Slowly rotating relativistic stars. V. Static stability analysis of n=3/2 polytropes

The static stability analysis of slowly and uniformly rotating relativistic stars is applied to the n-3/2 Tooper polytropes corresponding to an ideal nonrelativistic neutron gas. The method tests the stability of a sequence of stellar models against the modes of oscillation which correspond to radial modes in a nonrotating star. It involves a comparison of the uniformly rotating models to be tested with a sequence of models having a specified differential rotation. The equations of structure of these differentially rotating stars are derived and integrated, and the critical central density dividing the stable models from the unstable models is determined