A model for planetary igneous differentiation

Abstract

Numerical models for igneous activity on any planet must be based on thermal properties and melting relationships for realistic multicomponent systems. A consistent model for the composition of the earth's mantle may be obtained by considering a mixture of basalt and dunitc, as postulated by Ringwood and others, if the uranium, thorium, and potassium concentrations of the basalt are similar to that of basalts dredged from the deep ocean floors. Present evidence does not indicate that the bulk composition of the moon is appreciably different from that of the earth's mantle.On the basis of a review of existing phase equilibria and high pressure studies, we predict melting behavior as a function of pressure and temperature for a composition equivalent to 1 part basalt and 3 parts dunitc. The specific heat and fusion properties of the important minerals in this system are reviewed. The implications of these data for an understanding of magma generation are discussed.A review of the factors influencing the thermal conductivity of rocks indicates that when considering the details of heat conduction under conditions likely to be encountered within the earth's upper mantle and the moon, a model invoking constant phonon conductivity and temperature independent photon mean free path may be unrealistic. A more likely, but still oversimplified, model has a phonon conductivity inversely proportional to temperature, and, unless scattering dominates, a photon mean free path directly proportional to temperature over the range of interest. Pressure should not significantly affect the thermal conductivity within the upper mantle, except by changing the stable mineral assemblage. of the moon at the time of its formation were 0øC and the uranium content were 0.05 ppm, with Th/U and K/U in the ratio 3.7 and 10', respectively, melting would have begun about 1.5 X 10 • years after formation, the intensity being largely controlled by the thermal conductivity. At lower U, Th, and K contents, the onset of volcanism would have been delayed or suppressed completely, depending on the conductivity. Properly selected samples of the moon's surface rocks should thus make it possible to determine its initial temperature. The total thickness of extrusive and intrusive igneous rocks is shown to be critically dependent on the efficiency of radiative heat transfer in removing heat from the interior.

Icarus: Further Confirmation of the Relativistic Perihelion Precession

“…Heat-flow computations for the moon, taking into account the important fact that long-lived radioactivities concentrate in the first magma fraction to melt and ire redistributed by magma migrations, were made by McConnell et al [1967], Fricker et al [ 1967, andiee [1968], Kaula [1966] investigated the importance of tidal energy dissipation in the body of the moon as a source of heat. The effects of thermally driven rock con vection in the moon are discussed by Turcotte and Oxburgh [1969].…”

“…Heat-flow calculations for the terrestrial planets, in cluding the effect of igneous differentiation, were made fey McConnell et al [1967] and Lee [1968]. Vital lab oratory measurements of the radiative contribution to planetary thermal conductivity were made by Aronson et d [1967].…”

Density distribution of a steady-state homogeneous moon

“…Thermal histories of the moon have been derived by several workers leg., MacDonald, 1964;Fricker et al, 1967;McConnell et al, 1967]. As these solutions usually involve melting, partial melting, or differentiation, the calculation of density distributions using such results would be a very complex problem.…”

Thermal structure of the Moon

“…Many conduction calculations for the temperature within the moon have been made [Levin, 1962[Levin, , 1966MacDonald, 1961MacDonald, , 1963Phinney and Anderson, 1967;Urey, 1957Urey, , 1962Mayeva, 1971;Hays, 1972;Mizutani et al, 1972]. When either a chrondritic or a terrestrial [Wasserburg et al, 1964] concentration of ra-dioactive elements is used, these calculations [Fricker et' al., 1967;McConnell et al, 1967;Toksoz et al, 1972] show that a substantial portion of' the moon should be at least partly molten if conduction is the main heat transfer process within the moon. On the basis of our knowledge of the interior of the earth, we can conclude that significant solid-state convection will occur within the moon at temperatures considerably below those required for partial melting if there is a negative temperature gradient over a significant fraction of the lunar radius.…”