A model is presented for the thermal evolution of the Martian mantle and core and for the evolution of the Martian magnetic field. In the model, Mars is initially hot and completely differentiated into a core and mantle, consistent with evidence from SNC meteorites of early core formation in Mars. The subsequent evolution of Mars consists of a simple cooling, with interior temperature, surface heat flux, and core heat flux declining monotonically with time. Lithosphere thickness and mantle viscosity increase steadily through time. Heat transport across the mantle is accomplished by subsolidus convection which is parameterized by a Rayleigh number-Nusselt number relation. The core contains a light alloying constituent, assumed to be sulfur. Initial sulfur concentration xS is a principal parameter controlling core and magnetic field evolution. Model parameters such as core radius are functions of xS and are chosen consistent with the overall density and moment of inertia of Mars. The Martian mean moment of inertia I is allowed to vary between 0.365 Mpr2p and 0.345 Mpr2p (Mp is the mass of Mars and rp is the radius of Mars), in accordance with recent inferences of the planet's moment of inertia from measurements of its gravitational oblateness. Large, S-rich, low-density cores or small, S-poor, high-density cores are consistent with the density and moment of inertia of Mars. For a given xS, mantle density and core-mantle boundary pressure increase with increasing I, while core radius and pressure at the center of the core decrease with increasing I.

The decrease with time in mantle temperature and surface heat flow and the increase with time in lithosphere thickness are essentially independent of xS. The occurrence of inner core solidification depends mainly on xS and mantle viscosity &ngr;. For model in which inner core freezing takes place, present inner core radius increases with decreasing xS for a given &ngr; and also increases with decreasing &ngr; at fixed xS. For mantle viscosity about 1016 m2 s-1, inner core solidication requires less than about 16 wt % S in the core. With increasing &ngr;, the maximum xS for which inner core freezing occurs decreases; for &ngr;=5¿1016 m2 s-1 inner core freezeout requires xS less than about 10 wt %. Relatively small, S-poor cores would be largely solid at present, while relatively large, S-rich cores would be largely liquid at present. When inner core solidification occurs, the inner core grows rapidly at first and then more gradually as the core cools. The fraction of the core that is solid at present is almost independent of moment of inertia. Current estimates of the Martian dipole moment may be consistent with a small magnetic field driven by weak thermal convection in a completely fluid core. If Mars does not have a present magnetic field and xS is less than about 16 wt %, explanation may lie in the nearly complete solidification of the core or in the nonoperation of the dynamo; however, if xS is ≥16 wt %, then nonexistence of a magnetic field may be explained by the absence of an inner core or by nonoperation of the dynamo in a thermally or chemically convecting core.