- Email: [email protected]
Temperatures in the lunar interior and some implications
EARTH AND PLANETARY SCIENCE LETTERS 18 (1973) 158-162. NORTH-HOLLANDPUBLISHINGCOMPANY
[]
TEMPERATURES
IN T H E L U N A R I N T E R I O R
AND SOME IMPLICATIONS A. DUBA and A.E. RINGWOOD Department of Geophysics and Geochemistry, Australian National University, Canberra
Received 3 October 1972 Revised version received 14 December 1972
Data on the electrical conductivity of olivine and pyroxene obtained under redox conditions similar to those that exist in the moon indicate that the moon is at temperatures near the melting point at depths of 600-900 km. This temperature profile, combined with information on the distribution of radioactive elements and evidence of extensive differentiation of the moon, lead to the conclusion that the moon accreted at temperatures between 600-1000°C. This high accretion temperature can be reconciled with the presence of FeS and the probable FeO/MgO ratio in the lunar interior if the moon accreted from material which was depleted in H2 relative to the solar nebula.
1. Introduction The electrical conductivity distribution in the lunar interior has been obtained by Sonett and co-workers [ 1] from an analysis of the interaction of the moon with the solar wind. This, in turn, has been inverted to obtain a lunar temperature distribution, using existing experimental data on the relationship between electrical conductivity and temperature in olivine. The temperatures obtained were remarkably low, less than 800°C at a depth of 900 km [ 1]. Hays [2], among others, demonstrated the severe difficulties encountered in reconciling this temperature distribution with other constraints on lunar thermal history. Obviously, the weak point in Sonett et al.'s argument concerns the data used on electrical conductivity of olivine. Previously, one of us [3,4] has shown that the electrical conductivity of olivines from different terrestrial environments varies over a very wide range (for similar temperatures) and is possibly controlled by redox conditions. This is supported by some recent measurements by Housely and Morin [5] who demonstrated that the electrical conductivity of olivine decreases when heated in a mix of H2 and N2. Unfortunately, their data are subject to uncertainties as to
exact redox state attained, as well as the exact nature of the conducting species. Clearly, it would be necessary to measure the electrical conductivity of olivine under similar redox conditions to those believed to occur in the lunar interior. Furthermore, evidence has been presented elsewhere [6, 7] that pyroxenes (particularly orthopyroxene) probably constitute the most abundant minerals in the lunar interior. Information on the electrical conductivity of pyroxenes would therefore be of considerable interest in this context. For these reasons we have measured the electrical conductivities of several olivines and pyroxenes over a wide range of temperatures and redox conditions. The samples studied consisted of single crystals of olivine (Fo9o and Fo92) as well as a synthetic polycrystalline samples of FoBs prepared at 30 kb and 1300°C. We also studied the conductivities of three orthopyroxene single crystals, Enss, En93, En94.
2. Results Electrical conductivity measurements were carried out in the apparatus described previously [8]. Conductivity was measured by a capacitance bridge operating
159
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
TEMPERATURE(*C) 1400
1200
J"
t
1000
I
'
900
000
I
I
RADIUS i
(km I
800
1200
I
T
1500 I --
3
1501
7 =__, E
..=.
0 v
i,,.-
b
lOOl
0 m
I
I
12'00
IO'/T (°K) -1 Fig. 1. The electrical conductivity of pyroxene and olivine. Log fO2 (1200°C) is indicated by the negative number following the line label. 1. Ens5, crystallographic direction at fO2 = 10 - 8 atm. (1200°C) is indicated by a, b, c, 2. En94; 3. En93; 4A. Fo92 at fO2 = 10 -13 (1200°C); 4B. Fo96at fO2 = 10-~3 (1200°C). This sample 4A after half the fayalite was reduced to metallic iron plus silica; 5. Synthetic olivine powder, FoBs ; •
•
6.Olivine from the Red Sea area, fO2 = 10
- - 8
o
"
(1200 C), Fo90.
at 1592 Hz. Oxygen fugacity in the furnace was controlled by the ratio of CO2 to H2 supplied from a gasmixer of standard design. Conductivity measurements were performed for oxygen fugacities ranging from 10 -0.7 to 10 - i s atm. (at 1200°C). Special efforts were directed towards obtaining conductivity data over a wide range of temperatures at oxygen fugacities corresponding to equilibrium between the olivines and pyroxenes with metallic iron. These redox conditions are believed to correspond most closely to those in the lunar interior [9]. Conductivities of olivines were measured over the temperature interval 300-1650°C and of pyroxenes over 400-1400°C. A detailed account of these experiments and their application to considerations of lunar thermal history will be presented elsewhere [10]. An abbreviated summary of the pricipal results is presented in this paper. We confirm the great sensitivity of the conductivity of olivine to changes in oxidation state. For example, as the oxygen fugacity (fO2) decreases from 10 -0.7 to
800 DEPTH
"
I
J
400 ( km }
Fig. 2. Temperature distributions within the moon calculated from the electrical conductivity of olivine and pyroxene and •the conductivity-depth profile of Sonett et al. [ 1 ]. Temperatures calculated from olivioe conductivity fall within the dashed lines t~ose from pyroxene fall within the hashed area. The maximum of the profile calculated previously for the olivine from the Red Sea [32] is indicated by the dotted line. The solidus of the model lunar pyroxenite [6] is reproduced
for reference. 10-13 atm. (1200°C), the electrical conductivity measured at 950°C decreases by three orders of magnitude. Pyroxenes are poorer conductors than olivines after the effects of exsolution lammellae disappear [11]. Fig. 1 summarizes electrical conductivity data for oilvines and pyroxenes as a function of fO2 [8, 10, 11]. Using the conductivity-depth profile for the lunar interior obtained by Sonett et al. [1] and the experimental conductivity-temperature data on olivines and pyroxenes at oxygen fugacities varying from 10 -8 to 10 -~s arm. (1200°C), we have estimated the temperature distribution within the moon from the relationship: o = ox exp ( - A x / k T ) where o is the electrical conductivity, o x is a constant, A x is the activation energy, k is Boltzmann's constant and T is the temperature in °K. Results are shown in Fig. 2. The temperature envelopes include both the variation of conductivity as a function of fO2, composition and orientation and the uncertainties in our conductivity measurements and in the conductivity-depth profiles of Sonett et al. [1]. The temperature profiles
160
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
are very similar, with olivine yielding a somewhat higher temperature at depth than pyroxene. Considering all uncertainties, the temperature at a depth of 600 km in the moon ranges from 950 ° to 1560°C, or from about 500°C below to 100°C above the solidus as determined by Ringwood and Essene [6]. Two features of fig. 2 merit comment: (i) Temperatures in the lunar interior at depths of 500-900 km are much higher than previously obtained by Sonett et al. [1]. Contrary to much earlier speculation the lunar interior is hot, not cold. (ii) Temperatures in the lunar interior are at or near the solidus. One wonders whether this is a coincidence. Further discussion of the implications of fig. 2 requires a consideration of the role of radioactive heating in the lunar interior. We shall divert temporarily to this topic.
3. Radioactivity of deep lunar interior Observed compositions of lunar basalts suggest that a K/U ratio of 2000 and a Th/U ratio of 3.8 are appropriate for thermal history calculation [2]. We adopt these numbers. The remaining problem is to estimate the absolute abundance of uranium which was originally present in the deep lunar interior. Three sources of evidence bear on this problem: (i) Extensive investigations of the petrogenesis of maria basalts show that they have been formed by varying degrees of partial melting of source material at depths greater than 200 km [6, 7, 12-14]. These studies show that a sequence representing increasing degrees of partial melting is as follows: Apollo 11 (2-5%), Apollo 12 (~10%), Apollo 15 (15-20%) and Apollo 15 Green Glass (~50%). Following the same techniques which have been applied to derive the composition of the earth's mantle from the compositions of terrestrial basalts [ 15, 16], the composition of the lunar mantle can be derived [6, 7]. The inference that Apollo 15 Green Glass represents a 50% partial melt of source material implies, in conjunction with its observed uranium content (0.05 ppm [17]), that the uranium content of the source region is about 0.025 ppm. (ii) Ringwood and Essene [6] demonstrated t h a t the lunar interior cannot possess more than about 5% each of CaO and A1203.
Otherwise, phase changes to denser mineral assemblages with depth caused by these components would cause a density distribution in conflict with the moon's observed moment of inertia. A strong case can be made that the relative abundances of elements possessing highly involatile oxides (e.g., Ca, A1, Ti, Zr, rare earths, U and Th) in the moon are similar to those in chondrites. Taking the inferred Ca and A1 contents of the lunar interior [6], the chondritic U/Ca and U/A1 ratios would imply an absolute abundance of 0.025 ppm U in the lunar interior. (iii) The abundances of a wide range of elements possessing involatile oxides are higher in type 1 carbonaceous chondrites than in ordinary chondrites by a factor of about 1.4 [18]. Type 1 carbonaceous chondrites are believed to represent the closest approach to primordial solar system abundances. If we take the U/(Mg + Si) ratio occurring in type 1 carbonaceous chondrites [ 19] and apply it to the lunar interior assumed to consist dominantly of ferromagnesian sillicates [6], the uranium content of the moon is 0.022 ppm. We adopt this figure in subsequent discussion. With the above K/U, Th/U ratios and U abundance, the temperature rise caused by radioactive heating during the last 4.6 by would be 880°C. During the first 1.6 by after the moon's formation, the temperature increase would be 420°C. These radioactive element abundances would provide only about half of the heat flow observed at the Apollo 15 site. We are inclined to think that the heat flow distribution may not necessarily be uniform in a highly differentiated moon.
4. Palaeotemperature distributions within the moon Interpretations of the lunar maria as forming from magmas generated by partial melting at depths of 200-500 km in the lunar mantle [6] some 3 to 4 by ago implies that large volumes of the lunar interior were close to the solidus during this interval. From fig. 2 we see that this is still the case today. Two interpretations might be considered. Firstly, the region at depths of 200-900 km might have become completely differentiated by magmatism some 3 to 4 by ago and the radioactive heat sources transferred to regions near the surface where the heat can escape by conduction (this would imply incidentally that the maria represent only a small proportion of
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
the total magmas generated). Most of the magmas were presumably intruded as plutons in the outer cool lithosphere [20]. Thermal calculations [21,22] show that conductive cooling at depths of 500-900 km over the past 3 by has been quite small, so that the presently inferred temperatures at these depths are within 100-200°C of the temperatures present 3 by ago. Prior to this major differentiation, the source region would have been heated by radioactivity. With the abundances specified in section 3, this heating would amount to 420°C. It follows from this increment and from fig. 2 that the temperature at depths of 500-900 km when the moon was formed about 4.6 by ago must have been about 1000°C. This model therefore implies that the moon was born h o t throughout.
An alternative hypothesis is that the region at depths of 500-900 km has not yet differentiated to form maria-type magmas and is still in its primitive state. With the U, Th, K abundances previously adopted this would imply radioactive heating by 880°C over the past 4.6 by. Thus the temperature at 500-900 km in the lunar interior immediately after its formation was about 600°C. Even this temperature is substantially higher than had been previously considered likely according to some theories of lunar origin. Whilst both models are worthy of consideration, we favour the former on the following grounds: (i) It is extremely difficult to construct plausible thermal history models of the moon which account for a period of widespread magmatism of internal origin some 3 to 4 by ago, and at the same time, for the inferred paucity of magmatic activity over the last 3 by, without assuming the occurrence of nearly complete differentiation of the lunar interior around the time of maria volcanism [21-23]. (ii) The similarity between present internal temperatures and the solidus (fig. 2) is a direct consequence of the first model. According to the second model, it would be necessary to regard this as a coincidence.
5. Conclusions The preceding data and arguments strongly support the conclusion that the moon accreted under relatively
161
high temperature conditions (600-1000°C) and most probably at the higher end of this range. Many implications of this conclusion remain to be explored. A few are noted below. It is consistent with the strong depletion of volatile elements observed in lunar rocks. It relaxes the conditions required to cause extensive melting and differentiation of the outer part of the moon by means of partial conservation of gravitational energy of accretion during the moon's formation. This differentiation is necessary in order to explain the occurrence, chemical and petrological nature, and inferred age of the differentiated lunar highlands and crust. The deep interior of the moon is inferred always to have possessed low strength. Large molten bodies of iron-nickel- sulphide formed during the early near-surface differentiation would therefore be able to sink through the solid lunar mantle to form a core [24] which in turn might generate a magnetic field [25]. This possibility is examined in detail elsewhere [ 10]. The stresses in the outer part of the moon implied by the existence of mascons, and possibly, the non-hydrostatic figure of the moon, must therefore be supported by the strength of the thick (~300 km) cool lunar lithosphere. Our conclusions regarding lunar thermal history thus strongly support the interpretation advanced by Baldwin [26]. Finally, we note some cosmochemical implications. Lunar rocks cary substantial quantities of FeO and FeS. The FeO/(FeO + MgO) ratio of the source region of maria basalts is inferred to be 0.25 (molecular) [6] and maria basalts contain about 600 ppm S [24]. Probably, more FeS remained behind in the interior. It is difficult to understan the occurrence of these components if the moon accreted from the primordial solar nebula at the temperatures we have inferred ( 6 0 0 1000°C). Larimer and Anders [28] demonstrated that FeS would not condense until 400°C in the presence of the solar H2/H2S ratio, whilst sillicates with FeO/ (FeO + MgO) ~ 0.25 do not condense until about 330°C [27]. If the present composition of the material in the moon has been established by equilibrium with a gas phase at temperatures of 600-1000°C, then the gas phase must have been depleted in hydrogen relative to solar abundances by a factor of 10 to 50. The occurrence of FeO and FeS combined with the inferred high temperature .of accretion is readily explained ff the moon accreted from material which has equilibrated with a massive hot terrestrial atmosphere
162
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
o f CO a n d H2, b u t strongly d e p l e t e d in h y d r o g e n relative to the solar n e b u l a , as p r o p o s e d b y R i n g w o o d [29-31].
Acknowledgements A. Major a n d W.O. H i b b e r s o n were m o s t h e l p f u l in the e x p e r i m e n t a l studies. Discussions w i t h J.N. B o l a n d , R.C. L i e b e r m a n n a n d I.A. Nicholls were o f great benefit. T h e financial assistance o f the A u s t r a l i a n - A m e r i can E d u c a t i o n a l F o u n d a t i o n in the f o r m o f a Fullb r i g h t - H a y s P o s t d o c t o r a l F e l l o w s h i p was m u c h appreciated by one o f us (A.D.).
References [1 ] C.P. Sonett, D.S. Colburn, P. Dyal, C.W. Parkin, B.F. Smith, G. Schubert and K. Schwartz, Lunar electrical conductivity profile, Nature 230 (1971) 359. [2] J.F. Hays, Radioactive heat sources in the lunar interior, Phys. Earth Planet. Int. 5 (1972) 77. [ 3 ] A. Duba, The electrical conductivity of olivine as a function of temperature, pressure, composition and crystallographic orientation, Ph.D. thesis, University of Chicago (1971). [4] A. Duba, Electrical conductivity of olivine, J. Geophys. Res. 77 (1972) 2483. [5 ] R.M. Housley and F.J. Morin, Electrical conductivity of olivine and the lunar temperature profile, Moon 4 (1972) 35. [6] A.E. Ringwood and E. Essene, Petrogenesis of Apollo 11 basatts, internal constitution and origin of the moon, Geochim. Cosmochim. Acta, Suppl. 1 (1970) 769. [7] D.H. Green, A.E. Ringwood, N.G. Ware and W.O. Hibberson, Experimental petrology and petrogenesis of Apollo 14 basalts (1972) in press. [81 A. Duba and I.A. Nicholls, The influence of oxidation state on the electrical conductivity of olivine, Earth Planet. Sci. Letters 18 (1973) 59-64. 19l M. Sato and R.T. Helz, Oxygen fugacity of Apollo 12 basalts by the solid electrolyte method, Apollo 12 Lunar Science Conference, Houston, Texas (Jan. 1971). [10] A. Duba and A.E. Ringwood, Electrical conductivity, internal temperature and thermal evolution of the moon, (1973) in preparation. [ 11 ] A. Duba, J.N. Boland and A.E. Ringwood, Electrical conductivity of pyroxene (1973) in preparation. [ 12 ] D.H. Green and A.E. Ringwood, Significance of Apollo
15 basalts and primitive green glass in lunar petrogenesis in: The Apollo 15 Lunar Samples (eds. J.W. Chamberlain and C. Watkins), Lunar Science Institute, Houston (1972) in press. [13] D.H. Green and A.E. Ringwood, Significance of a primitive lunar basaltic composition present in Apollo 15 breccias, submitted. [14] A.E. Ringwood and D.H. Green, Petrogenesis of lunar basalt (1973) in preparation. [ 15 ] D.H. Green and A.E. Ringwood, The genesis of basaltic magmas, Contrib. Min. Pet. 15 (1967) 103. [16] A.E. Ringwood, Composition, Petrology and Origin of the Earth (McGraw-Hill, 1973) in press. [17] S.R. Taylor, personal communication, 1972. [18] J.W. Latimer, Composition of the earth: chondritic or achondritic? Geochim. Cosmochim. Acta 35 (1971) 769. [19] J.W. Morgan, Uranium (92), in: Handbook o f Elemental Abundances in Meteorites (ed. B. Mason) Gordon and Breach, New York (1971). [20] R.B. Baldwin, Summary of arguments for a hot moon, Science 170 (1970) 1297. [21] P.E. Fricker, R.T. Reynolds and A.L. Summers, Possible thermal history of the moon (1972) preprint. [221 M.N. ToksiSz, S.C. Solomon, J .W. Minear and D.H. Johnston, Thermal evolution of the moon, Moon 4 (1972) 190. [23] J.A. Wood, Petrology of the lunar soil and geophysical implications, J. Geophys. Res. 75 (1970) 6497. [24] R. Brett, Sulfur and the ancient lunar magnetic field, Trans. Am. Geophys. Union 53 (1972) 723. [25] S.K. Runcorn, Implications of the magnetism and figure of the moon, 1972 Lunar Science Conf. Abstracts (1972) p. 590. [26] R.B. Baldwin, The question of isostasy of the moon, Phys. Earth Planet. Int. 4 (1971) 167. [27] J.W. Larimer, Experimental studies on the system FeMgO-SiO2-02 and their bearing on the petrology of chondritic meteorites, Geochim. Cosmochim. Acta 32 (1968) 1187. [28] J.W. Larimer and E. Anders, Chemical fractionations in meteorites - III. Major element fractionation in chon, drites, Geochim. Cosmochim. Acta 34 (1970) 367. [29] A.E. Ringwood, Chemical evolution of the terrestrial planets, Geochim. Cosmochim. Acta 30 (1966) 41. [ 30] A.E. Ringwood, Petrogenesis of Apollo 11 lunar basalts and implications for lunar origin, J. Geophys. Res. 75 (1970) 6453. [31 ] A.E. Ringwood, Origin of the moon: The precipitation hypothesis, Earth Planet. Sci. Letters 8 (1970) 131. [32] A. Duba, H.C. Heard and R.N. Schock, The lunar temperature prof'de, Earth Planet. Sci. Letters 15 (1972) 301.
[]
TEMPERATURES
IN T H E L U N A R I N T E R I O R
AND SOME IMPLICATIONS A. DUBA and A.E. RINGWOOD Department of Geophysics and Geochemistry, Australian National University, Canberra
Received 3 October 1972 Revised version received 14 December 1972
Data on the electrical conductivity of olivine and pyroxene obtained under redox conditions similar to those that exist in the moon indicate that the moon is at temperatures near the melting point at depths of 600-900 km. This temperature profile, combined with information on the distribution of radioactive elements and evidence of extensive differentiation of the moon, lead to the conclusion that the moon accreted at temperatures between 600-1000°C. This high accretion temperature can be reconciled with the presence of FeS and the probable FeO/MgO ratio in the lunar interior if the moon accreted from material which was depleted in H2 relative to the solar nebula.
1. Introduction The electrical conductivity distribution in the lunar interior has been obtained by Sonett and co-workers [ 1] from an analysis of the interaction of the moon with the solar wind. This, in turn, has been inverted to obtain a lunar temperature distribution, using existing experimental data on the relationship between electrical conductivity and temperature in olivine. The temperatures obtained were remarkably low, less than 800°C at a depth of 900 km [ 1]. Hays [2], among others, demonstrated the severe difficulties encountered in reconciling this temperature distribution with other constraints on lunar thermal history. Obviously, the weak point in Sonett et al.'s argument concerns the data used on electrical conductivity of olivine. Previously, one of us [3,4] has shown that the electrical conductivity of olivines from different terrestrial environments varies over a very wide range (for similar temperatures) and is possibly controlled by redox conditions. This is supported by some recent measurements by Housely and Morin [5] who demonstrated that the electrical conductivity of olivine decreases when heated in a mix of H2 and N2. Unfortunately, their data are subject to uncertainties as to
exact redox state attained, as well as the exact nature of the conducting species. Clearly, it would be necessary to measure the electrical conductivity of olivine under similar redox conditions to those believed to occur in the lunar interior. Furthermore, evidence has been presented elsewhere [6, 7] that pyroxenes (particularly orthopyroxene) probably constitute the most abundant minerals in the lunar interior. Information on the electrical conductivity of pyroxenes would therefore be of considerable interest in this context. For these reasons we have measured the electrical conductivities of several olivines and pyroxenes over a wide range of temperatures and redox conditions. The samples studied consisted of single crystals of olivine (Fo9o and Fo92) as well as a synthetic polycrystalline samples of FoBs prepared at 30 kb and 1300°C. We also studied the conductivities of three orthopyroxene single crystals, Enss, En93, En94.
2. Results Electrical conductivity measurements were carried out in the apparatus described previously [8]. Conductivity was measured by a capacitance bridge operating
159
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
TEMPERATURE(*C) 1400
1200
J"
t
1000
I
'
900
000
I
I
RADIUS i
(km I
800
1200
I
T
1500 I --
3
1501
7 =__, E
..=.
0 v
i,,.-
b
lOOl
0 m
I
I
12'00
IO'/T (°K) -1 Fig. 1. The electrical conductivity of pyroxene and olivine. Log fO2 (1200°C) is indicated by the negative number following the line label. 1. Ens5, crystallographic direction at fO2 = 10 - 8 atm. (1200°C) is indicated by a, b, c, 2. En94; 3. En93; 4A. Fo92 at fO2 = 10 -13 (1200°C); 4B. Fo96at fO2 = 10-~3 (1200°C). This sample 4A after half the fayalite was reduced to metallic iron plus silica; 5. Synthetic olivine powder, FoBs ; •
•
6.Olivine from the Red Sea area, fO2 = 10
- - 8
o
"
(1200 C), Fo90.
at 1592 Hz. Oxygen fugacity in the furnace was controlled by the ratio of CO2 to H2 supplied from a gasmixer of standard design. Conductivity measurements were performed for oxygen fugacities ranging from 10 -0.7 to 10 - i s atm. (at 1200°C). Special efforts were directed towards obtaining conductivity data over a wide range of temperatures at oxygen fugacities corresponding to equilibrium between the olivines and pyroxenes with metallic iron. These redox conditions are believed to correspond most closely to those in the lunar interior [9]. Conductivities of olivines were measured over the temperature interval 300-1650°C and of pyroxenes over 400-1400°C. A detailed account of these experiments and their application to considerations of lunar thermal history will be presented elsewhere [10]. An abbreviated summary of the pricipal results is presented in this paper. We confirm the great sensitivity of the conductivity of olivine to changes in oxidation state. For example, as the oxygen fugacity (fO2) decreases from 10 -0.7 to
800 DEPTH
"
I
J
400 ( km }
Fig. 2. Temperature distributions within the moon calculated from the electrical conductivity of olivine and pyroxene and •the conductivity-depth profile of Sonett et al. [ 1 ]. Temperatures calculated from olivioe conductivity fall within the dashed lines t~ose from pyroxene fall within the hashed area. The maximum of the profile calculated previously for the olivine from the Red Sea [32] is indicated by the dotted line. The solidus of the model lunar pyroxenite [6] is reproduced
for reference. 10-13 atm. (1200°C), the electrical conductivity measured at 950°C decreases by three orders of magnitude. Pyroxenes are poorer conductors than olivines after the effects of exsolution lammellae disappear [11]. Fig. 1 summarizes electrical conductivity data for oilvines and pyroxenes as a function of fO2 [8, 10, 11]. Using the conductivity-depth profile for the lunar interior obtained by Sonett et al. [1] and the experimental conductivity-temperature data on olivines and pyroxenes at oxygen fugacities varying from 10 -8 to 10 -~s arm. (1200°C), we have estimated the temperature distribution within the moon from the relationship: o = ox exp ( - A x / k T ) where o is the electrical conductivity, o x is a constant, A x is the activation energy, k is Boltzmann's constant and T is the temperature in °K. Results are shown in Fig. 2. The temperature envelopes include both the variation of conductivity as a function of fO2, composition and orientation and the uncertainties in our conductivity measurements and in the conductivity-depth profiles of Sonett et al. [1]. The temperature profiles
160
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
are very similar, with olivine yielding a somewhat higher temperature at depth than pyroxene. Considering all uncertainties, the temperature at a depth of 600 km in the moon ranges from 950 ° to 1560°C, or from about 500°C below to 100°C above the solidus as determined by Ringwood and Essene [6]. Two features of fig. 2 merit comment: (i) Temperatures in the lunar interior at depths of 500-900 km are much higher than previously obtained by Sonett et al. [1]. Contrary to much earlier speculation the lunar interior is hot, not cold. (ii) Temperatures in the lunar interior are at or near the solidus. One wonders whether this is a coincidence. Further discussion of the implications of fig. 2 requires a consideration of the role of radioactive heating in the lunar interior. We shall divert temporarily to this topic.
3. Radioactivity of deep lunar interior Observed compositions of lunar basalts suggest that a K/U ratio of 2000 and a Th/U ratio of 3.8 are appropriate for thermal history calculation [2]. We adopt these numbers. The remaining problem is to estimate the absolute abundance of uranium which was originally present in the deep lunar interior. Three sources of evidence bear on this problem: (i) Extensive investigations of the petrogenesis of maria basalts show that they have been formed by varying degrees of partial melting of source material at depths greater than 200 km [6, 7, 12-14]. These studies show that a sequence representing increasing degrees of partial melting is as follows: Apollo 11 (2-5%), Apollo 12 (~10%), Apollo 15 (15-20%) and Apollo 15 Green Glass (~50%). Following the same techniques which have been applied to derive the composition of the earth's mantle from the compositions of terrestrial basalts [ 15, 16], the composition of the lunar mantle can be derived [6, 7]. The inference that Apollo 15 Green Glass represents a 50% partial melt of source material implies, in conjunction with its observed uranium content (0.05 ppm [17]), that the uranium content of the source region is about 0.025 ppm. (ii) Ringwood and Essene [6] demonstrated t h a t the lunar interior cannot possess more than about 5% each of CaO and A1203.
Otherwise, phase changes to denser mineral assemblages with depth caused by these components would cause a density distribution in conflict with the moon's observed moment of inertia. A strong case can be made that the relative abundances of elements possessing highly involatile oxides (e.g., Ca, A1, Ti, Zr, rare earths, U and Th) in the moon are similar to those in chondrites. Taking the inferred Ca and A1 contents of the lunar interior [6], the chondritic U/Ca and U/A1 ratios would imply an absolute abundance of 0.025 ppm U in the lunar interior. (iii) The abundances of a wide range of elements possessing involatile oxides are higher in type 1 carbonaceous chondrites than in ordinary chondrites by a factor of about 1.4 [18]. Type 1 carbonaceous chondrites are believed to represent the closest approach to primordial solar system abundances. If we take the U/(Mg + Si) ratio occurring in type 1 carbonaceous chondrites [ 19] and apply it to the lunar interior assumed to consist dominantly of ferromagnesian sillicates [6], the uranium content of the moon is 0.022 ppm. We adopt this figure in subsequent discussion. With the above K/U, Th/U ratios and U abundance, the temperature rise caused by radioactive heating during the last 4.6 by would be 880°C. During the first 1.6 by after the moon's formation, the temperature increase would be 420°C. These radioactive element abundances would provide only about half of the heat flow observed at the Apollo 15 site. We are inclined to think that the heat flow distribution may not necessarily be uniform in a highly differentiated moon.
4. Palaeotemperature distributions within the moon Interpretations of the lunar maria as forming from magmas generated by partial melting at depths of 200-500 km in the lunar mantle [6] some 3 to 4 by ago implies that large volumes of the lunar interior were close to the solidus during this interval. From fig. 2 we see that this is still the case today. Two interpretations might be considered. Firstly, the region at depths of 200-900 km might have become completely differentiated by magmatism some 3 to 4 by ago and the radioactive heat sources transferred to regions near the surface where the heat can escape by conduction (this would imply incidentally that the maria represent only a small proportion of
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
the total magmas generated). Most of the magmas were presumably intruded as plutons in the outer cool lithosphere [20]. Thermal calculations [21,22] show that conductive cooling at depths of 500-900 km over the past 3 by has been quite small, so that the presently inferred temperatures at these depths are within 100-200°C of the temperatures present 3 by ago. Prior to this major differentiation, the source region would have been heated by radioactivity. With the abundances specified in section 3, this heating would amount to 420°C. It follows from this increment and from fig. 2 that the temperature at depths of 500-900 km when the moon was formed about 4.6 by ago must have been about 1000°C. This model therefore implies that the moon was born h o t throughout.
An alternative hypothesis is that the region at depths of 500-900 km has not yet differentiated to form maria-type magmas and is still in its primitive state. With the U, Th, K abundances previously adopted this would imply radioactive heating by 880°C over the past 4.6 by. Thus the temperature at 500-900 km in the lunar interior immediately after its formation was about 600°C. Even this temperature is substantially higher than had been previously considered likely according to some theories of lunar origin. Whilst both models are worthy of consideration, we favour the former on the following grounds: (i) It is extremely difficult to construct plausible thermal history models of the moon which account for a period of widespread magmatism of internal origin some 3 to 4 by ago, and at the same time, for the inferred paucity of magmatic activity over the last 3 by, without assuming the occurrence of nearly complete differentiation of the lunar interior around the time of maria volcanism [21-23]. (ii) The similarity between present internal temperatures and the solidus (fig. 2) is a direct consequence of the first model. According to the second model, it would be necessary to regard this as a coincidence.
5. Conclusions The preceding data and arguments strongly support the conclusion that the moon accreted under relatively
161
high temperature conditions (600-1000°C) and most probably at the higher end of this range. Many implications of this conclusion remain to be explored. A few are noted below. It is consistent with the strong depletion of volatile elements observed in lunar rocks. It relaxes the conditions required to cause extensive melting and differentiation of the outer part of the moon by means of partial conservation of gravitational energy of accretion during the moon's formation. This differentiation is necessary in order to explain the occurrence, chemical and petrological nature, and inferred age of the differentiated lunar highlands and crust. The deep interior of the moon is inferred always to have possessed low strength. Large molten bodies of iron-nickel- sulphide formed during the early near-surface differentiation would therefore be able to sink through the solid lunar mantle to form a core [24] which in turn might generate a magnetic field [25]. This possibility is examined in detail elsewhere [ 10]. The stresses in the outer part of the moon implied by the existence of mascons, and possibly, the non-hydrostatic figure of the moon, must therefore be supported by the strength of the thick (~300 km) cool lunar lithosphere. Our conclusions regarding lunar thermal history thus strongly support the interpretation advanced by Baldwin [26]. Finally, we note some cosmochemical implications. Lunar rocks cary substantial quantities of FeO and FeS. The FeO/(FeO + MgO) ratio of the source region of maria basalts is inferred to be 0.25 (molecular) [6] and maria basalts contain about 600 ppm S [24]. Probably, more FeS remained behind in the interior. It is difficult to understan the occurrence of these components if the moon accreted from the primordial solar nebula at the temperatures we have inferred ( 6 0 0 1000°C). Larimer and Anders [28] demonstrated that FeS would not condense until 400°C in the presence of the solar H2/H2S ratio, whilst sillicates with FeO/ (FeO + MgO) ~ 0.25 do not condense until about 330°C [27]. If the present composition of the material in the moon has been established by equilibrium with a gas phase at temperatures of 600-1000°C, then the gas phase must have been depleted in hydrogen relative to solar abundances by a factor of 10 to 50. The occurrence of FeO and FeS combined with the inferred high temperature .of accretion is readily explained ff the moon accreted from material which has equilibrated with a massive hot terrestrial atmosphere
162
A. Duba, A.E. Ringwood, Temperatures in the lunar interior
o f CO a n d H2, b u t strongly d e p l e t e d in h y d r o g e n relative to the solar n e b u l a , as p r o p o s e d b y R i n g w o o d [29-31].
Acknowledgements A. Major a n d W.O. H i b b e r s o n were m o s t h e l p f u l in the e x p e r i m e n t a l studies. Discussions w i t h J.N. B o l a n d , R.C. L i e b e r m a n n a n d I.A. Nicholls were o f great benefit. T h e financial assistance o f the A u s t r a l i a n - A m e r i can E d u c a t i o n a l F o u n d a t i o n in the f o r m o f a Fullb r i g h t - H a y s P o s t d o c t o r a l F e l l o w s h i p was m u c h appreciated by one o f us (A.D.).
References [1 ] C.P. Sonett, D.S. Colburn, P. Dyal, C.W. Parkin, B.F. Smith, G. Schubert and K. Schwartz, Lunar electrical conductivity profile, Nature 230 (1971) 359. [2] J.F. Hays, Radioactive heat sources in the lunar interior, Phys. Earth Planet. Int. 5 (1972) 77. [ 3 ] A. Duba, The electrical conductivity of olivine as a function of temperature, pressure, composition and crystallographic orientation, Ph.D. thesis, University of Chicago (1971). [4] A. Duba, Electrical conductivity of olivine, J. Geophys. Res. 77 (1972) 2483. [5 ] R.M. Housley and F.J. Morin, Electrical conductivity of olivine and the lunar temperature profile, Moon 4 (1972) 35. [6] A.E. Ringwood and E. Essene, Petrogenesis of Apollo 11 basatts, internal constitution and origin of the moon, Geochim. Cosmochim. Acta, Suppl. 1 (1970) 769. [7] D.H. Green, A.E. Ringwood, N.G. Ware and W.O. Hibberson, Experimental petrology and petrogenesis of Apollo 14 basalts (1972) in press. [81 A. Duba and I.A. Nicholls, The influence of oxidation state on the electrical conductivity of olivine, Earth Planet. Sci. Letters 18 (1973) 59-64. 19l M. Sato and R.T. Helz, Oxygen fugacity of Apollo 12 basalts by the solid electrolyte method, Apollo 12 Lunar Science Conference, Houston, Texas (Jan. 1971). [10] A. Duba and A.E. Ringwood, Electrical conductivity, internal temperature and thermal evolution of the moon, (1973) in preparation. [ 11 ] A. Duba, J.N. Boland and A.E. Ringwood, Electrical conductivity of pyroxene (1973) in preparation. [ 12 ] D.H. Green and A.E. Ringwood, Significance of Apollo
15 basalts and primitive green glass in lunar petrogenesis in: The Apollo 15 Lunar Samples (eds. J.W. Chamberlain and C. Watkins), Lunar Science Institute, Houston (1972) in press. [13] D.H. Green and A.E. Ringwood, Significance of a primitive lunar basaltic composition present in Apollo 15 breccias, submitted. [14] A.E. Ringwood and D.H. Green, Petrogenesis of lunar basalt (1973) in preparation. [ 15 ] D.H. Green and A.E. Ringwood, The genesis of basaltic magmas, Contrib. Min. Pet. 15 (1967) 103. [16] A.E. Ringwood, Composition, Petrology and Origin of the Earth (McGraw-Hill, 1973) in press. [17] S.R. Taylor, personal communication, 1972. [18] J.W. Latimer, Composition of the earth: chondritic or achondritic? Geochim. Cosmochim. Acta 35 (1971) 769. [19] J.W. Morgan, Uranium (92), in: Handbook o f Elemental Abundances in Meteorites (ed. B. Mason) Gordon and Breach, New York (1971). [20] R.B. Baldwin, Summary of arguments for a hot moon, Science 170 (1970) 1297. [21] P.E. Fricker, R.T. Reynolds and A.L. Summers, Possible thermal history of the moon (1972) preprint. [221 M.N. ToksiSz, S.C. Solomon, J .W. Minear and D.H. Johnston, Thermal evolution of the moon, Moon 4 (1972) 190. [23] J.A. Wood, Petrology of the lunar soil and geophysical implications, J. Geophys. Res. 75 (1970) 6497. [24] R. Brett, Sulfur and the ancient lunar magnetic field, Trans. Am. Geophys. Union 53 (1972) 723. [25] S.K. Runcorn, Implications of the magnetism and figure of the moon, 1972 Lunar Science Conf. Abstracts (1972) p. 590. [26] R.B. Baldwin, The question of isostasy of the moon, Phys. Earth Planet. Int. 4 (1971) 167. [27] J.W. Larimer, Experimental studies on the system FeMgO-SiO2-02 and their bearing on the petrology of chondritic meteorites, Geochim. Cosmochim. Acta 32 (1968) 1187. [28] J.W. Larimer and E. Anders, Chemical fractionations in meteorites - III. Major element fractionation in chon, drites, Geochim. Cosmochim. Acta 34 (1970) 367. [29] A.E. Ringwood, Chemical evolution of the terrestrial planets, Geochim. Cosmochim. Acta 30 (1966) 41. [ 30] A.E. Ringwood, Petrogenesis of Apollo 11 lunar basalts and implications for lunar origin, J. Geophys. Res. 75 (1970) 6453. [31 ] A.E. Ringwood, Origin of the moon: The precipitation hypothesis, Earth Planet. Sci. Letters 8 (1970) 131. [32] A. Duba, H.C. Heard and R.N. Schock, The lunar temperature prof'de, Earth Planet. Sci. Letters 15 (1972) 301.