Inertial core-mantle coupling and libration of Mercury

¹ Royal Observatory of Belgium, 3 Avenue Circulaire, 1180 Brussels, Belgium e-mail: Nicolas.Rambaux@oma.be
² Depart. of Mathematics, Facultés Univ. N.D. de la Paix, 8 Rempart de la Vierge, 5000 Namur, Belgium
³ Observatoire de la Côte d'Azur, UMR CNRS Cassiopée, BP 4229, 06304 Nice Cedex 4, France

Received: 3 August 2005
Accepted: 24 February 2007

Abstract

The internal structure of Mercury is the most puzzling among the terrestrial planets. The space missions MESSENGER and the upcoming BepiColombo as well as ground-based radar measurements will play an important role in constraining our understanding of the structure, formation, and evolution of Mercury. The development of a complete theory of the coupled spin-orbit motion of Mercury within the Solar System is an essential complement to observational data and will improve significantly our knowledge of the planet. Prior work concerning the effect of core-mantle couplings on the rotation of Mercury has assumed that the obliquity of Mercury is equal to zero and that its orbit is Keplerian. This work deals with the Hermean core-mantle interactions in a realistic model of the orbital and rotational motions of Mercury. To this aim, we have used the SONYR model of the Solar System including Mercury's spin-orbit motion (SONYR is the acronym of Spin-Orbit N-bodY Relativistic model). We studied the dynamical behavior of the rotational motion of Mercury considered as a solid body including either a solid core or a liquid core. The liquid core and the mantle are assumed to be coupled through an inertial torque on the ellipsoidal core-mantle boundary. We determined Mercury's rotation for a large set of interior structure models of Mercury to be able to identify and to clarify the impact of the core motion on the librations. In this paper, we present a comparative study of the librations resulting from different models of the internal structure. The geophysical models have been calculated for a three-layer planet composed of a solid mantle, a liquid outer core, and a solid inner core. We find that (i) the influence of inertial coupling is of the order of a milliarcsecond for a core ellipticity of the order of 10^-4; (ii) the amplitude of the 88-day libration depends essentially on the radius of the core or, equivalently, on the concentration of sulfur in the core; and (iii) the range of amplitude values is 19 arcsec, indicating the possibility to discriminate between models of internal structure by using accurate libration measurements.