Solving the Darwin problem in the first post-Newtonian approximation of general relativity

TL;DR

This paper analytically investigates the equilibrium and stability of corotating binary stars in the first post-Newtonian approximation, revealing how relativistic effects influence the innermost stable orbit and orbital dynamics.

Contribution

It provides an analytical calculation of the equilibrium sequence and ISCCO in the first PN approximation, extending understanding beyond purely Newtonian models.

Findings

Orbital separation at ISCCO decreases with increased stellar compactness.

Orbital angular velocity at ISCCO increases with stellar compactness.

Results agree with previous numerical studies.

Abstract

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.