Condition for dust evacuation from the first galaxies
  Dust enables low-mass stars to form from low-metallicity gas by inducing
fragmentation of clouds via the cooling by its thermal emission. Dust may,
however, be evacuated from star-forming clouds due to radiation force from
massive stars. We here study the condition for the dust evacuation by comparing
the dust evacuation time with the time of cloud destruction due to either
expansion of HII regions or supernovae. The cloud destruction time has weak
dependence on the cloud radius, while the dust evacuation time becomes shorter
for a cloud with the smaller radius. The dust evacuation thus occurs in compact
star-forming clouds whose column density is $N_{\rm H} \simeq 10^{24} - 10^{26}
~{\rm cm^{-2}}$. The critical halo mass above which the dust evacuation occurs
becomes lower for higher formation redshift, e.g., $\sim 10^{9}~M_{\odot}$ at
redshift $z \sim 3$ and $\sim 10^{7}~M_{\odot}$ at $z \sim 9$. In addition,
metallicity of the gas should be less than $\sim 10^{-2} ~ Z_{\odot}$.
Otherwise the dust attenuation reduces the radiation force significantly. From
the dust-evacuated gas, massive stars are likely to form even with metallicity
above $\sim 10^{-5}~Z_{\odot}$, the critical value for low-mass star formation
due to the dust cooling. This can explain the dearth of ultra-metal poor stars
with the metallicity lower than $\sim 10^{-4}~Z_{\odot}$.
