How can we constrain the amount of heat producing elements in the interior of Mars?

The InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission to be launched in 2016 will study Mars' deep interior and help improving our knowledge about the interior structure and the thermal evolution of the planet - the latter is also directly linked to its volcanic history and atmospheric evolution. Measurements planned with the two main instruments, SEIS (Seismic Experiment for Interior Structure) and HP3 (Heat Flow and Physical Properties Package) aim to constrain the main structure of the planet, i.e. core, mantle and crust as well as the rate at which the planet loses the interior heat over its surface. Since the surface heat flow depends on the amount of radiogenic heat elements (HPE) present in the interior, it offers a measurable quantity which could constrain the heat budget. Being the principal agent regulating the heat budget which in turn influences partial melting in the interior, crustal and atmospheric evolution, the heat producing elements have a major impact on the entire the present temperature thermal history of the planet. To constrain the radiogenic heat elements of the planet from the surface heat flow is possible assuming that the urey number of the planet, which describes the contribution of internal heat production to the surface heat loss, is known. We have tested this assumption by calculating the thermal evolution of the planet with fully dynamical numerical simulations and by comparing the obtained present-day urey number for a set of different models/parameters (Fig. 1). For one-plate planets like Mars, numerical models show - in contrast to models for the Earth, where plate tectonics play a major role adding more complexity to the system - that the urey ratio is mainly sensitive to two effects: the efficiency of cooling due to the temperature-dependence of the viscosity and the mean half-life time of the long lived radiogenic isotopes. The temperature-dependence of the viscosity results in the so-called thermostat effect regulating the interior temperature such that the present-day temperatures are independent of the initial temperature distribution. If the thermostat effect is efficient as we show for the assumed Martian mantle rheology, and if the system is not dominated by radioactive isotopes like Thorium with a half-life much longer than the age of the planet as in the model of [3], all numerical simulations show similar today's values for the urey number (Fig. 1). Knowing the surface heat loss from the upcoming heat flow measurements planned for the InSight mission, one can distinguish then between different radiogenic heat source models [1, 2, 3, 4]. REFERENCES [1] Wänke et al., 94; [2] Lodders & Fegley, 97; [3] Morgan & Anders, 79; [4] Treiman et al., 86 Fig. 1: a) the influence of the reference viscosity and initial upper thermal boundary layer (TBL) on the urey ratio using HPE density from [1]; b) different models for HPE density; c) the urey ratio for different HPE models and 1e22 Pa s reference viscosity.