Low-$T/|W|$ instabilities in differentially rotating neutron stars resembling merger remnants

Abstract

We construct constant rest-mass sequences of equilibrium models of differentially rotating neutron stars which resemble binary neutron star post-merger remnants. For a more realistic description of the post-merger remnant, we impose that each model carries approximately $95\%$ of the angular momentum that a binary system with the same total rest-mass has at the moment of merging, based on an empirical relation informed from neutron star merger simulations. We account for equation of state effects by employing two distinct microphysical descriptions for high density matter. We dynamically evolve the equilibrium models with a three-dimensional general relativistic hydrodynamics code that employs the conformal flatness approximation. We investigate the connection between the occurrence of the instability and the existence of corotation radii within the stellar configurations and determine the instability window for both equation of state sequences. The occurrence of low-$T/|W|$ instabilities leads to pronounced gravitational wave emission in the range $0.13 \lessapprox\beta \lessapprox 0.2$, while models outside this range exhibit less pronounced features in the gravitational wave spectrum. The prominence of gravitational wave emission is primarily determined by $\beta$, while the equation of state seems to have a more minor effect. We present correlations between the strength of the gravitational wave emission associated with the instability and properties of the equilibrium models. Stellar configurations modelled by different equations of state display differences in the timescales over which the various dynamical features develop, as well as whether they exhibit a pronounced $m=1$ deformation. Potential relations between the instability growth timescales and properties of the stellar models are studied.