Computer Science – Sound
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..337g&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Computer Science
Sound
Scientific paper
Introduction: The current thermal state of Mars is a fundamental unknown in Mars science. Although is has a huge influence on the planet's current geodynamic activity and controls the possibility for basal melting at the polar caps [1], constraints on this quantities are very scarce. This situation has lately been improved by the study of lithospheric deformation at the north polar cap [2] which constrained the current Martian elastic lithosphere thickness Te, an indirect measure of the temperatures in the planetary interior. Using radar sounding data obtained bySHARAD, the shallow radar onboard the Mars Reconnaissance Orbiter, [2] found that the current Martian lithosphere is extremely stiff and Te is larger than 300 km today. This is surprising as this value is almost twice as large as previously estimated from theoretical considerations and flexure studies [3][1]. In order to be consistent with the planets thermal evolution, [2] argue that the amount of radioactive elements in the Martian interior needs to be subchondritic. This appears to be problematic as geochemical analysis of the SNC meteorites implies higher concentrations of radioactive elements [4]. Furthermore, if the concentration of heat producing elements is indeed reduced, the resulting low interior temperatures will inhibit partial mantle melting and magmatism. However, geological evidence suggests that Mars has been volcanically active in the recent past [5]. In order to address these inconsistencies, we reinvestigate the thermal evolution of Mars and examine its current thermal state for a wide range of initial condition using the current elastic thickness Te and the potential for partial mantle melting to constrain our models. Modeling: We investigate the thermal evolution of Mars by solving the energy balance equations for the core and mantle, treating the mantle energy transport by parametrized convection models. This is done using scaling laws for stagnant lid convection and our model is similar to that of [3]. We ignore crustal production and assume that the bulk of the crust is primordial. Starting from given initial conditions the thermal evolution of Mars is calculated and the current elastic thickness and mantle temperatures are evaluated. Elastic thicknesses are calculated using the strength envelope formalism for given crustal and mantle rheologies [3] and the potential for partial mantle melting is parameterized using the minimum temperature difference between the mantle temperature and the solidus of peridotite which is given by [6]. Partial melting will occur if temperatures locally exceeds the solidus of peridotite Tsol. As lateral inhomogeneities due to thickness variations of the insulating crust can locally increase temperatures by up to 100 K [7] and plumes rising from the coremantle boundary may further increase temperatures by up to 50 K, we will assume that partial mantle melting is feasible if temperatures are lower than Tsol by at most 150 K. Parameters: The current thermal state of Mars is most sensitive to the amount and distribution of radioactive ele- ments and the efficiency of mantle energy transport, which is a strong function of mantle viscosity. We vary the fraction of radiogenic elements in the crust between 20 and 80 % and the fraction of radiogenic elements with respect to the reference compositional model [4] between 30 and 100 %. The reference mantle viscosity at 1600 K was varied between 0 = 1019 and 1021 Pa s, corresponding to wet and dry olivine rheologies. Other parameters were kept constant and we use an initial upper mantle temperature of 1800 K, an initial core temperature of 2100 K, a crustal thermal conductivity of 3 W m-1 K-1, a mantle thermal conductivity of 4 W m-1 K-1 and a crustal thickness of 50 km. Fig. 1 shows the temperature structure of one model having 50 % of the radioactive elements in the crust ( = 0.5) and the fraction of radiogenic elements with respect to the reference model is 70 % = 0.7. As a comparison, the solidus and liquidus of peridotite are also given. The minimum temperature difference between mantle temperature and solidus is 250 K, not allowing for partial mantle melting. Results: Fig. 2 shows contour plots of the elastic thickness Te as a function of the fraction of radiogenic elements in the crust and the fraction of radiogenic elements with respect to the reference model [4] for (a) a wet mantle rheology and 0 = 1019 Pa s and (c) a dry mantle rheology and 0 = 1021 Pa s. Large elastic thicknesses require a small bulk concentration of radioactive elements or a large concentration of these elements in the crust . The gray areas in Fig.2 correspond to parameter combinations which satisfy the constrains given by Te > 300 km. Fig. 2 also shows contour plots of the minimum tempera- ture difference T as a function and for (b) wet and (d) dry mantle rheologies. Small T requires a large bulk concentration of radioactive elements or a small concentration of these elements in the crust . The gray areas correspond to parameter combinations which satisfy the constrains given by T < 150 K. There are no parameter combinations which satisfy both constrains given by Te > 300 km and T < 150 K for wet and dry mantle rheologies. The discrepancy is much larger for wet mantle rheologies than for dry ones. Conclusions: The constrains given by large elastic thicknesses and the potential for partial melting in the upper mantle cannot simultaneously be fulfilled using current models. This implies that either the elastic thickness is smaller than determined by [2], that the mantle solidus has been overestimated or that the polar caps are not currently in dynamic equilibrium. If the north polar cap contained CO2 ice, the permittivity of the cap would be reduced [8], allowing for larger deflections [2] and lower elastic thicknesses. This possibility needs to be investigated and the amount of CO2 ice necessary to sufficiently reduce Te should be determined in future work. Also, the solidus of mantle rocks depends on the rock'swater content and this effect should be incorporated into the models as a next step. Together, these effects will possibly allow for combinations of parameters and which satisfy the elastic thickness and partial melt constrains. Also, for the thermal models presented here, viscoelastic relaxation calculations should be carried out. References: [1] M.A.Wieczorek, Icarus, 10.1016/ j.icarus. 2007.10.026 (2008). [2] R.J. Phillips et al., Science 320, 5880, 1182 (2008) [3] M. Grott, D. Breuer, Icarus 193, 503 (2008). [4] H. Wänke and G. Dreibus, Philos. Trans. R. Soc. London Ser. A 349, 285 (1994). [5] G. Neukum et al., Nature 432, 971 (2004). [6] E. Takahashi, J. Geophys. Res. 95, B10, 1594115954 (1990). [7] S. Schumacher, D. Breuer, Geophys. Res. Lett., 34, 14, L14202 (2007) [8] E. Pettinelli et al, J. Geophyss Res. 108, E4, 101, 8029 (2003)
Breuer Doris
Grott Matthias
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