We consider the evolution of a binary system interacting due to tidal effects without restriction on the orientation of the orbital, and where significant, spin angular momenta, and orbital eccentricity. We work in the low tidal forcing frequency regime in the equilibrium tide approximation. Internal degrees of freedom are fully taken into account for one component, the primary. In the case of the companion the spin angular momentum is assumed small enough to be neglected but internal energy dissipation is allowed for as this can be significant for orbital circularisation in the case of planetary companions. We obtain a set of equations governing the evolution of the orbit resulting from tidal effects. These depend on the masses and radii of the binary components, the form and orientation of the orbit, and for each involved component, the spin rate, the Coriolis force, the normalised rate of energy dissipation associated with the equilibrium tide due to radiative processes and viscosity, and the classical apsidal motion constant. These depend on stellar parameters with no need of additional assumptions or a phenomenological approach as has been invoked in the past. They can be used to determine the evolution of systems with initial significant misalignment of spin and orbital angular momenta as hypothesised for systems containing Hot Jupiters. The inclusion of the Coriolis force may lead to evolution of the inclination between orbital and spin angular momenta and precession of the orbital plane which may have observational consequences.
تحميل البحث