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An Upper Mass Bound of a Two-Component Protogalaxy

We investigate the physical properties of a two-component virialized protogalaxy comprising a hot gas and cold clouds which are in pressure equilibrium under the assumptions that the protogalaxy is both spherical and homogeneous. Two conditions which we adopt are that the protogalaxy is in virial equilibrium and that the cooling time is less than the dynamical time. It is found that there exists an upper mass bound for such a two-component protogalaxy when the cloud mass is comparable to or greater than that of hot gas. We also consider the stability of the cold cloud against the Jeans instability and Kelvin-Helmholtz instability.