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 D_cr = [2.6-6.3] × 10^{-9}. The recently discovered Galactic halo star SDSS J102915+172927 has a stellar mass of 0.8 M_⊙ and a metallicity of Z ∼ 4.5 × 10^-5 Z_⊙ and represents an optimal candidate for the dust-induced low-mass star formation. Indeed, the critical dust-to-gas mass ratio can be overcome provided that at least 0.4 M_⊙ of dust condenses in Pop III supernova ejecta, allowing for moderate destruction by the reverse shock. Here, we show that grain growth during the collapse of the parent gas cloud is sufficiently rapid to activate dust cooling and fragmentation into low-mass stars, even if dust formation in the first supernovae is less efficient or strong dust destruction does occur. We find that carbon grains do not experience grain growth because at densities below n_H ∼ 10⁶ cm^-3 carbon atoms are locked into CO molecules. Silicates and magnetite grains accrete gas-phase species in the density range 10⁹ < n_H < 10¹² cm^-3, 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 10¹² < n_H < 10¹⁴ cm^-3, before the collapsing cloud becomes optically thick to continuum radiation.