Elsevier

Icarus

Volume 236, 1 July 2014, Pages 169-177
Icarus

Note
Shape, topography, gravity anomalies and tidal deformation of Titan

https://doi.org/10.1016/j.icarus.2014.03.018Get rights and content

Abstract

Gravity measurements and elevation data from the Cassini mission have been used to create shape, global topography and gravity anomaly models of Titan that enable an improved understanding of its outer ice I shell structure. We provide constraints on the averaged ice shell thickness and its long-wavelength lateral variations, as well as the density of the subsurface ocean using gravity anomalies, the tidal Love number k2 measurement and long-wavelength topography. We found that Titan’s surface topography is consistent with an approximate isostatically compensated ice shell of variable thickness, likely in a thermally conductive or in a subcritical convective state, overlying a relatively dense subsurface ocean.

Introduction

Gravity field measurements (Iess et al., 2010, Iess et al., 2012) and shape models (e.g., Zebker et al., 2009a) provide insight into the interior structure of Titan. Iess et al., 2010, Iess et al., 2012 determined the gravity field of Titan with a spherical harmonic expansion to degree three whereas the abundance of altimetry and SAR-Topography data have allowed the estimation of Titan’s shape up to degree 7 (Zebker et al., 2009a). Internal structure models of Titan are constrained, though not uniquely, by its moment of inertia, which can be estimated from the gravity field’s quadrupole moments neglecting non-hydrostatic components. The estimated normalized moment of inertia of Titan (Mol0.3414±0.0005) (Iess et al., 2010) is high relative to that of Ganymede, its closest twin in terms of mass and radius. Non-hydrostatic contributions to degree-2 gravity coefficients might produce an overestimate of the moment of inertia, and even if the more probable value of MoI is 0.34, a value of 0.33 must be considered as a lower bound value (Iess et al., 2010, Gao and Stevenson, 2013). To explain the relatively high moment of inertia, it has been suggested that Titan may have either a fully differentiated structure with a deep interior composed of hydrated silicates—for example, mineral antigorite (Castillo-Rogez and Lunine, 2010, Fortes, 2012) or else that the interior is only partially differentiated and at depth is composed of a mixture of ice and rock (Iess et al., 2010, Mitri et al., 2010a). Serpentines as antigorite are hydrous silicates formed on Earth from anhydrous Fe–Mg minerals during hydrothermal alteration of the oceanic lithosphere or from hydration of peridotide above subducting slabs (e.g. Hilairet et al., 2006). These minerals might be formed on Titan by hydrothermal alteration during differentiation as proposed by Castillo-Rogez and Lunine (2010).

The recently measured tidal Love number, k2, of Titan indicates that the outer ice I shell is decoupled from the deep interior by a global subsurface ocean (Iess et al., 2012). Previous analysis of Titan’s ice shell (Nimmo and Bills, 2010) argued that to explain the apparent non-hydrostaticity of Titan’s shape, its ice shell thickness must vary as a function of latitude thereby suggesting that the ice shell is in a conductive state (see also Hemingway et al., 2013). Nimmo and Bills (2010) analysis was based on the fluid Love number (kf = 1) derived from the quadrupole moments of the gravity field assuming the hydrostaticity of Titan (Iess et al., 2010) and the shape model of Zebker et al. (2009a).

We produced global topography and gravity anomaly models of Titan that enable an improved understanding of its outer ice I shell structure. We constrain the thermal state and thickness of Titan’s ice shell, as well as its lateral variation using as constraints the tidal Love number k2 (Iess et al., 2012), gravity anomalies and topographic shape models. The shape model used in our analysis of the ice shell is updated from the one presented in Zebker et al. (2009a) based on more recent SAR-Topography (Stiles et al., 2009) and altimetry datasets (Elachi et al., 2004). Then we show that the high measured value of k2 indicates that the outer ice shell is overlying a relatively dense subsurface ocean.

Section snippets

Method

In this section we present the methods used to provide the shape (Section 2.1), the gravity anomalies (Section 2.2) and to model the tidal deformation of the ice I shell (Section 2.3).

Shape

We determined the best-fit to Titan’s shape calculating the spherical harmonic expansion to the sixth order using surface elevations derived from Cassini RADAR altimetry and SAR-Topography (Stiles et al., 2009) data products. As the primary motivation for this work is to compare topography with gravity, which is only known to degree three, we did not need to solve for higher order shape coefficients and were able to limit the analysis to degree six and below, where unconstrained least squares

Conclusions

Gravity measurements and elevation data from the Cassini mission have been used to create shape, global topography and gravity anomaly models of Titan that enable an improved understanding of its outer ice I shell structure. Our models are consistent with a Titan interior in which the outer ice I shell is underlain by a dense subsurface water ocean containing a high concentration of dissolved salts. Assuming an upper limit of the density of the ocean equal to 1350 kg m−3, the upper limit of the

Acknowledgments

The authors thank Brian Stiles of the Jet Propulsion Laboratory for contributing the SAR-Topography data to this effort. GM thanks Luciano Iess for the discussions on Titan’s gravity field measurements. We thank two anonymous reviewers for their constructive comments. This work was in part supported by the Italian Space Agency (ASI). Part of the research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme

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