Disc kinematics and stability in high-mass star formation Linking simulations and observations

Context. In the disc-mediated accretion scenario for the formation of the most massive stars, high densities and high accretion rates could induce gravitational instabilities in the disc, forcing it to fragment and produce companion objects. Aims. We investigate the effects of inclination and spatial resolution on the observable kinematics and stability of discs in high-mass star formation. Methods. We studied a high-resolution 3D radiation-hydrodynamic simulation that leads to the fragmentation of a massive disc. Using RADMC-3D we produced 1.3 mm continuum and CH3CN line cubes at different inclinations. The model was set to different distances, and synthetic observations were created for ALMA at similar to 80 mas resolution and NOEMA at similar to 0.4 ''. Results. The synthetic ALMA observations resolve all fragments and their kinematics well. The synthetic NOEMA observations at 800 pc with linear resolution of similar to 300 au are able to resolve the fragments, while at 2000 pc with linear resolution of similar to 800 au only a single structure slightly elongated towards the brightest fragment is observed. The position-velocity (PV) plots show the differential rotation of material best in the edge-on views. A discontinuity is seen at a radius of similar to 250 au, corresponding to the position of the centrifugal barrier. As the observations become less resolved, the inner high-velocity components of the disc become blended with the envelope and the PV plots resemble rigid-body-like rotation. Protostellar mass estimates from PV plots of poorly resolved observations are therefore overestimated. We fit the emission of CH3CN(12(K)-11(K)) lines and produce maps of gas temperature with values in the range of 100-300 K. Studying the Toomre stability of the discs, we find low Q values below the critical value for stability against gravitational collapse at the positions of the fragments and in the arms connecting the fragments for the resolved observations. For the poorly resolved observations we find low Q values in the outskirts of the disc. Therefore, although we could not resolve any of the fragments, we are able to predict that the disc is unstable and fragmenting. This conclusion is valid regardless of our knowledge about the inclination of the disc. Conclusions. These synthetic observations reveal the potential and limitations of studying discs in high-mass star formation with current (millimetre) interferometers. While the extremely high spatial resolution of ALMA reveals objects in extraordinary detail, rotational structures and instabilities within accretion discs can also be identified in poorly resolved observations.