In-Situ Measurements of Lunar Heat FlowMarcus G. Langseth and Stephen J. Keihm

Lamont-Doherty Geological ObservatoryColumbia UniversityPalisades, New York

During the Apollo program two successful heat-flow measurements were made in situ onthe lunar surface. At the Apollo 15 site a value of 3.1 x.lO~*W/cma was measured, and atthe Apollo 17 site a value of 2.2 x lO^W/cm3 was determined. Both measurements haveuncertainty limits of ± 20 percent and have been corrected for perturbing topographiceffects. The apparent difference between the observations may correlate with observedvariations in the surface abundance of thorium. Comparison with earlier determinations ofheat flow, using the microwave emission spectrum from the Moon, gives support to thehigh gradients and heat flows observed in situ.

There has long been an interest in the rateat which heat is escaping from the Moon.The Moon is a planetary-sized body thatrepresents a significant sample of the solarsystem in the region of the terrestrial planets.On the other hand, the Moon is a smallenough body so that there is reason to believethat during its 4.6-b.y. history it has lost asignificant portion of its initial heat and, asa result, that the present heat flux mainlyresults from heat generated by radio isotopesin the interior to a depth of about 300 km.

Petrological and geochemical evidencegained from surface samples indicates thatthe Moon was radially differentiated earlyin its history. During this differentiation thelong-lived, heat-generating isotopes of 238U,235U, 40K, and ^Th were purged from theinterior and concentrated in the outer layerof the Moon. As a result, the surface heatflow from the Moon should very nearly re-flect the total abundance of isotopes in theMoon and thereby provide a valuable chemi-cal constraint on the Moon's bulk composition.

1 Lamont-Doherty Geological Observatory Con-tribution No. 2141

Prior to the Apollo missions, lunar heat-flow determinations were based on Earth-based observations of thermal emissions fromthe Moon in the microwave band. Because ofthe partial transparency of lunar materialto electromagnetic waves longer than 1 mm,the emission spectrum at wavelengths greaterthan 1 mm depends on temperatures in thesubsurface. If the electrical properties oflunar soil are known, the subsurface tem-perature profile can be determined from theemission spectrum.

The most comprehensive effort to detectheat flow from the interior by this techniquehas been made by Troitsky and colleagues(refs. 1 and 2) at the Radiophysical ResearchInstitute, Gorky, U.S.S.R. Their well-knowncurve, shown in figure 1, indicates an in-crease in brightness temperature with wave-length of about 0.6°C/cm. Using electricaland thermal properties deduced from micro-wave observations in the 1-mm to 3-cm range,Tikhonova and Troitsky (ref. 2) interpretedthis spectral gradient in terms of a heat flowof 3 X 10-« to 4 X lO^W/cm2. Such a heatflow is approximately one-half the mean ofobserved heat-flow values on the Earth.

283

284 COSMOCHEMISTRY OF THE MOON AND PLANETS

MICROWAVE EMISSION SPECTRUM

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Figure 1.—Data from microwave observations madein the Soviet Union between 1961 and 1964 usingthe "artificial Moon" technique (refs. 1 and 2). Theplot shows microwave brightness temperature ver-sus wavelength of the radiation.

In-Situ Measurements During theApollo Program

The manned lunar landings of the Apolloprogram provided an opportunity to makedirect measurements in the lunar surfacelayer relevant to the heat flow through thesurface. Successful measurements were madeat two of the landing sites: Hadley Rille,near the edge of the Imbrium basin—visitedon Apollo 15—and Taurus-Littrow, a narrowembayment on the southeastern margin of

Serenitatis—visited on Apollo 17 (see figure2).

At each location the astronauts buried twoprobes in the lunar soil to measure the tem-perature and thermal conductivity of the soil.At the Apollo 15 site the probes were buriedto depths of 1.0 and 1.4 m; at Apollo 17both probes were buried to a depth of 2.3 m.Each probe contains eight platinum resis-tance thermometers and four thermocoupleswhich detect temperature at 11 differentlevels in the subsurface. Four thermometerson each probe are surrounded by heaterswhich can be turned on by command fromEarth. These heaters are used to make in-situ determinations of thermal conductivity.The range and accuracy of measurementsmade by the heat-flow experiment are shownin table 1. The platinum resistance thermom-eters were carefully tested to demonstratethat they would retain their calibrationsafter experiencing the mechanical and ther-mal shocks of the lunar mission. Tempera-ture data from all the thermometers arerelayed to Earth every 7.2 min. At theApollo 15 site we presently have more than21/2 yr of data and more than 1 yr of dataat the Apollo 17 site.

A Summary of Results

The experiments installed on the Moonprovide extensive information on the tem-perature and thermal properties of the lunarsurface layer to a depth of 3 m, includingsurface temperature variations, near-surfacethermal properties, subsurface temperature

Table 1.—Heat-Flow Experiment Temperature Measurements

Measurement

Platinum Resistance Thermometers:Absolute Temperature

Temperature Difference

Cable Thermocouples:Absolute Temperature

Range

190-270 K

± 2 K

70-400 K

Accuracy

±0.05 K

± 0.001 K

±0.5 K

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286 COSMOCHEMISTRY OF THE MOON AND PLANETS

Figure 3.—The calculated surface temperaturethroughout a lunation based on the temperature ofa thermocouple inside a cable (see inset) which isexposed above the surface.

variations, and thermal conductivity. All ofthis information is essential to understandthe total heat budget near the lunar surfaceand the contribution of the flux from theinterior.

SURFACE TEMPERATURE VARIATIONS

Measurements by thermocouples in cablesabove the lunar surface provide informationon the surface temperature variation. Thecable is in radiative equilibrium with the lu-nar surface, except during times when thetemperature is changing rapidly, as duringan eclipse or at terminator crossing. Thelunar surface temperature can be readilycomputed from laws governing thermalradiation. In figure 3 we show the surfacetemperature variation at the Apollo 17 siteduring a complete lunation. During lunarday, the temperature deductions have large

errors because of uncertainties in the amountof solar radiation reflected from the lunarsurface, but at night the errors -are small.Similarly, surface temperatures can be de-duced quite accurately from thermocoupledata during the umbral phase of an eclipse.

In a manner similar to the classical meth-ods of Wesselink (ref. 3) and Jaeger (ref.4), the cool-down of the surface after sun-down and during an eclipse can be used todeduce the thermal properties of the regolithto a depth of about 15 cm. For analysis ofthe in-situ data we use a thermal model thatincludes many layers with thermal proper-ties that vary with depth and temperature.To explain the observed temperature varia-tions at lunar night and during an eclipse,the conductivity and density must vary withdepth. The variations of density and con-ductivity shown in figure 4 will explain thesurface temperature variations during thelunar night almost exactly, but these de-

CONDUCTIVITY WxlO/cm-K0.4 0.8 1.2

DENSITY gm/crr?2.2

Figure 4.—Profiles of thermal conductivity and den-sity, with depth in the lunar regolith that will ex-plain the observed surface temperature variationsshown in figure 3. Conductivity values shown arethose appropriate to the mean temperature at eachdepth.

IN-SITU MEASUREMENTS OF LUNAR HEAT FLOW 287

duced profiles are not necessarily unique.Two features of the profiles shown are essen-tial to explain the data:

1. The upper 1 to 2 cm must have an ex-tremely low thermal conductivity, andthis conductivity must be temperature-dependent. The conductivity at themean surface temperature (216 K)is approximately 1.5 X 10-5W/cm-K,which is in good agreement withmeasurements on returned lunar fines.

2. At a depth of about 2 cm, the conduc-tivity must increase greatly to values5 to 7 times greater than the surfacevalue.

THE NEAR-SURFACETURE GRADIENT

MEAN TEMPERA-

One of the most interesting features of the

subsurface temperature measurements is thevery large difference in mean temperature(i.e., the temperature averaged over onelunation) between the surface and depths ofa few centimeters. At the Apollo 15 site themean temperature 35 cm below the surfaceis 45 K higher than at the surface; the dif-ference at the Apollo 17 site is 40 K. Thislarge increase in mean temperature is dueprimarily to the temperature dependence ofthermal conductivity in the top 1 to 2 cm,which results from the nonlinear behavior ofradiative heat transfer. These large differ-ences require that the ratio of the radiativecomponent to conductive component at 350 Kbe about 2 to 3. Figure 5, from Keihm andLangseth (ref. 5), shows the variation ofmean temperature and the amplitude andphase of variations of lunation period withdepth in the regolith, based on the modelsshown in figure 4.

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Figure 5.—In the right plot, the expected peak-to-peak monthly variation of temperature as a function ofdepth. The left-hand plot shows mean temperature and phase lag of the monthly variation versus depth.These results are based on the conductivity and density models shown in figure 4.

288 COSMOCHEMISTRY OF THE MOON AND PLANETS

Subsurface Temperature Profiles

The probes are inserted inside the hollowfiberglass tubing which is drilled into the lu-nar soil. Figure 6 shows Charles Duke, anApollo 16 astronaut, drilling one of the heat-flow holes. Figure 7 shows the temperaturehistory of one of the probes after insertioninto the tube. The probes require approxi-mately 1 month to reach within a few thou-sandths of a degree of thermal equilibriumwith the surrounding regolith. The ther-mometers buried below 80-cm depths donot see any perceptible variation due to themonthly temperature cycle, and temperaturegradients should reflect heat flowing from

the lunar crust. The temperature profiles atfour of the probes are shown in figure 8.Very small corrections have been added tothese data to account for thermal shuntingeffects of the fiberglass tubes and probes, sothat these profiles should represent true un-disturbed regolith temperatures.

THERMAL CONDUCTIVITY

Thermal conductivity of the regolith canbe deduced from three different effects.First, and most important, were measure-ments made by in-situ experiments. The ef-fects of heaters turned on for a period of 36hours at low power were measured. From

Figure 6.—An astronaut drilling sections of fiberglass tubing into the Moon for the heat-flow probes.

IN-SITU MEASUREMENTS OF LUNAR HEAT FLOW 289

the rate of rise of temperature after 20hours it is possible to determine the conduc-tivity. Second, the initial cool-down of theprobes from high temperatures permits de-

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Figure 7.—The 10-month temperature history ofeight thermometers on one of the probes at theApollo 17 site. The inset shows the temperaturedepth profile after 75 days.

termination of conductivity based on theinitial energy input into the hole. Cool-downestimates can be made at all the gradientsensors, i.e., at eight different depths in eachhole. Third, temperature variations with amonthly period penetrate to approximately80 cm, and the annual variation of surfacetemperature is felt at all depths. The attenu-ation of these variations with depth dependsin part on the thermal conductivity of thesurrounding material. However, because ofradiative transfer along the fiberglass tub-ing, the attenuation data are difficult to in-terpret. Our analysis requires a thermalconductivity between 1 and 2 X 10^W/cm-Kto reproduce the attenuation observed. Theconductivities measured by the first twotechniques are shown versus depth in fig-ure 9. We note that the thermal conduc-tivity of the lunar soil lies between 1.4 and3.0 X 10^W/cm-K; this is approximatelya factor of 10 higher than the conductivityat the surface. The increase of conductivityat about a 2-cm depth appears to be mainly

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290 COSMOCHEMISTRY OF '.HE MOON AND PLANETS

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Figure 9.—A summary of thermal conductivity de-terminations at the heat-flow site. At the top ofthe plot the lines are the same as in figure 4.Deeper points are results of in-situ measurementsand analysis of probe cool-down data.

due to a large increase in the soil compactionand grain boundary contacts with depth. Itis likely that at this 2-cm depth the disrup-tive effects of micrometeorite bombardmentgive way to compactive effects. Conductivityvalues for regolith fines as high as 2 X 1Q-*W/cm-K have not been duplicated in thelaboratory, and further tests of highly com-pacted lunar soil should be made.

HEAT FLOW IN SITU

When the conductivity and gradient ob-servations are combined, the heat-flow valuesshown in table 2 result. The best value of

heat flow at the Hadley Rille site is 3.1 X10-°W/cm2 and at Taurus-Littrow 2.8 Xl(HW/cm2.

Temperature measurements at probe 2 atthe Apollo 17 site require special attention(see fig. 8). The profile indicates a verylarge decrease in gradient with depth at 130cm which, because the conductivity is rela-tively uniform, must reflect a change in heatflow with depth. Also, the heat flow in thelower part of the hole, about 1.9 W/cm2, isconsiderably lower than that at the othertwo locations. These results suggest that heatflow is locally disturbed, perhaps by a largerock buried very near where the probe is em-placed. The heat flow, using the temperaturesat 67 and 234 cm, gives a heat flow of 2.5 X10"6W/cm2, which is in reasonable agree-ment with the value at probe 1.

Possible Disturbance to theHeat Flow

How representative are the measurementsof the average heat loss from the Moon? Theanswer to this question depends on whetherthere are significant regional and local dis-turbances. Certain disturbing effects, such asthat of local topography, can be estimatedand corrected for.

The amounts of radioisotopes in the crustmay be anomalous in the region where theheat-flow observations are made. We haveorbital data on the distribution of thoriumand uranium on the surface that can be ap-plied to this problem.

Table 2.—Summary of Lunar Heat-Flow Results

Apollo 15Probe 1

Apollo 17Probe 1Probe 2

GradientK/m

1.75

1.361.30

ConductivityW x lO-'/cm K

1.78

2.062.00

Heat PlowW x 10-°/cm2

3.1

2.82.5

NOTE : The estimated error of heat-flow determination is ± 20 percent.

IN-SITU MEASUREMENTS OF LUNAR HEAT FLOW 291

Other effects, such as thermal conductivitycontrasts in the subsurface which can re-fract the heat-flow lines, are not directlyobservable, but geological observations canbe used as a guide for assuming subsurfaceconductivity geometries. From these assump-tions an appreciation of whether the mea-surements are anomalous may be obtained.

TOPOGRAPHY

Significant "disturbances of heat flow willoccur in the vicinity of craters having adiameter-to-depth ratio of 6 or less. Thedominant effect of such craters is to increasethe heat flow just outside the crater rim dueto the slightly higher mean temperature inthe crater floor. In the upper part of figure10 we show the heat-flow anomaly over acrater with a diameter-to-depth ratio of 6as a function of radius. It can be seen thatthe anomaly decreases very rapidly with dis-tance from the rim. By and large the astro-nauts were successful' in setting up theexperiment far from craters larger than 1 min diameter. At the Apollo 17 site, topo-

HfHT-FLO* ANOMALf

TiURUS—LITT/>0\V VALLEY

< 2O\

Figure 10.—In the upper part of the figure, the heat-flow anomaly expected over a crater with an aspectratio of 1.6. The lower part shows schematicallya cross section of Taurus-Littrow and the estimatedeffect on the heat flow, Aq.

graphic maps show three craters which weestimate have a combined effect that in-creases the heat flow by 0.3 W/cm2. That is,a correction of about —10 percent should beapplied to the Taurus-Littrow values for theeffect of craters. At the Hadley Rille sitethere were no craters in the vicinity of theprobes which would have a significant effecton the heat flow. Consequently, no correctionhas been applied.

At Hadley Rille both the rille and theApennine Front will affect the heat flow, butin opposite ways. Both effects are on the or-der of 5 percent and, thus, appear to be self-cancelling. Therefore, it appears that thebest value for the heat flow at Hadley Rilleis the uncorrected value, 3.1 X lO^W/cm2,with an estimated uncertainty of ± 20 per-cent.

The massifs that bound the Taurus-Littrow Valley on the north and south havea significant effect on the heat flow. We haveestimated the correction to be applied usinga method developed by Lachenbruch (ref.6). The valley is modeled as shown at thebottom of figure 10. Based on this model, weestimate that a correction of —15 to —20 per-cent should be applied to the Apollo 17 mea-surement. Applying all corrections, the bestvalue for heat flow in the Taurus-Littrow re-gion is 2.2 X 10-6W/cm2, with an estimateduncertainty of ± 20 percent.

SURFACE RADIOACTIVITY

When topographic effects are taken intoaccount, the heat flow at Taurus-Littrow is25 to 30 percent lower than at Hadley Rille.The results of the orbiting gamma-ray ex-periment reported by Metzger (ref. 7) gaveevidence of substantial variations in radio-active elements on the surface. One of theregions with the highest concentrations inradioactivity is the Hadley Rille area of MareImbrium. There the counts per second areabout twice those at Taurus-Littrow andthree to four times those observed over muchof the lunar farside. The difference in heatflow between these two sites may therefore

292 COSMOCHEM1STRY OF THE MOON AND PLANETS

reflect a real variation in radioactive heatproduction in the lunar crust. A similar cor-relation between surface heat flow and ra-dioactive heat production of surface rocks isobserved on the Earth. A most significantimplication is that two in-situ measurementsmay overestimate global heat flow, especiallyif the results of the gamma-ray experimentover the farside and nearside highlands arerepresentative, since the observed concentra-tions of radioactive isotopes are much lowerthere.

POSSIBLE SUBSURFACE EFFECTS

Both sites where the heat-flow experimentswere installed are at the margins of largemascon basins. These basins have beenflooded by basaltic lavas early in the Moon'shistory. As a result, it is possible that a con-ductivity contrast exists between the marebasalt and the underlying basin floor and ad-jacent highlands. It is not likely that thebulk conductivity of the basalt will be ashigh as that measured on returned solid sam-ples. The active seismic experiments byKovach and Watkins (ref. 8) indicate thatthese flows are highly fractured. Extensivefracturing of rocks in vacuum will decreasetheir conductivity appreciably. It may bepossible to entertain a conductivity contrastof mare fill material to underlying basinfloor material of 10.

Our observations, located at the margin ofbasins, may see an edge effect as a conse-quence of this contrast. If they lie withinthe basin as the Apollo 15 site appears to, anedge effect heat-flow anomaly would add tothe observed heat flow. If, on the other hand,the observation is outside the basin rim asmight be the case at Taurus-Littrow, the ob-served heat flow would be disturbed towardlower values. Uncertainties do not at thistime permit an accurate assessment of dis-turbance due to buried contacts betweenrocks of different thermal conductivity. Thebest estimate of the size of such an effect isby comparison with other estimates of heatflow from the Moon; e.g., those made fromEarth-based microwave measurements.

Comparison With Earth-BasedMicrowave Measurements

To compare our measurements with micro-wave measurements, we return to the set ofmeasurements of lunar brightness tempera-ture between 3 and 70 cm made by Troitskyand colleagues. Waves from 5 to 20 cm areemitted from depths comparable to thosemeasured by the heat-flow experiment. Wewill compare the spectral gradient in thisband of wavelengths with that expectedfrom a lunar surface layer, having the tem-peratures and thermal properties we mea-sured in situ. The greatest uncertainty insuch a comparison is the value of the powerabsorption length, le, of electromagneticwaves. In figure 11 we show the microwavedata compared with theoretical results usingdifferent absorption lengths. The model hasthe parameters given in the table at the topof the figure. The lowermost curve has apower absorption length that is a functionof A, i.e., le = 5.8 y1-48, which is an empiri-

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IN-SITU MEASUREMENTS OF LUNAR HEAT FLOW 293

cal fit to the experimental results. This rela-tion produces a good fit to radiotelescopicobservations of the attenuation of the varia-tions of microwaves over a monthly periodin the range from 1 mm to 3.2 cm. The resultis an increase in brightness temperature thatfits within the error bars but is a poor fit tothe observed spectral gradient. The tempera-ture gradient in the lunar surface layer wouldhave to be larger to better fit the microwavedata using this relation. The middle curvecorresponds to an le of 50\, which is nearthe mean of values reported by Gold et al.(ref. 9), based on measurements of lunarsamples at a wavelength of 68 cm. The bestfit to the spectral gradient would be obtainedfor an le of 80A. The principal result of thiscomparison at this point in our knowledge isthat gradients of 1.3°C/m or higher, as ob-served in situ, are supported by microwaveobservations. The heat flows deduced byTikhonova and Troitsky from 2.9 X 10-6

W/cm2 to 4 X lO^W/cm2 are in close agree-ment with our results.

Future Work

Several lines of future work can be pro-posed. First, more laboratory measurementsof the electromagnetic power absorptionlength of lunar fines in the wave band from5 to 20 cm would greatly improve the com-parisons made above. Second, further Earth-based measurements of microwave emissionsin the wavelength range from 5 to 30 cmwould be extremely valuable. Measurementswith sufficient resolution to detect variationsin emission spectra over the lunar diskwould be especially significant. Third, otherin-situ measurements in highland regions,using an automated lander, would be ex-tremely important. Finally, microwave ob-servations from lunar orbit could possiblymap heat flow variation over the entire Moon.

Acknowledgment

Columbia University's participation in theLunar Heat-Flow Program was made possible

through NASA contract NAS 9-6037. Theexperiment would not have been possiblewithout the efforts of many people at theBendix Aerospace Systems Division, AnnArbor, Mich.; Arthur D. Little, Inc., Cam-bridge, Mass.; Martin Marietta Corporation,Denver, Colo.; Gulton Industries, Inc., Albu-querque, N. Mex.; and Rosemount Engineer-ing Co., Minneapolis, Minn. The assistanceof John Chute, Jr., and K. Peters in theanalysis of the data is gratefully acknowl-edged. The drafting and manuscript werepatiently done by A. Trefzer.

References

1. KROTIKOV, V. D., AND V. S. TROITSKY, DetectingHeat Flow From the Interior of the Moon.Soviet Astron., Vol. 7, No. 6, 1964, pp. 822-826.

2. TIKHONOVA, T. V., AND V. S. TROITSKY, Effect ofHeat From Within the Moon on its RadioEmission for the Case of Lunar PropertiesWhich Vary With Depth. Soviet Astron., Vol.13, No. 1, 1969, pp. 120-128.

3. WESSELINK, A. F., Heat Conductivity and Natureof the Lunar Surface Material. Bull. Astron.Inst. of Netherlands, Vol. 10, 1948, p. 351.

4. JAEGER, J. C., The Surface Temperature of theMoon. Australian J. Phys., Vol. 6, 1953, p. 10.

5. KEIHM, S. J., AND M. G. LANGSETH, JR., SurfaceBrightness Temperatures at the Apollo 17Heat Flow Site: Thermal Conductivity of theUpper 15 cm of Regolith. Proc. Fourth LunarScience Conference, Geochimica et Cosmochi-mica Acta, Supplement 4, Vol. 3, 1973, pp.2503-2513.

6. LACHENBRUCK, A. H., Rapid Estimate of theTopographic Disturbance to Surficial ThermalGradients. Rev. Geophys., Vol. 6, No. 3, 1968,pp. 365-400.

7. METZGER, A. E., J. I. TROMBKA, L. E. PETERSON,R. C. REEDY, AND J. R. ARNOLD, Lunar SurfaceRadioactivity: Preliminary Results of theApollo 15 and Apollo 16 Gamma Ray Spec-trometer Experiments. Science, Vol. 179, 1973,pp. 800-803.

8. KOVACH, R. L., AND J. S. WATKINS, The VelocityStructure of the Lunar Crust. The Moon, Vol.7, 1973, pp. 63-75.

9. GOLD, T., E. BILSON, AND M. YERBURY, Grain SizeAnalysis and High-Frequency ElectricalProperties of Apollo 15 and 16 Samples. LunarScience, Vol. IV, Lunar Science Institute,Houston, 1973, pp. 293-295.