Can There Be Dissipation without Heat? Constraints on Tidal Dissipation in the Medium-sized Saturnian Satellites

Introduction: Much can be learned about tidal dissipation in icy bodies by studying the medium-sized Saturnian satellites. They have densities that range between 960 kg/m3 (Tethys) and ~1460 kg/m3 (Dione) [1]. They accreted very cold (e.g., [2]). Thermal models governed by the decay of long-lived radionuclides yield freezing of the smallest satellites, in a few hundred million years. A Maxwell-rheology model used to simulate body tides indicates that little dissipation, if any, is expected in these bodies. Even on the long term, tidal dissipation cannot build up a significant amount of heat. In the largest and densest ones (Rhea and Dione), the core temperatures reach the ice melting point while the lithosphere is thick (see also [3]). However these satellites show evidence that they underwent some tidal dissipation resulting in dynamical evolution (e.g., eccentricity damping) and endogenic activity which created geological features. Understanding the mechanisms of tidal dissipation in the cold Saturnian satellites has become especially urgent since the discovery of a geyser associated with a strong thermal anomaly at Enceladus’ South Pole [4]. We focus on some discrepancies between the observations and the state of our knowledge of the dissipation factor and the existing rheological models used to describe the tidal response of the satellites. In the present work, we especially want to address the following question: can tidal dissipation, (significant enough to drive dynamical changes and endogenic activity), start without being triggered by a thermal event which significantly raises the temperatures of at least part of the satellite? We argue that such triggering must indeed be the case. First, however, we provide a few examples that frequency-dependent rheological models that are mainly temperature-dependent, such as a Maxwell model, cannot realistically describe tidal dissipation in cold icy satellites, and that parameters describing the internal structure should also be taken into account. Frequency dependence modeling requires the understanding of material response at different scales: microscale, but also mesoscale, such as fractures, porosity, bubbles in fresh ice, grain size variations, relation between the rock and ice components. This problem concerns not only the dissipation factor, chiefly a function of viscosity and the frequency-dependent model, but also the tidal Love number k2, chiefly a function of the elastic properties of the model. It has been proposed [5] that faults significantly decrease the global rigidity of the Moon and increase k2 and tidal dissipation. Bodies as cold as the Saturnian medium-sized satellites are likely to be highly fractured and maintain such defects deep in their interiors [6] for at least part of their history, before some warming facilitates ice creeping and compaction [7]. Different rheological models include structural parameters in their description of the frequency dependence of material behavior [e.g., 8, 9]. However the actual structure of the cold icy satellites remains inaccessible, at least for now. The lack of data also applies to the rheological properties (viscosity and elastic parameters) for the range of temperatures encountered in the Saturnian satellites, i.e., 70 to 230K. A major difficulty of laboratory measurements is that the mechanisms taking place in the tidal friction should be reproduced at the same range of frequencies that occur in nature. For example, studies often refer to the measurement of ice dissipation factor at 100 K and frequencies of 1-10 Hz, which is ~300 [10]. However this measurement has been obtained at seismic frequency and using such a number can lead to substantial error. At least, if this number is used in coupled thermal-dynamical models of the Saturnian satellites, we show that it rapidly leads to full melting of the bodies and potential endogenic activity in the long run, which is discrepant with the observations. The lack of rheological data and understanding of the tidal response is a potential roadblock to future study. Assessing this problem is of special interest with regard to our recent study of Iapetus’ dynamical evolution, which Castillo et al. [11] propose to be triggered by heat from short-lived radiogenic species. But, this problem also applies to other puzzles in the Saturnian satellite systems, some of them outlined below.