The formation mass of a binary system via fragmentation of a rotating parent core with increasing total mass

We present a set of numerical simulations of the gravitational collapse of a uniform and rotating core, in which azimuthal symmetric mass seeds are initially implemented in order to favor the formation of a dense filament, out of which a binary system may be formed by direct fragmentation. We observe that this binary formation process is diminished when the total mass of the parent core M₀ is increased; then we increase the level of the ratio of rotational energy to the gravitational energy, denoted by β, initially supplied to the rotating core, in order to achieve the desired direct fragmentation of the filament. We measure the binary mass M_f obtained from an initial M₀ and then show a schematic diagram M₀ vs β, where the desired binary configurations are located. We also report some basic physical data of the fragments.