On the tilting of protostellar disks by resonant tidal effects

We consider the dynamics of a protostellar disk surrounding a star in a circular-orbit binary system. Our aim is to determine whether, if the disk is initially tilted with respect to the plane of the binary orbit, the inclination of the system will increase or decrease with time. The problem is conveniently formulated in the binary frame in which the tidal potential of the companion star is static. We may then consider a steady, flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations. The dynamics is controlled by the competing effects of the m = 0 and m = 2 azimuthal Fourier components of the tidal potential. In the presence of dissipation, the m = 0 component causes alignment of the system, while the m = 2 component has the opposite tendency. We find that disks that are sufficiently large, in particular those that extend to their tidal truncation radii, are generally stable and will therefore tend to alignment with the binary plane on a timescale comparable to that found in previous studies. However, the effect of the m = 2 component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency. Under such circumstances, the disk can be unstable to tilting and acquire a warped shape, even in the absence of dissipation. The outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius. For disks smaller than the primary resonance, the m = 2 component may be able to cause a very slow growth of inclination through the effect of a near resonance that occurs close to the disk center. We discuss these results in the light of recent observations of protostellar disks in binary systems.