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.
