Formation of Gravitationally Bound Primordial Gas Clouds

Abstract

The formation of gravitationally bound systems from primordial gas is studied by . means of Tolman's solution for dust-like matter. The critical values of density contrast and its growth rate at an initial epoch are derived, which are necessary for an inhomogeneity to condense into a bound system before the appearance of the oldest stars. The matter distributions in an . isolated inhomogeneity and an inhomogeneity included in a larger one (which will be a cluster of gas clouds) are followed with time by assuming simple models for inhomogeneities, and it is shown how the bound region spreads outwards. Moreover, the minimum mass of fragments into which the gas clouds may break up is examined. The formation of galaxies which are dispersed everywhere at present in the universe has been studied by many authors. Some of them have assumed that small density fluctuations in an early stage of cosmic evolution grow owing to gravitational instability, until they condense into protogalaxies. However, on Lifshitz's assumption!) that the early stage was very quiet and the fluctua­ tions were statistical, gravitational instability was not effective. This is because the density contrasts of the statistical fluctuations corresponding to galaxies are too small (r-J 10- 34 ) to grow to gravitationally bound systems within the cosmic age. The linearized theories were sufficient for the description of such small fluctuations. After Lifshitz, the behavior of the fluctuations has been studied successively in the linear approximation,2) while Lifshitz's assumption was not always used. On the other hand, it has been assumed that an early stage of the UnIverse was very turbulent and density fluctuations were not small. S ) At the stage when radiation density was larger than matter density and matter was wholly ionized, matter was strongly kicked by photon particles and hindered from condensing. But, once matter was neutrarized, density fluctuations condensed promptly into bound systems. However, we do not know at present how quiet or turbulent the early stages were. Accordingly, still we could assume the existence of fluctuations with vari­ ous amplitudes. In the process of their condensation, gravitation would have played the main role, and, as the density contrasts increased to the order o£