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 ( \lesssim 1 M _ { \odot } ) 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 { MgSiO _ { 3 } } grains grow sufficiently at gas densities n _ { { H } } = 10 ^ { 10 } , 10 ^ { 12 } , and 10 ^ { 14 } { cm ^ { -3 } } for metallicities Z = 10 ^ { -4 } , 10 ^ { -5 } , and 10 ^ { -6 } Z _ { \odot } , 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 } } \sim 10 ^ { -5.5 } Z _ { \odot } for the initial grain radius r _ { { MgSiO _ { 3 } } , 0 } \lesssim 0.01 { \mu m } and Z _ { { crit } } \sim 10 ^ { -4.5 } Z _ { \odot } for r _ { { MgSiO _ { 3 } } , 0 } \gtrsim 0.1 { \mu m } .
The formation of a recently discovered low-mass star with extremely low metallicity ( \leq 4.5 \times 10 ^ { -5 } Z _ { \odot } ) could have been triggered by grain growth .