Context. GG Tau is one of the most studied young multiple 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, a comprehensive understanding of the geometry of the GG Tau A system is still elusive. Given the significant role of dynamical interactions in shaping the evolution of these systems, it is relevant to characterise the stellar orbits and the discs' properties.
Aims: To determine the best orbital configuration of the GG Tau A system and its circumtriple disc, 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.
Methods: We tested the dynamical evolution of the two scenarios on short and long timescales. We obtained synthetic flux emission from our simulations at different timescales and we compared them with multi-wavelength observations of 1300 µm ALMA dust continuum emission and 1.67 µm SPHERE dust scattering to infer the most likely orbital arrangement.
Results: We extend the analysis of the binary orbital parameters using six new epochs from archival data, showing that the current measurements alone (and future observations coming in the next 5-10 yr) are not capable of fully breaking the degeneracy between families of coplanar and misaligned orbits, but finding that a modest misalignment is probable. We find that the timescale for the onset of the disc eccentricity growth, τ_ecc, is a fundamental timescale for the morphology of the system. Results from the numerical simulations obtained using the representative coplanar and misaligned (∆θ = 30°) orbits show that the best match between the position of the stars, the cavity size, and the dust ring size of GG Tau A is obtained with the misaligned configuration on timescales shorter than τ_ecc. The results exhibit an almost circular cavity and dust ring, favouring slightly misaligned (∆θ ~ 10-30°) low-eccentricity (e ~ 0.2-0.4) orbits. However, for both scenarios, the cavity size and its eccentricity quickly grow for timescales longer than τ_ecc and the models do not reproduce the observed morphology anymore. This implies that either the age of the system is shorter than τ_ecc or that the disc eccentricity growth is not triggered or dissipated in the system. This finding raises questions about the future evolution of the GG Tau A system and, more generally, the time evolution of eccentric binaries and their circumbinary discs.