Does mantle convection currently exist on Mercury?

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Abstract

The full equations of convective motion over the age of the solar system can be solved in a few hours (2D) to several weeks (3D) with numerical simulations in Cartesian or spherical geometry. Using the 2D, Cartesian geometry code, ConMan, we model the thermal evolution of Mercury. Our preferred calculation has an initial Rayleigh number of 8 × 104, no mantle internal heating, and a constant core heat flux of 9.75 mW/m2 in a non-Newtonian rheology. These values all fall within the range of previously estimated parameters from 1D calculations, and allow for weak mantle convection to persist until present, supporting the outer core dynamo explanation of Mercury's intrinsic magnetic field. Further, the peak dynamic topography and geoid anomalies from our model are about 179 m and 37 m, respectively—values that are not unrealistic and should be well within the range of observation by the MESSENGER spacecraft. Future spacecraft observations, yielding new and more accurate data, will help us better understand the thermal evolution of Mercury and the origin of its magnetic field.

Introduction

Mercury remains a mysterious place with little known about the planet. From moment of inertia calculations and density measurements, it is the densest of the four inner planets containing a large iron core up to 75% of the planetary radius (Siegfried and Solomon, 1974). It may be the only other terrestrial planet, aside from Earth, to possess an internal magnetic field. Whether this field is a result of a core dynamo (Ness et al., 1975, Stevenson, 1975, Gault et al., 1977, Gubbins, 1977, Stanley et al., 2005) or remnant magnetization (Stephenson, 1976, Sharpe and Strangway, 1976) remains uncertain. If the magnetic field is the result of a core dynamo, then the core heat flow can be used as a constraint on the thermal evolution of Mercury. In addition to the density and moment of inertia calculations of Mercury (e.g., Harder and Schubert, 2001), images from Mariner 10 reveal an ancient cratered surface and arcuate, tectonic structures commonly known as lobate scarps (Murray, 1975). These scarps stretch up to hundreds of kilometers long and up to a few kilometers in height (Strom et al., 1975, Watters et al., 1998). The proposed mechanism responsible for the formation of lobate scarps is related to cooling of the planet. It is expected that the planet radially contracted about 1–2 km since the end of the heavy bombardment period as a consequence of multiple processes including core (Strom et al., 1975, Watters et al., 1998), mantle and lithospheric cooling as well as a volume change in iron resulting from solidification of the inner core (e.g., Solomon, 1976, Solomon, 1977, Schubert et al., 1988, Hauck et al., 2004). Global contraction may be responsible for large thrust faulting that, in turn, produced the lobate scarps (Strom et al., 1975, Watters et al., 1998). Unfortunately, less than half of the surface was imaged from Mariner 10.

Other than lobate scarps, Mercury lacks recognizable tectonic features, making thermal history modeling challenging. A large increase in planetary volume is needed for core separation from an originally homogeneous planet (Solomon, 1976); however, there is no evidence for large-scale extension (i.e., tensional features) from known surface structures. The most probable scenario is that Mercury cooled rapidly allowing for differentiation to occur prior to the end of the period of heavy bombardment (Trask and Guest, 1975). Solomon (1977) proposed that Mercury had initial temperatures on the order of 1800 K allowing for complete global differentiation by 0.4 By In this model, radiogenic heat sources are concentrated in a low-density crust that formed during differentiation, allowing for rapid heat transfer from the mantle to the surface and extensive planetary cooling. With such efficient cooling, the radius of Mercury could have contracted by up to 7 km following differentiation (Solomon, 1977); however, in order to preserve a dynamo-driven internal magnetic field (e.g., Ness et al., 1975), a deep mantle heat source is required to maintain a largely molten core, offsetting heat loss due to mantle convection (Cassen et al., 1976). A smaller amount of contraction, spread over a longer time period, in conjunction with a smaller concentration of heat sources in the crust, could explain both the distribution of lobate scarps on the surface and preserve a core dynamo (Solomon, 1977).

Determining the thermal history of Mercury is made more challenging because the state of the present-day core is unknown. Two hypotheses for the origin of the magnetic field exist: remnant magnetization and a core dynamo. In order to obtain the magnitude of the present-day weak magnetic field from remnant magnetization, greater magnetizations than observed on Earth would be required (Schubert et al., 1988), and as a result of the cooling lithosphere, the internal dipole field would have had to maintain a single polarity lasting longer than the standard time interval between pole reversals on Earth (Schubert et al., 1988). In spite of this, remnant magnetization cannot be completely dismissed. Large remnant magnetic anomalies have been observed on Mars (Acuña et al., 1998). The core dynamo hypothesis requires a molten or partially molten outer core and the presence of an energy source to support convection within the molten layer (e.g., Merrill et al., 1998). This idea is more widely accepted and provides constraints for thermal evolution modeling (Hauck et al., 2004) such as core composition, ratio of inner core to outer core, and a minimum estimate for the core heat flux (Nimmo and Watters, 2004, Peale et al., 2002). The amount of core heat flux is an important constraint because it can be used as a boundary condition at the base of the mantle in thermal evolution calculations. Unfortunately, it is difficult to envision an external constraint on core heat flux; however, evidence of a convecting silicate mantle interior would be consistent with high core heat fluxes. Thus mantle convection could be an indirect observation of core heat flux. It is worthwhile considering this possibility because surface observables that are indicative of a presently convecting mantle (e.g., long-wavelength gravity and topography anomalies) will be mapped as a part of the MESSENGER mission (Solomon et al., 2001).

Currently, the best supporting evidence for present-day mantle convection on Mercury is the existing weak magnetic field, assuming a dynamo origin. This implies there may be sufficient heat flow from the core to maintain at least a sluggish mantle flow (Schubert et al., 1988, Stevenson et al., 1983). A caveat to this assumption exists in the core composition. If the core is solely made up of iron or iron and nickel, then it should have completely solidified by now, prohibiting a core dynamo (Solomon, 1976). However, complete core solidification would entail significantly more radial contraction than observed in surface tectonic features (Solomon, 1976). If a lighter element such as sulfur is mixed with iron, then the melting point of the core is reduced and a liquid outer core could exist at present (Siegfried and Solomon, 1974, Solomon, 1976, Schubert et al., 1988, Stevenson et al., 1983). Thus, although the present-day mantle may be depleted of radioactive elements, heat from a convecting outer core can be released into the mantle as the core solidifies, making it possible for mantle convection to persist to the present day.

Thus far, thermal history models of Mercury have been limited to 1D parameterized convection calculations (e.g., Schubert et al., 1988, Hauck et al., 2004, Stevenson et al., 1983). These calculations simplify the full equations of convective motion to a one-dimensional energy balance (Sleep, 1979). With advances in computing power, 2D numerical models solving the full equations of convective motion for the age of the solar system take only several hours to run for Mercury-like parameters and 3D calculations can be run on large clusters in several weeks. Hence, computing thermal history calculations with 2D convection simulations seems appropriate.

In this study we explore the state of the present-day mantle of Mercury to determine what range of core heat flux values are necessary to support mantle convection as well as a core dynamo. An intrinsic magnetic field implies that the outer core of Mercury is, at least, partially molten. This suggests heat may currently be released into the mantle because the cooling and solidifying of the outer core is an exothermic process. Mercury is likely depleted of heat-producing elements relative to Earth based on its proximity to the Sun (Wanke and Dreibus, 1988). Additionally, a large impact(s) may have stripped Mercury's outer layer early in its evolution (Cameron et al., 1988, Wetherill, 1988) further depleting the mantle and crust of heat-producing elements. Thus, there may be a small (compared to solar abundances) concentration of heat-producing elements in the mantle at present. It has been suggested by Lodders and Fegley (1998) that Mercury may have large mantle concentrations of uranium and thorium (possibly more than Earth) indicating internal heating may still be significant. However, we will show that, if the heat flux from the core is significant, mantle convection can occur at present without the presence of internal heating. Thus, we choose a conservative approach to our modeling efforts focusing mainly on the effect of core heat flux because the amount of internal heating is poorly constrained. If we add internal heating to our models it increases the likelihood of present day mantle convection, further supporting our results. Through numerical modeling we solve the full equations of convective motion for a Mercury-like mantle in 2D Cartesian geometry with a Newtonian and non-Newtonian rheology (e.g., Karato and Wu, 1993).

Section snippets

Numerical modeling

We model the thermal evolution of Mercury by solving the full equations of convective motion, assuming a creeping viscous fluid, with the two-dimensional, Cartesian geometry, finite element code, ConMan (King et al., 1990). Because the mantle of Mercury is only about 600 km, the assumption of Cartesian geometry is less restrictive than for other planets. The equations for incompressible convection in dimensionless form are the equations of momentum:(ηu)=p+Raθkˆcontinuity,u=0and energyθτ+

Results

In this study, we begin our calculations with an initially hot mantle in a dry, olivine stability field. We vary the initial Rayleigh number, rate of mantle internal heating as well as the core heat flux into the mantle and compare a Newtonian and non-Newtonian rheology. The calculations run for the age of the solar system so we can view the entire thermal history calculation up to present. The results of about 90 diffusion and dislocation creep computations are presented. Our goals are

Discussion

The origin of the weak magnetic field observed on Mercury remains controversial. A core dynamo requires at least partial core convection, and based on our results, if the mantle is no longer convecting, this would argue in favor of the remnant magnetization hypothesis for the present-day weak magnetic field (Stanley et al., 2005, Srnka, 1976) because the heat flux out of the core is not sufficient to power a dynamo. However, it is likely that Mercury's large iron/iron–nickel core has not

Conclusions

Advances in computing technology allow us to solve the full equations of convective motion in a short time with numerical simulations using Cartesian geometry in two or three dimensions. Through a series of calculations we have varied the Rayleigh number, amount of mantle internal heating, core heat flux and rheology in order to address the current state of the mantle of Mercury. If present-day mantle convection exists on Mercury, this would be consistent with the core dynamo hypothesis. In a

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    Now at MIT Lincoln Laboratory, Lexington, MA, United States.

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