Another twist in the f-mode instability - differential rotation of stars

The occurrence of an f-mode instability in a newly born uniformly rotating neutron star is in general prevented by the large bulk and shear viscosities of nuclear matter in those conditions and detailed calculations have shown that the instability is suppressed except for very large rotation rates, close to the mass-shedding limit [9]. However, there are elements which have improved our understanding of the instability and have again increased the expectations that the f-mode instability might characterize the earliest life stages of a newly formed neutron star. The first of these new elements was provided by [4, 18, 16] who have shown that, general relativistic effects tend to further destabilize the f-mode, lowering the critical value of the ratio between the stellar rotational kinetic energy and the absolute value of the gravitational energy, at which the secular f-mode instability is triggered. The second element was provided by [15], whose fully general relativistic hydrodynamical simulations have shown that the remnants of binary neutron star mergers could be, at least for polytropic equations of state, rapidly and differentially rotating stars. In addition to this, [12] have recently computed the structure of objects formed in accretion-induced collapse of rotating white dwarfs and found that these objects can rotate extremely rapidly and differentially.

In this revised picture, we have computed the eigenfrequencies of f-modes and determined the secular stability limits for rapidly rotating relativistic stars with differential rotation.