JOURNALOF GEOPHYSICALRESEARCH VOLUME 66. No. 9 SE•rX•a•E• 1961

The Behavior of Volatiles on the Lunar Surface

KENNETHWATSON, BRUCE C. •{URRAY,AND I-IARRISON BROWN

Division of GeologicalSciences, California Institute of Technology Pasadena, California

Abstract. Volatiles, and water in particular, have been thought to be unstable on the lunar sur- face becauseof the rapid removal of constituentsof the lunar atmosphereby solar radiation, solar wind, and gravitational escape.The limiting factor in removal of a volatile from the moon,however, is actually the evaporationrate of the solidphase, which will be collectedat the coldestpoints on the lunar surface.We present a detailed theory of the behavior of volatiles on the lunar surface basedon solid-vaporkinetic relationships,and show that water is far more stable there than the noblegases or other possibleconstituents of the lunar atmosphere.Numerical calculationsindicate the amount of water lost from the moon sincethe present surfaceconditions were initiated is only a few gramsper squarecentimeter of the lunar surface.The amount of ice eventually detectedin lunar 'cold traps' thus will provide a sensitiveindication of the degreeof chemicaldifferentiation of the moon.

1. INTRODUCTION on the lunar surfaceover the above time period. Previousanalyses of the behavior of volatiles Conversely, the absence of lunar ice would on the lunar surface [Spitzer, 1952; Kuiper, 1952; indicate an extremelysmall amount of chemical differentiation of the lunar mass. Urey, 1952; Opik and Singer, 1960; Vestine, 1958] have all indicated that volatiles could not We will first developthe theory of the behavior of volatiles on the lunar surface, and then survive there for extended periods of time, and that water is particularly unstablebecause of its investigate the best numerical values of the low molecular weight and ease of ionization. parametersof our model to use in numerical calculations. These investigationsdid not, however,recognize that the amount of any volatile in the vapor 2. THEORY OF MIGRATION AND TRAPPING OF phaseon the moon--and henceits massremoval VOLATILES AND THEIR ESCAPE FROM THE rate from the moon--is determined by the tem- LUNAR SURFACE peratureof the solid phaseat the coldestplace on the lunar surface. This was recently pointed In this section we shall develop a theory of the behavior of volatile substances on the lunar out by the authors[Watson, Murray, and Brown, 1961].We have now developeda detailedtheory surfacewhich is basedon two premises:(1) that of the behavior of volatiles on the lunar surface the lunar atmosphereis sorarefied that molecular which takes vapor pressure equilibrium into transportin the vapor phasecan be described account, and from it we show that water is purely in terms of dynamicaltrajectories; and actually by far the most stableof the naturally (2) that there are permanently shaded areas occurring volatile substancesthat might con- (cold traps) with temperaturesat least as low as 120øK. It will be convenient to discuss first ceivably have been releasedat some time on the lunar surface. We show further that the the steadyloss from the cold traps, and, second, total amount of water that could have been lossesof any newly liberated volatiles during removed since the time the moon's surface con- migrationto the coldtraps. By combiningthese ditions first evolved to essentiallytheir present resultswe will derive the equation governingthe total mass removal rates of volatiles from the characteristicsis quite small. Thus the present amount of lunar ice must bear a close relation- lunar surface. ship to the total amount of water ever present 2.1. Steady-stateloss o] volatiles]rom the cold trap. Once any substancecondenses in a per- • Contribution 1048, Division of Geological Sci- manently shadedarea, it will be subject to a ences,California Institute of Technology. continual evaporation loss, which may be 3033 3034 WATSON, MURRAY, AND BROWN

phase tha• depends only on the surface tem-

4 perature of that solid. The evaporation rate could be observed directly if the vapor were 2 removed as fast as it formed, i.e., by eliminating

0 condensation.On the other hand, evaporation and condensationrates are equal whenthe vapor -2 is saturated, if the accommodationcoefficient is

-4 unity. Accordingly,the equilibriumvapor pres- sure presentover a solid surfacecan be usedto -G estimate the characteristicevaporation rate at

-8 that temperature. The maximum evaporation rate can therefore be expressedas follows

o [Estermann,1955].

-12 - \

-14 - • - P•: 2•rRT tz_ 4374X ' 10-5X p• (2) Observeddata Extrapolated data \ \ -16 - where

-18 - /• = massloss in gramsper square centimeter per second. -20 - p- vapor pressure in dynes per square

-22 centimeter. /z - molecular weight. -24 I 000 .o•)2 .oo,• .o•e T = absolute temperature. I/T *K R = gas constant. Fig. 1. Evaporation rates. In orderto obtainvalues of/• in the vicinity of 120øK for a number of naturally occurring balancedin part by condensationback into the volatile substances,the appropriateequilibrium cold trap from the atmosphere. The mass loss vapor pressureshave been extrapolatedto low rate from the cold traps, rhs, is simply the temperaturesfor the present analysis [Inter- differencebetween evaporation and condensation nationalCritical Tables,1928]. The experimental rates: data are of the form log p - --A/T q- B (A •8 = KA(•- •) (1) and B are constants characteristic of the sub- stance), and linear extrapolationis reasonable where for our purposes,assuming that no solidphase K= fraction of lunar surface that is per- changesoccur at thesepressures. For ice, this manently shaded. assumptionis experimentallyvalidated by the A- total lunar surface area in square work of Bridgman[1957]. centimeters. The resultingmaximum evaporation rates for /• = evaporationrate of the substanceat the various volatiles as a function of temperature surface temperature of the cold trap, are plotted in Figure 1. taken to be 120øK as an upper limit for Thecondensation rate (7, unlike K, A, and/•, the moon in grams per squarecentimeter is not a simplecharacteristic property of either per second. the moonor of a particularsubstance because it • = condensationrate of the substancein also dependson the escaperate from the lunar question back into cold trap areas in atmosphereand the accommodationcoefficient gramsper squarecentimeter per second. in the cold traps. However,it is possibleto treat the migrationof moleculeson the lunar surface The fractionof the lunar surfacein permanent in termsof a simpleprobability model, provided shadow,K, will be estimatedlater in this paper that the averagetrajectory iump lengthof the to be about 5 X 10-3. The evaporationrate is a moleculesis comparableto or larger than the characteristicphysical property of any solid averagesize and separationof the cold traps. BEHAVIOR OF VOLATILES ON LUNAR SURFACE 3035 Thederivation of • in thisway is presented now. molecules from the lunar surface can be ade- Later we will demonstrate that the moon does quately describedby a cosinedistribution. The indeed satisfy the restriction regardingaverage average jump time 7, and the average jump jump length vs. sizeand separationof cold traps. distance/•,are, therefore' The followingparameters will be used' .866 X V t- 2 x t -- jump time, which is a function of the g velocity distribution at the surface as well as of the molecularweight and the lunarsurface gravity. • and/• are mean where jump time and mean iump length, respectively. V- rmsvelocity = •//3RT/•. a -- probability for a moleculeto escapefrom g - surfacegravitational acceleration the lunar atmosphereon a singlejump. R = gas constant. K -- fraction of the lunar surfaceoccupied by T = effectivesurface temperature (øK). permanentlyshaded areas. • = molecularweight of volatile. a- accommodation coefficient, the prob- We now examine the implications of our ability that an incident molecule will assumptions.If/• is at leastcomparable to the stick to the surface. size and separationof the permanently shaded The processesby whichthe moleculestransport areas, we can presume that for any individual themselvesthrough the rarefiedatmosphere and jump the probability of landing on a per- either escape or become trapped in the per- manently shaded area is proportional only to manentlyshaded areas are complicatedin detail. the total fractional area of permanentshade K, For our purposesit is sufficientto realize that and does not depend on the location of the the fraction of the molecules that condense .on a beginningpoint of the jump. Since a represents surface, as opposedto the fraction that are the escapeprobability duringan individual jump, reflected,is controlledby the microscopicrough- the probability of a particle landing on a cold- nessand chemicalnature of the surface,by the trap surface and not escapingis K (1 -- surface temperature, and by the molecular Finally, from our discussionof the coefficientof weight of the impacting molecules.A discussion accommodation,it is clear that of thoseparticles of this can be found in Loeb [1927], Langmuir landing on a cold trap a fraction a must remain [1917], and Knudsen [1910]. We shall assume trapped. Hence, on any individual jump' that the temperatureand microscopicroughness probability of a particle being trapped = K of the cold-trap surfacesare sufficientto ensure (1 -- a) a that the accommodation coefficient is close to where unity. We will, however, considerthe effect of varying a when numerical calculationsfor the a = probability of a particle escapingon a trapped fraction are performed.It is alsoreason- singlejump. able from the above to assume that molecules Now since we assumethat the jumps are un- reboundingfrom the warm surfaceswill approach correlated, the above discussionmust apply the surface temperature after a few jumps, for all particles during. a single jump. Hence regardlessof the velocity distribution at the a = 1 -- exp (--•/r) wherer is a characteristic source. decay time for many-particlejumps. Therefore, It is apparent that those moleculescaptured the fraction, y, of moleculesthat becomeper- in temporarily shadedareas, such as the dark manentlytrapped on any jump comparedto the side, cannotescape until the host area heatsup. total that either escapeor are trapped on the Hence, we can neglect the effect of these tem- jump is porarily shadedareas in the solutionof the problem, and consider only those molecules actually moving at any instant of time. ')' = Ka(1Ka(1-- o--0 oq-0 (5) We shall further assume,to avoid unnecessary complexity,that the reflectionand emissionof However, the net number of partiele• in the 3036 WATSON, MURRAY, AND BROWN lunar atmospheremust remain constant for a seriesof random impulsesof arbitrary constant escape probability c•, and certainly amounts. doesnot changesignificantly during the time of rhs, = massloss rate by escapeduring random a singlejump. Hence,the evaporationrate must migration of the moleculesfrom the be exactly equal to the condensationrate plus sourcepoint to a cold trapping surface, the escaperate. Therefore, in gramsper second. If we assume again that the end points of or molecularjumps are uncorrelatedwith beginning = (6) points, then the previous derivation for the condensationrate appliesto the presentproblem and, from equationsi and 6 as well. In particular, the fraction of newly • = ••(1 -- •) = (1 -- •)•,• (•) liberated moleculesthat get trapped on their first jump, or on any subsequentjump, is simply and from equation 5: 'y - [Ka(1 -- o•)]/[Ka(1--c•) + c•].Hence = - •h•= KA• Ka(1--o•) 2.3. Basic equations describing mass losses. This relationship clearly demonstrates im- Since the mass rate of removal by ewporation portant physical restrictionson •h•, the mass from the cold traps is independentof the rate loss rate. For very large values of the decay of liberation of any new volatile materials from time •, the probability of escapea, and •h•, are the lunar surface,the two lossrates • and •f• essentiallyzero. Thus, from equation1, /• is are independent.Therefore, from equations 7 equalto •, and the partialpressure of a par- and 9' ticular constituent in the lunar atmosphere is • = • • •s• just the equilibriumvapor pressurecorresponding to the temperature of the cold trap. For very = (1 -- •)(•s(max) + •f) (10) small values of • (rapid escape),a approaches1, when • is the total mass loss rate from the rh• becomesKAt• - •h• (•), and the partial lunar surface in grams per second and the pressure drops to zero. It is particularly im- accumulated loss over an interval of time portantto notethat thevalue KAt• = T• -- T• = AT is simply is an absoluteupper limit for the rate of removal of a condensedvolatile from all the cold traps = mat = (1 -,) on the moon. As Figure 2 illustrates,•h• is limited Tx by Ka and by the evaporationrate of a particular '(•(m•) + •) AT (11) volatile at 120øK, for example, rather than by the escape probability. For this reason, the The mass loss from cold traps only can be evaporation rate data of Figure 1 are a much expressedas more meaningful guide to stability of volaft]es on the lunar surfacethan are propertiessuch as molecular weight, ionizability, etc., that enter = ,m• -- (1 --,)m•(•> (12) into escapecomputations. m,(t) = m•(O) + yt• 2.2. Transient loss of newly liberatedvolatiles during migration to cold traps. We must also - (1 - (13) considerthe behavior of any new volatile mate- In the next section we Mll consider the actual rial that might be liberated at an arbitrary point on the lunar surface either sporadically or value of the parameters of the equation, and steadily. Let us define computem,(t) and t comparableto the lifetime of the moon. •h• = massinflux of newly liberated volatiles for the entire lunar surface, in grams 3. APPLICATIONS TO •HE LUNAR SURFACE per second.This can be consideredto 3.1. Introduction. It is first necessaryto show be either a smooth function or a that the environment of the lunar surface BEHAVIOR OF VOLATILES ON LUNAR SURFACE 3037

1.0

.8

equation (8) m'•rnax•.6

.'4

.2.

I I -2 -I

log C•

Fig. 2. Mass lossrate vs. escapeprobability. satisfiesthe two basic premisesof our model. interior heat flow and radiative cooling. Simple The existenceof a rarefiedatmosphere has been computationsindicate that the low conductivity proven observationallyby Doll•us [1952], Els- of the dust layer as proposedby Jaeger [1953] moreand Whitfield[1955], and Opik[1955]. and Wesselink [1948] will prevent even small The most recent studiesby Doll•us [1956] of areasof permanentshade from beingheated up polarization and by Elsmore [1957] of radio during the lunar day by horizontal conduction occultationshave verified the previous results from adjacent illuminated areas. and indicate that the lunar atmosphere is The next two sections are devoted to a dis- extremelyrarefied. The maximumdensity con- cussion of reasonable and limiting numerical sistentwith the measurementsof Elsinoreyields values for K, the fraction of permanent shade, a meanfree path of the orderof 10• km, which is and a, the probability of escape.Using these sufficientto justify the useof ballistictraiectories values, the mass removal rates for common for the mechanicsof moleculartransport in the volatile substanceswill be compared, and we lunar atmosphere,since the averagejump length will concludethat water, in the form of ice, is for molecules in equilibrium with the lunar the only commonvolatile that could be stable surface is of the order of 10'- km. for a period of time comparableto age of the Infrared studies of the lunar surface by moon. We then discusspossible sources for the Menzel [1923], Pettit and Nicholson[1930], and liberation of water from the lunar surface. Sinton [1955] indicate that the shaded areas of Finally, a discussionis presentedof the validity the lunar surfacehave maximum temperatures of the uncorrelated model as a description of of' the order of 120øK. Thus 120øK represents migration on the actual lunar surface. an upper limit for permanently shaded areas; 3.2. The amountand distributiono• permanently much lower temperatureswould be expectedif shadedareas on thelunar surface. The obliquity the surface temperature resulted principally of the moon'saxis of rotation with respectto the from the balance on that surface between an ecliptic is only 1ø32' [Allen, 1955]; there is 3038 WATSON, MURRAY, AND BROWN

S

Argelander

W

N

I0 0 I0 50 I00 km

! coordinatesSUN'Sof center ALTITUDE X= 5000 = 9 ø' 57 ,/9= -19000 ' SHADED AREA =-17.4%

Fig. 3. Tracing of the shaded area• near the crater Argelanderfor the sun's altitude of 9ø57'. virtually no seasonal variation on the moon. actual roughnessin the polar areas, and, then, Accordingly,many steep-walledcraters at high by measuringthe variation in per cent shaded lunar latitudes will be permanently shaded on area as a function of the sun'selevation, estimate the part of the wall and bottom of the crater K. The first techniquewas applied by Watson, nearest the equator. However, any terrestrial Murray, and Brown [1961] in order to get an observation of the moon is necessarilymade absolute lower limit of K -- 10 -4. The second from a selenodeticdirection that is also occupied approach, which is discussedbriefly in the by the sun at one time or another; hence, it is present paper and will be publishedelsewhere, impossible to study the permanently shaded yields an actual estimate of K -- 5 X 10-3 areas directly from the earth. One may attack (rather than just a lower limit). the problem, however, in at least two indirect Figure 3 is a tracing of the shadedareas in a ways: (1) definesome necessarily crude analytical small part of the lunar surfacesufficiently near model of a crater, compute its permanently k - 0, /• - 0, so that any bias in projectionis shaded area as a function of latitude, and use small. The character of the topographyin the some distribution function for lunar craters to test area is quite similar to that in the polar arrive at an estimate of K, the fractibn of areas' both display a densearray of craters of permanentlyshaded craters for the whole lunar random-size distribution. Mountains, valleys, surface,or (2) use photographsof upland areas and other linear topographicfeatures are almost near the equator to obtain estimates of the entirely restrictedto the bordersof the maria• BEHAVIOR OF VOLATILES ON LUNAR SURFACE 3039

TABLE 1. Estimation of Permanently Shaded Area on Lunar Surface

Permanently Latitude Total Lunar Upland in Total Shaded Area Shaded Area, % Zone, Surface, Latitude Zone, Upland, at Noon, (for reduction deg % % % % factor 0.5)

90-80 1.53 100 1 53 27.5 0.21 80-70 4 54 100 4 54 8.5 0.19 70-60 74l 94 5 7 01} 2.2 0.08 60-50 l0 O4 78 5 7 88 1 0 0. •}3 50-40 12 36 77 5 9 57 40-30 14 28 67 5 9 63 30-20 15 76 57 0 8 99 20-10 16 78 48 0 8 05 10-0 17 30 47 0 8 13

Total 65.3 Total 0.51% K =5 X10 -a

and, consequently,can be ignored when con- vs. latitude as a percentageof the total lunar sideringhigh latitudes where the permanently surface area is then merely the product of shaded areas are concentrated. columns4 and 5, reducedby the 1• factor. The relativeproportion of uplandas a function The main sourceof error leading to an over- of latitude for the visible face of the moon is estimate of K would arise from a poor choiceof shownin columnfour of Table 1. The percentage the reduction factor; K = 10-• would seem to of the test area shaded at different elevation be an absolutelower limit. Similarly, the facts anglesof the sun has been measuredfrom other that (1) there are less maria on the reverseside photographsof the samearea at differentlunar of the moon than on the visible one Barabashov, phases.Since the per cent shadedarea of any Michailov, and Lipski [1961], and (2) that crater on the equator at a sun's elevation of, cratersless than i km in diameterhave effectively for instance,20 ø, is about equal to the shaded been ignoredowing to limited resolution,might area that same crater would exhibit at local noon suggestthat the true value of K is higher than time if it were at a latitude of 90ø -- 20ø = 70ø, 5 X 10-•. An upper value of K = 10-'- seems it is possibleto usethe measurementof per cent appropriate. Accordingly, we conclude that K shadingvs. sun'selevation for an equatorialtest lies between 0.1 and 1 per cent, most likely area as a goodestimate of the per cent shaded about 0.5 per cent. area at noon time of similar topography at 3.3. Escapemechanisms. The most important higherlatitudes. The data from the photographs escapemechanisms proposed so far are ionization, are plottedin the fifth columnof Table i in this solar wind collision,and gravitation. manner,except that the 1ø 32' annual variation Opik and Singer[1960] have calculatedthe of the sun's elevation has been taken into half-life of krypton in an exospherein contact account. The annual variation, of course, is with the lunar surface under solar ultraviolet equivalentto increasingthe sun's elevationat radiation. They show that incident radiation all latitudesby that amount. For any crater the will ionize the atmosphereand also raise the minimum shadedarea occursat noon time, but electrostatic potential on the lunar surface by this shadow then is still larger than the per- photoionizationof silicates.By calculating the manently shaded area. This is becausethe screeninglength associatedwith this potential sun illuminatesa part of the border of the area and comparingit with the characteristic'scale coveredby the noon-timeshadow at other times height' of the atmosphere they calculated a during the lunar day, even thoughthe elevation half-life of 4.3 X 10•ø sees (r = 6 X 10•øseconds). angleis lessthan at noontime. We take a value 0pik and Singer(private communication) have of 0.5 as an average reduction factor for lunar also estimatedthe decay time for photodissocia- craters.The estimatedpermanently shaded area tion of water vapor in the lunar atmosphereby 3040 WATSON, MURRAY, AND BROWN

TABLE 2. Escape Parameters

Escape Probability,

Solar Solar Volatile u km sec Radiation Wind Gravitation

Mercury 200 26 133 1 X 10 -3 5 X 10 -74 Krypton 83 62 206 2 X 10 -9 2 X 10 -3 2 X 10 -30 Sulfur dioxide 64 61 236 2 X 10 -3 3 X 10 -a3 Carbon dioxide 44 118 285 3 X 10 -3 7 X 10 -•6 Hydrogen chloride 36 142 315 3 X 10 -3 4 X 10 -•3 Water 18 287 446 4 X 10 -3 4 X 10 -3 2 X 10 -6 Ammonia 17 304 458 5 )• 10 -3 4 X 10 -6 solar radiation to be of the order of 10 • seconds the mechanismswe have discussed,as well as or less, but the relevant calculations have not the valuesfor •, the averagejump time, and •), yet been published. the average jump length for selectedvolatiles. Herring and Licht [1959] have estimated the 3.4. Mass lossrates o• waterand othervolatiles. reductionin a lunar atmospheredue to the influx The mass loss rate per unit lunar surface area of the high-energyprotons in the solar wind. can be computedfrom equation8. We shall use Sincethe protonsare traveling with an assumed the value for K of 5 X 10TM, and, assuming velocity of 108 cm/sec they have an incident a - 1, we use Table 2 and the evaporation energyof about 5 kev. Inasmuchas the energy rates (Fig. 1) to compute •h•. Our assumption necessaryfor escapeof even the heavy volattics that a is unity for ice is justifiedby the work of from the lunar atmosphereis lessthan 5 ev it is Tschudin[1946] who measuredevaporation rates apparent that the energy transferredby pro- of ice in the range --60øC to --85øC and de- ton-moleculeimpact is more than sufficient to termined a value of .94 for a. The results are cause escape. The molecular diameter of the presentedin Table 3 and illustrated graphically volatticsis 3 X 10-8 cm, hencethe crosssection in Figure 4. for impact is about 10-• cm•.. For a solar wind It is apparent that mechanicalescape is far densityof 103particles/cm 3, the decaytime is too inefficientto be considereda significantloss (10-• X 103X 108)-• = 10• seconds. mechanism.A comparisonof the other lossrates The least rapid rate of removalis by direct leads us to the conclusionthat only water and escapeof that fraction attaining thermal veloci- mercurycould remain trapped for an appreciable ties greater than the escapevelocity. Spitzer fraction of lunar history. Because of the ex- [1952]has derivedthe equationsfor the escape tremely low abundanceof free mercury on the time. We shall assumethat the temperatureat earth's surface, it is reasonableto neglect it the base of the exosphereis the lunar surface from further lunar consideration.Accordingly, temperature of 400øK. Then water is the only volatile possiblyretained in significant quantities on the lunar surface. We ¾/• eY will use the mass loss rate associated with 3g Y photodissociationas a reasonableestimate for where the escapeof water. The total massloss rates of water are computed 3 V2• for two values of •: a 'reasonable' one corre- y- 2 V • spondingto • - 10• seconds,and a maximum one of • - 0 seconds(i.e., zero condensation), and where values for the latter will be given in V• = escapevelocity. brackets following the values associated with V = rms velocity associatedwith 400øK. the reasonable estimate. For water, r = 2.5 X 108seconds. In one billion years the massloss rate from the coldtraps is 4 g/cm• (9 g/cmos)(cm• refersto Table 2 gives a, the escapeprobability, for the whole lunar surface).This is equivalent to BEHAVIOR, OF VOI,ATILES ON LUNAR SURFACE 3041

TABLE 3. Mass Loss Rate Per Unit Area of the Lunar Surface m•/A(g/cm2/sec)

Maximum Solar Solar limited by Volatile Radiation Wind Mechanical evaporation

Mercury 6 X 10-26 2 X 10-9 3 X 10-25 Krypton 1 X 10-7 9 X 10-2 1 X 10-2s 3 X 10-• Sulfur dioxide 1 X 10 -9 2 X 10-29 4 X 10 -9 Carbon dioxide I X 10-6 I X 10-•s I X 10-5 Hydrogen chloride I X 10-4 2 X 10-14 3 X 10-4 Water 1 X 10 -16 1 X 10 -16 1 X 10 -•9 3 X 10 -16 Ammonia 3 X 10 -s 5 X 10 -u 6 X 10 -s a removal of a total of 8 meters (18 meters) of and Sahama,1950]. Approximately 6 kg of water ice from the cold traps. We now calculate the per squarecentimeter of the earth appearsto be necessaryamount of new water that would have bound in the sedimentsand, judging from the been liberated from the whole lunar surface to observedwater contents of basaltic materials, replenish the loss from the cold traps. From an additional50 kg/cm2 may still residein the equation 5 the mass addition rate to the cold crustabove the Mohorovicicdiscontinuity. Some traps owing to liberation of new volatticsis 30 kg of waterper squarecentimeter has perhaps Hence, for no net massloss from the cold traps, been lost over geologic time as the result of dissociationin the atmospherefollowed by the 'y•-= • (14) escapeof hydrogen.Thus, if the earth is well- degassodbelow the Mohorovicicdiscontinuity, and, from equations7 and 15 the primitive earth would have containedsome 370 kg of water per square centimeter. On this •f - m• ,max) basis the original earth material would have containedabout 0.03 per cent water, an amount Using our 'reasonable' estimate for rh•, the comparableto the apparentabundance of bound requiredliberation rate is 7 g/cm2m/billionyears. water in many chondritesof the noncarbonaceous 3.5. Productiono• water on the lunar surface. variety. Virtually all known silicate materials that fall Had primitive lunar material contained an upon the earth from space appear to contain equivalent concentration of water, the moon water in varying amounts, the' greater part of would have containedoriginally an amount of which is probably chemically bound. The water equal to about 60 kg of water per square hypersthene,bronzite, and enstatite chondrites centimeter of the lunar surface. This amount of containvery low concentrationsof water, starting water is equal to about 10a times the amount of at about 0.02 per cent, averaging about 0.25 water we estimateto have been lost per billion per cent, and seldom exceeding0.5 per cent. years from the lunar surface.Accordingly, it There is always the uncertainty tha• some of seems reasonable to assert that there should still the observedwater might be of terrestrial origin, be detectableamounts of ice in the permanently but water does appear to be present in fresh shaded areas of the moon if the moon has under- falls which have been analyzed shortly Mter gone a bulk chemical differentiation as small as recovery. Concentrationsrange upward to as about one one-thousandth that of the earth. high as 20 per cent in some carbonaceouschon- We may conclude,then, that ice shouldprove drites. In the latter casesthere is little question to be a most sensitive mineral indicator of the that the water is extraterrestrial. These mete- degree of chemicaldifferentiation of the moon, orites representsome 3 per cent of all observed a far moresensitive guide than the percentageof falls. silica in the surfacerocks, for instance. The visible water now on the surface of the It should be pointed out that accretionsof earth, which appears to have been present metcoritic water upon the moon are probably originally in chemicallybound form, amountsto small when comparedwith the amount of water somewhatover 280 kg/cm• of the earth [Rankama liberated from the interior of the moon itself. 3042 WATSON,MURRAY, AND BROWN

Maximum (limitedby evap. ) Mercury Water Sulfur Dioxide Ammonia Carbon Dioxide HydrogenChloride Krypfon

Solar Radiation

Water Krypton

Solar Wind

Nercury Water Sulfur Dioxide Ammonia Carbon Dioxide HydrogenChloride Krypton

Mechanical Mercury (-95.7) Sulfur Dioxide Krypfon Water Carbon Dioxid• HydrogenChloride

Ammonia i

I I i i -40 -$0 -20 --I0 Logß •/,"A Fig. 4. Massloss rate in g/cmm2/secforvarious escape mechanisms.

The frequencydistribution curve for meteoritic centof theaverage crustal thickness on the earth. massesindicates that at the presentrate of 3.6. Validity o! migrationmodel. It is now influx perhaps20 gramsof meteoriticmatter possibleto returnto the questionof the relative mayhave been deposited upon every square distancebetween cold traps as compared to the centimeterof the lunar surface during geologic average distance covered by a migratingmolecule time [Brown 1960, 1961]. This could have in a singlejump. It will berecalled from section 2 resultedin the liberationof no morethan about thatour theory assumes that the beginning and 0.2 gramsof waterper squarecentimeter of the endpoints of a singlejump are uncorrelatcd--in moon,largely from the carbonaceouschondrites. particular,that a moleculewill not find itself in It shouldalso be pointedout that the flux of an areadevoid of coldtraps which is large 'meteorites'composed primarily of ice of com- comparedto its averagejump length. Actually etary originis unknown.Such objects might sucha caseexists for watermolecules that are wellbe fairlyabundant, but theirvery nature releasedin an equatorialarea, but we will now wouldpreclude our observing them reliably from showthat this departurefrom our modelis not the earth's surface. significant.The 'barren'equatorial areas are Finally,it is interestingto comparethe approximatelycompensated by the polarareas requiredliberation rate of 7 g/cm•/billionyears wherethe proportionof coldtraps is much computedin the previoussection with the largerthan indicated by ouraverage value of K thicknessof a lunarcrust containing 0.03 per forthe entire moon, and the jump distances are centwater whichwould have to be differentiated lessbecause of the loweraverage surface tem- to producethat much water. The required thick- perature. nessis 78 meters,only about one-half of 1 per The oppositeextreme of our uncorrelated BEHAVIOR OF VOLATILES ON LUNAR SURFACE 3043 modelwould be the casewhere the iump lengths where AN is the difference between the number are so short compared with the separation of northerly component and the number of betweencold traps that there is httle migration, southerlycomponent iumps which compriseN. i.e. that the beginningand end pointsare highly But sincethe directionof iump is presumedto correlated in latitude. For instance, very few be random moleculesreleased in the equatorial areas could ever reach the higher latitudes to be trapped. AN = N '/2 (17) However, moleculesreleased in the polar areas and wouldbe confinedto thesehigher latitudes where the larger K would result in a higher proportion N = (7.5)• = 56 (lS) being captured. Hence, for the correlated case Since on each jump the probability of escapeis the lossrate from the coldtraps is reducedabout a, the probability of reaching50 ø latitude by 25 per cent (seeTable 1). We shall examinethe randomwalk without escapingis iust trapping of newly liberated volatiles for the correlated model by considering two cases: (1 -- oz)•v= 1-- Na (19) uniform liberation over the lunar surface, and since N•a 2 is negligible. the extremecase of liberationfrom the equatorial areas only. From Table 2, c• = 4 X 10TM The uniform liberation results in the loss rate duringmigration to the coldtraps being increased .'. (1 --oz)•r= 0.78 (20) about 50 per cent. The net effectwhen combined Hence, for the most extreme case, 22 per cent with the lower lossrate from the cold traps is to •f at the equator would be lost beforeentering increasethe required liberated flux to balance into the uncorrelated zone. The loss decreases cold-trap loss by about 10 per cent on the for sourceslocated between 0 ø and 50ø latitude, average. Clearly this differenceis insignificant and it is clear that the net preferentialselection in terms of the uncertainties in K and a, and effectionis insignificant.Thus, the uncorrelated the use of the uncorrelatedmodel is sufficiently model is indeed a valid descriptionof migration accurate for our purposes. as well as total trapping of volatiles on the The correlated and uncorrelated models do lunar surface. differ significantly,however, in regard to prefer- We have deferred until the present section a ential lossof volatilesliberated in the equatorial discussion of the effect on the mass loss rate of regions.A rigoroustreatment of this problemis variations in the parametersK, a, and a. It is involved,but the following analysis:]is sufficient clear from equations8 and 9 that K and a only to justify the uncorrelatedmodel. occuras the product Ka. If we double the value From Table 1 it will be seen that the fraction of Ka, we increase •, from .555 to .714. Thus of permanentlyshaded area becomes insignificant the total mass loss from the cold traps is in- for latitudes less than about 50ø . Accordingly, creased but the fraction of liberated volatiles the worst casefor a migrating moleculeto reach lost from the atmosphereis decreased;the net a cold trap is its releaseat the equator, 1500 km effect is to reducethe requiredliberated flux to from the 50ø latitude zone where the truly balancethe cold trap lossby a factor 2. If the uncorrelatedmodel begins to hold. The migration value of Ka is halved, or a is doubled, then 3' is presumedto be a random walk in arbitrary decreasesfrom .555 to .385, and the net effect directionswith an average jump distance, for a is to increasethe required liberated flux by a water molecule, of 280 km (Table 2). The factor 2. Obviously these changesin mass loss average component of northerly or southerly are insignificant compared to changes in the migrationper jump is then .707/• = 200 km. evaporation rates with temperature. We have We wish to find the expectednumber of jumps, used 120øK for the cold trap temperature,with E(N), for the moleculeto reach either 50øN or the understandingthat it representsa maximum. 50øS. This condition can be expressedas If a more likely temperature of 100øK is used, the massloss rate of water from the cold traps 1500 is reducedby four ordersof magnitude,and this AN- 200-- 7.5 (16) loss is insignificant over the lunar lifetime 3044 WATSON, MURRAY, AND BROWN

(equivalent to a maximum loss from the cold permits the use of simple dynamic trajectories trap surfaces of 2-mm thickness per billion over the lunar surface.Both these assumptions years). are validated by observations of the lunar Finally, we can summarize our conclusions surface.The model yields simple expressionsfor from this study by stating that the permanently the mass removal rates of volattics from the cold shadedareas are such an efficient trap that the traps and their migration to the cold traps discoveryof no ice in these areas on the moon following release from the lunar crust. In impliesthe stringentlimitations of an extremely particular' low productionof water from the lunar surface during its lifetime. m = (• --,)(•• + The atmosphericdensity that correspondsto where the vaporpressure of waterat 120øKis 3.5 X 104 molecules/cm3. It is interestingto note at this total mass removal rate of a volatile point that the degree of ionization of water from the moon(g/sec). producedby the solarwind is approximatelythe A • surfacearea of moon (cm•). escapeprobability a -- 4 X 10-8, since this fractionof surfacein permanentshadow. representsthe fraction of moleculesthat are evaporation rate of volatile at tem- ionized and escape; the ion density would be perature of cold trap (assumedto be 10•-/cm8. Clearly this result is compatiblewith 120øKin calculation)(g/cm•-/sec). the density of 108 electrons/cm3 observed by mass influx rate for liberation of new Elsmore [1957]. In addition, the logarithmic volatile material on lunar surface variation of vapor pressurewith inverse tem- (g//sec). perature implies that the vapor pressurede- Ka(1 -- a)/[Ka(1- a)-]- a]- ratio of creasesvery rapidly for a small temperature trapped fraction to trapped plus es- decrease. Since 120øK is an upper limit, we caping fractions. should actually expect to find even lower where densities. It has been suggestedin personal communi- a = the accommodation coefficient of the cations to the authors that sputtering [see cold traps. Webnet, 1955] might be a significanterostonal a = escapeprobability on a singlejump. mechanismacting on the ice in the cold traps. The parameters of the model have been Generally the threshold energy for sputtering examined in order to estimate reasonable and is at least an order of magnitude greater than also limiting values for water on the lunar the latent heat of vaporization. Recent calcula- surface. These are: tionsby Brandt[1961] suggest that Chamberlain's [1961] model of the solar corona with velocities K = 5 X 10-8 with a maximum range of of a few kilometersper secondand a density of 1X 10 -8 tolX 10-% around30 electrons/cm8at the earth's orbit is a = approximately 1. in agreementwith the deflectionof comet tails. a = 4 X 10-3 for photodissociationof The resulting energy flux is many orders of water. magnitudelower than the radiativeheat transfer amax= 1 for maximum lossby evaporation. from the cold trap surfacesand seemsto exclude The application of the model to common the possibility of sputtering having an ap- volatiles leads us to the conclusionthat only preciableeffect on the massremoval rate of ice water is relatively stable over periods com- from the cold traps. parableto the lunar lifetime. We have calculated the total mass loss rate of water from the cold 4. Sv•ARY trapsto be approximately4 g//cm2m/billionyears We have developeda modelof the stability of for the reasonable estimate. We also estimated volattics on the lunar surface. This model is the average liberation rate of water over the based upon the presumed existence of per- lunar surfacenecessary to condensein the cold manently shaded areas that act as cold traps trapsand balancethe lossto be 7 g/Cm2m/billion for volattics and a rarefied atmosphere that years. BEHAVIOR OF VOLATILES ON LUNAR SURFACE 3045

Finally we have discussedthe validity of our F. D. Rossini, Princeton University Press, pp. model and the effects of possible variations in 742-744, 1955. Herring, J. R., and A. L. Licht, Effect of solar wind the parameters a, K, and a. The model was on the lunar atmosphere,Science, 130, 266, 1959. found to be quite adequate, since the variation International Critical Tables,3, 201-246, McGraw- in parametersproduced effects which are negli- Hill Book Company, New York, 1928. gible comparedto the changein massloss rate Jaeger, J.C., The surface temperature of the moon, introduced by reducing the cold trap tem- Australian J. Phy., 6, 10-21, 1953. Knudsen, M., Die molekulare w•rmeleitung der peratures from the maximum of 120øK to a. gase und der akkommodationskoeffizient, Ann. more reasonabletemperature of 100øK. Physik, 34, 593-656, 1910. These resultsimply that the lack of ice in the Kuiper, G. P., Planetary atmospheresand their cold traps today would require that the libera- origin, in The Atmosphereof theEarth and Planets, revisededition, edited by G. P. Kuiper, University tion of water from the moon during its lifetime of Chicago Press, Chicago, p. 367, 1952. must have been extremely low compared with Langmuir, I., The condensationand evaporation of that on the earth and hencethe implication that gasmolecules, Phys. Rev.,3, 141-147, 1917. the chemical differentiation to form a lunar crust Loeb, L. B., Kinetic Theory of Gases, 1st ed., has been negligible. McGraw-Hill Book Company, Inc., New York, pp. 240-337, 1927. Menzel, D. H., Water-cell transmissions and Acknowledgement. This work has been supported planetary temperatures,Astrophys. J., 58, 65-74, in full by the National Aeronautics and Space 1923. Administration under Grant NsG 56-60. 0pik, E. J., The densityof the lunaratmosphere, Irish Astron. J., 3, 137-143, 1955. Opik,E. J., and S. F. Singer,Escape of gasesfrom REFERENCES the moon, J. Geophys.Research, 65, 3065-3070, 1960. Allen, C. W., Astrophysical Quantities, Athlone Pettit, E., Radiation measurementson the eclipsed Press, p. 162, 1955. moon, Astrophys.J., 91, 408-420, 1940. Barabashov, N. P., A. A. Michailov, V. N. Lipski, Pettit, E., and S. B. Nicholson, Lunar radiation editors of Atlas of the OppositeSide of the Moon, and temperatures, Astrophys. J., 71, 102-135, Academyof Sciences,USSR, 1961. 1930. Brandt, J. C., On the study of comet tails and Rankama, K., and Th. G. Sahama, Geochemistry, modelsof the interplanetary medium, Astrophys. University of Chicago Press, Chicago, 1950. J., 133, 1091-1092, 1961. Sinton, Wm., Observations of solar and lunar radia- Bridgman, P. W., High pressureeffects, in American tion at 1.5 millimeters, J. Opt. Soc. Am., 45, InstituteofPhysics Handbook, 1957. 975-979,1955. Brown,ofmeteoritic Harrison, bodiesThe density in_the. andneighborhood mass distribution ofthe S•'3•)• '•i*z^r 'kmL I' inJr., The The Atmosphereterrestrial atmosphereof the Earth above and earth'sorbit, J. Geophys.Research, 65,1679-1683, Planets,revised edition edited by G. P. Kuiper, 1960. University of ChicagoPress, Chicago, pp.239-244, Brown, Harrison, Addendum: The density and 1952. mass distribution of meteoritic bodies in the Tschudin, K., Die Verdampfungsgeschwindigkeit neighborhood of the earth's orbit, J. Geophys. yon Eis, HelveticPhysica Acta, 19, 91-102, 1946. Research,66, 1316-1317, 1961. Urey, H. C., The Planets, Their Origin and Develop- Chamberlain, J. W., Interplanetary gas, 3, A ment, Yale University Press, New Haven, pp. hydrodynamic model of the corona, Astrophys. 17-18, 1952. J., 133, 675-687, 1961. Vestine, E. H., Evolution and nature of the lunar Dollfus, A., Nouvelle recherche d'une atmosphere atmosphere, Rand Research Memo. RM-2106, au voisinagede la lune, Comptesrendus, Academie 1958. des Sciences,234, 2046-2049, Paris, 1952. Watson, K., B. Murray, and Harrison Brown, On Dollfus, A., Recherche d'une atmosphere autour the possiblepresence of ice on the moon, J. Geo- de la lune, Ann. d'Astrophys.,19, 71, 1956. phys. Research,66, 1598-1600, 1961. Elsmore, B., and G. R. Whitfield, Lunar occultation Wehner, G. K., Sputtering by ion bombardment, of • radio star and the derivation of an upper in Advancesin Electronicsand ElectronPhysics, 7, limit for the density of the lunar atmosphere, 239-298, Academic Press, 1955. Nature, 176, 457-458, 1955. Wesselink,A. J., Heat conductivity and the nature Elsmore, B., Radio observations of the lunar of the lunar surface material, Bull Astr. Inst. atmosphere, Phil. Mag., 2, 1040-1046, 1957. Netherlands,10, 351-363, 1948. Estermann, I., Gasesat low densities,in Thermody- namics and Physics of Matter, Vol. 1, High (Manuscript received June 9, 1961; SpeedAerodynamics and Jet Propulsion,edited by revised June 30, 1961.)