Probing the eccentricity in protostellar discs: Modelling kinematics and morphologies

Context. Protostellar discs are mostly modelled as circular structures of gas and dust orbiting a protostar. However, a number of physical mechanisms, for example, the presence of a (sub)stellar companion or initial axial asymmetry, can cause the gas and dust orbital motion to become eccentric. Theoretical studies have revealed that, when present, disc eccentricity is expected to occur with predictable profiles that can be long-lasting and potentially observable in protostellar systems. Aims. We construct an analytical model predicting the typical features of the kinematics and morphology of eccentric protostellar discs, with the final goal of characterising the observational appearance of eccentricity in discs. Methods. We validate the model using a numerical simulation of a circumbinary disc (where the binary makes the disc eccentric). We finally post-process the simulation with Monte Carlo radiative transfer to study how eccentric features would appear through the 'eyes' of ALMA. Results. Besides the motion of the material on eccentric Keplerian orbits in the disc orbital plane, the most characteristic eccentric feature emerging from the analytical model is strong vertical motion with a typical anti-symmetric pattern (with respect to the disc line of pericentres). A circumbinary disc with a ≈ 40 au eccentric cavity (ecav = 0.2), carved by an abin = 15 au binary, placed at a distance d = 130 pc, is expected to host in its upper emission surface vertical oscillations up to vz ∼ 400 m s-1 close to the cavity edge, that is to say, well within ALMA spectral and spatial resolution capabilities. A residual spiral pattern in the vertical velocity Δvz ∼ 150 m s-1 of the simulation cannot be captured by the theoretical model, we speculate it to be possibly linked to the presence of a companion in the system.