Smooth equations of state for high-accuracy simulations of neutron star binaries. (arXiv:1908.05277v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Foucart_F/0/1/0/all/0/1">Francois Foucart</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Duez_M/0/1/0/all/0/1">Matthew D. Duez</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Gudinas_A/0/1/0/all/0/1">Alana Gudinas</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Hebert_F/0/1/0/all/0/1">Francois Hebert</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Kidder_L/0/1/0/all/0/1">Lawrence E. Kidder</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Pfeiffer_H/0/1/0/all/0/1">Harald P. Pfeiffer</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Scheel_M/0/1/0/all/0/1">Mark A. Scheel</a>

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.

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.

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