Thermal evolution and Urey ratio of Mars

Abstract

The upcoming InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission, to be launched in 2016, will carry out the first in situ Martian heat flux measurement, thereby providing an important baseline to constrain the present‐day heat budget of the planet and, in turn, the thermal and chemical evolution of its interior. The surface heat flux can be used to constrain the amount of heat‐producing elements present in the interior if the Urey ratio (Ur)—the planet's heat production rate divided by heat loss—is known. We used numerical simulations of mantle convection to model the thermal evolution of Mars and determine the present‐day Urey ratio for a variety of models and parameters. We found that Ur is mainly sensitive to the efficiency of mantle cooling, which is associated with the temperature dependence of the viscosity (thermostat effect), and to the abundance of long‐lived radiogenic isotopes. If the thermostat effect is efficient, as expected for the Martian mantle, assuming typical solar system values for the thorium‐uranium ratio and a bulk thorium concentration, simulations show that the present‐day Urey ratio is approximately constant, independent of model parameters. Together with an estimate of the average surface heat flux as determined by InSight, models of the amount of heat‐producing elements present in the primitive mantle can be constrained.

Present-day heat flow model of Mars

“…For Mars, if we take into account a present-day radioactive heat production equivalent to a surface heat flow of 14.3 mW m −2 , according to the compositional model of Wänke and Dreibus37, and the average surface heat loss deduced from our model (19 mW m −2 ), then an Urey ratio of around 0.75 is obtained for the present-day Mars. This value is higher than the Ur (0.594 ± 0.024) proposed from some recent thermal evolution models38, but consistent with a more limited cooling deduced from lithospheric strength analysis1.…”

“…4). Our Ur values are clearly higher than those obtained from the 2D and 3D convective history models of Plesa and Breuer44 and Plesa et al 38,. which usually vary between 0.52 and 0.62 as a consequence of higher predicted heat flows; these models would suggest therefore a substantial amount of secular interior cooling.…”

“…For example, if HPE Mars /HPE Chondritic  =   0.9, the total radioactive heat production is equivalent to 12.8 mW m −2 , and the corresponding value of Ur is 0.68 and 0.61 for, respectively, the F NPR - and F SPR -based models. Thus, for obtaining Ur values similar to values found by Plesa et al 38. (between 0.5 and 0.6), requires an HPE Mars /HPE Chondritic ratio between 0.75 and 0.85, and a total radioactive heat production equivalent to ~10–12 mW m −2 .…”

The habitability of a stagnant-lid Earth

“…Grott et al 2011b;Morschhauser et al 2011) to simulate the thermal evolution of the interior of an Earth-like planet over 4.5 Gyr starting from a post-accretion scenario when core formation and magma ocean solidification are completed. Although this parameterized approach cannot capture the complexity of the dynamics of the mantle, it compares well with 2D and 3D simulations of the evolution of stagnant-lid bodies such as Mars and Mercury, both in terms of thermal evolution (Plesa et al 2015) and crust formation (Tosi et al 2013).…”

“…Although neglecting the time dependence in Eq. (4) could affect the earliest transient phases of the evolution, this approximation is sufficiently accurate to capture the long-term thermochemical behaviour of the interior reliably, as demonstrated by comparisons of this approach with the outcomes of fully dynamic simulations (Tosi et al 2013;Plesa et al 2015). The convective heat fluxes from the core into the mantle (q c ) and mantle into the stagnant lid (q l ) are obtained from boundary layer theory (e.g.…”