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 $\sim 10^{-4}~Z_{\odot}$.