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Density of the lunar interior
EARTH AND PLANETARY SCIENCE LETTERS 16 (1972J 299-305. NORTH-HOLLAND PUBLISHING COMPANY
DENSITY
OF THE LUNAR
INTERIOR
PAUL W. GAST and R. THOMAS GIULI NASA Manned Spacecra]? Center, Houston, Texas, [~rsA
Received 13 July 1972 Revised version received 12 September 1972
Tire characterization of a planet depends on our understanding of the physical and chemical state of its interior. The significance of a few physical parameters; i.e. the mean density, the moment of inertia, and the depth of several major discontinuities - the core mantle and crust mantle boundaries - was illustrated for the case of the earth in a series of classic papers written by Bullen between 1036 and 1940 [ 1-3]. Our knowledge of these parameters for tire moon is not as precise nor as extensive yet as it was for the earth 3 0 - 4 0 years ago. Nevertheless, a line of reasoning similar to that used by Bullen can be used to lnake inferences regarding tile composition of the lunar interior. The arguments for the moon are inherently more powerful than those for the earth simply because the moon has a much greater area-tovolume ratio. Thus, its surface and near-surface characteristics are more representative of the entire planet than those of tile earth, in this paper we will attempt to derive the constraints that can be placed on the density of the lunar interior from: (1) the mean density, (2) the moment of inertia, and (3) the mass and density of tile lunar crust that have been inferred from the seismic refraction data recorded by the passive seismoineter [4, 5]. The mean density and moment of inertia used in the calculations that follow are ~- = 3.36 g/cm 3, K - C / M R 2 = 0.395, 0.397, 0.399, 0.401. The uncertainty in our knowledge of the moon's moment of inertia is still sufficiently large to significantly affect the constraints placed on the interior densities. As will be seen from the results that follow, the value K = 0.395 allows a monotomically condensed lunar interior, whereas the other three values require an interior density inversion, more extreme for the higher
values of K. Since most of the conclusions which will be drawn here are simply exaggerated by increases in the value of K, we have somewhat arbitrarily emphasized calculations using the value 0.399, rather than the value most recently reported by Kaula [6] and Michael and Blackshear [7], 0.402 -+ 0.002. All of these authors indicate that the lowest acceptable value of K is 0.400. Even though the nloment of inertia of tile moon is ahnost identical with that of a homogeneous sphere, it is now rather clear that there probably are significant density variations in the lunar interior. These variations are largely due to tile relatively large, lowdensity crust which has been inferred from results obtained from both Lunar Orbiter and Apollo experiments. The recent seismic refraction studies [5] indicate that the earth-facing side of the moon has a major seismic discontinuity between 60 and 65 km which presumably separates the lunar crust and mantle. A more gradual transition occurs at 25 km [5]. In our calculations we assume a crust of this thickness comprising about 9% of the mass of the moon. It should be noted that tile lunar crust is qualitatively different from the crust of the earth, which makes up only l/2% of the mass of the planet. Constraints on tile density of file lunar crust can be inferred from: ( l ) the crustal P-wave velocity: i.e. 7.0 km per sec, (2) the mineralogy and chemical composition of common surface rocks, and (3) the density contrast within the crust that is required to produce the mascons. Toksoz et at. [4] have summarized file terrestrial rock types that have P-wave velocities similar to those found in the lunar crust. Their compilation includes rocks with plagioclase contents ranging from less than
300
P. 11'. C;ast, R.T. Giuli. Dcptxity +tl the lunar interior
50'.; to there than 9ff..:k. Since tile density difference between calcic plagioclase
tained on tile Apollo 14 and 15 missions [13, 14] suggest that the nlascons originate front circular plates with a tnass excess of 800 kg/cm 2. If these circular plates are less than 20 km thick, density contrasts ill excess of 0.4 g/cm 3 2re required to produce such mass concentrations. Such density contrasts are difficult to actlieve if tile crustal density is greater than 3.0 since they would require extensive surface plates of rocks that have intrinsic densities in excess of 3.4 g/cm 3. Such unusually dense rocks have not been observed in most mare regions. When all these factors are taken into account, we conclude that tile lower crust, taken to be 25 63 km in depth, probably has a density between 2.85 and "+ )3 g/cnl 3. A value of 2.90 has been used in tile calculations that follow. From tile reduced sound velocities reported bv ToksOz et at. [4] we inl0r a somewhat lower density for the upper crust. A value of 2.7 g/cm 3 is used for tile upper 25 km in tile calculations that follow. The implications of these crustal densities have been investigated by calculation of a variety of multilayer, spherically symmetric, solid body models. Two algebraic equations (tnotnent of inertia and nlass continuity) are solved sitnultaneously m tile approxitnation that tile htnar interior cotnprises n constant-densit,,,', radially symmetric layers. Tile specification of the two crustal layers in tile previous paragraph then requires that 2++ 7 of tile radii and densities of tile various zones tl/tlSt be specified beforehand as parameters. It is quite clear that tile observed monlent of inertia, mean htnar density, and low density crust require subcmstal regions with densities that exceed the mean density of tile moon. First, we consider four-laver nlodels { the two crustal layers specified above, and two interior layers). Calculations of the depth and tnagnitude of tile single density discontinuity between the two interior layers that would account |'or tile htnar tnotnent of inertia and mean density are summarized in fig. 1. Tile calculations reveal the vet 5' interesting result that a density discontinuity ranging t't-onl 6'.; at 500 km depth to IY.; at 900 km depth can compensate for tile low density crust i l K is taken at 0.399. A hi~ler moment of inertia (K = 0.401J requires tile density discontinuities to range from 10`5 to 2 I':': at tile corresponcling depths. Additional calculations for lower moments of inertia are illustrated in the inset in fig. l. (
_ .
-
P. It'. Gast. R. T. Giuli, Density ol the hmar interior
- - -
:
401
K :
399
K
397
K
395
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DEPTH (km) 25 63 1OO 200 300 400 500 600 800 IOOO VOLUME IO ,__. . . . o. . . . . 8. . . . . 7. . . . . 6. . ~ , ~ ,1 ! 5 4 3 2 O FRACTION Fig. 1. 1'our-layer models of the lunar interior, where the m o crustal la', ers are defined in the text. Proceeding inward, the respective densities of the interior layers are ,03 and P4, illustrated as a function of the location of the interior density discontinuity. That is, for any discontinuity location {abscissa), a point on the 0.~ curve appropriate to some K value defines the (constant) den~ity of the subcrustal layer, and the corresponding point on the P4 curve defines the I¢onstant) density of the interior layer. The curves are given for discontinuity locations anywhere in the interior for t~vo K values, and with an expanded density scale for all four K values for discontinuity locations between interior volume fractions of (I.25 and (I.65.
These indicate that a value of K lower than 0.396 is required to eliminate the density inversion. It is interesting to note that the magnitude of rite density contrast required ill die lower m o n t e n t of inertia models is quite comparable to that which occurs during melting of the c o m m o n silicate materials. (However, we recall that our calculations were t o n n u l a t e d with tire assumption of solid-body rotation; liquid-core models may not be adequately specified by our calculations. ) In addition, for all models ( e x c e p t for K = 0.305) where the interior density discontinuity lies at depths 500 900 kin, the subcrustal densities are quite high: 3.45 - 3.55 g/envY.In the e x t r e m e case where die interior density discontinuity is taken to lie at very shallow depths, the calculations show that a shallow layer just under the crust with a density of 7 (that is, similar to the density of metallic iron) would have to comprise at least 2.9q of the mass of the m o o n for K = 0.399, and at least 4.4(,4 for K = 0.401, to c o m p e n s a t e for the low crustal density used in our calculations. The mass of dlese shallow iron layers implies that
at least 7~1 . - - 3~ of the material that accreted during tile formation of the last 10 15'7; of the m o o n consisted of metallic iron. Thus, this portion of the m o o n would be substantially enriched in iron relative to primitive solar materials. This conclusion is a characteristic o f ahnost all models that e m p l o y an iron-rich layer to c o m p e n s a t e for the low-density crust. Fig.2 shows how the mass of such a layer must vary as a function of the depth of the layer, under the assumption that the densities of the layers adjacent to the iron are equal. The results indicate that the iron layer comprises at least 14% { 21% ) of the mass of the 'upper" layers when the iron layer is located 200 km below the surface, for K = 0.399 (0.401). In addition, we see that the mean density of the subcrustal m o o n is !ess than 3.36, significantly so when the iron lay'er is deeper than 300 kin. The effect of adding an iron core to the models illustrated in fig. 1 has also been calculated. If this core contains less than lr,'f of the mass of the m o o n , the effect upon the interior density discontinuities
t'. [?. (;axt. R. f. Gizfli, Dcllslrv ~LI tltc lunar iHrerior
302
~
/
for the K=0.BO9 model is to shift the curves toward, but not beyond, the curves illustrated for the K=0.401 model. Thus, adding a small, dense core to the fourzone model has about the ~ame effect upon the two subcrustal layers as increasing the m o m e n t olinertia of" the four-zone ntodel slightly. Several more complex models combining silicate layers with a single iron laver are illustrated in fig.3. Here we have arbitrarily assumed that high density silicate rocks form an upper mantle with illeatl d e l l sitv, _.,Iq ~g,,/Clll -~ , and an iron laver, t}l:Jt ntakes up _~',
,3 36
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~3 3
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o r 4~'; o f t h e mass ,.ff the m ~ l o n is s i t u a t e d at a d e p t h
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of 500 kin. The.',e models show that i l the abutidance of metallic iron is constrained so lh-it it comprises less than 10";- of the mass of the 'upper' layers, more than ~ or the mass of the moon must be made tip oI" a relatively dense silicate rock. They also require the density of the lower mantle and core to be le~s than 3.3 g/cnt ~. In fig. 4 we attempt to accotln[ l'or the hmar montent of inet tia b', imagininta a chemicalh' homo<,e-
\
\ 02
~
I00
200
3.0
300
Dj (km)
1 ig. 2. I'ive-layer models o f the lunar interior, where the two crustal layers are defined in die text. Q4 is tile fraction of hmar mass in a layer contained in a high density (7.0 g/cm 3) iron layer, as a function of the depth, D 3, of the top of this layer. The densities 03 and os of the layers adjacent to the iron layer are illustrated for tile case where P3 = 05- Density for basalt NM5 is taken from reference [171. The plotted densitie~ are for 12(10°C.
lleOtlS i l l a l l l J e COlllprisJllg Olle or lllOle r e p r e s e n t a t i v e
minerals and considering die a t l e n d a n t density varialion with depth due to a reasonable run of interior temperature and pressure. We also dis:~lay the four-
7
2563 5
--
I
453
I
522
I
(SEMI-DENSE LAYER EXTENDS BELOW IRON LAYER)
_.,j
3
K -- 401 Q = .04
K = 401 1
Q5 = 02
5
7
P
25 63 5-11
385
511
25
I
63
323
--II
522
I
(g/co)
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-.,J K = 399
K = 399
Q5 = 02 I
--
I
O
I 8
i
i .6
I
I 4
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I
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.04
Qs = I
I
I
I
I
I
.8 .6 .4 VOLUME FRACTION
i
I
.2
O
Fig. 3. Six-layer models of the hmar interior, xshere the two crustal layers are defined in the text. The top of a high density (7.0 g/cm 3 ) iron layer is located at a depth of 500 kin. A high density (3.5 g/cm 3) silicate layer is adjacent to the crust. The volume and depth of this layer, and the densities lassumed equal) of the layers adjacent to tile iron layer are illustrated for two assumed values of tile lunar mass fraction Os of the iron layer. The unlabelled numbers are the depths (kmJ of the density discontinuities which define tile respecti~ e layers.
P IC Gast. R.T. Giuli. DeHsit3' o / t h e hmar i#zterior
303
4
3P P (%)
2
o
-2
-4 2000
40
-
T I K)
T
J
IOOO
DEPTH (l(m) VOLUME FRACTION I
...,----"~""-'~ 63 1OO .9 .8
P (kbar)
I
i
I
200 .7
300
400
.6
.5
A
.4
20
I
600 .3
,
I
J I
O
800 1OOO .2 .I O
Fig. 4. Density variation of several minerals with respect to their room temperature and pressure values, AO/D0, as a function of a reasonable run of temperature, T, and presstlre, P, for the lunar interior. The minerals are: 1, olivine: 2, spinel and/or garnet (pyrope); 3, pyroxene (diopside); 4, plagioclase (labradorite). Also plotted is the ratio ,03/04 for a four-zone model (K=0.397) depicted in fig. I. Data for thermal expansion and compressibility are taken from Clark [21 ]. The temperatures for the lunar interior are based on the thermal models given by McConnell and Gast [22]. zone models of fig. 1 for K=0.397, which gives the tnagnitude of the density discontinuity required between the two interior layers, as a function of the location of the discontinuity. We see that, for K as low as 0.397, we still require density discontinuities of at least 2.5-3% at depths ranging from 275 km to 650 "kin, whereas none of the representative mineral densities decrease by more than 0.5% in this region. Further. the total density decrease of spinel or garnet, say, is perhaps 2% between the base of the crust and 600 knl. Considering the uncertainties in the composition and temperature of the lunar interior, no precise conclusion regarding the effect of thermal expansion is possible. Nevertheless, one can see that mantle densities decreasing downward due to thennal expansion of solid phases are probably insufficient explanation for models with K > 0.397.
Summary
The calculations summarized here clearly do n o t lead to a unique m o d e [ o f the density' o f the lunar interior. A l l o f the m o d e l s discussed above are in c o n f l i c t
with some inferences drawn from other observations. In particular, tile conchlsion that the moon has a substantial molten silicate core today may be in conflict with tire temperature profiles that have been inferred from conductivity profiles [15, 16] unless very low iron contents are assumed for the lunar interior. Nevertheless, we suggest that one explanation of the relatively low internal densities is that the present-day telnperatures below 700 900 km exceed the solidus of the lunar interior. We have already noted that the occurrence of iron at shallow depths requires ad hoc assumptions regarding the composition of initially accreted material. Moreover, such shallow conducting layers should have been discovered in the conductivity profiles [ 15]. There are 'also serious questions regarding the long-term stability of a system with such massive density contrasts. Several additional constraints on tire lunar interior may be considered in the context of the calculations presented here. Ringwood and Essene [17] have argued that the lunar moment of inertia and mean density exclude lunar compositions that resemble those of basalt due to the gabbro-eclogite transformation because it would restilt in excessively high densities
304
P. It'. Gast. R. T. (;htli. Density (,! the lunar mtcrk)r
for the deep interior of the m o o n . They state their conclusion :is follows: ""We c,,m'h¢de that th(' arcrage chemical composili+m o f lilt' m o o n cannot remoteh' resemble that o,/a basalt. This statement can be made categorically and is an important negative constraint, completely eliminating lunar compositional models of the kind proposed by Gast 118] and others." The calculations presented here show that the densit.,,' of the lunar interior can easily approach values as high as 3.5 for ~ _~ o f rite hmar mass. This density is quite consistent with the obsePted density o / g a r n e t granulites and eclogites. Green and R i n g w o o d [191 have recently summarized densities determined f o r t typical basalt composititm studied by lto and Kennedy 1201. This summary is superitnposed on the calculated densities given in fig. I. The comparison shows that the obselwed density ot'a typical basalt c o m p o s i t i o n probabl 5 never exceeds that calculated for the uPt)er ~ of the htnar mantle. We conclude that mean lunar cotnpositions with basaltic calcium and alumitmm concentrations camtot be exchtded front providing the m o m e n t of inertia and mean density of the moon. We also note that the lower mantle or core density found in our calculations ~ ould exclude chondritic mineral assemblages for the deep interior of the moon. The density' distributions found here also place some qualitative constrain ts on the early' differentiation o f the moon. One should note first of all that all density distributions involving iron lay'ers in the outer half o t the m o o n cannot evolve front a completely molten m o o n since metallic iron would quickly segregate the lunar interior during a contpletely molten condition. Sintilarlv, the decrease in density in the lower silicate mantle that we have inferred from the low-densit.,, crest is incunsistent with early gravitative ditterentiation of a c o m p l e t e l y molten ntoon. If such a difl+erentiation is driven by' gravitational potential energies, it mttst result in a density gradient that increases downward. It is doubtfttl that subsequent thermal evolution would overcome file density profile fl~at results ltOlll file c ~ ~tallization o f t cotnpletely tnoltetl tnoon. We suggest that the extensive upward enrichntent of radioactive and other lithophile elements duriilg a cotnpletely molten stage postulated by some autttors tnust be re-exanfined in the light o t tiffs constraint. Extensive chetnica[ dift'crentiation itt the outer two-thirds of the m o o n cannot be excluded
from the density.' profiles inferred hero. It would, however, imply primitive radial chemical differences to account for the relatively low density of the interior of the moon. In conchtsion, the non-uniqtteness of the models discussed here needs to be re-entphasized. The uncertainty in the ntean density of rite lunar crust, the unifomtity of its depth, and the tmcertainty ira the moment of inertia of the 1110011 may be greater than present estimates indicate. The effects of the hmar crust on constraints regarding the internal density clearly emphasize the intportance of a more accurate deterruination of the m o m e n t of inertia o f the moon.
Acknowledgement Many tb.anks to Frank Hsu and Eddie Nicholas of Houston Baptist College t'or programming and perfomting the calculations.
References [ 1 [ K.E. Bullen, Monthl.~ Notice~ Roy. Astron. Sot., Geophys. Suppl. 3 (1936) 395. [21 K.K, Bullen, Trans. Roy. Soc. New Zealand 67 (t938) 122. [3[ K.[5. Bullen, Bull. Seis. Sac. Am. 30 {1940) 235. [4] M.N. Toksoz, F. Press, K. Anderson, A. Dainty G. Latham. M. Fwing, ,I. Dorman, D. Lalnmlein, G. Sutton, I'. Duennebier and Y. Nakamura, Science 176 <1972P 1012. [5[ G.V. katham, M. Ewing, I.. Press, G. Sutton, J. Dorman, Y. Nakamura, N. "[oks6z, D. Lammlein and I. Duennebier, Apollo 15 Preliminary Science Report 8 l (1972). [61W.M. Kaula, Science 166 (1969) 1581. [7] W.I[. Michael, Jr. and W.T. Blackshear, The Moon 3 {1972) 388, [81 J,A. Wood, J.S. Dickey, JL, U.B. Marvin and B.N. Powell, I'roc. Apollo I 1 Lunar Sci. ('ont. I (1970) 965. [9] A.M. Reid, W.[. Ridley, J. Warner, R.S. tlarmon, R. Brett, P. Jake~ and R.W. Brm~ n, labstract), Lunar Science I11(1972}640. [10] I. Adler, J. Trombka, J. Gerard, P. Lm~ man, L. Yin, I[. Blodgett, P. Gorenstein and P. Bjorkholm, (abstract), Lunar Science I11(1972)4. [ 1 I I 1. Adler, J. Trombka, J. Gerard, R. Sclunadcbeck, I'. Lov,'man, 14. Blodgctt, L. Yin, I-. Eller, R. Lamothe, P. Gorcnstcin. P. Bjorkhohn, B, Harris and tf. Gursky, Apollo 15 Preliminar,', Science Report, 17-1 ( 1972L
P. It'. Gast, R. 7". Giuli, Density ~[ the lunar htterior [ 121 D.R. Stephens and E.M. Lillcy, Proc. Apollo 11 Lunar St_i. Conf. 3 (1970) 2427. [131W.L. Sjogren, labstract), Lunar Science 11111972) 707. [ 14] W.L. Sjogren, P. (;ottlieb, P.M. Muller and W.R. Wollenhaupt, Apollo 15 Preliminary Science Report 20-1 119721. [15] P. Dyal and C.W. Parkim J. Geophys. Res. (1971) 5947. [16[ D.L. Anderson and T.C. I Ianks, Science 11972~ in press.
305
[171A.E. Ringwood and E. Essene, Proc. Apollo 11 Lunar Sci. Conf. 1 (1970)769. [ 18] P.W. Gast, Science 159 (1968) 897. [19] D.II. Green and A.E, Ringwood, J. Geol. 80 J1972~ 277. [201 K. ho and G.C. Kennedy, Mineral. Soc. Am. Spec. Paper 3 (1970~ 77. [21] S.P. Clark, Jr., ed., Geol. Soc. Am. Mem. 97 (1966) 587 PP. [22] R.K. Mc('onnell, Jr. and P.W. Gast, The Moon (1972) in press.
DENSITY
OF THE LUNAR
INTERIOR
PAUL W. GAST and R. THOMAS GIULI NASA Manned Spacecra]? Center, Houston, Texas, [~rsA
Received 13 July 1972 Revised version received 12 September 1972
Tire characterization of a planet depends on our understanding of the physical and chemical state of its interior. The significance of a few physical parameters; i.e. the mean density, the moment of inertia, and the depth of several major discontinuities - the core mantle and crust mantle boundaries - was illustrated for the case of the earth in a series of classic papers written by Bullen between 1036 and 1940 [ 1-3]. Our knowledge of these parameters for tire moon is not as precise nor as extensive yet as it was for the earth 3 0 - 4 0 years ago. Nevertheless, a line of reasoning similar to that used by Bullen can be used to lnake inferences regarding tile composition of the lunar interior. The arguments for the moon are inherently more powerful than those for the earth simply because the moon has a much greater area-tovolume ratio. Thus, its surface and near-surface characteristics are more representative of the entire planet than those of tile earth, in this paper we will attempt to derive the constraints that can be placed on the density of the lunar interior from: (1) the mean density, (2) the moment of inertia, and (3) the mass and density of tile lunar crust that have been inferred from the seismic refraction data recorded by the passive seismoineter [4, 5]. The mean density and moment of inertia used in the calculations that follow are ~- = 3.36 g/cm 3, K - C / M R 2 = 0.395, 0.397, 0.399, 0.401. The uncertainty in our knowledge of the moon's moment of inertia is still sufficiently large to significantly affect the constraints placed on the interior densities. As will be seen from the results that follow, the value K = 0.395 allows a monotomically condensed lunar interior, whereas the other three values require an interior density inversion, more extreme for the higher
values of K. Since most of the conclusions which will be drawn here are simply exaggerated by increases in the value of K, we have somewhat arbitrarily emphasized calculations using the value 0.399, rather than the value most recently reported by Kaula [6] and Michael and Blackshear [7], 0.402 -+ 0.002. All of these authors indicate that the lowest acceptable value of K is 0.400. Even though the nloment of inertia of tile moon is ahnost identical with that of a homogeneous sphere, it is now rather clear that there probably are significant density variations in the lunar interior. These variations are largely due to tile relatively large, lowdensity crust which has been inferred from results obtained from both Lunar Orbiter and Apollo experiments. The recent seismic refraction studies [5] indicate that the earth-facing side of the moon has a major seismic discontinuity between 60 and 65 km which presumably separates the lunar crust and mantle. A more gradual transition occurs at 25 km [5]. In our calculations we assume a crust of this thickness comprising about 9% of the mass of the moon. It should be noted that tile lunar crust is qualitatively different from the crust of the earth, which makes up only l/2% of the mass of the planet. Constraints on tile density of file lunar crust can be inferred from: ( l ) the crustal P-wave velocity: i.e. 7.0 km per sec, (2) the mineralogy and chemical composition of common surface rocks, and (3) the density contrast within the crust that is required to produce the mascons. Toksoz et at. [4] have summarized file terrestrial rock types that have P-wave velocities similar to those found in the lunar crust. Their compilation includes rocks with plagioclase contents ranging from less than
300
P. 11'. C;ast, R.T. Giuli. Dcptxity +tl the lunar interior
50'.; to there than 9ff..:k. Since tile density difference between calcic plagioclase
tained on tile Apollo 14 and 15 missions [13, 14] suggest that the nlascons originate front circular plates with a tnass excess of 800 kg/cm 2. If these circular plates are less than 20 km thick, density contrasts ill excess of 0.4 g/cm 3 2re required to produce such mass concentrations. Such density contrasts are difficult to actlieve if tile crustal density is greater than 3.0 since they would require extensive surface plates of rocks that have intrinsic densities in excess of 3.4 g/cm 3. Such unusually dense rocks have not been observed in most mare regions. When all these factors are taken into account, we conclude that tile lower crust, taken to be 25 63 km in depth, probably has a density between 2.85 and "+ )3 g/cnl 3. A value of 2.90 has been used in tile calculations that follow. From tile reduced sound velocities reported bv ToksOz et at. [4] we inl0r a somewhat lower density for the upper crust. A value of 2.7 g/cm 3 is used for tile upper 25 km in tile calculations that follow. The implications of these crustal densities have been investigated by calculation of a variety of multilayer, spherically symmetric, solid body models. Two algebraic equations (tnotnent of inertia and nlass continuity) are solved sitnultaneously m tile approxitnation that tile htnar interior cotnprises n constant-densit,,,', radially symmetric layers. Tile specification of the two crustal layers in tile previous paragraph then requires that 2++ 7 of tile radii and densities of tile various zones tl/tlSt be specified beforehand as parameters. It is quite clear that tile observed monlent of inertia, mean htnar density, and low density crust require subcmstal regions with densities that exceed the mean density of tile moon. First, we consider four-laver nlodels { the two crustal layers specified above, and two interior layers). Calculations of the depth and tnagnitude of tile single density discontinuity between the two interior layers that would account |'or tile htnar tnotnent of inertia and mean density are summarized in fig. 1. Tile calculations reveal the vet 5' interesting result that a density discontinuity ranging t't-onl 6'.; at 500 km depth to IY.; at 900 km depth can compensate for tile low density crust i l K is taken at 0.399. A hi~ler moment of inertia (K = 0.401J requires tile density discontinuities to range from 10`5 to 2 I':': at tile corresponcling depths. Additional calculations for lower moments of inertia are illustrated in the inset in fig. l. (
_ .
-
P. It'. Gast. R. T. Giuli, Density ol the hmar interior
- - -
:
401
K :
399
K
397
K
395
K
-
-
..........
7
~
[ C ~
36
_7
~ ............ .............................................
5
(g
301
3
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2
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~
co)
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x \ \ 2 ;
- -
i
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--
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I
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I
DEPTH (km) 25 63 1OO 200 300 400 500 600 800 IOOO VOLUME IO ,__. . . . o. . . . . 8. . . . . 7. . . . . 6. . ~ , ~ ,1 ! 5 4 3 2 O FRACTION Fig. 1. 1'our-layer models of the lunar interior, where the m o crustal la', ers are defined in the text. Proceeding inward, the respective densities of the interior layers are ,03 and P4, illustrated as a function of the location of the interior density discontinuity. That is, for any discontinuity location {abscissa), a point on the 0.~ curve appropriate to some K value defines the (constant) den~ity of the subcrustal layer, and the corresponding point on the P4 curve defines the I¢onstant) density of the interior layer. The curves are given for discontinuity locations anywhere in the interior for t~vo K values, and with an expanded density scale for all four K values for discontinuity locations between interior volume fractions of (I.25 and (I.65.
These indicate that a value of K lower than 0.396 is required to eliminate the density inversion. It is interesting to note that the magnitude of rite density contrast required ill die lower m o n t e n t of inertia models is quite comparable to that which occurs during melting of the c o m m o n silicate materials. (However, we recall that our calculations were t o n n u l a t e d with tire assumption of solid-body rotation; liquid-core models may not be adequately specified by our calculations. ) In addition, for all models ( e x c e p t for K = 0.305) where the interior density discontinuity lies at depths 500 900 kin, the subcrustal densities are quite high: 3.45 - 3.55 g/envY.In the e x t r e m e case where die interior density discontinuity is taken to lie at very shallow depths, the calculations show that a shallow layer just under the crust with a density of 7 (that is, similar to the density of metallic iron) would have to comprise at least 2.9q of the mass of the m o o n for K = 0.399, and at least 4.4(,4 for K = 0.401, to c o m p e n s a t e for the low crustal density used in our calculations. The mass of dlese shallow iron layers implies that
at least 7~1 . - - 3~ of the material that accreted during tile formation of the last 10 15'7; of the m o o n consisted of metallic iron. Thus, this portion of the m o o n would be substantially enriched in iron relative to primitive solar materials. This conclusion is a characteristic o f ahnost all models that e m p l o y an iron-rich layer to c o m p e n s a t e for the low-density crust. Fig.2 shows how the mass of such a layer must vary as a function of the depth of the layer, under the assumption that the densities of the layers adjacent to the iron are equal. The results indicate that the iron layer comprises at least 14% { 21% ) of the mass of the 'upper" layers when the iron layer is located 200 km below the surface, for K = 0.399 (0.401). In addition, we see that the mean density of the subcrustal m o o n is !ess than 3.36, significantly so when the iron lay'er is deeper than 300 kin. The effect of adding an iron core to the models illustrated in fig. 1 has also been calculated. If this core contains less than lr,'f of the mass of the m o o n , the effect upon the interior density discontinuities
t'. [?. (;axt. R. f. Gizfli, Dcllslrv ~LI tltc lunar iHrerior
302
~
/
for the K=0.BO9 model is to shift the curves toward, but not beyond, the curves illustrated for the K=0.401 model. Thus, adding a small, dense core to the fourzone model has about the ~ame effect upon the two subcrustal layers as increasing the m o m e n t olinertia of" the four-zone ntodel slightly. Several more complex models combining silicate layers with a single iron laver are illustrated in fig.3. Here we have arbitrarily assumed that high density silicate rocks form an upper mantle with illeatl d e l l sitv, _.,Iq ~g,,/Clll -~ , and an iron laver, t}l:Jt ntakes up _~',
,3 36
18 // 14
- - - - - - K=401 -
,/~/
\.
K= 3 9 9
-
~3 3
3.2
~/ \
(g/~) o6
,
~
~
~
~
" ~ " ^
i
o r 4~'; o f t h e mass ,.ff the m ~ l o n is s i t u a t e d at a d e p t h
3l
~ \'\\
of 500 kin. The.',e models show that i l the abutidance of metallic iron is constrained so lh-it it comprises less than 10";- of the mass of the 'upper' layers, more than ~ or the mass of the moon must be made tip oI" a relatively dense silicate rock. They also require the density of the lower mantle and core to be le~s than 3.3 g/cnt ~. In fig. 4 we attempt to accotln[ l'or the hmar montent of inet tia b', imagininta a chemicalh' homo<,e-
\
\ 02
~
I00
200
3.0
300
Dj (km)
1 ig. 2. I'ive-layer models o f the lunar interior, where the two crustal layers are defined in die text. Q4 is tile fraction of hmar mass in a layer contained in a high density (7.0 g/cm 3) iron layer, as a function of the depth, D 3, of the top of this layer. The densities 03 and os of the layers adjacent to the iron layer are illustrated for tile case where P3 = 05- Density for basalt NM5 is taken from reference [171. The plotted densitie~ are for 12(10°C.
lleOtlS i l l a l l l J e COlllprisJllg Olle or lllOle r e p r e s e n t a t i v e
minerals and considering die a t l e n d a n t density varialion with depth due to a reasonable run of interior temperature and pressure. We also dis:~lay the four-
7
2563 5
--
I
453
I
522
I
(SEMI-DENSE LAYER EXTENDS BELOW IRON LAYER)
_.,j
3
K -- 401 Q = .04
K = 401 1
Q5 = 02
5
7
P
25 63 5-11
385
511
25
I
63
323
--II
522
I
(g/co)
31-.
-.,J K = 399
K = 399
Q5 = 02 I
--
I
O
I 8
i
i .6
I
I 4
i
I
.2
I
0 10
.04
Qs = I
I
I
I
I
I
.8 .6 .4 VOLUME FRACTION
i
I
.2
O
Fig. 3. Six-layer models of the hmar interior, xshere the two crustal layers are defined in the text. The top of a high density (7.0 g/cm 3 ) iron layer is located at a depth of 500 kin. A high density (3.5 g/cm 3) silicate layer is adjacent to the crust. The volume and depth of this layer, and the densities lassumed equal) of the layers adjacent to tile iron layer are illustrated for two assumed values of tile lunar mass fraction Os of the iron layer. The unlabelled numbers are the depths (kmJ of the density discontinuities which define tile respecti~ e layers.
P IC Gast. R.T. Giuli. DeHsit3' o / t h e hmar i#zterior
303
4
3P P (%)
2
o
-2
-4 2000
40
-
T I K)
T
J
IOOO
DEPTH (l(m) VOLUME FRACTION I
...,----"~""-'~ 63 1OO .9 .8
P (kbar)
I
i
I
200 .7
300
400
.6
.5
A
.4
20
I
600 .3
,
I
J I
O
800 1OOO .2 .I O
Fig. 4. Density variation of several minerals with respect to their room temperature and pressure values, AO/D0, as a function of a reasonable run of temperature, T, and presstlre, P, for the lunar interior. The minerals are: 1, olivine: 2, spinel and/or garnet (pyrope); 3, pyroxene (diopside); 4, plagioclase (labradorite). Also plotted is the ratio ,03/04 for a four-zone model (K=0.397) depicted in fig. I. Data for thermal expansion and compressibility are taken from Clark [21 ]. The temperatures for the lunar interior are based on the thermal models given by McConnell and Gast [22]. zone models of fig. 1 for K=0.397, which gives the tnagnitude of the density discontinuity required between the two interior layers, as a function of the location of the discontinuity. We see that, for K as low as 0.397, we still require density discontinuities of at least 2.5-3% at depths ranging from 275 km to 650 "kin, whereas none of the representative mineral densities decrease by more than 0.5% in this region. Further. the total density decrease of spinel or garnet, say, is perhaps 2% between the base of the crust and 600 knl. Considering the uncertainties in the composition and temperature of the lunar interior, no precise conclusion regarding the effect of thermal expansion is possible. Nevertheless, one can see that mantle densities decreasing downward due to thennal expansion of solid phases are probably insufficient explanation for models with K > 0.397.
Summary
The calculations summarized here clearly do n o t lead to a unique m o d e [ o f the density' o f the lunar interior. A l l o f the m o d e l s discussed above are in c o n f l i c t
with some inferences drawn from other observations. In particular, tile conchlsion that the moon has a substantial molten silicate core today may be in conflict with tire temperature profiles that have been inferred from conductivity profiles [15, 16] unless very low iron contents are assumed for the lunar interior. Nevertheless, we suggest that one explanation of the relatively low internal densities is that the present-day telnperatures below 700 900 km exceed the solidus of the lunar interior. We have already noted that the occurrence of iron at shallow depths requires ad hoc assumptions regarding the composition of initially accreted material. Moreover, such shallow conducting layers should have been discovered in the conductivity profiles [ 15]. There are 'also serious questions regarding the long-term stability of a system with such massive density contrasts. Several additional constraints on tire lunar interior may be considered in the context of the calculations presented here. Ringwood and Essene [17] have argued that the lunar moment of inertia and mean density exclude lunar compositions that resemble those of basalt due to the gabbro-eclogite transformation because it would restilt in excessively high densities
304
P. It'. Gast. R. T. (;htli. Density (,! the lunar mtcrk)r
for the deep interior of the m o o n . They state their conclusion :is follows: ""We c,,m'h¢de that th(' arcrage chemical composili+m o f lilt' m o o n cannot remoteh' resemble that o,/a basalt. This statement can be made categorically and is an important negative constraint, completely eliminating lunar compositional models of the kind proposed by Gast 118] and others." The calculations presented here show that the densit.,,' of the lunar interior can easily approach values as high as 3.5 for ~ _~ o f rite hmar mass. This density is quite consistent with the obsePted density o / g a r n e t granulites and eclogites. Green and R i n g w o o d [191 have recently summarized densities determined f o r t typical basalt composititm studied by lto and Kennedy 1201. This summary is superitnposed on the calculated densities given in fig. I. The comparison shows that the obselwed density ot'a typical basalt c o m p o s i t i o n probabl 5 never exceeds that calculated for the uPt)er ~ of the htnar mantle. We conclude that mean lunar cotnpositions with basaltic calcium and alumitmm concentrations camtot be exchtded front providing the m o m e n t of inertia and mean density of the moon. We also note that the lower mantle or core density found in our calculations ~ ould exclude chondritic mineral assemblages for the deep interior of the moon. The density' distributions found here also place some qualitative constrain ts on the early' differentiation o f the moon. One should note first of all that all density distributions involving iron lay'ers in the outer half o t the m o o n cannot evolve front a completely molten m o o n since metallic iron would quickly segregate the lunar interior during a contpletely molten condition. Sintilarlv, the decrease in density in the lower silicate mantle that we have inferred from the low-densit.,, crest is incunsistent with early gravitative ditterentiation of a c o m p l e t e l y molten ntoon. If such a difl+erentiation is driven by' gravitational potential energies, it mttst result in a density gradient that increases downward. It is doubtfttl that subsequent thermal evolution would overcome file density profile fl~at results ltOlll file c ~ ~tallization o f t cotnpletely tnoltetl tnoon. We suggest that the extensive upward enrichntent of radioactive and other lithophile elements duriilg a cotnpletely molten stage postulated by some autttors tnust be re-exanfined in the light o t tiffs constraint. Extensive chetnica[ dift'crentiation itt the outer two-thirds of the m o o n cannot be excluded
from the density.' profiles inferred hero. It would, however, imply primitive radial chemical differences to account for the relatively low density of the interior of the moon. In conchtsion, the non-uniqtteness of the models discussed here needs to be re-entphasized. The uncertainty in the ntean density of rite lunar crust, the unifomtity of its depth, and the tmcertainty ira the moment of inertia of the 1110011 may be greater than present estimates indicate. The effects of the hmar crust on constraints regarding the internal density clearly emphasize the intportance of a more accurate deterruination of the m o m e n t of inertia o f the moon.
Acknowledgement Many tb.anks to Frank Hsu and Eddie Nicholas of Houston Baptist College t'or programming and perfomting the calculations.
References [ 1 [ K.E. Bullen, Monthl.~ Notice~ Roy. Astron. Sot., Geophys. Suppl. 3 (1936) 395. [21 K.K, Bullen, Trans. Roy. Soc. New Zealand 67 (t938) 122. [3[ K.[5. Bullen, Bull. Seis. Sac. Am. 30 {1940) 235. [4] M.N. Toksoz, F. Press, K. Anderson, A. Dainty G. Latham. M. Fwing, ,I. Dorman, D. Lalnmlein, G. Sutton, I'. Duennebier and Y. Nakamura, Science 176 <1972P 1012. [5[ G.V. katham, M. Ewing, I.. Press, G. Sutton, J. Dorman, Y. Nakamura, N. "[oks6z, D. Lammlein and I. Duennebier, Apollo 15 Preliminary Science Report 8 l (1972). [61W.M. Kaula, Science 166 (1969) 1581. [7] W.I[. Michael, Jr. and W.T. Blackshear, The Moon 3 {1972) 388, [81 J,A. Wood, J.S. Dickey, JL, U.B. Marvin and B.N. Powell, I'roc. Apollo I 1 Lunar Sci. ('ont. I (1970) 965. [9] A.M. Reid, W.[. Ridley, J. Warner, R.S. tlarmon, R. Brett, P. Jake~ and R.W. Brm~ n, labstract), Lunar Science I11(1972}640. [10] I. Adler, J. Trombka, J. Gerard, P. Lm~ man, L. Yin, I[. Blodgett, P. Gorenstein and P. Bjorkholm, (abstract), Lunar Science I11(1972)4. [ 1 I I 1. Adler, J. Trombka, J. Gerard, R. Sclunadcbeck, I'. Lov,'man, 14. Blodgctt, L. Yin, I-. Eller, R. Lamothe, P. Gorcnstcin. P. Bjorkhohn, B, Harris and tf. Gursky, Apollo 15 Preliminar,', Science Report, 17-1 ( 1972L
P. It'. Gast, R. 7". Giuli, Density ~[ the lunar htterior [ 121 D.R. Stephens and E.M. Lillcy, Proc. Apollo 11 Lunar St_i. Conf. 3 (1970) 2427. [131W.L. Sjogren, labstract), Lunar Science 11111972) 707. [ 14] W.L. Sjogren, P. (;ottlieb, P.M. Muller and W.R. Wollenhaupt, Apollo 15 Preliminary Science Report 20-1 119721. [15] P. Dyal and C.W. Parkim J. Geophys. Res. (1971) 5947. [16[ D.L. Anderson and T.C. I Ianks, Science 11972~ in press.
305
[171A.E. Ringwood and E. Essene, Proc. Apollo 11 Lunar Sci. Conf. 1 (1970)769. [ 18] P.W. Gast, Science 159 (1968) 897. [19] D.II. Green and A.E, Ringwood, J. Geol. 80 J1972~ 277. [201 K. ho and G.C. Kennedy, Mineral. Soc. Am. Spec. Paper 3 (1970~ 77. [21] S.P. Clark, Jr., ed., Geol. Soc. Am. Mem. 97 (1966) 587 PP. [22] R.K. Mc('onnell, Jr. and P.W. Gast, The Moon (1972) in press.