Constant circulation sequences of binary neutron stars and their spin characterization

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 quasi-equilibria, 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 quasi-local, dimensionless spin parameter \(J/M^2\), or the circulation \(\mathcal{C}\), we first compute sequences of single, uniformly rotating stars and descibe 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.