Evolution of protobinary stars: The separation of equal-mass accreting binaries

Abstract We perform 3D smoothed particle hydrodynamics (SPH) simulations of gas accretion on to binary seeds until the mass, normalized by its initial value, reaches 20. Modeling the beginning of the accretion phase when the fragmentation has already occurred, our initial condition includes a seed binary and a surrounding envelope of self-gravitating isothermal gas with the angular momentum distribution $j \propto M$, where $j$ denotes the specific angular momentum of gas at a cylindrical radius and $M$ depicts the mass contained inside the radius. The results indicate that binary separation increases due to the accretion of mass and angular momentum from the gas. A circumbinary disk forms around binary stars and grows with the increasing binary separation. Both hydrodynamical calculations and semi-analytical investigations reveal that the binary separation, normalized by its initial value, follows a scaling proportional to $f^2$ times the normalized binary mass, where $f \sim 2/3$ corresponds to the ratio of the orbital to the total angular momentum of the binary seeds. Binary separation is sustained exclusively by the orbital angular momentum and not by the spin angular momentum. Furthermore, the case with the angular momentum distribution, $j \propto M^{\delta }$, is examined semi-analytically. The findings indicate that binary separation remains constant for $\delta = 1/2$, increases when $\delta > 1/2$, and decreases when $\delta < 1/2$ as the binary system grows. This dependence of separation evolution on the angular momentum distribution of the envelope suggests that the observed separations of binaries can be explained by the angular momentum distributions of molecular cloud cores.