One-armed Spiral Instability in Differentially Rotating Stars

We investigate the dynamical one-armed spiral instability in differentially rotating stars with both eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We find that the one-armed spiral mode is generated around the corotation radius of the star, and the distribution of angular momentum shifts inwards the corotation radius during the growth of one-armed spiral mode. We also find by investigating the distribution of the canonical angular momentum density that the low T/|W | dynamical instability for both m = 1 and m = 2 mode, where T is the rotational kinetic energy and W is the gravitational potential energy, is generated around the corotation point. Finally, we discuss the feature of gravitational waves generated from these modes. 1