The Formation Mass of a Binary System via Fragmentation of a Rotating Parent Core with Increasing Total Mass

Recent VLA and CARMA observations have shown proto-stars in binaries with unprecedented resolution. Specifically, the proto-stellar masses of systems such as CB230 IRS1 and L1165-SMM1 have been detected in the range of $0.1-0.25 \, M_{\odot}$. These are much more massive than the masses generally obtained by numerical simulations of binary formation, around $0.01 \, M_{\odot}$. Motivated by these discrepancies in mass, in this paper we study the formation mass of a binary system as a function of the total mass of its parent core. To achieve this objective, 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 first observed that this binary formation process is diminished when the total mass of the parent core $M_0$ is increased; then we increased the level of the ratio of kinetic energy to the gravitational energy, denoted by $\beta$, initially supplied to the rotating core, in order to achieve the desired direct fragmentation of the filament. Next, we found that the mass of the binary fragment increases with the mass of the parent core, as expected. In this paper we confirm this expectation and also measure the binary mass $M_f$ obtained from an initial $M_0$. We then show a schematic diagram $M_0$ vs $\beta$, where the desired binary configurations are located while the ratio of the thermal energy to the gravitational energy $\alpha$ is kept fixed. We also report some basic physical data of the proto-stellar fragments that form the binary system, including the formation mass $M_f$, and its corresponding $\alpha_f$ and $\beta_f$.