Conditions for the Formation of First-Star Binaries

The fragmentation process of primordial-gas cores during prestellar collapse is studied using three-dimensional nested-grid hydrodynamics. Starting from the initial central number density of n \sim10^3 cm^-3, we follow the evolution of rotating spherical cores up to the stellar density n \simeq 10^{22} cm^-3. An initial condition of the cores is specified by three parameters: the ratios of the rotation and thermal energies to the gravitational energy (\beta_0, and \alpha_0, respectively), and the amplitude of the bar-mode density perturbation (A_\phi). Cores with rotation \beta_0 > 10^{-6} are found to fragment during the collapse. The fragmentation condition hardly depends on either the initial thermal energy \alpha_0 or amplitude of bar-mode perturbation A_\phi. Since the critical rotation parameter for fragmentation is lower than that expected in the first star formation, binaries or multiples are also common for the first stars.