Elsevier

Icarus

Volume 169, Issue 2, June 2004, Pages 402-412
Icarus

A model for the interior structure, evolution, and differentiation of Callisto

https://doi.org/10.1016/j.icarus.2003.12.019Get rights and content

Abstract

The recently measured dimensionless moment of inertia (MoI) factor for Callisto of 0.3549±0.0042 (Anderson et al., 2001, Icarus, 153, 157–161) poses a problem: its value cannot be explained by a model in which Callisto is completely differentiated into an ice shell above a rock shell and an iron core such as its neighboring satellite Ganymede nor can it be explained by a model of a homogeneous, undifferentiated ice–rock satellite. We show that Callisto may be incompletely differentiated into an outer ice–rock shell in which the volumetric rock concentration is close to the primordial one at the surface and decreases approximately linearly with depth, an ice mantle mostly depleted of rock, and an about 1800 km rock–ice core in which the rock concentration is close to the close-packing limit. The ice–rock shell thickness depends on uncertain rheology parameters and the heat flow and can be roughly 50 to 150 km thick. We show that if Callisto accreted from a mix of metal bearing rock and ice and if the average size of the rocks was of the order of meters to tens of meters, then Callisto may have experienced a gradual, but still incomplete unmixing of the two components. An ocean in Callisto at a depth of 100–200 km is difficult to obtain if the ice is pure H2O and if the ice–rock lithosphere is 100 km or more thick; a water ocean is more plausible for ice contaminated by ammonia, methane or salts; or for pure H2O at a depth of 400–600 km.

Introduction

The gravity data returned by the Galileo mission from recent Callisto fly-bys allowed improved measurements of the mass and, for the first time, accurate measurements of the coefficient C22 of the gravity field (Anderson et al., 2001). From these, the dimensionless moment of inertia about the rotation axis C/MSRS2, where MS is the satellite mass and RS its radius, was estimated to be 0.3549±0.0042. C/MSRS2 can be calculated from C22 assuming a satellite in hydrostatic equilibrium and is usually taken to be approximately equal to the MoI-factor defined as the dimensionless average moment of inertia IMSRS2=1MSRS2∫ρ(r)r4sin3θdrdϕ, where ρ(r) is the density, r is the radial distance from the center and θ and ϕ are the co-latitude and longitude, respectively. The MoI-factor is an important quantity to constrain models of the interior structure of a planet or satellite because it measures the first moment of the interior density distribution. In the following, we will assume that C/MSRS2 equals the MoI-factor.

For a homogeneous satellite the MoI factor is 0.4. If the density increase due to self-compression under the action of gravity and due to ice phase transitions is taken into account, the MoI-factor for a homogeneous Callisto can be as small as 0.38 (McKinnon, 1997). The observationally constrained MoI-factor is thus smaller than the value for a homogeneous Callisto but it is considerably larger than the value of 0.3105±0.0018 found for Ganymede (Anderson et al., 1996). It was shown Anderson et al., 2001, Sohl et al., 2002 that it is impossible to construct 2- or 3-layer models of Callisto that will fit the MoI-factor and have a pure ice shell above a rock–iron core or shells of the pure phases ice, silicate, and iron, as it is possible and widely accepted for Ganymede. This is generally taken to suggest that differentiation in Callisto has not run to completion. Stevenson (1998), for example, has proposed a structure with pure ice I overlying an ocean and a rock/ice core.

While incomplete differentiation of Callisto appears to be a reasonable explanation, it is not clear how an icy satellite can evolve into such a state. It has been proposed that (partial) melting in near surface layers of undifferentiated Ganymede or Callisto sized satellites will lead to separation between the ice and the rock+metal components Friedson and Stevenson, 1983, McKinnon, 1997, Anderson et al., 2001. Mueller and McKinnon, 1988, McKinnon, 1997 have argued that convective layering due to the endothermic ice II to V phase transition and compositional layering may cause melting. These processes have not been modeled in detail, though, and in part rely on uncertain parameterizations of convective heat transport and compositionally driven flow. It is certainly true that the difference in gravitational energy between a homogeneous satellite and a satellite with an ice mantle and a rock+metal core is more than sufficient to provide the latent heat of ice melting. The gravitational energy stored in the rock sediment at the bottom of a 200 to 300 km deep ocean above an undifferentiated deeper interior, however, is not sufficient to melt the rest of the ice. A self-accelerating mechanism like the one proposed by Friedson and Stevenson (1983) has to be invoked. In any case, the consensus is that Callisto must have either formed cold such that melting can be avoided or must have differentiated so slowly as to remove the heat liberated upon differentiation. Recent models of the formation of the galilean satellites Canup and Ward, 2002, Mosqueira and Estrada, 2003a, Mosqueira and Estrada, 2003b, therefore, form Callisto cold. But these models do not explain why and how it is incompletely differentiated. In this paper, we present a model for the incomplete differentiation of a solid Callisto by the gradual and slow unmixing of rock and ice.

Section snippets

A simple model of incomplete differentiation

The mean density of Callisto of 1860 kgm−3 (Anderson et al., 2001) suggests that the satellite's volume fraction of rock (and metal), ε0, must be between roughly 20 and 40 vol%, mostly depending on the rock and the ice densities. If proto-Callisto consisted of a homogeneous mixture of metal bearing, perhaps hydrated rock and ice, then the density difference between the two phases will cause the rock particles to gradually settle towards the center if the ice deforms readily enough. The rate at

Model description

In this section we describe the results of more detailed calculations where we solve the one-field equations of Rudman (1997) for temperature and rock concentration dependent rheology in spherical geometry while taking into account high-pressure ice phase transformations as well as the dependence of gravity on depth and of radiogenic heat production on time (see also Nagel, 2001, for more details of the model calculations).

Solid-state creep of ice at the stress level expected in large icy

Discussion and conclusions

We presented a model capable of explaining an incompletely differentiated Callisto slowly evolving from a homogeneous initial state to one with an ice–rock lithosphere in which the rock concentration decreases with increasing depth, an ice mantle depleted to a large extent of rock, and a rock–ice core that can satisfy the mass and moment of inertia constraints. Our conclusions do not depend significantly on the value of the CPL. Internal consistency requires that the latter limit increase with

Acknowledgements

We have profited from discussions with G. Schubert, J.T. Wasson, W. McKinnon, and D.J. Stevenson. C. Sotin and D.J. Stevenson provided thoughtful reviews. This research was supported by the Deutsche Forschungsgemeinschaft.

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