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) similar to 10(3) cm(-3), we follow the evolution of rotating spherical cores up to the stellar density n(c) similar or equal to 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 (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 first-star formation, binaries or multiples are also common for the first stars.