2011A&A...528A..40F

A large fraction of stars, including young T Tauri stars, are observed to be members of binary or multiple systems. During the early stages of evolution when the individual binary stars are surrounded by a gaseous and dusty disc, the binary orbit plane and disc midplane may be mutually inclined. For the relatively thick protostellar discs associated with T Tauri stars, it is expected that in this scenario the disc will become mildly warped and undergo solid body precession around the angular momentum vector of the binary system. At the present time it is unclear how solid bodies such as planetesimals embedded in such a disc will evolve dynamically and affect the formation of planets. We investigate the dynamics of planetesimals embedded in gaseous protoplanetary disc models which are perturbed by a binary companion on a circular, inclined orbit. The main focus of this work is to examine the collisional velocities of the planetesimals in order to determine the conditions under which planetesimal growth through accretion is likely to occur, rather than erosion or catastrophic disruption. The parameters we consider are the binary inclination, γ_F, the binary separation, D, the disc mass, M_d, and planetesimal radius s_i. Our standard model has D=60AU, γ_F=45°, and a disc mass equivalent to that of the minimum mass solar nebula model. We use a 3-dimensional hydrodynamics code to model the evolution of the disc. The planetesimals are treated as non-interacting test particles which evolve because of gas drag, the gravitational force of the disc, and the gravitational perturbation due to the companion star. We detect the moment when two planetesimal orbits cross one another, and use these orbit crossing events to estimate the collisional velocities of the planetesimals. For binary systems with modest inclination (γ_F=25°), we find that the disc gravity prevents the planetesimal orbits from undergoing strong differential nodal precession (which they would do in the absence of the disc), and forces the planetesimals to precess with the disc on average. For planetesimals of different size, however, the orbit planes become modestly inclined with respect to one another, leading to collisional velocities that would clearly inhibit planetesimal growth. For larger binary inclinations (γ_F=45°), the Kozai effect is found to switch on, causing the growth of very large relative velocities which are on the order of a few kilometres per second. We conclude that planet formation via the mutual accretion of planetesimals is difficult to achieve in an inclined binary system with parameters similar to those considered in this paper, although more distant stellar companions than those we have studied should not present such a problem. For highly inclined systems in which the Kozai effect switches on, the prospects for forming planets would appear to be very remote indeed.