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 with incorporating baryonic streaming motions. We present a case where a significantly elongated gas cloud with $\sim\!10^4\,$solar masses (${\rm M_\odot}$) is formed in a pre-galactic ($\sim\!10^7\,{\rm M_\odot}$) dark halo. The gas streaming into the halo compresses and heats the massive filamentary cloud to a temperature of $\sim\!10,000\,$Kelvin. The gas cloud cools rapidly by atomic hydrogen cooling, and then by molecular hydrogen cooling down to $\sim\!400\,$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 $\sim\!50$-$120\,{\rm M_\odot}$. 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).