Dynamical stability of hypermassive neutron stars against quasi-radial perturbations

The dynamical stability of differentially rotating neutron stars, including hypermassive neutron stars, is of paramount importance in understanding the fate of the post-merger remnant of binary neutron stars mergers and the formation of a black hole during core collapse supernovae. We study systematically the dynamical stability of differentially rotating neutron stars within a broad range of masses, rotation rates and degrees of differential rotation, modeled as polytropes with $Γ=2$. We pay particular attention to quasi-toroidal configurations that are outside the parameter space region explored in previous works. We estimate the limits of the region of stability against quasi-radial perturbations by performing an extensive set of numerical simulations. We find that some of the stability criteria proposed in the past are not sufficient nor necessary to determine stability if differential rotation is present and propose a new more general criterion. We show that there is a large parameter space that allows for quasi-toroidal configurations that will not collapse immediately to a black hole and that can sustain masses up to $\sim 2.5$ times the maximum mass of a non-rotating neutron star.