Homogeneous spheres with constant adiabatic index

Compressible homogeneous spheres with constant adiabatic index gamma were s tudied for their dynamical stability by Chandrasekhar and he found that for each value of u (= mass to size ratio), there is a value of gamma = gamma (c), such that for gamma < gamma (c), the configuration is dynamically unst able. On examining the properties of the Chandrasekhar's spheres (homogeneo us spheres with constant gamma) it is found that these spheres are non-isen tropic, and the speed of sound within these spheres is finite. The authors find that (i) for the causality condition to be fulfilled throughout the co nfiguration, the value of gamma less than or equal to [2/(surface redshift) ], (ii) for a given value of u, the binding coefficient, alpha (r) = (M-r - M)/M, vanishes for some value of gamma = gamma (b) and for all the values o f gamma < gamma (b) the configurations are unbound, and (iii) for u less th an or equal to (1/3), one can find configurations which are bound, dynamica lly stable, and the speed of sound is less than that of light throughout th e configuration, whereas, for u > (1/3), the physically viable models of ho mogeneous density distribution are not possible. If the configuration is co nsidered to be isentropic, then both gamma and the speed of sound become in finite throughout the configuration.