JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. All, PAGES 26,833-26,849,NOVEMBER 1, 1998

Interplanetary Lyman observationsfrom Pioneer over a solar cycle from 1978 to 1992

WayneR. Pryor,1 Scott J. Lasica,1A. Ian F. Stewart,1Doyle T. Hall,1 SeanLineaweaver, l William B. Colwell,l JosephM. Ajello,2 OranR. White,3 and W. Kent Tobiska 4

Abstract. The PioneerVenus Orbiter ultravioletspectrometer (PVOUVS) routinelyobtained inter- planetaryhydrogen Lyman ot datawhile viewingecliptic latitudes near 30øS from 1978 to 1992 (dur- ing solarcycles 21 and 22). We describe"hot" models for this interplanetaryLyman otdata that include the solarcycle variation of (1) the solarflux, as a functionof latitudeand longitude;(2) the radiation pressureon hydrogenatoms; (3) the solarwind flux; (4) the solarEUV flux; and (5) the multiplescatter- ing correctionto an opticallythin radiativetransfer model. Thesemodels make use of solarradiation flux parameters(, solarEUV, and solarLyman or) from spacecraftand ground-basedsolar proxy observations.Comparison of the upwinddata and model indicates that the ratio of the solarLy- man ot line centerflux (responsiblefor the interplanetarysignal) to the observedsolar Lyman ot inte- gratedflux is constantto within-•20%, with an effectiveline width near 1.1 A. Averagingthe solar ra- diationpressure and hydrogenatom lifetime over 1 year beforethe observationreproduces the upwind intensitytime variationbut not the downwind. A betterfit to the downwindtime seriesis foundusing the 1 year averageappropriate for the time that the atomspassed closest to the sun. SolarLyman ot measurementsfrom two satellitesare usedin our models. Upper AtmosphereResearch Satellite (UARS) solarLyman ot measurementsare systematicallyhigher than SolarMesosphere Explorer (SME) values andhave a largersolar maximum to solarminimum ratio. UARS-basedmodels work better than SME- basedmodels in fitting the PVOUVS downwindtime seriesLyman ct data.

1. Introduction drogenatoms are also ionized by solar EUV radiation. Solar The interplanetaryLyman otglow comesfrom solarLyman ot Lyman ot resonancescattering from the surviving slow hydro- that hasbeen scattered by hydrogenatoms in the very local in- gen atoms createsthe observedglow. terstellarmedium. At a distance of perhaps30 AU upwind Modeling the interplanetary Lyman ot brightness pattern from the Sun, well inside the solar wind termination shock, requiresdetailed understanding of the processeslisted above. thesehydrogen atoms are currentlydescribed by a temperature The 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- cm-3[Ajello et al., 1994]. A recenttabulation of the rather esses and their variations, since the data were obtained over wide range of hydrogendensity values in the literature is more than a full solar cycle (December29, 1978, to April 18, givenby Puyoo,et al. [1997]. Their work finds a neutralden- 1992) at a nearly constantdistance of 0.72 AU fromthe Sun. sity at largedistances of n=0.25+0.08cm-3. Solargravity acts Other ( and Voyagers 1 and 2) have ob- to focus the hydrogen atoms as they pass the Sun, but is tained a long time series of interplanetaryLyman ct observa- largelycanceled by solar Lyman ot radiationpressure that re- tions, but thesedata sample a range of distancesfrom the Sun, pelsthe atoms. The ratioof the radiationpressure to the solar complicatingthe interpretation becauseof the possible pres- gravity is called g. Solar cycle variationsin g can makethe ence of outer heliosphericeffects [e.g., Hall, 1992; Hall et al., Sun eitherrepel the atomsor slightly focusthem downstream. 1993; Quemerais et al., 1995, 1996]. Successfulmodeling of Fastmoving solar wind protonscharge exchange with the thePVOUVS inner heliosphere data set is a firststep toward slowerinterstellar neutral hydrogen atoms, creating a popula- understanding theouter heliospheric data. tion of fastmoving hydrogen atoms DoI3pler-shifted outside The modeling described here builds on our earlier efforts. the solarLyman ot line and leaving behind a cavity depleted Ajello et al. [1987] examined the PVOUVS interplanetary Ly- in the slow neutralsthat scatter solar 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 Atmosphericand SpacePhysics, University of 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/NationalCenter for Astmospheric ecliptic latitudes during observations of Comet Halley. Im- Research, Boulder, Colorado. provementsin the model reflect subsequentefforts at modeling 4FederalData Corporation/JetPropulsion Laboratory, Pasadena, and Voyager data describedelsewhere [Pryor et al., California. 1992, 1996; Hall, 1992; Ajello et al., 1993, 1994]. This paper applies our latest models to the full PVOUVS data set. These Copyright1998 by the AmericanGeophysical Union. modelsexplicitly computethe solar Lyman otflux at each lati- Papernumber 98JA01918. tude and longitudeas a functionof time by using He 1083 nm 0148-0227/98/98JA-01918509.00 imagesas a proxy for solarLyman ot [Pryor et al., 1996].

26,833 26,834 PRYOR ET AL.: LYMAN ct OBSERVATIONS FROM PIONEER VENUS

2. Instrumentation hydrogencorona was necessary. We examinedthe brightness of the coronaas a functionof the closestapproach distance d of The PVOUVS instrument [Stewart, 1980] was a compact the look vectorto the centerof the planet[Lasica et al., 1993]. 1/8-m Ebert-Fastiespectrometer with a programmablegrating 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 Venus Orbiter 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 coronalcontamination was largestnear solar maximum and 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 slanted 60ø away Venus coronaand its variation over a solar cycle are discussed fromthe spin axis. Thus the instrumentfield of view (1.4ø x by Colwell [1997]. A time-dependentinstrumental back- 0.14ø) observeda smallcircular strip on the celestial sphere, ground of 7-12 R due to cosmicrays was subtractedfrom the with a 1.4ø width, at an ecliptic latitude 30+_5øS. The data. This background was largest near solar minimum and PVOUVS instrumentsensitivity at 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,dif- indicate that the Lyman (z sensitivity was nearly constant ferent fixed grating positionswere used to observethe Lyman over the course of the mission. (z line during different parts of the mission. The reported in- tensities were correctedto reflectthe part of the instrumental 3. Observations line profile being observed. No overall systematicoffsets be- tween data and model were identified that could be conclu- The PioneerVenus Orbiter maintaineda polar orbit around sively attributed to the use of these different grating 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 incompletelycorrecting for 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 in- strumentoperated in fixed gratingposition mode, typically us- ing a 32-ms integration. This integration period leads to a 5. Modeling spinsmearing of about0.9 ø . In orbits wheretwo setsof 240 ø Plate 1 includes a color display of the PVOUVS data se- arcswere taken, the data were combinedfor a full 360ø cover- lectedfor modeling,with time on the horizontalaxis and eclip- age in longitude. Figure 1 illustratesthe spacecraftorbit and tic longitude on the vertical axis. The data are brightest in the PVOUVS observinggeometry. upwind longitudes near ecliptic longitude 250ø and dimmest near the downwind direction, where slow neutrals have been 4. Data Reduction depleted by charge exchangeand photoionization. Data be- camesparser as the missionprogressed due to reducedground BecausePV obtainedinterplanetary Lyman c• data nearVe- station coverage. The brightest data are at the two ends of nus, carefulexclusion of the Lyman c• signatureof the Venus 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 = SUBSOLARPOINT AT VOl SPACECRAFT SPIN AXIS

Figure 1. Illustration of the Pioneer Venus Orbiter polar 24-hour orbit. The PVOUVS observedin longitude circles at -30 ø ecliptic latitude. InterplanetaryLyman (z data usedhere were obtainedwhere the distancefrom the instrumentlook vector to the planetcenter exceeded 5 Venus radii. Times from periapsisare indicated.VOI standsfor Venus Orbit Insertion. PRYOR ET AL.: LYMAN o(OBSERVATIONS FROM PIONEER VENUS 26,835

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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 chargeexchanging with the slow interstellar neutral hydrogen population, creating fast neutrals which are Doppler- shifted off the solar Lyman • line and are thereforeinvisible. The contour lines schematicallyillustrate the variations in the Lyman a volumeemission rate. It hasa local minimumcentered on the Sun, and a local maximum(the maximumemission region) upwind of the Sun, abouthalfway betweenthe Sun and the upwind cavity boundary. Waves visible in Plates 1 and 2 related to the motionof Venus(and the PV Orbiter) about the Sun are due to distancevariations betweenthe look vector in the upwind direction and the maximumemission region. The PVOUVS views in longitude circles near-30 ø ecliptic latitude. These instrumentlook directionsapproach the maximumemission region more closelywhen the spacecraftis upwind. taken from 1983 to 1987 are the least bright, correspondingto Throughoutthis paper, the PVOUVS values are scaledto the solar minimum. Galileo-basedmodel values. The scalingfactors are near 2 but The best fit 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 op- lb and 2b), and somewhatless apparent in the data, is a modu- posedto earlier modelsthat found n=0.07+0.01 cm-3[Ajello et lation or waviness in the upwind intensity associatedwith al., 1987], somewhat increasing the importance of multiple the 225-day orbital period of Venus. When the spacecraftis scattering. on the upwind side of the Sun (times marked with "U" in We prefer to use the more recent Galileo calibration for the Plates l a and 2a), it is closerto the upwind maximumemission following reasons. Becauseof launch delays, there was ade- region, increasing its angular extent (Figure 2). A parallax quatetime for extensivecharacterization and calibration of the shift in the direction to the maximumemission region due to Galileo UVS. The Galileo UVS laboratory absolute calibra- the orbital motion of Venus makesthese waves appeardiago- tion at wavelengthsgreater than 1300 A, basedon National nal in Figure2. The brightnessmaximum on eachwave tends Institute of Standardsand Technology (NIST) standard pho- to passthrough the upwind directionwhen the spacecraftis todiodes, is estimated to be accurate to better than 20%. We directlyupwind. In Plate 2 a diagonal variation is also visi- also obtained Galileo UVS laboratory spectraof electron im- ble correlatedwith the -25-day sidereal rotation period (28 pact on H2 and N2 that providea high-quality relative calibra- days as seenfrom Venus) of Lyman ct bright solar active re- tion in the FUV, includingLyman {x [Ajello et al., 1988; Hord gions. A detailed study of one such wave was presentedby et al., 1992]. The estimatedadditional uncertainty at Lyman {x Ajello et al. [1987]. with this technique is-20%. Comparisonof Galileo UVS The model developedfor fitting Galileo extremeultraviolet spectraof the star Sirius with rocket observations shows ex- spectrometerdata [Pryor et al., 1996] was used here. This cellentagreement (<20%) at wavelengthsgreater than 1300 A model is a versionof a "hot" density model describedby Tho- where sufficientstellar signal is present(W. McClintock, pri- mas [1978]. The model has evolved to include latitudinal vate communication,1998]. Based on these considerations, anisotropiesin the solar wind flux [Witt et al., 1979], as well the density derived from Galileo Lyman {x measurements,in- as latitudinal and longitudinal anisotropiesin the solar Ly- cludingestimated error bars from the calibrationonly, is -0.17 man{x flux [Pryor et al., 1992, 1996]. One troubling, persis- -I-0.05 cm'3 . tent problemfound in our modelingefforts is the differencein The density used here should also be comparedto neutral absolutecalibrations at Lyman {x betweendifferent spacecraft. hydrogendensity estimatesfrom pickup ion studies. Gloeck- PVOUVS 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 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. The relative calibration as a func- have overlappingerror bars. Another technique,measurement tion of time of SOLSTICE is closely monitoredby l:neasure- of the solar wind slowdown due to massloading, has been mentsof a suite of stars. The UARS Lyman ct fluxesare sys- studied by Richardson et al. [1995]. From a measuredsolar tematically higher than the SME measurements,by •-30% or wind slowdownof •-30 km s-• between 1 and 40 AU, they es- more,and have a larger solar maximumto solar minimumratio timatea low neutralhydrogen density of 0.05crn -3, based on [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 fluxes for the SME model. As we have previously slowdownof•-30 km s '• at 40 AU correspondsto a neutral suggested [Pryor et al., 1992; Ajello et al., 1994], the com- hydrogendensity of 0.1 cm-3, closer to the Gloeckleret al. re- puted polar Lyman ct flux is substantially (---20%)below the sults. Recentwork by Isenberg [1997] shows that a neutral equatorialflux at solar maxima.Figure 3b comparesthe SME- hydrogendensity of 0.125cm -3 near the termination shock is basedand UARS-basedecliptic Lyman ct fluxes. consistentwith an analysis of anomalouscosmic ray spectra A key assumptionin the modeling is that the unmeasured by Stoneet al. [1996]. Lymanct line centerflux (photonscm-2 s-1 fl,-i) responsiblefor The solar cycle variationsof five quantities are included in resonancescattering from interstellarneutral hydrogenequals the model as follows: about0.9 A-1 timesthe SME- or UARS-derivedintegrated so- lar Lyman ct flux (photonscm-2 s-i) throughoutthe solar cycle. 5.1. Solar Flux Variation Ajello et al. [1987] used PVOUVS data to show that this ratio is fairly constant over the solar cycle. The rough validity of Our model uses solar He 1083-nm imagesto computethe this assumptionis tested here by trying models that assume 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 ob- from recentmeasurements of the disc-integratedsolar Lyman ct tained at Kitt Peak provides a valuable indicator of the Sun's line shapeobtained at solar minimumby the Solar Ultraviolet Lyman ct distribution. The disc-averagedequivalent width is Measurementsof Emitted Radiation (SUMER) instrument on 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 factor of 1.0.A '•. SUMERresults provide the equivalent width as a function of latitude and from closerto solarmaximum may shedlight on this problemin longitudefor each solarrotation. TheseCarrington maps form the future. the basis for our calculation. First, holes and artifacts in these imageswere correctedby using informationfrom neighboring Carrington rotations. This proceduremay introduce someer- 5.2. Solar Radiation Pressure Variation rors in the record,particularly in the late 1970s when more Estimatesof the radiationparameter g alsorely on assuming data gapswere present. Next, an integralwas performedwhich the numericalcorrespondence between line center and inte- finds the disc-averagedequivalent width that would be seen gratedsolar Lyman ct emissions.The radiation pressurehas a above any solar latitude and longitude on any given day. latitude dependencedirectly causedby the latitude depend- This procedure reproducesin considerabledetail the previ- enceof the solar flux [Ajello et al., 1994]. Atoms that pass ously reporteddisc-integrated equivalent widths in the eclip- over the solar poles are exposedto a lower averageradiation tic plane. It was then assumedthat the same linear relation- pressurethan those that pass over more equatorial latitudes. ship that exists between the ecliptic plane disc-averaged This effectis crudely representedby averagingthe 12-month equivalent width of He 1083-nm and disc-integrated, line- averageecliptic value of g, with the lower polar value. The integrated Lyman ct flux [Tobiska, 1991] exists at all other time averageis used to compensatefor the varying pressures latitudes. Two different relationshipswere usedhere. The lin- experiencedby a hydrogenatom as it approachesand then re- ear relationship between the He 1083-nm equivalent width cedesfrom the Sun. During a 1-yearperiod a hydrogenatom (EW) and the Solar Mesosphere Explorer (SME) line- integratedsolar Lyman & measurementsis [Tobiska, 1991] travels4.2 AU at a velocityof 20 km s-•. This is roughly com- parableto the scale size of the system:the maximumemission regionis at distancesrc/2 from 2.25 to 3.35AU fromthe Sun, Lymanc•SME = 8.40x101ø+ 3.78x109xEW dependingon the hydrogenatom lifetime [Ajello et al., 1987]. Herer c isthe distance along the upwind axis from the Sun to in units of photons cm-2s-1 at 1 AU fromthe Sun. Measured the point where ionizationhas attenuatedthe original density valuesof EW rangefrom 39 to 97. The linear relationship be- by a factor of 1/e. tween the He 1083 nm equivalent width and the Upper At- Both the ecliptic value and polar values of g are estimated mosphereResearch Satellite (UARS) solarLyman ct time series fromthe He 1083-nm solar images. The solar flux information in the sameunits (throughthe end of 1995) is in Figures3a and 3b is usedto computethe equatorialand po- lar 1-year-averageratio of radiationpressure to solargravity. LymanctUARS=0.95x(2.10x 101ø+7.07x 109xEW). The computedpolar 1-year-averageradiation pressure is lower 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 equato- Experiment(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- bothshown for caseswith the line centerflux equalto 0.9 tral IrradianceMonitor (SUSIM)) reportsLyman ct values 10% and1.0 A-• timesthe line-integratedflux. Theradiation pres- lower than SOLSTICE. The UARS instrumentswere probably sureparameter g for the SME-basedLyman ct fluxesis gener- PRYORET AL.: LYMAN c•OBSERVATIONS FROM PIONEERVENUS 26,839

11 5.0x10

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o 11 ...... South .o 2.5x10 i North

11 Ecliptic 2.0x10 1980 1985 1990 199,5 Year

Figure3a. Thedaily SME-based solar Lyman (x line-integrated flux for the eclipticplane and for the two solarpoles for the PV period.Values are taken from the He 1083-nmcalculation using the proxy model described in thetext. Modelsin this paperuse the line centerflux, assumedto be 0.9 timesthe valuesshown.

7.0xlO11 l: ' I .... I .... I .... I '

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i c 11 o 3,0xt0 E

11 • 2.0x10

11 1.0x10 _- UARS-bosed - _ - _ : SME-bosed :

_

_

1980 1985 199o 1995 Year

Figure3b. TheSME- and UARS-based solar Lyman (x line-integratedecliptic flux computed t•om the He 1083-nmcalculation. Modelsin thispaper use the line centerflux, assumedto be 0.9 timesthe values shown. 26,840 PRYOR ET AL.: LYMAN •xOBSERVATIONS FROM PIONEER VENUS

o 0.5 ...... UARS-based

I ... SME-based

1980 1985 1990 1995 Year Figure3c. Assuminga one-to-onecorrespondence between the numericalvalues of line-integratedLyman (x solar flux (photons cm-2 s -]) andline center Lyman (x solar flux (photons cm-2 s'• A']) leadsto 1-yearaverage (before the indicated date) radiation pressureparameter p valuesfor SME andUARS fluxes. The averageof the northand south polar p valueshas been averagedwith the eclipticp valueto estimatethe "average"radiation pressure (solid lines). Modelsin this paperuse radiation pressurevalues (dashedlines) equalto 0.9 timesthe solid lines. The horizontalline at p=l separatesp valuesthat lead to a net solarattraction of hydrogenatoms by the sun (p 1).

ally less than 1, so the net effectin passing the Sun is focus- Our initial model approximatesthe varying solar wind ing. However, the UARS-based Lyman c• fluxes imply la gen- fluxesencountered by the interstellarneutrals by averaging erally >1, so the net effect is repulsion. the solarwind flux overthe 12 monthsbefore a given observa- tion. This is the sametimescale used for the radiation pressure 5.3. Solar Wind Flux Variation calculation, for the samereasons discussed above. Figure 4 shows the monthly averagehydrogen lifetime against solar Chargeexchange between slow (20 km s-l)interstellar hy- wind chargeexchange at 1 AU and the 12-month-averagelife- drogenatoms and faster (---300-700km s-l) solar wind protons time. The averagevalues range from -1.2 to 1.9xl 06 s. The ac- createsa cavity near the Sun depletedin slow neutralsthat can tual lifetime will be somewhatshorter due to solar EUV pho- scatterthe solar Lyman c• line. The rate of this processin the toionization of hydrogen. ecliptic is estimated l•om the National Space Science Data Center (NSSDC) on-line databaseof solar wind proton den- 5.4. Solar EUV Flux Variation sity and velocity measurementsat 1 AU. These measurements madeby the near-Earthspacecraft ISEE 1, ISEE 3, IMP 7, and A secondaryloss processfor ground state (ls) interstellar IMP 8 are documentedby King [1977a, b, 1979, 1983]. Most hydrogen is photoionization by photons with wavelengths of the data used here comel•om the IMP 8 spacecraft.Hydro- less than 91.2 nm. The solar EUV flux variation over a solar gen atom-protoncharge exchange cross sectionsare fi'omBar- cycle is not particularly well known. Ogawa et al., [1995] nett et al. [1990]. The rate of the charge exchangeprocess at evaluatedthe total photoionization rate [•, including a very other ecliptic latitudesis not well known; finding this rate is minor componentl•om loss of metastable(2s) hydrogen. Us- one goal of our modeling efforts. If x(0) is defined to be the ing Ogawa et al. 's, Table 3, we representthe total photoioni- time-averagedlifetime against solar wind charge exchangein zationrate at 1 AU, [•, in s-• as the ecliptic (ecliptic latitude 0 degrees),then the lifetime at eclipticlatitude [• is assumedto be of the form [•=1.50x10-7+ (2.42x10'7-1.50x10 -7) •(1•)=•(0)/[1. - ,t sin2(13)l 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 solar wind asymmetryparameter. 10-22 W m-2Hz-]. The photoionizationlifetime • is the recip- PRYOR ET AL.: LYMAN ct OBSERVATIONS FROM PIONEER VENUS 26,841

5.5x106 ' ' t .... I .... • .... I ' monthly average H lifetime against charge exchange ...... 12-month average H lifetime against charge exchange 5.0x106 - -- 12-month average H lifetime

'•' 2.5xl 06 • 2.0x106

:• 1.5x106

1.0x106

5.0x105

0 , , I , , , , I , , , 1980 1985 1990 1995 Yeor

Figure4. Thevariation in themonthly average hydrogen atom lifetime against solar wind chargeexchange. Also shownis the 12-monthaverage of the monthlyaverage lifetime before a giventime, for chargeexchange only; and for chargeexchange combinedwith photoionization.Values of solarwind densityand velocity are taken fi'om the National SpaceScience Data Center (NSSDC) database. rocalof[3. A valueofF10.7=62.7 is a very low solarminimum diationpressure and two values of the hydrogenatom lifetime value, while F10.7=214.0 is more typical of solar maximum at 1 AU. Linear interpolation betweenthese six caseswas conditions. For a solar minimum value of F!0.7-62.7, madeto derivethe multiple scatteringcorrections appropriate •=l.50x10-7 s-1 and x=6.67x106 s. For a solarmaximum value for a givenday. Thesecorrections were computedfor a space- of 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 photoionizationlifetime x is substantiallylonger outside the cavity but well inside the heliopause,of n=0.17 thanthe hydrogenatom lifetimeagainst solar wind chargeex- cm-3,v=20.0 km s-l, and T=8000K. Thedependence on dis- change. One-yearaverages of the photoionizationlifetime tance fi'omthe sun and on spacecraftecliptic longitude is as- were usedin the modelshere. Combiningthe photoionization sumedto be minor. The correctionsto an optically thin model lifetimeand the solar wind chargeexchange lifetime yields a brightness/thin are represented as surprisinglyconstant lifetime for slow neutralhydrogen (Fig- ure 4). Photoionizationis largestnear solar maximumwhen I(0)--/thin(0)q(0) the chargeexchange rate is smallest. The ecliptic lifetime found from solar wind and solar EUV flux measurements in Theangle fi'om the upwinddirection •is denoted 0. For 0=0, Figure4 is generallynear -t.2xtO 6 s. Thiscompares favorably upwind,the correctionsare negligible (<2%), while dow n' with the lifetime of 1.1x106sec derived fromparallax shifts of stream,0=180, theybecome important. The monotonicallyin- themaximum emission region in PioneerVenus interplanetary creasingfunction q(0), where0 is in degrees,can be well rep- data [Ajello et al., 1987]. resentedas a polynomial: 5.5. Multiple Scattering Correction q(O)=ao+a• 0+a 2 02+a 303 Next, the time dependenceof the multiple scatteringcorrec- tion was includedin our optically thin model. (Currentcom- Table 1 showsthe six casesused. This multiple scatteringcor- putationallimits favora hybrid approachbetween fast opti- rection scheme was used for all models shown. A similar cal- cally thin modelsand slow multiple scatteringcodes.) The culationfor n-0.10 cm-3 gave similar results (within 3%), in- multiplescattering model used [Hall, 1992; Ajello et al., dicatingthat the correctionfactors are not a strong function of 1994] assumescylindrical symmetry;no attemptis madeto densitybetween 0.10 and 0.17 cm'3. An independentcalcula- deal with latitudinal variations in the solar wind flux or the tion by Quemerais and Bertaux [1993, Table 3] found that q solarLyman c• flux. Multiple scatteringcorrections were com- increases from 1.09 to 1.23 to 1.30 to 1.34 to 1.36 in the putedfor six cases,involving threerealistic values of the ra- downwind multiple scatteringcorrection when the density 26,842 PRYOR ET AL.: LYMAN {xOBSERVATIONS FROM PIONEER VENUS

Table1. MultipleScattering Corrections % s !.t a0 a1 a2 a3 q(180) 1.4x106 0.75 0.99129 -2.1501x10-4 6.0459x10-6 2.6745x10-8 1.301 !.4x10• 1.10 0.98381 8.1145x10-5 -2.6860x10-• 9.5069x10-8 1.462 1.4x10• !.60 0.97097 6.0193x10-4 -1.873 lx10-5 2.1399x10-7 1.716 2.1x10• 0.75 !.0005 -3.1373x10-4 7.8907x10-6 -4.1819x10-!0 !.195 2.1x10• 1.10 0.99048 1.7690x10-5 -8.1105x10-7 7.06844xl 0-8 1.377 2.1x10• 1.60 0.97638 4.8491x10-4 -1.7107x10-5 1.9652x10-7 1.651 (n=0.17 cm-3)

increasesfrom 0.01 to 0.05 to 0.1 to 0.15 to 0.20 cm'3, for an genatom lifetime at 1 AU of 1.4x106 Sis fairly realistic; chang- observer1 AU fromthe Sun and 90ø fromthe upwind axis. ing to a 50% longerand less realisticlifetime of2.1xl06 s has Theirresults support the ideathat the multiplescattering cor- only a modesteffect on the correction. An extensive discus- rectionis not too sensitiveto densityvariations in the range sion of these radiativetransfer effects is presentedby 0.1-0.2 cm-3. Querneraisand Bertaux [ 1993]. Increasingradiation pressuredepletes the downwind den- sity, leadingto a very anisotropicdensity distribution. Mul- 6. Modeling Results tiple scatteringproduces a brightnessdistribution that is less anisotropicthan would be obtainedin a single-scattering An initialattempt was made to fit thetime series of the up- model. The derived multiple scatteringcorrections are a wind and downwinddata sets with an SME-basedmodel, strongfunction of the assumedradiation pressure. A hydro- wherethe radiationpressure, hydrogen atom lifetime, and mul-

i .... i , 700 ' ' .... OARSi UARS 'b)I-- SME Period iBegin_ i 1 500 o) t-- SMEPeriod --I Begin 600 500 • : 1000 400 300

5OO A=0.60 200 A=0.60 . RMS Fit = 9.79% Doto = . RMS Fit = 18.1% Dote = ß Foctor = 1.63 Model =-- 100 Foctor = 1.53 Model =-- SME-bosed Initiol Model , i , i i , i , , , , i , • 0 SME-bosedi i Inltio, I Model i • , , I , , , 1980 1985 1990 1980 1985 1990 Yeor Yeor

2.0 ...... 0A"S' c) SME Period Begin

. d) [--SME Period • + Begin: + + 1.5 + + + + ++ + +$ -½' + + o +** + • •,t+.%, * + 1.0 C3o10 ß +

+ 0.5 + A=0.60 0.5 -A=0.60 SME-bosed Initiol Model SME-bosed Initial Model

, I I 0.0 , i 0.0 • I I I 1980 1985 1990 1980 1985 1990 Yeor Yeor Figure5. Initialmodel fits to the time series PVOUVS interplanetary Lyman t• data.The data have been scaled upward to fit the modelderived for Galileodata of Pryor et al., [1996]. This scalingreflects calibration differences between instruments. This initialmodel uses solar radiation pressure, solar wind ionization, and photoionization values averaged over the 1 yearprior to theobservation. A solar wind asymmetry parameter of,4=0.6 was used. (a) Fit to the upwind data. Data represent the average of three10 ø binscentered on the upwind direction. Model points have been computed for each day and connected with a linefor clarity;data are shown as dots, the actual locations ofpoints can be more easily seen in Figures5c and5d. (b) Fit to the downwinddata with the samemodel. Data represent the averageof six 10ø binscentered on the downwinddirection. This modelfits the downwind time series poorly. (c) The time series of data divided by model in theupwind direction. (d) The time seriesof data dividedby model in the downwinddirection. PRYOR ET AL.' LYMAN ct OBSERVATIONS FROM PIONEER VENUS 26,843 tiple scatteringcorrection are all representedas a 1-yearaver- Physically, the light observed downwind is coming fi'om agebefore the time of the observation.The upwind and down- hydrogen atoms which passedthe sun in earlier years (see wind time series data with the Pioneer Venus calibration are Appendix A for morejustification). This travel time effectsug- independently scaled to the Galileo-based model. For suc- geststhat the 1-year-averagingscheme is not adequatefor de- cessfulmodels the two scaling factorsshould be similar and scribing the downwind hydrogen. Hydrogen atoms down- near 2 in order to match the cross-calibration results obtained wind at solarminimum may have passedthe Sun at solar maxi- when 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. Up- bins 10ø wide in ecliptic longitude centeredon the upwind wind volume emission rates are computedusing the radiation directionwere modeledseparately and then combinedto form pressureand hydrogen atom lifetimes averaged over 1 year the upwind set. Six of the dimmer10 ø bins centeredaround before the observation. For downwind volume elements the downwindwere combinedto provide countingstatistics simi- 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 ele- the star Iota Orionis was excluded. Each data point in this set ment crossa plane 6 monthsdownwind of the Sun, assuminga contains at least 85 counts, while most contain several hun- bulkhydrogen velocity of 20 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 1- the data are higher than the modelnear the two solar maxima year-averageecliptic data were used beginning in January and lower than the model near the solar minimum. 1975. Radiation pressure1-year-average data derived fi'omHe

I I | WARSt • 700 'b)[-- SME 'Period -- ' O^RS•Beglni _c 1 500 o) [-- SMEPeriod --{ Begin-[ • 600 • 500 o 1 000 n- 400 -o 500

5OO A=0.60 • 200 A=0.60 ß RMS Fit = 9.84% Data = ß RMS Fit = 13.2% Data = . Factor = 1.64 Model =-- o 100 Factor = 1.69 Model =-- SME,-b,os,ed ' Lo, gc•ed, Mgd ,el .... ca 0 S,ME,-b,os,ed, Lo, gg,ed, M,od,el , , .... 1980 1985 1990 1980 1985 1990 Yeor Yeor

2.0 2.0 ' i i I WARS WARS

Begin d) t-- SME+ Period Begin . ß

++ 1.5 + 1.5 • + + + -•.+ + o

+ + + -• + o10 + E3 ß + + ++ +

C + + c 0.5 A=0.60 . '• 0 I5 ßA=0.60 . • SME-bosedLogged Model c- SME-bosedLogged Model m 0.0 , , ...... o 0.0 ...... , .... , , , , 1980 1985 1990 1980 1985 1990 Year Year

Figure6. The fit of the bestSME-based lagged model (used in Plates 1 and 2 and Figures 6 and 7) to the time seriesPVOUVS interplanetaryLyman rt data. This model computesdownwind densities using solar radiation pressure and solar wind ionization and photoionization values averagedover the year when the downwind hydrogenatoms had crossedthe upwind- downwindplane, assuming a bulk downwind flow of 20 kms 4. Upwinddensities are computed for radiation 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 asymmetryparameter of A=0.6 was used. (a) Fit to theupwind data. Data(points) represent the average of three10 ø binscentered on the 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 model in the upwinddirection. (d) The time seriesof datadivided by modelin the downwinddirection. 26,844 PRYORET AL.: LYMAN ctOBSERVATIONS FROM PIONEER VENUS

1 ooo i i i i i J i 1 :24 Feb 1980 (Orbit 446) RMS Fit=7.13% • R=0.720 AU - • ,•,r47½•_ Factor= 1.53 -• X=0.082 AU 8OO - _ • • •'•.•..•'•T A=0.60 --• -I - •tt/t•'•.<-: ...... "*-.• A=0 25 q Y=0.71 5 AU Z=0.005 AU 600 ',.% x=o:oo...... S/C Angle=85.4ø -5 400 n-O. 1 7 cm T=8000 K v-20.O km s-' 200 - • SME-bosedLogged Model .... -• O! ;• Datawith 1cr Error Bars • 560 515 270 225 180 155 90 45 0 Ecliptic Longitude

000 • ...... •10 Jan 1985(Orbit 2227) RMSFit=6.55% R=0.722 AU •- Factor= 1.95 -1 X=0.586 AU 8OO •- • •;:• A=0.60 --- -1 I- z•,•"--• • A=0.25 - -- -- Y=0.610 AU 600 - Z=-0.01 AU S/C Angle=57.6ø -5 400 ../'/•. ::.•. 7...-....--.•t..:.... '-•...••,.A=O.O0 ...... n=0.1 7 cm T=8000 K 200 •- -- SME-bosedLogged Model'""-'--'-...--..".-.•."::'":" v=20.0 km s-' 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 interplanetaryLyman czdata from two "typical"days. Scalingfactors have been applied to the data to bring them into 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), duringsolar maximum. (b) For January10, 1985 (orbit 2227), duringsolar minimum.

1083 nm imageswas used beginining in July 1977. The val- the SME fluxes, and have a larger solar maximumto solar mini- ues for January1975 and July 1977 were used for the solar mumbrightness ratio. Woods and Rottrnan [1997] suggest wind and radiation pressuredata, respectively,when examin- scalingthe UARS SOLSTICE fluxes by 0.95 to reflectthe av- ing volume elementswhere the atomshad passedthe Sun be- erage of the UARS SOLSTICE and UARS SUSIM Lyman cz fore thosetwo dates. As our PV data span 1979-1992, this is measurements.This is done here for both the model solar Ly- not a majorhandicap in the modeling,except possibly in the man czflux andthe model radiation pressure. This model han- first year or two. Figures6a-6d showthe resultsof this SME- dlesthe time dependencein the sameway as in Figure 6. Fig- basedlagged model. The quality of the downwind fit to the ures 8a-8d show the UARS-based fit to the time series, in this data is now much closerto the quality of the upwind fit, sug- casefor A=0.75. The model brightnessesare not very different gestingthat this crudetime-dependent model has capturedthe •om before because increasing the radiation pressure has essenceof the effect. This lagged model also fits the upwind- largely compensatedfor the increasingsolar flux. The down- downwind variation observed on individual daily data sets. wind time seriesdata are now betterfit by the model. The large This is illustratedin Figure 7 for two "typical"days, one near radiation pressureassociated with the UARS fluxes depletes solarmaximum and one near solar minimum. Figure 7 also il- the downwind hydrogenmore than in an SME-basedmodel. lustratesthe effect of the solar wind asymmetryparameter A on For a UARS-based model with A=0.5 the scaling factors up- the upwind to downwindratio. Increasing`4 reducesthis ra- wind and downwindare ---20%different, with an upwind scal- tio, althoughwe shouldagain point out that manyfactors in- ing factorto applyto the dataof 1.99 and a downwindfactor of fluencethe upwindto downwind ratio and that the PVOUVS 1.65. Using A=0.75 provides somewhat better agreement data are not ideal for determiningA. (within ---10%) in scaling factors:upwind is 2.03 and down- Finally, we show a lagged model based on the UARS wind is 1.82. This asymmetryparameter corresponds to a polar SOLSTICE solar fluxes,which are systematicallyhigher than hydrogenatom lifetime 4 times longer than the equatorial one. PRYORET AL.:LYMAN c• OBSERVATIONS FROM PIONEER VENUS 26,845

[ [ , 700 ' UARS:: UARS• ' [ 'b') [-- SME'Period --• IBeglni o) t-- SMEPeriod --t Begin- • 600 ß . - 500 .. . i . •, 500 ß ! ß ß : ooo rY 400 -o 3oo

. • 200 500 A=0.75 A=0.75 ' :' RMS Fit = 9.68% Data = ß RMS Fit = 10.9% Data = . Factor = 2.0.:3 Model =- o 100 Factor = 1.82 Model =-- 0 U,AR,S-,bo,se,dL,og,ge,d Mo,del, , , , , m 0 U,AR,S-,bo?•,dL,og,g•,d ¾od,•,, , , , , 1980 1985 1990 1980 1985 1990 Year Year

, , 2.0 ' ' ' OARS UARS- c) SMEPeriod Begin d) [-- +SMEPeriod Begin] . . 1.5 • + +

1.0 ,•-+ + + g + +

0.5 A=0.75 UARS-bosed Lagged Model

0.0 , i , , , i I , , • o 0.0 1980 1985 1990 Yeor Figure8. Thefit of a UARS-basedlagged model (solid line) to thetime series PVOUVS interplanetary Lyman c• data. This modelcomputes downwind densities using solar radiation pressure and solarwind ionizationand photoionizationvalues averagedover the yearwhen the downwindhydrogen atoms had crossedthe upwind-downwindplane, assuming a bulk downwindflow of 20km s '•. Upwinddensities are computed forradiation pressure and ionization values averaged over one year beforethe observation. Scaling factors have been applied to thedata to bringthem into agreement with the model.A solarwind asymmetryparameter ofA=0.75 has been used. (a) Fit tothe upwind data. Data(points) represent the averageof three10 ø bins centeredon the upwind direction. (b) Fit to thedownwind data with the same model. Data (points) represent the averageof six 10ø bins centeredon the downwind direction. This model fits both time seriesbut does not simultaneouslyfit upwind and downwindwith the same scale factor. (c) Thetime series of datadivided by modelin theupwind direction. (d) Thetime series of data dividedby modelin the downwinddirection.

It is not entirelyclear that we are solvingfor the physical that damprapidly with heliocentricdistance. Outer helio- quantityA in this dataset because the look directionis al- sphericmodels of the downwindhydrogen (Pioneer 10 data) waysat -30ø . will needto incorporatethis effect in thefuture. A major assumptionin the modelingeffort wasthat the disc- integratedsolar line centerLyman c• flux, whichis r•sponsible 7. Discussion forthe resonance scattering (andradiation pressure) effects, A key resultin thisstudy is that the downwindbrightness has a constant line centerto line-integrated flux ratio of 0.9, is largerthan expected at solarmaximum and less than expected based on initial SOHO SUMER results at solar minimum [Le- at solarminimum in a 1-year-averagemodel. We have argued maire et al., 1998]. It would be of interest to see if spatially that this is due to the fact that downwind atoms reflect condi- resolved solar Lyman c• spectrafrom the Solar Max Mission tionsnear the Sunin earlieryears. A crudemodel of this effect (SMM) couldbe disc-integratedto test this conclusion,as has has improvedthe fits to the PioneerVenus Lyman c• data. been done for the O 130.4-nm emission [Gladstone, 1992]. Other workers have arguedthat such a time dependenceis Spatially resolvedSMM solar Lyman c• spectrahave a wide needed.Blum et al. [1993] useda Monte Carlo simulationto varietyof shapes,with differingdegrees of self-reversal[Fon- show that the downwind direction contains a series of hydro- tenla et al., 1988]. Their SMM quiet Sun profiles have a line gen densitywaves persisting to hundredsof AU resulting centerto integratedflux ratio of-•l.06. Their SMM active Sun fromthe time dependence of It. Kyrola et al. [1994], Rucinski profilesinclude both largerand smallerratios. Our successful and Bzowski[1995], and Summanen[1996] performedsimilar modelingefforts suggest that the disc-integratedflux and line calculationsshowing moremodest, but real, density waves centerflux must be roughly proportionalto eachother or the 26,846 PRYOR ET AL.: LYMAN ct OBSERVATIONS FROM PIONEER VENUS time seriesdata would not trackwith the model. The cavity would havea solarwind chargeexchange lifetime asymmetry shapealso dependson this ratio,through the radiationpres- factorof A=0.5. TheUlysses measurement is obviously more sureparameter g. Variationsin g substantiallyalter the ca¾ity direct and is in satisfactoryagreement with the SME-based shapeand affect our ability to simultaneouslyfit the datafrom Lymanct modelsdiscussed here. Summanenet al., [1997] ar- differentlongitudes. Our bestfitting modelparameters should guedthat the A representationdoes not very accuratelyrepre- not be considereda unique solution to the problem,as other sent the Ulysses solar wind data, which leads to an ionization effects,such as the time dependenceof the solar wind latitude ratethat is sharplypeaked near the eclipticplane. Theyfind asymmetry,may be involved. Solarwind monitoringsatellites that use of the A representationoverestimates the meanioniza- in the ecliptic do not recordsolar wind eventsat high solar tion rateby 20%. Pryor et al., [this issue]report on different latitudesthat might changethe latitudeasymmetry. representationsfor the solarwind massflux in fitting Ulysses The PVOUVS data modeledhere only sampleone ecliptic GAS Lymanat maps that are bettersuited for studyingthe so- latitude(-30ø), so they are not particularlywell suited for de- lar wind asymmetries. termining the value of A. A primarily affectsthe downwind We haveattempted to usethe bestavailable input parame- brightnessand may be a functionof time. We found that to si- ters in the models, but the uncertaintiesin some of them remain multaneouslyfit the PVOUVS dataobtained over a solarcycle uncomfortablylarge. Oneconcern is in thewide rangeof pub- in both the upwindand downwindhemispheres with an SME- lisheddensities for hydrogennear the terminationshock. The basedmodel requires an averagevalue of A=0.5-0.6. Fitting old standardpicture favored an inflowinghydrogen gas den- the UARS-basedmodels required a largervalue of,,1=0.75 or sity of n=0.06-0.08cm '3. However,"a consensushas been more. buildingfor a higherhydrogen density" [Isenberg, 1997, p. Our earlier modelingstudies of A used SME-basedmodels. 623]greater than 0.1 cm '3. Ourhydrogen density based on our Galileo EUVS Lyman c• data fromnear solar maximumfavor a GalileoUVS calibration of n=0.17+0.05 cm '3 is a bit higher low asymmetryparameter A--0 [Pryoret al., 1992, 1996]. This thanaverage, but the error bar overlaps with the recentpickup result may be comparedwith A=0.25+0.25 derived fromGali- ionresults of Gloeckleret al., [1997](n=0.115+0.05 cm '3) and leo UVS datafrom 1990 [Ajelloet al., 1994] at solar maximum. the Lymanct radiationanalysis of Quemeraiset al., [1994] Independentwork has foundA=0.30+0.05 fromsome special (n=0.165+0.035cm'3). Detection of a solarwind slowdown high-latitude PVOUVS observationsmade during the 1986 between1 and40 AU by Richardsonet al. [1995]was attrib- encounterwith Comet Halley at solar minimum [Lallement utedto a ratherlow hydrogendensity of 0.05cm -3. However, and Stewart, 1990]. The modelsare particularlysensitive to A thislow densityof 0.05 cm '3 requires only a modestmultiple at solarminimum when the solar Lyman c• flux is moresymmet- scattering correction for an observer at 1 AU from the Sun ric [Ajello 1990; Ajello et al., 1994]. A companionpaper lookingdownwind (from sidewind) of-•23% insteadof-35% [Pryor et al., this issue]reports evidence from Ulysses inter- forn=0.17 cm -3 [Quernerais and Bertaux, 1993, Table 3] and stellarneutral gas (GAS)Lyman c• mapsthat the asymmetry makes it somewhatharder to reconcilethe models with the ob- parameteris largerat solarminimum than solar maximum. servedupwind to downwindratios [Ajello et al., 1994]. The interplanetaryLyman c• datacan be comparedto other A secondmajor concern is thelarge difference between SME measurementsof the solar wind asymmetry. Radio observa- andUARS SOLSTICEsolar Lyman at fluxes. Tobiskaet al., tions combinedwith white light coronagraphobservations [1997] use the PioneerVenus data set fromthis paperto imply that in going fromsolar equator to solarpole, the solar bridge the gap in time betweenSME and UARS. As can be windmass flux (densityn• timesvelocity Vsw) decreases by a seenin Figure6, thereis no largejump in the ratio of the PV factorof 2.3 andsolar wind velocity v• increasesby a factorof datato themodel between the end of SMEand the beginning 2.2 at solarminimum [Woo and Goldstein,1994]. At a typical of UARS. Differencesbetween the largeUARS solarLyman eclipticsolar wind speedof 350 km s-i, the chargeexchange atirradiance values and smallerSME irradiancevalues proba- crosssection c• is 1.91xl0-lScm-2; at a polar wind speedof bly reflectabsolute calibration differences, as was also found 350x2.2=770km s-l, {J falls to 1.30x10-lScm '2 [Barnett et al., by Woodsand Rottrnan[1997] using other solar proxies. de 1990].Thus, if the lifetimeagainst charge exchange x of a hy- Toma et al. [1997] also found a calibration differencebetween drogenatom at 1 AU x=l/[mwv• o(v•w)],then SME and UARS by usingVoyager interplanetary Lyman at datato comparethe solarmeasurements. •pole/•equator Usinga UARS-basedmodel provides improved agreement with the PV downwindtime series data. However,the large radiation pressuresin the UARS-basedmodel make the de- =[n•v• {J(V•)]equator/[ns•V•{J(V,w)]poie=2.3(1.91/1.30)= 3.37. rivedasymmetry parameter A somewhatlarger than expected fromprevious work in orderto matchthe observedupwind to This ratio correspondsto A=0.70. This estimateis not too downwindratio. Otherfactors besides A maycontribute to different from the UARS-based models evaluated here. Direct theupwind to downwindratio. Forexample, a minor popula- solarwind measurementsby Ulyssesat solarminimum [Phil- tionof superthermalH atomsmay act to fill in the downwind lips et al., 1995] found the median massflux between -80.2 cavity. High spectralresolution Hubble SpaceTelescope latitude (September12, 1994) and 80.2 latitude (July 31, (HST)measurements [Clarke et al., 1995]of the hydrogencol- 1995) to be nearly constantwith latitude. However,the more umnbetween Earth and Marsalso indicate an unexpectedly relevantquantity for the hydrogendensity, the meanmass flux large amountof hydrogen(of noncometaryorigin) in the foundin thesesolar wind experiments,decreases by -•40% downwindcavity. Interplanetaryline shapemeasurements fromequator to pole [Summanen,1996; Summanenet al., fromthe Solar Wind Asymmetry(SWAN) experimenton 1997]. A "harmonic"representation of the Ulysses data SOHO and the Hydrogen DeuteriumAbsorption Cell (basedon the ionizationrates of Surnrnanenet al. [1997,Fig- (HDAC) experimenton Cassinimay help better characterize ure 2, after subtractionof the photoionizationcomponent) the downwind material. PRYOR ET AL.' LYMAN c• OBSERVATIONS FROM PIONEER VENUS 26,847

Appendix: Justificationfor a Model with a m is the massof a hydrogenatom. SinceI•=1, the acceleration "Lagged" Radiation Pressureand Lifetime due to effectivegravity is smallerthan that due to solar gravity. Findingthe trajectorydue to effectivegravity is First, consider the source function for emission, also analogousto a small angle Coulombscattering problem known as the volumeemission rate. Formally,it is the [Nicholson,1983). Define 0 as the anglebetween the ray productof the hydrogendensity n, the solar flux, the fromthe Sunin the upwind directionand the ray from the scatteringcross section, and the phasefunction. We usethe Sun to the atom. Define the impactparameter for an atom standardtable of hydrogendensities of Thomas[1978] to movingpast the Sun as the closestapproach distancep. evaluate the source function. The relative source function Then the perpendicularvelocity acquired in passingthe Sun for an observerat the Sunis simplythe productof density is and 1/r2, where r is the distancefrom the Sunin AU. Figure A1 illustratesthe relativedensity and sourcefunction. The vl= • dtFgl upwind sourcefunction is rather sharply peakednear the maximumemission region, 1-2 AU upwindof the Sun. The downwind source function is rather broad, with substantial =--• 7 dtGM(/•-l)sinO/.2 contributionsfrom a rangeof distances.This meansthat • dtGM(/•- 1)sin0 light comingfrom downwind is being scatteredfrom = • (p/sinO)2 hydrogenatoms that passedthe Sun at varioustimes in the previousfew years,when solar conditionswere different from the current conditions. We show below that a Let x be theposition at timet, givenan initial velocityv 0 reasonablefirst approximationis to model the source along the upwind-downwind direction. Assumingthe functionfor eachdownwind volumeelement using the solar upwind-downwindplane is crossedat t=0, then conditionsduring the year when thehydrogen atoms in that volumeelement moving at thebulk velocity passed the Sun. x= Vot =-rcos0 =-pcos0 =Vot The ionization,radiation pressure, and solar gravity all sin0 havea 1/r2 dependence.The ratio of theLyrnan cc radiation so that pressureforce on a hydrogenatom to solar gravityis called pdO I•. Definethe effective gravity force Fg=GMm(Iz-1) / r2 where at -- • G is thegravitational constant, M is themass of theSun, and vo sin 2 0

1.0

>, 0.8 Thomos 1978 Toble 20 Density

ß 0.6

-> 0.4 o + a: 0.2 + +

+ 0.0 - • , , , I , , , , , , , , , i +,-!-•.,ii -I- , , , , , , , • , , , , , 2O 10 0 -10 Upwindto Downwind(Sun ot O) in AU

.... , ...... ! ...... , ...... I ...... i ....

• 0.08 _ _ c - + - oo6 _ + Thomos1978 Teble2o SourceFunction o

c ._o 0.04

+ + "0.02

_ _

o 0.00 .... + ...... '•.•+ + + t + 20 10 0 -10 -20 Upwindto Downwind(Sun ot O) in AU FigureA1. Table2a of Thomas[1978] presents relative hydrogen densities for the case of initialdensity n=l cm'3, velocity v=20 kms -•, andtemperature T=10,000 K, ionizationrate at 1 AU •=5.x10'7 s-1, and !.t=0.75. (a) Therelative densities from that table along the upwind-downwindaxis are shown. Upwind is on the left. (b) The relative sourcefunction (volume emissionrate) is shownin arbitraryunits. Note the broad downwindsource function. 26,848 PRYOR ET AL.: LYMAN ct OBSERVATIONS FROM PIONEER VENUS and finally E. Simmons,and D. T. Hall, Observationsof interplanetaryLyman c• with the Galileo ultravioletspectrometer: Multiple scatteringeffects at solarmaximum, Astron. Astrophys., 289, 283-303, 1994. GM(I.t-1)idOsin 0 Barnett,C. F., ed., Collisionsof H, H2, He and Li atomsand ionswith at- vop o omsand molecules,Oak RidgeNatl. Lab., Rep. ORNL-6086/VI, Vol. 1, Oak Ridge, Tenn., 1990. Thelast integral numerically equals 2. For atomstraveling Bertaux,J.-L., R. Lallement, V. G. Kurt, and E. N. Mironova, Charac- teristics of the local interstellar hydrogen determined from at thebulk velocityV 0 = 20 kms -1, a distanceof 4.2 AU is PROGNOZ 5 and 6 interplanetaryLyman alpha line, Astron.Astro- traveledin 1 year, for example,from 2.1 AU upwindto 2.1 phys.,150, 1-20, 1985. AU downwindin 1 year. Consideran atomwith impact Blum,P., P. Gangopadhyay,H. S. Ogawa,and D. L. Judge,Solar-driven parameterp=2.1 AU. In that 1-yearinterval, 0 variesfrom neutraldensity waves, Astron. Astrophys., 272, 549-554,1993. --45ø to--135ø , if the effectivegravity is small. The same Clarke, J. T., R. Lallement, J.-L. Bertaux,and E. Quemerais,HST ob- servationsof the interplanetarymedium downwind and in the inner integralevaluated from 45 ø to 135ø numericallyequals solarsystem, Astrophys. d., 448, 893-904,1995. 1.414. In this case, 1.414/2.0=71% of the transverse Colwell,W., VenusLyman alpha: A morphologicaland radiativetrans- velocityis acquiredin theyear of closestapproach to the fer analysis,Ph.D. dissertation,Univ. of Colo.,Boulder, 1997. Sun. For atomswith a few AU impact parameterthe de Toma, G., E. Quemerais,and B. R. Sandel,Long-term variation of the interplanetaryH Lya glow:Voyager UVS measurementsand im- radiationpressure and effective gravity during the year of plicationsfor the solarH Lya irradiance,Astrophys. d., 491, 980-992, closestapproach to theSun control the trajectory. 1997. We alsoestimate the relative importanceof ionization at Fontenla,J., E. J. Reichmann,and E. Tandberg-Hanssen,The Lyman al- differentdistances. This is importantfor evaluatingthe pha line in varioussolar features,I, Observations,Astrophys. J., 329, rightimpact parameters p for thepreceding estimate: if p is 464-481, 1988. Gladstone,G. R., SolarO I 1304-Atriplet line profiles, J. Geophys.Res., toosmall, ionization may leaveno downwindslow neutral 97, 19519-19525, 1992. component.A table of interplanetaryhydrogen densities Gloeckler, G., L. A. Fisk, and J. Geiss, Anomalouslysmall magnetic presentedby Thomas[1978, Table 2a) indicatesthat for an field in the local interstellar cloud, Nature, 386, 374-377, 1997. impactparameter of 1 AU, the densityat the upwind- Hall, D. T., Ultravioletresonance scattering and the structureof the he- downwindplane crossing is only 3% of theinitial density. liosphere,Ph.D. thesis,Phys. Dept., Univ. of Ariz., Tucson,1992. Hall, D. T., D. E. Shemansky,D. L. Judge,P. Gangopadhyay,and M. A. For a 4-AU impactparameter, the densityat planecrossing Gruntman,Heliospheric hydrogen beyond 15 AU: Evidencefor a is 30% of the initial density. A few. AU seemsto be a terminationshock, J. Geophys.Res., 98, 15185-15192,1993. reasonableestimate for the impactparameter to use in the Harvey,J. W., Helium10830 A irradiance:1975-1983, in Solar Irradi- precedingcalculation on transversevelocities. This ance Variationson Active Region Time Scales, edited by B. J. LaBonte,NASA Conf. Publ., 2310, 197-211, 1984. discussionsuggests that a 1-yearaverage of ionizationrates Harvey,J. W., andW. C. Livingston,Variability of the solarHe I 10830 andradiation pressures for theperiod centered on upwind- A triplet,in lnJ•aredSolar Physics, IAU Syrup.154, edited by D. M. downwindplane crossing is a usefulfirst approximationto Rabin, J. T. Jefferies, and C. Lindsey,pp. 59-64, Kluwer Acad., usein evaluatingdownwind densities at differentphases of Norwell, Mass., 1994. the solar cycle. Hord,C. W., et al., Galileo ultravioletspectrometer experiment, Space Sci. Rev., 60, 503-530, 1992. Isenberg,P. A., Interactionof the solarwind with interstellarneutral hy- Acknowledgments.This research was supported by thePioneer Ve- drogen:Three-fluid model, J. 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SpaceSci. Data Cent.,Greenbelt, Md., 1979. tivelyby NSF/NOAO,NASA/GSFC, and NOAA/SEL. We acknowl- King, J. H., InterplanetaryMedium Data Book, 83-01, GoddardSpace edgeuseful discussions with Tom Woods,Eric Quemerais,Giuliana de Flight Cent.,Natl. SpaceSci. Data Cent.,Greenbelt, Md., 1983. Toma,Randy Gladstone, and Bill McClintock. Kyrola,E., T. Summahen,and P. Raback,Solar cycle and interplanetary The Editorthanks two anonymousreferees for their assistancein hydrogen,Astron. Astrophys., 288, 299-314, 1994. Lallement,R., and A. I. F. Stewart, Out-of-eclipticLyman alpha obser- evaluatingthis paper. vationswith PioneerVenus: Solar wind anisotropydegree in 1986, Astron.Astrophys., 227, 600-608, 1990. Lasica, S. J., W. B. Colwell, W. R. Pryor, A. I. F. Stewart, and J. M. References Ajello, Solarcycle effect on the VenusLyman alpha corona,Bull. Am. Astron. Soc., 25, 1096, 1993. Ajello, J. M., Solar minimumLyman c• sky backgroundobservations Lee, M. 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