We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.Comment: 32 pages, accepted for publication in MNRA

Abridged/ We present numerical results on the properties of young binary and multiple stellar systems. Our analysis is based on a series of SPH + Nbody simulations of the fragmentation of small molecular clouds, that fully resolve the opacity limit for fragmentation. We have produced a statistically significant number of stable multiple systems, with components separations in the range 1-1000 AU. At the end of the hydrodynamical evolution (0.5 Myr) we find that ~60% of stars and brown dwarfs are members of multiples systems, with about a third of these being low mass, weakly bound outliers in wide eccentric orbits. Our results imply that in the stellar regime most stars are in multiples (~80%) and that this fraction is an increasing function of primary mass. After Nbody integration to 10.5 Myr, the percentage of bound objects has dropped to ~40%, as most very low mass stars and brown dwarfs have been released to the field. Brown dwarfs are never found to be very close companions to stars (brown dwarf desert at very small separations), but one case exists of a brown dwarf companion at intermediate separations (10 AU). Our simulations can accommodate the existence of brown dwarf companions at large separations, but only if the primaries of these systems are themselves multiples. We have compared the outcome of our simulations with the properties of real stellar systems as deduced from the IR CM diagram of the Praesepe cluster and from spectroscopic and high-resolution imaging surveys of young clusters and the field.Comment: 14 pages, 4 figures, 1 table, accepted by MNRA

We present results from high‐resolution hydrodynamical simulations that explore the effects of small‐scale clustering in star‐forming regions. A large ensemble of small‐N clusters with five stellar seeds have been modelled and the resulting properties of stars and brown dwarfs statistically derived and compared with observational data. Close dynamical interactions between the protostars and competitive accretion driven by the cloud collapse are shown to produce a distribution of final masses that is bimodal, with most of the mass residing in the binary components. When convolved with a suitable core mass function, the final distribution of masses resembles the observed initial mass function, in both the stellar and substellar regimes. Binaries and single stars are found to constitute two kinematically distinct populations, with about half of the singles attaining velocities ≥2 km s−1, which might deprive low‐mass star‐forming regions of their lightest members in a few crossing times. The eccentricity distribution of binaries and multiples is found to follow a distribution similar to that of observed long‐period (uncircularized) binaries. The results obtained support a mechanism in which a significant fraction of brown dwarfs form under similar circumstances as those of normal stars but are ejected from the common envelope of unstable multiple systems before their masses exceed the hydrogen burning limit. We predict that many close binary stars should have wide brown dwarf companions. Brown dwarfs, and, in general, very low‐mass stars, would be rare as pure binary companions. The binary fraction should be a decreasing function of primary mass, with low‐mass or substellar primaries being scarce. Where such binaries exist, they are expected either to be close enough (semimajor axis ∼10 au) to survive strong interactions with more massive binaries or to be born in very small molecular cloud cores.