Numerical simulations of oscillating and differentially rotating neutron stars

Abstract: The remnants of binary neutron star mergers are expected to be massive, rapidly rotating stars whose oscillations produce gravitational waves in the kilohertz band. The degree of differential rotation and the rotation profiles strongly influence their structure, stability and oscillation spectrum, and must therefore be taken into account when modeling their dynamics. We extend the pseudospectral code ROXAS (Relativistic Oscillations of non-aXisymmetric neutron stArS) to enable the dynamical evolution of oscillating, differentially rotating neutron stars. Using the updated code, we aim to study the star's oscillation frequencies. We extend the previous formalism, based on primitive variables and the conformal flatness approximation, to differential rotation. Within this framework, we run a series of axisymmetric and non-axisymmetric simulations of perturbed, differentially rotating neutron stars with different rotation rates, and extract their oscillation frequencies. Axisymmetric modes, as well as those under the Cowling approximation, show excellent agreement with published results. We show that the secondary fundamental mode in the Cowling approximation is an artifact that does not appear in dynamical spacetimes. In addition, we provide, for the first time, frequency values for non-axisymmetric modes in differentially rotating configurations evolved in conformal flatness. This extension broadens the range of physical scenarios that can be studied with ROXAS, and represents a step toward more realistic modeling of post-merger remnants and their gravitational-wave emission.