Numerical simulations of oscillating and differentially rotating neutron stars

TL;DR

The paper extends the ROXAS code to model oscillating, differentially rotating neutron stars within the conformal flatness approximation, enabling systematic study of both axisymmetric and non-axisymmetric oscillation modes under KEH differential rotation. By implementing a well-balanced formulation and differential rotation in LORENE, the authors validate axisymmetric frequencies against literature and, for the first time in CFC, report non-axisymmetric mode frequencies. A key finding is that the secondary fundamental mode seen in the Cowling approximation is an artifact and disappears in full dynamical spacetimes, while non-axisymmetric frequencies $^2f_2$ and $^2f_{-2}$ are newly reported in CFC. The work demonstrates that ROXAS remains a fast, versatile tool for exploring post-merger neutron-star remnants and their gravitational-wave signatures, with future work aimed at more realistic rotation laws and equations of state.

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.

Figures (9)

• Figure 1: Radial profile in different directions of the initial enthalpy perturbation of the non-axisymmetric B4 simulations.
• Figure 2: Slice in the $xz$ plane of the initial enthalpy perturbation of the non-axisymmetric B4 simulations. The green dashed lines correspond to the boundaries between the different domains of the metric grid, as described in Subsection \ref{['ssec:sim_params']}.
• Figure 3: Angular velocity profiles in different directions for an unperturbed B4 simulation. The solid lines correspond to the initial profiles, while the superimposed points are plotted after 25 ms of dynamical evolution in CFC.
• Figure 4: GW spectrum of the non-axisymmetric B4 simulation in the Cowling approximation.
• Figure 5: Fourier spectrum of the $l=m=0$$R_S$ coefficient for the non-axisymmetric B4 simulation in the Cowling approximation (left) and a dynamical spacetime (right).