In a low-metallicity gas, rapid cooling by dust thermal emission is considered to induce cloud fragmentation and play a vital role in the formation of low-mass stars (≲ 1 M⊙) in metal-poor environments. We investigate how the growth of dust grains through accretion of heavy elements in the gas phase onto grain surfaces alters the thermal evolution and fragmentation properties of a collapsing gas cloud. We directly calculate grain growth and dust emission cooling in a self-consistent manner. We show that MgSiO3 grains grow sufficiently at gas densities n H = 1010, 1012, and 1014 cm-3 for metallicities Z = 10-4, 10-5, and 10-6 Z ⊙, respectively, where the cooling of the collapsing gas cloud is enhanced. The condition for efficient dust cooling is insensitive to the initial condensation factor of pre-existing grains within the realistic range of 0.001-0.1, but sensitive to metallicity. The critical metallicity is Z ⊙crit ∼ 10-5.5 Z⊙ for the initial grain radius and Z⊙crit ∼ 10-4.5 Z ⊙ for . The formation of a recently discovered low-mass star with extremely low metallicity (≤4.5 × 10-5 Z ⊙) could have been triggered by grain growth.
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