# Testing Modified Gravity with Wide Binaries in GAIA DR2

## TL;DR

This study tests modified gravity theories using a large sample of wide binary stars from GAIA DR2, finding that MOND-like theories without external field effects are inconsistent with observed stellar velocities, supporting Newtonian gravity.

## Contribution

It provides an observational test of modified gravity theories using GAIA DR2 data, specifically analyzing wide binary star velocities to distinguish between Newtonian and MOND-like predictions.

## Key findings

- Observed velocity distributions align with Newtonian expectations.
- MOND-like theories without external field effects are inconsistent with data.
- High-velocity tail analysis offers potential for future tests.

## Abstract

Several recent studies have shown that very wide binary stars can potentially provide an interesting test for modified-gravity theories which attempt to emulate dark matter; these systems should be almost Newtonian according to standard dark-matter theories, while the predictions for MOND-like theories are distinctly different, if the various observational issues can be overcome. Here we explore an observational application of the test from the recent GAIA DR2 data release: we select a large sample of $\sim 24,000$ candidate wide binary stars with distance $< 200$ parsec and magnitudes $G < 16$ from GAIA DR2, and estimated component masses using a main-sequence mass-luminosity relation. We then compare the frequency distribution of pairwise relative projected velocity (relative to circular-orbit value) as a function of projected separation; these distributions show a clear peak at a value close to Newtonian expectations, along with a long `tail' which extends to much larger velocity ratios; the `tail' is considerably more numerous than in control samples constructed from DR2 with randomised positions, so its origin is unclear. Comparing the velocity histograms with simulated data, we conclude that MOND-like theories without an external field effect are strongly inconsistent with the observed data since they predict a peak-shift in clear disagreement with the data; testing MOND-like theories with an external field effect is not decisive at present, but has good prospects to become decisive in future with improved modelling or understanding of the high-velocity tail, and additional spectroscopic data.