A STUDY OF DYNAMICAL STABILITY OF A ROTATING N=1.5 POLYTROPE

A hydrodynamic code is used to study the growth of three-dimensional i nstability for a rapidly rotating n = 1.5 polytrope (this equation of state is valid for a degenerate nonrelativistic free Fermi gas, e.g., in a neutron star) with a rotation law such that the ratio of the cent rifugal-to-gravitational force in the equatorial plane is constant for the dimensionless rotational energies beta = -E(rot)/W = 0.268 and 0. 313. The m = 2 mode is shown to grow for the initial data with beta = 0.313. The sectorial mode in an approximate analytical tensor virial a pproach corresponds to this type of perturbation. The oscillation freq uency found for the in = 2 mode for beta = 0.313 and the stability of the configuration with beta = 0.268 are consistent with the results of the tensor virial approach. These calculations also refine independen t numerical calculations of the stability of a rotating polytrope and confirm the legitimacy of the stability criterion beta less than or eq ual to 0.27 used in a previous study to determine the range of paramet ers for a collapsing stellar core which may undergo a two-stage collap se and supernova explosion, The collapse of a rotating stellar core is expected to be studied later in order to check this mechanism directl y.