Secondary instability of Jeans mode in a gravitating fluid with uniform rotation

Abstract

An axisymmetric rotating gas in a gravitational field is examined for its stability to two dimensional disturbances with first azimuthal mode. It is shown that a quasi-equilibrium is established when pressure and Coriolis force act against primary Jeans instability. A linear perturbation on this inhomogeneous equilibrium gives rise to secondary instability, which grows differently from homogeneous case. A stationary phase integral method demonstrates that the instability grows algebraically due to the free energy associated with the axisymmetric equilibrium. This secondary Jeans instability may have some bearing with the structure formations in the universe.