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The Behavior of Volatiles on the Lunar Surface

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The Behavior of Volatiles on the Lunar Surface 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 fraction of 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
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