Context. Abridged. Many stars are members of binary systems. During early phases when the stars are surrounded by discs, the binary orbit and disc midplane may be mutually inclined. The discs around T Tauri stars will become mildly warped and undergo solid body precession around the angular momentum vector of the binary system. It is unclear how planetesimals in such a disc will evolve and affect planet formation. Aims. We investigate the dynamics of planetesimals embedded in discs that are perturbed by a binary companion on a circular, inclined orbit. We examine collisional velocities of the planetesimals to determine when they can grow through accretion. We vary the binary inclination, binary separation, D, disc mass, and planetesimal radius. Our standard model has D=60 AU, inclination=45 deg, and a disc mass equivalent to the MMSN. Methods. We use a 3D hydrodynamics code to model the disc. Planetesimals are test particles which experience gas drag, the gravitational force of the disc, the companion star gravity. Planetesimal orbit crossing events are detected and used to estimate collisional velocities. Results. For binary systems with modest inclination (25 deg), disc gravity prevents planetesimal orbits from undergoing strong differential nodal precession (which occurs in absence of the disc), and forces planetesimals to precess with the disc on average. For bodies of different size the orbit planes become modestly mutually inclined, leading to collisional velocities that inhibit growth. For larger inclinations (45 degrees), the Kozai effect operates, leading to destructively large relative velocities. Conclusions. Planet formation via planetesimal accretion is difficult in an inclined binary system with parameters similar to those considered in this paper. For systems in which the Kozai mechanism operates, the prospects for forming planets are very remote.
We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.
Numerical simulations of planets embedded in protoplanetary gaseous discs are a precious tool for studying the planetary migration ; however, some approximations have to be made. Most often, the selfgravity of the gas is neglected. In that case, it is not clear in the literature how the material inside the Roche lobe of the planet should be taken into account. Here, we want to address this issue by studying the influence of various methods so far used by different authors on the migration rate. We performed high-resolution numerical simulations of giant planets embedded in discs. We compared the migration rates with and without gas selfgravity, testing various ways of taking the circum-planetary disc (CPD) into account. Different methods lead to significantly different migration rates. Adding the mass of the CPD to the perturbing mass of the planet accelerates the migration. Excluding a part of the Hill sphere is a very touchy parameter that may lead to an artificial suppression of the type III, runaway migration. In fact, the CPD is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill radius and using a smooth filter. Alternatively, the CPD can be given the acceleration felt by the planet from the rest of the protoplanetary disc. The gas inside the Roche lobe of the planet should be very carefully taken into account in numerical simulations without any selfgravity of the gas. The entire Hill sphere should not be excluded. The method used should be explicitly given. However, no method is equivalent to computing the full selfgravity of the gas.
