Growth of dust grains in a low-metallicity gas and its effect on the cloud fragmentation

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_sun) 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 calculate directly grain growth and dust emission cooling in a self-consistent manner. We show that MgSiO3 grains grow sufficiently at gas densities nH = 10^10, 10^12, and 10^14 /cc for metallicities Z = 10^-4, 10^-5, and 10^-6 Zsun, 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 Zcrit ~ 10^-5.5 Zsun for the initial grain radius r_MgSiO3,0 <~ 0.01 um and Zcrit ~ 10^-4.5 Zsun for r_MgSiO3,0 >~ 0.1 um. The formation of a recently discovered low-mass star with extremely low metallicity (<= 4.5x10^-5 Zsun) could have been triggered by grain growth.