The concept of reduced variables is revisited with regard to van der Waals’ theory and an application is made to polytropic spheres, where the reduced radial coordinate is , R radius, and the reduced density is , central density. Reduced density profiles are plotted for several polytropic indexes within the range, 0≤n≤5, disclosing two noticeable features. First, any point of coordinates, (w, v), 0≤w≤1, 0≤v≤1, belongs to a reduced density profile of the kind considered. Second, sufficiently steep i.e. large reduced density profiles exhibit an oblique inflection point, where the threshold is found to be located at n=nth=0.888715. Reduced pressure profiles,, central pressure, Lane-Emden fucntions, , and polytropic curves,?q=q(v), are also plotted. The method can be extended to nonspherical polytropes with regard to a selected direction,.?The results can be extended to polytropic spheres made of collisionless particles, for polytropic index within a more restricted range,?1/2≤n≤5 .
展开▼
