A new insight into the Galactic potential: A simple secular model for the evolution of binary systems in the solar neighbourhood

Context. Among the main effects that the Milky Way exerts in binary systems, the Galactic tide is the only one that is not probabilistic and can be deduced from a potential. Therefore, it is possible to perform an analysis of the global structure of the phase space of binary systems in the solar neighbourhood using the Galactic potential. Aims. The aim of this work is to obtain a simple model to study the collisionless dynamical evolution of generic wide binaries systems in the solar neighbourhood. Methods. Through an averaging process, we reduced the three-dimensional potential of the Galaxy to a secular one-degree of freedom model. The accuracy of this model was tested by comparing its predictions with numerical simulations of the exact equations of motion of a two-body problem disturbed by the Galaxy. Results. Using the one-degree of freedom model, we developed a detailed dynamical study, finding that the secular Galactic tide period changes as a function of the separation of the pair, which also gives a dynamical explanation for the arbitrary classification between “wide” and “tight” binaries. Moreover, the secular phase space for a generic gravitationally bound pair is similar to the dynamical structure of a Lidov-Kozai resonance, but surprisingly this structure is independent of the masses and semimajor axis of the binary system. Thus, the Galactic potential is able to excite the initially circular orbit of binary systems to high values of eccentricity, which has important implications for studies of binary star systems (with and without exoplanets), comets, and Oort cloud objects