## Title: Stability of Neutron Star Remnants from Binary Mergers: A Roadmap for Future

arXiv:2403.05642v1 Announce Type: new

Abstract: Binary neutron star mergers produce massive, hot, rapidly differentially rotating neutron star remnants; electromagnetic and gravitational wave signals associated with the subsequent evolution depend on the stability of these remnants. Stability of relativistic stars has previously been studied for uniform rotation and for a class of differential rotation with monotonic angular velocity profiles. Stability of those equilibria to axisymmetric perturbations was found to respect a turning point criterion: along a constant angular momentum sequence, the onset of unstable stars is found at maximum density less than but close to the density of maximum mass. In this paper, we test this turning point criterion for non-monotonic angular velocity profiles and non-isentropic entropy profiles, both chosen to more realistically model post-merger equilibria. Stability is assessed by evolving perturbed equilibria in 2D using the Spectral Einstein Code. We present tests of the code’s new capability for axisymmetric metric evolution. We confirm the turning point theorem and determine the region of our rotation law parameter space that provides highest maximum mass for a given angular momentum.

**Conclusion:** This study investigates the stability of neutron star remnants produced by binary neutron star mergers. The stability of these remnants is crucial for understanding the electromagnetic and gravitational wave signals associated with their evolution. Previous studies have shown that stable equilibria respect a turning point criterion, which states that unstable stars occur at a maximum density close to the density of maximum mass. This paper tests this turning point criterion for more realistic models of post-merger equilibria with non-monotonic angular velocity profiles and non-isentropic entropy profiles.

## Roadmap for the Future

### 1. Further Testing of Turning Point Criterion

Future research should continue to test the turning point criterion for a wider range of non-monotonic angular velocity profiles and non-isentropic entropy profiles. This will help to validate and refine the criterion and its applicability to different scenarios.

### 2. Exploration of Stability in 3D

While this study focuses on the stability of neutron star remnants in 2D, future investigations should expand to 3D simulations. This will provide a more comprehensive understanding of the stability properties of these remnants and their evolution.

### 3. Comparison with Observations

The stability analysis presented in this study should be compared with observations of neutron star remnants in order to validate the theoretical predictions. Utilizing data from electromagnetic and gravitational wave signals, researchers can assess whether the turning point criterion holds true in real-world scenarios and potentially refine the models accordingly.

### 4. Optimization of Rotation Law

The study determines the region of rotation law parameter space that provides the highest maximum mass for a given angular momentum. Future investigations can focus on optimizing the rotation law further to enhance the stability and properties of neutron star remnants. This can lead to improved understanding of the post-merger evolution and potential applications in astrophysical models.

## Challenges and Opportunities

**Challenges:**Conducting 3D simulations of neutron star remnants can be computationally demanding and require significant computational resources. Additionally, comparing theoretical predictions with observational data may present challenges due to the complex nature of astrophysical observations.**Opportunities:**Further exploration of the stability properties of neutron star remnants can lead to advancements in our understanding of their evolution and properties. This can have broader implications in the field of astrophysics and gravitational wave astronomy. Additionally, optimizing the rotation law can potentially improve the stability and properties of neutron star remnants, opening up possibilities for new astrophysical models and applications.