Water and Carbon Dioxide in the Martian Magma Ocean: Early Atmospheric Growth, Subsequent Mantle Compositions, and Planetary Cooling Rates

Introduction: Volatile content of a planetary magma ocean has significant effects on the process of magma ocean solidification, on formation of an initial planetary atmosphere, and on subsequent mantle composition [1-5]. The heterogeneous partitioning of volatile phases during accretion and differentiation of the Earth and Mars can account for current volatile budgets without the need to invoke a late veneer [4]. This abstract report results from initial models of a Martian magma ocean degassing carbon dioxide and water into an early atmosphere, and subsequent planetary mantle compositions. Efficient degassing requires rapid convective velocities to carry liquid to pressures lower than the solubility pressure of the gases in question, and until the magma ocean is almost entirely liquid velocities are significantly inhibited. Retention of some level of volatiles through the magma ocean stage of planetary evolution, therefore, is a reasonable initial assumption. Any material degassed during accretion may also be partially retained by the gravity of the growing planet. For example, even in the case of an impact of a Marssized body into the early Earth, the Earth would retain between 20 and 70% of its existing atmosphere [6]. For the purposes of calculating the cooling rate of the magma ocean and the time to solidification of the planet, the most important gases entering the early atmosphere are water and carbon dioxide. These two components, both relatively common in the potential planetary disk building blocks of Mars, are strong greenhouse gases and will significantly slow planetary cooling and retain a high temperature at the surface of the magma ocean. The importance of an early water atmosphere has been recognized and studied by Abe and Matsui [7] and Matsui and Abe [8] and further explored by Elkins-Tanton and Parmentier [5]. Here we add carbon dioxide to the calculations of magma ocean solidification and atmospheric growth. Models: Possible chondritic materials for building Mars have been investigated by Mohapatra and Murty [9], who find that a ratio of 74:26 of enstatite to ordinary chondrites are consistent with the major element estimates of present-day bulk Mars, implying an initial C concentration of 3.1 wt%. In general, data from Brearley and Jones [10] suggests such a mixture might begin with up to 3 wt% water and 2 wt% carbon dioxide. Models presented here assume an initial 1.5 wt% water and 1 wt% carbon dioxide. Carbon dioxide and water behave differently in magma ocean processes. Both can dissolve into silicate melts at quantities greater than 10 wt% at pressures above their degassing pressures [e.g. 11]. However, water largely comes out of solution and forms bubbles in silicate melts at approximately 0.5 GPa, and carbon dioxide at ~3 GPa [12,13]. Prior to degassing, both OH and CO partition between crystallizing solids and the evolving magma ocean liquids. At pressures and temperatures of magma ocean crystallization no hydrous or carbonate minerals will crystallize [14,15]. Nominally anhydrous minerals can contain a dynamically and petrologically significant amount of OH [16-20] (as much as 1000 ppm, and with contributions from minimal interstitial liquids, resulting mantle solids can retain 0.25 to 0.5 wt% H2O [5]). Carbon dioxide, in contrast, cannot partition into mantle minerals in as significant quantities [21]. In this simple model all carbon dioxide degasses to the atmosphere from magma ocean liquids that move below 3 GPa pressure, and all but 0.5 wt% of water degasses below 0.5 GPa. Though turbulent eddies and high magma ocean velocities might entrain bubbles and prevent their escape, detailed calculations of these processes await further work. Magma ocean fluid dynamics differ significantly from the dynamics of solid mantles, and are closely modeled by the dynamics of atmospheres, as noted by Solomatov [4]. Heat is transported from the interior to the surface by cold thermal plumes descending from the upper boundary layer, accompanied by more diffuse return flow of hotter material from the interior. Heat is transmitted conductively from the upper boundary layer into any existing early atmosphere, which in turn inhibits radiation into space by its level of emissivity. Proceeding from the work of Priestley [22,23], similarly to Abe [2], heat flux from the top of the magma ocean can be expressed as heat flux across the viscous upper boundary of the magma ocean, and must be equivalent to the Stefan-Boltzmann radiation from the planet’s atmosphere, tempered by its emissivity ε: