Models of helically symmetric binary systems

TL;DR

This paper explores helically symmetric models for binary systems, including scalar fields and neutron stars, highlighting convergence behaviors and the approximation accuracy of such models compared to waveless formalisms.

Contribution

It introduces a convergent helically symmetric binary neutron star code and analyzes the effects of nonlinear terms and boundary conditions on convergence and accuracy.

Findings

Scalar field models show convergence sensitivity to nonlinear term signs.

Neutron star code achieves convergence under specific boundary conditions.

Helically symmetric solutions are comparable in accuracy to waveless formalisms.

Abstract

Results from helically symmetric scalar field models and first results from a convergent helically symmetric binary neutron star code are reported here; these are models stationary in the rotating frame of a source with constant angular velocity omega. In the scalar field models and the neutron star code, helical symmetry leads to a system of mixed elliptic-hyperbolic character. The scalar field models involve nonlinear terms that mimic nonlinear terms of the Einstein equation. Convergence is strikingly different for different signs of each nonlinear term; it is typically insensitive to the iterative method used; and it improves with an outer boundary in the near zone. In the neutron star code, one has no control on the sign of the source, and convergence has been achieved only for an outer boundary less than approximately 1 wavelength from the source or for a code that imposes helical symmetry only inside a near zone of that size. The inaccuracy of helically symmetric solutions with appropriate boundary conditions should be comparable to the inaccuracy of a waveless formalism that neglects gravitational waves; and the (near zone) solutions we obtain for waveless and helically symmetric BNS codes with the same boundary conditions nearly coincide.