It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key rôle in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars.We have carried out a series of simulations of disc-star interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism.A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars. When the disc-spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20% of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically-triggered star formation, then new companions are formed in approximately 50% of encounters.

Abstract. -Smoothed particle hydrodynamics (SPH) is a particle method for modelling hydrodynamical flows that has been successfully applied to a wide range of astrophysical problems. One of its main weaknesses, however, has been its inability to treat viscosity in a rigorous manner. We present a new method that can be used to solve the Navier-Stokes equation for an arbitrary viscosity. We compare the accuracy of the method to alternative methods for treating viscosity in SPH, and apply the method to a series of tests for which there exist analytic solutions. We find that the new method is significantly more accurate than other existing methods, computationally efficient, and that the results of simulations carried out using the method are in excellent agreement with the theory.

No abstract

A Lagrangian, particle-based numerical method (tree code gravity plus smoothed particle hydrodynamics) was used to simulate clump-clump collisions occurring within GMCs. The collisions formed shock-compressed layers, out of which condensed approximately co-planar protostellar discs of 7-60 solar masses and 500-1000AU radius. Binary and multiple systems were the usual final state. Lower mass objects were also produced, but commonly underwent disruption or merger. Such objects occasionally survived by being ejected via a three-body slingshot event resulting from an encounter with a binary system. Varying the impact parameter, b, altered the processes by which the protostellar systems formed. At low b a single central disc formed initially, and was then spun-up by an accretion flow, causing it to produce secondaries via rotational instabilities. At mid b the shocked layer w hich formed initially broke up into fragments, and discs were then formed via fragment merger. At large b single objects formed within the compressed leading edge of each clump. These became unbound from each other as b was increased further. The effect of changing numerical factors was examined by : (i) colliding clumps which had been re-oriented before the collision (thus altering the initial particle noise), and (ii) by quadrupling the number of particles in each clump (thus increasing the resolution of the simulation). Both changes were found to affect the small-scale details of a collision, but leave the large scale morphology largely unaltered. It was concluded that clump-clump collisions provide a natural mechanism by which multiple protostellar systems may form.Comment: 15 pages, 12 low resolution figures in 50 files, accepted by MNRA

It is expected that an average protostar will undergo at least one impulsive interaction with a neighbouring protostar whilst a large fraction of its mass is still in a massive, extended disc. Such interactions must have a significant impact upon the evolution of the protostars and their discs.  We have carried out a series of simulations of coplanar encounters between two stars, each possessing a massive circumstellar disc, using an SPH code that models gravitational, hydrodynamic and viscous forces. We find that during a coplanar encounter, disc material is swept up into a shock layer between the two interacting stars, and the layer then fragments to produce new protostellar condensations. The truncated remains of the discs may subsequently fragment; and the outer regions of the discs may be thrown off to form circumbinary disc‐like structures around the stars. Thus coplanar disc–disc encounters lead efficiently to the formation of multiple star systems and small‐N clusters, including substellar objects.

It is expected that an average protostar will undergo at least one impulsive interaction with a neighbouring protostar whilst a large fraction of its mass is still in a massive, extended disc. If protostars are formed individually within a cluster before falling together and interacting, there should be no preferred orientation for such interactions. As star formation within clusters is believed to be coeval, it is probable that during interactions, both protostars possess massive, extended discs.We have used an SPH code to carry out a series of simulations of non-colpanar disc-disc interactions. We find that non-coplanar interactions trigger gravitational instabilities in the discs, which may then fragment to form new companions to the existing stars. (This is different from coplanar interactions, in which most of the new companion stars form after material in the discs has been swept up into a shock layer, and this then fragments.) The original stars may also capture each other, leading to the formation of a small-N cluster. If every star undergoes a randomly oriented discdisc interaction, then the outcome will be the birth of many new stars. Approximately two-thirds of the stars will end up in multiple systems.

1. Ox corneal stromal swelling pressure (gel pressure) may be measured by osmometry: polyethylene glycol of nominal molecular mass 10,000 Da (PEG 10K) is a suitable non‐penetrating solute. 2. Corneal hydrations equilibrate within 4 h of exposure to 154 mM‐NaCl including various concentrations (2‐8%) of PEG 10K, providing that the epithelium covers the anterior surface and Descemet's membrane covers the posterior surface. At equilibrium hydration, corneal gel pressure equals the external osmotic pressure contributed by PEG 10K. 3. The osmotic pressure of PEG 10K may be calibrated using Descemet's membrane as the semi‐permeable membrane. 4. Corneal gel pressure decreases with increasing hydration. 5. The relationship may be adequately explained by the Donnan theory of corneal swelling with a fixed negative matrix charge of 39.5 +/‐ 0.8 mequiv l‐1 at physiological hydration of 3.2 at this salt concentration (154 mM‐NaCl).

No abstract