Galactic tides in the Solar System within a non-axisymmetric Milky Way model adjusted to Gaia data
Context. Galactic tides are external differential forces acting on extended systems immersed in the Galactic potential. They play a key role in the dynamics of comets in the Oort cloud. Aims. We aim to establish the strength of Galactic tides from the non-axisymmetric potential of the Milky Way revealed by the Gaia mission, and how this strength evolves along the Galactic trajectory of the Solar System. Methods. We derived expressions for Galactic tide parameters independently of any simplified trajectory for a star in the Galaxy or any specific symmetry of the Galactic potential. We obtained six parameters, $G_1$ to $G_6$, that quantify the influence of tides. Using the most up-to-date Galactic potential model, extended here to three dimensions, we studied the time evolution of these parameters along the Sun's trajectory using a statistical approach. Results. Even for Galactic trajectories featuring modest radial and vertical excursions, as investigated here, the dominant Galactic parameter, $G_3$, is found to vary by an order of magnitude along the solar trajectory. $G_1$ and $G_2$ reach up to about one half and one quarter, respectively, of $G_3$ along the solar trajectory, whilst parameters $G_4$ to $G_6$ reach up to one tenth of $G_3$. Conclusions. Contrary to what is often assumed, all Galactic tide parameters vary widely along the Galactic trajectory of the Solar System. Two consequences can be expected: First, $G_3$ directly affects the flux of observable long-period comets and the extent of the fossilised Sednoids region; second, $G_1$ and $G_2$, and to a lesser extent, $G_4$ to $G_6$, break the integrability of the dynamics, potentially affecting the long-term structure of the Oort cloud. Additionally, the new parameters $G_4$ to $G_6$, while small for the Solar System, may strongly impact extrasolar systems with a large out-of-the-plane excursion in the Galaxy.