Effects of a radially varying electrical conductivity on 3D numerical dynamos

Effects of a radially varying electrical conductivity on 3D numerical dynamos Natalia G´omez-P´erez∗,a, Moritz Heimpelb, Johannes Wichtc aDepartment of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road N.W., Washington, DC 20015-1305 bDepartment of Physics, Room 238 CEB, 11322 - 89 Av., University of Alberta, Edmonton, Alberta, Canada T6G 2G7 c Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau Abstract The transition from liquid metal to silicate rock in the cores of the terrestrial planets is likely to be accompanied by a gradient in the composition of the outer core liquid. The electrical conductivity of a volatile enriched liquid alloy can be substantially lower than a light-element-depleted fluid found close to the inner core boundary. In this paper, we investigate the effect of radially variable elec- trical conductivity on planetary dynamo action using an electrical conductivity that decreases exponentially as a function of radius. We find that numerical solutions with continuous, radially outward decreasing electrical conductivity profiles result in strongly modified flow and magnetic field dynamics, compared to solutions with homogeneous electrical conductivity. The force balances at the top of the simulated fluid determine the overall character of the flow. The rela- tionship between Coriolis and Lorentz forces near the outer boundary controls the flow and magnetic field intensity and morphology of the system. Our results imply that a low conductivity layer near the top of Mercury’s liquid outer core is consistent with its weak magnetic field. Key words: Variable electrical conductivity, numerical dynamos, Geodynamo, Mercury 1. Introduction Variations in the physical properties of fluids in planetary dynamos define the character of the observed intrinsic magnetic field (e.g., strength, geometry and time variability). Changes in the electrical conductivity of the fluid as a function of depth may become relevant in the context of terrestrial and gas giant ∗Corresponding author Email address: ngomezperez@ciw.edu (Natalia G´omez-P´erez) Preprint submitted to Physics of the Earth and planetary Interiors October 27, 2018 arXiv:1003.4192v1 [astro-ph.EP] 19 Mar 2010 planets. In this paper we explore (with a focus on the terrestrial planets) how the radial variation of electrical conductivity in planetary cores may result in changes to dynamo-generated magnetic fields. 1.1. Terrestrial planets The cores of the terrestrial planets are composed principally of iron, with minor but significant amounts of nickel and lighter elements. It has long been known that an iron-nickel core would have too high a density to be compati- ble with Earth’s moment of inertia and seismic data (e.g., Birch, 1952; Poirier, 1994). A compatible Earth core density model can result from the inclusion of about 8% by weight of one or more light elements. Detailed models of core com- position are based primarily on the constraints of seismology, mineral physics, geochemistry, metallurgy, and cosmochemisty. Silicon, sulphur and oxygen are the primary candidates for the light elements. Sulphur is likely to be a signifi- cant component but the depletion of light elements in the process of accretion in the inner solar system limits sulphur to about 2 wt% in the core. Recent reviews of core differentiation and composition distinguish between models considering Silicon versus those considering Oxygen as the primary light element. Composition models give weight percents of Fe ≃85%-88%, Ni ≃5% Si ≃0-7%, O ≃0-4% and S ≃2% (e.g McDonough, 2003; Wood et al., 2006). Solidification of a more or less pure iron-nickel inner core may exclude the lighter elements, which would then be enriched in the outer core. The ratio of the inner core radius (1221 km) to the core radius (3480 km) is 0.35 and the mass of the inner core is only about 5% of the total core mass. So the bulk composition of the outer core is only slightly different than that of the whole core. Convection in the liquid outer core is driven by a combination of compo- sitional and/or thermal buoyancy. Thermal buoyancy available to drive con- vection and dynamo action originates primarily from the latent heat of solid- ification at the inner core boundary (ICB) and possibly from cooling at the core-mantle boundary (CMB). Secular cooling at the CMB does not guarantee a source of convective instability since heat can be conducted through a stably stratified layer (a super-adiabatic heat flux is needed). Compositional buoyancy originates at the ICB due to light element enrichment in the residual liquid as- sociated with inner core solidification. A source of compositional buoyancy near the CMB could come from precipitation from a silicate enriched layer at the top of the core, leaving a light element depleted, heavy residual liquid and a silicate sediment layer at the CMB (Buffett et al., 2000). Temperature and pressure dependence of electrical condu

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