DENSITY of the MANTLE of MARS Kenneth A. Goettel, Dept. of Earth and Planetary Sciences, Mcdonnell Center for the Space Sciences, Washington, University, St

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DENSITY OF THE MANTLE OF MARS Kenneth A. Goettel, Dept. of Earth and Planetary Sciences, McDonnell Center for the Space Sciences, Washington, University, St. Louis, MO 63130 The zero pressure density of the Martian mantle is an important constraint on the composition and mineralogy of the mantle. The mean density and moment of inertia factor of Mars constrain the density of the Martian mantle, but do not define it uniquely. The mean density of Mars, 3.933+0.002 g/cm3 (1) is well determined. The estimated moment of inertia factor wFich Mars would have if Mars were in hydrostatic equilibrium, 0.365 (2,3), may still be significantly model dependent. With these constraints, the estimated zero pressure density of the Martian mantle varies as a function of the core composition assumed and as a function of the elastic data chosen as representative of the Martian interior. Recent estimates of the zero pressure density of the Martian mantle are shown in Table 1. The results of Johnston et a1 . (4) were based on a value of 0.377 for the moment of inertia factor of Mars. The results of Johnston and ToksBz (5) and Okal and Anderson (6) were both based on the revised (2,3) value of 0.365 for the moment of inertia factor. The results of (5) and (6) are not completely comparable, since (5) did not give the densities assumed for their core compositions, and (6) did not give compositions corresponding to their core densities. Part of the motivation for the present work was to explore the reasons for the differences between the results of (5) and (6). The purpose of the present investigation was to define as rigorously as possible the present bounds on the zero pressure density of the Martian mantle by utilizing fully existing high pressure, high temperature elastic data, and by investigating systematically the sensitivity of the computed density models to uncertainties in the input parameters. More than 80 models for the density distribution within Mars, each consistent with the mean density and moment of inertia factor of Mars, were computed by numerical integration of the equations of hydrostatic equilibrium, using the Murnaghan equation of state. Mars was modeled with 4 or 5 main zones: crust, upper and lower mantle (above and below the olivine to spinel phase change) and core (with a phase change, if appropriate). Each of these zones was characterized by: zero pressure density, bulk modulus (K), pressure derivative of the bulk modulus (Kt ) , temperature derivative of the bul k modulus (dK/dT) , and thermal expansion coefficient (a). Temperatures as a function of radius were taken from the thermal models of ToksBz et a1 . (7). Results of these calculations are shown in Table 2. The range of zero pressure mantle densities shown in Table 2, computed for the geochemically plausible range of core compositions, provides a minimum estimate of the present uncertainty in the density of the Martian mantle. Uncertainties in the requisite input parameters for the calculations contribute uncertainties to each of the densities shown in Table 2. Estimated la uncertainties in 9 of the input parameters (listed in Table 3) result in la uncertainties in the computed zero pressure mantle densities greater than 0.01 g/cm3. Assuming zero covariance between input parameters and combining errors results in formal estimated la uncertainties in the zero ressure mantle density of 0.04 g/cm3 for the Fe core model and 0.05 g/cm S for the FeS core model. Differences between the present results and the results of Okal and Anderson (6) are probably largely attributable to the very simple equation of state (linear increase in density with depth) used by (6). About 0.05 g/cm3

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Goettel , K.A. of the difference between the present results and the results of Johnston and Toksbz (6) is attributable to their use of a higher mean density (3.96 g/cm3) and a thicker crust; the remainder of the differences presumably reflect differences in elastic data chosen as representative of the Martian interior. Combining uncertainties due to uncertainty about the composition of the Martian core and uncertainties due to uncertainties in the input parameters results in an estimate of 3.44 0.06 g/cm3 for the zero pressure density of the Martian mantle. Thus, the Martian mantle does appear to be enriched in FeO, compared to the terrestrial mantle, but the amount of enrichment is much less than estimated by some previous authors (5,8). The present models are still oversimplifications (e.g., the effects of possible lateral or radial variations in chemical or physical properties have not been consid- ered). Work in progress includes assessment of the imp1 i cati ons of these results with respect to: a) mineralogy of the Martian mantle, b) the petrologic evolution of Mars, and c) the bulk composition of Mars. References cited (1) Bills and Ferrari (1978), J. Geophys. Res. 83, 3497-3508. (2) Reasenburg (1977), J. Geophys. Res. 82, 369375. (3) Kaula (1979), Geophys . Res. Lett. 6,194-196. (4) Johnston, McGetchin and Toksbz (1974), J. Geophys. Res. 3,3959-3971. (5) Johnston and Toksbz (1977), Icarus 32, 73-84. (6) Okal and Anderson (1978) 1carus,514-528. (7) Toksbz, Hsui and ~ohnston~8),~oonand Planets 18, 281-320. (8) McGetchin and Smyth (1978), --Icarus 34, 512-536. TABLE 1 ZERO PRESSURE DENSITY OF THE MARTIAN MANTLE mantle density (g/cm3) cores Johnston et al. (4) 3.71 - 3.74 FeS - Feg5S1 Johnston and Toksbz (5) 3.47 - 3.58 FeS Fe85S15 3 Okal and Anderson (6) 3.33 - 3.41 5.4 - 8.1 g/~m TABLE 2 ZERO PRESSURE DENSITY OF THE MARTIAN MANTLE core core density1 core mass mantl e density composition (g/m3) fwt.% of Mars (g/cm3)

FeS 5.77 26.3 3.409 'zero pressure density of the relevant high pressure phase: Ni, y-Fe, Fe304 before and after the 250 kb phase change and FeS-111.

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Goettel , K.A.

TABLE 3 UNCERTAINTY IN CALCULATED MANTLE DENSITIES

parameter parameter mantle densi tyl parameter value 0 u v moment of inertia factor 0.365 0.001 0.01 29

temperature profi 1 e ----- 2 50 0.0186 crust density 3.0 0.25 0.0123

mantle Ko(upper) 1.25 0.10 0.0122 4 mantle dKo/dT -2 x 10- 0.5 x 0.0127

mantle a 3 0.5 x 0.0235

FeS KO 1 .OO 0.125 0.01 66 4 FeS dKo/dT -2 x 10- 0.5 0.01 53

FeS a 10 lo-5 2.5 x loe5 0.0163

'q/cm3

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