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Protostellar-disc fragmentation across all metallicities

Cosmic metallicity evolution possibly creates the diversity of star formation modes at different epochs. Gravitational fragmentation of circumstellar discs provides an important formation channel of multiple star systems, including close binaries. We here study the nature of disc fragmentation, systematically performing a suite of two-dimensional radiation-hydrodynamic simulations, in a broad range of metallicities, from the primordial to the solar values. In particular, we follow relatively long-term disc evolution over 15 kyr after the disc formation, incorporating the effect of heating by the protostellar irradiation. Our results show that the disc fragmentation occurs at all metallicities $1$--$0$ $Z_{\odot}$, yielding self-gravitating clumps. Physical properties of the clumps, such as their number and mass distributions, change with the metallicity due to different gas thermal evolution. For instance, the number of clumps is the largest for the intermediate metallicity range of $10^{-2}$--$10^{-5}$ $Z_{\odot}$, where the dust cooling is effective exclusively in a dense part of the disc and causes the fragmentation of spiral arms. The disc fragmentation is more modest for $1$--$0.1$ $Z_{\odot}$ thanks to the disc stabilization by the stellar irradiation. Such metallicity dependence agrees with the observed trend that the close binary fraction increases with decreasing metallicity in the range of $1$--$10^{-3}$ $Z_{\odot}$.