# Smooth equations of state for high-accuracy simulations of neutron star binaries

## TL;DR

This paper introduces spectral equations of state for neutron star simulations, enabling high-accuracy results at lower computational costs and highlighting the importance of low-density modeling choices.

## Contribution

The authors implement spectral equations of state in the Spectral Einstein Code, demonstrating improved accuracy and efficiency over traditional methods.

## Key findings

- Spectral equations of state enable high-accuracy neutron star merger simulations.
- Different low-density spectral models significantly affect simulation cost and accuracy.
- Trade-offs exist between physical realism and computational efficiency in choosing equations of state.

## Abstract

High-accuracy numerical simulations of merging neutron stars play an important role in testing and calibrating the waveform models used by gravitational wave observatories. Obtaining high-accuracy waveforms at a reasonable computational cost, however, remains a significant challenge. One issue is that high-order convergence of the solution requires the use of smooth evolution variables, while many of the equations of state used to model the neutron star matter have discontinuities, typically in the first derivative of the pressure. Spectral formulations of the equation of state have been proposed as a potential solution to this problem. Here, we report on the numerical implementation of spectral equations of state in the Spectral Einstein Code. We show that, in our code, spectral equations of state allow for high-accuracy simulations at a lower computational cost than commonly used `piecewise polytrope' equations state. We also demonstrate that not all spectral equations of state are equally useful: different choices for the low-density part of the equation of state can significantly impact the cost and accuracy of simulations. As a result, simulations of neutron star mergers present us with a trade-off between the cost of simulations and the physical realism of the chosen equation of state.