Constant circulation sequences of binary neutron stars and their spin characterization

TL;DR

This paper extends a computational code to analyze binary neutron star systems with constant circulation, comparing different spin measures and exploring differential rotation, advancing understanding of neutron star spin characterization.

Contribution

It introduces an extension of the extsc{cocal} code to compute constant circulation sequences and compares them with existing models, including differential rotation.

Findings

Circulation provides an exact measure of neutron star spin.

Sequences of constant circulation differ from corotating and irrotational models.

The study links circulation to various spin diagnostics and explores differential rotation.

Abstract

For isentropic fluids, dynamical evolution of a binary system conserves the baryonic mass and circulation; therefore, sequences of constant rest mass and constant circulation are of particular importance. In this work, we present the extension of our Compact Object CALculator (\cocal{}) code to compute such quasiequilibria and compare them with the well-known corotating and irrotational sequences, the latter being the simplest, zero-circulation case. The circulation as a measure of the spin for a neutron star in a binary system has the advantage of being exactly calculable since it is a local quantity. To assess the different measures of spin, such as the angular velocity of the star, the quasilocal, dimensionless spin parameter $J/M^2$, or the circulation $\mathcal{C}$, we first compute sequences of single, uniformly rotating stars and describe how the different spin diagnostics are related to each other. The connection to spinning binary systems is accomplished through the concept of circulation and the use of the constant rotational velocity formulation. Finally, we explore a modification of the latter formulation that naturally leads to differentially rotating binary systems.