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

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.

💡 Research Summary

The paper addresses a long‑standing limitation in the construction of binary neutron‑star (BNS) initial data: the prevailing assumption that the fluid flow is either perfectly corotational (the stars spin with the orbital motion) or perfectly irrotational (no intrinsic circulation). While these two extremes simplify the relativistic Euler equation—reducing it to an algebraic relation—their physical realism is questionable. Real neutron stars may retain a non‑zero amount of spin or circulation due to their formation history, magnetic torques, or prior mass transfer. Consequently, a formalism that can describe arbitrary intermediate circulation is essential for generating more accurate BNS models, especially as gravitational‑wave detectors become sensitive to subtle waveform features.

The authors start by decomposing the fluid 4‑velocity (u^\mu) into a corotational part proportional to the orbital Killing vector (\xi^\mu) and a gradient of a new scalar potential (\Psi): \