Astrometric signatures of self-gravitating protoplanetary discs

We use high-resolution numerical simulations to study whether gravitational instabilities within circumstellar discs can produce astrometrically detectable motion of the central star. For discs with masses of M_disc= 0.1M_*, which are permanently stable against fragmentation, we find that the magnitude of the astrometric signal depends upon the efficiency of disc cooling. Short cooling times produce prominent filamentary spiral structures in the disc, and lead to stellar motions that are potentially observable with future high precision astrometric experiments. For a disc that is marginally unstable within radii of ~10 au, we estimate astrometric displacements of 10-10²μ arcsec on decade time-scales for a star at a distance of 100 pc. The predicted displacement is suppressed by a factor of several in more stable discs in which the cooling time exceeds the local dynamical time by an order of magnitude. We find that the largest contribution comes from material in the outer regions of the disc and hence, in the most pessimistic scenario, the stellar motions caused by the disc could confuse astrometric searches for low-mass planets orbiting at large radii. They are, however, unlikely to present any complications in searches for embedded planets orbiting at small radii, relative to the disc size, or Jupiter-mass planets or greater orbiting at large radii.