The Stellar Initial Mass Function in Primordial Galaxies

In the context of star formation through fragmentation of an extremely metal-deficient protogalactic cloud, the gravitational collapse of filamentary gas clouds is explored with 1D numerical hydrodynamics coupled with non-equilibrium chemistry of H${}_2$ and HD. It is found that the cloud evolution is governed mainly by the initial central density ($n_{\mathrm{c},0}$) and H${}_2$ abundance ($x_{{\mathrm{H}}_2,0}$). In particular, the evolution of low-density filaments bifurcates at a threshold H${}_2$ abundance of $x_{\rm H_2,cr}\simeq 3 \times 10^{-3}$,beyondwhichHDcoolingoverwhelmsH$2$ cooling. The contraction of a low density filament with $x{\rm H_2, 0}\gtrsim x_{\rm H_2,cr}$isstronglydeceleratedwhen$n_{\rm c}$ reaches a critical density of HD, and the filament is expected to fragment at $\sim {10}^7$ cm${}^{-3}$. The fragment mass is lowered to be $\approx 10M_{\odot }$. In contrast, the contraction of a low density filament with $x_{\rm H_2, 0}\lesssim x_{\rm H_2,cr}$isregulatedbyH$_2$ cooling. In this case, the fragment mass is as high as $\approx {10}^2{M}_{\odot }$. For a high-density filament, the cloud evolution is governed by H${}_2$ cooling. The fragmentation is not expected to take place until the cloud becomes opaque in H${}_2$ lines at $n_{\mathrm{c},0}\sim {10}^{12-13}$ cm${}^{-3}$, so that the fragment mass is reduced to 1-2 M${}_{\odot }$. As a result, the stellar IMF could be bimodal and deficient in sub-solar mass stars, where the high mass peak is around $10M_{\odot }$ or ${10}^2{M}_{\odot }$, dependently on $n_{\mathrm{c},0}$ and $x_{{\mathrm{H}}_2,0}$.