Generalized polytropes: Stellar structure with a boltzmann factor

In order to study the structure of a chemically homogeneous star in equilibrium, a density profile of the form T ^N exp(–µm(–)/kT) is suggested. As for polytropes, qualitative aspects of the resulting stellar model can be discussed analytically. In particular it is shown that one reobtains forN=3 Eddington's standard model, whereas forN<3 nearly polytropic models result. WhenN>3, the effective polytropic index does vary appreciably over the star. Numerical results indicate that the proposed density profile is quite reasonable in view of the simplicity of the model. From a comparison of the degree of precision of a polytropic approximation with that of the newly proposed model it follows that the new approximation is definitely better than the polytropic one. It is suggested that the model may be useful to study the structure of stellar clouds, clusters and (spherical) galaxies.Now at Department of Applied Mathematics, Queen Mary College, University of London, England.