Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration

• Published in: Icarus (New York, N.Y. 1962) N.Y. 1962), 2020-06, Vol.343, p.113610, Article 113610
• Main Authors: Gevorgyan, Yeva, Boué, Gwenaël, Ragazzo, Clodoaldo, Ruiz, Lucas S., Correia, Alexandre C.M.
• Format: Article
• Language: English
• Subjects: Astrophysics; Enceladus; Librations; Maxwell; Physics; Rheology: Andrade; Tides
• ISSN: 0019-1035; 1090-2643
• DOI: 10.1016/j.icarus.2019.113610

The main purpose of this work is to present a time-domain implementation of the Andrade rheology, instead of the traditional expansion in terms of a Fourier series of the tidal potential. This approach can be used in any fully three dimensional numerical simulation of the dynamics of a system of many deformable bodies. In particular, it allows large eccentricities, large mutual inclinations, and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, such as chaotic motions, transient events, and resonant librations. The results are presented by means of a concrete application: the analysis of the libration of Enceladus. This is done by means of both analytic formulas in the frequency domain and direct numerical simulations. We do not a priori assume that Enceladus has a triaxial shape, the eventual triaxiality is a consequence of the satellite motion and its rheology. As a result we obtain an analytic formula for the amplitude of libration that incorporates a new correction due to the rheology. Our results provide an estimation of the amplitude of libration of the core of Enceladus as 0.6% of that of the shell. They also reproduce the observed 10 GW of tidal heat generated by Enceladus with a value of 0.17 × 1014 Pa⋅s for the global effective viscosity under both Maxwell and Andrade rheology. •We address a direct implementation of the Andrade rheology in the time domain.•Our approach allows for large eccentricities and non-periodic perturbations of the orbit.•Our analytic formula for the amplitude of libration incorporates a new correction due to the rheology.•We provide an estimation of the amplitude of libration of the core of Enceladus.•Our model reproduces the observed tidal heat generated by Enceladus.