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Can the Growth of Dust Grains in Low-Metallicity Star-Forming Clouds Affect the Formation of Metal-Poor Low-Mass Stars?

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.