The Stellar Initial Mass Function in Primordial Galaxies

Abstract

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 $x_{{\mathrm{H}}_2,\mathrm{cr}}\simeq 3\times 10^{-3}$, beyond which HD cooling overwhelms H${}_2$ cooling. The contraction of a low density filament with $x_{{\mathrm{H}}_2,0}\gtrsim x_{{\mathrm{H}}_2,\mathrm{cr}}$ is strongly decelerated when $n_{\mathrm{c}}$ 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 $x_{{\mathrm{H}}_2,0}\lesssim x_{{\mathrm{H}}_2,\mathrm{cr}}$ is regulated by H${}_2$ 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 $x_{{\mathrm{H}}_2,0}$.

10 pages, 6 figures, accepted by ApJ

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