Detailed numerical implementation of the wide binary test

TL;DR

This paper outlines a detailed numerical plan to test Milgromian dynamics (MOND) against Newtonian gravity using wide binary stars, emphasizing computational strategies and feasibility with current technology.

Contribution

It provides a comprehensive, cost-effective numerical implementation plan for the wide binary test to distinguish between dark matter and modified gravity theories.

Findings

Cost function can be evaluated deterministically in seconds.

The test is feasible with current computational resources.

Embedding in MCMC allows robust model fitting.

Abstract

The observed flat rotation curves of galaxies are among a number of astrophysical phenomena which require a larger acceleration than can be provided by the Newtonian gravity of the detected baryons. The main proposed solutions are additional undetected mass in the form of dark matter, or a low-acceleration modification to Newtonian gravity known as Milgromian dynamics (MOND). It is possible to directly test MOND using wide binary stars in the Solar neighbourhood, as these systems should contain a dynamically insignificant amount of dark matter even if it comprises most of the Galaxy. However, local wide binaries in MOND should orbit each other $\approx 20\%$ faster than in Newtonian dynamics. We describe the detailed plan for how this wide binary test will be conducted, focusing especially on stages with a high numerical cost. The computational costs and memory requirements are estimated for the main stages in the plan. Our overall assessment is that the critically important cost function can be evaluated deterministically at a marginal cost of a few seconds, giving the absolute binomial likelihood of a model. This will allow the cost function to be embedded within a Markov Chain Monte Carlo sampler, or a less expensive gradient descent stage designed to reveal the best-fitting model parameters. Therefore, the wide binary test should be feasible using currently available technology.