A one-armed spiral instability has been found to develop in differentially rotating stellar models that have a relatively stiff , n = 1 polytropic equation of state and a wide range of rotational energies .
This suggests that such instabilities can arise in neutron stars that are differentially , although not necessarily rapidly , rotating .
The instability seems to be directly triggered by the presence of a corotation resonance inside the star .
Our analysis also suggests that a resonant cavity resulting from a local minimum in the radial vortensity profile of the star plays an important role in amplifying the unstable mode .
Hence , it appears as through this instability is closely related to the so-called “ Rossby wave instability ” ( 21 ) that has been found to arise in accretion disks .
In addition to the one-armed ( m = 1 ) spiral mode , we have found that higher-order ( m = 2 and m = 3 ) nonaxisymmetric modes also can become unstable if corotation points that resonate with the eigenfrequencies of these higher-order modes also appear inside the star .
The growth rate of each mode seems to depend on the location of its corotation radius with respect to the vortensity profile ( or on the depth of its corotation radius inside the vortensity well ) .
The existence of such instabilities makes the stability criterion for differentially rotating neutron stars non-unique .
Also , the gravitational-waves emitted from such unstable systems generally will not have a monochromatic frequency spectrum .