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Non-axisymmetric dynamical instability of differentially rotating, self-gravitating masses


 We investigate the dynamical stability of differentially rotating, self-gravitating, homogeneous masses. Besides the classical bar-like instability we obtain a new non-axisymmetric Kelvin-Helmholtz-like instability which resembles the Papaloi-zou-Pringle instability in shearing accretion tori. We define the flattening parameter, f, as the ratio of the polar to the equatorial radius. The growth-rate curve can be divided into two components. For low angular velocities (f ≤ 1), the instability grows on a linear time-scale. The growth rate then rises towards a peak value. This occurs near the point where the uniformly rotating Maclaurin sequence exhibits a non-axisymmetric bifurcation point. For m = 2 this is the Jacobi bifurcation point. The instability is reduced for small values of f due to the stabilizing effect of the gravitational force. The results are almost independent of the form of the rotation law. Maximum instability occurs for intermediate values of m. A comparison is made with results obtained in the absence of self-gravitation. We discuss possible implications on stellar evolution