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_c ∼ 10³ cm^-3, we follow the evolution of rotating spherical cores up to the stellar density n_c ≃ 10²² 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 ( β₀ and α₀, respectively), and the amplitude of the bar-mode density perturbation (A_Φ). Cores with rotation β₀ > 10^-6 are found to fragment during the collapse. The fragmentation condition hardly depends on either the initial thermal energy α₀ or amplitude of bar-mode perturbation A_Φ. Since the critical rotation parameter for fragmentation is lower than that expected in first-star formation, binaries or multiples are also common for the first stars.