To simulate the outgassing of CO2 and water from Martian mantle, I used a two-dimensional numerical model of magmatism in the convecting mantle. The mantle is internally heated by incompatible heat-producing elements (HPEs) that decay with time. Mantle convection is driven by thermal, compositional, and melt-buoyancy. Mantle convection causes magmatism, that is, a decompression melting of upwelling mantle materials and upward permeable flow of the generated basaltic magma through the convecting mantle. Water is incompatible and concentrates to magma in a partially molten region, while there is a saturation limit for CO2 in magma that depends on the oxygen fugacity. Water and CO2 in magma are transported upward to the surface by migrating magma and are outgassed to the atmosphere when they ascend to the top of the mantle. Both water and CO2 reduces the solidus temperature and the viscosity of solid mantle materials. The calculated mantle evolves in four stages: in Stage I, an extensive magmatism forms the crust and compositionally differentiates the mantle; in Stage II, the resulting compositional stratification of the mantle suppresses magmatism and mantle convection for tens to hundreds of millions of years to allow heat to build up in the deep mantle; in Stage III, magma is generated at depth, and the buoyancy of generated magma induces plumes that ascend through the stratified mantle to cause an episodic magmatism; in Stage IV, the magmatism subsides due to extraction of HPEs from the mantle by the magmatism itself. The episodic magmatism in Stage III outgasses water and CO2. The total amount of outgassed water is typically 100-200 m GEL (global equivalent layer), while that of outgassed CO2 is around 105 Pa s or less, when the oxygen fugacity of the mantle is in the range of Iron-Wustite (IW) buffer to one log-unit higher. This amount of CO2 is not large enough to account for the clement surface environment of early Mars by itself even when H2O enhances the greenhouse effect of CO2. Other greenhouse gasses or a remnant of the CO2 that was supplied at the time of planetary formation may have played an important role in realizing the surface environment of early Mars that was favorable to life.

To understand the overall features of the history of magmatic activities and surface environment on Mars, I used a numerical model of magmatism in the convecting mantle that is nominally anhydrous and internally heated. Magmatism occurs as an upward permeable flow of basaltic magma generated by decompression melting through matrix. The modeled mantle evolves in four stages. In Stage I, high initial temperature in the uppermost mantle causes an extensive magmatism intensified by two types of positive feedback that operate between magmatism and mantle upwelling flow, the MMUb and MMUc feedback: the buoyancy and volume change of matrix, respectively, caused by migrating magma that a mantle upwelling flow generates intensify the flow itself to generate more magma. The stratification suppresses mantle convection and magmatism for the next tens to hundreds of millions of years, allowing heat to build up in the mantle by internal heating (Stage II). Eventually, magma is generated at depth, and the MMUb feedback operates to cause an episodic plume magmatism that releases water from the interior of Mars (Stage III). The plume magmatism also stirs the mantle to make it more homogeneous and extracts heat producing elements from the deep mantle to let the magmatism itself wane and cease. In the final stage IV, mantle convection becomes more like a thermal convection. The episodic magmatism and water outgassing in Stage III account for the magmatism and clement surface environment observed for early Mars.

We present a three-dimensional numerical model of tectonic plates that self-consistently develop in the convecting mantle. The viscosity depends on stress-history as well as temperature. The lithosphere develops as the upper highly viscous part of the thermal boundary layer along the surface boundary owing to a strong dependence of the viscosity on temperature. When the stress S exceeds a threshold Sp in the lithosphere, however, we assumed that the viscosity drops by orders of magnitude and keeps the low value, even when S is reduced below Sp, provided that S remains higher than the other threshold Sm (< Sp). Sp corresponds to the rupture strength of the tectonic plates, while Sm to that at plate margins. The viscosity is a two-valued function of the stress S in the range of (Sm, Sp), and which of the two values the lithosphere chooses is determined by whether or not S has exceeded Sp in the past. When the model parameters are tuned so that the stress in the lithosphere stays in the range, the lithosphere is rifted into several highly viscous pieces, or tectonic plates, separated by narrow plate margins where the viscosity takes the lower value, and the tectonic plates rigidly and stably move and occasionally rotate for several hundred million years or longer. (See the planform of the plate motion shown in the figure. The arrows show the velocity, while the color shows the relative viscosity on the surface.) Because of the rather stable plate motion, the heat flow decreases with the distance from the spreading centers L in their vicinity as 1/sqrt(L), and the secondary convection occurs beneath the plates in the form of two-dimensional rolls with their axes aligned with the direction of plate motions.