A formalism for the construction of binary neutron stars with arbitrary circulation

TL;DR

This paper introduces a new formalism for constructing binary neutron star models with arbitrary circulation, extending beyond the traditional corotational and irrotational assumptions, by formulating the Euler equation as an elliptic equation.

Contribution

It generalizes the flow equations for binary neutron stars, enabling modeling of intermediate circulation states not previously accessible.

Findings

Developed an elliptic equation formulation for arbitrary circulation

Proposed a parameterized decomposition of stellar fluid flow

Extended the modeling capabilities for binary neutron star systems

Abstract

Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the hydrodynamic equations of stationary equilibrium. In this paper we develop a new formalism for the construction of binary stars with circulation intermediate between corotational and irrotational. Generalizing the equations for irrotational flow we cast the Euler equation, which is an algebraic equation in the case of corotational or irrotational fluid flow, as an elliptic equation for a new auxiliary quantity. We also suggest a parameterized decomposition of the fluid flow that allows for a variation of the stellar circulation.