Tilt Instability of Retrograde Disk Around One Component of a Binary

Be/X-ray binaries are systems containing a massive Be main sequence star and a compact object companion. The Be star contains a disc of material that flows from the Be star, and may interact with the companion. In this work we consider a neutron star companion. With hydrodynamic simulations, we show that a coplanar disc around one component of a binary can be unstable to global tilting when the disc orbits in a retrograde direction relative to the binary. The disc experiences the largest inclination growth relative to the binary orbit in the outermost radii of the disc, closest to the companion. This tilt instability also occurs for test particles. A retrograde disc is much larger than a prograde disc since it is not tidally truncated and instead spreads outwards to the orbit of the companion. The coplanar retrograde disc remains circular while a coplanar prograde disc can become eccentric. We suggest that the inclination instability is due to a disc resonance caused by the interaction of the tilt with the tidal field of the binary. This model is applicable to Be/X-ray binaries in which the Be star disc may be retrograde relative to the binary orbit if there was a sufficiently strong kick from the supernova that formed the neutron star companion. The accretion on to the neutron star and the resulting X-ray outbursts are weaker in the retrograde case compared to the prograde case.