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We perform a set of cosmological simulations of early structure formationwith incorporating baryonic streaming motions. We present a case where asignificantly elongated gas cloud with $\sim\!10^4\,$solar masses (${\rmM_\odot}$) 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 filamentarycloud to a temperature of $\sim\!10,000\,$Kelvin. The gas cloud cools rapidlyby atomic hydrogen cooling, and then by molecular hydrogen cooling down to$\sim\!400\,$Kelvin. The rapid decrease of the temperature and hence of theJeans mass triggers fragmentation of the filament to yield multiple gas clumpswith a few hundred solar masses. We estimate the mass of the primordial starformed in each fragment by adopting an analytic model based on a large set ofradiation hydrodynamics simulations of protostellar evolution. The resultingstellar masses are in the range of $\sim\!50$-$120\,{\rm M_\odot}$. The massivestars gravitationally attract each other and form a compact star cluster. Wefollow the dynamics of the star cluster using a hybrid $N$-body simulation. Weshow that massive star binaries are formed in a few million years throughmulti-body interactions at the cluster center. The eventual formation of theremnant black holes will leave a massive black hole binary, which can be aprogenitor of strong gravitational wave sources similar to those recentlydetected by the Advanced Laser Interferometer Gravitational-Wave Observatory(LIGO).

Formation of the first star clusters and massive star binaries by fragmentation of filamentary primordial gas clouds