Maximum mass and stability of differentially rotating neutrons stars

We present our study of stability of differentially rotating, axisymmetric neutron stars described by a polytropic equation of state with $\mathrm{\Gamma }=2$. We focus on quasi-toroidal solutions with a degree of differential rotation $\tilde{A}=1$. Our results show that for a wide range of parameters hypermassive, quasi-toroidal neutron stars are dynamically stable against quasi-radial perturbations, which may have implications for newly born neutron stars and binary neutron stars mergers.