The reflex instability: exponential growth of a large-scale m = 1 mode in astrophysical discs

We report the finding of a linear, non-axisymmetric, global instability in gas discs around stars (and which may be relevant to other astrophysical discs). It takes the form of an m=1 mode that grows in the disc density distribution while the star-barycentre distance rises exponentially with a characteristic timescale that is orders of magnitude longer than the orbital period, but potentially shorter than a protoplanetary disc lifetime. Hydrodynamical simulations with various codes and numerical methods all consistently show an unstable mode growing exponentially. A feedback loop is identified as a possible origin, whereby the acceleration of the star excites the eccentricity of the disc, yielding an m=1 mode in the density distribution which, in turn, pulls the star. The instability disappears if, and only if, the reflex motion of the star due to the disc's asymmetry is not taken into account in the simulations. For this reason we refer to this instability as the reflex instability. After a short presentation of the physics at play and the various indirect terms that can be implemented to model the stellar acceleration in a stello-centric frame, a study of the growth timescale as a function of the various parameters at play will be presented, and the potential consequences on planet formation will be discussed.