19 67ApJ. . .150 . .327P -2 The AstrophysicalJournal,Vol.150,October1967 Jones, andLilley1964).Thisresult,togetherwith otherlinesofevidence(Walkerand planetary radiiofthesurfaceVenus.Atwo-channelmicrowaveradiometerwas results. Ontheotherhandscatteringmodelfailsforthissituation.Anupperlimitonsurfacepres- near thetopofatmosphere;andanaerosolscatteringparticles,arbitrarilydistributedwithaltitude. predictions offivedifferentopacitymodels:pressure-inducedtransitionsCO2andN2,continuously phase effect(PollackandSagan1965&;henceforth called“PaperII”),andthedifference but isinqualitativeagreementwithradiationarising fromahotsurfaceandatmosphere. bright sideoftheplanet—theemissionsatwavelengths13.5and19mmwererecorded with thoseinferredfromthe3-and10-cmphaseeffects. way forthedetailsofpassiveinterferometric microwave observations(Pollackand ous limbdarkeningwasobservedinthe19-mm channel (Barath,Barrett,Copeland, atmosphere; buthailstonesorlargeraindropsarealsopossible.Forallscatteringmodels,particleradii scattering modelstheopacityisperhapsbestrealizedbydustcontinuouslydistributedthrough layer, wouldberequiredtoexplainboththisdatumandtheMariner2observations. the absorbingcloudmodelcanaccountforMariner2dataandoffernoinconsistencieswithradar The CO2-N2,thewatervapor,andabsorbingdustmodelsinwhichthesematerialsaresolesources distributed throughouttheatmosphere;non-resonantandresonantabsorptionbywatervapor,similarly a modelhavingbothcontinuouslydistributedopacity,aswelleitheranabsorbingcloudorscattering of theatmosphere.Finallysizablelongitudinaltemperaturegradientsareindicated,whichconsistent sure ofbetween16and150atm,dependingontheCO2mixingratio,isderivedfromfailure of microwaveopacityareinconsistentwiththeMariner2results. distributed; anaerosolofabsorbingdust,arbitrarilyisothermalcloudlayer, craft Mariner2arehereanalyzedinahot-surfacecontext.Theobservedpeakbrightnesstemperatures meter wavelengthsaswell. consistency ofthehot-surface modelinexplainingtheobservedlimbdarkening atmilli- between opticalandradardiameters.Inthepresent paperweundertaketostudythe Furthermore, thehypothesisofahotsurfacecan accountinaperfectlyself-consistent tenable. Italsoseemstoruleoutelectricaldischarge models(PollackandSagan1967) Sagan 1966),renderstheionosphericmodelof Cythereanmicrowaveemissionun- as afunctionofpositiononthedisk.Withantenna polarizationadopted,unambigu- aboard thespacecraft.Duringthreescans—ofdarkside,terminator,and very closeto0.5mmarerequired.Suchparticleshaveterminalvelocitiesofseveraltensmilesperhour. Sagan 1965a;henceforthcalled“PaperI”;Clark and Kuz’min1965)ofthemicrowave CO2-Ñ2 opacitymodel,andsimilarlyanupperboundof640gmcmisplacedonthewater-vaporcontent rp nearthecenterofeachscan(darkside,terminator,brightside)at19mmarecomparedwith B © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem On December14,1962theUnitedStatesspacecraftMariner2passedwithin6 The limb-darkeningobservationsofVenusmadebythe19-mmchannelUnitedStatesspace- Liquid waterdropletsarethemostprobablesourceofopacityforanabsorbingcloudlayer.In If thelowradarcross-sectionat3.8cmisderivedingoodmeasurefromatmosphericattenuation,then If thelowradarcross-sectionat3.8cmisattributedtoadielectricconstantof1.45forsurface, AN ANALYSISOFTHEMARINER2MICROWAVE Harvard UniversityandSmithsonianAstrophysicalObservatory Received May13,1966;revisedFebruary16,1967 Smithsonian AstrophysicalObservatory OBSERVATIONS OFVENUS James B.Pollack I. INTRODUCTION Carl Sagan ABSTRACT AND 327 19 67ApJ. . .150 . .327P mospheric opacity.Suggestedsourcesofthisattenuationincludegaseousconstituents 328 the atmosphere,particularlyCO2andN2mixtures,H2O(Barrett1961;Barrett rather markedly,aphenomenongenerallyattributedtosharpincreaseintheat- In thepresentpaperwewilldetermineextenttowhicheachoftheseattenuatorscan water (SaganandGiver1961;Rasool1963;Salomonovich1964;Diermendjian1964). Staelin 1964;Thaddeus1965);atmosphericdust(Öpik1961);andcloudscomposedof millimeter opacity—verylowsurfacepressuresandanexcessivewater-vapormixing plausibility oftheimpressedsubsidiaryconditions.Forpressure-induceddipoletransi- edge, inthecontextofhot-surfacemodel,naturemillimeterattenuator explain theMariner2limb-darkeningobservations.Insodoingwewillgainsomeknowl- illuminated hemisphere,gaveresultsconsistentwith theobservations. invoked cloudsofuniformopacity,oratmospheric dustpreferentiallypresentintheun- match thespectraldata.Thelowercloud-bottomtemperaturesofsuchamodelwould urements (e.g.,SintonandStrong1960).Infact,BrasharinovKutuza(1965)have ratio arerequired.However,BarrettandStaelin,followingSalomonovich(1964),place unlikely circumstanceprevailsthatcondensationofsomeatmosphericconstituentoc- with thatderivedfrominfraredandopticaldataforaconvectiveatmosphereunlessthe sources ofopacityhavebeenmadebyBarrettandStaelin(1964),Pollack and ofthedistributionsurfacetemperatureoverCythereansurface. mospheric regionfilledwithabsorbersorscatterers havesurvivedthepreliminary higher surfacetemperaturesfortheilluminatedhemisphereofVenus.When8-mm help eliminatetheaboveinconsistencies. atm isrequired,accordingtoBarrettandStaelin.Thispressureappearsincompatible the putativeattenuators.Itwasfoundthateachattenuatorcouldmatchobserva- ence ofbrightnesstemperatureonwavelengthwiththespectrumpredictedbyeach Sagan (PaperII).BarrettandStaelinhavecomparedtheobservedfunctionaldepend- shown thatsupercooledwater,whichisacommonconstituentofterrestrialclouds,can curs throughoutmostoftheCythereanatmosphere(Sagan1962). tions ofCO2-N2mixturestoexplaintheobservations,asurfacepressureinexcess200 tions undercertaincircumstances;achoiceamongthemdepends,therefore,onthe length. Thebrightnesstemperatures Jbdisplayedtherearethepeak temperatures millimeter waveattenuators. observation ofthephaseeffectwerefoundtobe discordant at8mm;butmodelsthat opacity wasattributedtoCO2-N2mixtures,or atmospheric watervapor,theoryand the cloudsatahighertemperaturethanwouldnecessarilybeimpliedbyinfraredmeas- while modelsincorporatingacloudlayer—particularly awater-cloudlayer—oranat- on therealityof3-and10-cmphaseeffects,theirinterpretationinterms with theparticlesizeprogressivelydecreasingaltitude. so theyMiescatteraswellabsorbmicrowaveradiation—BarrettandStaelinshowed analyses. Oneobjectiveofthepresentpaperistodiscriminate furtheramongalternative to discriminateamongvariouspotentialmicrowaveattenuators.Theargumentdepends that suchclouds,too,canprovideasuitablewavelengthdependenceofbrightness CO2-N2 mixturesandwatervaporunlikelyassolesources ofmillimeteropacityonVenus, temperature. Theseauthorsemployed100-/4particlesatthebaseofatmosphere, p © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem At wavelengthsshorterthan3cm,thebrightnesstemperatureofVenusdeclines Previous theoreticalstudiesdesignedtodiscriminateamongthevariouspostulated Other inconsistenciesarisewhenwatervaporandcloudsjointlyprovidethe In short,ground-basedobservationshaverendered suchatmosphericabsorbersas In Table1wesummarize theresultsofMariner2observationsat19-mm wave- In PaperIItheobserved8-mmphasedependenceofbrightnesstemperaturewasused If thehypothesizedCythereandustparticlesarehundredsofmicronsindiameter— JAMES B.POLLACKANDCARLSAGAN II. THEOBSERVATIONS Vol. 150 19 67ApJ. . .150 . .327P _ planetary normalatthemomentofpeakbrightness temperatureofeachscan. from thecenterofeachscan;wehavethereforechosentoconsideronlypeaktempera- recorded ineachscan.Thesignal-to-noiseratiowasobservedtodecreasesharplyaway longitude istakentopassthroughthesubsolarpoint duringencounter.Thesecoordinates face andisnotpreciselyidenticaltotheequator oftheaxisrotation.Thezero follows thatthedirectivitycanberepresentedadequatelybyaGaussianfunction, viewed bytheantennabeamwasisothermal.Inmodelsweconsiderbelow, receiver timeconstantsandforthefactthatbeamisincompletelyfilledbyplanet. tures, obtainednearthescancenters.Thebrightnesstemperaturesarecorrectedfor No. 1,1967 scan. Wewilllatercomparethe19-mmresultswith thoseatneighboringfrequenciesto brightness temperatureinthe19-mmchannelhave beenreducedtosome6percent,or not treatthe13.5-mmobservations inthisdiscussion. of aninherentlylowersignal-to-noiseratio,andinstrumental difficultiesassociatedwith confirm thattheabsolutecalibrationofthisMariner 2channelisfairlyaccurate.Because Table 1representtherandomerrorsdeducedfrom thescatterofpointswithinagiven are usedtocomputethesecantofanglebetween thelineofsightandlocal The zerooflatitudeistheprojectionorbitalplaneVenusonplanetarysur- antenna beamatthemomentineachscanofmaximumrecordedbrightnesstemperature. 2.6 X10V;risthedistancefromspacecrafttosurfaceareaviewed.Since brightness temperatureTbwillbeallowedtovaryovertheantennabeam.Inthiscase, correction factorforthefinitebeamwilllaterbefoundtosmall,wehaveneglected where xandyareCartesiancoordinatesperpendiculartothelineofsight,v^ carried outonlyovertheentireplanetarydisk.Thebulkofradiationisreceivedby where GisthedirectivityorantennapatternanddQ,elementofsolidangleat In addition,thesetemperatureswerederivedassumingthesurfaceareainstantaneously the sidelobesinaboverepresentationofG. spacecraft subtendedbyanelementofareaontheplanetarysurface.Theintegrationis the centrallobeofantennapattern.FromdiscussionBarathetal.(1964),it the phasesynchronyofchopping (leadingtoavariableanduncertainbase line), wewill about 35°K(Jones1964,1965).Theerrorsin brightness temperaturesdisplayedin (For observationsnearthelimb,planetdidnotcompletelyfillantennabeam.) rp andTbarerelatedby B © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The latitudesandlongitudesofTable1refertothepositioncenter As domostradiotelescopes, theMariner2antennaacceptedonlyonecomponent of By preflightandin-flightcalibrationofthemicrowave radiometer,absoluteerrorsin Scan * (Barathetal1964;Jones1965). Peak TemperatureObservedbyMariner2,19-mmChannel* Terminator, t Bright side,b Dark side,d Location MICROWAVE OBSERVATIONSOFVENUS 2 Fb =xT-üGdOi^J'^GdQi,U) p G =Goexp[—(%+y)/or],(2) Latitude, £ - 6° -13 6 -18 7 TABLE 1 Longitude, 77 137° 27 88 3 490 +11 511 +14 595 +12 TbpCK) sec 2 04 1 00 1 49 329 19 67ApJ. . .150 . .327P , -1 polarization. Iftheplaneofincidenceisdefinedbylocalsurfacenormal(atpoint 330 intercepted bytheantennaaxis)andlineofsightfromspacecrafttosurface, limb darkeningandbrighteningforobservationsofanidenticalsource. in extremecasesthedirectionofantennapolarizationmaymakedifferencebetween electric vectoroftheCythereanemissionacceptedbyantennalayperpendicularto sphere. Sincerp(t)—p(b)=ATßpOob)ju(cl),dataimmediatelysuggestmeansurface the planeofincidence,nearcentereachscan.Thisisapointsomeimportance; variables: TÇK^rjjZe),thetemperatureofeffectiveemittinglayerCytherean temperature onthebrightsideexceedsthatdark.Wewilllaterextractnumerical attenuator underinvestigationatthepositionandwavelengthinquestion;£(\;£,?7,/¿), latitude andlongitude.Therelationamongtheobservedbrightnesstemperature, subsurface atthepositionandwavelengthinquestion;r(Xtheopticaldepthof effectively emittingatwavelengthX,and£rjare,respectively,theplanetocentric the emissivityofpointobserved.HereXrepresentswavelengthobservation leigh-Jeans approximationtothePlanckfunction is validatmicrowavefrequenciesand investigate whethereachofthepostulatedopacitysourcesisabletoreproduceob- reasonable variationsinrandTatthebright-dark-sidescanpositions,wewill ployed toinferr(19mm,t)andT(19t,z).Wewillthencheckthesevaluesby radiative transferforagivenopacitysource.Ground-basedobservationswillbeem- relevant equationsoftransferforallpostulatedopacitysources:CO2andNdistributed BBp served valuesofr(X;ju;b)andX;M;d).Inthepresentsectionwewritedown of theatmosphere: following expressionforthebrightnesstemperature detectedbyanobserveratthetop The formalsolutiontotheequationofradiative transfer thenyields,forthiscase,the atmosphere—as appliestotheCO2-N2,H0,andabsorbing dustmodels.SincetheRay- arbitrary mannerthroughouttheatmosphere. dust particles,arbitrarilydistributed;anabsorbingcloudlayer,localizednearthetop continuously throughouttheatmosphere;watervapor,similarlydistributed;absorbing computing r(19mm,t)andcomparingwiththeobservedvalue.Thenallowingfor the absorberisdistributedcontinuouslyandwith plane-parallelgeometrythroughthe of theatmosphere;and,finally,anarraymicrowavescatterersdistributedin Tp(X;/z;£,r7), T(k;^r)Ze),e,andisspecifiedbythesolutionofequation (primarily 19mmintheensuingdiscussion),zissubsurfacedepthoflayer Cytherean temperatures,thespecificintensitywill beproportionaltothetemperature. e 2 Bp 2 Bp By e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem It issignificantthatthebrightnesstemperaturesofbothdarksideandbright The peakbrightnesstemperatureof,e.g.,theterminatorscan,isafunctionofthree We beginbycalculatingthebrightnesstemperature ofagivenlocaleonVenuswhen — III. EQUATIONSOETRANSFEREORTHEPOSTULATEDOPACITYSOURCES + [1—e(/u)]exp(“ )j( Ur]exp£ x = e(ß)T(\^,v,z)eP(-7)+(~£) y e JAMES B.POLLACKANDCARLSAGAN b) ContinuousDistributionofAbsorbers a) Over-allStrategy Vol. 150 (3) 19 67ApJ. . .150 . .327P brightness temperatureof234°K(SintonandStrong 1960),whichisclosetotheequi- Here risthetotalopticaldepthofcloudsand the factor1—exp(—r//x)represents vided byalayerofisothermalclouds: distribution ofpurelyscattering particles.Sincethescattererscontribute noradiation of positiononthedisk,inagreementwithinfra-red observations(see,e.g.,Sintonand for thebrightnesstemperaturedetectedfromabovewhenmillimeteropacityispro- possible forabsorbingdust(PaperII).ThequantitiestandTqarethesurfaceoptical librium temperatureoftheplanetdeducedfrom bolometricalbedo. Strong 1960;Murray,Wildey,andWestphal1963). Weinitiallyadoptan8-to13-/z the cloudemissivity.ThetemperaturesTare assumedindependent,tofirstorder, depth andsurfacetemperatureatsomereferencelocaleontheplanet. where m—n=3.6forCO2-N2mixtures,2.125watervapor,andarangeofvaluesis surface ifTsovaries.Sincethepressureisinvariantover(see,e.g., where thereismicrowaveattenuation.Detailednon-graymodelatmospherecalculations The surfacetemperatureisT.Throughoutthispaperwewillassumethattherean No. 1,1967MICROWAVEOBSERVATIONSOFVENUS331 tend toconfirmthisassumption. w >3.6fordustthattendstosettletowardthebottomofatmosphere(PaperII). vapor withaconstantmixingratio,^3.6fordustand where, foranadiabaticlapserate,3.6CO2-N2mixtures,5.075water perature ateachlevelintheatmosphereoncorrespondingopticaldepth.For Ingalls, Rainville,andSilva1966).Wenotethatnumericalresultstobeextractedfrom Here e(/x)istheemissivityforplaneofpolarizationacceptedbyobserver,and observations at12.5cmand3.8showVenustobesmooth(Carpenter1964;Evans, sents theenergyradiateddirectlytospacebyattenuator.Thethirdtermrepresents Paper II),thelateralvariationofrwithTmaybewritten adiabatic lapseratepresentatthethreescanpositionsinportionofatmosphere equation (3)andfromanalogoussubsequentequationsareveryinsensitivetothe explicit assumptionsregardingsurfaceroughness. the reflectivity,throughKirchhofPslaw.Wehaveassumed,inlasttermofequation and transmittedbackthroughtheattenuatortospace;factor1—¿(/z)represents the radiationemittedbyattenuatorthatisincidentonsurface,reflectedfromit, escaping directlytospacethroughtheoverlyingattenuators.Thesecondtermrepre- of thethreeabsorbers,T—trelationcanbewrittenas t =(A)isthetotalopticaldepthofatmosphereinverticalsection. c c s0s (3), that19-mmradiationisspecularlyreflectedfromtheCythereansurface.Radar c s s s& s5 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We nowconsiderourfinal opacitysource,aplane-parallel,butotherwise arbitrary, A derivationanalogoustothatusedforequation(3)leadsthefollowingexpression The totalopticaldepthatthesurface,r,maybeexpectedtovaryoverplanetary The firstterminequation(3)representstheradiationemittedbysubsurfaceand Essential tothesolutionofequation(3)isknowledgedependencetem- 8 +r[l -exp(-T/ß)]{l+[1e(ß)]exp(—t/ju)¡ . c = e(ß)T(\;t,Ti,z)exp(—t/m) ec d) PureIsotropicScattering Ts =To(7Vr)”™,(5) 5s 1/w c) IsothermalClouds T =r(r/T),(4) 8 (6) 19 67ApJ. . .150 . .327P 332 JAMESB.POLLACKANDCARLSAGANVol.150 of theirown,theobservedbrightnesstemperaturewilldependonscatterersonly of scatterers.Werestrictthepresentdiscussiontoisotropicscattering. through thetotalopticaldepthrandwillnotbeafunctionofverticaldistribution within aconeofsolidangle¿O'.Thequantity'istheazimuthalinspherical coordinate systemwithpolaraxisalongthelocalsurfacenormal;ix'iscosineof atmosphere inthedirectionwillberelatedto^')by coordinate angleorthogonalto'.Thespecificintensity,/(0,/q),atthetopof ing andb(x,x')istheDiracdeltafunction.Nowintegratingequation(7)overallsolid planetary surface,wehavegeneralizedfromtheusualcase(Chandrasekhar1950)of incident fromallanglesatthebottomofatmosphere,viz., pression forTb: radiation incidentonascatteringmediumfromonedirectiononly.Wenowproceedto angles O',weobtainthespecificintensityattopofatmosphereduetoradiation intensity ofthermalemissionfromtheground,whichhasbeenreflecteddownward Note thatinthepresentcase,wherethermalradiationisemittedintoallanglesby where t(ß)representsanangularaverageofthetransmission functionandisdefinedin where theangularbracketsdenoteasolidangleaverage;S(ß')andNrepresent s employed byChandrasekhar(1950),Imayberelatedto: the scatteringlayer,andthenupwardoffsurface.Inamanneranalogoustothat the specificintensityofthermalemissiondirectlyfromground,andJ, express equation(8)inaformmoretractabletonumericalstudies. between specificintensityandbrightnesstemperature,wearriveatthefollowingex- for eachassumedopacity source.TherearefivereasonsthatTbwillvaryfrom onescan surface reflectivity. (see Chandrasekhar1950).Here£(/x,/z')isthetransmissionmatrixforisotropicscatter- Chandrasekhar andElbert(1952). averages ofthescatteringmatrixandaredefinedinChandrasekharasbook,Ris Chandrasekhar’s book;/(¿i),S(ß),andhavebeen tabulatedforvariousßandtby to thenext: rg r © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Let bethespecificintensityreceivedatbottomofatmosphere The radiationincidentonthescatteringlayerfrombelowhastwocomponents; Finally, insertingequation(9)into(8)andemployingtheproportionality Equations (3),(6),and(10)givethefunctionalform ofthebrightnesstemperature 1. Theemissivitywillvary fromscantobecausee=e{ß). T(\;v,I>;£,v) =j[ b I(0,ß,(i>) =exp(—t/m)+d(j>'.(8) s IV. APPROXIMATIONSANDSPECIFICATIONOFPARAMETERS r d/(0,M,4>) =I{r,ixexp(— s f XT(\'£,r,Ze), /,(/,') =[(1-e)/(l(RS))}(I)S(ß,(9) 0 a) ApproximationsfortheBrightnessTemperature ë(l-e)S(iO (1 —{RS)) »]“■>(“ if) ë_t(ß) (l-(RS)) ß (io) (7) 19 67ApJ. . .150 . .327P 344 ■ .1965(privatecommunication). Barrett, A.H.1961,Ap.133,281. Barath, F.T.,Barrett,A.H.,Copeland,J.,Jones,D.E.,andLilley,E.1964,AJ.,69,49. Thaddeus, P.1965(privatecommunication). .1967,Ap.J.,149,731. ■ .1965c,J.Geophys.Res.,70,4403. .19656,Icarus,4,62(PaperII). .1966,ibid.,71,142. Basharinov, A.E.,Vetukhnovskaya,Y.N.,Kuz’min,D.,Kutuza,B.G.,andSalomonovich,E. Basharinov, A.E.,andKutuza,B.G.1965,RadioSei.,69Z>,1580. Barrett, A.H.,andStaelin,D.H.1964,SpaceSei.Rev.,3,109. .1967,submittedtoAp.J. Walker, R.,andSagan,C.1966,Icarus,5,105. Ryan, J.A.1964,Geophys.Res.,69,3759. Rasool, S.I.1963,Proc.XlthInternat.Ap.Symp.,Liège,Belgium,1962,p.367. Murray, B.C.,Wildey,R.L.,andWestphal,J.A.1963,/.Geophys.Res.,68,4813. Lippincott, E.R.,Eck,R.V.,Dayhofï,M.O.,andSagan,C.1967,147,753. Jones, D.E.1964,thesis,BrighamYoungUniversity. Sinton, W.M.,andStrong,J.1960,Ap.J.,131,470. Salomonovich, A.E.1964,LifeSciencesandSpaceResearch,ed.M.FlorkinDollfus(Amsterdam: Sagan, C.1962,Icarus,1,151. Pollack, J.B.,andSagan,C.1965a,Ap.J.,141,1161(PaperI). Pendorf, R.1956,GeophysicalResearchPaperNo.45(CambridgeAirForceCenter). Karp, D.,Morrow,W.E.,Jr.,andSmith,B.1964,Icarus,3,473. .1965(privatecommunication). Hulst, H.C.vande.1957,LightScatteringbySmallParticles(NewYork:JohnWiley&Sons). Ho, W.,Osborn,R.,andThaddeus,P.1963,ColumbiaRad.Lab.,FourthQuart.Progr.Rept.,58. Deirmendjian, D.1964,Icarus,3,109. Carpenter, R.L.1964,A.J.,69,2. Sagan, C.,andGiver,L.1961,PaperdeliveredatAm.Geophys.UnionSymp.onRadioEmission Öpik, E.J.1961,Geophys.Res.,66,2807. Kaplan, L.D.1963,/.Quant.Spectrosc.andRad.Trans.,3,537. Evans, J.V.,Ingalls,R.P.,Rainville,L.andSilva,1966,A.J.,71,902. Copeland, J.,andTyler,W.C.1964,Ap.139,409. Chandrasekhar, S.,andElbert,D.1952,Ap.J.,115,269. Chandrasekhar, S.1950,RadiativeTransfer(Oxford:ClarendonPress). Chamberlain, J.W.1965,Ap.J.,141,1184. Spinrad, H.1962,Pub.A.S.P.,74,187. Gunn, R.,andKinzer,G.D.1949,J.Meteorol.,6,243. Clark, B.G.,andKuz’min,A.D.1965,Ap.J.,142,23. Goody, R.M.,andRobinson,A.1966,Ap.J.,146,339. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem North-Holland PublishingCo.),Vol.2. Thermal StructureoftheVenusAtmosphere(U.C.L.A.)(seealsoRept.NASAgrantNsG-126-61). 1964, Astr.Zh.,41,707. JAMES B.POLLACKANDCARLSAGAN Copyright 1967TheUniversityofChicagoPrintedinUSA. REFERENCES 19 67ApJ. . .150 . .327P , Mrs. AndreaDupreefor assistancewithdeskandelectroniccomputers thecalcu- Lilley ofHarvardCollege Observatory.ItisapleasuretothankMrs.Elinore Greenand lations. We alsogratefullyacknowledgeafruitfuldiscussion withexperimenterProf.A.E. Jones oftheJetPropulsionLaboratoryandBrigham YoungUniversityforagenerous of determiningthedistributionandtotalabundance ofwatervapordowntothesurface meter measurementsneartheantisolarpointandrotationalpoleswillpermita model donotsatisfytheMariner2observations,aconclusionheverifiedforrangeof Jones alsoconcludedthatthepressure-inducedCO2-N2modelandwater-vapor mm channel,whichwascharacterizedbylowsignal-to-noiseandanerraticbaseline. tion. WeareparticularlyindebtedtoMariner2 microwaveexperimenterDr.D.E. and bygrantNGR-09-015-023fromtheNational AeronauticsandSpaceAdministra- of Venus. for watervaporacquiremostoftheirphotonsfromthevicinityclouds.Incon- better specificationtobemadeofthenatureandthree-dimensionaldistributionmicro- and detaileddiscussionoftheinstrumentation,observational errors,anddatareduction. adjacent channelsatnearbywavelengthstotestline shape,isthemosteffectivemethod trast, anoperating13.5-mmexperimentwitha highsignal-to-noiseratio,andwith opacity withdecreasingtemperatures—ontheover-allopticaldepth.Infraredsearches wave attenuators,andofthesurfacetemperaturedistribution.High-resolutionmilli- values oftheopticaldepth. problem intheVenusatmospherehasyetbeenpublished. materials. Further,someskepticismhasbeenexpressed(Spinrad1965)aboutthereality check ontheinfluenceofCO2-N2mixturesandwatervapor—^materialsthatincreasein desirable. Measurementsmadewithhightopographicalresolutionwillpermitamuch indicated than350°Kabsorbingcloudsofsomeunspecifiedcarbonaceousmaterial. water aredifferentfromthoseofabove0°C,andcanaccountforthemillimeter Kutuza (1965)haverecentlyshownthattheabsorptionpropertiesofsupercooled with liquid-watercloudshasbeennoticedbyseveralworkers(SaganandGiver1961; Mariner 2.AcloudatT=350°Kcannotbemadeofwater;Kaplansuggestedhydro- Accordingly, weconcludethat234°Kabsorbingwatercloudsaremuchmorestrongly spectrum. Weprefertotreatwithsomecautionanyconclusiondrawnfromthe13.5- Rasool 1963;Salomonovich1964;BarrettandStaelin1964).However,Basharinov greenhouse modelsofthehigh-surfacetemperaturetobeconstructed.However,thermo- window intheCO2,N2,andH0atmosphereofVenus,whichmustbefilledforsuccessful with liquid-watercloudsatT~234°K;and(3)thedifficultyinaccounting of the/-numberdoublemaximum,and,inanycase,nosolutionthisline-formation carbons (PaperII);andthe3.5-/*windowiseffectivelypluggedeitherbywaterorother carbons, someofwhichcondenseat350°K,andallabsorb3.5m,anapparent dynamic equilibriumstudiesshowhydrocarbonsandotherorganicmoleculestobe 230° Kcloudsfortheapparentabsenceoflimbdarkeningat13.5mmasobservedby Kaplan (1963)andbasedontheground-basedobservationsofSpinrad(1962);(2) of the7820ÂCO2band,withonepeaktemperatureatabout300°K,aspointedoutby limb-darkening observationscanbesecured.Jonesprefers350°Kcloudsprimarilyfor No. 1,1967 extremely unstableintheCythereanatmosphere(Lippincott,Eck,Dayhofï,andSagan apparent difficultyinfittingboth4-mmand8-mmground-basedbrightnesstemperatures from ourpreviousdiscussionthataslongT<3C,agreementwiththeMariner2 three reasons:(1)theapparentbimodalBoltzmanndistributionofrotationallines 1967); theradarobservationsareinconsistentwithlargequantitiesofsurfacehydro- c 2 C cs © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem This researchwassupportedinpartbyanawardfrom theAlfredP.SloanFoundation The apparentdifficultyinmatching4-mmand8-mmobservationssimultaneously Future microwaveobservationsofVenusfromflybyororbiterspacecraftareclearly MICROWAVE OBSERVATIONSOFVENUS 343 19 67ApJ. . .150 . .327P 2 perature, Forthiscase,theabsolutevalueofTb{^9mm,t)placesonlyweak 342 JAMESB.POLLACKANDCARLSAGANVol.150 mm). Whenwedemandthattheabsolutevalueof^(19mm,t)andlimbdarkening compatible withtheextrapolatedvalueofr(19mm)foundfrom8-mmobservations. constraints onr(19mm)becauseoftheerrorsmeasurement;aswehaveseen,itis brightness temperatureoftheground,eT,ishighat19mm,implyingalargeropacity and henceasmallervalueofg.Forthiscase,becauseeTissubstantiallyhigherthan lies between0.20and0.35.Allowingfora10percenterrorintheabsolutevalueof be adequatelyreproducedwithintheconstraintAT^bjt)>Ar(t,d)wefindr(19mm) When edeclinesfromavalueof3.6atdecimeterwavelengthsto1.4519mm,thenthe ^100° K—betweentheequatorialterminatorand thesubsolarpoint.Asimilardiffer- value ofthesurfacedielectricconstant,asdeterminedby3.6-cmradarobservations.If measurements. Wehavefoundthatwatervapor,CO2-N2mixturesatelevatedpressures, vapor content,who,oftheatmosphere.Wehave foundPlessthan16-150atm— phase effect(PaperII).TheexclusionoftheCO2-N2 andthewater-vapormodelsfor haps themostlikelysourceofopacityforcloudmodelsandarecompatiblewith of overlapissmall. with thecorrespondingtheoreticalvaluesforwater-dropletclouds,althoughregion and 1.6fora253°Kcloud0.31.9293°K.Thesevaluesofgareconsistent based observations,ofavarietymodelsthe19-mmMariner2limb-darkening and derivedspectraldependencesissomewhatmarginal. narrow rangeofparticlesizescanreproducetheobservations.Waterdropletsareper- generation ofthescatterersisrequiredbytheirsizablefallvelocities;and(2)onlya depending ontheCO2mixingratio;further,who <640gm/cm. € =1.45hasprovidedusefulupperlimitsonthesurface pressure,P,andthetotalwater- temperature gradientsareingoodagreementwith thosededucedfromthemicrowave formed inthecloudsarepossiblealternatives. observations forthe€(19mm)=1.45case,althoughagreementbetweenpredicted Tb(19 mm,t)fairlyrigidconstraintsareplacedbytheMariner2observationsonr(19 tributed withaltitude.Adiscriminantagainstthesuccessfulmodelsisprovidedby 1(e.g.,vandeHulst1957).Wedenotethesevaluesofbyx*. particle sizemustbeatleastaslargeax.Thecalculationsoftheterminalvelocities Katuza (1965)andothers haveshownthatforc(19mm)=3.6,water-droplet clouds tween 8and19mmemploydatagivenbyBasharinov andKatuza(1965),weobtain of dustintheCythereanatmosphere.Thisassignment ofparticlesizetendstojustify centered abouta0.5mm.SimilarparticlesizeswerederivedbyBarrettandStaelin velocities, whichpresentaproblemforthismodel.Table7showstheterminalvelocities Venus atmosphereitishardtoseehowdustcouldbelocalizedinahigh-altituderegion for liquidwater,itwouldappearthatthephaseofawatercloudmustbere- can satisfactorilyreproduce thewavelengthvariationofobservedbrightness tem- our previousassumptionofapproximatelyisotropic scattering,sincex(19mm)0.3 Table 7,wefindthattheyarecompatibleonlywithaverysmallrangeinparticlesize, constant. TheobservedbrightnesstemperatureofVenusdeclinessteadilyfromX=3 ment foranefficientscouringofthegroundbywindstoregeneratedustparticles of theatmosphere,ascancondensablesubstancessuchwater. sponsible forthemicrowaveattenuation.Becauseofturbulenceexpectedin absorbing cloudmodel.Becausee¿foriceisthreeordersofmagnitudesmallerthane* crystals anddustparticleswillabsorblittleofthelighttransmittedthroughthemin lets willbecomealmosttotalreflectorsbecauseofthehighvalueseand€¿,whileice cm toX=3mm.Thusthescatteringmodelrequiresthatlargestvalueofxat3-mm tends tooscillate,aparticlesizedistributionwilltenddamptheoscillations;thus efficient reachesanapproximatelyconstantvaluewhenx>2;thecorresponding ture towardshortermillimeterwavelengths.Fordustandice,thetotalextinctionco- scatterer modelshouldreproducetheobservedsharpdeclineofbrightnesstempera- a possibility,itdoesseemunlikely.Evenwithdustasthescattererthereisrequire- small hailstoneswouldhavetobegeneratedingreatnumbersthecloudsreplace Ryan (1964).Becauseofthesizablevalueterminalvelocity,largeraindropsor incorporated deviationsfromStokes’slawgivenbyGunnandKinzer(1949) associated withax-Theseareminimumvelocitiesforthescatterermodel,since the particlesizeisgivenbyxrit-Anupperboundsupplieddemandthat that arecontinuallyfallingtothegroundatmoderatelyhighvelocities. those fallingtoloweraltitudesandtherebeingvaporized.Whilewecannotexcludesuch quasi-geometrical region,exceptforverylargesizes(vandeHulst1957). If theparticleradiusislargerthanax,scatteringwillingeneraldominate:waterdrop- While, foragivenparticlesize,andlargex,thetotalextinctioncross-section,Qxt, 0max givesanupperlimittoparticleradiicompatiblewiththeabsorbingcloudmodel. No. 1,1967 (TbÍX)) perhapsonlyforthee(19mm)=1.45case (BarrettandStaelin1964).Wenow (cf. Penndorf1956). (1964) inanattempttomatchthemicrowavespectrumwithacontinuousdistribution 19 mm)>Xcrit-Comparingtheseconstraintswiththevaluesofxritandx*givenin 19 mm.Thustheconstraintsonscatteringmodelarex(X=3mm)atmequation at surfacepressuresinexcessof100bars(GoodyandRobinson1966). But fromexistingspectroscopiccloudpressuresforalternativescatteringmodels ment withthevaluescomputed(Table4)fromground-basedobservations.TheMariner case. Forthismodeltoreproducetheobservations,asubstantiallongitudinaltempera- ported at3-and10-cmwavelength. examination oftheMariner2data. ture gradientisrequired—aswehavealreadyqualitativelyinferredfromapreliminary (14) toestablishanupperlimitonwho,wemustfirsthavealowerP.From That is,theMariner2observationsleadtoestimatesofP^b)andP^d)ingoodagree- P >15atm.Theseconclusionsare,however,dependentonthescatteringmodelused. chosen analyticformiscompatiblewiththeactual temperaturedistribution.Toac- 8 8 complish thisgoalwemustcorrectforthelatitudinal temperaturedifferencebetween of Pi(0,0),fromAP(t,b)andt,d).Agreementthetwoestimatesimpliesthat analytic formofthetemperaturedistribution,wecangaintwoindependentestimates (14) yieldswho<640gmcm.Wenotethatevenfore=3.6,ze>Hisfarbelowthe (Chamberlain 1965),itseemssafetoconcludethatP>2atm.Ifr(19mm,H0)< 28 Paper I.Table6summarizesthesecalculations. Paper II,andthefouranalyticformsforsurface temperaturedistributiongivenin equator-to-pole gradientandthevalueofthermal dampingparametergivenin the scanlatitudesandequator,aswellallow fordampingofthethermalwaveat solar point,asmeasuredalongtheequator.Forthissuccessfulmodelandaparticular 2 observationstend,therefore,toconfirmtherealityofmicrowavephaseeffectre- 8 the effectivedepthofemission.Weadoptinterferometrically derivedvalueofthe 2 the entriesofallthreelinesinTable6.Thisisaccomplished onlyfortheanalyticform not good,indicatinganequatorial latitudinaltemperaturegradientsomewhat shallower Pi (0,0),thesurfacetemperaturedifferencebetweenterminatorandsubsolaroranti- 8 gradients neartheequator.Eveninthiscase, agreement withphase-effectresultsis [Po(0,£), Pi0,£)Lwhichischaracterizedby very modestlatitudinaltemperature 28 s still. ye 2 8s2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem In asimilarfashiontheamountofwatervapormayberelatedtor(19mm)andP: We nowturnourattentiontothesuccessfulabsorbingcloudmodelfore=1.45 We canalsoestimateP(b)andTd)fromTable5: 8 Our presentimmediateobjectiveistoobtainfromtheMariner2dataanestimateof For agreementbetweentheoryandobservationwe requireroughagreementamong &0 MICROWAVE OBSERVATIONSOFVENUS VIII. SURFACE-TEMPERATUREDISTRIBUTIONIN 31 who =2.5X10Prt(19mm,H0),(i4) 2 T(b) ~760°K,d)630°K. 0g THE ABSORBINGCLOUDMODEL 339 19 67ApJ. . .150 . .327P 338 bound onP.BothCO2andN2undergopressure-induced dipoletransitionsatsufficient- model indetail. mechanism oflimb-darkening.BecausetheCO2-N2,watervapor,anddistributedab- ly elevatedpressures.Atagivenpressure,CO2 isamoreefficientpressure-induced pressure, andonwho,thetotalwater-vaporabundanceVenusfore=1.45case. Thaddeus (1963).Carryingouttheintegrationr =fadzovertheverticaldistance,z, section perunitvolume,k,ofaCO2-N2mixturederived fromdataofHo,Osborn,and 0.9 and1.6,respectively.Wecanconsiderthattheactualopticaldepthfortheseopacity large amountofwatervaporbelowthecloud.Inalaterpaperwewillconsidersuch ing low-temperaturecloudorascatteringlayer.Suchtwo-componentmodelsarise volume mixingratio,q,by surface pressureisrelatedtotheopticaldepth at 19mm,r(19mm),andtheCO2 sources islessthanone-thirdofthesevalues,viz.,r(19mm,H0)<0.5and opacity at19mm.ThisresultallowsustosetupperlimitsonP,thetotalsurface then attributetheradardeclinetoatmosphericattenuation,amodelincludingseveral with theMariner2results.Thedistributed-scattererandcloudmodelsaresuccessful generally by(TbCA)).Asaresult,thecontributionofgroundemissionisdiminished, and undertheassumptionsofanadiabaticlapse rateandT=700°K,wefindthe absorber thanN2.BarrettandStaelin(1964)give an expressionfortheabsorptioncross- For CO2-N2orwatervaportobethesolesourcesofopacity,r(19mm)wasfound naturally inthecaseofawatercloudcontainingliquiddroplets,sincetherewouldbe opacity sourceswouldthenseemtoberequiredaccountforbothsetsofresults:one optical depths,areinconsistentbythemselveswiththeMariner2observations.Ifwe ness temperaturesforthesemodels(cf.Table3).Ontheotherhand,wehaveseenabove cloud model. scattering doesnotgiveaspronouncedalimbdarkeningexp(-—r/V)inthe in the6(19mm)=3.6casebecauser(19issufficientlysmalltoallowalargecon- and theemissivitylimb-darkeningeffectissmall.Againbecauseofcontinuousdis- of r(19mm)isimpliedbythe8-mmbrightnesstemperatureobservationsandmore sorbers attenuateateachlevelintheatmosphere,alargevalueofr(8mm)andhence CO2-N2) <0.3. component wouldbeacontinuouslydistributedattenuator;theothereitheranabsorb- that continuouslydistributedatmosphericattenuators,whichcouldhavesuchlarge about unityat3.8cmandof41.9cm—farhigherthanallowedbythebright- with the€=3.6case,inwhichweattributedeclineradarcross-sectionat3.8cm ing fromthesubstantialtemperaturedifferencebetweencloudsandground.For tribution ofattenuators,theopacitylimbdarkeningistoosmalltoproduceagreement and lowere.Thesuccessofthemodelisaresultaneffectiver/¡jllimbdarkeningaris- to microwaveattenuation.Thelowcross-sectionwouldrequireanopticaldepthof tribution fromtheemissivitylimbdarkening.Thecloudmodelstillworksfore(19mm)= e =1.45,thescatterermodelisnotsuccessful,i.e.,AT^^jb)AZt,d). pendence parameters,weagainencounterthesamedifficultiesintrinsictounsuccess- opacity, aconclusionalreadyreachedfromanexaminationofthe8-mmphaseeffect temperature variesandtheatmosphereexperiencesnodiurnalchanges(cf. Ar(t,b) willbedecreasedmorethanAZ't,d)increased,andagreementwiththe and TbÍó)decreases.Thiscomesaboutintwoways,becauseofthevariationsurface CO2-N2, water-vapor,anddistributedabsorbingdustmodelsareunabletoreproducethe letting ^(Brewster)=700°K.Becauseoftheslant pathsinvolved,theresultswerein no increaseinTetowardtheBrewsterangle,and Tb(Brewster)<615°K.Totestthe reaches unityattheBrewsterangle,arctane.However, the19-mmobservationsshow from thecenterofdisk,withinterminator scan,e~e\\andwillincreaseuntilit force afitwithobservation.Accordingly,wereject thismodelasunsatisfactory. uniform opacity.Asweallowforsuchgradients,findthat,e.g.,Z^byT^t)> ful CO2-N2andwater-vapormodels.However,weherehavemorefreedomtovarythe conclude thatCO2-N2andwatervaporarenottheonlyimportantsourcesofmillimeter atmosphere aresubject,leadtodecreasedlimbdarkening,sincetheterminatorpeak ster) mustbelessthan700° Kbecauseofthepolewarddecreasesurfacetemperature— compatibility ofourtwosuccessfulmodels,wehave computedTb(Brewster)forthem, significantly decreased,andthevalueofAr(t,d) predictedbythemodelwillbemuch A7(t,b) intoagreementwithobservation.However,atthesametime,r(d)willbe values ofAr(t,d)andATß^b)forasubstantiallateraltemperaturegradientbut those betweendarksideandterminator.Thus,asweallowforanon-isothermalsurface, [cf. equation(5)].Ourestimateofthesurfacetemperaturevariation—given,e.g.,inTable the Cythereanatmosphere.Itisclearthat,regardlessofourchoicepressure-de- all casesinaccordwiththeobservationalupperlimit of615°K.Inactuality,T(Brew- absorbing dustmodelpossesses,extremedifficulties areencounteredinattemptingto lates theopticaldepthsattwolocalesonVenustocorrespondingsurfacetempera- smaller thanobserved.Evenwiththemanydegrees offreedomthatthedistributed tures andbrightnesstemperatures.ThesixthmodelentryinTable5showsthepredicted opacity withpositionovertheplanet.Mighttherebesomefelicitousdistributionofdust there mustbesubstantialtemperaturegradientsacrosstheplanet.Equation(12)re- a circumstancethatfurther lowersZ(Brewster)andstrengthensourconclusions. Thus, the successfulmodelsare compatiblewiththeabsenceofBrewsterhighlights. that securesagreementwiththeMariner2data?Foropacitytovarysignificantly, (Paper II). Z(b)/rt), andso,fromequation(12),r(b)>r(t).Itisthuspossibletobring i/ B i/i; B B B B s B B © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem In thenexttwoparagraphsweconsiderunsuccessfulCO2-N2,water-vapor,and Our comparisonofresultsissummarizedinTable5.ThesymbolsAJBCtjd)and The terminatorscanatitspeakseesessentiallye±(p =1)1).Aswescan Consider nowthemodelinwhichabsorbingdustisdistributedcontinuouslythrough MICROWAVE OBSERVATIONSOFVENUS 337 19 67ApJ. . .150 . .327P 336 center ofeachMariner2scan.Formodel,weinitiallyusethevaluer(19mm,t) suggested byTable3andtestwhetherityieldsavalueofTb(19mm,t)inagreement unsuccessful, werequireittofailreproducetheobservationsforallreasonablesurface surface. WeseefromTable5thatthevaluesofrin3leadtoacceptable manner, therejectionofamodelwillnotdependonvalidityotheranalyses,such estimate ofthesubsurfacetemperature.Thesamevaluewillalsoholdforanisothermal Predictions ofmodels: scatterer models,withintheconstraintsestablishedbyphaseeffect. neglect possiblesystematicvariationoftheamountattenuatorsoverbrightas as thepredictedvariationofTandwithpositiongiveninTable4.Weinitially temperature distributions—includingtheunlikelycaseofanisothermalsurface.Inthis the othertwoscanscanbereproduced;i.e.,weseekvaluesofT^b)andX^d)suchthat abundance ofattenuatorswithposition,fordistributed-absorberanddistributed- compared withthedarksidesofVenus.Wewilllaterconsidereffectsvarying the observedvaluesofTßCb)andTb(Í)areaccountedfor.Inorderforamodeltoprove with theobservedvalue.AccordingtoTable4,2^(19mm,t)700°Kourbest r(t). Withthisvalueofwenowaskwhethertheobservedbrightnesstemperature Observed byMariner2. sg B Absorbing dustwith5=0.4 Absorbing dustwith5=0 Absorbing cloudr=234°K Absorbing dustwith5=0 Distributed scatterers © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem c Using equation(11)andTable2,wecancalculatethebrightnesstemperatureat * Foranatmospherecompletelydecoupled fromthediurnalsurfacetemperaturevariation, f With40percentdepolarization. or CO2-N2mixture. or watervapor VI. COMPARISONOPTHEMODELSANDOBSERVATIONS Predicted andObservedValuesofr(19mm)(Tin°K) B JAMES B.POLLACKANDCARLSAGAN Estimates ofTand7^(19mm)Appropriate s for theMariner2Scans,Calculated from Ground-basedObservations Scan \3 6 Jl 45 13 6* 3 6 3 6f 3 6 1 45 1 45 1 45 6 6f 6 620 +45 885 +25 730 +5 TABLE 4 T(°K) TABLE 5 S 0 9 0 9 0 9 0 9 0 10 0 10 0 15 0 25 0 33 0 15 1 6 1 6 Ta(t) 700 700 700 700 700 700 700 700 700 700 700 700 T(l9 mm)(°K) T(d) g g 600 600 700 635 675 700 700 640 670 635 700 635 845+40 630 +60 700 +15 Tn(b) 800 800 700 835 700 700 700 740 730 795 760 725 595+35 T(t) B 580 580 590 580 575 575 590 590 595 595 595 590 105 +25 AT(t,d) B 120 105 105 105 105 105 105 45 45 45 45 65 Vol. 150 Ar(t,b) 85 +25 B 80 80 80 85 85 85 80 70 85 85 85 10 19 67ApJ. . .150 . .327P nw -2 -2 -1-2 pressions for1,<7^(8mm))willapproximatelyequalthetemperatureof from thephase-averagedbrightnesstemperatureat8mm,withwavelength,asdescribedbelow.InallothercasesaXvariationisneeded the sthpowerofpressure,n—3.6(1+s). and thewater-vaporabsorbermodelsalsoimplyaXscaling. to reproducetheobservedvaluesof(TbÍX))(BarrettandStaelin1964).TheCO2-N2 1.45, at(\)dependencelyingbetweenXandcanreproducetheobservedvariation s B We willcheckthesederivedvaluesbycomputingTb(19mm,t)andcomparingwith When theparametersdescribinglongitudinaland latitudinaltemperaturevariations we havegivenfourpossibleanalyticformsfor the surfacetemperaturedistribution. scan, usingground-basedobservationsatlongerwavelengths alone.InPapersIandII, the observedvalue. found. (Becauseofthelargeequator-to-poletemperature gradient,itisnotvalidtocon- Kuz’min 1965),respectively,thesurfacetemperature atthethreescanpositionsmaybe are assignedfromphase-effectobservationsandinterferometric observations(Clarkand sider onlythelongitudinaltemperaturegradient.) Thephase-effectobservationsalso of the19-mmradiationandtemperatureTat this levelforeachofthescans.Table4 permissible analyticformsofthesurfacetemperature distribution(PapersIandII). summarizes thesecalculations.Theerrorsgiven in thistablereflectthedifferences allow anestimatetobemadeofthedamping thermalwaveatthesubsurfacelevel We notethatthereisvery littleuncertaintyintheestimatesofTand Tforthe terminator point. g s g © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The opticaldepthat19mmfortheterminatorscan,r(19mm,t),maybeestimated The quantityr(19mm)isreadilyobtainedfromr(8byusingtheappropriate Table 3summarizesthevaluesofr(19mm,t)derivedinmanneroutlinedabove. We nowobtainestimatesofsurfaceandsubsurfacetemperaturesappropriateforeach 3 6 1 45 1 45. b) EstimatesofSurfaceTemperaturesAppropriatefortheMariner2Scans Dielectric (8-19 mm Constant Emitting Surface Levels) Estimates oft(19mm)atQuadraturefromEarth-based MICROWAVE OBSERVATIONSOFVENUS X-Depend- ENCE OFr 2 1 X-2 X“ X' Measurements oft(8mm) or Uniformly Dust (5=0) Absorbing CO2-N2 Mixed TABLE 3 Dust (s=04) or Uniformly Absorbing Mixed H2O 1 6 1 6 Model (r=234°K) c Isothermal Clouds 0 20 0 09 0 07 Distributed Arbitrarily Scatterers 0 15 0 12 0 35 335 19 67ApJ. . .150 . .327P 334 Rx denotesthereflectivityforEvectornormaltoplaneofincidence.Inturn,is plane. Forotherpositionsinthebeam,ewillbeahybridofe\\ande±withdominating. will alsobeconsidered.Forapointnearthecenterofbeamandforsmoothsurface, tions atlongerwavelengths(Carpenter1964;Evansetal.1966).However,theeffectsof a partiallyroughsurface,whichtendstoeliminatethelimbdarkeningdueemissivity, e inourequationsequalsßj.,theemissivitywithEvectornormaltoincident mm). mm) =1.45.Notethatthe3.6-cmradarresultsrefertoadepthaboutequal2(19 vations at12.5cmyieldavalueofe~3.6(Carpenter1964,1966),andsimilar,but related to¡xande,thedielectricconstant,throughFresnelequations.Radarobser- Fortunately, samplecalculationsindicatethatthebeam-averagedvalueofefallswithin wavelengths isacorrespondingdeclineinthedielectricconstant.Inthiscasee(3.6 ever, thereportedreflectivityat3.6cmis0.009±0.003(Karp,Morrow,andSmith cm) ^1.45.Otherinterpretationsofthelowreflectivityhavebeenproposed,however somewhat largervaluesarededucedfromthereflectivitiesatlongerwavelengths.How- measurement. Averyconservativesummaryoftheseobservationsisthattocomparewiththephase-effectobservations(cf. however, concernslargetemperaturegradients,asprobablyexist(PapersIandII). these modelscouldbemadetomatchtheMariner2observationstrivially,simplyby cloud, distributedscatterer,andabsorbermodels.Withoutsuchconstraints, for theilluminatedhemisphereofVenusisbetween 0°Kand120°higherthan(Tb If weaverageequations(3),(6),and(10)oversolidangles,obtaindisk-integrated some limitstobesetonT(b)/r(d)fortheisothermal cloud,distributedscatterer,and Vetukhnovskaya, Kuz’min,Kutuza,andSalomonovich(1964)byCopeland expect theopacitiestobeindependentofpositionondisk.Thecaseinterest, 1964). Oneinterpretation(PaperII)ofthedeclineinradarreflectivitytowardshorter Papers IandII). wavelengths, (T^b))800°Kand(T^d))~650° K(cf.PapersIandII)wefindthat distributed absorbermodels.Forexample,ifwe choose,fromobservationsatlonger 8-mm phaseeffectwiththetheoreticaldisk-averaged brightnesstemperaturespermits this crudeinformationonsurfacetemperatures, a comparisonoftheselimitsonthe Tyler (1964);theseobservationsagreewitheachotherwithintheprobableerrorsof (Paper II).Inourcalculationswewillemploybothvalues:6(19mm)=3.6,ande(19 e equation (4)whenwenotethatr(8mm)^>>1and so(Tb)—T(t=f). (8 mm))forthedarkside.At90°phaseangle,isabout425°K.Evenwith © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We assumeinitiallythatthesurfaceissmoothat1.9cm,inaccordwithradarobserva- The quantityej.(ju)isevaluatedasfollows:ByKirchhofFslaw,ex=1—R±,where Observations ofthevariationbrightnesstemperaturewithphaseangleat8-mm Recent measurementsofthe8-mmphaseeffecthavebeenmadebyBasharinov, The boundsonr(b)/r(d)forthedistributed-absorber modelfollowreadilyfrom V. OPACITIESANDTEMPERATURESFROMGROUND-BASEDOBSERVATIONS clouds: 0.7/r (d)]-. (12) s 8B Vol. 150 19 67ApJ. . .150 . .327P 1-1 We willassume,however,thatthedielectricconstantdoesnotvaryoverdisk. because theopacitymaybetemperature-dependent.Equation(5)givesexplicit No. 1,1967MICROWAVEOBSERVATIONSOFVENUS333 lower Tbonthedarksideandraiseitbrightside.Forremainingmodels dependence ofronTforCO2-N2mixturesandwatervapor.Thus,throughthe to ju“.Bothfactors1and3produceadecreaseofTbwithincreasing/z gradient ofsurfacetemperaturedirectly;sinceTisexpectedtobegreateronthebright judiciously choosingT(^,rj)forthesethreemodels,apointwediscussinmoredetaillater. vational data,itwouldbeatrivialproblemtoexplaintheMariner2observationsby cooling towardthepoles,willhelptolowerTbinbothhemispheres;but,forafixed temperature dependenceofopacity,alatitudinalsurface-temperaturegradient,with terminator temperature,alongitudinalgradientofsurfacetemperaturewillhelpto side, thiswilltenddirectlytoincreaseTbintheilluminatedhemisphere. the dependenceofopticaldepthonsurfacelocale.Iftherewerenootherrelevantobser- should beadequate. pression forTb(/z)isinsertedintoequation(1),weformallyobtain differs fromTb(m=Mo)byatmost25°K,anamount comparabletotheprobableerrors where Q(a)isalwaysslightlylessthanunity.InTable 2areshownthecomputedvalues where aisconstantand/zothevalueof/zatcenterbeam.Whenthisex- use thetemperatureatbeamcenterincalculations below.Thus,itispossibleto of measurement(cf.Table1),andfortheaccuracy ofthepresentproblem,equation(11) of Q(a)fortworepresentativevaluesa,and eachofthethreescans.ThusTb tures Tbtotheobservedpeakvalues.Weinitiallyneglectvariationsinground (absorbing dust,acloudlayer,andscatteringaerosol)thereisnoprioriconstrainton Paper Iwereemployed.Inallcasesthetwotemperatures agreedwithin10°K,wewill representations ofthevariationtemperaturewith positiononthediskasgivenin ground temperatureswoulddifferfromthevalue at thebeamcenter.Forthispurpose can berepresentedadequatelybyapower-lawdependenceon/z:Tb(/z)=TbGzoXm/mo)“, temperature andtheopacityoverbeamconsideronlyexplicitvariationof s We calculateTb(m=Mo), fromequation(11),determineafor¿x=no,and thenuse reduce considerablythe labor ofcomputingTbwithoutappreciableloss ofaccuracy. s s Tb with/z.Asisthecaseforinfraredlimbdarkening(PollackandSagan1965c),Tb(/z) Table 2tofindQ(a)and Tb. p p p p © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 3. Theequivalentatmosphericopticaldepthviewedbythespacecraftisproportional 4. Theatmosphericopticaldepthmayvarywithpositiononthedisk,forexample 2. Theremaybearealvariationofdielectricconstantwithpositiononthesurface. 5. AfinalfactorinfluencingthevariationofTbfromscantoislongitudinal We nowconsidertheuseofequation(1)torelatetheoreticalbrightnesstempera- Sample calculationsweremadetodetermineby whatamountthebeam-weighted d t . b. Scan Representative ValuesofQ(a) Tp =(mPo)Q(a),dU Bb 2 04 1 49 1 00 Mo TABLE 2 0 975 0 979 0 997 0 25 0 962 0 965 0 995 0 50