# A new line on the wide binary test of gravity

## TL;DR

This paper evaluates the feasibility of testing gravity laws using wide binary stars by analyzing their relative velocities with a novel 'line velocity' method, showing current data nearly suffice to distinguish Newtonian gravity from alternatives like MOND.

## Contribution

Introduces and applies the 'line velocity' technique to improve velocity measurements of wide binaries, assessing its potential for testing gravity theories with existing and future data.

## Key findings

- Line velocity method reduces velocity uncertainty to ~30 m/s.
- Current data nearly distinguish Newtonian gravity from modified theories.
- Approximately 1000 wide binary systems are needed for conclusive tests.

## Abstract

The relative velocity distribution of wide binary (WB) stars is sensitive to the law of gravity at the low accelerations typical of galactic outskirts. I consider the feasibility of this wide binary test using the `line velocity' method. This involves considering only the velocity components along the direction within the sky plane orthogonal to the systemic proper motion of each WB. I apply this technique to the WB sample of Hernandez et. al. (2019), carefully accounting for large-angle effects at one order beyond leading. Based on Monte Carlo trials, the uncertainty in the one-dimensional velocity dispersion is $\approx 100$ m/s when using sky-projected relative velocities. Using line velocities reduces this to $\approx 30$ m/s because these are much less affected by distance uncertainties. My analysis does not support the Hernandez et. al. (2019) claim of a clear departure from Newtonian dynamics beyond a radius of $\approx 10$ kAU, partly because I use $2\sigma$ outlier rejection to clean their sample first. Nonetheless, the uncertainties are small enough that existing WB data are nearly sufficient to distinguish Newtonian dynamics from Modified Newtonian Dynamics. I estimate that $\approx 1000$ WB systems will be required for this purpose if using only line velocities. In addition to a larger sample, it will also be important to control for systematics like undetected companions and moving groups. This could be done statistically. The contamination can be minimized by considering a narrow theoretically motivated range of parameters and focusing on how different theories predict different proportions of WBs in this region.