GEOP}!YSiCAI. RESEARCI! I.ETTERS, VOL. 17, NO. 10, PAGES I725-1728, SEPTEMBER 1990

NITR•EN ION CLU• IN TR1TON'S

Mona L Delitsky JetPropulsion Laboratory, California Institute of Technflogy,Pasadena, CA

Richard P. Tar•

Depaxtmentof Atnx)sphericSciences, University of California,Los Angeles, CA

Mark Z. Jacobson

Departmereof Atmo•h•c Sciences,University of California,Los Angeles, CA

Abstract. The formation of cluster ions composition,themodynamics and meteorologyof 's [•2*(•h, N*(N2)• shouldocmar easily in Triton'sthin cold atmosphere. •-•gen atmosphere.These ions are formed stepwiseas: •on Ch• As on , the interaction of cosmic-rays or At lowaltitudes, themaxxtynamics (temperature and press•) precipitatingmagnetospheric particles with nitrogem mo•u!es t avc•cluster sizes up to andincluding N2+0•2)4o. Such ions results in the formation of ions and neutral atoms: • closem the threshold(critical size) to nucleate,forming a •-'• Mtrogenice aerosolseen as exteadedhazes in Voyager N2+e* ---> N•+e+e (1) '• .mage•of Tri•n's limb.The critical ion radius for nucleation N2 + e* ---> N + + N + e+e is about 8.3 A. As temperatureincreases and pressure ....deranges with altitude, cluster ion formation becomes less The primaryions, N2+ and N+, are transformedinto f .;•bte and small clustersizes predominate. At altitudes largerions by clust•ing with N2 in a seriesof steps(Bobroe et >200•, clus• are thexmodynamical!yunstable and only al., 1969;HeadIcy et al., !982): •* :andN* am present.Because electron •bination with • 'runs(N +) is very slow,a denseionosp •here should form N2+ + N2+ M '-• N2+(N2)+ M •ere N* recombination via N* clustering with N2 is -•mfavorable. Model calculations yield peak electron coaceatra'uonsabove 200 kin, -asdetected by Voyagerradio ,oe••on measure•ts. The sha• ledgeat the bouomof N2+(N2)+ N2 + M • N2+(N2)2+ M (2) '•:-.•"maos•ea• is causedby the onsetof rapid electron-ion .., • .r•m•inaxkm•ted with cluster ion formation. N2+(N•+ N2+ M • N2+(N2)•t+M

The first close-upimages taken by of (speciessuch as N2+(N2)2can alsobe writtenN•+). Each ,•.:me's satelliteTriton revealeda thin, hazy atmosphere. forwardclusr•ing re,on sty: (k•) hasan associated reverse CIoMa,pa•ehes of fogand local amx•heaSc phenomena such dissociationreaction step (1•). Hence,the clusters will igrow vmting plumeswere obse•ed, •dicating that weather until they reach an equilibrium distribution of s•zes, •• oa thissatellite. The atmosphereis madeup mostlyof con-espondingto the local teanpemtum and pressure, in whi,•ch •..imgen,with small amountsof ,as predictedby cluster formation and thermal diq•odation rates are in .balance. -.••ank et al. (!983, 1984) six years earlier, and The resultingdistribution of cl.m• size•is gaussian-like,with •.• by 'theVoyager UVS experiment(Broadfoot et al. thepe• correspondingto the thermodymcally "pref--" •,•),These hazes and in theatmosp• resultfrom fluctuationsin the thermodynamicstate of the The thermodynamicsof nitrogencluster formation is •phem. which induce nitrogen to nucleate on ions describedby Hariokaand Nakajima (1988). The enthalpyof ,:•• bycosmic ray- or magnetospirit partiQe-induced formation of NJ from N2+ (reaction1) is very l'd•, 25.8 'ti•, or on solidparticles ejected by Tritons geysers. kcal/mol½,and the reactionis stronglyfavored at low paperdescri•s thenitrogen ion chemistrythat controls !m•aperatm'es.The forward rate coefficient is givenby Boh•r•e '•c composition,and may be responsive for the (!969) as1.9 x 10'e• cmS/mole•-sec at280K; a teanpexamm- dependentrate coefficient,1.7! x 10'2½ (300/T)I's Thevolat-fie - in • caseN2 and C• -- will tend cmS/mo!½c2-•c,was derived from the data of Boltme. Highex-ordexclusters have a lowerenthalpy of frm!mtion(for -,mupemunu,which is defied bythe radiative balance •pl½, 2.76kca!/mole for the clustering ofNJ ,.d-•,•s of Triton'satmosph•. The temuperature atthe theirentropy v•ues remainalmost cons.rant from oae s•ze to •• ofTriton w:as detcm•2ned to be roughly 37 K (Conruth tl• neat.Nev•½ss, higherclusters can • easilyform at i:'989),giving a nitr•ea sinfacevapor procure of about the cold temperams of Triton'slower atmo,•:•. The 10•!:'0 's bar, .and• ptussureof roughly 7x10 -m bar. As a •ui!ilxiam conrot for • dusmdngstep .'m givm by, of this:• of • press=cs,nitrogen d.omi• the

C•y•i•t 1990 by ,•he American Geophysical Union. whexeK2,, 'm .the .•uilibrium cons/mr for ..the .nth clust•g step,[ ] '•tes a concmtmti.on•m_too. numberß 90GL01732 Gi•bbsfree energychange for '•e reacfoa, • ka is the '•,-8276/90 / 9•L-0173250'3. •, Bo!tzmanncous-rot. it f .o!!owsfrom Eq. (3)

1725 1720 Dclit.,,k5ct ztl.: Nitrogen!on Clustersin Triton's Atmosphere clustersize increaseswith decreasingtemperature and interactionreduces the free energy of the cluster (see below) increasingnitrogen partial pressure, and thus varies rapidly andallows the formation of stableembryos. Heterogenm-m with altitude. nucleationof nitrogenabove geysers would produce locali• Clusteringreactions with N+ asthe coreion (K•,,•, hazes.Ion-induced nucleation could occur wherever clus•m n=l ....) yield a seriesof ionswith anodd number of nitrogen ionsare found, provided the atmosphere is sufficiently atoms -- N3*, Ns+,N7+, etc. This series of clusters has a supersaturated(perhaps as a resultof dynamicalforcing). slightlydifferent rate constant for formation(Bohme, 1969), Hence,global haze layers seen in theVoyager Triton irra•s but in generalbehaves similarly to the N2*-basedclusters. rnayhave theirorigin in ion nucleation. Recombinationof the N + seriesof ionswith electrons yields N The freeenergy expression for ion-inducednuclmti• atoms,which eventually recombine to form N2. However,as upona sphericalcluster of radiusr containingn nitrogen thisprocess is fairly slow,some build-up of N atomsin the molecules(noting that n=4/3•rr3p/mo, where p is thecluster Triton atmosphereis expected.In fact, ultravioletemissions densityand mo is the molecular mass of nitrogen)isgiven •, fromN* as well asN atomswere detected at thetop of the atmosphereby theVoyager UVS experiment(Broadfoot et al., - 1989). AG(r)=-nk•TlnS +4,nrr2o'+ /•-•X 1-••• •) Forward rate coefficients in each cluster series were whereri is the radiusof the ionic core of the cluster,wi-• assumedto be similarfor all clusteringsteps, being equal to chargeq, ande is thedielectric constant. The firstterm re•t• the valuesof Bohme(1969) for the initial N2 association the supersaturation(S), (i.e., theratio of thevap• •a reactionswith N2+ and N +. The reverserate coefficientswere pressureto the thermodynamicequilibrium va•r pressam calculatedusing the forward rate coefficient and equilibrium overthe bulkcondensed material) to thefree energy, aM t.M constantfor eachclustering step (see Eq. 3). The equilibrium second term takes into account the surface tension of constantswere calculatedusing the thermodynamicdata of nucleation embryo. Nitrogen has a much lower surf• Hariokaand N-_akajima (1989). Largeclusters have enthalpies tension(10.5 dynedcm) than does water (80 dyne/cm);•, and emropiesof reaction,AH andAS, respectively,that nucleationand particle fo,wnation is 'easier' in nitrogencl,-•s approachthe latentheat of condensationand the entropy than in water clouds under the same relative conditionsof change,respectively, for condensationof N2 (Harioka and supersaturation(i.e., the positive surface tension term in F•. 4 Nakajima,1988); the clustersare then actingas liquid is smaller for nitrogen). Since the radius of the clusteris surfacesfor N2condensation. Accordingly, all clust-erslarger always larger than the ionic core radius, the electrostatic thanN24' were assignedbulk valuesfor the enthalpyand conu-ibutionto the free energyis negative,and ion-irdm• entropyof formation. nucleati• is favoredover homogeneous nucleation. The clusteringof N atomswith N2+ was alsoincluded Tbeion-induced nucleation rate can be expressed m: usinga ramcoefficient of 2.5x10-29 cm6/molec2-sec at 300 K (Good, 1975). (The reaction was assumedto have a similar temperature-dependenceasfor clusteringreactions of N2 with j=/½[N2•(r,)Z(r a )Nia 'ex•.AG(ra)-AG(F*)] ksT (5) ions.)Charge exchange reaction rate coefficients (e.g., for N In thisequation, kc is the collisioncoefficient for N2 with + N2+ --> N + + N2) weretaken from Delitsky et al. (1989). clusters,r* is the critical size that a cluster must reach be• The recombination coefficient for N2+ ions with cannucleate and grow into a droplet,ra is theprefened clua• electronsis 3.5x10 -7(300fF) ø• cm3/nmlec-sec(Krasnopolsky, size (i.e., the maximumin the distributionof sizes),Z(r*) 1986). All cluster ion-electron recombination reactions were the Zeldovich factor (which is a correction for the s.• assumedto have a rate coefficientof 3.0x10-6(300,rI')ø-• departurefrom an equilibriumdistribution of clustersizes dm to nucleationof the largestions), Z(ra) accountsf•- crn3_hnolec--•. Atomic ion-electron recombination, occurring equilibriumdistribution of clustersizes, Nion is the at low pressuresvia photonemission, is at least 105 times ion concentration,and the exponential term t•es intoac•omt slowerthan molecular ion-electron dissociative recombination; thedifferen• in .freeenergy between the preferred clus• :• the N + recombinationcoefficient is ~10 '12 cm3/molec-sec. andthe critical size for nucleationand phase change; if Hence,N + losscan be dominated by clusteringto N2 followed differencein energiesis large,then the ion clustersare by electron/cluster-ionrecombination (- 10 -6 cm3/molec-sec). likelyto nucleateinto growing particles. They will simply• Ionsremain in thegas phase until they either recombine with andsubtract nitrogen molecules over time to changesi•s, • electronsor nucleateinto haze particles (see below). sothe duster distribution will eventuallyreach a steadystate. The Voyagerradio experiment measured an unprecedentedelectron concentration of about40,000/cm 3 at M•I Inputsa_r•l Calculations thepeak in theionosphere (Tyler et a1.,1989),compared with Cluster size distributions were calculated with a the peak in 's ionosphereof about3000/cm 3. Sucha st.and• Gearintegration package (Gear, 1969). The highelectron density was unexpected in the thin atmosphere of codeis designedto solvea set of stiff chemicalkinetic Triton. The formationof clusterions at low altitudes,and the •uations suchas those encountered in ionization p_robte :m. accumulationof atomicions (N +) at high altitudeswhere Thecomputations were run until equilibrium was achiev• clusterswill not form, can explainthese observations (see typicallywithin lx105 seconds(~1 day). The Results). atn•sphereused for thesecalculations has been taken frtan Ion Nucleation VoyagerUVS results(Broadfoot et a1.,1989). The Tdt• surfacetemperature is 37 K, decreasingto a tro•pau• A neutral can nucleate into an aerosol temperata_reof 32 K, andthen increasing to an exosff•-• homogeneouslywhen the partialpressure of the g• exceeds temperatureof 95 K above400 km. Atmosphericni•Qen the vaporpressure of the condensedphase by a substantial pani•press-• •re calculatedusing the hydrostatic equa• margin(a factorof 2 or more). The gasmay alsonucleate withthe gravity constant for Triton. Temperature-de•r heterogeneouslyonto the surfacesof solid pa•icles (which vapor pressuresof nitrogengas over might be injected into the atmosphereby geysers, for obt'•nedfrom t• AIP Hat,,•k (1972). example),or ontolarge cluster ions. Ion nucleationtheory is There•-e t'm•princi_pal sources of ionJ-zati•in Tn•.• reviewed by Keesee (1989). Generally, the fo.rmationof area>sphere:ch•ged particles precipitating from N•pm•'s aerosolson ions is aided by the electrostaticinteraction magnetosphere,an• photoionization.The magnet between'the core ion andthe impinginggas n•lecules; this clcctronsdrainate at low•titudes. Analysisof •tc• Dclitsk 5 ct z•l.: Nitrogen Ion Cluster• in Triton's Atmosphere I _

250 (79) 200 (73) 150(65)

50(4• 35(43) 25 (40) •0 (32) 0 (3•

species

Fig. 1. Variationin nitrogenion clustersizes in Triton'satmosphere as a functionof altitude.Near Triton's surface,large cluster sizes are favored at thevery cold temperatures found there; at 10km the peak size is roughly a: Ns,_+. The ion size distributionis well-resolvedonly aboveabout 25 km. As altitude(and temperature) increases,intermediate ion sizespredominate, as is seenbetween 25 and 100km. Clusterion formationis not fa•ored at higheraltitudes, leading to largeconcentrations of N + (andan equivalent electron content).

. earonspectra from the Voyager LECP experiment[Krimigis the nucleation(particle formation) rate is negligible. As the •.al. 1989]gives an energy input of 7.5x10-8 ergtcm3-secfor supersaturationincreases, the preferredion sizeincreases, the numberof critical-•izeclusters increases, and some nucleation e magnetosphericelectrons, and 4.1x10 -9 erg/cm3-secfor gneospheric protons at Triton's surface. This yields an canoccur (limited by the ratethat critical-size ions are formed from smallerclusters). As the preferredsize approachesthe .. proximateion-electron pair production rate of 1300/cm3-seccritical size, essentiallyall of the ions may nucleateinto brthe electrons and 71/cm3-sec forthe protons (A. Eviltar, growing particles; i.e., the thermodynamic barrier to personalcommunication). The ion pair productionrate is nucleation has been removed. •fitudedependent, and was scaledlinearly with pressure. To determine the radius of the critical-size clusters for Energy deposition rates for all other sources of ion nucleation,equation (21) from Keesee(1989) wassolved. 'onizafionon Triton -- due to solar photolysis, Nearthe surface of Triton,this cluster radius is around8.3 'nterplanetaryelectron impact, and cosmic ray bombardment-- which correspondsto an ion clusterNs2* (-- N2*[N2h0). ereobtained by scalingfrom the rateson Titan, correcting In the rangeof Triton's surfacetemperature of 37 K, or d/fferencesin atmospherictemperatures, pressures and nitrogenhas an extremelysteep vapor pressure dependence 'stancesfrom the sun. The energydeposition rates for Titan e gi,,enby Sagan and Thompson(1984). To scale the withtemperature. The vapor pressure at37 K is lx 10-5 bar ergydeposition accurately, altiitudes of equivalentnitrogen (10 pbar);at 34 K, thepressure is lx104 bar,and at 31 K, •erburden were calculated for the Titan and Triton lxlO -? bar. Accordingly,the local surfacetemperature on •-mospheres.The Titan atmosphereused in thesecalculations Triton needonly drop2-3 degreesKelvin for the atmosphere as obtained from Lellouch and Hunten (1987). The to suddenlyachieve a supersaturationof 10. The critical .1obally-a•eragedphotoionization rates of Sagan and cluster size and preferred cluster size are equal at a , mpson(1984) havebeen multiplied by a factorof four. supersaturationof about 6.5 (i.e.,at a temperatureof about 35 Reaction rate data were discussed in an earlier section. K). If an air parcelat thesurface of Tritoncooled from 37 to 35 K, then the nucleationrate (Eq. 5) would increasefrom Results zero (4x10-•4 particles/cm3-secat 36 K) to 5x10s Dgure 1 showsthe calculateddistribution of nitrogen particles•cm3-sec(at35 K). ß clt.s,er sizes as a function of altitude. The clusters are The tropopausealtitude of---9 km, with its minimum g nearthe surfacebecause the temperaturesare colder; temperature,is the point where haze particles are most likely to lersizea are more prevalent at higheraltitudes because the form by ion nucleation.This correlateswith the Voyager •peraturesare warmer. In the ionosphere, where observationthat haze layers occur in thelowest -10 km of ßemperatures axe (relatively) high and pressuresare low, Triton'satmosphere. The eruption of a geysercould generate ecludingcluster ion formation, only N* andN2* are present. a local disequilibrium by creating a high nitrogen Ho ever,N* is dominantbecause its electronrecombination supersaturationin the vicinity of thestabilizing plume. The •,. ½ntis 'some10 '• smallerthan that of N2*. nitrogenwould then condense on ejected particles, or nucleate Calculatedion clustersizes axe plotted in Figure 1 to onto ionsentrained into the plume. \• ' [-=N..*(N2)•?]. At low altitudes,the preferred cluster Figure2 givesthe calculated electron concentration as a •ze arelarger than N36'. The peakin theion sizedistribution functionof altitude,and compares the theoretical results v, ith r theconditions prevailing at theselower altitudes can be Voyagerradio occultation measurements (Tyler et al., 1989). cram.ted from thermodynamicrelationships given, for Thepredicted electron concentrations are< 103/cm• below 200 •ample,by keesee(1989). At low levelsof supersaturation, kmand increase almost two orders of magnitudeto4x 104/cm 3 e preferred cluster size is much smaller than the critical near350 km. The increaseis dueto thephotoionization of N2 •,a•tersize. Hence, essentially no •ons reach critical size and and N, whichcreates N *. The N* ionsrecombine very slov,ly 1728 Delitsky ctal.: Nitrogen Ion Clusters in Triton's Atmosphere

1,200 ion clusteringat the high temperaturesand low pres..•sm• prevailingabove 200 km.

ingress Acknowledgements.We are gratefulto R. G. 80O for his helpful explanationsof nucleationtheory, W. "' egress' '" Thompsonwho provided us with a detailedenergy profilefor Triton, and J. K. Lewfor his work on the andformatting of thispaper. We alsothank Jolm App•by 4OO Dan McCleese for their continuingencouragement support. 20O References

•- ,, ,, i ...... • , .., , I Bohme,D. K., Flowing afterglowstudies of ion-molec•ut½ 0 20,000 40,000 60,000 80,000 associationreactions, J. Chem.Phys., 51, 863, 1 electron(number/cm 3) Broadfoot,A.L., et al., Ultraviolet spectrometerobserv of Neptuneand Triton, Science,246, 1459, !989. Conrath,B., et al., Infraredobservations of the N• Fig. 2. Calculatedversus observe• electron density system,Science, 246, !454, 1989. profiles for Triton's atmosphere. Solid curves labeled Cruiksh•, D. P., R. H. Brown and R. N. Clark, 'ingress'and 'egress'are from Voyagerradio occultation surfaceand atmosphere of Triton,IAU 77 measurements(Tyler et al., 1989). Ingressoccultation was 'Natural Satellites',Ithaca, N.Y., July 1983. on the 'night' side of Triton, egresson the 'day' side. The Cmikshank,D. P., R. H. Brownand R. N. Cla•, N';• dotted curve is the calculated electron concentration. The on Triton, icarus, 58, 293, 1984. electron content is low at altitudes below 200 km due to the De•tsky, M. L., A. Eviatarand J. D. Richardson,A .• formationof ionclusters and their subsequent efficient cleon'on Triton plasma toms in 's magnet.osphere, recombination. Above 200 km, clusters can not form, and Geophys.Res. Len., 16, 215, 1989. atomic ions, N +, (and electrons) accumulate to form the Gear, C. W., The automaticintegration of stiff observedionosphere. differentialequations, in InformationProce•=i•, 68, edited by A.J.H. Mottel, pp. !87-193,: with e!ecuDns,and also very slowlyform clusterions at these Holland, Amsterdam, 1969. altitudes(>200 km), becauseof thehigh temperatures and low Good, A., Third-order ion-molecule clustering nitrogenpressures. Accordingly,our model predictsthe Chem. Rev, 75, 561, 1975. existenceof a denseionosphere above about 200 km. Small Harioka, K., and G. Nakajima, A determinationof variationsin temperaturehave a greateffect on the availablity stabilifiesof N2*(N2)n and O2+(N2),,with n=l-11 from of clusterions and, hence, predicted electron concentrations. measurementsof the gas-phaseion cquilibr'• d. C• The additionof methanereactions into the ion chemistry Phys., 88, 7709, 1988. scheme(using CH4 concentrationsdeduced from the UVS Head!ey,J. V., R. S. Mason and K. R. Jennings,K/• experiment)had no effecton thecalculated ion composition. equilibriaand diffusion of ionsproduced in N•, • Extrapolationof theUVS datayields a C!• concentrationof about102/cm 3 at theelectron ledge; a concentrationof more CO•, studiedas a functionof temperatureusing a •hi•- than 10•/cms would be neededto cause N + and electron pressurepulsed mass spectrometer•, J. C' Soc.,Faraday Trans. 1, 78, 933, 1982. depletion. Keesee,R. G., Nucleationand particle formation in .:the...:. The ionosphereis not a simpleChapman layer because atomsphere,J. Geophys.Res, 94, 14683, 1989. theionization rate does not havea steepcutoff at low alfit_,des. Kram•opolsky,V. A., P .•hotochemistryof t.he a•sp .her•s The sharpionization ledge at 200 kin, observedby Voyager,is ...and Venus, 334 pp, S•ger-Verlag, New-Y. associated with the onset of cluster ion formation, which 1986. rapidlydepletes electrons through electron-ion recombination. Krimigis, S. M., Hot plasmaand energeticparficl• Conclusions Neptune'smagnetosphere, Science, 246, 1483,1989• Lel!ouch, E., and D. M. Hunten, Titan at !) Nitrogencluster ion formationshould readily occur eng'mecaSngmodel, ESA Publication, ESI.AB 87- in Triton's thin, cold atmosphere. Solar ultraviolet !987. photoionizationand magnetosphericparticle bombardment Sagan, C., and W. R. Thompson,Productio• create the core ions, N2+ and N*, which accrete nitrogen condensa•onof organicgases in the atmo•:•h• moleculesto form larger ion clusters; e.g., N2+(N2)nand Titan.,Icarus, 59, !33, 19'84. N*(N2),,. Theseclustered ion speciesshould be dominant Tyler,G. L., et al., Voyagerradio science ob•.•_•rvat/m.l Wow about200 km in Triton'satmosphere. Neptuneand Triton, Science, 246, 1466, !989. 2) The verylow temperaturesof Triton'satmosphere implythat these clustered ions can nucleate into solid nitrogen particles,creating the extended visible hazes recorded in the i...... M2•L. Delitsky, JetPropulsion Laboratory, Voyagerirnages of Trimn'slimb. Suchhaze forrn•on is .•titute of Tec •hno!ogy,183-•1, Pasadena,CA 91 ! pre•cted to occurat alfit•es belowabout 10 km where R. P. Turco, Dept. of AtmosphericSc.ieac• sufficientnitrogen ropersaturation islikely m exist.At higher U•versityof California,Los Angdes, California •24., altitudes,cluster ions continueto form •t rcrrmlngaseous, M. Z. Jacobson,Dept. of Atmospheric andno nitrogenhazes are forecast. Universfly:of Ca•fomia, Los Angeles, Califomi'a 3) A _modelbased on thechemic-al k•etics of nim•gen

isprodu• by•omionization atth• altitudes,w-,•eh cre•es (Received April 9, 1990; revised July 12, 1990; accepted July 18, 199,0)