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

Author(s)

Gevorgyan, Yeva ^{[1, 2]} ; Boue, Gwenael ^[2] ; Ragazzo, Clodoaldo ^[1] ; Ruiz, Lucas S. ^[3] ; Correia, Alexandre C. M. ^[4]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

^[2] Sorbonne Univ, PSL Univ, Observ Paris, ASD, IMCCE, CNRS, UMR8028, 77 Ave Denfert Rochereau, F-75014 Paris - France

^[3] Univ Fed Itajuba, Inst Matemat & Comp, BR-37500903 Itajuba, MG - Brazil

^[4] Univ Coimbra, Dept Phys, CFisUC, P-3004516 Coimbra - Portugal

• Document type: Journal article
• Source: ICARUS; v. 343, JUN 2020.
• Web of Science Citations: 0

Abstract

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 x 10(14) Pa.s for the global effective viscosity under both Maxwell and Andrade rheology. (AU)

• FAPESP's process: 16/25053-8 - Dynamics and geometry in low dimensions
• Grantee: André Salles de Carvalho
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/26253-8 - Tidal effects on the dynamics of two- and three-body systems under gravitational forces
• Grantee: Yeva Gevorgyan de Mendonça
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 18/02905-4 - A rheological model for the deformation and orbital dynamics of celestial bodies
• Grantee: Yeva Gevorgyan de Mendonça
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate