Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits

TL;DR

This paper develops a new formulation for numerically computing binary neutron stars in quasicircular orbits, ensuring they satisfy key physical relations and improving initial data for merger simulations.

Contribution

The authors derive relations between key physical quantities and propose a full Einstein equation solution approach with specific gauge conditions for better quasiequilibrium models.

Findings

Formulated relations between $M_{ADM}$ and $M_K$, and between $ abla M_{ADM}$ and $ abla J$.

Developed a new numerical method solving the full Einstein equations with maximal slicing and transverse gauge.

Produced solutions expected to be accurate initial data for neutron star merger simulations.

Abstract

Two relations, the virial relation $M_{\rm ADM}=M_{\rm K}$ and the first law in the form $\delta M_{\rm ADM}=\Omega \delta J$, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, $M_{\rm ADM}$, $M_{\rm K}$, $J$, and $\Omega$ are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $\delta$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between $M_{\rm ADM}$ and $M_{\rm K}$ and between $\delta M_{\rm ADM}$ and $\Omega \delta J$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.