##### Xiaoyi Xie (University of Southampton)

Using nonlinear, fully relativistic, simulations we investigate the dynamics and gravitational-wave signature associated with instabilities in neutron star post-merger remnants. For simplified models of the remnant, we establish the presence of instability in stars with moderate T/|W|, the ratio between the kinetic and the gravitational potential energies. Detailed analysis of the density oscillation pattern reveals a local instability in the inner region of the more realistic differential rotation profile. We apply Rayleigh’s inflection theorem and Fjørtoft’s theorem to analyze the stability criteria concluding that this inner local instability originates from a shear instability close to the peak of the angular velocity profile and that it later evolves into a fast-rotating m 1⁄4 2 oscillation pattern. We discuss the importance of the presence of a corotation point in the fluid, its connection with the shear instability, and comparisons to the Rossby wave and Papaloizou-Pringle instabilities considered in the wider literature.

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