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 one-dimensional numerical hydrodynamics coupled with nonequilibrium chemistry of H 2 and HD. It is found that the cloud evolution is governed mainly by the initial central density ( n c , 0 ) and H 2 abundance ( x ). In particular, the evolution of low-density filaments ( n c , 0 ≲ 10 5 cm -3 ) bifurcates at a threshold H 2 abundance of x ≃ 3 × 10 -3 , beyond which HD cooling overwhelms H 2 cooling. The contraction of a filament with n c , 0 ≲ 10 5 cm -3 and x ≳ x is strongly decelerated when the central density ( n c ) reaches a critical density of HD at which LTE level populations are achieved, and therefore the filament is expected to fragment at ~10 7 cm -3 . The fragment mass is lowered to be ≈10 M ☉ . In contrast, the contraction of a filament with n c , 0 ≲ 10 5 cm -3 and x ≲ x is regulated by H 2 cooling. In this case, the filament tends to fragment at lower density as ~10 4 cm -3 owing to the low critical density of H 2 , and the fragment mass is as high as ≈10 2 M ☉ . For a high-density filament with n c , 0 ≳ 10 5 cm -3 , the temperature stays at a relatively high value because both H 2 and HD cooling saturate, and the cloud evolution is governed by H 2 cooling. The contraction of a high-density filament is accelerated by effective three-body H 2 formation when the density reaches 10 8 -10 9 cm -3 . Fragmentation is not expected to take place until the cloud becomes opaque in H 2 lines at n c , 0 ~ 10 12 -10 13 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 10 2 M ☉ , dependent on n c , 0 and x . If the protogalactic clouds are ionized by UV radiation or strong shocks, the H 2 abundance could exceed x ≃ 3 × 10 -3 by reactions of H + e → H - + h ν and H + H - → H 2 + e . The high-mass peak would then be O (10) M ☉ .