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 cooling by thermal emission. Dust may, however, be evacuated from star-forming clouds due to the radiation force from massive stars. We study here the condition for 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 a weak dependence on cloud radius, while the dust evacuation time is shorter for a cloud with a smaller radius. Dust evacuation, thus, occurs in compact star-forming clouds whose column density is N_H ≃ 10²⁴-10²⁶ cm^-2. The critical halo mass above which dust evacuation occurs is lower for higher formation red shift, e.g. ~10⁹M_⊙ at red shift z ~ 3 and ~10⁷M_⊙ at z ~ 9. In addition, the metallicity of the gas should be less than ~10^-2 Z_⊙, otherwise attenuation by dust reduces the radiation force significantly. From the dust-evacuated gas, massive stars are likely to form, even with a metallicity above ~10^-5 Z_⊙, the critical value for low-mass star formation due to dust cooling. This can explain the dearth of ultra-metal-poor stars with a metallicity lower than ~10^-4 Z_⊙.