NONTHERMAL ESCAPEOF THE ATMOSPHERES OF VENUS, EARTH, AND MARS

BernieD. Shizgal• andGregory G. Arkos Department of Earth and Ocean Sciences, Universityof British Columbia, Vancouver, British Columbia, Canada

Abstract. Atmospheric loss from planetary atmo- sphere. The translationalenergy required for escape spheresis an importantgeophysical problem with impli- could be thermal energyand proportionalto the ambi- cations for planetary evolution. This is a multidisci- ent temperatureor the result of some collisionalpro- plinaryresearch field that requiresan expertisein a wide cessesenergizing the speciesabove thermal energies. range of subjectsincluding statisticalmechanics, fluid These collisionalprocesses, which include charge ex- mechanics,plasma physics, collision theory, and surface change and dissociativerecombination between ener- science.This paper is a reviewof the current stateof our getic ions, neutrals, and electrons, are referred to as understandingof atmosphericloss from the terrestrial nonthermalescape processes. We highlightthe similar- planets.A detailed discussionis provided of the basic itiesand differencesin the importantescape mechanisms conceptsrequired to understandthe processesoccurring on the terrestrialplanets and commenton applicationof in the high-altitudeportion of a planetaryatmosphere thesemechanisms to evolutionarytheories of the terres- referred to as the exosphere.Light atomic specieswith trial atmospheres.The emphasisin this paper is directed sufficienttranslational energy can escapefrom an atmo- toward the need to considerthe exosphereas collisional.

1. INTRODUCTION processesthat are referred to as nonthermal escape mechanisms.An example of such collisionalprocesses One of the more challengingmultidisciplinary prob- are collisionsbetween hot protonsand coolerhydrogen lems in geophysicsand atmosphericscience is the study atoms resulting in energetic hydrogen atoms that can of the evolutionand escapeof planetaryatmospheres. escape.There are many other nonthermal processes An atmosphereis boundincompletely to a planet by the includingphotodissociation, sputtering [Johnson, 1994], planetary gravitational field. At very high altitudes, and solar wind pickup. Hunten [1982] has provided a atomic speciesof low mass,such as hydrogenand he- comprehensivelist of the varioustypes of nonthermal lium, can attain speedsin excessof the escapespeed of processesthat occurin planetaryatmospheres. Since the the planet and escape,provided they suffer no further particledensities of the exosphereare small,an approx- collision.The escapeflux referred to as thermal escape imate model of the exosphere[Chamberlain, 1963] as- or Jeans[1925] escapedepends on the ambienttemper- sumesthat exosphericatoms move, without colliding, ature and occursover a range of altitudes where the under the influenceof the planetarygravitational field. atmosphereis approximatelycollisionless, which is in the The studyof exosphericprocesses and escapemech- vicinity of the exobase.The exobaseis the altitude for anismsfrom the planets is of considerableinterest to whichthe mean free path of atmosphericconstituents is planetary scientistsin their effort not only to better equal to the densityscale height and is defined in detail understandthe present state of planetaryatmospheres in section2. The region abovethe exobaseis referred to but also to model atmosphericevolution. This is a mul- as the exosphere.For Earth the exobaseis at approxi- tidisciplinarystudy which involvescoupling of different mately 500 km, and the exosphere,in the vicinityof the atmosphericregions in addition to the interactionof the exobase,is predominantlyatomic oxygen with hydrogen exospherewith the solarwind plasmaand the planetary and helium as minor species.Heavier speciessuch as surface.The expertiseof scientistsin atmosphericchem- oxygen,nitrogen, and carboncan escapefrom the atmo- istry and dynamics,ionospheric plasma properties, geol- spheresof the terrestrialplanets as a resultof collisional ogy and planetarysurface morphology, planetary mag- netic fields, the solar wind plasma, and other fields is required. •Also at Departmentof Chemistry,University of British There havebeen severalexcellent reviews which pro- Columbia, Vancouver, British Columbia, Canada. vide a good overviewof the basicconcepts involved in

Copyright1996 by the American GeophysicalUnion. Reviewsof Geophysics,34, 4 / November 1996 pages 483-505 8755-1209/96/96 RG-02213515.00 Paper number 96RG02213 ß 483 ß 484 ß Shizgaland Arkos:NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

the study of exospheres.The review by Chamberlain translationallyexcited. Some of the exothermicityof the [1963]provides a very detailedtheoretical description of reaction appearsas translationalenergy of the product the collisionlessexosphere. Several additional reviews atoms,and a large populationof energeticor hot atoms have been written by Hunten and Donahue [1976], Tin- is produced. sley[1978], Fahr and Shizgal[1983], Hunten [1982,1990], Hot oxygenatoms resulting from dissociativerecom- andMahajan and Kar [1990].This reviewis motivatedby bination were predicted to occur on both Mars and the need to emphasizethe importanceof nonthermal Venus by McElroy et al. [1982a] and Rodriguezet al. processesin planetary exospheresand to reconsider [1984]. The presenceof hot oxygenon Venus was con- currentexospheric models. This reviewis appropriateat firmed by the 130.4-nm measurementof the ultraviolet this time in view of upcomingmissions to Mars and the spectrometeron the Pioneer Venus Orbiter [Nagyet al., importantobservational constraints on theoreticalmod- 1981]. A hot corona of atomic oxygenhas also been els that the new data will provide.Our aim in this paper observedfor the terrestrialexosphere [Yee et al., 1980]. is to provide the geophysicscommunity with a back- Theoretical estimates of the nonthermal character and ground of the basic conceptsin exosphericphysics as extentof thesehot oxygencoronae in the exospheresof well as an understandingof the important outstanding the terrestrial planets have been provided by several researchproblems. While someof the topicscovered in researchers[Nagy and Cravens,1988; Nagy et al., 1995; the previousreviews are repeatedfor completeness,the Ip, 1988, 1990;Lammer and Bauer, 1991;Shematovich et main emphasisof this paper will be collisionalphenom- al., 1994]. Enhanced loss of hydrogenwith respect to ena and nonthermal processes.We provide an up-to- deuterium,as implied by the D/H ratio observedby the date review, and we cite primarily the most recent pa- Pioneer Venus Orbiter, if coupledwith an appropriate pers sinceabout 1980which impacton currentresearch lossof oxygen,may be indicativeof the lossof water. in this area. We refer the reader interested in the his- The observed Pioneer Venus Orbiter D/H ratio has led torical developmentof the subjectto the reviewsmen- to suggestionsthat an Earth equivalentocean of water tioned previouslyand the exhaustivereference lists con- existedon Venus in the distantpast and hasdissipated as tained in those works. a result of this loss of atomic hydrogen and oxygen. The presentunderstanding of planetaryexospheres is Other isotopicfractionations, such as the enrichmentof determinedlargely by satelliteand ground-basedobser- •SNover •4N on Mars,can be explainedon the basis of vationswhich are predominantlymeasurements of the similar nonthermalprocesses. emissionsof exosphericconstituents. These includeLy- Nonthermal processeshave also been employedin man a and Lyman • emissionsof atomic hydrogenat order to understanda discrepancyin the terrestrial he- 121.6nm and 102.6nm, respectively,emission of helium lium budget [Axford, 1968; Bates and McDowell, 1959; at 58.4 nm, and emissionof atomic oxygenat 130.4 nm. Lie-Svendsenet al., 1992].The productionof 4He is These observationsof the exospheretogether with in predominantlyfrom the radioactive decay of 238U,with situ massspectrometric measurements provide density anestimated flux of Fprod • (0.9-1.9)x 106 cm-2 s-• and temperatureprofiles of neutral and chargedconstit- [Torgerson,1989]. For helium the exosphericescape uents.For example,data from the Pioneer Venus large energy on Earth is approximately2.5 eV, and for a probe neutral mass spectrometerindicated an enrich- densityof 106 cm-3 andtemperature of 1000K at the ment of the deuteriumto hydrogen(D/H) ratio in the exobasethe thermal Jeans flux is Fj = 0.4 cm-2 s-• (see exosphereof Venus by a factor of 100 relative to the section2), so that Fprod/F J • (2.3-4.8)x 106.Clearly, terrestrialvalue [Donahueet al., 1982]. As discussedin the calculatedrate of outgassingof 4He is far greater section 3, this enrichment of deuterium relative to hy- than the loss due to thermal Jeans escape, and the drogenis believedto arisefrom the enhancedescape of atmospherichelium contentshould be far abovewhat is hydrogen due to nonthermal processes.Nonthermal observed.Furthermore, as helium is chemicallyinert, processesrefer to collisionsbetween exospheric species there are no reactive processesto accountfor the ob- and translationallyenergetic species (both ionsand elec- serveddiscrepancy. In order to reconcilethis, there must trons), generally of ionosphericorigin. This includes exist additional loss processeswhich remove helium processessuch as the collision of hot plasmaspheric from the atmosphere.Lie-Svendsen et al. [1992] and protonswith exospherichydrogen, H + + H -• H* + Lie-Svendsenand Rees[1996a, b] recentlystudied several H +, whicheffectively converts the energeticprotons to potential nonthermal mechanismsand suggestedthat translationallyexcited hydrogen atoms H*, with speeds the exothermiccharge exchange reaction He + + N2 --> in excessof the escape speed. Such nonthermal pro- He + N•- + 9 eV, originallyproposed by Maier [1968], cessesprovide an importantescape mechanism and also couldproduce He atomsof sufficientenergy for escape. make possiblethe escapeof heavier species,such as Given the importanceof nonthermalcollisional pro- oxygen,nitrogen, and carbon, for which the thermal cessesto many exosphericsituations, it is very clear that escape rate is very small. An important nonthermal exosphericconditions are determinedto a large extent processin the exospheresof Mars and Venus is the by collisionalprocesses and the collisionlessmodels have dissociativerecombination of O•- with electrons,that is, to be reconsidered. Nonthermal mechanisms are dis- O•- + e- -• O* + O*, with the productoxygen atoms cussedat length in section3, with emphasison the need 34, 4 / REVIEWSOF GEOPHYSICS Shizgaland Arkos' NONTHERMAL ESCAPEß 485

Escaping

Ballistic

Exobase -•

Satellite

CollisionlessExosphere Hydrodynamic Expansion

BOLTZMANN EQUATION

Collisionless models Fluid Models

Kn-o:,o K_n=l Kn--,•)

Figure 1. Regimesof validityfor hydrodynamicsand kinetic theoryversus the Knudsennumber, Kn = l/H. The hydrodynamicexpansion of the atmospherewith radial velocity u(r) is shown on the right. The collisionlessexosphere [Chamberlain, 1963], characterized by differentparticle classes, is depictedon the left. Collisionlesskinetic theory modelsare valid in the limit Kn -• c•, whereashydrodynamic models are valid when the mean free path is very smalland Kn --• O. The Boltzmannequation of kinetictheory is valid for the whole range of Knudsennumber.

to reconsidertheoretical models of the exosphereto Scherer,1973; Fahr and Shizgal, 1983], and planetary include collisionalprocesses in a consistentmanner. In magnetospheresalso exists, although the conditions particular,the classicmodel of thermal or Jeansescape there are more nearly collisionlessthan for the dense will be addressedin terms of a collisionalapproach, in (primordial) atmospheres.Figure 1 is a depiction of contrastto the standardview of a thermal evaporative these different physicalsituations. The diagram on the processfrom an exobase. left showsa planet surroundedby a thick atmosphere, Thermal and nonthermal escape mechanismsare above which is a collisionlessexosphere with particles basedon kinetictheory and individualparticle dynamics. executingescaping, ballistic, and satelliteorbits [Cham- An alternative model of atmosphericloss whereby the berlain, 1963;Fahr and Shizgal,1983]. The diagram on atmosphereis viewed as a dense fluid which expands the right showsa fluid-like atmosphereexpanding radi- radially outwardhas alsobeen employed.This approach ally outward.The bottom portion of Figure 1 refers to is analogousto the solar and polar wind expansions the different theoretical approachesemployed to de- [Chamberlain,1961; Parker, 1965; Banks and Holzer, scribeatmospheric loss and is discussedlater. 1968; Axford, 1968; Brandt, 1970; Hundhausen, 1972; The important interactionof the solar wind with the Lemaireand Scherer,1973]. The polar wind refers to the lossof terrestrialH + andHe + alongopen magnetic field exospheresof Venus and Mars, with no or vanishingly lines at high latitudes.These fluid-like expansionsare smallplanetary magnetic fields, is presentedin section4. basedon the hydrodynamicequations of fluid mechan- The solar wind plasma can penetrate deep into the ics.Such models have recently been employedto explain extendedexospheres of theseplanets, ionize the neutral the observedisotopic fractionations on Mars and Venus speciesthere, and sweep them up in the embedded [Huntenet al., 1987;Zahnle and Kasting,1986; Zahnle et interplanetarymagnetic field. Severalprocesses, includ- al., 1990;Pepin, 1991, 1992, 1994]. An important theo- ing scavenging,mass loading, and sputtering, are dis- retical problemis the reconciliationof kinetic theoryand cussedin detail. Nonthermal escape of helium from hydrodynamicmodels of an expandingexosphere. An Mars arisingfrom the interactionof the solar wind and analogousproblem in other areasof geophysics,notably the Martian ionospherehas been discussedby Barabash models of the solar and polar winds [Lemaire and et al. [1995]. The solar wind penetratesdeep into the 486 ß Shizgal and Arkos: NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

corona,and He + ionsare picked up andswept out of the nonthermalprocesses and will provide the impetusfor atmosphere. the further developmentof theoreticalmodels of atmo- The impact of nonthermal processesin planetary sphericevolution and planetaryclimate change. exosphereson the developmentof evolutionarymodels In section2 we presenta brief overviewof exospheric is discussedin section 5. As already mentioned, the theory [Chamberlain,1963]. This is a kinetic theory Pioneer Venus Orbiter measurements of D/H enrich- description,based on particle distributionfunctions, and ment on Venus have led to the suggestionof a layer of could be extended to include collisionalprocesses as water tensto hundredsof metersthick in the distantpast discussedby Fahr and Shizgal[1983]. The importantidea [Donahue, 1995]. For Mars a similar history of past of diffusion-limitedflux in the lower part of the atmo- water abundancehas been suggested[Squyres and Kast- sphere as controlling the escapeis also presented.In ing, 1994], based on estimatesof water abundanceand section 3 the important role of nonthermal processes, surfacemorphology from satellite data [Pollacket al., which is the main emphasisof the paper, is discussed. 1987], Earth-basedspectroscopy of HDO [Owenet al., Section4 is devotedto the important interactionof the 1988], and measurementsof isotopic fractionation of solarwind with the extendedcorona of energizedor hot gasestrapped in shergottite-nakhlite-chassignite(SNC) atoms of Mars and Venus. The implicationsof atmo- meteorites[Pepin, 1991; McSween, 1994]. However, the sphericloss to the understandingof the evolutionof the processeswhich have led to the loss of water on Mars atmospheresof the terrestrial planets and climate are and Venus appear to be somewhatdifferent. Venus briefly discussedin section5. probably had its water primarily in the form of water vapor [Hunten,1993] because of the higheratmospheric and surfacetemperatures. This large amount of atmo- 2. AN OVERVIEW OF THE EXOSPHERIC sphericwater vapor would have created a densepopu- PROBLEM: A TUTORIAL lation of atomic hydrogen via photodissociation,and conditionswould have been favorablefor bulk hydrody- 2.1. CollisionlessExosphere: Thermal Escape namic loss.This processhas been suggestedto explain The basicconcepts of planetaryatmospheric escape both the observedisotopic fractionation of noble gases were givenby Jeans [1925] and extendedto the collision- and the removalof large amountsof hydrogenand thus, less thermal escapemodel by Chamberlain[1963] and possibly,water. Unless exospherictemperatures were Chamberlainand Hunten [1987].The lowerregion of the higher in the past than today, it appearsthat thermal atmospherewhere turbulent mixing of gasesleads to a escape is, in general, negligible on Venus. On Mars, homogenouscomposition is called the homosphere. nonthermaland thermal processesmay haveboth played Above this region, turbulencebecomes less important a large role in removing much of the original water, relative to molecular diffusion as a form of vertical possiblyaided by impact erosion early in the planet's transport, and the vertical distributionof individual at- history [Hunten, 1993; Squyresand Kasting,1994]. It is mospheric gases is determined by their respective still uncertainwhether the relative escaperates of H and masses.In this region, called the heterosphere,the den- O correspondstoichiometrically to the escapeof water sityprofile hi(r) of the ith constituentis determinedby [Fox, 1993a]. Another important indication of atmo- the balanceof gravityand gaspressure. The equationfor spheric evolution is the observedpatterns of isotopic hydrostaticequilibrium [Bauer, 1973; Banks and Kock- fractionationin the noble gasesof the terrestrial atmo- arts,1973], dpi = GMnimidr/r2, togetherwith the ideal spheres.Their deviationfrom the patternsfound in the gas law, P i = n ikT, can be integratedto give the baro- solarwind and meteoritesimpart importantinformation metric densityvariation with radial distancer, and constraintson the historyof atmosphericevolution [Hunten et al., 1987; Zahnle et al., 1990;Pepin, 1991]. This review is important in view of the upcoming n,(r)- n,(ro)exp Hiir) Hi(to)rø1 (1) international effort to observe both the surface and where G is the gravitationalconstant, M is the planetary atmosphereof Mars. The Martian neutral atmosphere, mass,m i is the molecularmass of the ith species,and r 0 ionosphere,and the solar wind plasma interactionwill is some reference level. A constant temperature T is be measuredby instrumentsaboard satellitesto Mars assumedin the derivationof (1). Each speciesis distrib- toward the end of the decade. These include Planet B uted accordingto its own scaleheight, defined by [Tsuruda and Yamamoto, 1995] and Mars 96 and 98 [Zakharov,1994]. Some of the plannedmissions to Mars Hi(r) = kTr2/GMmi= kT/mig(r) (2) involve experimentsto obtain signaturesof the hot co- where k is the Boltzmann constantand #(r) is the ronae in the Martian exosphere[Nagy and C•;avens, gravitational acceleration.If we set r = r 0 + z and 1988]. Additional measurementswill be obtainedwith expand the first term of the exponentialup to linear the Hubble SpaceTelescope and instrumentsaboard the terms in z, we find the exponentialdensity profile, Mars Surveyorand Pathfinderorbiter/lander pairs to be launchedin 1996 and 1998, respectively.These satellite 11i(r)= 11i(rO)exp missionswill collectivelyyield important informationon H,(r0) (3) 34, 4 / REVIEWSOF GEOPHYSICS Shizgal and Arkos: NONTHERMAL ESCAPEß 487

The atmosphericscale height in (2) shouldbe distin- TABLE 1. Planetary Escape Velocities and Energies guishedfrom the pressurescale height Hpi = d In Planet rc, km Vesc•km s- 1 E H.... eV Eesc'0 eV n i/dz + d In T/dz which includesthe effectof a varying temperature.The exobaseor criticallevel r c is definedas Earth 500 10.8 0.61 9.69 the altitude for which the mean free path, the average Venus 200 10.2 0.54 8.64 distancebetween particle collisions,given by Mars 250 4.8 0.12 1.91 l - 1/x/•n(r (4) is equal to the barometric scale height of the major low exospherictemperature. For Venus,thermal escape constituent,that is, l(rc) = H(rc). In (4), •r is the energy is insignificantat present, and nonthermal processes independentcollision cross section for collisionswith the (section3) play a dominant role. However, Donahue major constituent,and n is the total density. [1986] has discussedthe escapeof primordial atmo- In the standard model [Jeans,1925; Chamberlain, spheresfrom planetesimalsfor which Xc is small and 1963] the atmosphereabove the exobaseis considered Jeansflux is significant. collisionless,while below, it is collision dominated. Par- It is importantto note that in (7) the three-dimen- ticles that reach the exobase from below and move sionalvelocity integral is carriedout only over the upper upwardwith speedsin excessof the escapespeed given half of the velocityspace (0 -> 0). Sincethe Maxwellian by distributionfunction is isotropic,the flux would be zero if the lower hemisphereof the velocity spacewas in- Uesc-- N/2GM/F (S) cluded.This model of atmosphericescape is an oversim- will escapefrom the gravitationalfield of the planet. plification.The actual distributionfunction at the exo- This model assumesthat abovethe exobasethe particles base is not Maxwellian, because the escape process move on collision-freetrajectories determined by the preferentiallyremoves energetic particles and nonther- planetarygravitational field. The classificationof exo- mal processesintroduce them. The distributionthat sphericspecies into classesof particlessuch as ballistic, leads to an outward flow must include an anisotropic satellite,and escapingbased on this model is discussed part so that the drift velocityis givenby at length by Chamberlain[1963] and Fahr and Shizgal [1983] and is not repeated here. In these models a Maxwelliandistribution of particlevelocities u(r)- fLnisotropic (r,v)v dv (10) fmax(v)= n(m/2,rkr) 3/2exp [-mv2/2kr] (6) wherefanisotropic (r, v) dependson the velocity direction is assumedto exist at the exobase.The escapeflux of as well as the speed. It is reasonableto expect that particlesmoving radially outward at the criticallevel is escapingparticles originate not only from a singlealti- determinedby averagingover the outward directedve- tude at the exobasebut from a range of radial positions locityfor speedsgreater than the escapespeed, that is, in the vicinity of the exobase.Hence the escapeflux is F(r) = n(r)u(r), where u(r) is givenby (10) and de- pends on the radial position. The total escapeflux is F: = 27r fmaxCOS 0v 3 d(cos 0) dv (7) determinedby the integralof F(r) over a rangeof radial esc ='tr/2 distancesin the vicinity of the exobase.This picture of atmosphericescape, which considersboth thermal and so that the thermal or Jeansescape flux is given by nonthermalescape as collisionallyinduced phenomena, is discussedat greater length in section3. Fa-•- nc•2kTc (1+Xc)e -•c (8)2.2. HydrodynamicEscape In (8), Tc andn c are the temperatureand densityof the The thermalescape mechanism described by (8) is often escapingspecies at the exobase,respectively, and the referredto asevaporative escape. This impliesa process escapeparameter Xc is definedby with a flow speed,u(r)' = Ffin(r), which is very small relativeto the speedof sound,vs = X/•/kT/m,where hc = Eesc/kTc (9) • 2 The wherethe total energy for escapeis E esc = • mVesc- TABLE 2. Planetary Exospheric Values for Hydrogen escapespeeds and escapeenergies for H andO from the Escape terrestrialplanets are shownin Table 1. Mars, the small- est of the three, has the lowest escapeenergy. The Planet rc, km Tc, K )tc F/nc, cm S-1 escapeflux is determinedby the ratio of the escape energyrelative to the thermal energy,that is, by hc in Earth 500 1000 7.06 7.94 x 102 Venus 200 275 22.89 1.65 x 10 -4 (9). Table 2 comparesthe valuesof hc for the terrestrial Mars 250 300 4.65 3.39 x 102 planets.The very largevalue for Venus arisesfrom the 488 ß Shizgaland Arkos' NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

•l - Cp/Cv,the ratio of specificheats. For Earth's exo- wherethe massdensity p(r) = n(r)m. In (12), p(r) = spherewe find,using the datain Table2 andwith Vs• n(r)kT(r)is the hydrostaticpressure, assumed to be given 300 m s-1, that U/Vs• 0.027. Thiscan be compared bythe equation of state[Kundu, 1990]. If in (12)du/dr = 0, with the expansionof the solar atmosphere,which at theatmosphere isnot expanding, and we have the equation Earth orbit is supersonicwith a ratio of U/Vs• 1-1.5 of hydrostaticequilibrium used to derive(1) and(3). Equa- [Chamberlain,1961; Parker, 1965; Axford, 1968; Brandt, tions(12) and(13) do not includeviscous effects and an 1970; Hundhausen,1972; Lemaire and Scherer,1973]. anisotropicpressure tensor related to velocitygradients The exosphericmodel developed by Chamberlain[1960] [Chapmanand Cowling,1964; Kundu, 1990]. For a plan- for thesolar wind expansion gave a bulkflow at Earthorbit etaryatmosphere, energy transport occurs both from the that was lessthan observed.Lemaire and Scherer[1973] loweratmosphere and as solarEUV absorptionin the showedthat an exosphericmodel of the solarwind with middle-to-upperatmosphere [Watson et al., 1981].Many the correctself-consistent electric field gavea supersonic aspectsof hydrodynamicmodels applied to planetary flow speedin accordwith observations.A detailedre- atmosphereshave been discussedby Hunten [1979], view of the solarand polar wind theoriesis beyondthe Watsonet al. [1981],Zahnle and Kasting[1986], Kasting scopeof thisreview and hasbeen presented elsewhere and Pollack[1983], and Zahnleet al. [1990]. [Lemaireand Scherer,1973; Fahr andShizgal, 1983]. In Figure1 we contrastthe kineticand hydrodynamic The solarand polar winds are generallyconsidered to approachesto atmosphericescape with regardto the be fluid-like or hydrodynamicand can be describedby Knudsennumber, Kn = l/H. In the collision-dominated consideringthe equationsof hydrodynamicsrather than regimeat low altitudethe meanfree path is small,Kn << the particlepicture of the collisionlessexosphere. The 1, andthe hydrodynamic approach is valid. In thecollision- theoryof hydrodynamicescape of an atmosphere,as it lessregime at highaltitude the mean free path is extremely appliesto the solarwind, is describedin standardrefer- long,Kn >> 1, andthe independentparticle model with ences[Parker, 1958; Brandt, 1970; Hundhausen, 1972]. differentparticle classes is a goodapproximation. In order Similar hydrodynamicmodels have been used to de- to describephenomena over the whole range of Kn values scribethe lossof a planetaryatmosphere for whichthe the Boltzmannequation must be employed.However, the escapeparameter X• is smalland the flowspeed is large solutionof the Boltzmannequation over the wholerange [Watsonet al., 1981;Kasting and Pollack,1983]. Such of Knudsennumber is driftcult,especially for Kn • 1. largeflow speedsmay haveexisted during early plane- tary atmosphericformation, when hydrogenrich pro- 2.3. Diffusion-Limited Flux toatmospheresare exposedto highlevels of solarEUV The escapeof particlesfrom the exobaseis, under flux.Hydrodynamic models of atmosphericescape have certaincircumstances, determined by the flux from lower been usedto explainthe enrichmentof the isotopesof altitudesin the atmosphere.If the fluxfrom below is low, the noblegases [Hunten et al., 1987;Zahnle and Kasting, then the densityat the criticallevel is adjustedso that 1986; Zahnle et al., 1990]. the escapeflux at the exobaseis consistentwith the flux The basisfor the hydrodynamicformulation used to at lower altitudes. This important concept has been describeatmospheric expansions is the equationsof con- reviewedby Hunten [1990], who provideda detailed servationof mass,momentum, and energy [Chapman accountof the historicaldevelopment of what is referred and Cowling,1964; Kundu, 1990]. It is a contractionof to as diffusion-limitedflux. We follow the presentation the kinetictheory description based on the lower-order of Hunten[1973a, b] andHunten and Donahue[1976]. momentsof the nonequilibriumdistribution function. The verticalflux 4)of a minorcomponent (denoted by 1) The lower-order moments of the distribution function diffusingthrough a backgroundcomponent (denoted by are the density,n(r, t) = f f(r, t) dr; the bulk velocity, 2) is givenby Banksand Kockarts[1973], u(r, t) = (I/n) • v f(r, t) dr; and the temperature

3nkT(r,2 t) - • (m/2)[v - u(r, t)]2 f(r, t) dv. This correspondsto the five-momentmodels used by St. Mau- (b-- --DFtl•11• -I-'• --KFt 1•11 -•- -I-'•2e2 (14) rice and Schunk[1979] for a similardescription of ion- wherethe equilibriumscale heights are definedby osphericphenomena. For steadyflow in a spherical 1 mig (1 + o•) dT geometrythe conservationequations without massor = + He1 kT T dz energysources or sinksare 1 d 1 m2#1 dT (15) r2 dr (r2pu) - 0 (11) He2 k T T dz

du dp GM The first term of the right-handside of (14) representsa pu dr dr p r2 (12) flux due to molecular diffusion,where D is the molecular diffusion coefficient and o• is the thermal diffusion coef- 1 d GM ficient. The second term describes the contribution of r2 dr (r2pu) - pu r2 turbulentmixing to the verticalflux, where K is the eddy diffusioncoefficient. In the homosphere,K >> D, andin 34, 4 / REVIEWSOF GEOPHYSICS Shizgaland Arkos:NONTHERMAL ESCAPEß 489 the heterosphere,D >> K. At the boundaryof thesetwo specifiedby the mixing ratio there. If, for example, regionscalled the homopause,K • D so that both terms exospherictemperature is changed,the densityat the mustbe considered.The phenomenonof turbulentmix- exobase,n c, adjustsso that F s = 4)l. The densitydistri- ing is not well understood[Rodrigo et al., 1990], and bution of the minor speciesessentially follows the dis- valuesfor the eddy diffusioncoefficient K are uncertain, tributionof the backgroundsince f is nearlyconstant. If whereas the molecular diffusion coefficient D can be there is a lossmechanism in additionto thermalescape calculatedrigorously from kinetic theory [Chapmanand (see section3), then the sumof all escapefluxes would Cowling,1964]. In someapplications the eddy diffusion be equalto the limiting flux. As conditionschange, such coefficientserves as an adiustableparameter. Values of as the exospherictemperature, the contributionsfrom K have also been estimated from the distribution of each mechanismwill adjust,but the sum would remain minor species[l/on Zahn et al., 1980]. the same. The flux 4) can be expressedas a function of the mixing ratio, defined asf = n•/n2, and the gradient of the mixing ratio with altitude, df/dz. If we take the 3. COLLISIONAL NONTHERMAL PROCESSES logarithmicderivative of n • = fn2, we have that AND ATMOSPHERIC ESCAPE 1 dnl 1 1 The kinetic theory of nonthermal escapehas been nldz H/+H2 (16) previouslyreviewed by Fahr and Shizgal [1983], who wherewe have used Hœ- -f- • df/dz.If wenow define provided a very detailed accountof the literature to that the binarydiffusion parameter, b • = Dn2, and substitute date. Hunten [1982, 1990, 1993] has also presented a for n•-• dn•/dzfrom (16) into (14), we havethat personal and historical account of the introduction of nonthermal processesto explain the observationsof planetaryexospheres. In this paper we .willhighlight the 4)- blf t•2 H1+ • (Knl+ blf) (17) advances that have been made since about 1980 and refer the reader to the previousreviews for the literature If we usef = nl/n2 andreplace Hf by its definition,we have that prior to that date. However,there is someoverlap with the previous reviews in order to make the discussion af presentedhere reasonablycomplete. 4,= (in: + Nonthermal processesgenerally refer to collisional processesbetween exospheric constituents with charged In (18), speciesto produce atoms that are translationallyener- getic and incompletely thermalized. The charge ex- changereactions of energeticprotons or deuteriumions (I),- •2-2 1-•2 (19) with hydrogenor oxygen is the limiting flux, which for a light gas diffusingin a H + + H-• H* + H + (21) heavierbackground simplifies to H + + 0 -• H* + O + (22) 4)l• blf /m2 (20) D + + H-• D* + H + (23) Jeans escapeat the exobaserequires an adequate supplyof atoms from below, and in some instancesthe are prototypenonthermal processes. On Earth the pro- escapeflux is controlledby diffusionat lower altitudes.If tons are of ionosphericand/or plasmasphericorigin and diffusiveequilibrium exists and both densityprofiles are at a temperature of about 2000-10,000 K, whereas exo- barometric,then df/dz > 0 for m 2 >> m •, and 4) < 4)lß spherichydrogen is at about750-1250 K. Reaction(21) If the two componentsare completelymixed and they convertsthe cooler hydrogeninto a nonthermalpopu- follow the same densitydistribution, then f is constant lation of translationallyenergetic hydrogen atoms H* and 4) = 4)l. The exactsituation for a particularplane- that can escapewith an enhancedrate relative to the tary atmospherewill be somewherebetween these two thermalJeans escape rate. We presentin the firstpart of extremes. Hunten [1973b] and Hunten and Donahue this section an overview of several such nonthermal [1976] haveprovided a criterionas to whether a partic- processesthat occurin the atmospheresof the terrestrial ular situationcorresponds to the limiting flow situation planets. A more detailed discussionof the important or not. Applied to Earth, the limitingflux givenby (19) current theoretical issues follows later. The discussion of correspondsto a flow speedat the homopauseof Wh = the importantnonthermal process involving direct inter- D/H 2 • 1.4 cms -•. Table2 showsthat the flow speed action of the solarwind with the upper atmospheresof for Jeansescape is approximately8 x 102cm s -•. In this Mars and Venus is deferred to section4, as the physics caseit is clear that diffusionis the controllingprocess. of this processis somewhatdifferent from the collision- The flux throughoutthe atmosphereand at the exobase ally inducedprocesses discussed in this section. is equal to the value at the homopauselevel which is On Venus the chargeexchange reactions (21) and 490 ß Shizgaland Arkos' NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

scale heightsas shownin Figure 2. The scale heights 40-•

_ correspondedto different H atom populations,a ther-

_

_ mal componentat about150-275 K and densityl0 s cm-3 anda hot componentat approximately800-1500 16'0- K anda densityof 103cm -3 [Stewartet al., 1979;Takacs 8'0- et al., 1980]. 4.0-_T:1020øK • In additionto the chargeexchange reactions (21) to (23) other mechanismscan produce energeticatoms. The dissociativerecombination of O•-, 1.6- ,,,; "',,,• •N,x • Observe d O•- + e--• O* + O* (24)

0.8- ß • ,. • -. is an importantreaction for producingenergetic atomic 0'4- •• "' '.. - • -.. - • -.. oxygenon Earth, Venus, and Mars [McElroyand Yung, • '-... 1976;Yee and Hays, 1980;Knudsen, 1973, 1990;Zhang et 0.2 6 8 10 14 1 18 20 al., 1993a].Reaction (24) indirectlyproduces additional DistancefromCenter ofVenus, Rv (103 km) energetichydrogen and/or deuteriumby virtue of the elasticenergy transfer collisions Figure 2. Dual hydrogencorona of Venus obtainedby Mar- iner 5. The observedemission in kilorayleighsversus radial O* +H-•O+H* (25) position is fitted to a thermal componentat 275 K and a nonthermal componentat 1020 K (adapted from Anderson O* +D-•O+D* (26) [1976]). This combinationof processeshas been consideredas important escapemechanisms for H and D from Venus (23) are the dominant escapemechanisms since the [McElroyet al., 1982b].The hydrogenescape rate result- thermal escapeis very slow becauseof the low exo- ing from reaction (25) is estimatedby Rodriguezet al. spherictemperature; see (8) and Table 2. Reaction(22) [1984]to be about 8 x 106cm -2 s-1, whereasthe escape is not importantbecause the protondensity and temper- rateresulting from reaction (21) is 2.8 x 107cm -2 s-1 ature are low near the exobasewhere the oxygendensity [Hodgesand Tinsley,1986]. The energytransfer reaction is significant[Cravens et al., 1980;Hodges and Tinsley, (25) couldbe a significantcontribution to the escapeflux 1986]. The existenceof a population of energeticH for low ionospherictemperatures. A summary of the atomson Venuswas confirmedby observationswith the situation for Venus as obtained from theoretical models ultravioletphotometer on Mariner 5 [Barthet al., 1967; is shownin Figure 3. The densityprofiles of hot H and O Anderson,1976]. The Lyman ot emissionindicated an are shownrelative to the profilesof the thermal compo- altitudedependence characterized by two very different nentsand other constituents.In Figure 4 we showfor the Martian exospherethe calculateddensity profiles of hot H and O relative to the cold components.The detailsof the theoretical models are discussed later in this section. It is clear that both Venus and Mars have extended 1050- \ColdH ß coronaeof hot oxygen.There is an importantinteraction _

_ \ :, HotO of the exosphereswith the solar wind as discussedin 900- • , (Nagyet al., 1981) section4. Reaction (24) is also believedto be the im- _

_ \ portant mechanismfor the productionof translationally ß energeticoxygen on Earth. A hot oxygengeocorona has

750-_

600 Hot H 107 - 450 • : 106- ,, • '. ' Thermal oxygen

300 •,•• 104-•- '•- ...... Thermalhydrogen ß• 103- .,• 150 , , , , , , •o 102- 'M,,. ' Hotoxygen 2 3 4 5 6 7 8 9 102- a--'Ho• Logn (cm") 0 10'00 2(•00 3000 Figure 3. Altitude profiles of neutral atmosphericconstitu- Altitude (km) ents of Venus. The extended coronae of H and O were calcu- lated with theoreticalmodels (adapted from Luhmann [1986, Figure 4. The hot corona of Mars. Calculatedthermal and Figure W] with kind permissionfrom Kluwer AcademicPub- hot hydrogenand oxygendensity profiles (adapted from Nagy lishers). et al. [1990, Figure 6]). 34, 4 / REVIEWSOF GEOPHYSICS Shizgal and Arkos' NONTHERMAL ESCAPEß 491

TABLE 3. Variation of the Charge Exchange and Jeans Flux With Exospheric Temperature

T•, øK rc , km noc ' 107 cm-3 ni•,c 104cm -3 Fi•+,.a Fj F.+,./Fj F.+,i• + Fj

750 370 6.35 20.0 1.36 0.16 8.50 1.52 1000 450 5.00 8.7 0.82 0.73 1.10 1.55 1250 535 3.89 3.5 0.48 1.21 0.40 1.69 1500 615 3.17 1.6 0.30 2.33 0.13 2.63

Adapted from Shizgaland LindenfeM[1982]). aAll fluxesare in unitsof 10s cm-2 s-i; (rO,H= 33 x 10-16 cm2;(rH+,H = 50 x 10-16 cm2;nia+ = 2 X 104cm-3; and Ti•+ = 4000K. beenverified by measurements of the O+(2P) emission that the flux of hydrogenin all forms is equal to approx- at 731.9 nm by Yee et al. [1980] with estimatesof the imately1.5 x l0s cm-2 s-• independentof Tc.It isnow densityof hotoxygen of 10s cm-• at 550km. recognized[Chamberlain, 1977; Shizgaland Lindenfeld, Similar processesmay act to form hot coronae of 1982;Bertaux, 1975; Hodges et al., 1981;He, 1995] that other species.The dissociativerecombination process the charge exchangeinduced escapeflux from reaction (21) decreaseswith increasingexospheric temperature, N•- + e--• N + N (27) whereas the Jeans flux increaseswith increasingexo- can create a population of energeticnitrogen on Mars spherictemperature. The sum of the two fluxesis con- [Brinkmann,1971; Fox and Dalgarno, 1980, 1983; Ip, stant at about the limiting flux value at the homopause 1988, 1990;Lainmet and Bauer, 1991;Fox, 1993b].The and independentof exospherictemperature. massspectrometers on the Viking landersmeasured an This has been demonstratedvery clearly by Shizgal isotopicratio of 6.0 x 10-3 for •SN/•4N,which is about and Lindenfeld [1982], who employed a simple colli- 1.62 times the terrestrial value of 3.68 x 10-3. This sional model to obtain an expressionof the charge isotopic enhancementor fractionation of the heavier exchangeinduced flux that can be comparedwith the isotopewith respectto the lighter one is due to the fact thermalescape flux. They showed that the chargeex- that the energygiven to the productsis just enoughfor changeinduced escapeFce is given by the •4N to escapebut too smallfor the heavier•SN. Measurementsof suchisotopic fractionations yield sig- Fce- 1•. -'[-x/ 2k Tc / •T rn H e - Xc[(1 + 'r) - •1 + 're nificant information about early planetary volatile bud- (2s) getsand form importantconstraints on the development = 2kce•r+n•r of evolutionary models of the terrestrial atmospheres [Hodges,1993a; Pepin, 1994;Jakosky et al., 1994; Rich- where the important parameter is -r = Tc/Tr•+ - 1 and ards et al., 1994]. Another well-known example is the •r•+ is an effective density [Shizgaland Lindenfeld, enhancement of the D/H ratio on Venus over the ter- 1982]. For sufficientlylarge Tr•+/T c temperatureratios, restrial ratio recordedby the massspectrometer on the (28) givesa rate coefficientof the form Pioneer Venus Orbiter. With D/H valuesof 1.6 x 10-2 kce- 3.6 x 10-6 S-l/(1 -- Tc/T•+) (29) on Venus and 1.56 x 10-4 on Earth the ratio on Venus exceedsthat on Earth by a factor of 100 [Kastingand For Try+ = 4000 K and T c - 1000 K, this givesa value Pollack, 1983]. We addressthe evolutionaryaspects of of 4.8 x 10-6 s- • close to the estimate of 4.3 x 10-6 s- • this and other isotopicfractionations in section5. obtained by Bertaux [1975]. The variation of the charge Nonthermalprocesses have been consideredtheoret- exchangeflux versusexospheric temperature from Shiz- ically at some length by numerous researchers.The gal and LindenfeM [1982] is shown in Table 3 which chargeexchange reaction (21) was originallysuggested should be compared with the observationsof Bertaux by Cole [1966] and was reconsideredby Chamberlain [1975] reproducedin Figure 5. The main result in both [1977], Tinsley[1978], Kumar et al. [1978], Shizgaland casesis the increaseof the chargeexchange flux and the LindenfeM [1979], Cravenset al. [1980], Hodgeset al. decreaseof the thermal flux with decreasingexospheric [1981],Hodgesand Tinsley[1981],McElroy et al. [1982b], temperature, and the total flux remains essentiallycon- Shizgal[1985, 1987],Hodges and Breig[1991, 1993], and stant. This is consistent with the results of Liu and Hodges[1993a, 1994]. Donahue [1974a,b, c] and Yunget al. [1989], who dem- An importantfeature of the chargeexchange process onstratedthat the escapeflux should be approximately on Earth is the temperature dependenceof the charge 1.8 x 10-8 cm-2 s-•. The independenceof the escape exchangeinduced escaperelative to the Jeans escape. flux can be related to the result that hydrogenescape is The thermalflux (equation(8)) clearlyincreases with an diffusion-limited. increase in the exospherictemperature Tc. This is in The resultin (28) is an oversimplification,but it does conflict with the results obtained by Liu and Donahue illustratein a clearway the essentialconcepts involved in [1974a,b, c] and Hunten and Strobel[1974] and verified nonthermal escape.This result has been employed re- recentlyby Yunget al. [1989]which demonstrated clearly cently to interpret ground-basedBalmer ot observations 492 ß Shizgaland Arkos:NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

15 their velocity so as to preclude their escape.Since the density decreasesapproximately barometrically (see 14 (3)), the rate of collisionsdecreases with increasing 13 altitude, and hence the population of translationally 12- energized particles decreases.However, with the de-

11- creasein the densitythe mean free path increases,and the probabilityof escapeincreases. Hence the rate of 10- ",,,F•=kn•H• escapeas a functionof altitudeattains a maximumvalue 9- that occursin the vicinity of the exobase.We can write •,, // 8- the total escapeflux as an integral over radial position, that is, 7-

6- 5- Ftotal-frlF(r)dr (30) 4- T,, (Kø) In (30), r0 is some radial positionin the atmosphere 3 5900 1000 ;oo •4D0T• (Kø) where escapeis zero, and F(r) is the total production rate of energeticatoms escapingfrom radial positionr Figure 5. The terrestrial Jeans escapeflux Fj and charge and given by exchangeflux Fce versusexospheric temperature Tc. The two curvesfor Fj, indicated by solid and dashedcurves, are for slightlydifferent schemes used in the Lyman a data reduction. p(r, v)Q(r, v)dv (31) The total flux,Fj + Fce, denotedby squares,is nearlyconstant F(r)=ff over the temperaturerange considered (adapted from Bertaux [1975]). where Q(r, v) is the velocitydependent production rate of energetic particles at radial position r. The other quantity,p(r, v), is the probabilitythat a particlewith speedv at positionr will escapeand has a weak depen- of geocoronalhydrogen [Kerr et al., 1993;He, 1995]. A denceon the speed.The explicitform ofp(r, v) is given more realistic model which includesthe actual density by LindenfeMand Shizgal[1979]. This quantitytakes into and temperatureprofiles was carried out by Maher and accountthe effect of the overlyingatmosphere above r Tinsley[1977]. Their estimatesof the escapefluxes for and whether the particle will suffer a further collision low and middlelatitudes are 1.5 x 108cm -2 s-•, in mitigatingescape. The probabilityfor escape,p(r, v), agreementwith the value obtainedby Shizgaland Lin- increasesto unity with altitude, whereasthe production denfeld[1982]. of energeticparticles through collisions,Q(r, v), de- The theoretical structure of the exospheremust be creaseswith altitude.The productionof fast particlesfor reconsidered in order to include these collisional non- escapeis enhancedby collisions,while the probabilityof thermal processes.The collisionlesspicture is not a true escapeis hindered by them. This involvesthe product reflection of the actual exosphere,although one could p(r, v)Q(r, v), and there is a maximumin the contri- considerthe exosphereas almost collisionlesswith in- bution to the total escapeflux as shownby the dashed frequent nonthermalcollisional processes as a first-or- curve in Figure 6. der perturbation,as done by Chamberlain[1977] and The rate of production of fast moving particlesde- Hodgesand Tinsley[1981]. The notionof an exobasethat pendson the rate of binary encountersbetween the two dividesthe atmospherediscontinuously between colli- collidingspecies and is given by sion-dominated(hydrodynamic) and collisionless (kinet- ic) regimes has to abandoned.The escape process Q(r, v) - n • (r)n2(r) shouldbe consideredas occurringfrom a range of alti- tudes above and below the exobase. These concepts were discussedby Shizgaland LindenfeM [1979] and emphasizedin the review by Fahr and Shizgal[1983]. ff v2)go'*(g,II)dft dv' (32) They originate in the older works of Biutner [1958], where the speciesdensities are n • (r) and n2(r) and the Jensen[1963], and Jockers[1970] and are found in the speciesdistribution functions are f•(r, v) and f2(r, v), recent papersby Johnson[1992, 1994]. respectively.If the distributionfunctions are Maxwellian The basic concept for nonthermal escape is that (see(6)) asused in the calculationof the thermalescape, translationallyenergetic species are producedby elastic the altitude dependencealso enters implicitly in termsof or reactivecollisions. These energeticparticles are mov- the temperatureprofile T(r). A major difficultyis that ing in all directions,but only those moving radially the distributionfunctions of nonthermalspecies are far outwardcan escape,provided they do not sufferfurther from equilibriumand the distributionfunctions are not collisionsthat change the direction and magnitude of Maxwellian. In (32), # is the relative velocity of the 34, 4 / REVIEWSOF GEOPHYSICS Shizgaland Arkos:NONTHERMAL ESCAPEß 493

10 with regard to the collisioncross section, and the nature \\ of the distribution functions that enter into the calcula- tion of the escapeflux. Density and temperatureprofiles are obtained from observationor atmosphericmodels. Collision crosssections are determinedtheoretically or from laboratoryexperiments. The distributionfunctions are determined from the solution of the Boltzmann equation or from Monte Carlo simulations.Observa-

4 ' I I I tions are then required to put a constrainton the theo- 0 1 2 3 4 retical modelsthat are constructedin this way. n2 (104cm '3) In recent years it has become increasinglyclear that the details of the collisionalprocess are important to Figure 6. Altitude variationof the thermal escapeflux. Solid curves are the density profiles of hydrogen (curve a) and determinequantitative escape fluxes. For example,the details of the cross sections for dissociative recombina- backgroundoxygen (curve b). The dashedcurve showsthe altitudedependence of the flux proportionalto the productof tion of O•- the hydrogenand oxygendensities and the escapeprobability 0•- + e---> O(3p) + O(3p) + 6.98 eV nilhop(r) (adaptedfrom Lindenfeldand Shizgal[1979, Figure 6] copyright(1979) with kind permissionfrom ElsevierScience -• O(3p) + O(•D) + 5.02 eV Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK). -• O('D) + O(1D) + 3.05 eV -• O(3p) + O(•S) + 2.79 eV collidingpair, 12 is the scatteringangle that givesthe orientationof the final relative velocityg' relative to the -• O(•D) + O(1S)+ 0.83 eV (33) initial relativevelocity g, and (r*(#, 12) is the differential remain uncertain [Guberman,1988, 1991; Fox, 1993a]. scatteringcross section, which describesthe details of a Sincethe escapeenergy for oxygenfrom Mars is 1.91 eV binary collision.The details of such a reactive binary (seeTable 1), only the first two channelsare important. collisionare shownin Figure 7 for the process(23). The Much of the dynamicalinformation for suchprocesses, distributionsin (32) are for the incomingparticles, and suchas the branchingratios of theseprocesses, is lack- the integrationis overthe velocityof the productH + ing, and the detailsof the crosssection for this process ion. Equation(32) thusgives the velocitydependent rate are necessary.An added complicationis that the colli- of productionof energeticD*. With the kinematicsof sion crosssections also dependon the vibrationalstate the collisionthe velocitiesof the products(v, v') can be of the molecularion [Yunget al., 1989;Guberman, 1987, related to the velocitiesof the reactants(v•, v2) so that 1988, 1991;Bates and Mitchell, 1991;Fox and Bougher, the final resultQ(r, v) is a functionof the velocityof the 1991;Gurwell and Yung,1993], and so the productionof translationallyenergetic D* atom. It is the angular de- fast oxygenatoms will also depend on the vibrational pendent differentialcross section (r*(#, 12) that is re- distributionfunction (which is not shown explicitlyin quired in (32), and whichmay play an importantrole in (32)). There are similaruncertainties in the correspond- the velocitydependence of Q(r, v). The angleindepen- ing dissociativerecombination reactions of N•- [Fox, dent total crosssection is O'tot(#)= f O'*(#, 12) dfi. 1993b];the majorchannel for N•- in the groundstate is This formulationof nonthermalescape, developed by theone that yields N(4S) and N(2D). Further details can LindenfeM and Shizgal [1979], Shizgaland LindenfeM be found in the recent paper by Fox [1993b]. [1982],and Shizgal [1985, 1987] is rigorousprovided that The theoreticaltreatment of the (H +, H) charge one has all the detailed informationwith regard to the exchangereaction is comparativelyeasy and can be densityand temperatureprofiles, dynamical information consideredto be quite standard,despite being imple- mented only recently [Shizgal,1985, 1987; Hodgesand Breig, 1991, 1993; Hodges, 1993b; Clarke and Shizgal, 1994].For the chargeexchange reactions (21) and (23), Shizgal[1985] pointed out that the approximationthat only large impact parameters contribute to the cross section(that is, that the proton trajectoryremains es- sentially linear during a collision and little energy is transferred)is incorrect.Detailed quantummechanical Figure 7. Schematicof a charge exchangebinary collision. differentialcross sections for the chargeexchange pro- D + and H enter into a collisionwith velocitiesVl and v2, cessare required to correctlydescribe the kinematicsof respectively.The productsof the collisionare H + and trans- the process[Shizgal, 1985, 1987;Hodges and Breig,1991, lationallyenergetic D* with relativevelocities v' and v, respec- 1993;Hodges, 1993a, 1994]. The approachbased on the tively. solution of the radial Schroedingerequation and the 494 ß Shizgaland Arkos:NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

calculationof the quantum mechanicalphase shifts is gain. The collisionoperator can be written in the form standardand well known in the chemicalphysics com- [Chapmanand Cowling,1964] munity [Rodbergand Thaler, 1967; Shizgal,1987]. The recentcalculations by Hedgesand Breig[1993] confirmed the earlier suggestionsby Shizgal[1985] that the simple linear trajectoryapproximation is invalidfor this system. 4f]--ff[f(v)f,aX(V2) Shizgal [1987] compared the escapefluxes for Venus ll)dll dv' (36) calculated with the exact differential cross section with the resultsfor the linear trajectoryapproximation. This where it is assumedthat the backgroundmoderator was also examinedby Clarke and Shizgal [1994] with speciesis in large excessand at equilibriumso that it is respectto the relaxationproperties of hot protonsin a describedby a Maxwellianf •uax. This assumptionimplies thermal bath of atomic hydrogen. that J[f] is a linear operator. The velocities of the Gurwelland Yung[1993] consideredthe productionof collidingparticles before and after a collisionare shown hot oxygenfrom dissociativerecombination (24) and the in Figure 7. The first term in the integral representsthe subsequentenergy transfer reactions (25) and (26). They gain of particles, whereas the second is the loss of employedaccurate analytic fits to the differential cross particles from a given interval. At equilibrium, in the sectionsfor these processes.The importance of the absenceof Q(r, v), the gain and lossare equal,detailed angular distributionof the products,as determined by balance exists, and the distribution function of the es- the differentialcross sections, is emphasizedin this pa- capingspecies f becomesMaxwellian. per. The distributionsof hot hydrogencalculated in this The Boltzmann equation takes into account, in a way for Venus did not yield temperaturesin goodagree- statisticalmanner, the cascadingor degradationin en- ment with the observedtwo-temperature exosphere. An ergy of hot atoms through a seriesof reversiblecolli- importantconsideration may involvethe partial thermal- sionalevents. This could be simulatedby Monte Carlo ization of the energeticatoms produced owing to colli- methods[Hedges, 1994]. Shizgaland LindenfeM [1979] sionswith other ambient species,such as atomic oxygen determinedthe solutionof such a Boltzmann equation on Earth and CO2 on Mars and Venus. This requiresa which includedthe departurefrom a Maxwellian distri- statisticalor kinetic theory treatment to take into ac- bution owing to the loss of energeticparticles due to count the thermalization processin competition with thermal escape.A brief outline for the use of the Boltz- chargeexchange reactions. Fahr and Shizgal[1983] and mann equation to take into account the competition Johnson[1994] have emphasizedthe need to considera betweenproduction of energeticparticles and thermal- detailed treatment of the collisionalprocesses with the ization with thermal ambient specieswas given several Boltzmann equation and realistic differentialcross sec- years later [Shizgal,1987]. A very similar approachfor tions. the thermal escapeproblem based on solutionsof the The rigorous kinetic theory treatment involves the Boltzmannequation was alsoreported by Stamneset al. solutionof the Boltzmannequation for the systemunder [1991].A Boltzmannequation analysis was also carried consideration.The Boltzmannequation for the distribu- out by Lie-Svendsenet al. [1992] and Lie-Svendsenand tion functionf(r, v) of somespecies that couldescape is Rees [1996a, b] in their recent study of the collisional given by productionof energetichelium from the reaction

of F He + + N2--->He* + N•- + 9 eV Ot+ ¾'•7rf + m--' Vvf- J[• + Q(r,v) (34) They employedan elastic,hard spherecross section to model the thermalization due to He-O collisions and The left-handside of (34) describesthe time and space suggestedthat the details of the differential crosswere evolution of the distribution function in the absence of not too important.The resultsof their calculationsindi- collisions,as determinedby diffusion(the term in v. X7rf) catedthat thischarge exchange mechanism is potentially and the planetarygravitational field (F/m).X7vf, where importantas a lossof He andthe resolution of the4He F = (GM/r2)r). On the right-handside the collision budget problem. The methodologyused in these calcu- operatorJ[f] describesthe effectsof thermalizingcolli- lationsis very similar to that employedpreviously in the sionsrestoring the distributionfunction to Maxwellian, solutionof the so-calledMilne problem [LindenfeMand in competitionwith the productionof fast atoms,Q(r, Shizgal,1983; Barrettet al., 1992; Barakat and Lemaire, v). A simplifiedlocal description of hot atomproduction 1990]. and thermalizationcan be obtainedfrom (34), Similar techniqueswere usedto studythe population Of/Ot= j[je] + Q(r, v) (35) of nonthermalO(3p) atomsin thethermosphere of the Earth [LindenfeMand Shizgal,1979], aswell as nonther- where the systemis assumedto be spatiallyhomoge- malO(•D) [Schmittet al., 1981]and hot N(4S)atoms neous and the effectsof gravity are neglected.The col- [Lie-Svendsenet al., 1991], although hard sphere cross lisionoperator is similarin form to (32), but there is also sectionswere generallyemployed for thermalizingcolli- a lossof atomsfrom a givenvelocity interval aswell as a sions.A similar studywas carried out by Shematevichet 34, 4 / REVIEWSOF GEOPHYSICS Shizgaland Arkos:NONTHERMAL ESCAPE ß 495 al. [1991], where they claim that there is a sufficient of Mars was also consideredby Ip [1988, 1990]. His populationof hot nitrogen atomsto have a significant treatment is also a Monte Carlo simulation and not a role in the odd nitrogen chemistryof the lower atmo- direct solution of the Boltzmann equation. As men- sphere.Sharma et al. [1996] have recently reported a tionedearlier, there are manyuncertainties in the dy- calculationof the energy distributionof fast nitrogen namicaland atmosphericparameters, and thesecalcula- atomsin the nighttimeterrestrial atmosphere. Our pri- tions only approximate the actual exosphere. maryinterest in thispaper is with regardto processesin Nevertheless,the existenceof an extendedoxygen co- the upper thermosphereand exosphere,and there is rona on both Venus and Mars is clear. It is far more only a minor overlap with these studiesin the lower extendedon Mars than on Venus owing to the smaller thermosphere.However, the techniquesfor the studyof gravitational field. There is considerable theoretical similarnonthermal process are of considerableinterest, work to be consideredto developquantitative models. and there is some potential couplingbetween the two Shematovichet al. [1994]presented a detailedkinetic regions. theoryanalysis of the formationof the oxygengeocorona Thesemethods based on a Boltzmannequation are fromdissociative recombination of O•- (reaction(24)) as rigorous.Other researchershave employed similar tech- well as from the reaction niquesthat havetheir originin radiativetransfer theory. Calculations based on the so-called two-stream model NO + + e--• N(4S)q- O(3p)q- 2.75 eV were carried out by Nagy and coworkers[Nagy et al., -• N(2D) + O(3p)+ 0.38 eV (37) 1981; Nagy and Cravens,1988] and reviewedrecently [Nagy et al., 1990]. The two-streammodel splits the Theyalso include the resonant charge exchange process distributionfunction in a plane-parallelatmosphere into O + +O-•O* +O + (38) two parts;one, f+(r, v), representsparticles moving upward,whereas the other,f-(r, v), representsparticles They beginwith a set of Boltzmann-typekinetic equa- movingdownward. This is a very simplifieddescription tionssimilar to (34), whichinclude source terms for the of the actual anisotropicvelocity distributionfunction. production of energetic oxygen atoms as well as the In the first paper [Nagyet al., 1981] theseworkers con- thermalization processes,and considereda stochastic/ sideredthe two-streamapproximation in addition to a Monte Carlo method of solution.Since they consider diffusionapproach to model the productionand ther- collisionsof hot oxygenwith thermal oxygen,the colli- malizationof hot oxygenin the Venus exosphere.The sion operator used in their approachis not linear, in thermalizationis with the ambient CO2, O, and H and contrastto (36). Solutionsof the nonlinearBoltzmann modeledby a hard spherecross section. Since the energy equation for the thermal escapeof a one-component distributionof the productoxygen atoms from dissocia- exospherewere provided by MerryfieM and Shizgal tive recombination is not known, this was modeled as a [1994].Marconi et al. [1996]carried out a detailedMonte Gaussianwith each productatom sharingthe available Carlo study of a one-componentescaping exosphere. energy. There are additional uncertainties with the Severalyears ago, Weinert and Shizgal[1987] considered model regardingthe ion and electrondensities and tem- a simple analytic solution of the nonlinear Boltzmann peratures.Nevertheless, their calculationsclearly indi- equation for a one-componentplanetary atmosphere. cated the existenceof an extendedoxygen corona on These considerations of the nonlinear Boltzmann are Venus.The PioneerVenus ultraviolet spectrometer ver- important, and the solutionsare difficultto obtain. ified, from signaturesof the O I resonancetriplet near Shematovichet al. [1994] showedthat the oxygen 130.4 nm, the existenceof a hot oxygen component geocoronais formed primarily by energizationof the above 350 km and extending out to 1500 km. These thermaloxygen component with superthermalO(•D) observationswere cautiouslyconfirmed by Venera 11 andO(•S) atomsproduced from 02 photodissociation observations[Bertaux et al., 1981]. Nagy and Cravens anddissociative recombination of O•- andNO+. At 600 [1988] employedmore realistic densityprofiles and a km the hot oxygenhas a temperatureof 4100 K and a differentvalue of the hard spherecross section which densityof 104 cm-3. Theirsolutions were valid through controls the rate of thermalization, and their revised the transitionregion of the atmospherein the vicinityof calculations lowered the estimated densities of hot at- the exobase.The measurementsby Yeeet al. [1980]and oms to givebetter agreementwith the observations. Hedin[1989] suggest that at 550km thetemperature of Lammerand Bauer [1991]carried out a Monte Carlo the neutral atmosphereis 4000-5000 K and the densities simulationof the oxygencorona on Mars that arises are of the order105-106 cm -3. Richardset al. [1994] from dissociativerecombination (reaction (24)) and es- suggestedthat there are numerous other sources of timatedthe escape flux of atomicoxygen at 6 x 106cm -2 terrestrialhot oxygenfrom the quenchingof metastable s- • correspondingto a lossof oxygenatoms at a rateof speciessuch as O+(2D), O+(•D), N+(2D), O+(2P), 0.14 kg s-•. The oxygenenergy distribution can be and vibrationallyexcited N 2 by atomicoxygen. representedby two Maxwellian distributionsat 850 K The theoreticaltreatment of nonthermalprocesses in and 7800 K with densitiesof 2 x 103 cm-3 and 1.5 x 104 the atmospheresof the terrestrialplanets requires cross- cm-3, respectively.The formation of theoxygen corona sectiondata for binary collisionsand temperatureand 496 ß Shizgaland Arkos:NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

densityprofiles (preferably global) including solar cycle Phobos 2 data, Mars does not appear to possessan variability.In addition,the nature of thenonequilibrium intrinsicmagnetic field, and they set the upper limit at distribution functions from below to well above the 2.2• 1022 G cm3. This is a verycontroversial subject and exobaseare requiredfrom solutionsof the appropriate a definitive conclusionregarding the intrinsic field of transportor Boltzmannequations. Observations are re- Mars may be forthcomingfrom the data from the up- quired to provide an importantconstraint on the theo- comingsatellite missions. retical models. The interaction of the solar wind plasmawith Mars and Venus is substantiallydifferent from the interaction with Earth. For Venus and Mars the interactionis pri- 4. SOLAR WIND INDUCED ESCAPE marily with the high-altitudeportion of the atmosphere and involves both neutral and charged species.For Mars and Venus have little or no planetarymagnetic Earth the interactionis predominantlywith the geomag- fields, in contrast to the Earth's moderate field with a netic field which deflectsthe flow around the planet. In magneticmoment of 8.06x 1025G cm3. The interaction all three cases the interaction results in the formation of of the solar wind with the strongmagnetic field of the a stationarybow shock.This regionis similarto a typical Earth resultsin the solar wind being largely deflected shockwave front, acting as a boundary or transitional around the planet. This resultsin a large standoffdis- region betweensupersonic and subsonicflow. In terms tance of the solar wind of about 10 Earth radii. By of the respectiveplanetary radii the bow shockis located contrast,the solar wind interactsdirectly with the iono- at 10 R e for Earth, whereasit is of the order of 1.2-1.5 spheresof Mars and Venusand perhapsa smallintrinsic planetary radii for Mars [Luhmann and Brace, 1991; magneticfield, so that the standoffdistance is much Luhmann et al., 1992b] and Venus [Breus,1986]. The smallerand of the order of 1.5 planetaryradii. Detailed positionof the bow shockdepends on many different reviewsof this subjectcan be found in the collectionof physicalconditions and is highlyvariable [Zhang et al., papersedited by Luhmannet al. [1992a,b] and Gombosi 1990]. The situation for Venus is much better under- [1993], as well as in SpaceScience Reviews, 55, 1-498, stoodthan for Mars primarilybecause of PioneerVenus 1991. data. An excellentdiscussion of the basicphysics of the The nature of the interiors of the terrestrial planets interaction of the solar wind with Venus and Mars has and the conditionsnecessary for a dynamoeffect leading been givenby Luhmann [1995]. to an intrinsicmagnetic field are beyondthe scopeof this The ionopauseis the upper boundaryof the thermal paper, and further detailscan be found elsewhere[Par- ionosphereand occurswhere the solar wind dynamic kinson,1983]. There is a wealth of data for the magnetic pressure is balanced by the thermal pressure of the field strengthin the vicinity of Earth, some for Venus ionosphericplasma. The location of the ionopauseis primarily from the Pioneer Venus Mission,and a little highlyvariable, dependingon many factors.At Venus it for Mars from Mars 2, 3, and 5 and Phobos 2. Russell is between an altitude of about 300 and 400 km most of [1978]estimates the magneticmoment of Venus at 6.5 x the time during solar cyclemaximum [Breus, 1986; Lu- 1022 G cm3. The situation for Mars is uncertain and hmann,1986; Mahajan and Magr, 1990;Brace and Kliore, controversial[Nagy et al., 1995]. Hanson and Mantas 1991; Luhmann et al., 1992b], while for Mars it can [1988] analyzedthe Martian electrontemperature pro- estimated at about 400 km [Shinagawaand Cravens, files obtained from Viking retardingpotential analyzer 1988, 1989, 1992;Lammer and Bauer, 1992;Ip, 1992;Ip data and concludedthat the data do not uniquelyestab- et al., 1994]. The thicknessof the ionopausefor both lish whether the magneticfield is intrinsic or induced. planets is of the order of several tens of kilometers. Axford [1991]estimates the magneticmoment of Mars at There is some evidence that for Mars the thermal ion- 0.5 X 1022 G cm3. Slavin and Holzer [1982] estimate the osphericpressure is at times insufficientto balancethe Martianmagnetic moment at 2.6x 1022 G cm3. Vaisberg solar wind dynamicpressure, and the ionopauseis not [1992] has provided a history of the estimatesof the clearly defined [Hansonand Mantas, 1988; Luhmann, intrinsicmagnetic moments of Mars whichhover around 1995].Between the bow shockand the ionopauseis the 2 x 1022G cm3. Dolginov and Zhuzgov [1991] estimate a ionosheath(or magnetosheath). Martianmagnetic moment of 1.22x 1022 G cm3. Lam- The solar wind interaction with the atmospheresof merand Bauer [1992] suggest an upperlimit at somewhat Mars and Venus alters the conditions of the atmo- lessthan 10 22 G cm3 froma simulationof theheavy ion spheres,which in turn affectsthe shockedsolar wind in escapefrom Mars. Krymskiieta!. [1995]have very re- the magnetosheath.For example,the ionizationof the cently suggested,from an examinationof the observed neutral atmosphereby the solarwind plasma(or solar electrondensity profiles, that Mars musthave an intrin- photons)results in ions that producecurrents which sicmagnetic field. A weak intrinsicmagnetic field would deflect the solar wind plasma. The neutrals that have make the profiles depend on the zenith angle and also been ionized can be acceleratedfrom an escapingtra- on the magneticlatitude and longitudedefined by the jectoryback into the atmosphere.These accelerated ions intrinsicfield. Trotignonet al. [1996] suggestthat from of planetary origin can collide and energize neutral their studyof solar wind measurementsnear Mars with particles into escapingtrajectories. This process,re- 34, 4 / REVIEWSOF GEOPHYSICS Shizgaland Arkos:NONTHERMAL ESCAPEß 497

interplanetary magneticfield Solar photoion radiation "pickup"by solar wind

WindSolar 4X/X7' . [?'_ tail

"precipitating"photoion-- / arnospheric/ Ionosphere neural atoms

Figure8. Schematicof the solarwind interactionwith Venus and Mars and the solarwind inducedescape of ions. Ions producedin the region of solarwind by photoionizationand/or chargeexchange are either removedby the solarwind or redirectedinto the lower atmosphere(adapted from Luhmann and Kozyra [1991]). ferred to asknock on, is analogousto the energytransfer mann and Kozyra[1991], is a depictionof the interaction processesdiscussed in section3 [Cooperet al., 1984]. If of the solar wind and Venus and shows the ionosheath the incident energy of an ion is high, there can be a (or magnetosheath)between the ionopauseand the bow degradation or thermalization due to a successionof shock.Neutral atomsare ionized, executehelical type chargeexchange collisions that cyclethrough ionization trajectorieswith very large Larmor radii, and are swept and neutralization. out of the atmosphereby the solarwind magneticfield. A theoreticaltreatment of the solarwind-atmosphere The main topic of interestin the presentpaper is the interaction must considerboth systems,the solar wind way in which this interactionleads to the lossof atmo- and the atmosphere,simultaneously. The models often sphericconstituents. This can be significant,since the usedto studythis interactionare mainly fluid modelsof hydrogenand oxygencoronae of the planets,discussed the solarwind [Tanaka, 1995;Murawski and Steinolfson, in section3, extendto largeradial distancesand the solar 1996],and excellentreviews have been provided recently wind plasmaextends to fairly low altitudes.In either case by Johnson[1994], Luhmann et al. [1992b], and Breus the extendedhot coronaeof these planetsextend well [1986]. Johnson[1994] and Shapiroet al. [1995] have beyond the ionopause,and a strong solar wind-iono- emphasizedkinetic theory aspectsof the interactionand sphere interaction is to be expected.There can be a other associatedphysical processes such as sputtering. significantatmospheric loss as a consequenceof this Luhmann and Kozyra [1991] consideredthe interaction interaction. of the solarwind plasmawith the exospheresof Venus The main mechanismfor lossof atmosphericconstit- and Mars with regardto the scavengingof planetaryions uents appearsto be the ionization of the neutral atmo- and the associatedproblem of the heating of the iono- sphere by photoionization,by impact with solar wind sphere,leading to anomalousplasma density and tem- electrons,or by charge exchangewith solar wind ions perature profiles.They employeda combinationof the such as reaction (22). The product ion can then be hydrodynamicmodel of Spreiterand Stahara[1980] for capturedin the solar interplanetarymagnetic field and the solar wind and the exosphericmodels of Nagy and sweptaway from the planet and/or acceleratedin the v x Cravens[1988]. The energy loss of a fast oxygenion B drift. The accelerated ion can also reenter the atmo- passingthrough a backgroundof neutral oxygenis sim- sphere and transfer its energy to a neutral atom in a ulated with a Monte Carlo scheme. The models of the subsequentcollision. This processhas been referred to extendedexospheric coronae of the planets,such as the as sputtering[Johnson, 1994], in analogyto a similar hot oxygen coronae of Mars and Venus, are almost laboratoryprocess when a plasma is in contactwith a collisionless. These different treatments of these two metal surface.As pointed out by Johnson[1994], the interactingsystems, the solar wind and the exosphere, correct treatment of this nonequilibriumprocess re- shouldbe reconsidered.Figure 8, adapted from Luh- quires the solution of the Boltzmann equation. The 498 ß Shizgal and Arkos: NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

details of the energytransfer processesrequire the ap- reiterate that energeticO + formed by ionizationof propriate set of collisioncross sections. neutral O in the hot coronaof Mars can be pickedup by The processby which atmosphericions become an the magneticfield lines of the solarwind and that this is integral part of the solar wind plasma is referred to as a significantloss mechanism. They also add that the loss massloading [Breus,1986; Breus et al., 1989;Dubinin et of 36Arand 38Ar, 2øNe and 22Ne, and •4N and •SN is even al., 1994] in the sensethat additional mass has been more significantowing to their increasedabundance at added to the solar wind. In more quantitative terms it the exobase.Jakosky et al. constructelaborate evolu- implies that the continuity equation for the hydrody- tionary models and consider the fractionation of the namicdescription of the solarwind (equation(11)) must isotopesof theinert gases as well as that of •60, •80, •2C, be augmented by a source term to account for the and•3C. They find that the solarwind induced escape additional massof planetary origin. This mass-loading does not account for any significantfractionation of effect and the escapeof the planetary atmospherehave 180/160 or of 13C/12C.Of interestis their conclusionthat an important effect on both the exosphereand the solar a period of hydrodynamicescape is not required to wind. reproducethe fractionation of 36Ar/38Ar. Luhmann et al. [1992b] and Luhmann [1995] have provided an excellentoverview of the interaction of the solar wind with Mars and Venus. The situation for 5. EVOLUTIONARY ASPECTS OF NONTHERMAL Venus was reviewedby Luhmann [1986], and a discus- ESCAPE FOR VENUS AND MARS sion of the mass-loadingeffect was presentedby Breus [1986].Comparisons between available satellite data and Nonthermal processesin planetary exospheres,re- theoreticalmodels were provided.There is somediscus- viewed in Sections 3 and 4, have an impact on the sion by Breus[1986] as to the applicabilityof magneto- evolution of planetary atmospheres.Evolutionary pro- hydrodynamic(MHD) theory to massloading, that is, cessesinvolve the interplay of numerousphenomena in the interactionof a fluid-like(though rarefied) plasma of severaldifferent disciplines.The most difficult aspectis the solar wind and an extended, nearly collisionless, the extrapolation of present-day observationsto the planetary corona.The conclusionwas that MHD theory distant past on geologictimescales. One of several ex- can provide usefulmodels of the solarwind-atmosphere tremely important items is the evolutionaryhistory of interaction.Ip et al. [1994] studiedthe effect of charge the Sun and the variabilityover time of its EUV output. exchangeas a lossprocess for solarwind protonsinter- In this sectionwe review recent discussionsof possible acting with the exosphereof Mars and demonstrated scenariosof evolutionfor the atmospheresand surfaces that this processaffects the formation of the planeto- of Mars and Venus and, in particular, the question of pause-magnetopauseboundary. They mention that a whether water existed in abundanceon either planet. quantitativeassessment would require a kinetic simula- We presentthis subjectnot as activepractitioners in this tion of the solar wind-Mars interaction and the colli- extremelydifficult and controversialarea but rather as sional losseffect by chargeexchange. interestedbystanders with researchinterests that over- The interaction of the solar wind with the Martian lap work in the field. exospherecan lead to a significantloss of oxygen.As As discussedin the introduction and in section 3, the mentionedpreviously, this could be an important mech- Pioneer Venus Orbiter determined that Venus has a anism for the loss of water if the net loss of oxygenis D/H ratio approximately100 times that of Earth. This accompaniedby the appropriate stoichiometricloss of value hasbeen confirmedusing Earth-based observation hydrogen.The original inventoryof water on Mars could of HDO and H20 absorptionspectra [De Berghet al., be equivalentto severaltens of kilometersin depth or 1991]. If Venus and Earth both developedwith similar more. The oxygenatoms in the Martian exosphereare initial D/H ratios, this would seem to indicate that dur- convertedto ionsby photoionization,electron impact, or ing early atmosphericevolution, Venus had over 100 charge exchange.The ions are swept out by the solar times its present amount of water. The mixing ratio of wind or reenter the atmospherewhere they can sputter waterin thelower Venusian atmosphere (about 10 -4 by neutralsfrom near the exobase(see Figure 8) [Luhmann volume) can be used to calculatea rough global water and Kozyra,1991]. Luhmann et al. [1992c]and Zhang et inventory for present day Venus of about 0.0014% of al. [1993a,b] have estimatedthe oxygenloss rates from that of Earth [Kastingand Pollack, 1983].When consid- Mars. Typical resultsfor the neutral oxygenescape rate ered in addition to the D/H ratio, this seemsto suggest andO + pickupare of 8 x 1025O atomss- • and6 x 1024 that Venus had an initial volumeof water of only 0.14% ionss -•, respectively.These energetic O + ionsreimpact of that of Earth. It has been argued that Venus could the exobaseand create additional energetic neutral O have had a much lower initial budget of water due to its thatis ejectedat a rateof 3 x 1023 O atomss-•. These accretion from dessicated materials in the much warmer estimatesare very model dependent. region of the solar nebula near the Sun [Lewis, 1970; Jakoskyet al. [1994] have presenteda detailed study Lewis and Kreimendahl,1980]. The gradient of mean of the solarwind inducedescape from Mars and the way planetarydensities does provide someevidence that the this process can lead to isotopic fractionation. They initial bulk compositionsof the terrestrial planets may 34, 4 / REVIEWSOF GEOPHYSICS Shizgal and Arkos: NONTHERMAL ESCAPEß 499 not havebeen uniform [Hunten,1993]. The view of a wet tration may not be indicativeof the value during forma- Venus was also questionedby Grinspoon[1987, 1993], tion of the initial atmosphere[Hunten, 1993]. A constant who suggestedthat Venus may exist in a steadystate deuterium concentration would result in higher D/H with regardto water, with volcanicoutgassing or impacts ratios than are currently observedand would increase of volatilerich bodies (such as comets) providing a water the implied early volume of water on Venus or Mars. source with an enhanced D/H ratio. He attributes the Since the D/H ratio is sensitive to initial deuterium current D/H ratio to a signatureof some catastrophic concentrations,processes which may enhancethe escape injectionof water into the atmospherefollowed by mas- of both deuterium and hydrogenmust be closelyexam- sive fractionatingescape (possiblydiffusion limited) ined, as discussedin section 3. Hunten [1990] has re- within the last billion years,rather than to a signatureof viewedpublished estimates of the globallyaveraged hy- a primordialocean. However, most explanations offered drogen flux from Venus for various nonthermal to accountfor the measuredD/H ratio seem to imply a processes,and currentvalues are at about (0.2-2.7) x higherwater contenton Venus in the past. 107cm -2 s-•. It mayhave been 1000 times larger in an The standardview of Martian atmosphericevolution early atmospheremuch richer in hydrogen[Kasting and [Fanaleet al., 1992; Squyreset al., 1992;Hunten, 1993] Pollack, 1983]. Deuterium escapevia the analogousre- has Mars much as it is today for the last 3 Gyr: a thin action (23) is thoughtto be approximatelyone tenth as atmosphereof predominantlyCO2 with someamount of efficient [Kastingand Pollack, 1983]. McElroy et al. water incorporatedinto the regolith as permafrostor [1982b] estimated the escape flux of hydrogen from frozen at the polar capsbut with abundantliquid water Venusfrom dissociativerecombination of O•- and sub- before about 3.5 Gyr ago [Jakoskyand Jones, 1994]. sequentenergy transfer to hydrogen(processes (24)- Recently, there have been suggestions[Kerr, 1993; (26))at 8 x 106cm -2 s-•. Thehydrogen escape flux due Hunten,1993] of cyclicwarming over the lastfew billions to chargeexchange with hot protons (reaction (21)) is of years on Mars to explainobserved surface morphol- approximately1.2 x 107cm -2 s-1 [Kumaret al., 1983]. ogy. These theorieshypothesize massive outgassing of The combined effect of these loss processesis only CO2 to increasethe surfacepressure to the point that sufficientto removeapproximately 40 cm of water plan- liquid water is stableand estimatethat an equivalentof etwide [Huntenet al., 1989;Atreya et al., 1989].On Mars, a planetwidelayer of water a few hundredmeters deep estimatesof the hydrogenescape flux are in the rangeof is released.If at least someof the observedmorphology (1-2) x 108cm -2 s-• [Barthet al., 1972;Anderson, 1974]. of the Martian surfaceis relativelyrecent (<3 Gyr), a Kastingand Pollack [1983] mention that the escapeof significantamount of water must be availablefor ex- hydrogenis only one aspectof the problem of loss of changewith the surfacefrom subsurface,polar cap, and water. Oxygenmust alsobe removedat a rate consistent atmosphericreservoirs, since the amount of water re- with the stoichiometryof water. This is particularlydif- quired to form these featurescould not have escaped ficult on Venus where the escapeenergy of suchmassive from the planet in the time sinceformation, given the constituentsis high.McElroy et al. [1982a]estimated the availableloss mechanisms[Squyres et al., 1992]. How- averageescape flux of oxygendue to ionizationof ther- ever, there are many other factorswhich complicatean mal and nonthermaloxygen atoms above the Venusian estimate of the current Martian water reservoir. For plasmapauseand subsequentpickup by the solarwind at example,it hasbeen noted [Kieffer et al., 1992;Kieffer and 6 x 106cm -2 s-•. Thisis approximatelyhalf the hydro- Zent, 1992] that changesin Martian obliquity strongly gen escaperate and implies that the hydrogenand affect the amount and distribution of absorbed solar oxygenloss is equivalentto the lossof water. This loss radiation and can subsequentlyhave important effects rate, however, would account for only the loss of a on the exchangeof volatilesbetween surface and atmo- fraction of an Earth equivalent ocean of water. The sphericreservoirs. model of massivehydrogen loss by hydrodynamicescape The lossof water from an atmosphereis stronglytied duringearly atmosphereformation such as employedby to the breakdownand escapeof hydrogenousconstitu- Kastingand Pollack [1983] to remove water does not ents.The photodissociationof watervapor in the middle addressthe removal of the oxygenthat is left behind. It or upper atmospherefollowed by the escapeof hydro- has been suggestedthat the excessoxygen could react gen,if accompaniedby the appropriateloss of oxygen,is with iron in crustalrocks or early magmas[Watson et al., the suggestedprincipal mechanism for the lossof water. 1981; Kastingand Pollack, 1983]. The rate of surface The excessoxygen could be lost from the atmosphereor rejuvenationand the level of geologicactivity required removedthrough reactions with gasesin the atmosphere for sucha processhave been questioned[Kasting and or compoundsat the planet'ssurface [Kasting and Pol- Pollack, 1983; Richardsonet al., 1984]. Recent radar lack, 1983].The interpretationof measuredD/H ratiosis imagingresults from Venera and Magellan spacecraft basedon the assumptionthat the amountof deuterium appearto indicatewidespread and relativelyrecent geo- in a planetaryatmosphere has remainedroughly con- logic and volcanic activity on Venus [Hunten, 1993], stant from early atmosphericformation. However, cur- althoughit is unclearwhether theseprocesses have been rent modelsof atmosphericescape indicate that there is sufficientlyvigorous over geologictimescales to absorb some escapeof deuterium,and so the presentconcen- the required excessoxygen. 500 ß Shizgaland Arkos:NONTHERMAL ESCAPE 34, 4 / REVIEWSOF GEOPHYSICS

Other mechanismsnot requiring sinks similar to [Kastingand Pollack, 1983]. The hydrodynamicformula- those of the crustal incorporation model have been tion of the escapeproblem was describedin section2.2. suggestedto augmentthe removalof water. Richardson This hydrodynamicdrag-induced escape has important et al. [1984] investigatedthe reaction consequencesfor isotopicfractionations observed in the noble gaseson Venus, Earth, and Mars. CO + H20--> CO2 + H2 The various theories to explain both Martian and Venusianatmospheric evolution are stronglyinfluenced which links the removal of oxygento the availabilityof by the efficiencyat which water loss processeshave carbon monoxide.However, it is necessaryto postulate operated over the evolution of their respectiveatmo- C/H ratios of the order of 5 times that of Earth in order spheres.Many of the current limits on the history and to create a sufficientatmospheric CO abundance.Bauer abundanceof Martian water are implied from D/H mea- [1983]and Hunten [1993]both mentionthe possibilityof surementsfrom Earth and of SNC meteorites[Owen et a solar T Tauri phase,which could have enhancedhy- al., 1988;Pepin, 1991, 1992, 1994] and alsofrom analysis drodynamicescape of heavierspecies through increased of imagesof surfacemorphology from past missionsto EUV outputin additionto increasingdirect mass loss by the planet, mostnotably the Viking missions[Pollack et photoionizationof neutralsand subsequentincorpora- al., 1987]. For Venus the strikingly large D/H ratio tion into the much more activesolar wind (see section recordedby the PioneerVenus Orbiter (and confirmed 4). The removalof oxygenfrom Mars is more straight- by Earth-basedobservations) is the primary constraint forward than for Venus because of the much lower on the modelingof past water abundances.Images and escapeenergy. As we can see from comparisonsof the data from upcomingMars missionswill help to resolve requiredescape energy in Table 1, both thermal oxygen many of the current uncertaintiesin geologicinterpre- and hot oxygengenerated by the chargeexchange reac- tation and atmosphericmodeling which make it difficult tion givenby process(24) can escapedirectly from the to commentwith certaintyon the originsof the observed upperatmosphere of Mars.McElroy [1972], Lammer and featuresof Mars [Kerr,1993]. The improvedconstraints Bauer [1991],and Fox [1993a]estimated the escapeflux on some of the model parameters may also aid the of oxygenfrom Mars at (6-7) x 107cm -2 s-1, 6 x 106 interpretationof atmosphericevolution on Venus. cm-2 s-1, and3 x 106cm -2 s-1, respectively.The latter The noble gasesare important indicatorsof atmo- two estimatesare significantlyless than half the hydro- sphericevolutionary history. With the exceptionof he- gen escapeflux. Other mechanismsfor the removal of lium, the noble gases are too heavy to have escaped oxygenthrough sputteringand the interactionwith the thermally from the terrestrial atmospheresover a time- solar wind have also been proposed [Luhmann and scalecomparable with the age of the solarsystem. They Kozyra,1991; Zhang et al., 1993a,b; Johnson,1994; Kass are also chemicallyinert and do not react with atmo- and Yung, 1995; Fox, 1993a]. On Venus, exospheric sphericor crustalconstituents and are thus expectedto oxygenis largelygravitationally bound and thus contrib- have remained in the planetary atmospheresfollowing utes to nonthermal escapemainly through momentum accretion[Hunten, 1993]. It is thoughtthat fractionation transferreactions such as (25) and (26). Lossof oxygen of the noble gasesmust thus be the result of drag- from Mars alsooccurs through the solarwind interaction inducedescape during massivehydrodynamic hydrogen with the planet'sionosphere. The thicker atmosphereof outflow during early planetaryhistory [Kasting and Pol- Venus and the correspondinglylarger standoffdistance lack, 1983; Zahnle et al., 1990]. of the bow shock make direct removal of oxygen less The rapid hydrodynamicescape of molecularhydro- important. As can be seen from Table 1, even for an gen from a dense primordial atmospherecould have early Earth and Venus, at nearly their present masses resultedin a massdependent fractionation. Such a pro- the relativelyhigh escapevelocities may have made this cesscould explainthe massdependent depletion of the processinefficient. Mars, however,would have remained noble gasesobserved in the Martian atmosphere.En- vulnerable to this processfor a much longer period hanced solar UV fluxesfrom a young Sun would have [Hunten, 1993]. providedthe energeticsfor this expansion.The method- For an early Venus with a much higher water vapor ology developedby Kastingand Pollack [1983], Zahnle content in the upper atmosphere,photodissociation by and Kasting[1986], and Zahnle et al. [1990] is basedon EUV radiation would have created atomic hydrogenin the solutionof the hydrodynamicequations analogous to much greater amountsthan at present. For this dense thoseused for the solarwind expansion.A more analytic corona of hydrogen, escape may have been hydrody- approachwas developedby Hunten et al. [1987] and namic rather than kinetic in nature [Watsonet al., 1981]. reviewed by Hunten [1990]. The fractionation occurs The hydrodynamic escape of hydrogen could have becauseof the competitionbetween the downwardforce draggedmore massiveconstituents, such as xenon, ar- on an atom (or molecule)and the upward drag force gon, and others,with it. This would mean, for example, whichdepends on the diffusionparameter b (seesection that the deuterium enrichment on Venus would reflect 2.3) which is independentof mass.Hunten et al. [1987] only enhancedhydrogen loss after hydrodynamicescape showedthat at some crossovermass m c the two forces fluxesfell below the level required to removedeuterium are equal. Their final result is that the inventory of 34, 4 / REVIEWSOF GEOPHYSICS Shizgal and Arkos: NONTHERMAL ESCAPEß 501 component2 at time t relativeto the originalabundance Atreya, S. K., J. B. Pollack,and M. S. Matthews(Eds.), Origin at timet o, N2/N2ø, is dependenton the massm2 and and Evolutionof Planetaryand SatelliteAtmospheres, Univ. of Ariz. Press, Tucson, 1989. given by Axford, W. I., The polar wind and the terrestrial helium budget,J. Geophys.Res., 73, 6855-6859, 1968. Axford, W. I., A commentaryon our presentunderstanding of In • : -•-• m0LN• (t2- to) (39) the Martian magnetosphere,Planet. Space Sci., 39, 167-173, 1991. whereF• is the fluxat somereference level r 0. Using Banks, P.M., and T. E. Holzer, The polar wind, J. Geophys. (39), Huntenet al. [1987]studied the massfractionation Res., 73, 6846-6854, 1968. of the isotopesof xenon as a result of large hydrody- Banks, P.M., and G. Kockarts, Aeronomy Part A and B, Academic, San Diego, Calif., 1973. namic escapefluxes, or blowoff,of hydrogen.The result Barabash, S., E. Kallio, R. Lundin, and H. Koskinen, Measure- of their study showed a linear relationship between ments of the nonthermal helium escape from Mars, J. relative abundanceand mass of each isotope. Similar Geophys.Res., 100, 21,307-21,316, 1995. studiesof hydrodynamicescape induced fractionation Barakat, A. R., and J. 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