Possible factors affecting magnetic field generation in Mercury
With the two flybys of Mercury by MESSENGER in 2008, new data have been collected that allow us to study in more detail the interior of the planet closest to the Sun. The recognition of a molten interior (Margot et. al., 2007), as well as the new flyby data, indicates that magnetic field generation in Mercury is very likely to be caused by an internal dynamo (Anderson et al., 2008). The operation of a traditional dynamo in Mercury poses important questions, not the least of which is that the magnetic field at Mercury is measured to be more than two orders of magnitude too small for a magnetostrophic dynamo-generated field. In this paper I address the effects of two independent phenomena that may modify Mercury's internal dynamics. First, the active and small magnetosphere may have an effect on magnetic field generation. The dynamo regime does not depend exclusively on the thermal state of the planet, but also on the interaction between the external and internal magnetic fields. Second, the consequences of a light-element enriched core have been studied. If mixing of core elements is not efficient, and a thin liquid layer enriched in light elements is located at the top of the core, the effects on magnetic field generation may also be significant. I will present two scenarios that may affect magnetic field generation in Mercury and, on the basis of numerical modelling, constrain the conditions under which those variables become important in magnetic field generation in the terrestrial planets.
Dynamo models Incorporating Iron "Snow Zones" Consistent with Mercury's Weak Observed Magnetic Field
The Mariner 10 and MESSENGER probes have revealed that Mercury possesses a field of internal origin, with a dipole moment between 230 and 290 nT-RM3 (RM is the mean radius of Mercury). The field is dominated by an axial dipole, and is approximately 100 times weaker than Earth's. Although it is likely caused by a planetary dynamo, a field as weak as Mercury's is difficult to produce with an Earth-like dynamo. This disparity in field strengths implies that the core dynamics of Mercury differ markedly from Earth's, and that an exotic internal field partitioning should be expected. Recent experimental work by Chen et al. (2008) indicates that convection in Mercury's outer core may be compositionally driven at multiple points by an iron precipitate, or "snow". Using the Kuang-Bloxham numerical dynamo model, we investigate the effects of these iron snow zones on the dynamo to determine whether these layers can help explain Mercury's weak field. We find that when snow zones are placed both midway through the core, and at the core mantle boundary, the observed dipole field is reproduced. Because the geometry of these layers is dependent on the chemical makeup of the core, the results can be used to provide constraints on the sulphur content in Mercury's core.
Modelling the effect of radially variable conductivity on dynamo action and zonal flow in the Giant planets
The surface winds and magnetic fields of Jupiter and Saturn are observed to be broadly comparable. Both planets have strong and prograde equatorial jet and weaker jets, flowing in alternating directions at higher latitudes. Also, both planets exhibit relatively strong, dipolar magnetic fields. Saturn's magnetic field is weaker and more axisymmetric than that of Jupiter. In addition, Saturn's equatorial jet is broader and stronger than that of Jupiter. We have performed a set of numerical simulations of rotating convection and dynamo action in spherical shells. The model fluid is Boussinesq with radially varying electrical conductivity. The electrical conductivity, which is nearly constant in the deeper parts of the shell, exponentially decreases outward, starting at a chosen radius parameter. We find that the character of the dynamo-generated magnetic field, and the fluid flow structure are strongly affected by the afore-mentioned radius parameter, as well as by the size of the inner boundary radius and the temperature boundary conditions. In some of the simulations a strong, magnetostrophic, mainly dipolar dynamo develops in the deeper region of high electrical conductivity. In most cases, a strong zonal flow with an equatorial jet develops near the low-conductivity, free slip outer surface, and penetrates to a depth associated with the conductivity profile. The zonal flow is attenuated by Lorentz forces at depth and is, in some cases, greatly diminished in the dynamo region. The relationship between the structure of equatorial jets and the magnetic fields generated in our models implies that major differences between the surface zonal flow and magnetic fields of Jupiter and Saturn can arise from the presence of a rocky core, and the depth of transition from their low-conductivity molecular envelopes to their liquid metal interiors.
Digital Imaging Velocimetry is used to Analyze Particle Motion in a Rotating Fluid Sphere and Spherical Shell
Some of the inertial modes of a sphere and a spherical shell proportional to the Earth's fluid core are excited using mechanical means. A camera and a laser module are mounted in the rotating frame so that when at solid body rotation there are minimal particle motions relative to the camera. Particle motions are then captured using Digital Imaging Velocimetry (DIV) when a mode is excited. We will show that both the particle velocity vectors and the modal frequencies match well with the predicted values. Although some of these modes had been observed using different means, the present set up provides new means to study particle motion in the Earth's fluid core.
Updated Scaling Laws for Mantle Convection from 3D Spherical Simulations
A newly developed 3D spherical code with the ability to handle strongly spatially varying viscosities was applied to simulate a planetary mantle within a parameter study of 88 cases to constrain parameterized laws for purely internally heated convection in a spherical shell. The aspect ratio was fixed to 0.55, similar to the estimated value of the Earth. The rheology bases on a linearized Arrhenius law, commonly known as the Frank- Kamenetskii approximation. Three regimes of convection that were explored with bottom-heated convection in previous studies could be identified with purely internally heated convection as well, with the addition of a low-degree-regime that occurs instead of the sluggish regime known from purely bottom-heated convection. This new regime produces long wavelengths in the same parametric range as the sluggish regime. The surface is completely mobile and the transition to the stag-nant lid regime is rather abrupt. Present and newly developed indicators for the different regimes were validated to distinguish between them as this is the first parametric study that follows the transition of the regimes with purely internally heated convection in a spherical shell. The thermal boundary layer was closely analyzed with common and new methods to establish scaling laws for the heat flow and the thickness of the stagnant lid that occurs as the viscosity contrast becomes higher than five orders of magnitude. Due to the high viscosity close to the surface an immobile lid forms on top of the convecting part. Within the stagnant-lid, heat is transported only by conduction. This stagnant lid is especially interesting for planetary formation as its thickness can reveal properties of the planetary crust and the overall heat budget. The boundary layer that is below this lid or directly below the surface for mobile regimes reveals the temperature of the convecting interior and the strength of convection, usually expressed as the Nusselt number. Scaling laws help to quickly calculate these quantities to avoid time consuming computations of three-dimensional simulations. Apart from updated scaling laws, a new method was developed to reconstruct the complete heat flow profile, and therefore temperature, as a radial function with parameterized incomplete gamma functions. Another key interest lies in the structural composition of mantle convection. As mentioned earlier, a low-degree regime could be identified, although the parametric range of occurrence is rather unrealistic. Within the more realistic stagnant-lid regime, a relation between the internal Rayleigh number and a structural indicator, the dominant degree, could be identified. The weighted mode is an indicator close to the dominant degree on which one is able to determine the average area that a plume covers on the surface. The correlation was identified for the time-dependent stagnant lid regime, whereas for steady-state convection a lower limit of around degree five seems to be the lowest possible mode beneath the stagnant lid under these simplified circumstances. This is not affected by the presence of pressure dependence. This lower limit is bound to the employed radius ratio of 0.55 and is likely to be lower with a smaller core.
Implementing Heat Sinks in a Vigorously Convecting Plane Layer to Simulate Spherical Shell Geometry Temperatures
Plane layer convection is characterized by higher mean temperatures than those found in corresponding spherical shell systems with the same heating parameters. For a given Rayleigh number (convective vigor), we seek to identify heating modes in isoviscous Cartesian calculations which yield temperature profiles (geotherms) that are similar to the temperatures found in spherical shell convection. The study is motivated by estimates of the mean temperatures of vigorously convecting spherical shell systems obtained using a previously derived predictive equation. The predictive equation estimates the temperature of a spherical shell system with an isothermal surface heated by both a relatively hot isothermal core and internal sources. In a spherical shell with a core to surface radii ratio, f, equal to that inferred for the Earth, specifying heating parameters similar to the Earth's produces a mean temperature that is less than half the average of the surface and core temperatures. The minimum mean temperature obtainable in plane layer Boussinesq convection is half the average of the boundary temperatures. Consequently, the use of heat sinks is required to lower the mean temperature of Cartesian systems to bring their thermal structure into agreement with spherical shell models. In order to simulate spherical shell temperature profiles, we examine uniform and stratified cooling rates. In Cartesian geometry calculations, we vary the cooling rates as a function of depth to match the radial change in total volume of fixed thickness layers in a sphere. We also examine the effect of different vertical gradients in the rate of cooling in an attempt to emulate convection in spherical shells with different values of f. In addition, we consider the effect of aspect ratio on convective planforms and temperature profiles. Systems featuring lower Rayleigh numbers (105-106) and internal heating rates (H=5) have temperatures and planforms that are more dependent on aspect ratio. Our results show promise for improving the similarity of the geotherms found in Cartesian systems and those observed in spherical shell convection. The findings are particularly relevant to studies implementing temperature-dependent parameters in Cartesian geometry mantle convection studies.
Fe-Si alloys in the lowermost mantle and the outer core
Chemical arguments suggest that iron silicon alloys can result from the reaction of the Fe-rich perovskite and post-perovskites in the D" layer of the mantle with the Fe of the liquid core . These iron-silicon alloys could accumulate in the lower parts of D", in particular the ultra-low velocity zones (ULVZ) or in the outermost part of the core, like slag. Physical arguments (high density) and seismological arguments (low velocities) plead for their existence in these regions . Here we compute the thermal equation of state, the temperature- dependent electronic conductivity and the elasticity of iron-silicon alloys from density-functional perturbation theory. From the phonons and electron-phonon coupling we solve the Boltzmann transport equations to give the electrical and thermal conductivities . We find that iron-silicon has lower seismic wave velocities than the lower mantle and higher than the outer core. Silicon also reduces the electrical conductivity of iron. For example, the electrical resistivity of FeSi at lower mantle and outer core conditions is on the order of 3.5-4.0 micro Ohm.m at 2500-3000K. This is about twice the resistivity of Fe in the same conditions, and is similar to the assumed resistivity of the outer core. If present in significant amounts, then the large values of the conductivity computed here suggest iron-silicon as the major conducting phase in the D" and ULVZ, and the mineral phase that would ensure the electromagnetic coupling between the mantle and the core.  E. Knittle and R. Jeanloz, Science, 251, 1438 (1991).  R. Caracas and R.M. Wentzcovitch, Geophys. Res. Lett. 31, No. 20, 10.1029/2004GL020601 (2004)  S.Y. Savrasov and D.Y. Savrasov, Phys. Rev. B, 54, 16487 (1996).
The Combined Effects of Continental Coverage and the 660-km Depth Endothermic Phase Transition on the Planform and Heat Transport Efficiency of Mantle Convection
The thermal insulation caused by partial continental coverage induces very large aspect ratio convection cells in mantle convection models with upwellings beneath the continents. The ability of upwellings and downwellings to penetrate the 660-km depth endothermic phase boundary has been shown to increase with the wavelength of convection. In this study, we present a large suite of numerical models in which we vary the degree of continental coverage from 0 to full coverage and we vary the Clapeyron slope of the 660-km depth endothermic phase transition. We will demonstrate that even with very large magnitudes of the Clapeyron slope, the planform of convection is only weakly affected when there is partial continental coverage and there is very little reduction in the surface heat flow compared with models with free-slip surfaces. The planform of convection in models with complete continental coverage is very strongly affected by the magnitude of the Clapeyron slope of the phase boundary where the strongly layered cases have a large number of rolls in the upper mantle and a small number of rolls in the lower mantle. We will also demonstrate that the heat transport efficiency under continents actually increases with phase boundary induced layering leading to relatively modest decrease in the surface heat flow with the magnitude of the phase boundary. We will also demonstrate that the very long wavelength flows that occur with partial continental coverage and with large magnitudes of the Clapeyron slope cause large amounts of horizontal advection which lead to subadiabatic mantle geotherms, even in the absence of internal heating.