Identification of stellar-mass black hole binaries and the validity of linear orbital motion approximation in microlensing

TL;DR

This paper investigates the detection challenges of binary black holes via microlensing, highlighting the limitations of parallax detection and the validity of the linear orbital motion approximation in modeling such events.

Contribution

It demonstrates that the microlensing parallax effect is often undetectable in binary black hole events and assesses the accuracy of the linear orbital motion approximation in modeling binary microlensing.

Findings

Microlensing parallax effect is rarely detectable in binary BH events.

The linear orbital motion approximation is valid in over 93% of simulated events.

Non-detection of binary BHs may be due to parallax measurement limitations.

Abstract

Gravitational microlensing is unique in detecting binary black (BH) holes with wide (a few au) separations. Models predict that about $1\%$ of microlensing binaries should be due to binary BHs, and yet zero has been robustly identified. Using simulated events with binary BH lenses, we show that the microlensing parallax effect in a typical binary BH event cannot be reliably detected. Given the crucial role of the parallax parameter in determining the mass of dark microlenses, this may explain the non-detection of binary BHs. Additionally, we show that in only a small fraction ($\lesssim7\%$) of the simulated events the full orbital motion of the binary lens cannot be modeled with the linear orbital motion approximation. This approximation has been frequently used in modelings of binary microlensing events.