On the origin of the lump in circumbinary discs

Abstract: Accreting binary black holes (BBHs) are multi-messenger sources, emitting copious electromagnetic (EM) and gravitational waves. One of their most promising EM signatures is the lightcurve modulation caused by a strong, unique and extended azimuthal overdensity structure orbiting at the inner edge of the circumbinary disc (CBD), dubbed "lump". In this paper, we investigate the origin of this structure using 2D general-relativistic (GR) hydrodynamical simulations of a CBD in an approximate BBH spacetime. First, we use the symmetric mass-ratio case to study the transition from the natural m = 2 mode to m = 1. The asymmetry with respect to m = 2 grows exponentially, pointing to an instability origin. We indeed find that the CBD edge is prone to a (magneto-)hydrodynamical instability owing to the disc edge density sharpness: the Rossby Wave Instability (RWI). The RWI criterion is naturally fullfilled at the CBD edge and we report the presence of vortices, which are typical structures of the RWI. The RWI is also at work in the asymmetric mass-ratio cases (from 0.1 to 0.5). However, the CBD edge sharpness decreases with a decreasing mass ratio, and so the lump. By proposing a scenario for this lump formation, our work further supports its existence in astrophysical CBDs and potential source for an EM signature of BBHs. Finally, because the RWI is not caused by GR effects, it is also a robust candidate for the lump origin in CBDs around non-compact objects, e.g. binary protostars.