Journalof GeophysicalResearch

VOLUME 77 FEBRUARY 10., 1972 NUMBER 15

Internal Constitution of Mars

Do• L. ANDERSON

SeismologicalLaboratory, California Institute o/ Technology Pasadena, California 91109

Models for the internal structure of Mars that are consistentwith its mass, radius, and moment of inertia have been constructed.Mars cannot be homogeneousbut must have a core, the size of which dependson its density and, therefore, on its composition.A meteorite model for Mars implies an Fe-S-Ni core (12% by massof the planet) and an Fe- or FeO-rich mantle with a zero-pressuredensity of approximately 3.54 g/cm•. Mars has an iron content of 25 wt %, which is significantly less than the iron content of the earth, Mercury, or Venus but is close to the total iron content of ordinary and carbonaceouschondrites. A satisfactory model for Mars can be obtained by exposing ordinary chondrites to relatively modest temperatures. Core formation will start when temperaturesexceed the cutecftc temperature in the system Fe-FeS (•990øC) but will not go to completionunless temperatures exceed the liquidus through- out most of the planet. No high-temperature reduction stage is required. The size and density of the core and the density of the mantle indicate that approximately63% of the potential core-forming material (Fe-S-Ni) has entered the core. Therefore, Mars, in contrast to the earth, is an incompletely differentiated planet, and its core is substantially richer in sulfur than the earth's core. The thermal energy associated with core formation in Mars is negligible. The absenceof a magnetic field can be explained by lack of lunar precessional torques and by the small size and high resistivity of the Martian core.

Most calculations of the internal structure of son and Phinney, 1967; Hanks and Anderson, Mars have assumedthat the coreof the planet, 1969] have been used to support the arguments if there is any, has the density of iron or the againstthe developmentof an extensivemolten- density of the earth's core suitably correctedfor iron core in Mars, as has the lack of a detect- the effects of pressure.On the basis of this able magneticfield. However, solar and meteor- assumptionand the observedmoment of inertia, itic abundancessuggest that iron is not the only it has been concludedthat Mars is a nearly candidate for the material in a planetary core. homogeneousbody with, at most, an iron core Cosmic abundances,for example, and melting of 1-6% of the planer's mass [MacDonald, relationships•indicate that sulfur should be an 1962; Binder, 1969]. Urey [1957] and Bullen abundant elemen• in the core, particularly in [1966] concludedthat it is unlikely that Mars small relatively cold planets. has a core.Thermal-history calculations lander- The two measurableparameters that are per- tinent' to the internal structure of Mars are the x Contribution 2034 of the Division of Geologi- mean density and th• moment of inertia. These cal and Planetary Sciences,California Institute of data can be usedto determineonly two param- Technology. eters of the interior. The behavior of solids, Copyright ¸ 1972 by the American Geophysical Union. such as silicatesand metals, under pressureis

789 790 DON L. ANDERSON fairly well known from high-pressureand shock- CALCULATIONS wave studies and from the known structure of For present purposes,we take an extremely the interior of the earth. For example,we know simple form for the equation of state: the equationsof state and the locationsof phase changesfor most of the materialsthat might be P = Poq- a[1 -- (r/R)] expectedto be important in the interiorsof the where pois the zero-pressuredensity of a given terrestrial planets. With this information, we regionof the planet, R is the radius of Mars, p can eomplet.ely define the structure of a two- is the density at radius r, and a is a constant zone planet (for example, one containing a taken as 0.565 g/cm8. This equation gives re- mantleand a core) in termsof the zero-pressure sults consistent with those of Kovach and An- densities of the mantle and the core and the derson [1965] and Binder [1969], who used a radius of the core.For Mars two of these pa- rameters can be found as a function of the third. differentapproach. The mantle of Mars is pre- This procedureis to be preferredto preassign- sumably composedmainly of silicates, which ing one of the parameters,since such preassign- can be expectedto undergoone or two major ment would be equivalentto assumingthat the phase changes,each involving a 10% increase compositionof one of the regionsof the planet in density. To a good approximation, these is known. It is particularly dangerousto assign phas•changes will occurat x/3and 2/• of the the densityof the core,since the relativepropor- radius of Mars. The deeper phase changewill tions of iron, nickel,sulfur, and silicon,elements not occur if the radius of the core exceeds• of that may be in the core in appreciableabun- the radius of the planet. With these parameters dances,depend critically on conditionsduring we can solve for the radius and density of the accretion of the planet, present internal tem- core, given the density of the mantle and the peratures, degree of differentiation, and, of observablemass, radius, and moment of inertia course,the compositionand oxidizationstate of for Mars. The results are given in Table 1. the originalmaterial. If siliconis the light alloy- The curve in Figure 1 gives these results in ing element in the earth's core [Ringwood, terms of the density of the core and the radius 1966], the density of the core will decreaseas of the core. The curve is the locus of possible it grows; silicatesare reducedonly in the later Mars models.Clearly, the data can accommodate high-temperature stages of accretion. Mars, a small dense core or a large light core. The beinga smallerbody than the earth, wouldhave upper limit to the density of the core is prob- lesssilicon in its core, and the core would have ably closeto the density of iron. This density a larger zero-pressuredensity. On the other value provides a lower limit to the radius of the hand, if sulfur is the light alloying element in core of 0.36 of the radius of Mars, or about 8% the core [Andersonet al., 1971], the densityof of the massof the planet. To determinea lower the core will increaseas it growsand becomes limi• to the density,one must considerpossible fieher in iron because of the nature of the major componentsof the core. Of the potential Fe-FeS phase diagram [Anderson,1971]. Mars core-formingmaterials, Fe, S, and Ni are by wouldthus be expectedto have a coreless dense far the most abundant elements,both in me- than the earth.This effectwould be compounded by the greater efficiencyof Mars in retaining TABLE 1. Parameters for Mars Models sulfur, by the smaller aeeretionalenergies in- volvedin its growth,and by the inferreddeple- Rc/R Pm Pc Mc/M tion of iron in Mars relative to the earth. In any ease,a Martian core is unlikely to be of 0.20 3.557 2 0.1 * 0.25 3.554 I 2.6 * pure iron or of the same compositionas the 0.30 3.550 9.22 0.06 earth's core. 0.33 3.548 7.93 0.07 0.40 3.541 6.30 0.10 Accordingly,we have constructeda suite of 0.50 3.522 5.27 0.17 planets that satisfy the observableproperties 0.60 3.492 4.80 0.26 for Mars and that are independentof com- positionalassumptions. *Not computed. INTERNAL CONSTITUTION OF MARS 791 fractional core radius of 0.6 and a fractional massof 26%. On thesegrounds, the massof the 10- \ MARS 3 - Martian core can be considered to lie between Prn"'3.54 g/cm 8 and 24% of the massof the planet. "') 9 - METEORITES\ _ This range can be narrowed considerablyby further considerationof the compositionsof meteorites. The points in Figure 1 represent most of the major categories of stony me- 0'•8-- 0 /OSll. •/0 m • _ teorites. The size and density of the 'core' have X - -o , been computed from the amounts of iron, sul- • •-Eorfhs Core• •Hyp.C.•o O.,C,;,. o' Enstl o" fur, and nickel in the meteorite. No single class o 6 - Arnph. '•.,g' of meteorites, fully differentiated into core and --P:3O kb• Eutect,c'•C3 • mantle, would satisfy the data for Mars, al- •--P= 0 kbJ m•x. • thoughcarbonaceous chondrites and hypersthene (low iron) chondrites come close. The open

0 0.2 0.4 0.6 circles indicate silicate (mantle) densities less than the inferred density for the mantle of Core redius (Rc/R) Mars; the closedcircles indicate silicate densi- Fig. 1. l•adius of the core versus the density ties that are too high. The meteoritesabove the of the core for planetary models that have the curve can be migrated downwardand to the left mass, radius, and moment of inertia of Mars. The by placing some of the iron of the core in the density of the mantle varies along the solid curve (Table 1). The densities of the Fe-FeS cutecftc mantle and thereby increasingthe density of compositions are determined from data of Brett the mantle and decreasingthe density and and Bell [1969]. The points are for various radius of the core. Physically, the result would meteorite classes with all the FeS and free Fe and correspondto a meteoritemodel that has been Ni differentiated in a core. The dashed line shows how core density is related to core size in the Fe- only partially differentiated,i.e., has undergone FeS system. The density and amount of melt in- an incompleteseparation of mantle and core. crease as the temperature is raised above the If chondritesare an appropriate guide to the eutectic. The level of the line is adjusted to ordi- compositionof Mars, possiblecore sizeswould nary chondfific abundances.The slope is calcu- be further restricted to 12-15% by mass. Al- lated from the phase diagram. ternatively,the closedcircles could be migrated to the locusof possibleMars modelsby reduc- teoritesand in the sun. In ordinary high-iron ing someof the FeO in the silicatephase and chondrites,the free iron contentaverages 17.2% allowingthe iron to enter the core.This proce- by weight. The FeS contentis approximately dure is much more drastic and requires high 5.4% (3.4% Fe, 2.0% S), and the Ni contentis temperatures and, probably, the presenceof 1.6%. A planet assembledfrom such material, carbon to effect the reduction. It is interesting if completelydifferentiated, would yield a core that the meteoritesin questiondo contain sub- of 24% of the massof the planet, with Fe:S:Ni stantial amounts of carbon. The resulting cores in the approximate proportionsof 21:2:2 by would be about the same size as was previously weight. Low-iron chondriteswould yield a core inferred. of 15% of the mass of the planet, with pro- A third possibilitywould be to assembleMars portions of 12:1:2. from a mixture of meteorites that fall above Carbonaceous chondrites have little or no and below the curve. The meteorites below the free iron but contain 7-25% by weight FeS and curve, however, are relatively rare, although about 1.5% Ni. The average core size for a the earth may not be collectinga representative planet made of carbonaceouschondrites would sample. be 15% by mass,Fe:S:Ni beingin the propor- The first alternative seems particularly at- tions 9' 5' 1.5. An absolute minimum core den- tractive becauseof its simplicity and becauseit sity can probably be taken as 4.8 g/cm•. This followsnaturally from the phaserelations in the value correspondsto a pure FeS core with a Fe-FeS system for the compositionsfound in 792 DoN L. ANdErSON ordinary and enstatite chondrites.That is to say, the iron contentof these meteoritesis on EARTH'SCORE the iron-rich side of the eutectic composition, and partial meltingwould producea sulfur-rich melt and leave iron behind in the mantle. Liquid Many other alternatives are possible.The mantle need not be homogeneous;all parts of Fe+L•quld the mantle need not contribute equally to the core. Some parts of the mantle may be more effectively stripped of their iron than other parts. The compositionof the melt dependson SULPHURRICHCORE!•/• temperature and pressure.Unfortunately, the EulecllcTemp.I ,/Liquld+FeS data restrict us to a discuussionof two parame- ter models. In addition, the phase diagram for Fe+FeS(Solid) the Fe-FeS system is not known at high pres- Fe • • • F•S sures. High-pressurephases will eertainly in- H E L CC tervene, but it is unlikely that the qualitative •ig. 2. Schematic diagram for the system •e- argumentsgiven above will be invalidated. FeS, adapted from •re• e•g Beg[ [1969] and •ge• eng Anger}o [1958]. The composRioas DISCUSSION of high-iroa (•), ]o•-Jroa (L), eas•atJ•e (•), aad carboaaceous choadrRes (CC) are sho•n a]oag Phase relations in the system Fe-FeS have •he bottom. These compositioas are calculated beenworked out by Hansenand Anderko [1958] from •he free Fe aad FeS coateats of •hese and by Brett and Bell [1969]. The cuteerictem- meteorites. The shape of the dia•am aad the •empera•ure scale depead on pressure. The me]t- perature is 990øC and is relatively insensitive Jag •empera•ures of the cad members (Fe to pressure,at least to 30 kb. The cuteericcom- FeS) Jutrede •ith temperature. The eu•ectic positionshifts from about 69 wt % Fe at zero •emperature is fairly Jadepeadea• of temperature, pressureto 74 wt % Fe at 30 kb. The cuteeric bu• •he eu•ec•i.e compositioA migrates •o •he ]ef• phasediagram for the Fe-FeS systemis shown (i.e., becomesricher iA iroa) as pressureiacreases. schematicallyin Figure 2. Several poinls should be noted. First, if sulfur is the light alloying and the eutectic and liquidus curves. For the element in the earth's core, estimates of its model much of the interior of Mars is between density and temperature would place it well the eutectic and liquidus temperatures. This above the liquidus temperature in this system. condition suggests partial rather than total This result would suggestthat the separation melting and incompleteseparation of potential of core and mantle is probably well advanced core-formingmaterial. Preliminary calculations or completein the earth. Second,for composi- on the thermal effect of core formation indicates tions to the left of the cuteeric compositionthe that this sourceof energy is negligiblefor Mars. melt and presumably the core become pro- We have argued above, qualitatively, that gressivelyricher in iron and denseras tempera- partial melting of certain classesof meteorites ture increasesand me]ting proceeds.The con- will move them toward the locus of Mars trary is true for FeS-rich systems, such as models. The phase diagram for the iron-sulfur carbonaceouschondrites. For ordinary and en- system allows us to compute, at least at low staritc chondrites partial melting accompanied pressures, the relation between the relative by complete separationof melt from the solid amount of melt and its compositionor density. would result in an iron-rich mantle and a sulfur- The dashed line in Figure 1 shows how these rich core. An estimate of the conditions in the two quantitiesare related for a certainstarting Martian core are shown in the hatched region compositionclose to that of ordinary chondrites. of Figure 2. At the intersection of the curves the mass of Figure 3 showstemperature profiles in Mars the core is 12% of the massof the planet and as a function of time from thermal-history cal- the density of the core is 5.85 g/cm8. An aver- culations [Hanks and Anderson, 1969]. Also age ordinary chondrite contains 11.7% Fe, shown are estimatesof the iron melting curve 1.3% Ni, and 5.9% FeS, or 19% potentialcore- INTERNAL CONSTITUTION OF MARS 793

3000 MARS2'D tacc:3xlO5 years (0.8 Terrestrialabu'ndances) ,--Iron MeltingCu FeSliquidus, (Strong,1959) 2000 -__-2 ...... • - •-

iooo

. • Eutect• o I I I 0 0.2 0.4 0.6 0.8 1.0 Radius, (Fraction of Mars Radius) Fig. 3. Temperatures in Mars as a function of radius and time (adapted from Ha•ks and Anderson [1969]). Also shown are estimates of the melting temperature of pure iron and the eutectic and liquidus temperaturesin the Fe-FeS system. The thermal effects of convection, latent heat, and core formation have been ignored.

formingmaterial. From the phasediagram and high FeO content of type III carbonaceous the assumption that the Ni/Fe ratio stays chondrites. Type II carbonaceouschondrites constant,we determinethat the core consistsof and amphoterites (Soko-Banjites) also have 5.7% Fe, 0.6% Ni, and 5.7% S, relative to the high FeO contents. massof the planet. Thus, the total core is 12% One interesting result of this model is that of the massof the planet. Most of the original the total iron content of Mars is almost inde- sulfur has entered the core, but considerable pendentof the size of the core or assumptions amounts of Fe and Ni remain solid and in the on how the iron is distributed.For example,the mantle. The density of the silicate phase plus total inferred iron content for Mars varies from the residual iron and nickel yields a mant]e 25 to 28% for models in which the mass of the density of 3.54 g/cm8, which agrees well with core rangesfrom 10 to 26%. This range of core the required value (Table 1). Thus, it appears sizesjust about coversthe range of core densi- that a satisfactory model can be obtained for ties from pure iron to pure FeS. This range of Mars by melting 63% of the potential core- valuesfor Mars can be comparedwith the iron forming material in an ordinary chondrite.This content of the earth (about 35%) and verifies situationwould hold if internal temperaturesin previous conclusionsthat Mars is less rich in Mars averaged about 1300ø-1600øC. Bronzite iron than the earth. or high-iron chondrites provide mantles that Table 2 gives the compositionof the mantle are slightly too dense (3.62 g/cm8) when mi- and core of Mars for the two meteorite models grated back to the Mars locus by the above just discussed.Mode] I is the meteorite mix procedures. model, with 75% type III carbonaceouschon- An alternative meteorite model for Mars drites and 25% ordinary chondrites.Complete that would accommodatehigher temperatures segregationof the core from the mantle is as- and complete separation of core and mantle sumed. Model 2 is the partially differentiated can be constructed.For example, if type III ordinary chondrite model, with 63.5% of the carbonaceous chondrites are mixed with ordi- potential core-forming material me]ted and nary chondritesto give the correct density,the settled to the core. Both models contain 25% core will be 12% by weight and will have a iron, and both have a core of about 12% of the density of 5.78 g/cm•. These values are closeto mass of the planet. the values required to satisfy the mass and The Orgueil type I carbonaceouschondrite moment of inertia of Mars. The high density has been consideredby some authors to be the of the mantle in this exampleis a result of the best available sample of primordial material. 794 DoN L. ANDERSON TABLE 2. Mars Models This meteoriteis extremelyrich in such low- temperaturecondensates as I-I20 and FeS, as Element Model 1' Model 2ñ well as carbon and 'organicmatter.' If we ignorethe waterand carbon compounds, a fully Mantle differentiatedplanet of this compositionwould Si% 34.9 38.3 Mg0 23.9 23.9 havea coreof 15% by mass,composed mainly Fe0 21.2 12.0 of FeS (13.6% FeS, 1.4 Ni), and a mantlewith A1203 2.7 2.7 Ca0 2.2 1.9 a densityof about 3.5 g/cm•. However,this Na20 0.7 0.9 meteoritealso containsabout 19% I-I20, most K20 0.06 0.1 Cr203 0.5 0.4 of which must have escapedif Mars is to be •0 0.2 0.3 madeup primarilyof this material.Otherwise, Ti02 0.1 0.1 P205 0.3 0.2 the mantlewould not be denseenough. NiO 0.2 0.0 Figure 4 givesseveral possible Mars models H20 0.8 0.3 Fe 6.0 in terms of density as a functionof fractional Ni 0.7 radius. These models are consistent with the FeS 0.2 meandensity and momentof inertia.The range Total 87.8 88.0 of possiblesolutions can be considerablyre- Core duced,as mentionedbefore, if chondriticcom- Fe 4.6 5.7 positions are used as an additional constraint. Ni 1.1 0.6 FeS 6.1 $ .7 MAGNETIC FIELD Total 11.8 12.0 The presence of a substantial core rich in

*Mix; 75% type 3 carbonaceouschondrites, 25% molteniron, impliedby previoussections, and ordinary ½hondrites. the observedrapid rotationof Mars provide ñPartially differentiated ordinary ½hondrite' two of the conditionsthat are thoughtnecessary Pe = 5.85, Pm= 3.54. for the generationof a magneticfield. One

I I I I

MARS

Fe ---•

Earth's Core CHONDRITICMODELS

Eutectlcmix{pP:30 0 kbkb-.-- '-•'• FeS --•

MANTLE

Earth's Mantle I I I 0 02 0.4 0.6 0 8 1.0 r/R Fig.4. Densityversus radius for somerepresentative Mars models that have the proper meandensity and moment of inertia.Models with chondritic compositions fall in thehatched region.Note that all modelshave approximately the same mantle density. INTERNAL CONSTITUTION OF MARS 795 might, therefore, expect Mars to have a mag- tures inferred from thermal-history calculations. netic field. However, a differential precessional The absenceof a magnetic field can be ex- torque acting on the core and mantle is prob- plained by the lack of significantlunar torques. ably the ultimate driving mechanismfor the The presenceof large amountsof sulfur in the geomagnetic dynamo [Malkus, 1968]. The core and its small size, as comparedwith the moon and the sun are much less effective in earth's core, also serve to suppressthe impor- generatingsuch a torque for Mars becauseof tance of dynamo action in the Martian core. the distance of Mars from the sun and Mars' lack of a substantial moon. Acknowledgments. This researchwas supported The small size of the Martian core and, if by National Aeronautics and Space Administra- tion grant NGL 05-002-069. sulfur is abundant, its high resistivity would lower the magnetic Reynolds number. These REFERENCES effects alone could eliminate the possibility of Anderson,D. L., Sulfur in the core: Implications regenerativedynamo action. Other factors that for the earth and Mars, CommentsEarth Sci. must be consideredare the core's viscosity, Geophys., 1, 133-137, 1971. which is highly dependenton temperature and Anderson,D. L., and R. A. Phinney,Early thermal pressure,and the shieldingeffect of an iron- history of the terrestrial planets,in Mantles o/ the Earth and Terrestrial Planets, edited by rich mantle. All things considered,it seemsun- S. K. Runcorn, pp. 113-126, Interscience, New likely that Mars ever had a substantialmagnetic York, 1967. field of internal origin. Anderson,D. L., C. Sammis, and T. Jordan, Com- position and evolution of the mantle and core, CONCLUSIONS Science, 171, 1103-1112, 1971. The present astronomicaldata for Mars re- Binder, A. B., The internal structure of Mars, J. Geophys.Res., 74, 3110-3118,1969. quire that it have a densecore. Brett, R., and P. Bell, Melting relations in the The size of the core and its density can be Fe-rich portion of the system Fe-FeS at 30 kb traded off. By using the density of pure iron pressure, Earth Planet. Sci. Lett., 6, 479-482, and the density of pure trollire (FeS) as rea- 1969. Bullen, K. E., On the constitution of Mars III, sonableupper and lower boundsfor the density Mon. Notic. Roy. Astron. Soc., 133, 229-238, of the core, its radius can be consideredto lie 1966. between 0.36 and 0.60 of the radius of the Hanks, T. C., and D. L. Anderson,The early planet. thermal history of the earth, Phys. Earth The zero-pressuredensity of the mantle is Planet. Interiors, 2, 19-29, 1969. Hansen,M., and K. Anderko,Constitution o/ the confined to the range 3.54-3.49 g/cm". This Binary Alloys, 2nd ed., pp. 1-720, McGraw- range implies an FeO content of 21-24 wt % Hill, New York, 1958. unlesssome free iron has been retained by the Kovach, R. L., and D. L. Anderson,The interiors mantle. of the terrestrial planets, J. Geophys. Res., 70, 2873-2882, 1965. If chondrites are an appropriate guide to MacDonald, G. J. F., On the internal constitution the major element compositionof Mars, the of the inner planets, J. Geophys. Res., 67, 2945- core of Mars is smaller and less dense than the 2974, 1962. core of the earth, and the mantle of Mars is Malkus, W. V. R., Precessionof the earth as the denser than that of the earth. cause of geomagnetism,Science, 160, 25'9, 1968. Ringwood, A. E., Chemical evolution of the ter- Mars contains 25-28% iron, independent of restrial planets, Geochim. Cosmochim.Acta, 30, assumptionsabout the over-all compositionor 41-104, 1966. distribution of the iron. The earth is clearly Strong, H. M., The experimental fusion curve of enrichedin iron when comparedwith Mars or iron to 96,000 atmospheres,J. Geophys. Res., 64, 653-660, 1959. most classes of chondritic meteorites. Urey, It. C., Progressin Physics arid Chemistry Meteorite models for Mars that contain 25 o/ the Earth., vol. 2, p. 46, Pergamon, New wt % iron and 12 wt % core have been con- York, 1957. structed. If sulfur is retained in Mars, the presenceof (Received June 9, 1971; a core is not inconsistentwith the low tempera- revised October 27, 1971.)