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Recent VLA and CARMA observations have shown proto-stars in binaries withunprecedented resolution. Specifically, the proto-stellar masses of systemssuch 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 obtainedby numerical simulations of binary formation, around $0.01 \, M_{\odot}$.Motivated by these discrepancies in mass, in this paper we study the formationmass of a binary system as a function of the total mass of its parent core. Toachieve this objective, we present a set of numerical simulations of thegravitational collapse of a uniform and rotating core, in which azimuthalsymmetric mass seeds are initially implemented in order to favor the formationof a dense filament, out of which a binary system may be formed by directfragmentation. We first observed that this binary formation process isdiminished when the total mass of the parent core $M_0$ is increased; then weincreased the level of the ratio of kinetic energy to the gravitational energy,denoted by $\beta$, initially supplied to the rotating core, in order toachieve the desired direct fragmentation of the filament. Next, we found thatthe mass of the binary fragment increases with the mass of the parent core, asexpected. In this paper we confirm this expectation and also measure the binarymass $M_f$ obtained from an initial $M_0$. We then show a schematic diagram$M_0$ vs $\beta$, where the desired binary configurations are located while theratio of the thermal energy to the gravitational energy $\alpha$ is kept fixed.We also report some basic physical data of the proto-stellar fragments thatform the binary system, including the formation mass $M_f$, and itscorresponding $\alpha_f$ and $\beta_f$.

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