The Stellar Initial Mass Function in Primordial Galaxies
Nakamura, Fumitaka, & Umemura, Masayuki
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$_H2$,0). In particular, the evolution of low-density filaments (n$_c,0$<åisebox-0.5ex~10$^5$ cm$^-3$) bifurcates at a threshold H$_2$ abundance of x$_H< SUB>2$,cr\i̊sebox-0.5ex~=3×10 $^-3$, beyond which HD cooling overwhelms H$_2$ cooling. The contraction of a filament with n$_c,0$<\rs̊ebox-0.5ex~10$^5$ cm$^-3$ and x$_H2$,0>\rae̊box-0.5ex\textas ciitildex$_H2$,cr 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 \raib̊ox-0.5ex~10$^7$ cm$^-3$. The fragment mass is lowered to be \raiso̊x-0.5ex~10 M$_solar$. In contrast, the contraction of a filament with n$_c,0$<\raisex̊-0.5ex~10$^5$ cm$^-3$ and x$_H2$,0<\raiseb̊-0.5ex\textas ciitildex$_H2$,cr is regulated by H$_2$ cooling. In this case, the filament tends to fragment at lower density as \raisebo-̊0.5ex~10$^4$ cm$^-3$ owing to the low critical density of H$_2$, and the fragment mass is as high as \raisebox0̊.5ex~10$^2$ M$_solar$. For a high-density filament with n$_c,0$>\raisebox.̊5ex~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$_c,0$\raisebox-5̊ex~10$^12$-10$^13$ cm$^-3$, so that the fragment mass is reduced to 1-2 M$_solar$. 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$_solar$, dependent on n$_c,0$ and x$_H2$,0. If the protogalactic clouds are ionized by UV radiation or strong shocks, the H$_2$ abundance could exceed x$_H2$,cr\raisebox-0e̊x~=3×10$^-3$ by reactions of H+e-->H$^-$+h\ensuremathν and H+H$^-$-->H$_2$+e. The high-mass peak would then be O(10)M$_solar$.