5:15 PM - 6:30 PM
[MGI35-P02] Numerical studies of convective stability of the lunar mantle by three-dimensional spherical calculation
Keywords:the Moon, thermal history, mantle convection, convective stability, three-dimensional spherical simulation
The observations of mare volcanism and gravity field on the Moon allow us to explore the evolution of the interior of the Moon as an example of simple rocky planets. The giant impact hypothesis suggests that the lunar interior was initially hot and mostly molten. The thermal history of the Moon predicted from numerical models that start from this initial thermal state is, however, in conflict with the observed history of expansion/contraction, that of volcanic activity, and present thermal structure of the Moon. To resolve these conflicts, we assumed that the temperature was relatively low in the deep mantle at the beginning of the history and reevaluated the effects of mantle convection on lunar thermal evolution. More specifically, we calculated a thermal convection of a Newtonian fluid with temperature-dependent viscosity in an internally heated spherical shell mantle. According to a linear stability analysis of thermal convection, the Rayleigh number (RaH ) corresponding to such initial thermal state of the Moon is lower than the critical Rayleigh number. Therefore, it is expected that mantle convection did not occur in the early stage of the lunar history.
To constrain this initial temperature distribution more quantitatively, we first calculated the thermal history caused by diffusion in a spherically symmetric shell. We found that a model of the lunar thermal history that fits in with the observed expansion/contraction history of the Moon can be obtained, if the initial temperature at the CMB is around 1000 K and the depth of the magma ocean is around 300 km. We applied this initial temperature distribution to 3D spherical calculation of thermal convection.
In 3D simulation, first, we started our simulation for the cases where heat producing elements (HPEs) are uniformly distributed in the mantle. Second, we introduced a thin layer whose thermal conductivity is lower than that of the mantle just beneath the surface in order to see the blanket effect of the lunar crust and regolith layer on thermal evolution. Third, we introduced a non-uniform distribution of HPEs with an enriched region beneath the nearside surface as a model of the Procellarum KREEP Terrane.
Our calculation demonstrates that the lunar thermal evolution is dominated by thermal conduction, when the temperature-dependence of viscosity is strong, since the Rayleigh number (RaH ) is smaller than the critical Rayleigh number. This thermal evolution model predicts a history of radius change that meshes with the observed one for the Moon: the modeled Moon radially expands by about 1 km for the first 1 Gyr and then shrinks at a rate of about 1km/Gyr. However, we could not reproduce the early expansion, when we introduced a model of the PKT, because the HPEs are concentrated to the PKT region and the average mantle is more depleted in them. To understand the thermal history of the Moon, it is important to consider the effects of volume change by mantle melting, transport of energy and HPEs by magma-migration, and mantle differentiation by the magma ocean.
To constrain this initial temperature distribution more quantitatively, we first calculated the thermal history caused by diffusion in a spherically symmetric shell. We found that a model of the lunar thermal history that fits in with the observed expansion/contraction history of the Moon can be obtained, if the initial temperature at the CMB is around 1000 K and the depth of the magma ocean is around 300 km. We applied this initial temperature distribution to 3D spherical calculation of thermal convection.
In 3D simulation, first, we started our simulation for the cases where heat producing elements (HPEs) are uniformly distributed in the mantle. Second, we introduced a thin layer whose thermal conductivity is lower than that of the mantle just beneath the surface in order to see the blanket effect of the lunar crust and regolith layer on thermal evolution. Third, we introduced a non-uniform distribution of HPEs with an enriched region beneath the nearside surface as a model of the Procellarum KREEP Terrane.
Our calculation demonstrates that the lunar thermal evolution is dominated by thermal conduction, when the temperature-dependence of viscosity is strong, since the Rayleigh number (RaH ) is smaller than the critical Rayleigh number. This thermal evolution model predicts a history of radius change that meshes with the observed one for the Moon: the modeled Moon radially expands by about 1 km for the first 1 Gyr and then shrinks at a rate of about 1km/Gyr. However, we could not reproduce the early expansion, when we introduced a model of the PKT, because the HPEs are concentrated to the PKT region and the average mantle is more depleted in them. To understand the thermal history of the Moon, it is important to consider the effects of volume change by mantle melting, transport of energy and HPEs by magma-migration, and mantle differentiation by the magma ocean.