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 one-dimensional numerical hydrodynamics coupled with nonequilibrium chemistry of H2 and HD. It is found that the cloud evolution is governed mainly by the initial central density (nc, 0) and H2 abundance (x). In particular, the evolution of low-density filaments (nc, 0 ≲ 105 cm-3) bifurcates at a threshold H2 abundance of x ≃ 3 × 10-3, beyond which HD cooling overwhelms H2 cooling. The contraction of a filament with nc, 0 ≲ 105 cm-3 and x ≳ x is strongly decelerated when the central density (nc) reaches a critical density of HD at which LTE level populations are achieved, and therefore the filament is expected to fragment at ~107 cm-3. The fragment mass is lowered to be ≈10 M☉. In contrast, the contraction of a filament with nc, 0 ≲ 105 cm-3 and x ≲ x is regulated by H2 cooling. In this case, the filament tends to fragment at lower density as ~104 cm-3 owing to the low critical density of H2, and the fragment mass is as high as ≈102 M☉. For a high-density filament with nc, 0 ≳ 105 cm-3, the temperature stays at a relatively high value because both H2 and HD cooling saturate, and the cloud evolution is governed by H2 cooling. The contraction of a high-density filament is accelerated by effective three-body H2 formation when the density reaches 108-109 cm-3. Fragmentation is not expected to take place until the cloud becomes opaque in H2 lines at nc, 0 ~ 1012-1013 cm-3, so that the fragment mass is reduced to 1-2 M☉. As a result, the stellar initial mass function could be bimodal and deficient in sub-solar mass stars, where the high-mass peak is around 10 or 102 M☉, dependent on nc, 0 and x. If the protogalactic clouds are ionized by UV radiation or strong shocks, the H2 abundance could exceed x ≃ 3 × 10-3 by reactions of H + e → H- + hν and H + H- → H2 + e. The high-mass peak would then be O(10) M☉.