial Model
I
I
I
1980
1985
1990
Yeor
Figure
5. Initialmodel
fitstothetimeseries
PVOUVS
interplanetary
Lyman
t• data.Thedatahavebeenscaled
upward
to fitthe
modelderivedfor Galileodataof Pryor et al., [1996]. This scalingreflectscalibrationdifferences
betweeninstruments.
This
initialmodel
uses
solar
radiation
pressure,
solar
windionization,
andphotoionization
values
averaged
overthe1 yearpriorto
theobservation.
A solar
windasymmetry
parameter
of,4=0.6
wasused.
(a)Fittotheupwind
data.Datarepresent
theaverage
of
three10øbinscentered
ontheupwind
direction.
Modelpointshavebeencomputed
foreachdayandconnected
witha linefor
clarity;
dataareshown
asdots,theactual
locations
ofpoints
canbemore
easilyseenin Figures
5cand5d. (b)Fit to the
downwinddatawith the samemodel.Datarepresent
the average
of six 10ø binscentered
on the downwinddirection.This
model
fitsthedownwind
timeseries
poorly.
(c)Thetimeseries
ofdatadivided
bymodel
in theupwind
direction.
(d)Thetime
seriesof datadividedby modelin the downwinddirection.
PRYOR ET AL.' LYMAN ct OBSERVATIONS FROM PIONEER VENUS
26,843
Physically, the light observed downwind is coming fi'om
hydrogen atoms which passedthe sun in earlier years (see
wind time series data with the Pioneer Venus calibration are
AppendixA for morejustification). This travel time effectsugindependently scaled to the Galileo-based model. For suc- geststhat the 1-year-averagingschemeis not adequatefor decessfulmodelsthe two scaling factorsshould be similar and scribing the downwind hydrogen. Hydrogen atoms downnear 2 in order to match the cross-calibration results obtained
wind at solarminimum may have passedthe Sun at solar maxiwhen both PV and Galileo were near Venus. A solar wind
mum, when the radiation pressureis much larger. A variation
asymmetryfactor of A=0.6 was used (Figures 5a-5d). Three on the model was constructedto account for the time lag. Upbins 10ø wide in ecliptic longitude centeredon the upwind wind volume emissionrates are computedusing the radiation
directionwere modeledseparatelyand then combinedto form pressureand hydrogen atom lifetimes averagedover 1 year
the upwind set. Six of the dimmer10ø bins centeredaround before the observation. For downwind volume elements the
downwindwere combinedto provide countingstatisticssimi- radiation pressureand hydrogen atom lifetimes are averaged
lar to thoseof the upwindset. The downwind bin containing over 1 year beforethe time when the atomsin that volume elethe star Iota Orionis was excluded. Each data point in this set ment crossa plane6 monthsdownwindof the Sun, assuminga
tiple scatteringcorrectionare all representedas a 1-yearaveragebeforethetime of the observation.The upwind and down-
contains at least 85 counts, while most contain several hun-
bulkhydrogen
velocityof20 kms'1. Thisapproximation
as-
dred counts. The upwind data are in fair agreementwith the sumesthat the largest effecton the atoms occurs in the year
model,but the downwind data lead to a systematicproblem: when they are closestto the sun (AppendixA). Solar wind 1the data are higher than the modelnearthe two solar maxima year-averageecliptic data were used beginning in January
and lower than the model near the solar minimum.
1975. Radiationpressure1-year-averagedata derived fi'omHe
_c
I
| WARSt
o) [-- SME
Period
--{
1 500
o
I
Begin-[
1 000
•
700
•
600
•
500
n-
400
'Period
'b)[--SME
-- ' O^RS•
Begln
i
-o 500
5OO
•
A=0.60
RMS Fit = 9.84%
Factor
= 1.64
Data =
ß
Model =--
1985
A=0.60
ß
RMS Fit = 13.2%
Factor = 1.69
Data =
.
Model =--
o 100
os,ed,
Lo,
gg,ed,
M,od,el
, , ....
ca
0 S,ME,-b,
SME,-b,
os,ed
' Lo,
gc•ed,
Mgd,el ....
1980
200
1980
1990
1985
1990
Yeor
Yeor
2.0
2.0
WARS
Begin
'
i
i
I
WARS
d) t--SME
Period
Begin
+
ß
.
1.5
•
1.5
+
+
++
+
o
+ -•.+ +
+
+ +
+
o10
-• +
E3
ß
+
+
++
+
c
0.5
•
m
.
A=0.60
SME-bosed
Logged
Model
0.0
, , ............
1980
1985
Year
1990
C
+
'• 0I5 ßA=0.60
co 0.0
+
SME-bosedLoggedModel
......
, ....
1980
1985
.
, , , ,
1990
Year
Figure6. The fit of the bestSME-basedlaggedmodel(usedin Plates 1 and 2 and Figures6 and 7) to the time seriesPVOUVS
interplanetaryLyman rt data. This model computesdownwind densities using solar radiation pressureand solar wind
ionization and photoionizationvalues averagedover the year when the downwind hydrogenatomshad crossedthe upwind-
downwind
plane,assuming
a bulkdownwind
flowof20 kms4. Upwinddensities
arecomputed
forradiation
pressure
and
ionization values averagedover 1 year beforethe observation. Scaling factorshave been applied to the data with the PV
calibrationto bring them into agreementwith the Galileo-derivedmodel. A solar wind asymmetryparameterof A=0.6 was used.
(a) Fit to theupwinddata. Data(points)represent
theaverage
of three10ø binscentered
onthe upwinddirection.(b) Fit to the
downwinddata with the samemodel. Data (points) representthe averageof six 10ø bins centeredon the downwind direction.
This model does better at fitting the downwind time seriesthan the model in Figure 5. (c) The time seriesof data divided by
modelin the upwinddirection. (d) The time seriesof datadividedby modelin the downwinddirection.
26,844
PRYORET AL.: LYMAN ctOBSERVATIONS
FROMPIONEERVENUS
1 ooo
i
i
i
i
i
J
i
1
:24 Feb 1980 (Orbit 446)
RMS Fit=7.13%
•
R=0.720
AU
-
Factor= 1.53
-•
X=0.082
AU
A=0 25
q
Y=0.71
• ,•,r47½•_
8OO -
_ • • •'•.•..•'•T
-
A=0.60
•tt/t•'•.<-:
....... "*-.•
--•
-I
',.% x=o:oo
........
600
5 AU
Z=0.005
S/C Angle=85.4ø
n-O.
400
1 7 cm
T=8000
200
v-20.O
- • SME-bosed
Logged
Model .... -•
O! ;•Data
with
1crError
Bars
560
515
270
225
180
155
90
AU
-5
K
km s-'
•
45
0
Ecliptic Longitude
000
•
.......
•10 Jan1985(Orbit2227)
•8OO •-
• •;:•
I-
600
400
z•,•"--•
•
RMSFit=6.55%
Factor= 1.95
A=0.60 ---
A=0.25 - --
-1
-1
--
R=0.722
AU
X=0.586
AU
Y=0.610
AU
Z=-0.01
AU
../'/•.::.
•.7...-....--.•t..:....
'-•...••,.
A
=O.
O0
.........
S/C Angle=57.6ø
n=0.1
T=8000
v=20.0
7 cm
-5
K
km s-'
200 •- -- SME-bosed
Logged
Model'""-'--'-...--..".-.•."::'":"
oL
560
515
270
225
180
155
90
45
0
Ecliptic Longitude
Figure 7. The fit of the best (A=0.6) SME-basedlagged model (used in Plates 1 and 2 and Figures 6 and 7) to PVOUVS
interplanetary
Lyman czdatafrom two "typical"days. Scalingfactorshavebeenappliedto the data to bring theminto agreement
with the solar wind asymmetryparameter
A=0.6 model. Also shown are modelswith ,4=0.25 and ,4=0.0. (a) For February24,
1980 (orbit 446), duringsolarmaximum. (b) For January10, 1985 (orbit2227), duringsolarminimum.
1083nm imageswas used beginining in July 1977. The values for January1975 and July 1977 were used for the solar
wind and radiation pressuredata,respectively,when examining volume elementswhere the atomshad passedthe Sun before thosetwo dates. As our PV data span 1979-1992, this is
not a majorhandicapin the modeling,exceptpossibly in the
first year or two. Figures6a-6d showthe resultsof this SMEbasedlaggedmodel. The quality of the downwind fit to the
datais now muchcloserto the quality of the upwind fit, suggestingthat this crudetime-dependent
model has capturedthe
essenceof the effect. This lagged modelalso fits the upwinddownwind variation observed on individual daily data sets.
This is illustratedin Figure 7 for two "typical"days, one near
solarmaximumand one near solar minimum. Figure 7 also illustratesthe effect of the solar wind asymmetryparameterA on
the upwindto downwindratio. Increasing`4 reducesthis ratio, althoughwe shouldagain point out that manyfactorsinfluencethe upwindto downwind ratio and that the PVOUVS
data are not ideal for determiningA.
Finally, we show a lagged model based on the UARS
SOLSTICE solar fluxes,which are systematicallyhigher than
the SME fluxes,and have a largersolar maximumto solar minimumbrightnessratio. Woods and Rottrnan [1997] suggest
scalingthe UARS SOLSTICE fluxes by 0.95 to reflectthe averageof the UARS SOLSTICE and UARS SUSIM Lyman cz
measurements.This is done here for both the model solar Lymanczflux andthe model radiation pressure. This modelhandlesthe time dependence
in the sameway as in Figure 6. Figures 8a-8d show the UARS-based fit to the time series, in this
casefor A=0.75. The modelbrightnessesare not very different
•om before because increasing the radiation pressure has
largely compensatedfor the increasingsolar flux. The downwind time seriesdataare now betterfit by the model. The large
radiation pressureassociatedwith the UARS fluxes depletes
the downwind hydrogenmorethan in an SME-basedmodel.
For a UARS-based model with A=0.5 the scaling factorsupwind and downwindare ---20%different,with an upwind scaling factorto applyto the dataof 1.99 and a downwindfactorof
1.65. Using A=0.75 provides somewhatbetter agreement
(within ---10%) in scaling factors:upwind is 2.03 and downwind is 1.82. This asymmetryparametercorresponds
to a polar
hydrogenatom lifetime 4 times longer than the equatorialone.
PRYORET AL.:LYMANc•OBSERVATIONS
FROMPIONEER
VENUS
[
500
..
.
[
,
UARS•
o) t-- SMEPeriod
--t
Begin-
i
700
•
600
26,845
' [ 'b') [-- SME
'Period
--•
ß
'
UARS::
IBegln
i
-
.
.
ß
•, 500
rY 400
ooo
!
ß
ß:
-o 3oo
.
500
0
•
A=0.75
RMS Fit = 9.68%
Factor = 2.0.:3
Data =
ß
Model =-
o
m
U,AR,S-,bo,se,d
L,og,ge,d
Mo,del,, , , ,
1980
1985
200
100
0
A=0.75
'
RMS Fit = 10.9%
Factor = 1.82
Data =
.
Model =--
U,AR,S-,bo?•,d
L,og,g•,d¾od,•,, , , , ,
1980
1990
,
'
'
c)
1985
1990
Year
Year
2.0
:'
'
SMEPeriod
OARS
,
d) [-- +SME
Period
Begin
UAR
S-
Begin]
.
.
1.5
•
+
+
1.0
,•-+
+
+
g
+
+
0.5
A=0.75
UARS-bosed Lagged Model
0.0
,
i
,
,
1980
,
i
I
,
1985
,
o
•
0.0
1990
Yeor
Figure8. Thefit of a UARS-based
laggedmodel(solidline)to thetimeseriesPVOUVSinterplanetary
Lymanc•data. This
modelcomputes
downwinddensities
usingsolarradiationpressure
andsolarwind ionizationandphotoionization
values
averaged
overthe yearwhenthe downwindhydrogenatomshad crossed
the upwind-downwind
plane,assuming
a bulk
downwind
flowof20kms'•. Upwind
densities
arecomputed
forradiation
pressure
andionization
values
averaged
overoneyear
beforetheobservation.
Scalingfactors
havebeenapplied
to thedatato bringthemintoagreement
withthe model.A solarwind
asymmetry
parameter
ofA=0.75hasbeenused.(a)Fittotheupwinddata.Data(points)represent
theaverage
of three10ø bins
centered
ontheupwinddirection.(b) Fit to thedownwind
datawiththesamemodel.Data(points)represent
the average
of six
10ø bins centeredon the downwind direction. This modelfits both time seriesbut does not simultaneouslyfit upwind and
downwind
withthesamescalefactor.(c) Thetimeseriesof datadividedby modelin theupwinddirection.(d) Thetimeseriesof
datadividedby modelin the downwinddirection.
It is not entirelyclearthat we aresolvingfor the physical that damprapidlywith heliocentric
distance.OuterhelioquantityA in this datasetbecause
the look directionis al- sphericmodelsof the downwindhydrogen
(Pioneer10 data)
waysat -30ø.
will needto incorporate
thiseffectin thefuture.
A majorassumption
in the modelingeffort wasthatthe discintegrated
solarline centerLymanc•flux, whichis r•sponsible
7. Discussion
fortheresonance
scattering
(and
radiation
pressure)
effects,
A key resultin thisstudyis thatthe downwindbrightness
is largerthanexpected
at solarmaximum
andlessthanexpected
at solarminimumin a 1-year-average
model. We haveargued
has a constant line centerto line-integrated flux ratio of 0.9,
based on initial SOHO SUMER results at solar minimum [Lemaire et al., 1998]. It would be of interestto see if spatially
resolved solar Lyman c• spectrafrom the Solar Max Mission
(SMM) couldbe disc-integrated
to testthis conclusion,as has
been done for the O 130.4-nm emission [Gladstone, 1992].
Spatially resolvedSMM solar Lyman c• spectrahave a wide
varietyof shapes,with differingdegreesof self-reversal[Fontenla et al., 1988]. Their SMM quiet Sun profiles have a line
centerto integratedflux ratio of-•l.06. Their SMM active Sun
profilesincludebothlargerand smallerratios. Our successful
modelingeffortssuggestthat the disc-integratedflux and line
centerflux mustbe roughly proportionalto eachother or the
that this is due to the fact that downwind atoms reflect condi-
tionsnearthe Sunin earlieryears. A crudemodelof this effect
has improvedthe fits to the PioneerVenusLyman c• data.
Other workershave arguedthat such a time dependenceis
needed.Blumet al. [1993] useda Monte Carlo simulationto
show that the downwind direction contains a seriesof hydro-
gen densitywavespersistingto hundredsof AU resulting
fromthetimedependence
of It. Kyrola et al. [1994],Rucinski
and Bzowski[1995],andSummanen[1996] performed
similar
calculationsshowing moremodest,but real, density waves
26,846
PRYOR ET AL.: LYMAN ct OBSERVATIONS FROM PIONEER VENUS
time seriesdatawould not trackwith the model. The cavity
shapealso dependson this ratio,throughthe radiationpressureparameterg. Variationsin g substantiallyalter the ca¾ity
shapeandaffectourability to simultaneously
fit the datafrom
differentlongitudes.Our bestfitting modelparameters
should
not be considereda unique solution to the problem,as other
effects,suchasthe time dependenceof the solar wind latitude
asymmetry,may be involved. Solarwind monitoringsatellites
in the ecliptic do not recordsolarwind eventsat high solar
latitudesthat mightchangethe latitudeasymmetry.
The PVOUVS datamodeledhereonly sampleone ecliptic
latitude(-30ø), so they are not particularlywell suitedfor determining the value of A. A primarily affectsthe downwind
wouldhavea solarwind chargeexchange
lifetimeasymmetry
factorof A=0.5. TheUlyssesmeasurement
is obviouslymore
direct and is in satisfactory
agreement
with the SME-based
Lymanct modelsdiscussed
here. Summanenet al., [1997] arguedthattheA representation
doesnot very accurately
representthe Ulysses solar wind data, which leadsto an ionization
ratethat is sharplypeakednearthe eclipticplane. Theyfind
that use of the A representation
overestimates
the meanioniza-
tionrateby 20%. Pryor et al., [this issue]reporton different
representations
for the solarwind massflux in fitting Ulysses
GAS Lymanatmapsthatare bettersuitedfor studyingthe solar wind asymmetries.
We haveattempted
to usethe bestavailableinput parame-
brightness
andmay be a functionof time. We found that to si-
ters in the models, but the uncertaintiesin some of them remain
multaneously
fit the PVOUVS dataobtainedovera solarcycle
in boththe upwindand downwindhemispheres
with an SMEbasedmodelrequiresan averagevalueof A=0.5-0.6. Fitting
the UARS-basedmodelsrequireda largervalue of,,1=0.75 or
uncomfortably
large. Oneconcern
is in thewide rangeof publisheddensitiesfor hydrogennearthe terminationshock. The
old standardpicturefavoredan inflowinghydrogengasdensity of n=0.06-0.08cm'3. However,"a consensus
hasbeen
buildingfora higherhydrogendensity"[Isenberg,1997,p.
more.
Our earlier modelingstudiesof A used SME-basedmodels. 623]greater
than0.1cm'3. Ourhydrogen
density
based
onour
Galileo EUVS Lyman c• data fromnear solar maximumfavor a GalileoUVScalibration
ofn=0.17+0.05
cm'3 is a bit higher
low asymmetryparameter
A--0 [Pryoret al., 1992, 1996]. This thanaverage,
buttheerrorbaroverlaps
with the recentpickup
result may be comparedwith A=0.25+0.25 derived fromGali- ionresults
of Gloeckler
et al., [1997](n=0.115+0.05
cm'3)and
leo UVS datafrom 1990 [Ajelloet al., 1994] at solar maximum. the Lymanctradiationanalysisof Quemeraiset al., [1994]
Independentwork has foundA=0.30+0.05 fromsomespecial
high-latitudePVOUVS observationsmadeduring the 1986
encounterwith Comet Halley at solar minimum[Lallement
and Stewart,1990]. The modelsare particularlysensitiveto A
at solarminimumwhenthesolarLymanc•flux is moresymmetric [Ajello 1990; Ajello et al., 1994]. A companionpaper
[Pryor et al., this issue]reportsevidencefromUlyssesinter-
(n=0.165+0.035
cm'3).Detection
of a solarwind slowdown
between1 and40 AU by Richardson
et al. [1995]wasattributedto a ratherlowhydrogen
densityof0.05cm-3. However,
thislowdensity
of0.05cm'3requires
onlya modest
multiple
scattering correction for an observer at 1 AU from the Sun
lookingdownwind(fromsidewind)
of-•23% insteadof-35%
forn=0.17cm-3[Quernerais
andBertaux,
1993,Table3] and
stellarneutralgas(GAS)Lymanc• mapsthat the asymmetry makesit somewhatharderto reconcilethe models with the observedupwindto downwind
ratios[Ajelloet al., 1994].
A second
majorconcern
is thelargedifference
betweenSME
The interplanetary
Lymanc• datacanbe compared
to other
measurements
of the solar wind asymmetry. Radio observa- andUARS SOLSTICEsolarLymanat fluxes. Tobiskaet al.,
tions combinedwith white light coronagraphobservations [1997] usethe PioneerVenusdata set fromthis paperto
imply that in goingfromsolarequatorto solarpole,the solar bridge the gap in time betweenSME and UARS. As can be
windmassflux(densityn• timesvelocityVsw)
decreases
by a seenin Figure6, thereis no largejump in the ratio of the PV
theendof SMEandthebeginning
factorof 2.3 andsolarwindvelocityv• increases
by a factorof datatothemodelbetween
between
thelargeUARS solarLyman
2.2 at solarminimum[Wooand Goldstein,1994]. At a typical of UARS. Differences
valuesandsmaller
SMEirradiance
valuesprobaeclipticsolarwind speedof 350 km s-i, the chargeexchange atirradiance
as was also found
crosssectionc•is 1.91xl0-lScm-2;at a polar wind speedof bly reflectabsolutecalibrationdifferences,
350x2.2=770
kms-l,{Jfallsto 1.30x10-lS
cm'2[Barnettet al., by Woodsand Rottrnan[1997]usingothersolarproxies.de
1990].Thus,if the lifetimeagainstchargeexchange
x of a hy- Toma et al. [1997] also found a calibration differencebetween
SME and UARS by usingVoyagerinterplanetary
Lymanat
drogenatomat 1 AU x=l/[mwv• o(v•w)],then
parameteris largerat solarminimumthansolarmaximum.
datato comparethe solarmeasurements.
•pole/•equator
=[n•v• {J(V•)]equator/[ns•V•
{J(V,w)]poie=2.3(1.91/1.30)=
3.37.
Usinga UARS-based
modelprovidesimproved
agreement
with thePV downwindtimeseriesdata.However,
the large
radiation pressuresin the UARS-basedmodel makethe de-
rivedasymmetry
parameter
A somewhat
largerthanexpected
fromprevious
workin orderto matchthe observed
upwindto
This ratio correspondsto A=0.70. This estimateis not too downwindratio. OtherfactorsbesidesA maycontributeto
different from the UARS-based models evaluated here. Direct
theupwindto downwind
ratio. Forexample,
a minorpopulasolarwind measurements
by Ulyssesat solarminimum
[Phil- tionof superthermal
H atomsmayactto fill in the downwind
lips et al., 1995] found the median massflux between -80.2 cavity. High spectralresolutionHubbleSpaceTelescope
latitude (September12, 1994) and 80.2 latitude (July 31, (HST)measurements
[Clarkeet al., 1995]of thehydrogencol1995) to be nearlyconstantwith latitude. However,the more umnbetweenEarthandMarsalsoindicatean unexpectedly
relevantquantityfor the hydrogendensity,the meanmassflux largeamountof hydrogen(of noncometary
origin) in the
foundin thesesolarwind experiments,
decreases
by -•40% downwindcavity. Interplanetary
line shapemeasurements
fromequatorto pole [Summanen,1996; Summanenet al., fromthe Solar Wind Asymmetry
(SWAN) experiment
on
1997]. A "harmonic"representation
of the Ulysses data SOHO and the Hydrogen DeuteriumAbsorption Cell
(basedon the ionization
ratesof Surnrnanen
et al. [1997,Fig- (HDAC) experimenton Cassinimayhelp bettercharacterize
ure 2, after subtractionof the photoionizationcomponent) the downwind material.
PRYOR ET AL.' LYMAN c•OBSERVATIONS FROM PIONEER VENUS
Appendix: Justificationfor a Model with a
"Lagged" Radiation Pressureand Lifetime
First, consider the source function for emission, also
known as the volumeemissionrate. Formally,it is the
productof the hydrogendensityn, the solar flux, the
scattering
crosssection,andthe phasefunction.We usethe
standardtable of hydrogendensitiesof Thomas[1978] to
evaluate the source function. The relative source function
for an observerat the Sunis simplytheproductof density
and 1/r2, wherer is the distancefrom theSunin AU. Figure
A1 illustratesthe relativedensityand sourcefunction.The
upwindsourcefunctionis rather sharplypeakednear the
maximum
emissionregion,1-2 AU upwindof the Sun. The
m is the massof a hydrogenatom. SinceI•=1,the acceleration
due to effectivegravity is smallerthan that due to solar
gravity. Findingthe trajectorydue to effectivegravity is
analogousto a small angle Coulombscatteringproblem
[Nicholson,1983). Define 0 as the anglebetweenthe ray
fromthe Sunin the upwind directionand the ray from the
Sunto the atom. Definethe impactparameterfor an atom
movingpast the Sun as the closestapproach distancep.
Thenthe perpendicularvelocityacquiredin passingthe Sun
is
vl=• dtFg
l
=--•
7dtGM(/•-l)sinO
/.2
downwind source function is rather broad, with substantial
• dtGM(/•- 1)sin0
contributionsfrom a rangeof distances.This meansthat
light comingfrom downwind is being scatteredfrom
hydrogen
atomsthat passedtheSunat varioustimesin the
previousfew years,when solar conditionswere different
from
the current
conditions.
We
show
below
that
a
26,847
=• (p/sinO)2
Let x be thepositionat timet, givenan initial velocityv0
reasonablefirst approximationis to model the source along the upwind-downwind direction. Assumingthe
at t=0,then
functionfor eachdownwind volumeelementusingthe solar upwind-downwindplaneis crossed
conditions
duringtheyearwhen thehydrogenatomsin that
volumeelementmovingatthebulkvelocitypassed
theSun.
x=Vot
=-rcos0
=-pcos0
=Vot
sin0
The ionization,radiationpressure,and solar gravity all
havea 1/r2 dependence.
Theratioof theLyrnanccradiation so that
pressure
forceona hydrogen
atomto solargravityis called
I•. Definetheeffective
gravityforceFg=GMm(Iz-1)
/ r2 where
G isthegravitational
constant,
M isthemassof theSun,and
pdO
at -- •
vosin20
1.0
>, 0.8
ß
Thomos 1978 Toble 20 Density
0.6
-> 0.4
o
+
+
a: 0.2
0.0
-
•
,
,
,
I
,
,
,
,
,
,
,
2O
,
,
+
+,-!-•.,
-I-
i
ii
10
,
+
,
,
,
,
0
,
,
•
,
,
,
,
,
-10
Upwindto Downwind(Sun ot O) in AU
•
0.08
....
,
.........
!
.........
,
.........
I
.........
i
....
_
_
c
-
+
oo6 _
-
+ Thomos1978 Teble2o SourceFunction
o
c
._o 0.04
+
+
"0.02
_
o
0.00
_
....
+ ...................
20
'•.•+
10
0
+
+
t
+
-10
-20
Upwindto Downwind
(Sun ot O) in AU
FigureA1.Table2aof Thomas
[1978]presents
relative
hydrogen
densities
forthecaseof initialdensity
n=l cm'3,velocityv=20
kms-•, andtemperature
T=10,000
K, ionization
rateat 1 AU •=5.x10
'7s-1,and!.t=0.75.
(a)Therelativedensities
fromthattable
along the upwind-downwindaxis are shown. Upwind is on the left. (b) The relative sourcefunction (volume emissionrate) is
shownin arbitraryunits. Note the broaddownwindsourcefunction.
26,848
PRYOR ET AL.: LYMAN ctOBSERVATIONS FROM PIONEER VENUS
and finally
GM(I.t1)idOsin
0
vop
o
Thelastintegralnumerically
equals2. For atomstraveling
atthebulkvelocityV0 = 20 kms-1,a distance
of 4.2 AU is
traveledin 1 year,for example,
from2.1 AU upwindto 2.1
AU downwindin 1 year. Consideran atomwith impact
parameter
p=2.1AU. In that1-yearinterval,0 variesfrom
--45ø to--135ø, if the effectivegravity is small. The same
integralevaluatedfrom45ø to 135ø numericallyequals
1.414.
In this case, 1.414/2.0=71%
of the transverse
velocityis acquiredin theyearof closestapproachto the
Sun. For atomswith a few AU impactparameterthe
radiationpressureandeffectivegravityduringthe year of
closest
approachto theSuncontrolthetrajectory.
We alsoestimatethe relative importance
of ionizationat
differentdistances.This is importantfor evaluatingthe
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with the Galileo ultravioletspectrometer:
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rightimpactparameters
p for thepreceding
estimate:
if p is
G. R., SolarO I 1304-Atripletlineprofiles,
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toosmall,ionizationmayleaveno downwindslow neutral Gladstone,
97, 19519-19525, 1992.
component.
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presented
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[1978,Table2a) indicates
thatfor an
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Hall, D. T., D. E. Shemansky,
D. L. Judge,P. Gangopadhyay,
and M. A.
Fora 4-AU impactparameter,
thedensityat planecrossing Gruntman,Heliospherichydrogenbeyond15 AU: Evidencefor a
is 30% of the initial density. A few. AU seemsto be a
terminationshock,J. Geophys.Res.,98, 15185-15192,1993.
1975-1983,
in Solar Irradireasonableestimatefor theimpactparameterto usein the Harvey,J.W., Helium10830A irradiance:
ance Variationson Active Region Time Scales, edited by B. J.
precedingcalculationon transversevelocities. This
LaBonte,NASA Conf. Publ., 2310, 197-211, 1984.
discussion
suggests
thata 1-yearaverageof ionizationrates Harvey,J. W., andW. C. Livingston,Variabilityof thesolarHe I 10830
andradiationpressures
for theperiodcentered
on upwind- A triplet,inlnJ•aredSolarPhysics,
IAU Syrup.154,editedby D. M.
Rabin, J. T. Jefferies, and C. Lindsey,pp. 59-64, Kluwer Acad.,
downwindplanecrossing
is a usefulfirst approximation
to
Norwell, Mass., 1994.
usein evaluatingdownwinddensities
at differentphasesof
the solarcycle.
Hord,C. W., et al., Galileo ultravioletspectrometer
experiment,Space
Sci. Rev., 60, 503-530, 1992.
Isenberg,P. A., Interactionof the solarwindwith interstellar
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Isenberg,
P. A., A weakersolarwind termination
shock,Geophys.Res.
Acknowledgments.
Thisresearch
wassupported
by thePioneerVenus GuestInvestigatorProgram,the SpacePhysicsHeliosphericReLett., 24, 623-626, 1997.
searchProgram,thePioneerVenusProject,the GalileoProject,andthe
UpperAtmosphere
Research
SatelliteGuestInvestigator
Program.Fred King, J. H., InterplanetaryMedium Data Book, 77-04, GoddardSpace
LacyandWarrenAkersassisted
in the preparation
of the PV database Flight Cent.,Natl. SpaceSci. Data Cent.,Greenbelt,Md., 1977a.
usedhere. Alan Lazarus and the NSSDC suppliedthe necessarysolar King, J..H., InterplanetaryMediumData Book,77-04A, GoddardSpace
FlightCent.,Natl. SpaceSci.Data Cent.,Greenbelt,Md., 1977b.
wind fluxes. Gary Rottmanand Barry Knappprovidedthe SME solar
Lymanc•database,
whichincludes
thesolarF10.7cmfluxes. JackHar- King, J. H., InterplanetaryMedium Data Book,79-08, GoddardSpace
Flight Cent.,Natl. SpaceSci. Data Cent.,Greenbelt,Md., 1979.
vey'sNSO/KittPeakHe 1083nmdatausedhereare producedcooperativelyby NSF/NOAO,NASA/GSFC,and NOAA/SEL. We acknowl- King, J. H., InterplanetaryMedium Data Book, 83-01, GoddardSpace
FlightCent.,Natl. SpaceSci. Data Cent.,Greenbelt,Md., 1983.
edgeusefuldiscussions
with Tom Woods,Eric Quemerais,
Giulianade
Toma,RandyGladstone,
andBill McClintock.
The Editorthankstwo anonymous
refereesfor their assistance
in
evaluatingthis paper.
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acceptedJune2, 1998.)