Orbital dynamics in the GG Tau A system: investigating its enigmatic disc

GG Tau is one of the most studied multiple young stellar systems: GG Tau A is a hierarchical triple surrounded by a massive disc and its companion, GG Tau B, is also a binary. Despite numerous observational attempts, an understanding of the geometry of the GG Tau A system is still elusive. We provide new astrometric measures of the system and we run a set of hydrodynamical simulations with two representative orbits to test how they impact a disc composed of dust and gas. We test the dynamical evolution of the two scenarios on short and long timescales. We obtain synthetic flux emission from our simulations and we compare them with 1300 $\mu$m ALMA dust continuum emission and 1.67 $\mu$m SPHERE dust scattering images to infer the most likely orbital arrangement. We extend the analysis of the binary orbital parameters using six new epochs from archival data, showing that the current measurements alone are not capable of breaking the degeneracy between families of coplanar and misaligned orbits. We found that the time-scale for the onset of the disc eccentricity growth, $\tau_{ecc}$, is a fundamental time-scale for the morphology of the system. Results from numerical simulations show that the best match between is obtained with the misaligned configuration ($\Delta\theta= 30^\circ$) on timescales shorter than $\tau_{ecc}$. The results exhibit an almost circular cavity and dust ring. However, for both scenarios, the cavity size and its eccentricity quickly grow for timescales longer than $\tau_{ecc}$ and the models do not reproduce the observed morphology anymore. This implies that either the age of the system is shorter than $\tau_{ecc}$ or that the disc eccentricity growth is not triggered or dissipated. This finding raises questions on the future evolution of the GG Tau A system and, more in general, on the time evolution of eccentric binaries and their circumbinary discs.