A model for the interior structure, evolution, and differentiation of Callisto
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 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 (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.
References (50)
- et al.
Shape, mean radius, gravity field and interior structure of Callisto
Icarus
(2001) - et al.
Convection and lithospheric strength in Dione, an icy satellite of Saturn
Icarus
(1991) - et al.
Viscosity of rock–ice mixtures and applications to the evolution of icy satellites
Icarus
(1983) - et al.
The ammonia–water system and the chemical differentiation of icy satellites
Icarus
(1997) - et al.
Thermal evolution of a differentiated Ganymede and implications for surface features
Icarus
(1987) Tidal origin of the Laplace resonance and the resurfacing of Ganymede
Icarus
(1991)Mystery of Callisto: is it undifferentiated?
Icarus
(1997)- et al.
Numerical modelling of 26Al-induced radioactive melting of planetesimals considering accretion
Icarus
(2002) - et al.
Three-layered models of Ganymede and Callisto, compositions, structures, and aspects of evolution
Icarus
(1988) - et al.
Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites
Icarus
(2003)
Formation of the regular satellites of giant planets in an extended gaseous nebula II: satellite migration and survival
Icarus
Two-phase natural convection: implications for crystal settling in magma chambers
Phys. Earth Planet. Inter.
Implications from Galileo observations on the interior structure and chemistry of the galilean satellites
Icarus
Oceans in the galilean satellites of Jupiter?
Icarus
Subsurface oceans on Europa and Callisto: constraints from Galileo magnetometer observations
Icarus
Gravitational constraints on the internal structure of Ganymede
Nature
Phase transitions and convection in icy satellites
Geophys. Res. Let.
Formation of the galilean satellites: conditions of accretion
Astrophys. J.
Thermodynamic properties and equation of state of high-pressure ice phases
Prikl. Mek. i Tekhn. Fiz.
Convection with pressure- and temperature-dependent non-Newtonian rheology
Geophys. J. R. Astron. Soc.
Transient high-Rayleigh-number thermal convection with large viscosity variations
J. Fluid Mech.
Rheological properties of water ice—application to satellites of the outer planets
Annu. Rev. Earth Planet. Sci.
Effects of dispersed particulates on the rheology of water ice at planetary conditions
J. Geophys. Res.
Glow of ice in the ammonia–water system
J. Geophys. Res.
Creep of water ices at planetary conditions: a compilation
J. Geophys. Res.
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