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Dust grain growth and the formation of the extremely primitive star SDSS J102915+172927

Dust grains in low-metallicity star-forming regions may be responsible for the formation of the first low-mass stars. The minimal conditions to activate dust-induced fragmentation require the gas to be pre-enriched above a critical dust-to-gas mass ratio Dcr=[2.6--6.3]x10^-9 with the spread reflecting the dependence on the grain properties. The recently discovered Galactic halo star SDSS J102915+172927 has a stellar mass of 0.8 Msun and a metallicity of Z=4.5x10^-5 Zsun and represents an optimal candidate for the dust-induced low-mass star formation. Indeed, for the two most plausible Population III supernova progenitors, with 20 Msun and 35 Msun, the critical dust-to-gas mass ratio can be overcome provided that at least 0.4 Msun of dust condenses in the ejecta, allowing for moderate destruction by the reverse shock. Here we show that even if dust formation in the first supernovae is less efficient or strong dust destruction does occur, grain growth during the collapse of the parent gas cloud is sufficiently rapid to activate dust cooling and likely fragmentation into low-mass and long-lived stars. Silicates and magnetite grains can experience significant grain growth in the density range 10^9 /cc < nH<10^12 /cc by accreting gas-phase species (SiO, SiO2, and Fe) until their gas-phase abundance drops to zero, reaching condensation efficiencies =1. The corresponding increase in the dust-to-gas mass ratio allows dust-induced cooling and fragmentation to be activated at 10^12 /cc < nH < 10^14 /cc, before the collapsing cloud becomes optically thick to continuum radiation. We show that for all the initial conditions that apply to the parent cloud of SDSS J102915+172927, dust-driven fragmentation is able to account for the formation of the star.