The sodium and potassium atmosphere of the moon and its interaction with the surface

ICARUS 96, 27-42

(1992)

The Sodium and Potassium Atmosphere of the Moon and Its Interaction with the Surface A. L. SPRAGUE’ NASA Ames Research

Center, Moffett Field, California 94035

R. W. H. KOZLOWSKI~, D. M. HUNTEN, AND W. K. WELLS Lunar and Planetary

Laboratory, The University of Arizona, Tucson, Arizona 85721 AND

F. A. GROSSE’ Susquehanna

University, Selinsgrove,

Pennsylvania

17870

Received September 3, 1991; revised December 23, 1991

hundred km altitude can be on escape trajectories. We apply these ideas to the budget of atomic oxygen. We suggest that the inventory of oxygen atoms is greatly reduced because they stick to the surface with high efficiency similar to that of the alkalis, and subsequently recombine with each other or with partially reduced oxides of such atoms as Mg, Fe, Al, and Si. o 1992 Academic PRSS, IIX.

Observations of lunar atmospheric sodium and potassium from May 1988 to July 1991 are reported and analyzed. Densities at 80“ north and south are less than equatorial ones by a factor of 2-3. For our observations, which do not reach above 800 km from the limb, the apparent scale heights for the intensity are 119-611 km for Na, and 85 and 154 km for K; most of these are much larger than would be expected for atoms thermalized to the surface temperature. However, the intensity drops off with increasing radius at a much greater rate than would be observed for an atmosphere that is mostly escaping. We interpret our data using both singleand two-component analyses. We amplify an earlier suggestion that source atoms are quickly redistributed into thermal and suprathermal populations by “competing release mechanisms” acting at the surface. The suprathermal distributions are produced by solar radiation releasing atoms adsorbed on the surface (photodesorption). We present reasons why the energy distribution seems to mimic a Maxwellian. The competing release mechanisms explain an obvious trend of decreasing apparent scale heights toward the subsolar point, where the density in the lowest 100 km appears to be dominated by thermally desorbed atoms. The suprathermal component is expected to appear at greater altitudes, but the early subsolar data do not extend high enough to reveal it. Six of the data sets are tentatively resolved into thermal and suprathermal components. The variation with latitude is naturally explained if a larger fraction of the atoms at large solar zenith angles are adsorbed to the surface, rather than being visible in the atmosphere. Migration to the dark side may also play a role. It is shown that at most a very small fraction of the observed atoms below a few

1. INTRODUCTION

Study of the Moon’s atmosphere was a significant part of the Apollo program, with mass spectrometers on landed packages and in orbit, and an ultraviolet spectrometer also in orbit. This work is summarized by Hodges et al. (1973) and Hodges (1975), and more briefly by Morgan and Shemansky (1991). Gases observed were 4He and 36Ar from the solar wind and 40Ar of lunar origin. The original suggestions of *‘Ne are no longer considered reliable. Most of the results are from the landed instruments, which could not function during the day because of overwhelming background from outgassing of residual hardware in the vicinity. There were serious problems even at night. Nevertheless, slightly more than half of the diurnal variation could be pieced together. Densities of helium and neon showed marked nighttime maxima, while argon had peaks at dusk and dawn, with a decay of 2 or more orders of magnitude during the night. The number density (n) of the lighter gases was well described by the relationship: n oc T-j”, where T is the IocaI surface temperature. This behavior stems from the more rapid diffusive transport away from a warm region relative to a cold one (Hodges and Johnson 1968, Chamberlain and Hunten 1987). Argon

’ Also at The University of Arizona, Tucson, AZ 85721. ’ Also at Susquehanna University, Selinsgrove, PA 17870. 27

0019-1035192 $3.00 Copyright 0 1992by Academic Press, Inc. Ail rights of reproduction

in any form reserved.

2x

SPRAGUE ETAL

must in addition adsorb to the cold nighttime surface, with the desorption time exceeding 10’ set when temperatures are below 150 K (Hodges 1974, 1980, 1982). The remarkable deficiency of molecular species, especially those containing carbon, is discussed by Hoffman and Hodges (1975). The Apollo 14 mission included the Suprathermal Ion Detector Experiment (SIDE). A reanalysis of these data by Freeman and Hills (1991) concludes that the intense flux of ions whose mass is consistent with water vapor is most likely associated with the ascent and descent stage rockets or residual water in the descent stage tanks. The orbiting ultraviolet spectrometer (Fastie et al. 1973) set extremely low upper limits on the abundance of several gases, notably atomic hydrogen and oxygen. Morgan and Shemansky (1991) have discussed the oxygen budget in detail, using the Fastie et ul. oxygen upper limit and concluded that the source strength is several orders of magnitude greater than the conventional sink (photoionization). Feldman and Morrison (1991), in a reanalysis of the Apollo 17 UVS data, have revised the upper limit for oxygen upward by a factor of six. We suggest that loss by Jeans escape and by oxidation of regolith materials will diminish the atomic oxygen abundance after formation and will remove the remaining discrepancy. There is no direct evidence in the Apollo data on the temperature (or velocity distribution) of the gases; all models made the natural assumption that the gases were in equilibrium with the local surface. This assumption seems to be confirmed by the reasonable fit of the data to the T m~5’2 behavior, even though the range of temperatures with usable data is restricted to the night and twilight periods. A body of related work followed the Mercury encounters by Mariner 10 and the UV observations of H and He; a thorough review is given by Hunten et al. (1988). It was quickly noticed (Smith et ul. 1978) that the distribution of He between the day and the night (actually, twilight) sides did not fit the expected T-“” behavior based on rapid thermalization to the local surface temperature. This led to the suggestion that such thermalization is very inefficient. This process is usually described by the accommodation coefficient, which apparently must be unusually small for He atoms scattering from a clean rocky surface. Errors in earlier Monte-Carlo treatments were also found and explained (Shemansky and Broadfoot 1977). Even so, it was still taken as obvious that thermalization to the local surface would occur; it would just take more collisions. Interest in these problems was revived once more by the unexpected discovery of bright sodium emission from Mercury (Potter and Morgan 1985), shortly followed by potassium (Potter and Morgan 1986). Attempts to detect similar emission from the Moon failed for some time, as mentioned by Hunten et al. (1988). Independent observing programs resulted in the first report by Potter and Morgan

(1988a), and the slightly later one by ourselves (Tyler et al. 1988). The key was to observe along a path just grazing the sunlit limb, to enhance the feeble intensity by a long path length. An important additional feature is that the height distribution of intensity is obtained, although in these initial observations the maximum height was limited. Potter and Morgan (1988a), observing a region at a solar zenith angle near 14”, found a scale height of 120 + 40 km, but their observations extended only to 40 km. Our data for June 1988 were obtained for a solar zenith angle of 3” to a height of 106 km. The scale height given by Tyler et al. (1988) is 86 t 25 km, and is slightly revised here. This happy state of affairs was upset by the startling discovery (Potter and Morgan 1988b) of substantial sodium densities at heights as great as 1200 km, seemingly inconsistent with the scale height of around 100 km obtained earlier that year and described above. Their data for 2 and 3 October 1988 could not be fitted by the scale height obtained earlier, and a two-temperature distribution was suggested. Morgan and Shemansky (1991) have fitted the same data to a single distribution. Potter and Morgan (1991) have given a reanalysis of the 2 and 3 October 1988 data, along with three new data sets. As we show below, we see good evidence for a two-component distribution, revealed most clearly by the fact that low temperatures are closely associated with the subsolar region. These results are readily explained by a model of competing release mechanisms with different dependences on solar zenith angle. 2. OBSERVATIONS The spectrograph used for all the observations is the “LPL Cchelle” (Hunten et al. 1991b) with a CCD camera supplied by Dr. U. Fink. The spectral resolution is about 0.1 A and the range covered by a single exposure about 10 A. We can therefore obtain both sodium lines (5890, 5895 A) at once, but only the one potassium line at 7699 A. The stronger of the pair, at 7665 A, cannot be observed because it is absorbed by a strong telluric line of 0,. The telescope is the 153-cm instrument of the University of Arizona Observatories on Mount Bigelow, with a scale of 10 arcsec/mm. A rotatable tailpiece was used to place the slit parallel to the radial direction. The lo-mm slit length ideally covers 100 arcsec, or 200 km at the mean distance of the Moon. In actual operation, the coverage has typically been 170 km. Higher altitidues are reached, on some occasions, by placing three fields end-to-end or guiding the telescope to a prescribed distance from the center of the disk. The sensitivity of the instrument limits the radial extent to which we can measure the extremely faint emissions. Table I shows the date, time, exposure time, lunar

SODIUM AND POTASSIUM

INTERACTION TABLE

29

WITH THE MOON’S SURFACE

I

Measurements of Sodium and Potassium

Date

24 7 I6 29 I2 I2 I3 I3 I3 I4 I4 I9

Time (UT) hr mitt

Exposure time (set)

May 1988 June 1988 July 1990 Aug 1990 Ott 1990 Ott 1990 Ott 1990 Ott 1990 Ott 1990 Ott 1990 Ott 1990 July 1991

404 II 47 IO 38 4 I6 I2 20 9 43 IO 40 IO 52 IO 20 II 18 II 45 3 49

400 3600 1200, 600 3 x 900 1200 1200, 2 x 1800 900 2400 1200 1200 1200 1200, 1800

29 April 1989 I8 July 1990

IO 41 IO 45

1800 4800

Local solar zenith angle

Calibration surface brightness (kR/A)

Slit location perpendicular to limb at

Calibration factor (kR sec/DN)”

Sodium D? 90 0 93 3 103 28 81 9 106 80 Same I6 II9 29 Same 81 Same 81 I31 41 Same 83 96 6

Equator Equator 25”s Equator 80”s Equator Equator 80% 80”N Equator 80”s Equator

None 102 None 10.8 5.4 Same Same Same Same 5.3 Same None

None l.03b None 1050’ 5300d Same Same Same Same Same Same None

Potassium D, 97 7 130 40

Equator Equator

187.0 41.0

4200d 1330’

Phase angle (deg)

0 For emission line shown. b Obtained for Earth’s D2 twilight (kRID2 line); revised to 1.03 kRD2 line during reanalysis. c From Saturn’s South Equatorial Belt. d From Jupiter’s North Tropical Zone. y From Saturn’s North Tropical Zone.

phase, local solar zenith angle, and slit location. Absolute intensity calibration is obtained from specific areas on Jupiter’s or Saturn’s disk. These have been carefully compared with standard stars (using the same instrument) by Karkoschka (1990). Because the albedo depends slightly on the particular location on the planet, care was taken to obtain the calibration from a stable, well-characterized region. The last two columns of Table I show the sensitivity of the instrument and the surface brightness of the calibration standard. For June 1988 the only available standard was the D,/D, ratio in the twilight (Tyler et al. 1988); the revised value corrects for the actual zenith angle of the calibration exposure. The sodium observations of May 1988 and July 1990 and 1991 could not be absolutely calibrated because of forest-fire haze, cirrus clouds, and limited clear time, respectively; however, the scale heights are still useful. 3. ANALYSIS

The principal steps in the processing are subtraction of a dark frame and normalization to a “flat field” obtained from incandescent lamps illuminating the inside of the telescope dome. An image of day sky was used to correct for variations in width along the length of the slit. Next the frames were rectified to remove the tilt and curvature

of the spectral lines and the slightly nonuniform dispersion, with the information taken from an exposure to a standard Th-Ar source. The tilt is caused by the out-ofplane mounting of the Cchelle grating (Hunten et al. 1991b). The resulting spectrum is still dominated by the continuum scattered from the Moon’s surface, which must be subtracted before photometry of the emission lines can be done. Sample spectra are shown by Tyler et al. (1988) and Hunten et al. (1991b). Occasionally (Kozlowski et al. 1990), it has been possible to perform a satisfactory subtraction on an entire frame, but more often it has been necessary to collapse the spectra along the slit in bins of -20-30 km before the subtraction is performed. This procedure gives the six to eight points per exposure typically seen in Figs. l-4. Uncertainties in the derived intensities are dominated by the continuum subtraction, which is most difficult near the limb. For this reason the first data point is taken 10 or so km above the lunar surface and is assigned the lowest weight in determining the best-fitting slope to the line-ofsight intensities. Within a single exposure, we estimate that errors for an individual point are within ?5%, and twice as great for the point nearest the surface, in the sense of a 95% confidence. For most of the measurements, noise is negligible, perhaps +-2%, but it is occasionally greater where the intensity is low (for example D, in Fig.

30

SPRAGUE

lal POTbSSlUM I8 JULY 1990 eq

‘;$+jF&1 ‘J/,,:‘1”::--:1 1990 tl0’N

0

50

100

150

0

50

100

150

If I 14 OCT 1990 80’

ET AL

solar flux is slightly augmented by the lunar albedo contribution and the - 1 km/set Sun-Moon Doppler shift. These corrections, which can amount to as much as 15%, are easily included. If z, is the minimum height of the line of sight, the abundance N(z,) from (1) must next be converted to n(z,), the number density as a function of height z. In previous work we have used the approximate relation N(z,) = n(z,) w, which is valid for a barometric atmosphere whose scale height His much smaller than the radius. The lunar atmosphere is not barometric and we observe scale heights as large as one-fifth of the radius just above the surface, and even larger at greater altitudes. Variable gravity can be allowed for by use of geopotential height ZFP = Y&Y,, + Z) or the dimensionless potential-energy variable

S

h = GMm r kTr =6’

I 0

GEOPOTENTIAL

A

I,

1,.

50

HEIGHT ABOVE LIMB

,,

I..

100

.,

12,

150

I

(km)

FIG. 1. Log of intensity as a function of geopotential height of the line of sight above the limb. (a) Potassium D,, July 18, 1990: (b) sodium D?, July 16, 1990. The point at 520 km (geometrical height 740 km) is an average for the whole slit; (c) both sodium lines. Oct. 13, 1990 at the equator; (d) both sodium lines, Oct. 13, 1990 at 80” north latitude: (et both sodium lines, Oct. 13. 1990 at 80” south latitude; (f) both sodium lines, Oct. 14, 1990 at 80” south latitude. In each panel, the line is a leastsquares ftt from which the apparent scale height H" is obtained.

where G is the gravitational constant, M and m are the masses of the Moon and of the atom, k is Boltzmann’s constant, T is a temperature, and r0 is the radius of the Moon. It is important to remember that A decreases away from the body, while geopotential height starts off nearly equal to geometrical height, becoming equal to r, at infinite distance. The real difficulty is in representing the atmospheric density distribution. It is conventional to compare the lunar atmosphere (and that of Mercury) to an exosphere,

5ooop

2b above 250 km). The absolute calibrations are good to ?15% or better; a major contribution to the absolute uncertainty is possible variations of sky transparency between exposures. An example can be seen in the results for October 12, 1990 at the equator (Fig. 4a), which are made up of three exposures to extend the height coverage. It is obvious that the points in the middle lie systematically high by -11%. The twilight airglow calibration for June 1988 has up to 60% absolute uncertainty. Scale heights, if obtained from a single exposure, are not affected by the absolute intensity calibration. If the abundance along the line of sight is N (atoms cm-?), the observed photon intensity I, multiplied by 4n x 10Ph to express it in rayleighs, is

(bl

29 AUGUST

1990 eq

E r FJ 5

SUPRATHERMAL

500-

too 0

50

5000

200

,

300

11

400 1

,

- .

-!s

1000 .

4rI = gN,

(1)

5ooo’Llo GEOPOTENTIAL

where the g-factor (Chamberlain and Hunten 1987) depends on the transition probability, the phase function, and the incident flux. As outlined by Tyler rt al. (1988), the phase function is not quite isotropic for D2, and the

HEIGHT

ABOVE

LIMB

Ikml

FIG. 2. (a. bottom) same as Fig. I. sodium Dz on June 7, 1988 at the equator; (top) Dz two-term fit with suprdthermat component guided by modeling. (b) The same, for August 29, 1990, but showing both sodium lines at bottom.

SODIUM AND POTASSIUM INTERACTION 4000

f

I

I

r

,

I

I

I

I,,

1 I

I,

I

I’

!

I

I,(,,1!,,,,,,,,

la) 14 OCTOBER 1990 eq

z ‘;

31

WITH THE MOON’S SURFACE

Ib) 14 OCTOBER

2000_5

z 2 z

.

0,

.-

.

Ic) 12 OCTOBER 1990 .90’S

GEOPOTENTIAL

HEIGHT

ABOVE

LIMB

1 km)

FIG. 3. (a) Same as Fig. 2b, for both sodium lines on Oct. 14, 1990 at the equator; (b) the same Dz data with a two-term fit; (c, d) the same, for Oct. 12, 1990 at 80” South. The line fitted to D, in (c) corresponds to the 1112-km apparent scale height shown in Table 3, not the smaller adopted value.

but in fact they cannot have Maxwellian distribution functions even if the flux emitted from the surface is Maxwellian. Trajectories in a collisionless atmosphere can be classified as ballistic, escaping, and satellite (Chamberlain 1963, Chamberlain and Hunten 1987). The distribution function can be strictly Maxwellian only if all three classes are fully represented, and if the escaping particles are replaced by the same quantity of incoming particles. Not only are the incoming particles missing, the short atmospheric lifetime for alkali metals assures that the satellite

population is also essentially absent. The major source of satellites at low altitudes is scattering from other atmospheric atoms or molecules. To estimate its probability, we must assume a value for the total atmospheric density, and we take 500 cm-3, the observational upper limit for 0 atoms. With a collision cross section of 3 x lo-” cm3 set-‘, the lifetime against scattering is nearly 10’ set, at least two orders of magnitude greater than the ionization lifetime. If some unmeasured constituent were present at around 10’ cm-3, the two lifetimes would be comparable,

ICI JULY 19, 1991

GEOPOTENTIAL

FIG. 4.

fdl JULY I9

TANGENT

HEIGHT

I km 1

Same as Fig. 3, for Oct. 12, 1990 and July 19, 1991, both at the equator.

i

32

SPRAGUE

TABLE 11 Chamberlain Parameters for Na

A, I 1.5 2 2,s 3 3.5 3.9 4 5 6 7 x 9 IO 12 14 17 20 24.3

H” 1011 950 865 765 697 620 567 561 452 37x 317 273 239 2 10 170 142 II4 95 72

7*

7.

r)

4529 4256 3875 3427 3123 277x 2540 2513 2025 1693 1420 I223 1071 941 762 636 511 426 323

7786 5191 3893 3114 25% 222s 2000 1947 1557 12% I I12 973 X65 770 649 556 45x 3x9 321

3.60 3.66 3.78 3.94 4.09 4.27 4.44 4.46 4.90 5.33 5.79 6.25 6.73 7.17 7.07 8.74 9.x3 10.77 II.93

and the satellite population might approach half the equilibrium value. It is thus an excellent approximation to regard the atmosphere as consisting of only ballistic and escaping atoms. In this paper we neglect the effect of radiation acceleration, which is 1.5% of surface gravity and 3% at an altitude of 700 km. At much higher altitudes it becomes important and could be a significant source of satellite particles and solar-antisolar asymmetry. Chamberlain (1963) has developed methods for computing exospheric densities above a critical level which emits atoms in an isotropic Maxwellian flux distribution. The appendix gives details, along with some additional computations to supplement Chamberlain’s tables which are reproduced in Chamberlain and Hunten (1987). Over the height region covered by our data, the integrated density, proportional to the line-of-sight intensity, can be represented by N = N,,e~;w’~‘“,

(3)

where the apparent scale height H*, obtained from the computations, is given in Table II. The corresponding apparent temperature T* is shown in both Table II and Eq. (A2), along with the airmass factor q described below. As described in the appendix, the temperature T (which enters the computations through the value of A) must be adjusted for the atomic mass, and must be multiplied by 1.70 for potassium. There is no guarantee a priori that the lunar atmosphere can be represented by a theory based on a Maxwellian flux distribution. If the observed line-of-

ET AL

sight abundances are adequately fitted by an exponential function of geopotential height, then it can be concluded that the theory is adequate for further analysis. Although our results below are limited in their precision and altitude coverage, each individual one can be so represented and therefore does define a “temperature,” which is generally found to be much hotter than the surface and should be regarded as a convenient parameter to represent the distribution. However, when we examine the ensemble of the measurements, we find a marked change in “temperature, ” increasing with distance from the subsolar point. We are therefore driven to the working hypothesis that the sodium atmosphere consists of two components, a “hot” or suprathrrmal one distributed over the entire day side and a “cooler,” thermal one, consistent with the actual surface temperature and concentrated in the subsolar region. Each component has its own value of H* and therefore of A, and temperature T. Conversion by Eq. (A2) or Table II is carried out separately for each component. For the optically thin lines observed, this procedure is valid as long as each component is horizontally uniform over a sufficient distance. This condition is almost certainly satisfied for the suprathermal component, but for the thermal component it may be marginal . A line of sight grazing the surface has an altitude of approximately (R,,/2)8’ at angular distance 13(in radians), or -100 km at 20” from the tangent point. This height is somewhat greater than the scale height ascribed to the thermal component, which must therefore occupy a circle at least 20” in radius to be regarded as sufficiently uniform. This issue deserves more attention, but we shall defer it to another occasion. Once the temperature and scale height are found by fitting the data and using the appendix, we can then use the effective path length 2K(O, h,) to obtain the number density at the surface. The line-of-sight column abundance just above the limb can be converted to the vertical column abundance by use of the airmass factor q. The abundance does not seem to vary significantly as long as attention is confined to the equatorial region, and the mean for the 1990 results is 10.7 x 10’ atoms cm- ‘. The polar values are smaller by a factor of 2-3. and are discussed in Section 5. The data have been analyzed in two different ways, referred to as single-component and two-component. We believe that the two-component version has a more reasonable physical basis, but the advantage of a singlecomponent analysis is that it makes fewer assumptions. A fit to the line-of-sight intensities gives an empirical scale height H*, and a corresponding “temperature” through (A2) for the observed atoms. The two-component analysis is described below. A summary of the results is given in Table III. Figure 1 shows six profiles for which only single-component anal-

SODIUM AND POTASSIUM INTERACTION

33

WITH THE MOON’S SURFACE

TABLE III Sodium and Potassium Apparent Scale Heights and Amounts Tangent

Date

Location

height (km) (geop)

24 May 1988 7 June 1988 reanalysis 16 July 1990 29 Aug 1990 12 Ott 1990 13 Ott 1990 14 Ott 1990 12 Ott 1990 Same 13 Ott 1990 14 Ott 1990 13 Ott 1990 19 July 1991

Equator Equator

100 100

25”s Equator Equator Equator Equator 80”s 8O”S” 80”s 80”s 80”N Equator

410 400 450 170 170 170 170 170 170 150 300

29 April 1989 18 July 1990

Equator Equator

106 170

Surface H”

(210) (km)

(2) Wlw,)

(kR)

Column abundance (zenith) ( IOx cmm2)

Surface number density (cme3)

Chamberlain temperature

emission rate

WI

119(38) 407(2 1) 354(2 1) SOO(45) 556(55) 611(72) 1112(196) 527(35) 517(35) 421(61) 516(35) 379( 15)

Sodium Dz 70 86 106 307 270 379 429 485 1535 397 394 317 393 287

310 385 476 1376 1210 1699 1924 2175 6878 1780 1764 1421 1760 1287

3.4 2.5 3.7 3.4 3.7 2.8 1.0 I.1 1.4 2.2 1.0 -

4.9 4.1 9.9 11 12 10 4.4 3.8 4.9 6.5 4.3 -

57 34 26 17 20 16 5 7 9 14 6 -

85(9) 154(23)

Potassium D, 80 136

610 1033

2.1 2.8

0.45 1.3

10 9

Note. Emission rates in the seventh column are for the line shown. u Values calculated using upper limit on limb data point.

yses were done; the remaining six are presented in Figs. 2-4, which include the two-component analyses as well. The line-of-sight scale heights H* and single-component temperatures were obtained by least-squares fitting. Estimated standard errors are shown in parentheses in the fourth column of Table III. The figures do not include the potassium data from 29 April 1989 (Kozlowski et al. 1990), but the reanalyzed sodium results from June 1988 are shown in Fig. 2. We paid special attention to this set because its small scale height stands out and it was strongly questioned by Morgan and Shemansky (1991). The new scale height is slightly but not significantly larger than the original one. The largest permissible geopotential scale height is 156 km, corresponding to a temperature of 700 K. Our very first observation, in May 1988, is very noisy because of poor equipment performance, and uncalibrated because we were observing through haze from a local forest fire, but it is a useful confirmation because it gives the low temperature of 310 + 100 K. Because both these data sets came from within a few degrees of the subsolar point, it is reasonable that the apparent scale height is dominated by the thermal component. A significant contribution from the suprathermal component at unobserved high altitudes would not be apparent in these observations. To test these hypotheses we made a special effort to obtain one more set of measurements at a small solar

zenith angle, and succeeded on July 19, 1991 (see Figs. 4c and 4d). Although conditions were not ideal and the telluric water lines were strong, we obtained uncalibrated data up to 300 geopotential km. The apparent scale height for the points below 100 km is 252 geopotential km, and for the entire data set it is 379 geopotential km. These numbers suggest that we did observe the transition from a mixture of thermal and suprathermal to mainly suprathermal atoms, as illustrated by the two-component fit of Fig. 4d. The two-component analysis was applied to a selected set covering a range of solar zenith angles from 3 to 82”; these results are shown in Figs. 2-4. As discussed above and in Kozlowski et al. (1990), there is no unique way to carry out this decomposition without data to much higher altitudes, and it is necessary to make some plausible assumptions. We have chosen to fix the apparent scale heights for the two components, guided by the computations in the appendix and by our data which required high Chamberlain temperatures on 13 and 14 October, 1991. For the thermal component we used the temperatures given below in the third column of Table V and the third line of Table VI (Keihm and Langseth 1972), calculating individual values of H* as described in the appendix. Our choice for the suprathermal component was H* = 620 km, with A, = 3.89 and T = 2000 K. A suitable combination of these slopes was then chosen to fit the data. Figure Sa shows the single-component apparent scale

34

SPRAGUE

1

-z

.

(a)

~1000 -

TO 150- 400

-

km

500 -

8

.

_

,OTO 100 km / do

-

._----

OO IOOr

(b)

l

POTASSIUM

301

60 I

90

I

I

I

SUPRATHERMAL

\

90

SOLAR

ZENITH ANGLE

(degrees)

5. (a) Apparent geopotential scale height of the line-of-sight intensities as a function of local solar zenith angle. Open circles show fits to data from 0 to 100 geopotential km; solid circles go to higher tangent heights. (b) The partitioning of sodium between thermal and suprathermal components in the atmosphere, and adsorbed on the surface, according to Table 6. The distances between the curves represent the fraction of the total for each component.

heights as a function of solar zenith angle. The marked trend, which is also present for the two potassium points, is the basis for our hypothesis of two atmospheric components and two competing release processes. The open circles near the origin represent measurements limited to 100 km, and include this part of the July 1991 results, while the entire height range is shown by a solid dot. All these results are further analyzed and discussed in Section 5. 4. RELEVANT

Adsorption

PROCESSES

und Desorption

On collision with the surface an atom may be scattered, adsorbed, or chemically bound. After a sufficient number of scattering events, if nothing else intervenes, the atoms must reach a Maxwellian distribution at the surface temperature, and the rate of approach is described by the accommodation coefficient. Both accommodation coefficients and adsorption energies have been computed by Shemansky and Kunc, for an ideal surface of a-quartz; this work is summarized in the review chapter by Hunten et al. (1988). The adsorption energies D are given as 0.26 eV for Na and 0.24 eV for K, small enough to predict a sticking time less than a second even at nighttime temperatures. It was argued that these values should apply to the different composition and physical state of the Mercurian

ET AL.

(and, by extension, lunar) surface, and that the atoms should quickly be accommodated to the surface temperature. Morgan and Shemansky (1991) assume that any tighter bonding must be chemical in nature and postulate that there is an appreciable activation energy. In consequence, for tight, or “chemical-scale,” bonding to occur, atoms must strike at a considerable velocity. Although simple molecules in the gas phase often show such behavior, we see no reason why it should apply to the interaction of an atom with a surface. For example, it would imply that oxygen in a flask, once dissociated into atoms, would remain in that state indefinitely, or recombine very slowly, at room temperature. The lunar atmospheric observations indicate that atoms remain on the surface for longer times and thermal accommodation is less efficient than predicted by Shemansky and Kunc. Our interpretation of the atmospheric data suggests that sodium and potassium atoms typically adsorb to the lunar surface with an energy of around 1 eV. Although the bonding could be chemical in nature, it seems more reasonable to us that it is physical; it can be described as an udsorption. As suggested by Kozlowski et al. (1990), the lunar surface is likely to be covered with dangling chemical bonds. Sputtering by solar-wind protons and UV photons, some having energies of tens of electron volts and higher, will break silicate bonds. Bombardment by micrometeoroids will have the same effect. Most atoms and molecules (including Si, Al, Mg, and Fe and their oxides) released by these agents must undergo a ballistic orbit and fall back to the surface, where they will lie or wander around and undergo further chemistry. The surface, on an atomic scale, must resemble a brush pile more than an ordered crystal. Because oxygen is lost to the system more rapidly than the more refractory molecules and atoms, the material is likely to be deficient in, and ready to react with, oxygen. Some of the consequences have been examined on returned samples and in related theoretical studies, but even if such a layer survived sampling, return to Earth, and subsequent handling, no analytical tools exist to study it on an atomic scale. Scanning electron microscopy (McDonnell 1977) has illustrated the “accreta” at the submicrometer scale, but studies of erosion by sputtering have had to be much less direct. Monte-Carlo studies (Carey and McDonnell 1976) indicate that many sputtered atoms are intercepted by other gains near their source; this is illustrated by Johnson and Baragiola (1991). Most of the rest execute ballistic orbits and fall back to the surface, and a few may be able to escape. The reaccreted atoms and molecules are believed to account for the very small sputtering rates inferred by various indirect methods (McDonnell 1977, Kerridge and Kaplan 1978, Kerridge 1991). A detailed and quantitative compendium of sput-

SODIUM

AND POTASSIUM

INTERACTION

tering effects on surface materials is given by Johnson (1990); see also Johnson and Baragiola (1991). Taken together, these physical processes have a profound influence on the fate of an impinging atom; on a macroscopic scale one could imagine dropping a marble on a grassy lawn, while the theoretically ideal surface would be more like the sidewalk. In such a molecular “brush pile” it is probable that an alkali atom would see around three bonding sites of greater strength than could exist for a perfect crystal, and we therefore suggest that an adsorption energy of 1 eV or even greater is reasonable. There is substantial in situ evidence for strong adsorption of Ar at nightside temperatures (Hodges 1980, 1982). Instead of the large nighttime maximum of atmospheric density observed for helium and expected for a T - 5’2behavior, the landed mass spectrometer found a transient maximum after sunset, followed by a decay to a minimum just before sunrise. The adsorption energy derived from this behavior is 6-7 kcal/mole, or 0.28 eV. Laboratory experiments by Bernatowicz and Podosek (1991) show a similar value for a freshly crushed sample, although it seems that the strongest sites are quickly saturated by impurities, either in the vacuum system or, as suggested by the authors, released from the sample. Such impurities are much less prevalent on the Moon. In view of the inertness of argon, it seems likely that the adsorption energy for chemically active atoms, including alkalis, is much greater. Our data seem to require two desorption processes, one producing atoms at the surface temperature and the other producing a highly suprathermal energy distribution. We suggest that these two processes are thermal desorption and photodesorption by solar photons. The thermal desorption time [Hunten et al. 1988; Eq. (Bl)] can be estimated from ^- loTth

13eDlkT

(4)

the product of a vibrational period and the reciprocal of a Boltzmann factor, representing the number of attempts necessary to overcome the energy barrier of height D. The rate of thermal desorption is extremely sensitive to the surface temperature; between 200 and 400 K it can change by 12 orders of magnitude. For D = 1 eV and a representative dayside temperature of 350 K, the lifetime is 25 sec. On the night side, adsorption would be essentially permanent until after sunrise. Although we have no independent way of estimating D to anything like the required accuracy, we suggest that the desorption time near the subsolar point is likely to be a few tens of seconds, competitive with a reasonable photodesorption time. Ip (1986) and McGrath et al. (1986) suggested the importance of “photosputtering” for Na at Mercury. McGrath et al. used -2 eV for both bound and adsorbed atoms and

WITH THE MOON’S

SURFACE

35

predicted a nonthermal, extended Na component along with a component from thermal desorption. These ideas were taken up by Kozlowski et al. (1990) and applied to lunar sodium and potassium. They (and we) preferred to use the term “photodesorption” for the release of atoms adsorbed on the surface with energies - 1 eV, by photons of wavelengths in the 3000-8000 A range. Whether photosputtered or photodesorbed, ejected atoms are likely to have some spread of kinetic energy, reflecting the shape of the solar spectrum and the photon absorption cross section, as well as the complicated sharing of energy between the various interatomic bonds and vibrational modes in the vicinity. In some cases, sputtered atoms are found to have a power-law energy distribution (Johnson, 1990). The probability of photodesorption can be expressed as the product of a solar flux and a cross section. For the flux we shall retain our earlier estimate (Kozlowski et al. 1990), which rounds to 3 x 10” photons cm-2 see-’ for the 3000-8000 A range. Most of the photons in this range are between 5000 and 8000 A. Atomic and molecular cross sections can be as large as 10-l’ cm’, but we shall adopt a more modest value of 10m20cm2 for the environment of an adsorbed atom. The product of flux and cross section, the desorption rate factor, is J = 3 x 10m3 set-‘. In the absence of information we shall use the same value for Na, K, and 0. Several estimates for photosputtering rates exist in the literature. Ip (1986) quotes cross sections in the range 1O-24to lo-l8 cm2; the corresponding desorption coefficient is J = 0.3 see-’ or less. McGrath et al. (1986) estimate J = 10m4to 10m3see-‘. Morgan and Shemansky (1991) give a probability instead of a cross section; multiplication by IO-l7 cm2 gives values one or two orders of magnitude smaller than the one we adopt. Our values are generally compatible given that photodesorption would be expected to be more probable than photosputtering. The photodesorption lifetime 7rd is J -’ at the subsolar point and will vary as the cosine of the solar zenith angle. The surface residence time is 7, and 7thand 7rd are properly called “partial lifetimes. ” Empirically, the suprathermal atmospheric component can be represented by a “temperature” of -2000 K, and presumably includes a velocity tail above the escape velocity. Whatever the distribution may be, it is continually regenerated on every photodesorption event. The Jeans formula, used with the number density of the supratherma1 component, should therefore give a reasonable estimate of the corresponding escape flux, as suggested for meteoroid impact by Morgan and Shemansky (1991). The relevant values of the escape parameter h, at 2000 K are given in Table IV. Characteristic loss times, referred to the atmospheric inventory, are of order lo4 set for Na and even shorter for 0 (if it too has a 2000 K temperature). If comparable quantities are adsorbed to the surface, the

36

SPRAGUE

ET AL.

Production

TABLE IV Ballistic Quantities

Luterrrl Migration

Morgan, Zook, and Potter (1989) have shown that vaporization of regolith by micrometeoroid bombardment is a probable source of alkali atoms. For impact velocities below -20 km set-‘, the velocity of the vapor plume is small, and most of the vapor is retained by the Moon. Morgan and Shemansky (1991), however, neglect this component in favor of the faster impactors that give velocities large enough to escape. Thus, an ejected atom either escapes from the Moon or makes a single ballistic hop of the sort described above. During this first hop it is described as a source particle, following Hunten et al. (1988). It then joins the ambient population, and if the “temperature” is 2000 K it continues to hop around until it reaches the night side or is photoionized. As estimated above, there are about 12 ambient atoms aloft for each source atom, and detection of the latter is difficult or impossible. The dilution increases rapidly for lower temperatures. Sprague (1990a) has proposed another source, diffusion through the regolith from a depth of a few km; such atoms would be released in a thermal distribution that is even harder to resolve from ambient atoms. However, it may be that this source is much more important on Mercury than the Moon.

Atmospheric atoms move over the surface in a series of ballistic hops. Table IV shows typical hop times and distances for Maxwellian distributions at 360 and 2000 K. The average range is approximately equal to the scale height, and the corresponding ballistic time is t, = (2/g) V%?%; for the examples shown, this time is between 7 and 26 min and the scale height between 47 and 640 km. Migration over greater distances is a random walk. If a typical distance of interest is taken as the lunar radius Y, the necessary number of hops is of the order of the square of r/H, or of the surface value h, as defined in Eq. (4). The migration times shown do not include time spent adsorbed to the surface and are therefore lower limits. For the example of sodium at 2000 K, the time is at least 20,000 set (5.6 hr) and the number of hops is 4’ = 16. The mean life of sodium against photoionization is 14 hr, and during this time the number of hops would be 39 if the atom did not reach the night side first. If an atom requires 16 hops to reach the night side, and is also subject to photoionization, the average net number of hops is about 12. At 360 K, A, = 21.6, the migration time becomes 2.6 x 10’ set, while photoionization occurs after 90 hops. All the numbers shown in Table IV are for parabolic rather than elliptical trajectories, but the correction is minor even for small values of A,. For the elliptical orbit the mean range in radians is approximately I/(& - l), to be compared with l/X, for the parabolic case. The difference is negligible in view of all the other uncertainties.

A major conclusion of Morgan and Shemansky (1991) is that 99.5% of the sodium atmosphere escapes without ever reimpacting the surface. The continuity equation for this situation is nur2 = constant, where u is the radial component of the velocity at distance r. For a constant velocity, n varies as r-’ and the line-of-sight abundance as r- ‘. With a more reasonable value of the initial velocity, the velocity diminishes substantially over the first few lunar radii to an asymptotic value, and the density has the inverse behavior superposed on the r-‘. It is easy to show that the index for the density is initially - 2, asymptotically approaching - 2 at large distances. The form of the integrated density is no longer easy to derive, but clearly the index must start out near - ?2and then approach - 1. If the observed index is more negative than - 1, there must be a significant component that is gravitationally bound. Similar results are given by Chamberlain (1963). Mendillo et al. (1991) have clearly shown that the intentsity in the solar direction varies with an index around ~ 4 between 2 and 5 lunar radii, and that the data of Potter and Morgan (1988b) fall close to the same curve. A similar demonstration is given in Fig. 6 for two of our data sets that reach substantial altitudes, as well as those of Potter and Morgan. None of the data resemble the dashed line, which has a slope of - 1; rather, they show slopes between

Temperature

(K)

360

Scale height H = range (km) h = RIH Hop time (set) Migration time ( 10J set) Ionization time (IO see) Escape energy (eV)

2000

0

Na

K

0

Na

K

116 is 669 I5 250 0.47

80 22 5% 26 s.2 0.68

47 37 429 57 3.5 I.18

642 2.7 1578 I.3 250 0.47

446 3.9 1316 2.0 5.2 0.68

263 6.6 1011 4.4 3.5 I.18

loss times for the total inventory would be doubled. This “suprathermal escape” rate is competitive with the ionization process for sodium and potassium, and much faster for atomic oxygen. However, our estimate of the Na escape flux is considerably smaller than the -30 x lo4 cm-’ set-’ given by Morgan and Shemansky (1991); we obtain 3 x IO4 cmm2 set’.

SODIUM

AND POTASSIUM

INTERACTION

2000

RADIAL DISTANCE(km1 FIG. 6. Log-log plots for the three available data sets that extend to high altitudes. From top to bottom, they are from Potter and Morgan (1988b), Fig. 2b, and Fig. 4a. The dashed line has an index of - 1, representing the steepest slope that an escaping component can show.

-2.6 and -3.5, corresponding to -3.6 to -4.5 for the number density. Both these results and those of Mendillo ef al. (1991) demonstrate that at most a small fraction of the observed sodium is escaping. This does not necessarily mean that theflux is small, because fast-moving atoms make a small contribution to the density relative to slow ones. 5. INTERPRETATION

Competing

OF DATA

Release Mechanisms

As mentioned in Section 3, the chief reason for the hypothesis of a two-component atmosphere is the trend of increasing apparent scale height with local solar zenith angle (Table III and Fig. 5a). Table V gives additional details on the five selected data sets of the six illustrated in Figs. 2-4. The solar zenith angles and Chamberlain temperatures of Table V show the trend of the singlecomponent temperature analysis. Although we have only two measurements for potassium, they show the same behavior between solar zenith angles of 7” and 40”, but considerably smaller scale heights. A two-component distribution is well known for H at Venus (Wallace 1969, Chamberlain and Hunten 1987) and was used for lunar Na by Potter and Morgan (1988b), and for K by Kozlowski er al. (1990). However, this interpretation was rejected by Morgan and Shemansky (1991). The 385 K (revised to 476 K) sodium temperature for June 1988 becomes a natural end member, with its solar zenith angle of only 3”. Confirmation is offered by the very first result of 310 K (see Table III) obtained just 2

WITH THE MOON’S

SURFACE

37

weeks earlier right at the subsolar point, although the data are rather noisy and reach only 100 km altitude, and by the July 1991 results, which were obtained to test the twocomponent hypothesis. We now show that these trends can be explained in terms of the competition between thermal and photon-induced desorption. Thermal desorption dominates near the subsolar point while photodesorption dominates at high zenith angles. Confinement of a substantial thermal component to the region of the subsolar point occurs through the exponential dependence of the thermal desorption rate on the ratio D/T of adsorption energy and surface temperature, Eq. (4). On the other hand, photodesorption varies only as the cosine of the solar zenith angle. Table V shows sample values of the partial lifetimes for thermal desorption calculated from Eq. (4) for the five selected cases. Lifetimes r,,, range between 7.9 and 21,000 set, if D = I. 1 eV, and over an even wider range if D has some other value. Photodesorption times rpd are also shown in Table V for a reasonable range ofcross sections and including the effect of solar zenith angle. Focusing on a cross section of 10m2” cm’, we see times of 330 set (subsolar) to 1920 set (lo” from the terminator). In the subsolar region, thermal desorption is more probable than photodesorption; most of the atoms should be in a thermal distribution with a scale height close to the expected value of 87 km for a fully accommodated atmosphere. Near the terminator, photodesorption dominates the release of atoms and controls the energy and height distributions. The surface residence timer, is given by l/7, = l/~,~ + l/~. Such a trend is obvious in the data sets collected in Table V. As the solar zenith angle goes from 3” to 80”, the Chamberlain or single-component temperature varies monotonically from 476 to 1804 K. In the two-component interpretation, this variation reflects a shift from mostly thermal to mostly suprathermal atoms. In a previous paper (Kozlowski et al. 1990) we formulated and solved a set of equations for the statistical equilibrium of this system, including the redistribution of potassium atoms between thermal and suprathermal populations by photodesorption and inelastic collisions with the surface. More detail is given in Sprague (1990b). We adopt an unspecified source and equate it to half the loss by ionization. Figure 7 illustrates the atmospheric populations and their redistribution from one to another. Atoms are divided among thermals, suprathermals, and atoms residing temporarily on the surface. An unspecified source (box shown at the left) provides atoms at the same rate they are lost by ionization and Jeans escape. Half of the ions are assumed to be recycled by surface impact. The rates are dependent upon the choice of sticking coefficient (S) and accommodation factor (A), which are here given the values 0.8 and 0.2. The standard accommodation coefficient a is defined in terms of the excess energy E’ = E - Et,, lost in the

38

SPRAGUE ET AL.

TABLE V Relevant Desorption Lifetimes

Date

Solar zenith angle (deg)

7 June 88” 29 Aug 90” 12 Ott 90” 14 Ott 90” I2 Ott 9oh

3 9 I6 41 80

Surface temperature (K) 399 395 392 358 321

Chamberlain temperature (K) 476 1210 1617 1706 1804

Thermal desorption lifetimes 7th (set) Bonding energy (eV)

Photodesorption lifetimes 7pd (set) Cross section (cm?)

I.1

1.2

IO-‘9

,()-?,I

7.9 10.8 13.9 310 2 I ,000

144 205 268 7,800 790,000

33 34 35 44 I92

330 340 350 440 1920

” Equatorial observation ’ 805 latitude.

average collision, where E is the incident energy and Et,, is the thermal energy corresponding to the surface temperature. After a number n of collisions, the excess energy will be reduced from its initial value by the factor emu”; the number of collisions necessary for this factor to be l/r is therefore II, = l/a. Our accommodation factor A enters the equations as the probability that an atom will be thermalized in a single collision, and can be equated to I/n, = CY. Table VI shows solutions for the five selected cases (June 1988, August 1990, 12 October 1990 Equator and S polar, and 14 October 1990). The correlated increases in solar zenith angle and sticking time and the importance of photodesorption are seen by comparing the populations shown in Table VI and illustrated in Fig. 5b. Particularly notable is the increase in the number of atoms residing on the surface as solar zenith angle increases and surface

52 SOURCE

REFLECTED -______-.-.__ RPTION

/

EVAPORATION

FIG. 7. Flow chart for thermal and suprathermdl numbers for five cases are given in Table 6.

sodium atoms:

temperature drops. These numbers illustrate that the twocomponent models shown in Figs. 2-4 are all consistent within a single framework. The requirements are that at least 80% of the atoms that impact the surface stick to be later desorbed, and the other 20% of the impacting atoms have an accommodation efficiency of 0.2. The two-component models span the entire range from almost exclusively accommodated atoms (June 1988) to entirely suprathermal (Ott 12, 805). High-Latitude

Observations

The last column in Table VI is for 80” south, while the others refer to low-latitude observations. Although the atmospheric inventory near the pole is less than half as great as the low-latitude mean, the difference is made up to a considerable degree by a larger quantitiy on the surface. The reason, of course, is that both desorption processes are diminished at large solar zenith angles. Within the accuracy of the budgeting and the natural fluctuations of the data, it appears that the total inventory may be independent of latitude. The dominant loss processes, migration to the night side and photoionization, both depend on the amount in the atmosphere, although the migration rate is increased by the proximity of the terminator and mildly augmented by solar radiation pressure. The suprathermal Jeans part falls off with the cosine of the solar zenith angle. The high-latitude average for all four nights is 5 x lo* cm-‘, still much less than the low-latitude mean of 9.4 x IO*. If the increase at 80” south latitude on 13 and 14 October 1990 is a special event such as a meteor shower (Hunten et al. 1991a), the average is 4 x lo8 cm-‘. Thus, the total inventory (atmosphere plus surface) would still be somewhat reduced relative to low latitudes. Potter and Morgan (1991), however, find rather different results. They present three polar observations which,

SODIUM AND POTASSIUM

INTERACTION

39

WITH THE MOON’S SURFACE

TABLE VI Solutions for Redistribution of Sodium Date:

7 June 88O

Solar zenith angle (“) Surface temperature (K)

3 399

Thermal Suprathermal Surface Total

30 19 4.9 53

Thermals-adsorbed Suprathermals-adsorbed Desorbed-thermals Desorbed-suprathermals Thermals-Reflected Suprathermals-reflected Reflected-thermals Reflected-suprathermals

32 7.2 32 7.7 8.1 1.8 8.4 1.5

29 Aug 90” 9 395

12 Ott 90” 16 392

Inventories (10’ atoms cm-Z) 40 13 84 100 9.6 9.9 130 120 Production rates (lo4 atoms cm-* set-‘) 28 14 33 39 27 12 35 41 7.0 3.5 8.1 9.6 8.6 5.4 6.7 7.9

14 Ott 90” 41 358

4.8 97 22 120 5.5 37 3.6 40 1.4 9.3 3.3 7.6

12 Ott 906 80 321

0.63 39 38 77 0.77 1.5 .016 16 0.19 3.7 0.95 3.0

a Equatorial observation. b 80”s latitude.

on average, have roughly the same abundance as the equatorial ones. Evidently more observations are required to define the typical behavior. 6. DISCUSSION Our observations of Na and K in the lunar atmosphere show a wide range of scale heights, single-component temperatures, and surface number densities although the column abundances remain within a factor of 3. We can explain the observed trends, including the hitherto puzzling observations of June 1988, with a model of competing release mechanisms and resulting two-component atmospheres. Observations made at the warm subsolar point show a predominantly thermal energy distribution, consistent with small thermal desorption times for alkali atoms. These observations do not extend high enough to reveal the expected suprathermal component. As the solar zenith angle increases and the surface temperature drops, the atoms stay on the surface longer and are released by photodesorption, which imparts a more energetic velocity distribution, resembling a Maxwellian at 2000 K. Thus mixtures of different relative proportions of thermal and suprathermal atoms exist until temperatures are so low at high latitudes and near the terminators that there is little or no thermal desorption. There the energy distribution is almost purely generated by photodesorption. Our existing data set is consistent with this pattern but does not demand it. Most urgently needed are observations extending to at least 1000 km altitude, so that the deduced suprathermal component will be fully resolved

even at small solar zenith angles. The July 1991 data shown in Figs. 4c and 4d are a good beginning, but the solar zenith angle is still 6”, and neither the height coverage nor the signal-to-noise ratio is fully adequate. We have not attempted a similar resolution of our two potassium measurements, but there is a hint that the suprathermal “temperature” may be lower than for sodium (see Fig. 5a). Ifthis is verified by additional measurements, it will imply different atomic parameters (adsorption energy and the atomic vibrations that determine the desorption behavior). For a reasonable probability of photodesorption, and to keep the rate of thermal desorption in the same range, it is necessary to assume that the adsorption energy of Na to the lunar surface is a little greater than 1 eV. We believe that this rather strong binding is reasonable for the lunar surface, which must be as rough and disordered on the atomic scale as it is on the millimeter and centimeter scale. The modeling of vertical distribution in the appendix assumes that atoms are emitted from the surface in aMaxwellian flux distribution. This assumption is reasonable for the thermal component, but for suprathermal atoms is mainly a convenience. Our data have neither the precision nor the height coverage to resolve any deviations from the Chamberlain theory. If the desorption threshold is roughly equal to theadsorptionenergy, 1 eV(12,000A), 75%oftheactive photons in the solar spectrum are still below 2 eV (6000 A). Such a modest excess of energy may help explain why the observed “temperature” of the photodesorbed sodium is only 2000 K. Undoubtedly, just as in the photoelectric effect, most of the desorbed atoms retain only a fraction of the photon energy.

SPRAGUE

40

As shown in Fig. 6 and discussed in Section 4, log-log plots of intensity as a function of radial distance have slopes between - 2.6 and - 3.5. The power-law index for the number density is therefore in the range - 3.6 to -4.5, incompatible with the suggestion by Morgan and Shemansky (1991) that the bulk of the observed sodium is on escape trajectories. Mendillo et uf. (1991) find that on the sunward side, their intensities can be represented by a power law of index -4 which, as they point out, corresponds to a density law of index - 5. If an I’ ’ curve, characteristic of an atmosphere in rapid escape, is adjusted to their point at 5 lunar radii, it gives an intensity of about 50 R at the surface, only about I% of the total observed there by Potter and Morgan and by ourselves. Although solar radiation pressure is becoming important at the highest altitudes, allowance for it will not change the conclusion that we are observing a ballistic atmosphere. Any escaping component must be a very small fraction of the observed density. Implications

jeer-the Oxygen Budget

A rather tight upper limit on the abundance of atomic oxygen was set by Fastie rt al. (1973) and somewhat relaxed by Feldman and Morrison (1991). Photoionization is rather slow for 0, with a characteristic time of 2.5 x 10h set, and the dayside lifetime on the average is twice as great because half the ions are returned to the surface. Morgan and Shemansky (1991) conclude that the abundance should be about 160 times greater than the (revised) observational limit. They reject the idea that 0 atoms might efficiently react with surface constituents, unless they arrive with enough energy to overcome an activation barrier. To increase the loss rate they postulate a novel sink: migration to the night side, followed by pickup of an electron from the surface. The resulting negative ion is rapidly lost. The effective lifetime is now the migration time to the night side, between 1.2 x lo4 and 1.5 x 10 set according to Table IV. We suggest that adsorption (and, perhaps, subsequent chemical reaction) could be as efficient for 0 as we find it must be for Na and K, giving a loss rate much greater than photoionization in the atmosphere. For a sticking efficiency of 0.5, the characteristic time for adsorption is around 3 hop times, or 1500 to 3000 set according to Table IV. This rate is faster than migration to the night side by a factor of 10. Another potentially important sink is Jeanslike escape of the faster atoms as they are ejected from the surface, as discussed for Na in Section 4. For example, an energy distribution resembling a 2000 K temperature would give a Jeans lifetime of about lo4 sec. In addition, the sources of 0 were examined by Johnson and Bardgiola (1991), and suggested to be much more modest than those of Morgan and Shemansky. We agree that there is no need to postulate any novel sink process.

ET AL. 7. CONCLUSIONS

Our observations of Na and K in the lunar atmosphere show a wide range of scale heights, equivalent temperatures, and surface number densities although the column abundances remain within a factor of 3 of one another. We can explain all of the observed differences, including the previously puzzling observations of June 1988, with a model of “competing release mechanisms” and resulting two-component atmospheres. The atmosphere in the subsolar region is dominated by thermal desorption, which gives a scale height corresponding to the surface temperature. In cooler regions farther from the subsolar point, the rate of thermal desorption drops rapidly; the atoms stay on the surface longer and are released by photodesorption, which imparts a more energetic velocity distribution. Thus different mixtures of thermal and suprathermal atoms exist until temperatures are so low at high latitudes and near the terminators that there is little or no thermal desorption. There the atmosphere, almost entirely generated through photodesorption, has an energy distribution that appears like a Maxwellian at -2000 K. For this competition to work as inferred, the rates of thermal and photodesorption must be in a rather specific ratio, although there is more flexibility in the absolute values. Suitable values are 1.1 eV for the adsorption energy and 300 set for the partial lifetime against photodesorption at the subsolar point. It is likely (Morgan and Shemansky 1991) that source atoms, those released by a process such as meteoroid impact, have fairly high energies, or temperatures, 2500 K or higher. Such fast atoms, if they could be observed, could be a signature allowing the dominant source to be identified. Unfortunately, they are almost certainly submerged in the much larger density of recycled “ambient” atoms, which also are found to have high temperatures. We find that the polar Na abundance in the atmosphere is only one-third of that at low latitudes, although the total amounts (atmosphere plus surface) are similar. This result is based on four measurements obtained over 3 days, and is not confirmed by the results of Potter and Morgan (1991). More observations are needed to define the average behavior. If the total polar inventory does turn out to be reduced, a possible explanation is the drain by migration to the night side. In a related paper (Hunten et al. 1991a) we suggest that our southern high-latitude data contain evidence for an otherwise undetected meteor shower. We suggest that oxygen atoms, like sodium atoms, stick efficiently to the surface, but then react with surface materials. This gives them a very short atmospheric lifetime which helps explain the fact that they have not been detected.

SODIUM AND POTASSIUM

INTERACTION

41

WITH THE MOON’S SURFACE

corresponding apparent temperature T* is defined as mgoH */k, where go is the acceleration of gravity at the surface. Over the range A, = 2 to 20 (temperatures 2’ of 3893 to 389 K for sodium), the relation between the real temperature and apparent scale height is represented to 1% by

i 2997 2355 3077 1482 1867 1172_ rgw 5=,

NUMBER DENSITY (n, cni31 FIG. 8. The Chamberlain model atmosphere for Na emitted at 2000 K, corresponding to A, = 3.89. The barometric number density at the surface was arbitrarily taken as 1000 cme3, about 60 times greater than observed. Dotted lines show the escaping and ballistic components of the total density. Also shown are the line-of-sight integrated density N and its slope H*.

APPENDIX:

ATMOSPHERIC

DENSITY

T = 4.488

= 4.488 * 1.0179 - &

t &

L42)

Table II shows the actual computed data, including the airmass factors that can be used to obtain the zenith column abundance. For potassium, the factor 4.48 becomes 7.62, and the temperatures T in Table II must be adjusted by the mass ratio 1.70. As pointed out in Section 3, there is reason to doubt that sodium atoms are emitted into the lunar atmosphere with a Maxwellian distribution, which is the basis for all the results given here. But they are the best we have until there is information about the actual energy distribution. As discussed in Section 6, observations to very high altitude are usefully represented in terms of the logarithms of intensity and radial distance r. Chamberlain (1963) showed that power-law behavior is expected at great distances. The integrated-density expression is reproduced as Eq. (7.1.67) in Chamberlain and Hunten (1987).

PROFILES ACKNOWLEDGMENTS

If the flux distribution of emitted atoms is Maxwellian, the height distribution can be obtained by the methods given by Chamberlain (1963) and reproduced in Chamberlain and Hunten (1987); the following equation numbers are for that book. The barometric density is multiplied by the appropriate partitionfunctions &,aland <,,, for the ballistic and escaping components [Eqs. (7.1.34) and (7.1.43)]. Although the expressions look forbidding, they are easily evaluated with the help of a subroutine for incomplete y functions. Figure 8 illustrates the barometric density that would be realized for a fully populated atmosphere, the actual total density, and its ballistic and escaping components. The temperature was 2000 K (A, = 3.89), the value used for the suprathermal component in Figs. 2-4. These densities can then be integrated numerically along any line of sight; for present purposes the relevant equation is (7. I S2) with F, set equal to zero for a horizontal line of observation. The path-length factor 2K(O, A,) multiplies the number density and the true scale height, referred to the gravity at the tangent point, to give the column abundance. The zenith abundance is obtained by use of another path-length factor K( I, A,), where the subscript c refers to the critical level or surface. This abundance can be obtained more directly by multiplying the line-of-sight column density just above the limb by the airmassfactor 7, defined as

2K(O, A,) rl = K(l,h,) .

(Al)

Appendix IX of Chamberlain and Hunten (1987) tabulates the partition functions and path-length factors for selected cases; we have supplemented them on a finer grid of A,. If the logarithms of these line-of-sight integrated densities are plotted against geopotential height (as shown by a dashed line in Fig. 8), it is found that the slope (represented by an empirical scale height H*) is constant within 1 or 2% up to heights of about 500 km geopotential, or 702 km geometrical. This height is sufficient for the data reported here; at greater heights the computed geopotential scale height H* begins to fall off. This behavior is also shown in Fig. 8; for the very small value of h, used there, the variation with height, while still modest over the relevant height range, is somewhat greater than mentioned above. The

We are grateful to Dr. D. Housley and Mr. Dan Hughes, both of Susquehanna University, for help with observations. Useful comments and criticisms were received from R. Hodges, R. Johnson, T. Morgan, and D. Shemansky. Special thanks is given to an anonymous reviewer for a complete annotation of the text. Support was received from NASA Grant NAGW-596 to Hunten, the Research Corporation and the NASA JOVE program to Kozlowski, and an NRC Associateship at Ames Research Center to Sprague.

REFERENCES BERNATOWICZ,T. J., AND F. A. PODOSEK1991. Argon adsorption and the lunar atmosphere. Proc. Lunar Planetary Sci. Conf. 21st, 307-3 13. CAREY,

W. C. AND J. A. M. MCDONNELL 1976. Lunar surface sputter erosion: A Monte Carlo approach to microcrater erosion and sputter redeposition. Proc. Lunar Sci. ConJ: 7th, 913-926.

CHAMBERL.AIN,J. W. 1961. Theory of the Aurora and Air&w. demic Press, Orlando.

Aca-

CHAMBERLAIN,J. W. 1963. Planetary coronae and atmospheric evaporation. Planet. Space Sci. 11,901-960. CHAMBERL.AIN,J. W., AND D. M. HUNTEN 1987. Theory ofPIanetary Atmospheres. Academic Press, Orlando. FASTIE, W. G., P. D. FELDMAN. R. C. HENRY, H. W. Moos, AND T. M. DONAHUE1973. A search for far-ultraviolet emissions from the lunar atmosphere. Science 182, 710-711. FELDMAN, P. D., AND D. MORRISON1991. The Apollo 17 ultraviolet spectrometer: Lunar atmosphere measurements revisited. Geophys. Res. Lett. 18,2105-2109. FREEMAN,J. W. AND H. K. HILLS 1991. The Apollo lunar surface water vapor event revisited. Geophys. Res. Left. 18, 2109-2112. HODGES, R. R., JR., AND F. S. JOHNSON 1968. Lateral transport planetary atmospheres. J. Geophys. Res. 73, 7307-7317. HODGES,R. R., JR., J. H. HOFFMAN, AND

in

F. S. JOHNSON1973. Compo-

42

SPRAGUE ETAL

sition and dynamics

of lunar atmosphere.

Proc. Luncrr Sci. Conj: 4th,

2855-2864. HODGES, R. R., JR. 1974. Episodic

the Moon.

Pro<,. Lunar

release of aAr from the interior Sci. Coqf: 5th, 2955-2962.

of

HODGES, R. R., JR., J. H. HOFFMAN, AND F. S. JOHNSON 1974. The lunar atmosphere. Icunrs 21, 415-426. HODGES, R. R., JR. 1975. Formation

of the lunar atmosphere.

1~. W.-H. 1986. The sodium exosphere Geoph>js. Res. Lett. 13, 423-426.

echelle

Res. in lunar

species

in the

N. M. SCHNEIDER, spectrograph. Pub.

and magnetosphere

studies

on Apollo

12054,58: In-situ lunar surface microparticle flux rate and solar wind sputter rate defined. Proc. Lunar Sci. Con,f. 8th, 3835-3858.

MENDILI.O, M., J. BAUMGARDNER, AND B. FLYNN 1991. Imagingobservations of the extended sodium atmosphere of the Moon. Geophys.

HUNTEN, D. M., R. W. H. KOZLOWSKI, AND A. L. SPRAGUE 1991a. A possible meteor shower on the Moon. Geophys. Res. Lett. 18, 2101-2104. BROWN,

particle

Groph~s.

on argon-

HUNTEN, 0. M.. T. H. MORGAN, AND Il. E. SHEMANSKY 1988. The Mercury atmosphere. In Mercury (F. Vilas, C. R. Chapman, and M. S. Matthews, Eds.), pp. 562-612.

HUNTEN. D. M.. W. K. WELLS, R. A. AND R. L. HILLIARD 199lb. A Cassegrain Astron. Sot. Prcc$c 103, 1187- 1192.

J. A. M. 1977. Accretionary

lunar atmosphere.

MCGRATH, M. A., R. E. JOHNSON. AND L. J. LANZEROTTI 1986. Sputtering of sodium on the planet Mercury. Nature 323, 694-696.

HODGES, R. R., JR. 1982. Adsorption of exospheric argon-40 regolith. Lunar Planet. Sci. XIII, 329-330. [Abstract]. HOFFMAN, J. H. AND R. R. HODGES, JR. 1975. Molecular lunar atmosphere. The Moon 14, 1.59-167.

MCDONNELL,

in the tenuous

The Moon

14, 139-157. HODGES, R. R., JR. 1980. Lunar cold traps and their influence 40 Proc. Luncw Sci. Conf. llth, 2463-2477.

Observations of potassium Rex. Lett. 17, 2253-2256.

Lett.

18, 2097-2100.

MORGAN, T. H., H. A. ZOOK, AND A. E. POTTER 1989. Production sodium vapor from exposed regolith in the inner solar system. Luntrr Pltrn. SC,;. Conj: IYth, 297-304.

of

Proc.

MORGAN. T. H. AND D. E. SHEMANSKY 1991. Limits to the lunar atmosphere. J. Geophys. Res. 96, 1351-1367. POTTER, A. E.. AND T. H. MORGAN 1985. Discovery atmosphere of Mercury. Science 229, 651-653. POTTER, A. E.. AND T. H. MORGAN 1986. Potassium of Mercury. Icrrrus 67, 336-340.

of sodium

in the

in the atmosphere

POTTER, A. E., AND T. H. MORGAN 1988a. Discovery of sodium and potassium vapor in the atmosphere of the Moon. Science 241, 675-680.

of Mercury.

JOHNSON, R. E. 1990. Energetic Chuged-Par-ticlc Interrrctiom Atmospheres und Surfuces. Springer-Verlag, Berlin.

with

POTTER, A. E. AND T. H. MORGAN 1988b. Extended sodiumatmosphere of the Moon. Geophys. Res. Lett. 15,1515-1518. POTTER, A. E., AND T. H. MORGAN 1991. Observations sodium exosphere. Geophys. Res. Lett. 18, 2089-2092.

of the lunar

JOHNSON, R. E., AND BARAGIOLA. R. 1991. Lunar surface: Sputtering and secondary ion mass spectrometry. Geopkvs. Re.s. Lett. 18, 2169-2172.

SHEMANSKY. D. E.. AND A. L. BROADFOOT 1977. Interaction of the surfaces of the Moon and Mercury with their exospheric atmospheres. Rev. Geophys. Space Phys. 15, 491-499.

KARKOSCHKA, E. 1990. Suturn’s Atmosphere in the Vi.sihle rind Nrtrr Infrared, 1986-1989. Ph.D dissertation, University of Arizona.

SMITH. G. R., D. E. SHEMANSKY, A. L. BROADFOOT, AND L. WALI.ACE 1978. Monte Carlo modeling of exospheric bodies: Mercury. J. Geephy~. Rrs. 83, 3783-3790.

KEIHM, S. J., AND LANGSETH. M. G. JR. 1972. Surface brightness temperatures at the Apollo 17 heat flow site: Thermal conductivity of the upper 15 cm of regolith. PVOC. 4t/1 Luncrr Sc,ienc,e Cortf S~ppl. 4 Grochirn. Cosmochirn. Acts, 3, 2503-2513. KERRIDGE. J. E. 1991. A reevaluation of the solar-wind sputtering on the lunar surface. Proc. Luntrr Sci. Conf: Zlst. 301-306.

rate

KERRIDGE, J. E., AND I. R. KAPLAN 1978. Sputtering: Its relationship to isotopic fractionation on the lunar surface. Proc,. L//nor Sci. Conj: 9th, 1687-1709. KOZLOWSK~, R. W. H..

A. L. SPRAGUE, AND D. M. HUNTEN 1990

SPRAGUE, A. L. 1990a. A diffusion source for sodium and potassium the atmospheres of Mercury and the Moon. Icarus 84, 93-105.

in

SPRAGUE, A. L. 1990b. An Ohservutionul Comparison of Mercrrry and the Moort. Ph.D. dissertation, University of Arizona. TYLER, A. L., R. W. H. KOZLOWSKI, AND D. M. HUNTEN 1988. Observations of sodium in the tenuous lunar atmosphere. Geophy.t. Rrs. Lett. 15, 1141-I 144. WALLACE, L. 1969. Analysis of the Lyman-alpha observations made from Mariner 5. J. Geopl~vs. Res. 74, 115-13 I

of Venus