Formation of the First Star Clusters and Massive Star Binaries by Fragmentation of Filamentary Primordial Gas Clouds

We perform a set of cosmological simulations of early structure formation incorporating baryonic streaming motions. We present a case where a significantly elongated gas cloud with similar to 10(4) solar mass (M-circle dot) is formed in a pre-galactic (similar to 10(7) M-circle dot) dark halo. The gas streaming into the halo compresses and heats the massive filamentary cloud to a temperature of similar to 10,000 Kelvin. The gas cloud cools rapidly by atomic hydrogen cooling, and then by molecular hydrogen cooling down to similar to 400 Kelvin. The rapid decrease of the temperature and hence of the Jeans mass triggers fragmentation of the filament to yield multiple gas clumps with a few hundred solar masses. We estimate the mass of the primordial star formed in each fragment by adopting an analytic model based on a large set of radiation hydrodynamics simulations of protostellar evolution. The resulting stellar masses are in the range of similar to 50-120 M-circle dot. The massive stars gravitationally attract each other and form a compact star cluster. We follow the dynamics of the star cluster using a hybrid N-body simulation. We show that massive star binaries are formed in a few million years through multi-body interactions at the cluster center. The eventual formation of the remnant black holes will leave a massive black hole binary, which can be a progenitor of strong gravitational wave sources similar to those recently detected by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO).