Librational response of a deformed 3-layer Titan perturbed by non-Keplerian orbit and atmospheric couplings

Abstract

The analyses of Titan's gravity field obtained by Cassini space mission suggest the presence of an internal ocean beneath its icy surface. The characterization of the geophysical parameters of the icy shell and the ocean is important to constrain the evolution models of Titan. The knowledge of the librations, that are periodic oscillations around a uniform rotational motion, can bring piece of information on the interior parameters.The objective of this paper is to study the librational response in longitude from an analytical approach for Titan composed of a deep atmosphere, an elastic icy shell, an internal ocean, and an elastic rocky core perturbed by the gravitational interactions with Saturn. We start from the librational equations developed for a rigid satellite in synchronous spin-orbit resonance. We introduce explicitly the atmospheric torque acting on the surface computed from the Titan IPSL GCM (Institut Pierre Simon Laplace General Circulation Model) and the periodic deformations of elastic solid layers due to the tides. We investigate the librational response for various interior models in order to compare and to identify the influence of the geophysical parameters and the impact of the elasticity.The main librations arise at two well-separated forcing frequency ranges: low forcing frequencies dominated by the Saturnian annual and semi-annual frequencies, and a high forcing frequency regime dominated by Titan's or- bital frequency around Saturn. At low forcing frequency, the librational response is dominated by the Saturnian gravitational torque and the atmospheric torque has a small effect. In addition, the libration amplitude in that case is almost equal to the magnitude of the perturbation. The modulation of the gravitational torque amplitude at the orbital frequency with periodic deformation induces long-period terms in the librational response which contain information on the internal structure. At high forcing frequency the libration depends on the inertia of the layers and the elasticity can strongly reduce its amplitude at orbital frequency. For example, the amplitude of diurnal libration for oceanic models goes from about 320 − 390 meters if the icy shell is purely rigid to 60 − 85 meters when the elasticity is included, i.e. a reduction of about 80%. For models without ocean, diurnal libration goes from 52 meters in a rigid case to 50 meters for an elastic case, a very low reduction due to the weak deformation of an entirely solid satellite compared to the deformation of a thin icy shell. Oceanic models with elastic solid layers have the same order of libration amplitude than the oceanless models, which makes more challenging to differentiate them by the interpretation of librational motion.

Interpreting the librations of a synchronous satellite – How their phase assesses Mimas’ global ocean

“…(Vienne & Duriez 1995), and the mean motions of Janus and Epimetheus, taken from (Noyelles 2010). The masses come from (Jacobson et al 2006(Jacobson et al , 2008, and the Stokes coefficients from (Iess et al 2014;Tortora et al 2016;Iess et al 2010 Richard et al (2014) This study…”

Titan's atmosphere and climate

“…Observations that Titan's spin rate differs from synchronous [Lorenz et al, 2008a;Stiles et al, 2008Stiles et al, , 2010 have been explained by the exchange of angular momentum between Titan's massive atmosphere and its surface assuming the presence of a subsurface ocean [Lorenz et al, 2008a]. This exchange may lead to seasonal variations in Titan's rotation rate because the seasonal reversal of the meridional circulation produces a torque; the exact details of this interaction are still being explored [see, e.g., Tokano and Neubauer, 2005;Karatekin et al, 2008;Lorenz et al, 2008a;Mitchell, 2009;Van Hoolst et al, 2009;Goldreich and Mitchell, 2010;Tokano et al, 2011;Richard et al, 2014;Tokano et al, 2014].…”

The obliquity of Enceladus

“…with the subscript (l−1) referring to the layer located beneath layer j. Note that expression (32) has been corrected with respect to the expression used in Baland et al (2011Baland et al ( , 2012Baland et al ( , 2014. This correction has limited impact on the results reported in these studies.…”

“…In this paper, we propose a new theoretical model for the Cassini state, taking into account that Enceladus experiences a nonuniform orbital precession (see Bills, 2005 for an application to the Galilean satellites), may harbor an internal global ocean (see Baland et al, 2011, for the first application of such a model to Titan), and experiences periodic elastic deformations. To our knowledge, a theoretical model for the spin precession of a synchronous satellite under the influence of periodic tides does not exist yet, contrary to the case of the librations (Van Hoolst et al, 2013; Richard et al, 2014;Jara-Orué and Vermeersen, 2014). With this new model, we will assess the possibility of a resonant amplification of the solution (due to the non uniformity of the orbital precession and/or the presence of the internal global ocean and/or the elastic deformations of the solid layers).…”