One-armed spiral instability in differentially rotating stars

We investigate the dynamical instability of the one-armed spiral m = 1 mode in differentially rotating stars by means of 3 + 1 hydrodynamical simulations in Newtonian gravitation. We find that both a soft equation of state and a high degree of differential rotation in the equilibrium star are necessary to excite a dynamical m = 1 mode as the dominant instability at small values of the ratio of rotational kinetic to gravitational potential energy, T/|W|. We find that this spiral mode propagates outward from its point of origin near the maximum density at the center to the surface over several central orbital periods. An unstable m = 1 mode triggers a secondary m = 2 bar mode of smaller amplitude, and the bar mode can excite gravitational waves. As the spiral mode propagates to the surface it weakens, simultaneously damping the emitted gravitational wave signal. This behavior is in contrast to waves triggered by a dynamical m = 2 bar instability, which persist for many rotation periods and decay only after a radiation reaction-damping timescale.