On the Initial Mass Function of Low-Metallicity Stars: The Importance of Dust Cooling

The first stars to form in the universe are believed to have distribution of masses biased toward massive stars. This contrasts with the present-day initial mass function, which has a predominance of stars with masses lower than 1 M ☉. Therefore, the mode of star formation must have changed as the universe evolved. Such a transition is attributed to a more efficient cooling provided by increasing metallicity. Especially dust cooling can overcome the compressional heating, which lowers the gas temperature thus increasing its instability to fragmentation. The purpose of this paper is to verify if dust cooling can efficiently cool the gas, and enhance the fragmentation of gas clouds at the early stages of the universe. To confirm that, we calculate a set of hydrodynamic simulations that include sink particles, which represent contracting protostars. The thermal evolution of the gas during the collapse is followed by making use of a primordial chemical network and also a recipe for dust cooling. We model four clouds with different amounts of metals (10–4, 10–5, 10–6 Z ☉, and 0), and analyze how this property affect the fragmentation of star-forming clouds. We find evidence for fragmentation in all four cases, and hence conclude that there is no critical metallicity below which fragmentation is impossible. Nevertheless, there is a clear change in the behavior of the clouds at Z <~ 10–5 Z ☉, caused by the fact that at this metallicity, fragmentation takes longer to occur than accretion, leading to a flat mass function at lower metallicities.