Deflection of light by the field of a binary system

TL;DR

This paper analyzes how light deflection occurs in a binary system's gravitational field, proposing methods to detect such effects with high-precision astrometry, and identifying two cumulative effects on photon paths.

Contribution

It introduces a model for photon motion in a binary system's gravitational field, incorporating tidal forces, and suggests observational detection of light deflection effects.

Findings

Potential detection of light deflection effects with microarcsecond astrometry.

Identification of two cumulative effects on photon paths.

Conditions under which deflection effects are detectable.

Abstract

We examine the motion of a photon in the gravitational field of a binary system. The equations of motion are geodesic equations in a Schwarzchild background with a tidal force. We specialize the equations to that of an edge-on binary and use the method of osculating elements to integrate them. This work helps to identify a binary system through the gravitational light deflection of one member in the gravitational field of the other member. It is found that the effects of the companion body on a photon passing the edge of the star can be potentially detected by astrometric satellites with $\mu$as precision, if the ratio of the Schwarzchid radius to the star radius, $\frac{Gm}{c^2 R}\geq 10^{-5}$. Two different cumulative effects on the photon path are identified.