Accretion during binary star formation .1. Ballistic accretion

We consider the effects of accretion, during binary star formation, on the mass ratio and separation of a 'seed' binary system. Numerical fragmentation calculations show that 'seed' binary systems may be formed during the gravitational collapse of molecular cloud cores. When initially formed, however, these protobinaries typically contain only a small fraction of the total mass of the cloud core. For the star formation process to reach completion, a protobinary system must grow in mass via accretion from the remainder of the infalling cloud. The accretion of, and interaction with, this matter affects the mass ratio, separation and eccentricity of the protobinary, and thus the final state of the system cannot be determined unless the effects of the accretion are known. In this paper, the effects of accretion on the mass ratio and separation of an initially circular protobinary system are determined as functions of the initial mass ratio of the protobinary and the specific angular momentum of the infalling cloud material. The effects are studied by modelling the cloud ballistically, with non-interacting particles which are accreted by the protostars. Qualitatively, it is found that the mass ratio and separation decrease for the accretion of matter with low specific angular momentum, and increase for the accretion of material of high specific angular momentum. The quantitative results, however, are found to depend critically on the assumed sizes of the protostars. As well as the effects on mass ratio and separation, the spin angular momentum of the accreted material is examined, and evidence is found that the circumstellar discs formed in a binary system may differ considerably between the two components. The implications for the formation of binary stellar systems are discussed.