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We investigate the formation of dust in a stellar wind during thered-supergiant (RSG) phase of a very massive Population III star with thezero-age main sequence mass of 500 M_sun. We show that, in a carbon-rich windwith a constant velocity, carbon grains can form with a lognormal-like sizedistribution, and that all of the carbon available for dust formation finallycondense into dust for wide ranges of the mass-loss rate ((0.1-3)x10^{-3} M_sunyr^{-1}) and wind velocity (1-100 km s^{-1}). We also find that theacceleration of the wind driven by newly formed dust suppresses the graingrowth but still allows more than half of gas-phase carbon to be finally lockedup in dust grains. These results indicate that at most 1.7 M_sun of carbongrains can form in total during the RSG phase of 500 M_sun Population IIIstars. Such a high dust yield could place very massive primordial stars asimportant sources of dust at the very early epoch of the universe if theinitial mass function of Population III stars was top-heavy. We also brieflydiscuss a new formation scenario of carbon-rich ultra-metal-poor starsconsidering the feedback from very massive Population III stars.

Dust Production Factories in the Early Universe: Formation of Carbon Grains in Red-supergiant Winds of Very Massive Population III Stars