key words [modelling multicomponent mineral system]

A method for solution of the inverse geophysical problem was developed on the basis of thermodynamic modeling of phase relations and physical properties of multicomponent mineral systems. The problem is to restore the total chemical composition and thermal regime of the lunar mantle [1] and the size of the lunar core from geophysical data. The seismic velocity and density values necessary for the calculations were determined using the THERMOSEISM software complex [2] which allows the estimation of the composition of a multicomponent system and its physical properties (three-dimensional wave velocities, density, and other characteristics).

Two modeling versions were adopted: (1) the core radius is known and (2) the core radius is determined by optimization. For geophysical reasons, the core radius is tolerated to range from O (core is absent) to 670 km (of which 440 km correspond to -Fe core). The model of the Moon without core was obtained at high FeO contents (16-17 wt %) in the lower mantle. From the calculations at a fixed core radius, the lunar mantle model was derived that described the chemical composition of the lunar mantle without density inversion for all tolerable core radius values and fitted all the geophysical limitations. The most probable values of the lunar core radius obtained at minimum limitations range within 500-590 km for the FeS core and 330-390 km for the -Fe core.

The estimates of chemical composition and temperature in various mantle zones are presented in Table 1. The upper lunar mantle is evident to be enriched in silica and depleted in ferrous oxide relative to the middle mantle, whereas the middle mantle is enriched in silica and iron relative to the lower mantle. Al₂O₃ and CaO contents in the upper lunar mantle are equal to or lower than those in the middle mantle and half as high as lower than those in the lower mantle [3]. The nature of the middle lunar mantle (zone of lower wave velocities) [4] is explained by more ferrous composition compared to the outer and inner lunar shells. This fact conforms with the conclusion that the lunar mantle is stratified by chemical composition and testifies that the pyroxenites of the upper and middle lunar mantle differ in chemical composition from the peridotites of the upper earth's mantle. The total composition of the silicate portion of the Moon (crust + mantle) is as follows (wt %): 26<MgO<31, 11<FeO<12, 5<Al₂O₃<7, 3.6<CaO<5.0, and 48.5<SiO₂<51.

Note: The lunar core radius was calculated at two density values at the lower boundary crust-mantle ( _cr-m); H_cr = 58 km; _cr= 3.0 g/cm³.

1. Kronrod V.A. and Kuskov O.L. (1996) // Geokhimiya, no. 1, p. 80.
2. Kuskov O.L. (1995) // Phys. Earth Planet Inter., 90:50.
3. Kuskov O.L. (1995) // Geokhimiya, N.12, p. 1683.
4. Nakamura Y. (1983) // J. Geophys. Res., vol. 88, N. B1, p.677.

key words [volatiles planet simal]

Could planetesimals form at the earliest stage of the solar and protoplanet disk evolution? If they could, what was their composition and what was their influence on the composition of future planets?

To clarify this, we compared the typical duration of such important processes as radial transportation of the matter within the protoplanet disk, accretion of the dust to bodies, pressure and temperature variations. Some estimates were taken from the literature [1, 2]. To estimate the rates of temperature and pressure changes, a numerical model was developed [3], with parameters chosen on the basis of recent astrophysical data on young low-mass stars with disks. Some results are presented in figure. Each curve shows the radial distribution of temperature in the equatorial plain of the disk for four instants of time. The maximum values correspond to the end of the collapse, when the disk had radius of about 20 a.u. and mass close to 20% of the present-day solar mass.

From the comparison of these temperatures with temperatures of condensation from the solar gas of iron and magnesian silicates, plagioclase and pyrite formation, and aqueous ice condensation, the conclusion was made that during the disk formation the dust did not contain alkalies, sulfur, nor especially water at radii of 3 a.u.

The vertical structure of the disk at r = 2.5 - 3 a.u. was an important feature. There was a zone near the equatorial plain, where temperature was maintained equal to the condensation temperature of iron and magnesian silicates and depended only on pressure. This zone was as much as a half of the disk in thickness but concentrated the major mass of the disk. Dust evaporation and condensation were in equilibrium in this zone, so that fine particles disappeared while coarse particles grew. The physical conditions of this zone favored the collapse of the dust in the equatorial plain of the disk and formation of dense dust layer. The silicate dust content and, therefore, oxygen partial pressure in this layer exceeded significantly those in surrounding gas of solar composition. In addition to rising condensation temperatures of magnesian silicates, this was responsible for condensation of not only metallic iron but also several percent of iron oxide.

Planetesimals 1-10 km in diameter formed from the dust layer as a result of gravitational instability or by growth when smaller bodies collided. Planetesimals of this size were not carried out of this zone for the characteristic time of 10⁵ years and could constitute terrestrial planets as a result of subsequent accretion. The accretion was followed by differentiation, whereby the cores depleted of sulfur but containing FeO formed.

Moreover, the particles to 0.01 cm in size chemically isolated from gas also formed. These particles together with the gas can be carried out of this zone to the radius of 5-6 a.u. for the characteristic time of 10⁵ years. In further evolution, they can constitute the planetesimals forming at these radii or return to be involved in planet growth.

Thus, planetesimals depleted of volatiles and moderately volatile components (component A in models by [4, 5]) but containing FeO as an admixture could originate in the protoplanet disk at radii of no more than 3 a.u. The dust of the same composition was carried out to radii of up to 5 a.u. and was partially captured by parental meteorite and planet bodies. This mechanism is a possible explanation to the deficit of alkalies and volatiles of the terrestrial planets and meteorites.

1. Ruzmaikina T.V. and Maeva S.V. (1986) Astronomicheskii vestnik, vol. 20, p. 212.
2. Cassen P. (1994) Icarus. vol. 112, pp. 405-429.
3. Dorofeyeva V.A. and Makalkin (1994) A.B. LPS XXVII, vol. 1, pp. 321-322.
4. Ringwood A.E. (1982) Origin of the Earth and the Moon. Moscow: Nedra, p. 293.
5. Wenke H. (1981) Constitution of Terrestrial Planets, Pholos. Trans. Roy.Soc., London A, vol. 303, pp. 287-302.