Dissipation in a tidally perturbed body librating in longitude

Abstract

Internal dissipation in a tidally perturbed librating body differs from the tidal dissipation in a steadily spinning rotator. First, libration changes the spectral distribution of tidal damping across the tidal modes, as compared to the case of steady spin. This changes both the tidal heating rate and the tidal torque. Second, while a non-librating rotator experiences alternating deformation only due to the potential force exerted on it by the perturber, a librating body is also subject to a toroidal force proportional to the angular acceleration. Third, while the centrifugal force in a steadily spinning body renders only a permanent deformation, in a librating body this force contains two alternating components $-$ one radial, another a degree-2 potential force. Both contribute to heating, as well as to the tidal torque and potential. We build a formalism to describe dissipation in a homogeneous terrestrial body performing small-amplitude libration in longitude. This formalism incorporates a linear rheological law defining the response of the material to forcing. While the formalism can work with an arbitrary linear rheology, we consider a simple example of a Maxwell material. We show that, independent of rheology, the forced libration in longitude can provide a considerable and even leading input in the tidal heating. Based on the observed parameters, this input amounts to 52% in Phobos, 33% in Mimas, 23% in Enceladus, and 96% in Epimetheus. This supports the hypothesis by Makarov & Efroimsky (2014) that the additional damping due to forced libration may have participated in the early heating up of some moons. As one possibility, a moon could have been chipped by collisions $-$ whereby it acquired a higher triaxiality and a higher forced-libration magnitude and, consequently, a higher heating rate. After the moon warms up, its triaxiality reduces, and so does the tidal heating.