# Achievements & Publications

## On the Initial Mass Function of Population III Stars

### Nakamura, Fumitaka,   & Umemura, Masayuki

##### Abstract
The collapse and fragmentation of filamentary primordial gas clouds are explored using one- and two-dimensional hydrodynamical simulations coupled with the nonequilibrium processes of hydrogen molecule formation. The cloud evolution is computed from the initial central density n$_c$=10-10$^6$ cm$^-3$. The simulations show that depending on the initial density, there are two occasions for the fragmentation of primordial filaments. If a filament has relatively low initial density such as n$_c$<åisebox-0.5ex~10$^5$ cm$^-3$, the radial contraction is slow as a result of less effective H$_2$ cooling and appreciably decelerates at densities higher than a critical density, where LTE populations are achieved for the rotational levels of H$_2$ molecules and the cooling timescale becomes accordingly longer than the free- fall timescale. This filament tends to fragment into dense clumps before the central density reaches 10$^8$-10$^9$ cm$^-3$, where H$_2$ cooling by three-body reactions is effective and the fragment mass is more massive than some tens of M$_solar$. In contrast, if a filament is initially as dense as n$_c$>\i̊sebox-0.5ex~10$^5$ cm$^-3$, the more effective H$_2$ cooling with the help of three-body reactions allows the filament to contract up to n\rs̊ebox-0.5ex~10$^12$ cm$^-3$. After the density reaches n\rae̊box-0.5ex~10$^12$ cm$^-3$, the filament becomes optically thick to H$_2$ lines and the radial contraction subsequently almost stops. At this final hydrostatic stage, the fragment mass is lowered down to \raib̊ox-0.5ex~1 M$_solar$ because of the high density of the filament. The dependence of the fragment mass upon the initial density could be translated into the dependence on the local amplitude of random Gaussian density fields or the epoch of the collapse of a parent cloud. Hence, it is predicted that the initial mass function of Population III stars is likely to be bimodal with peaks of \raiso̊x-0.5ex~10$^2$ and \raisex̊-0.5ex~1 M$_solar$, where the relative heights could be a function of the collapse epoch. Implications for the metal enrichment by Population III stars at high redshifts and baryonic dark matter are briefly discussed.