Dynamics of Self-Gravitating Gaseous Spheres--II: Collapses of Gas Spheres with Cooling and the Behaviour of Polytropic Gas Spheres

Abstract

Numerical integrations of the full non-linear hydrodynamic equations are given for a number of different self-gravitating flows with spherical symmetry. The collapse of a sphere of gas to form a galaxy is studied under the effects of cooling by bremsstrahlung and recombination radiation and heating by cosmic rays and the results show a state of free fall soon develops. The collapse of a Bok globule to form a star is also computed under the effects of cosmic ray heating and ionic cooling. In this case it is found that the flow is essentially similar to that obtained assuming isothermality. The behaviour of adiabatic spheres with different values of γ are exlored and here the results show that over-reliance on energy arguments leads to a false picture of the behaviour of γ=4/3 spheres. It is also suggested that the hydrodynamics of the centre of a variable star may be of more importance than hitherto supposed. Finally and of most general significance, self-gravitating flows are classified according to various dimensionless ratios governing their behaviour. The effects of these ratios are discussed and a 'dimensionless cooling time' and a 'Jeans number' are defined. The effect on thermal instability of self-gravitation is also discussed and a criterion for instability is given.