The discovery of a low-mass star with such low metallicity as < 4.5x10^{ -5} Z_sun reveals the critical role of dust in the formation of extremely metal-poor stars. In this paper we explore the effect of the growth of dust grains through accretion of gaseous refractory elements in very low-metallicity pre-stellar cores on the cloud fragmentation induced by the dust emission cooling. Employing a simple model of grain growth in a gravitationally collapsing gas, we show that Fe and Si grains can grow efficiently at hydrogen densities of ~10^{ 10}-10^{ 14} cm^{ -3} in the clouds with metal abundances of -5 <~ [Fe, Si/H] <~ -3. The critical metal number abundances, above which the grain growth could induce the fragmentation of the gas clouds, are estimated to be A_{ crit} ~ 10^{ -9}-10^{ -8}, unless the initial grain radius is too large (>~ 1 um) or the sticking probability is too small (<~ 0.01). We find that even if the initial dust-to-gas mass ratio is well below the minimum value required for the dust-induced fragmentation, the grain growth increases the dust mass high enough to cause the gas fragmentation into sub-solar mass clumps. We suggest that as long as the critical metal abundance is satisfied, the grain growth could play an important role in the formation of low-mass stars with metallicity as low as 10^{ -5} Z_sun.
Categories: astro-ph.SR astro-ph.GA