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 { \cal D } _ { cr } = [ 2.6 – 6.3 ] \times 10 ^ { -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 M _ { \odot } and a metallicity of Z \sim 4.5 \times 10 ^ { -5 } Z _ { \odot } 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 M _ { \odot } and 35 M _ { \odot } , the critical dust-to-gas mass ratio can be overcome provided that at least 0.4 M _ { \odot } 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 .
We find that the size distribution of carbon grains is not modified by grain growth because at small densities , below n _ { { H } } \sim 10 ^ { 6 } { cm ^ { -3 } } , carbon atoms have been locked into CO molecules .
Silicates and magnetite grains can experience significant grain growth in the density range 10 ^ { 9 } { cm ^ { -3 } } < n _ { { H } } < 10 ^ { 12 } { cm ^ { -3 } } by accreting gas-phase species ( SiO , SiO _ { 2 } , and Fe ) until their gas-phase abundance drops to zero , reaching condensation efficiencies \approx 1 .
The corresponding increase in the dust-to-gas mass ratio allows dust-induced cooling and fragmentation to be activated at 10 ^ { 12 } { cm ^ { -3 } } < n _ { { H } } < 10 ^ { 14 } { cm ^ { -3 } } , 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 .
We discuss the implication of this finding for the formation of the first low-mass stars in the Universe and derive some minimum critical abundances of refractory elements by our results : [ Mg / H ] _ { cr } = [ -5.02 : -4.73 ] , [ Si / H ] _ { cr } = [ -5.24 : -4.73 ] , and [ Fe / H ] _ { cr } = [ -5.43 : -3.70 ] .