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_csimeq 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_phi). 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_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.