The Formation of Population I Stars: Part I. Gravitational Contraction

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Abstract
The present paper is preliminary to the second part in which it will be suggested that the gravitational contraction that is primarily significant for the formation of Population I stars is that of the material destined to form a cluster of such stars. The relevant type of gravitational instability is that recently studied by Ebert and by Bonnor, which concerns material under external pressure. A more elementary treatment than theirs is here developed from a general form of the virial theorem. This shows that the essential features of their results hold good under somewhat relaxed conditions which may be more like those encountered in applications. But also it shows that if we employ the exact results of Ebert and Bonnor we may have to regard them as applying to somewhat larger masses (up to about fifty per cent larger) than those to which they explicitly refer, on account of incomplete realization of the theoretical conditions. The present treatment appears to afford some additional physical insight into the results obtained by Ebert and Bonnor and their relation to other criteria for gravitational instability. This is aided by its extension to cylindrical and plane-stratified distributions, which had been shown by Ebert to provide instructive comparisons. Among more detailed results we exhibit the behaviour for varying temperature of isothermal gravitating material under given external pressure and we note some numerical results required for subsequent use.

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