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Internal Constitution of Mars

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Internal Constitution of Mars 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.
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